Affinité chimique — Wikipédia

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class="vector-toc-link" href="#Définitions"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Définitions</span> </div> </a> <button aria-controls="toc-Définitions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Définitions</span> </button> <ul id="toc-Définitions-sublist" class="vector-toc-list"> <li id="toc-Définition_générale" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Définition_générale"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Définition générale</span> </div> </a> <ul id="toc-Définition_générale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relation_avec_les_potentiels_thermodynamiques" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relation_avec_les_potentiels_thermodynamiques"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Relation avec les potentiels thermodynamiques</span> </div> </a> <ul id="toc-Relation_avec_les_potentiels_thermodynamiques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dépendance_à_l'écriture_de_la_réaction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dépendance_à_l'écriture_de_la_réaction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Dépendance à l'écriture de la réaction</span> </div> </a> <ul id="toc-Dépendance_à_l'écriture_de_la_réaction-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Condition_d'évolution_spontanée_d'un_système_chimique" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Condition_d'évolution_spontanée_d'un_système_chimique"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Condition d'évolution spontanée d'un système chimique</span> </div> </a> <button aria-controls="toc-Condition_d'évolution_spontanée_d'un_système_chimique-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Condition d'évolution spontanée d'un système chimique</span> </button> <ul id="toc-Condition_d'évolution_spontanée_d'un_système_chimique-sublist" class="vector-toc-list"> <li id="toc-Rappels_sur_l'avancement_de_réaction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rappels_sur_l'avancement_de_réaction"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Rappels sur l'avancement de réaction</span> </div> </a> <ul id="toc-Rappels_sur_l'avancement_de_réaction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relation_avec_l'entropie_du_système_réactionnel" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relation_avec_l'entropie_du_système_réactionnel"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Relation avec l'entropie du système réactionnel</span> </div> </a> <ul id="toc-Relation_avec_l'entropie_du_système_réactionnel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formulation_générale" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formulation_générale"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Formulation générale</span> </div> </a> <ul id="toc-Formulation_générale-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formulations_avec_les_potentiels_thermodynamiques" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Formulations_avec_les_potentiels_thermodynamiques"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Formulations avec les potentiels thermodynamiques</span> </div> </a> <ul id="toc-Formulations_avec_les_potentiels_thermodynamiques-sublist" class="vector-toc-list"> <li id="toc-Cas_général" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Cas_général"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.1</span> <span>Cas général</span> </div> </a> <ul id="toc-Cas_général-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cas_d'une_réaction_à_volume_et_température_constants" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Cas_d'une_réaction_à_volume_et_température_constants"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.2</span> <span>Cas d'une réaction à volume et température constants</span> </div> </a> <ul id="toc-Cas_d'une_réaction_à_volume_et_température_constants-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cas_d'une_réaction_à_pression_et_température_constantes" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Cas_d'une_réaction_à_pression_et_température_constantes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.3</span> <span>Cas d'une réaction à pression et température constantes</span> </div> </a> <ul id="toc-Cas_d'une_réaction_à_pression_et_température_constantes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Condition_de_stabilité_de_l'équilibre" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Condition_de_stabilité_de_l'équilibre"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Condition de stabilité de l'équilibre</span> </div> </a> <ul id="toc-Condition_de_stabilité_de_l'équilibre-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Récapitulatif" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Récapitulatif"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Récapitulatif</span> </div> </a> <ul id="toc-Récapitulatif-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_et_références" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_et_références"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes et références</span> </div> </a> <button aria-controls="toc-Notes_et_références-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Notes et références</span> </button> <ul id="toc-Notes_et_références-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliographie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliographie"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Bibliographie</span> </div> </a> <ul id="toc-Bibliographie-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Articles_connexes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Articles_connexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Articles connexes</span> </div> </a> <ul id="toc-Articles_connexes-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Basculer la table des matières" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Basculer la table des matières</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Affinité chimique</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Aller à un article dans une autre langue. Disponible en 30 langues." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-30" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">30 langues</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Chemiese_affiniteit" title="Chemiese affiniteit – afrikaans" lang="af" hreflang="af" data-title="Chemiese affiniteit" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D9%84%D9%81%D8%A9_%D9%83%D9%8A%D9%85%D9%8A%D8%A7%D8%A6%D9%8A%D8%A9" title="ألفة كيميائية – arabe" lang="ar" hreflang="ar" data-title="ألفة كيميائية" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Afinitat_qu%C3%ADmica" title="Afinitat química – catalan" lang="ca" hreflang="ca" data-title="Afinitat química" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Chemick%C3%A1_afinita" title="Chemická afinita – tchèque" lang="cs" hreflang="cs" data-title="Chemická afinita" data-language-autonym="Čeština" data-language-local-name="tchèque" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Affinitet" title="Affinitet – danois" lang="da" hreflang="da" data-title="Affinitet" data-language-autonym="Dansk" data-language-local-name="danois" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Affinit%C3%A4t_(Chemie)" title="Affinität (Chemie) – allemand" lang="de" hreflang="de" data-title="Affinität (Chemie)" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CE%B7%CE%BC%CE%B9%CE%BA%CE%AE_%CF%83%CF%85%CE%B3%CE%B3%CE%AD%CE%BD%CE%B5%CE%B9%CE%B1" title="Χημική συγγένεια – grec" lang="el" hreflang="el" data-title="Χημική συγγένεια" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Chemical_affinity" title="Chemical affinity – anglais" lang="en" hreflang="en" data-title="Chemical affinity" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Afinidad_qu%C3%ADmica" title="Afinidad química – espagnol" lang="es" hreflang="es" data-title="Afinidad química" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Keemiline_afiinsus" title="Keemiline afiinsus – estonien" lang="et" hreflang="et" data-title="Keemiline afiinsus" data-language-autonym="Eesti" data-language-local-name="estonien" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%81%D9%86%DB%8C%D8%AA%D9%87_%D8%B4%DB%8C%D9%85%DB%8C%D8%A7%DB%8C%DB%8C" title="آفنیته شیمیایی – persan" lang="fa" hreflang="fa" data-title="آفنیته شیمیایی" data-language-autonym="فارسی" data-language-local-name="persan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Affiniteetti" title="Affiniteetti – finnois" lang="fi" hreflang="fi" data-title="Affiniteetti" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A4%D7%99%D7%A0%D7%99%D7%95%D7%AA_(%D7%9B%D7%99%D7%9E%D7%99%D7%94)" title="אפיניות (כימיה) – hébreu" lang="he" hreflang="he" data-title="אפיניות (כימיה)" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kemijski_afinitet" title="Kemijski afinitet – croate" lang="hr" hreflang="hr" data-title="Kemijski afinitet" data-language-autonym="Hrvatski" data-language-local-name="croate" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Afinitas_kimia" title="Afinitas kimia – indonésien" lang="id" hreflang="id" data-title="Afinitas kimia" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Affinit%C3%A0_chimica" title="Affinità chimica – italien" lang="it" hreflang="it" data-title="Affinità chimica" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8C%96%E5%AD%A6%E8%A6%AA%E5%92%8C%E5%8A%9B" title="化学親和力 – japonais" lang="ja" hreflang="ja" data-title="化学親和力" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%99%94%ED%95%99_%EC%B9%9C%ED%99%94%EB%A0%A5" title="화학 친화력 – coréen" lang="ko" hreflang="ko" data-title="화학 친화력" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Affinit%C3%A4t_(Chemie)" title="Affinität (Chemie) – bas-allemand" lang="nds" hreflang="nds" data-title="Affinität (Chemie)" data-language-autonym="Plattdüütsch" data-language-local-name="bas-allemand" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Chemische_affiniteit" title="Chemische affiniteit – néerlandais" lang="nl" hreflang="nl" data-title="Chemische affiniteit" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Affinitet" title="Affinitet – norvégien bokmål" lang="nb" hreflang="nb" data-title="Affinitet" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Powinowactwo_chemiczne" title="Powinowactwo chemiczne – polonais" lang="pl" hreflang="pl" data-title="Powinowactwo chemiczne" data-language-autonym="Polski" data-language-local-name="polonais" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Afinitate_chimic%C4%83" title="Afinitate chimică – roumain" lang="ro" hreflang="ro" data-title="Afinitate chimică" data-language-autonym="Română" data-language-local-name="roumain" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D1%84%D1%84%D0%B8%D0%BD%D0%BD%D0%BE%D1%81%D1%82%D1%8C" title="Аффинность – russe" lang="ru" hreflang="ru" data-title="Аффинность" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Afiniteti" title="Afiniteti – albanais" lang="sq" hreflang="sq" data-title="Afiniteti" data-language-autonym="Shqip" data-language-local-name="albanais" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Affinitet" title="Affinitet – suédois" lang="sv" hreflang="sv" data-title="Affinitet" data-language-autonym="Svenska" data-language-local-name="suédois" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%84%E0%B8%A5%E0%B9%89%E0%B8%B2%E0%B8%A2%E0%B8%84%E0%B8%A5%E0%B8%B6%E0%B8%87%E0%B8%97%E0%B8%B2%E0%B8%87%E0%B9%80%E0%B8%84%E0%B8%A1%E0%B8%B5" title="ความคล้ายคลึงทางเคมี – thaï" lang="th" hreflang="th" data-title="ความคล้ายคลึงทางเคมี" data-language-autonym="ไทย" data-language-local-name="thaï" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%BE%D1%80%D1%96%D0%B4%D0%BD%D0%B5%D0%BD%D1%96%D1%81%D1%82%D1%8C_(%D1%85%D1%96%D0%BC%D1%96%D1%8F)" title="Спорідненість (хімія) – ukrainien" lang="uk" hreflang="uk" data-title="Спорідненість (хімія)" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C3%81i_l%E1%BB%B1c_h%C3%B3a_h%E1%BB%8Dc" title="Ái lực hóa học – vietnamien" lang="vi" hreflang="vi" data-title="Ái lực hóa học" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamien" 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aria-label="Apparence"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Apparence</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">déplacer vers la barre latérale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">masquer</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Un article de Wikipédia, l'encyclopédie libre.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="fr" dir="ltr"><div class="bandeau-container metadata homonymie hatnote"><div class="bandeau-cell bandeau-icone" style="display:table-cell;padding-right:0.5em"><span class="noviewer" typeof="mw:File"><a href="/wiki/Aide:Homonymie" title="Aide:Homonymie"><img alt="Page d’aide sur l’homonymie" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Confusion_colour.svg/20px-Confusion_colour.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Confusion_colour.svg/30px-Confusion_colour.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Confusion_colour.svg/40px-Confusion_colour.svg.png 2x" data-file-width="260" data-file-height="200" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Ne doit pas être confondu avec <a href="/wiki/Affinit%C3%A9_%C3%A9lectronique" title="Affinité électronique">affinité électronique</a>. </p> </div></div> <div class="infobox_v3 infobox infobox--frwiki noarchive"> <div class="entete" style=""> <div>Affinité chimique</div> </div> <table><caption class="hidden" style="">Données clés</caption> <tbody><tr> <th scope="row"><a href="/wiki/Unit%C3%A9s_de_base_du_Syst%C3%A8me_international" title="Unités de base du Système international">Unités SI</a></th> <td> <a href="/wiki/Joule" title="Joule">joule</a> par <a href="/wiki/Mole_(unit%C3%A9)" title="Mole (unité)">mole</a> (J/mol)</td> </tr> <tr> <th scope="row"><a href="/wiki/Dimension_(physique)" title="Dimension (physique)">Dimension</a></th> <td> <span class="nowrap"><a href="/wiki/Masse" title="Masse">M</a>·<a href="/wiki/Longueur" title="Longueur">L</a><sup> 2</sup>·<a href="/wiki/Temps_(physique)" title="Temps (physique)">T</a><sup> −2</sup>·<a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">N</a><sup> −1</sup></span></td> </tr> <tr> <th scope="row">Nature</th> <td> Grandeur <a href="/wiki/Scalaire_(physique)" title="Scalaire (physique)">scalaire</a> <a href="/wiki/Grandeur_intensive" class="mw-redirect" title="Grandeur intensive">intensive</a></td> </tr> <tr> <th scope="row">Symbole usuel</th> <td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/280ae03440942ab348c2ca9b8db6b56ffa9618f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.903ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span></td> </tr> <tr> <th scope="row">Lien à d'autres grandeurs</th> <td> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=-\sum _{i=1}^{N}\nu _{i}\mu _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=-\sum _{i=1}^{N}\nu _{i}\mu _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/123c59beec6684526e0f7bd5d53dad36be7d685a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.089ex; height:7.343ex;" alt="{\displaystyle {\mathcal {A}}=-\sum _{i=1}^{N}\nu _{i}\mu _{i}}"></span></td> </tr> <tr> <th scope="row"><a href="/wiki/Variables_conjugu%C3%A9es_(thermodynamique)" title="Variables conjuguées (thermodynamique)">Conjuguée</a></th> <td> <a href="/wiki/Avancement_de_r%C3%A9action" title="Avancement de réaction">Avancement de réaction</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span></td> </tr> </tbody></table><p class="navbar bordered noprint" style=""><span class="plainlinks navigation-not-searchable"><a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Affinit%C3%A9_chimique&action=edit">modifier</a></span> <span typeof="mw:File"><a href="/wiki/Mod%C3%A8le:Infobox_Grandeur_physique" title="Consultez la documentation du modèle"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Info_Simple.svg/12px-Info_Simple.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Info_Simple.svg/18px-Info_Simple.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Info_Simple.svg/24px-Info_Simple.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></p></div> <p>L'<b>affinité chimique</b> en <a href="/wiki/Thermodynamique" title="Thermodynamique">thermodynamique</a> est une <a href="/wiki/Fonction_d%27%C3%A9tat" title="Fonction d'état">fonction d'état</a> permettant de prévoir le sens de l'évolution d'une <a href="/wiki/R%C3%A9action_chimique" title="Réaction chimique">réaction chimique</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historique">Historique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=1" title="Modifier la section : Historique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=1" title="Modifier le code source de la section : Historique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La notion d'affinité chimique, héritée de l'<a href="/wiki/Alchimie" title="Alchimie">alchimie</a> (elle est mentionnée au <abbr class="abbr" title="13ᵉ siècle"><span class="romain">XIII</span><sup style="font-size:72%">e</sup></abbr> siècle dans les travaux d'<a href="/wiki/Albert_le_Grand" title="Albert le Grand">Albert le Grand</a>), est longtemps évoquée sans être formellement définie par les savants étudiant les réactions chimiques. En 1718 et 1720, <a href="/wiki/%C3%89tienne-Fran%C3%A7ois_Geoffroy" title="Étienne-François Geoffroy">Geoffroy</a> présente à l'<a href="/wiki/Acad%C3%A9mie_des_sciences_(France)" title="Académie des sciences (France)">Académie des sciences</a> sa <i><a href="/wiki/Table_des_diff%C3%A9rents_rapports_observ%C3%A9s_en_Chimie_entre_diff%C3%A9rentes_substances" title="Table des différents rapports observés en Chimie entre différentes substances">table des rapports</a></i>, listes d'affinités chimiques obtenues par l'observation des réactions des substances les unes avec les autres. En 1733, pour <a href="/wiki/Herman_Boerhaave" title="Herman Boerhaave">Boerhaave</a>, médecin de <a href="/wiki/Leyde" title="Leyde">Leyde</a>, l'affinité chimique est la force en vertu de laquelle les particules des corps se recherchent, s'unissent et se retiennent<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup>. <a href="/wiki/Claude-Louis_Berthollet" title="Claude-Louis Berthollet">Berthollet</a>, qui le premier évoque en 1803 la notion d'<a href="/wiki/%C3%89quilibre_chimique" title="Équilibre chimique">équilibre chimique</a>, utilise la notion d'affinité chimique sans lui donner une définition claire, tout en la rapprochant de la <a href="/wiki/Loi_universelle_de_la_gravitation" title="Loi universelle de la gravitation">loi universelle de la gravitation</a><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite_crochet">[</span>4<span class="cite_crochet">]</span></a></sup>. Peu après, à la suite des récentes découvertes dans le domaine de l'électricité, et notamment l'électrolyse de certains sels par <a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a>, <a href="/wiki/J%C3%B6ns_Jacob_Berzelius" title="Jöns Jacob Berzelius">Berzelius</a> exprime la notion d'affinité chimique en termes d'attraction et de répulsion de pôles chargés sur ce que l'on ne nommait pas encore les <a href="/wiki/Mol%C3%A9cule" title="Molécule">molécules</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite_crochet">[</span>5<span class="cite_crochet">]</span></a></sup>. En 1879, <a href="/wiki/Marcellin_Berthelot" title="Marcellin Berthelot">Berthelot</a> énonce son principe de travail maximum, tentant de relier l'affinité à la chaleur dégagée par la réaction, qui selon lui ne pouvait être que positive<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite_crochet">[</span>6<span class="cite_crochet">]</span></a></sup>. </p><p>La définition formelle actuelle de l'affinité chimique par <a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">de Donder</a>, qui la relie au <a href="/wiki/Deuxi%C3%A8me_principe_de_la_thermodynamique" title="Deuxième principe de la thermodynamique">deuxième principe de la thermodynamique</a>, date de 1922<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite_crochet">[</span>7<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite_crochet">[</span>8<span class="cite_crochet">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Définitions"><span id="D.C3.A9finitions"></span>Définitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=2" title="Modifier la section : Définitions" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=2" title="Modifier le code source de la section : Définitions"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Définition_générale"><span id="D.C3.A9finition_g.C3.A9n.C3.A9rale"></span>Définition générale</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=3" title="Modifier la section : Définition générale" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=3" title="Modifier le code source de la section : Définition générale"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Soit une <a href="/wiki/R%C3%A9action_chimique" title="Réaction chimique">réaction chimique</a> dont l'<a href="/wiki/%C3%89quation_chimique" title="Équation chimique">équation bilan</a> est écrite selon la <a href="/wiki/St%C5%93chiom%C3%A9trie#Nombres_stœchiométriques_négatifs" title="Stœchiométrie">convention stœchiométrique</a><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite_crochet">[</span>9<span class="cite_crochet">]</span></a></sup> : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{1}\,{\rm {C}}_{1}+\nu _{2}\,{\rm {C}}_{2}+\cdots +\nu _{N}\,{\rm {C}}_{N}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{1}\,{\rm {C}}_{1}+\nu _{2}\,{\rm {C}}_{2}+\cdots +\nu _{N}\,{\rm {C}}_{N}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b09ecb23d1efd1be3de26e64b802d6e0ae2b845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.746ex; height:2.509ex;" alt="{\displaystyle \nu _{1}\,{\rm {C}}_{1}+\nu _{2}\,{\rm {C}}_{2}+\cdots +\nu _{N}\,{\rm {C}}_{N}=0}"></span></center> <p>en attribuant une valeur négative aux coefficients stœchiométriques des réactifs et positive à ceux des produits : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aeee4853b360ba323e932acb72159b1c9c357841" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}<0}"></span> pour un <a href="/wiki/R%C3%A9actif_(chimie)" title="Réactif (chimie)">réactif</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44d9c0eac121342f83f680ea9963901ddfded18f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}>0}"></span> pour un <a href="/wiki/Produit_de_r%C3%A9action" title="Produit de réaction">produit</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d370e94d86d8182d557ea2b10e8d6f7d63a1145c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}=0}"></span> pour un <a href="/wiki/Inerte_(chimie)" title="Inerte (chimie)">inerte</a>.</li></ul> <p>L'<b>affinité chimique</b>, notée <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/280ae03440942ab348c2ca9b8db6b56ffa9618f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.903ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}}"></span> ou <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>, est formellement définie<sup id="cite_ref-IUPACnotation_10-0" class="reference"><a href="#cite_note-IUPACnotation-10"><span class="cite_crochet">[</span>10<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-R2_11-0" class="reference"><a href="#cite_note-R2-11"><span class="cite_crochet">[</span>11<span class="cite_crochet">]</span></a></sup>, en introduisant les <a href="/wiki/Potentiel_chimique" title="Potentiel chimique">potentiels chimiques</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dea0a0293841cce9eef98b55e53a92b82ae59ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.201ex; height:2.176ex;" alt="{\displaystyle \mu _{i}}"></span> des <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> constituants (réactifs, produits et inertes) du mélange réactionnel, par : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Affinité chimique :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=-\sum _{i=1}^{N}\nu _{i}\mu _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=-\sum _{i=1}^{N}\nu _{i}\mu _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/123c59beec6684526e0f7bd5d53dad36be7d685a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.089ex; height:7.343ex;" alt="{\displaystyle {\mathcal {A}}=-\sum _{i=1}^{N}\nu _{i}\mu _{i}}"></span> </td></tr></tbody></table> </center> <p>Par exemple, si l'on écrit l'<a href="/wiki/%C3%89quilibre_chimique" title="Équilibre chimique">équilibre</a> du <a href="/wiki/Dioxyde_de_soufre" title="Dioxyde de soufre">dioxyde</a> et du <a href="/wiki/Trioxyde_de_soufre" title="Trioxyde de soufre">trioxyde de soufre</a> en présence d'<a href="/wiki/Dioxyg%C3%A8ne" title="Dioxygène">oxygène</a> : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇄</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d684659bf8c7c10802281e8516ff20c63a4ad97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.191ex; height:2.843ex;" alt="{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}"></span></dd></dl> <p>soit, selon la convention stœchiométrique : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4aaf1cfe63166fa45d9d4a8c65db9354ac1fda5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.486ex; height:2.843ex;" alt="{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}"></span></dd></dl> <p>on a l'expression de l'affinité chimique : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=-\left(-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}+2\,\mu _{\rm {SO_{3}}}\right)=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=-\left(-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}+2\,\mu _{\rm {SO_{3}}}\right)=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/739a57d7f769e1d5220f2584296c515cafe607cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:60.692ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}=-\left(-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}+2\,\mu _{\rm {SO_{3}}}\right)=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}"></span></dd></dl> <p>L'affinité chimique est <a href="/wiki/Homog%C3%A9n%C3%A9it%C3%A9_(physique)" title="Homogénéité (physique)">homogène</a> avec une <a href="/wiki/%C3%89nergie" title="Énergie">énergie</a> rapportée à une <a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">quantité de matière</a>, elle s'exprime par exemple en <a href="/wiki/Joule" title="Joule">joules</a> par <a href="/wiki/Mole_(unit%C3%A9)" title="Mole (unité)">mole</a>, J/mol. L'affinité chimique <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/280ae03440942ab348c2ca9b8db6b56ffa9618f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.903ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}}"></span> est la variable <a href="/wiki/Extensivit%C3%A9_et_intensivit%C3%A9_(physique)" title="Extensivité et intensivité (physique)">intensive</a> <a href="/wiki/Variables_conjugu%C3%A9es_(thermodynamique)" title="Variables conjuguées (thermodynamique)">conjuguée</a> de la variable <a href="/wiki/Extensivit%C3%A9_et_intensivit%C3%A9_(physique)" title="Extensivité et intensivité (physique)">extensive</a> <a href="/wiki/Avancement_de_r%C3%A9action" title="Avancement de réaction">avancement de réaction</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span>. Autrement dit, le produit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feb515d545dd4ce9e7a27498fde7c3d0cc31f8c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.613ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi }"></span> est homogène avec une énergie. </p> <div class="mw-heading mw-heading3"><h3 id="Relation_avec_les_potentiels_thermodynamiques">Relation avec les potentiels thermodynamiques</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=4" title="Modifier la section : Relation avec les potentiels thermodynamiques" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=4" title="Modifier le code source de la section : Relation avec les potentiels thermodynamiques"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Les variations <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fc7e08f0268800efa7d45d5bff48ed1013c2c35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.487ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} n_{i}}"></span> des <a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">quantités</a> (nombres de <a href="/wiki/Mole_(unit%C3%A9)" title="Mole (unité)">moles</a>) des espèces chimiques <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> intervenant dans la réaction chimique sont liées par l'équation bilan de la réaction. En introduisant l'<a href="/wiki/Avancement_de_r%C3%A9action" title="Avancement de réaction">avancement de réaction</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span> (lui aussi défini par de Donder) on a les relations : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi ={\frac {\mathrm {d} n_{i}}{\nu _{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi ={\frac {\mathrm {d} n_{i}}{\nu _{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9a4142d9f828903bf61a8091d65b02903088563" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:9.744ex; height:5.676ex;" alt="{\displaystyle \mathrm {d} \xi ={\frac {\mathrm {d} n_{i}}{\nu _{i}}}}"></span> pour tout <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\in [1,\cdots ,N]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>N</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\in [1,\cdots ,N]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b408c2723c4b77edc723df1fdc3eab75284902b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.341ex; height:2.843ex;" alt="{\displaystyle i\in [1,\cdots ,N]}"></span></dd></dl> <p>soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{i}=\nu _{i}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{i}=\nu _{i}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db816598fc363335a8ee8ef1c3446d03be1dc6ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.243ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} n_{i}=\nu _{i}\,\mathrm {d} \xi }"></span> pour tout <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\in [1,\cdots ,N]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>N</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\in [1,\cdots ,N]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b408c2723c4b77edc723df1fdc3eab75284902b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.341ex; height:2.843ex;" alt="{\displaystyle i\in [1,\cdots ,N]}"></span> (pour un inerte <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{i}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{i}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe7cbb1099e41accd7f4b3fd33f4da4a90eb756" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.748ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} n_{i}=0}"></span>) ; d'où : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =-\left(\sum _{i=1}^{N}\mu _{i}\nu _{i}\right)\,\mathrm {d} \xi =-\sum _{i=1}^{N}\mu _{i}\left(\nu _{i}\,\mathrm {d} \xi \right)=-\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =-\left(\sum _{i=1}^{N}\mu _{i}\nu _{i}\right)\,\mathrm {d} \xi =-\sum _{i=1}^{N}\mu _{i}\left(\nu _{i}\,\mathrm {d} \xi \right)=-\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7b199d5fbd41eded72f05c4dadc0efd82bf640b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:57.779ex; height:7.509ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =-\left(\sum _{i=1}^{N}\mu _{i}\nu _{i}\right)\,\mathrm {d} \xi =-\sum _{i=1}^{N}\mu _{i}\left(\nu _{i}\,\mathrm {d} \xi \right)=-\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}}"></span></dd></dl> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Affinité chimique :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05026f05a43ddbd82ad8906e1a366004865cfeb1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:19.337ex; height:7.343ex;" alt="{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}}"></span> </td></tr></tbody></table> </center> <p>Reprenons l'exemple de l'équilibre du dioxyde et du trioxyde de soufre en présence d'oxygène : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4aaf1cfe63166fa45d9d4a8c65db9354ac1fda5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.486ex; height:2.843ex;" alt="{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}"></span></dd></dl> <p>On a la variation de l'avancement de réaction : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi ={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi ={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05e42753d4244607720ecf895297b6da3d1a5291" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:31.043ex; height:5.843ex;" alt="{\displaystyle \mathrm {d} \xi ={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"></span></dd></dl> <p>d'où : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =-2\,\mu _{\rm {SO_{2}}}\,\mathrm {d} \xi -1\,\mu _{\rm {O_{2}}}\,\mathrm {d} \xi +2\,\mu _{\rm {SO_{3}}}\,\mathrm {d} \xi =-2\,\mu _{\rm {SO_{2}}}\,{\mathrm {d} n_{\rm {SO_{2}}} \over -2}-1\,\mu _{\rm {O_{2}}}\,{\mathrm {d} n_{\rm {O_{2}}} \over -1}+2\,\mu _{\rm {SO_{3}}}\,{\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =-2\,\mu _{\rm {SO_{2}}}\,\mathrm {d} \xi -1\,\mu _{\rm {O_{2}}}\,\mathrm {d} \xi +2\,\mu _{\rm {SO_{3}}}\,\mathrm {d} \xi =-2\,\mu _{\rm {SO_{2}}}\,{\mathrm {d} n_{\rm {SO_{2}}} \over -2}-1\,\mu _{\rm {O_{2}}}\,{\mathrm {d} n_{\rm {O_{2}}} \over -1}+2\,\mu _{\rm {SO_{3}}}\,{\mathrm {d} n_{\rm {SO_{3}}} \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8b78344181a0834955d4d04ebf03037f1321d80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:91.729ex; height:5.843ex;" alt="{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =-2\,\mu _{\rm {SO_{2}}}\,\mathrm {d} \xi -1\,\mu _{\rm {O_{2}}}\,\mathrm {d} \xi +2\,\mu _{\rm {SO_{3}}}\,\mathrm {d} \xi =-2\,\mu _{\rm {SO_{2}}}\,{\mathrm {d} n_{\rm {SO_{2}}} \over -2}-1\,\mu _{\rm {O_{2}}}\,{\mathrm {d} n_{\rm {O_{2}}} \over -1}+2\,\mu _{\rm {SO_{3}}}\,{\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"></span></dd></dl> <p>et finalement la relation : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =\mu _{\rm {SO_{2}}}\,\mathrm {d} n_{\rm {SO_{2}}}+\mu _{\rm {O_{2}}}\,\mathrm {d} n_{\rm {O_{2}}}+\mu _{\rm {SO_{3}}}\,\mathrm {d} n_{\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =\mu _{\rm {SO_{2}}}\,\mathrm {d} n_{\rm {SO_{2}}}+\mu _{\rm {O_{2}}}\,\mathrm {d} n_{\rm {O_{2}}}+\mu _{\rm {SO_{3}}}\,\mathrm {d} n_{\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38374214dc5e88439405085517043300c12097e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:46.339ex; height:3.009ex;" alt="{\displaystyle -{\mathcal {A}}\,\mathrm {d} \xi =\mu _{\rm {SO_{2}}}\,\mathrm {d} n_{\rm {SO_{2}}}+\mu _{\rm {O_{2}}}\,\mathrm {d} n_{\rm {O_{2}}}+\mu _{\rm {SO_{3}}}\,\mathrm {d} n_{\rm {SO_{3}}}}"></span></dd></dl> <p>Les <a href="/wiki/Diff%C3%A9rentielle" title="Différentielle">différentielles</a> des quatre <a href="/wiki/Potentiel_thermodynamique" title="Potentiel thermodynamique">potentiels thermodynamiques</a> s'écrivent : </p> <ul><li><a href="/wiki/%C3%89nergie_interne" title="Énergie interne">énergie interne</a> :</li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U=-P\,\mathrm {d} V+T\,\mathrm {d} S+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=-P\,\mathrm {d} V+T\,\mathrm {d} S-{\mathcal {A}}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>=</mo> <mo>−</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>+</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>+</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U=-P\,\mathrm {d} V+T\,\mathrm {d} S+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=-P\,\mathrm {d} V+T\,\mathrm {d} S-{\mathcal {A}}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557722c82f1bb7250cc2c6b499c240464bf9277a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:58.735ex; height:7.343ex;" alt="{\displaystyle \mathrm {d} U=-P\,\mathrm {d} V+T\,\mathrm {d} S+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=-P\,\mathrm {d} V+T\,\mathrm {d} S-{\mathcal {A}}\,\mathrm {d} \xi }"></span></dd></dl> <ul><li><a href="/wiki/%C3%89nergie_libre" title="Énergie libre">énergie libre</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c80d36ac52e52be78ce8bb9111b0fdf05378ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.598ex; height:2.343ex;" alt="{\displaystyle F=U-TS}"></span></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} F=-P\,\mathrm {d} V-S\,\mathrm {d} T+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=-P\,\mathrm {d} V-S\,\mathrm {d} T-{\mathcal {A}}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>F</mi> <mo>=</mo> <mo>−</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} F=-P\,\mathrm {d} V-S\,\mathrm {d} T+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=-P\,\mathrm {d} V-S\,\mathrm {d} T-{\mathcal {A}}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09f42fbf48097416b4bcccb130ea70a4f87d2a79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:58.693ex; height:7.343ex;" alt="{\displaystyle \mathrm {d} F=-P\,\mathrm {d} V-S\,\mathrm {d} T+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=-P\,\mathrm {d} V-S\,\mathrm {d} T-{\mathcal {A}}\,\mathrm {d} \xi }"></span></dd></dl> <ul><li><a href="/wiki/Enthalpie" title="Enthalpie">enthalpie</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H=U+PV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>P</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H=U+PV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff8a8679f9f841c71be73152fedca0199b673fb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.318ex; height:2.343ex;" alt="{\displaystyle H=U+PV}"></span></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} H=V\,\mathrm {d} P+T\,\mathrm {d} S+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=V\,\mathrm {d} P+T\,\mathrm {d} S-{\mathcal {A}}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>H</mi> <mo>=</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>+</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>+</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>S</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} H=V\,\mathrm {d} P+T\,\mathrm {d} S+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=V\,\mathrm {d} P+T\,\mathrm {d} S-{\mathcal {A}}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b65dc4f6635b667bad3397976361794dc944e2cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:55.4ex; height:7.343ex;" alt="{\displaystyle \mathrm {d} H=V\,\mathrm {d} P+T\,\mathrm {d} S+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=V\,\mathrm {d} P+T\,\mathrm {d} S-{\mathcal {A}}\,\mathrm {d} \xi }"></span></dd></dl> <ul><li><a href="/wiki/Enthalpie_libre" title="Enthalpie libre">enthalpie libre</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G=H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G=H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31abc549d1a3b34b4d49d0785f8f90abbd2396fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.965ex; height:2.343ex;" alt="{\displaystyle G=H-TS}"></span></li></ul> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} G=V\,\mathrm {d} P-S\,\mathrm {d} T+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=V\,\mathrm {d} P-S\,\mathrm {d} T-{\mathcal {A}}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <mo>=</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>V</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G=V\,\mathrm {d} P-S\,\mathrm {d} T+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=V\,\mathrm {d} P-S\,\mathrm {d} T-{\mathcal {A}}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e04f292ffd458eb1723cb50a5d77b8bb3bc78a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:55.163ex; height:7.343ex;" alt="{\displaystyle \mathrm {d} G=V\,\mathrm {d} P-S\,\mathrm {d} T+\sum _{i=1}^{N}\mu _{i}\,\mathrm {d} n_{i}=V\,\mathrm {d} P-S\,\mathrm {d} T-{\mathcal {A}}\,\mathrm {d} \xi }"></span></dd></dl> <p>avec : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> la <a href="/wiki/Pression" title="Pression">pression</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> la <a href="/wiki/Temp%C3%A9rature" title="Température">température</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> le <a href="/wiki/Volume" title="Volume">volume</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> l'<a href="/wiki/Entropie_(thermodynamique)" title="Entropie (thermodynamique)">entropie</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57f87f905ba5a4d8c691ccaecd65fc47bd007ba4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.194ex; height:2.009ex;" alt="{\displaystyle n_{i}}"></span> la <a href="/wiki/Quantit%C3%A9_de_mati%C3%A8re" title="Quantité de matière">quantité</a> du constituant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>.</li></ul> <p>On a donc également les relations suivantes pouvant définir l'<b>affinité chimique</b><sup id="cite_ref-Mesplède-45_12-0" class="reference"><a href="#cite_note-Mesplède-45-12"><span class="cite_crochet">[</span>12<span class="cite_crochet">]</span></a></sup> : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Affinité chimique :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=-\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=-\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=-\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=-\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=-\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00075579dde11aa06d7c3c0fe8afa07dadf505a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:63.434ex; height:6.509ex;" alt="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=-\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=-\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}}"></span> </td></tr></tbody></table> </center> <div class="mw-heading mw-heading3"><h3 id="Dépendance_à_l'écriture_de_la_réaction"><span id="D.C3.A9pendance_.C3.A0_l.27.C3.A9criture_de_la_r.C3.A9action"></span>Dépendance à l'écriture de la réaction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=5" title="Modifier la section : Dépendance à l'écriture de la réaction" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=5" title="Modifier le code source de la section : Dépendance à l'écriture de la réaction"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Puisque les coefficients stœchiométriques entrent dans l'expression de l'affinité chimique, celle-ci dépend de la façon dont la réaction est écrite. Reprenons l'exemple de l'équilibre du dioxyde et du trioxyde de soufre en présence d'oxygène : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇄</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d684659bf8c7c10802281e8516ff20c63a4ad97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.191ex; height:2.843ex;" alt="{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}"></span></dd></dl> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4aaf1cfe63166fa45d9d4a8c65db9354ac1fda5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.486ex; height:2.843ex;" alt="{\displaystyle {\rm {-2\,SO_{2}(g)-1\,O_{2}(g)+2\,SO_{3}(g)=0}}}"></span></center> <p>on a une première expression de l'affinité et de l'avancement de réaction : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}=-\left(-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}+2\,\mu _{\rm {SO_{3}}}\right)=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}=-\left(-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}+2\,\mu _{\rm {SO_{3}}}\right)=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5f2f1aea91513ca00d51d7c7869ee19fb4c9757" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:61.697ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}_{1}=-\left(-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}+2\,\mu _{\rm {SO_{3}}}\right)=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}"></span></center> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{1}={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{1}={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f5acb69516b7018bf93b9b465cacfdd75cc522" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.086ex; height:5.843ex;" alt="{\displaystyle \mathrm {d} \xi _{1}={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"></span></dd></dl> <p>Si l'on inverse l'écriture de la réaction : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {2\,SO_{3}(g)\rightleftarrows 2\,SO_{2}(g)+1\,O_{2}(g)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇄</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {2\,SO_{3}(g)\rightleftarrows 2\,SO_{2}(g)+1\,O_{2}(g)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bd0fe0c41737e8cd8d17d32275d1d5ea49df2fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.191ex; height:2.843ex;" alt="{\displaystyle {\rm {2\,SO_{3}(g)\rightleftarrows 2\,SO_{2}(g)+1\,O_{2}(g)}}}"></span></dd></dl> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {-2\,SO_{3}(g)+2\,SO_{2}(g)+1\,O_{2}(g)=0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {-2\,SO_{3}(g)+2\,SO_{2}(g)+1\,O_{2}(g)=0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e50f40d8e03c8d6f212017a3794771fff7c777b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.486ex; height:2.843ex;" alt="{\displaystyle {\rm {-2\,SO_{3}(g)+2\,SO_{2}(g)+1\,O_{2}(g)=0}}}"></span></center> <p>on a une deuxième expression de l'affinité et de l'avancement de réaction : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{2}=-\left(-2\,\mu _{\rm {SO_{3}}}+2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}\right)=2\,\mu _{\rm {SO_{3}}}-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{2}=-\left(-2\,\mu _{\rm {SO_{3}}}+2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}\right)=2\,\mu _{\rm {SO_{3}}}-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6775c1f779eb47c79eba3ab8a05e0e76bbbccd92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:61.697ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}_{2}=-\left(-2\,\mu _{\rm {SO_{3}}}+2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}\right)=2\,\mu _{\rm {SO_{3}}}-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}}"></span></center> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{2}={\mathrm {d} n_{\rm {SO_{2}}} \over 2}={\mathrm {d} n_{\rm {O_{2}}} \over 1}={\mathrm {d} n_{\rm {SO_{3}}} \over -2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{2}={\mathrm {d} n_{\rm {SO_{2}}} \over 2}={\mathrm {d} n_{\rm {O_{2}}} \over 1}={\mathrm {d} n_{\rm {SO_{3}}} \over -2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8d67715d3d9327c01f65852160076b56f433db7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.086ex; height:5.843ex;" alt="{\displaystyle \mathrm {d} \xi _{2}={\mathrm {d} n_{\rm {SO_{2}}} \over 2}={\mathrm {d} n_{\rm {O_{2}}} \over 1}={\mathrm {d} n_{\rm {SO_{3}}} \over -2}}"></span></dd></dl> <p>Et si l'on écrit la réaction d'une troisième façon, en divisant par deux les coefficients stœchiométriques de la première écriture : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {1\,SO_{2}(g)+{1 \over 2}\,O_{2}(g)\rightleftarrows 1\,SO_{3}(g)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇄</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {1\,SO_{2}(g)+{1 \over 2}\,O_{2}(g)\rightleftarrows 1\,SO_{3}(g)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bef2c0093a37ba5112e995c45d15a1025e7201c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:32.027ex; height:5.176ex;" alt="{\displaystyle {\rm {1\,SO_{2}(g)+{1 \over 2}\,O_{2}(g)\rightleftarrows 1\,SO_{3}(g)}}}"></span></dd></dl> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {-1\,SO_{2}(g)-{1 \over 2}\,O_{2}(g)+1\,SO_{3}(g)=0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {-1\,SO_{2}(g)-{1 \over 2}\,O_{2}(g)+1\,SO_{3}(g)=0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5b80ca7e35bc2fcbdef83e243f4902fb5fb1c93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:37.322ex; height:5.176ex;" alt="{\displaystyle {\rm {-1\,SO_{2}(g)-{1 \over 2}\,O_{2}(g)+1\,SO_{3}(g)=0}}}"></span></center> <p>on a une troisième expression de l'affinité et de l'avancement de réaction : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{3}=-\left(-1\,\mu _{\rm {SO_{2}}}-{1 \over 2}\,\mu _{\rm {O_{2}}}+1\,\mu _{\rm {SO_{3}}}\right)=1\,\mu _{\rm {SO_{2}}}+{1 \over 2}\,\mu _{\rm {O_{2}}}-1\,\mu _{\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{3}=-\left(-1\,\mu _{\rm {SO_{2}}}-{1 \over 2}\,\mu _{\rm {O_{2}}}+1\,\mu _{\rm {SO_{3}}}\right)=1\,\mu _{\rm {SO_{2}}}+{1 \over 2}\,\mu _{\rm {O_{2}}}-1\,\mu _{\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb77398b34b5843367325c3e66de26f983623d04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:64.982ex; height:6.176ex;" alt="{\displaystyle {\mathcal {A}}_{3}=-\left(-1\,\mu _{\rm {SO_{2}}}-{1 \over 2}\,\mu _{\rm {O_{2}}}+1\,\mu _{\rm {SO_{3}}}\right)=1\,\mu _{\rm {SO_{2}}}+{1 \over 2}\,\mu _{\rm {O_{2}}}-1\,\mu _{\rm {SO_{3}}}}"></span></center> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{3}={\mathrm {d} n_{\rm {SO_{2}}} \over -1}={\mathrm {d} n_{\rm {O_{2}}} \over -{1 \over 2}}={\mathrm {d} n_{\rm {SO_{3}}} \over 1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>1</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{3}={\mathrm {d} n_{\rm {SO_{2}}} \over -1}={\mathrm {d} n_{\rm {O_{2}}} \over -{1 \over 2}}={\mathrm {d} n_{\rm {SO_{3}}} \over 1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f39d7587ed1c1cf179ec61b64e3cc0531966aa42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:32.086ex; height:7.176ex;" alt="{\displaystyle \mathrm {d} \xi _{3}={\mathrm {d} n_{\rm {SO_{2}}} \over -1}={\mathrm {d} n_{\rm {O_{2}}} \over -{1 \over 2}}={\mathrm {d} n_{\rm {SO_{3}}} \over 1}}"></span></dd></dl> <p>On a ainsi, selon la façon d'écrire la réaction : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}=-{\mathcal {A}}_{2}=2\,{\mathcal {A}}_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}=-{\mathcal {A}}_{2}=2\,{\mathcal {A}}_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/928201327c112a795aba6bb7e4d3bca38bf5424c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.281ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{1}=-{\mathcal {A}}_{2}=2\,{\mathcal {A}}_{3}}"></span></center> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{1}=-\mathrm {d} \xi _{2}={1 \over 2}\,\mathrm {d} \xi _{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{1}=-\mathrm {d} \xi _{2}={1 \over 2}\,\mathrm {d} \xi _{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2936b2d643159a74750610146ec4c8a069636d63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.486ex; height:5.176ex;" alt="{\displaystyle \mathrm {d} \xi _{1}=-\mathrm {d} \xi _{2}={1 \over 2}\,\mathrm {d} \xi _{3}}"></span></center> <p>Il est donc nécessaire, pour utiliser l'affinité, de connaitre la façon dont la réaction a été écrite. En particulier, les première et deuxième écritures de la réaction donnent des affinités de signes opposés. Néanmoins, quelle que soit la façon d'écrire la réaction, on a : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\mathcal {A}}_{1}\,\mathrm {d} \xi _{1}=-{\mathcal {A}}_{2}\,\mathrm {d} \xi _{2}=-{\mathcal {A}}_{3}\,\mathrm {d} \xi _{3}=\mu _{\rm {SO_{2}}}\,\mathrm {d} n_{\rm {SO_{2}}}+\mu _{\rm {O_{2}}}\,\mathrm {d} n_{\rm {O_{2}}}+\mu _{\rm {SO_{3}}}\,\mathrm {d} n_{\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\mathcal {A}}_{1}\,\mathrm {d} \xi _{1}=-{\mathcal {A}}_{2}\,\mathrm {d} \xi _{2}=-{\mathcal {A}}_{3}\,\mathrm {d} \xi _{3}=\mu _{\rm {SO_{2}}}\,\mathrm {d} n_{\rm {SO_{2}}}+\mu _{\rm {O_{2}}}\,\mathrm {d} n_{\rm {O_{2}}}+\mu _{\rm {SO_{3}}}\,\mathrm {d} n_{\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c937fba6b0de76099c35648192a7b279cf52b98a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:71.522ex; height:3.009ex;" alt="{\displaystyle -{\mathcal {A}}_{1}\,\mathrm {d} \xi _{1}=-{\mathcal {A}}_{2}\,\mathrm {d} \xi _{2}=-{\mathcal {A}}_{3}\,\mathrm {d} \xi _{3}=\mu _{\rm {SO_{2}}}\,\mathrm {d} n_{\rm {SO_{2}}}+\mu _{\rm {O_{2}}}\,\mathrm {d} n_{\rm {O_{2}}}+\mu _{\rm {SO_{3}}}\,\mathrm {d} n_{\rm {SO_{3}}}}"></span></center> <div class="mw-heading mw-heading2"><h2 id="Condition_d'évolution_spontanée_d'un_système_chimique"><span id="Condition_d.27.C3.A9volution_spontan.C3.A9e_d.27un_syst.C3.A8me_chimique"></span>Condition d'évolution spontanée d'un système chimique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=6" title="Modifier la section : Condition d'évolution spontanée d'un système chimique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=6" title="Modifier le code source de la section : Condition d'évolution spontanée d'un système chimique"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Rappels_sur_l'avancement_de_réaction"><span id="Rappels_sur_l.27avancement_de_r.C3.A9action"></span>Rappels sur l'avancement de réaction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=7" title="Modifier la section : Rappels sur l'avancement de réaction" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=7" title="Modifier le code source de la section : Rappels sur l'avancement de réaction"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/Avancement_de_r%C3%A9action" title="Avancement de réaction">Avancement de réaction</a>.</div></div> <p>Nous considérons une réaction chimique dont l'<a href="/wiki/%C3%89quation_chimique" title="Équation chimique">équation bilan</a> est écrite selon la <a href="/wiki/St%C5%93chiom%C3%A9trie#Nombres_stœchiométriques_négatifs" title="Stœchiométrie">convention stœchiométrique</a> : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{1}\,{\rm {C}}_{1}+\nu _{2}\,{\rm {C}}_{2}+\cdots +\nu _{N}\,{\rm {C}}_{N}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{1}\,{\rm {C}}_{1}+\nu _{2}\,{\rm {C}}_{2}+\cdots +\nu _{N}\,{\rm {C}}_{N}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b09ecb23d1efd1be3de26e64b802d6e0ae2b845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.746ex; height:2.509ex;" alt="{\displaystyle \nu _{1}\,{\rm {C}}_{1}+\nu _{2}\,{\rm {C}}_{2}+\cdots +\nu _{N}\,{\rm {C}}_{N}=0}"></span></center> <p>en attribuant une valeur négative aux coefficients stœchiométriques des réactifs et positive à ceux des produits : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aeee4853b360ba323e932acb72159b1c9c357841" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}<0}"></span> pour un <a href="/wiki/R%C3%A9actif_(chimie)" title="Réactif (chimie)">réactif</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44d9c0eac121342f83f680ea9963901ddfded18f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}>0}"></span> pour un <a href="/wiki/Produit_de_r%C3%A9action" title="Produit de réaction">produit</a> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d370e94d86d8182d557ea2b10e8d6f7d63a1145c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}=0}"></span> pour un <a href="/wiki/Inerte_(chimie)" title="Inerte (chimie)">inerte</a>.</li></ul> <p>La réaction progresse en respectant la stœchiométrie de l'équation bilan, aussi si la quantité de l'espèce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> varie de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca6bcd8599eb508c8c4bf626eaa65f9533f573cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.741ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} n_{1}}"></span>, la quantité de toute autre espèce <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\in [1,\cdots ,N]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>1</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>N</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\in [1,\cdots ,N]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b408c2723c4b77edc723df1fdc3eab75284902b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.341ex; height:2.843ex;" alt="{\displaystyle i\in [1,\cdots ,N]}"></span> varie de : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{i}={\nu _{i} \over \nu _{1}}\,\mathrm {d} n_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{i}={\nu _{i} \over \nu _{1}}\,\mathrm {d} n_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa636772ba931732ab0a681cf038b7ba9fe25713" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.753ex; height:5.009ex;" alt="{\displaystyle \mathrm {d} n_{i}={\nu _{i} \over \nu _{1}}\,\mathrm {d} n_{1}}"></span>, ce qui implique que tous les rapports <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathrm {d} n_{i} \over \nu _{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathrm {d} n_{i} \over \nu _{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d9d5fd29d8c2737c6e50415ee18c02cdd23acca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:4.323ex; height:5.676ex;" alt="{\displaystyle {\mathrm {d} n_{i} \over \nu _{i}}}"></span> sont égaux. On définit ainsi le paramètre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span> appelé <b>avancement de la réaction</b> : </p> <center><b>Avancement de la réaction :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi ={\frac {\mathrm {d} n_{1}}{\nu _{1}}}=\cdots ={\frac {\mathrm {d} n_{i}}{\nu _{i}}}=\cdots ={\frac {\mathrm {d} n_{N}}{\nu _{N}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mo>⋯</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mo>⋯</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> </mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi ={\frac {\mathrm {d} n_{1}}{\nu _{1}}}=\cdots ={\frac {\mathrm {d} n_{i}}{\nu _{i}}}=\cdots ={\frac {\mathrm {d} n_{N}}{\nu _{N}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26d0432efc9b044e402fbb09b275b6495271bd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:37.377ex; height:5.676ex;" alt="{\displaystyle \mathrm {d} \xi ={\frac {\mathrm {d} n_{1}}{\nu _{1}}}=\cdots ={\frac {\mathrm {d} n_{i}}{\nu _{i}}}=\cdots ={\frac {\mathrm {d} n_{N}}{\nu _{N}}}}"></span></center> <p>L'avancement est donc défini pour toutes les espèces du mélange réactionnel, y compris les inertes pour lesquels <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d370e94d86d8182d557ea2b10e8d6f7d63a1145c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}=0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{i}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{i}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe7cbb1099e41accd7f4b3fd33f4da4a90eb756" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.748ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} n_{i}=0}"></span>. </p><p>Lorsque la quantité d'une espèce augmente, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{i}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{i}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/155d8d0b211441148e5c904cd2882e350ea08146" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.748ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} n_{i}>0}"></span> : </p> <ul><li>s'il s'agit d'un produit, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44d9c0eac121342f83f680ea9963901ddfded18f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}>0}"></span>, alors <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c18566664fa065930257ba762160b7c7aafd9ad4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi >0}"></span> ;</li> <li>s'il s'agit d'un réactif, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aeee4853b360ba323e932acb72159b1c9c357841" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}<0}"></span>, alors <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31903c372b25d62f311cde0c68ac07c738eeea90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi <0}"></span>.</li></ul> <p>Inversement, lorsque la quantité d'une espèce diminue, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{i}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{i}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9cc17d41f3b6f6c0369aaca89fa39699d1f8cf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.748ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} n_{i}<0}"></span> : </p> <ul><li>s'il s'agit d'un produit, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44d9c0eac121342f83f680ea9963901ddfded18f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}>0}"></span>, alors <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31903c372b25d62f311cde0c68ac07c738eeea90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi <0}"></span> ;</li> <li>s'il s'agit d'un réactif, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aeee4853b360ba323e932acb72159b1c9c357841" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.209ex; height:2.509ex;" alt="{\displaystyle \nu _{i}<0}"></span>, alors <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c18566664fa065930257ba762160b7c7aafd9ad4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi >0}"></span>.</li></ul> <p>En conséquence : </p> <ul><li>lorsque les réactifs disparaissent et que les produits apparaissent, c'est-à-dire lorsque <b>la réaction progresse</b> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c18566664fa065930257ba762160b7c7aafd9ad4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi >0}"></span> ;</li> <li>lorsque les réactifs apparaissent et que les produits disparaissent, c'est-à-dire lorsque <b>la réaction régresse</b> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31903c372b25d62f311cde0c68ac07c738eeea90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi <0}"></span>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Relation_avec_l'entropie_du_système_réactionnel"><span id="Relation_avec_l.27entropie_du_syst.C3.A8me_r.C3.A9actionnel"></span>Relation avec l'entropie du système réactionnel</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=8" title="Modifier la section : Relation avec l'entropie du système réactionnel" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=8" title="Modifier le code source de la section : Relation avec l'entropie du système réactionnel"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Soit un <a href="/wiki/Syst%C3%A8me_ferm%C3%A9" title="Système fermé">système fermé</a> dans lequel s'effectue une réaction chimique. L'énergie interne de ce système évolue donc selon : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}+T_{\text{sys}}\,\mathrm {d} S_{\text{sys}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta W_{\text{sys}}+\delta Q_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}+T_{\text{sys}}\,\mathrm {d} S_{\text{sys}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta W_{\text{sys}}+\delta Q_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ebd80b2bb55fbe54d9e3ef483af9677c28ecb99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:55.91ex; height:3.009ex;" alt="{\displaystyle \mathrm {d} U_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}+T_{\text{sys}}\,\mathrm {d} S_{\text{sys}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta W_{\text{sys}}+\delta Q_{\text{sys}}}"></span></dd></dl> <p>avec : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fa1c5ce59c589a5df63722738f280d64ded5b27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.984ex; height:2.843ex;" alt="{\displaystyle U_{\text{sys}}}"></span> l'énergie interne du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1493cbe8417c409c709f70b2d268655e7d218c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.888ex; height:2.843ex;" alt="{\displaystyle P_{\text{sys}}}"></span> la pression du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36b10aae702b78c349e9ee9b9285868d243fe282" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.751ex; height:2.843ex;" alt="{\displaystyle V_{\text{sys}}}"></span> le volume du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1eea018d6eb4316bb7e30220904e12fc7707fd87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.754ex; height:2.843ex;" alt="{\displaystyle T_{\text{sys}}}"></span> la température du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/caae3e59006bba7ce971db2ca550fe2a823f84f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.821ex; height:2.843ex;" alt="{\displaystyle S_{\text{sys}}}"></span> l'entropie du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dbafbf31f3124ee871e3dd955ee4ff27e755bb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.864ex; height:3.009ex;" alt="{\displaystyle \delta W_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}}"></span> le travail des forces de pression du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d0efb231c6683dad72faf9a6bfefbef2814648c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.283ex; height:3.009ex;" alt="{\displaystyle \delta Q_{\text{sys}}}"></span> la chaleur échangée par le système avec l'extérieur.</li></ul> <p>Pour l'extérieur du système, qui n'est pas le siège d'une réaction chimique, l'énergie interne évolue selon : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}+T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}=\delta W_{\text{ext}}+\delta Q_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}+T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}=\delta W_{\text{ext}}+\delta Q_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df97ac801e341376f3e97856fa4b56e0bae22246" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:48.974ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} U_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}+T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}=\delta W_{\text{ext}}+\delta Q_{\text{ext}}}"></span></dd></dl> <p>avec : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82a87886cf3c995298a11efa82b2a59d372d6f3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.057ex; height:2.509ex;" alt="{\displaystyle U_{\text{ext}}}"></span> l'énergie interne de l'extérieur ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90b10336e64007b8bef3510cca421475746fe94a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.962ex; height:2.509ex;" alt="{\displaystyle P_{\text{ext}}}"></span> la pression de l'extérieur ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76dc8f9e2829ce2e63e9a1fad9c352035b42ad00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.825ex; height:2.509ex;" alt="{\displaystyle V_{\text{ext}}}"></span> le volume de l'extérieur ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64dc9881db151a09ac92062e78db87d70ca3db12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.827ex; height:2.509ex;" alt="{\displaystyle T_{\text{ext}}}"></span> la température de l'extérieur ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27243d5e9fac9ee81fb45adb538ffa7ee2640d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.895ex; height:2.509ex;" alt="{\displaystyle S_{\text{ext}}}"></span> l'entropie de l'extérieur ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71bd40b1aacfc7d052fb8a39c04c7dc76991d49b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.086ex; height:2.676ex;" alt="{\displaystyle \delta W_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}}"></span> le travail des forces de pression de l'extérieur ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q_{\text{ext}}=T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{\text{ext}}=T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f37b2187e7dac16f02bdf47ff08d1164f8979af8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.857ex; height:2.676ex;" alt="{\displaystyle \delta Q_{\text{ext}}=T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}}"></span> la chaleur échangée par l'extérieur avec le système.</li></ul> <p>Nous supposerons que le système et l'extérieur forment un <a href="/wiki/Syst%C3%A8me_isol%C3%A9" title="Système isolé">système isolé</a> lors de la réaction. Le <a href="/wiki/Premier_principe_de_la_thermodynamique" title="Premier principe de la thermodynamique">premier principe de la thermodynamique</a> implique la conservation globale de l'énergie du système et de l'extérieur, soit : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U_{\text{sys}}+\mathrm {d} U_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U_{\text{sys}}+\mathrm {d} U_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce14fa8409006ed24f4ce52f99ac8d48c56dd5b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.727ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} U_{\text{sys}}+\mathrm {d} U_{\text{ext}}=0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}+T_{\text{sys}}\,\mathrm {d} S_{\text{sys}}+T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta W_{\text{sys}}+\delta W_{\text{ext}}+\delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}+T_{\text{sys}}\,\mathrm {d} S_{\text{sys}}+T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta W_{\text{sys}}+\delta W_{\text{ext}}+\delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a25d70ee49746a69779581487451a311802aac0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:93.096ex; height:3.009ex;" alt="{\displaystyle -P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}+T_{\text{sys}}\,\mathrm {d} S_{\text{sys}}+T_{\text{ext}}\,\mathrm {d} S_{\text{ext}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta W_{\text{sys}}+\delta W_{\text{ext}}+\delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}"></span></dd></dl> <p>Le système et l'extérieur : </p> <ul><li>forment un ensemble à volume constant, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} V_{\text{sys}}+\mathrm {d} V_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} V_{\text{sys}}+\mathrm {d} V_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ceef0808ba5df8686cc81b94e35f5460dac112d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.263ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} V_{\text{sys}}+\mathrm {d} V_{\text{ext}}=0}"></span> à tout instant (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36b10aae702b78c349e9ee9b9285868d243fe282" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.751ex; height:2.843ex;" alt="{\displaystyle V_{\text{sys}}}"></span> pouvant varier au cours de la réaction) ;</li> <li>sont en équilibre mécanique permanent, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\text{sys}}=P_{\text{ext}}=P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\text{sys}}=P_{\text{ext}}=P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/143e47f0cb258dbf86c83f05c6a33e21c2ebda63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.793ex; height:2.843ex;" alt="{\displaystyle P_{\text{sys}}=P_{\text{ext}}=P}"></span> à tout instant (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> pouvant varier au cours de la réaction) ;</li> <li>sont en <a href="/wiki/%C3%89quilibre_thermique" title="Équilibre thermique">équilibre thermique</a> permanent, soit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\text{sys}}=T_{\text{ext}}=T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\text{sys}}=T_{\text{ext}}=T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d800dedc5427af3b00e348bf42b0528198982fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.414ex; height:2.843ex;" alt="{\displaystyle T_{\text{sys}}=T_{\text{ext}}=T}"></span> à tout instant (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> pouvant varier au cours de la réaction).</li></ul> <p>Nous avons donc pour le travail des forces de pression : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}=-P\,\mathrm {d} V_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}=-P\,\mathrm {d} V_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f0342132cbef55295dde10c7be442c766e171e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:31.947ex; height:3.009ex;" alt="{\displaystyle \delta W_{\text{sys}}=-P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}=-P\,\mathrm {d} V_{\text{sys}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}=P\,\mathrm {d} V_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}=P\,\mathrm {d} V_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a4fa523da5e8cb742b90049fb6be31a552298c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:30.361ex; height:3.009ex;" alt="{\displaystyle \delta W_{\text{ext}}=-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}=P\,\mathrm {d} V_{\text{sys}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5929a4128f3d7d9668cd6c2a1c17de18240db8f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.696ex; height:2.843ex;" alt="{\displaystyle -P_{\text{sys}}\,\mathrm {d} V_{\text{sys}}-P_{\text{ext}}\,\mathrm {d} V_{\text{ext}}=0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W_{\text{sys}}+\delta W_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta W_{\text{sys}}+\delta W_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d7c0f95230c4c7629ddddff7bf1f5b66f42318b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.452ex; height:3.009ex;" alt="{\displaystyle \delta W_{\text{sys}}+\delta W_{\text{ext}}=0}"></span></dd></dl> <p>Par conséquent : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U_{\text{sys}}+\mathrm {d} U_{\text{ext}}=T\,\mathrm {d} S_{\text{sys}}+T\,\mathrm {d} S_{\text{ext}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U_{\text{sys}}+\mathrm {d} U_{\text{ext}}=T\,\mathrm {d} S_{\text{sys}}+T\,\mathrm {d} S_{\text{ext}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a48e69a763ea18138d4c6444e9e72a46e9fe175" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:62.046ex; height:3.009ex;" alt="{\displaystyle \mathrm {d} U_{\text{sys}}+\mathrm {d} U_{\text{ext}}=T\,\mathrm {d} S_{\text{sys}}+T\,\mathrm {d} S_{\text{ext}}-{\mathcal {A}}\,\mathrm {d} \xi =\delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}"></span></dd></dl> <p>et donc pour la chaleur : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc62fa6bee0d680d1595b513d631c38e9eca5bae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.741ex; height:3.009ex;" alt="{\displaystyle \delta Q_{\text{sys}}+\delta Q_{\text{ext}}=0}"></span></dd></dl> <p>Il s'ensuit également la relation qui relie affinité chimique et entropie : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Affinité chimique :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}=\mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}=\mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/414822029ab2ccd4730c41a58bc9b6d8bc185fa7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.689ex; height:5.509ex;" alt="{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}=\mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}}"></span> </td></tr></tbody></table> </center> <p>L'expression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mrow> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a05f3fa21ac692b59f0461105abb74a640c43569" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.449ex; height:5.509ex;" alt="{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}}"></span> est donc <b>l'entropie créée par la réaction</b>. </p><p>On peut également écrire, puisque : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} S_{\text{ext}}={\delta Q_{\text{ext}} \over T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mrow> <mi>T</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} S_{\text{ext}}={\delta Q_{\text{ext}} \over T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c545b338a13926444ce11592691f7a7666f39a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.479ex; height:5.343ex;" alt="{\displaystyle \mathrm {d} S_{\text{ext}}={\delta Q_{\text{ext}} \over T}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q_{\text{ext}}=-\delta Q_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{\text{ext}}=-\delta Q_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd8051119e815e90f9a5210cd8fef38ce480c16e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.546ex; height:3.009ex;" alt="{\displaystyle \delta Q_{\text{ext}}=-\delta Q_{\text{sys}}}"></span></dd></dl> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Affinité chimique :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\delta Q_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\delta Q_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1325ef9ad8809c7296acf929fabd2f1181ef603" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.972ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\delta Q_{\text{sys}}}"></span> </td></tr></tbody></table> </center> <p>L'expression <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feb515d545dd4ce9e7a27498fde7c3d0cc31f8c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.613ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi }"></span> est donc la chaleur créée par la réaction qui n'est pas échangée avec l'extérieur, c'est-à-dire la « <b>chaleur non compensée</b> » de Clausius. </p> <div class="mw-heading mw-heading3"><h3 id="Formulation_générale"><span id="Formulation_g.C3.A9n.C3.A9rale"></span>Formulation générale</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=9" title="Modifier la section : Formulation générale" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=9" title="Modifier le code source de la section : Formulation générale"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le <a href="/wiki/Deuxi%C3%A8me_principe_de_la_thermodynamique" title="Deuxième principe de la thermodynamique">deuxième principe de la thermodynamique</a> implique que l'entropie globale du système et de l'extérieur ne peut qu'augmenter, d'où : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}=\mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mrow> <mi>T</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}=\mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}\geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c0ec4e26121a8b9c721484edf389736d102e271" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.95ex; height:5.509ex;" alt="{\displaystyle {{\mathcal {A}}\,\mathrm {d} \xi \over T}=\mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}\geq 0}"></span></dd></dl> <p>On en tire la <b>condition d'évolution spontanée</b> de toute réaction chimique (la température absolue <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> étant toujours positive)<sup id="cite_ref-Mesplède-45_12-1" class="reference"><a href="#cite_note-Mesplède-45-12"><span class="cite_crochet">[</span>12<span class="cite_crochet">]</span></a></sup> : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Condition d'évolution spontanée :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e884df098d1c5068f1cba8c0346d3cb141fa401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"></span> </td></tr></tbody></table> </center> <p>Une réaction ne peut être <i>spontanée</i> que si <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e95b9672fc07c391ba02a1b943360e546c1e47a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi >0}"></span> ; dans ce cas la réaction libère une forme d'énergie, elle est dite <i><a href="/wiki/R%C3%A9action_exergonique" title="Réaction exergonique">exergonique</a></i>. Une réaction dans laquelle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/323d62d8dfdda94ab82d52d933199b4ce67ef678" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi <0}"></span> <i>n'est pas impossible</i>, mais elle doit être <i>provoquée</i> par un apport d'énergie, elle est alors dite <i><a href="/wiki/R%C3%A9action_endergonique" title="Réaction endergonique">endergonique</a></i>. Une réaction endergonique peut par exemple avoir lieu en présence d'une autre réaction créant suffisamment d'entropie pour que le bilan entropique global des deux réactions soit positif conformément au deuxième principe de la thermodynamique. </p><p>Dans une réaction spontanée <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/280ae03440942ab348c2ca9b8db6b56ffa9618f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.903ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89dad203ae5bdf94199adc19c338525861e04e86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.323ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi }"></span> ne peuvent donc être que de même signe : </p> <ul><li>une progression est associée à un signe positif : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c18566664fa065930257ba762160b7c7aafd9ad4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi >0}"></span> et par conséquent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba3c2b0a70538e75f9cbe69c1a29647fc296369f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.164ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}>0}"></span>, <b>la réaction progresse</b> : des réactifs sont consommés, des produits apparaissent ;</li> <li>une régression est associée à un signe négatif : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31903c372b25d62f311cde0c68ac07c738eeea90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi <0}"></span> et par conséquent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beca201aa44ce1453cdddb777517834c09727227" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.164ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}<0}"></span>, <b>la réaction régresse</b> : des produits sont consommés, des réactifs apparaissent.</li></ul> <p>Cette relation permet de prédire le sens d'évolution spontanée de la réaction à partir du signe de l'affinité chimique. L'affinité chimique étant une <a href="/wiki/Fonction_d%27%C3%A9tat" title="Fonction d'état">fonction d'état</a>, il suffit de la calculer dans les conditions opératoires initiales pour savoir dans quel sens la réaction va s'effectuer spontanément. </p><p>Rappelons toutefois que l'expression de l'affinité chimique dépend de la façon dont la réaction est écrite. Cette écriture conditionne par conséquent le signe de l'affinité. Reprenons l'exemple de l'équilibre du trioxyde et du dioxyde de soufre en présence d'oxygène, nous avons notamment une première écriture : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇄</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d684659bf8c7c10802281e8516ff20c63a4ad97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.191ex; height:2.843ex;" alt="{\displaystyle {\rm {2\,SO_{2}(g)+1\,O_{2}(g)\rightleftarrows 2\,SO_{3}(g)}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9ae01447c8488899d5de78f75dfd4119fb10533" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.397ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}_{1}=2\,\mu _{\rm {SO_{2}}}+1\,\mu _{\rm {O_{2}}}-2\,\mu _{\rm {SO_{3}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{1}={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{1}={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f5acb69516b7018bf93b9b465cacfdd75cc522" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.086ex; height:5.843ex;" alt="{\displaystyle \mathrm {d} \xi _{1}={\mathrm {d} n_{\rm {SO_{2}}} \over -2}={\mathrm {d} n_{\rm {O_{2}}} \over -1}={\mathrm {d} n_{\rm {SO_{3}}} \over 2}}"></span></dd></dl> <p>et une deuxième écriture avec l'écriture inverse : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {2\,SO_{3}(g)\rightleftarrows 2\,SO_{2}(g)+1\,O_{2}(g)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇄</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">g</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {2\,SO_{3}(g)\rightleftarrows 2\,SO_{2}(g)+1\,O_{2}(g)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bd0fe0c41737e8cd8d17d32275d1d5ea49df2fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.191ex; height:2.843ex;" alt="{\displaystyle {\rm {2\,SO_{3}(g)\rightleftarrows 2\,SO_{2}(g)+1\,O_{2}(g)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{2}=2\,\mu _{\rm {SO_{3}}}-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{2}=2\,\mu _{\rm {SO_{3}}}-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9620a4d92766bf8c755f6d7ea9a9bd53edc51009" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.397ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}_{2}=2\,\mu _{\rm {SO_{3}}}-2\,\mu _{\rm {SO_{2}}}-1\,\mu _{\rm {O_{2}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{2}={\mathrm {d} n_{\rm {SO_{2}}} \over 2}={\mathrm {d} n_{\rm {O_{2}}} \over 1}={\mathrm {d} n_{\rm {SO_{3}}} \over -2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{2}={\mathrm {d} n_{\rm {SO_{2}}} \over 2}={\mathrm {d} n_{\rm {O_{2}}} \over 1}={\mathrm {d} n_{\rm {SO_{3}}} \over -2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8d67715d3d9327c01f65852160076b56f433db7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.086ex; height:5.843ex;" alt="{\displaystyle \mathrm {d} \xi _{2}={\mathrm {d} n_{\rm {SO_{2}}} \over 2}={\mathrm {d} n_{\rm {O_{2}}} \over 1}={\mathrm {d} n_{\rm {SO_{3}}} \over -2}}"></span></dd></dl> <p>Quelle que soit l'écriture, une affinité positive signifie que la réaction progresse, qu'elle se déplace de la gauche vers la droite (sens direct <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"></span>) ; cependant : </p> <ul><li>selon la première écriture : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/607763a364e8168c76081f53643a8f3c702dd82b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{1}>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{1}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{1}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90a92c26b5a598e9f02e1647c5649e85d5b264a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.626ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi _{1}>0}"></span>, donc <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d2ff2e82009b934d8ff19fd32ff6c27a3f8bb65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e928774444d6b512e617ad7170fe86f96a68a1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}<0}"></span>, c'est la formation du trioxyde de soufre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5620b3732625bb46b96b5bbcf7ff38cfd6b6d01b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.155ex; height:2.509ex;" alt="{\displaystyle {\rm {SO_{3}}}}"></span> qui est favorisée ;</li> <li>selon la deuxième écriture : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{2}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{2}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d476588b8898d9b18ec1d7e409e53f958f6247a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{2}>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{2}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{2}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/519718c2f1b59a35a0b5d091b4d6d12dc1fab780" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.626ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi _{2}>0}"></span>, donc <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0879dcfd12bdb98c0200e1de4d27234df354467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7e7ff442400d89577ba719874d49aad76c0804d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}<0}"></span>, c'est la formation du dioxyde de soufre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {SO_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {SO_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd2d8693e91d14a6b118887fe0efa16335e5f7ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.155ex; height:2.509ex;" alt="{\displaystyle {\rm {SO_{2}}}}"></span> qui est favorisée.</li></ul> <p>Inversement, une affinité négative signifie que la réaction régresse, qu'elle se déplace de la droite vers la gauche (sens inverse <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span>) ; cependant : </p> <ul><li>selon la première écriture : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9146ca7771b51776f69c1bb01f0d9ce87a2bae17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{1}<0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{1}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{1}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70eab658b259d2d9116e7b86de72230a2706ceb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.626ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi _{1}<0}"></span>, donc <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0879dcfd12bdb98c0200e1de4d27234df354467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7e7ff442400d89577ba719874d49aad76c0804d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}<0}"></span>, c'est la formation du dioxyde de soufre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {SO_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {SO_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd2d8693e91d14a6b118887fe0efa16335e5f7ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.155ex; height:2.509ex;" alt="{\displaystyle {\rm {SO_{2}}}}"></span> qui est favorisée ;</li> <li>selon la deuxième écriture : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{2}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{2}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c32c359fe3ccd8f316507c73bf75a287f4698a53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{2}<0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi _{2}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi _{2}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05748f9e566060d03b5b604c48137cb9d26d1c93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.626ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi _{2}<0}"></span>, donc <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d2ff2e82009b934d8ff19fd32ff6c27a3f8bb65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{3}}}>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e928774444d6b512e617ad7170fe86f96a68a1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.204ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} n_{\rm {SO_{2}}}<0}"></span>, c'est la formation du trioxyde de soufre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5620b3732625bb46b96b5bbcf7ff38cfd6b6d01b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.155ex; height:2.509ex;" alt="{\displaystyle {\rm {SO_{3}}}}"></span> qui est favorisée.</li></ul> <p>On a donc deux cas selon le produit recherché : </p> <ul><li>la production de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {SO_{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {SO_{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5620b3732625bb46b96b5bbcf7ff38cfd6b6d01b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.155ex; height:2.509ex;" alt="{\displaystyle {\rm {SO_{3}}}}"></span> est favorisée si <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/607763a364e8168c76081f53643a8f3c702dd82b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{1}>0}"></span> ou <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{2}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{2}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c32c359fe3ccd8f316507c73bf75a287f4698a53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{2}<0}"></span> ;</li> <li>la production de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\rm {SO_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\rm {SO_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd2d8693e91d14a6b118887fe0efa16335e5f7ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.155ex; height:2.509ex;" alt="{\displaystyle {\rm {SO_{2}}}}"></span> est favorisée si <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9146ca7771b51776f69c1bb01f0d9ce87a2bae17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{1}<0}"></span> ou <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{2}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{2}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d476588b8898d9b18ec1d7e409e53f958f6247a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.17ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{2}>0}"></span>.</li></ul> <p>Cet exemple illustre la nécessité de connaitre la façon dont la réaction est écrite dans l'utilisation de l'affinité chimique. Néanmoins, quelle que soit l'écriture et quel que soit le sens de déplacement de la réaction, on a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}\,\mathrm {d} \xi _{1}={\mathcal {A}}_{2}\,\mathrm {d} \xi _{2}\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}\,\mathrm {d} \xi _{1}={\mathcal {A}}_{2}\,\mathrm {d} \xi _{2}\geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3968d845d3f315defa464bce6f246f688df6072e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.682ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{1}\,\mathrm {d} \xi _{1}={\mathcal {A}}_{2}\,\mathrm {d} \xi _{2}\geq 0}"></span>. </p><p>À l'équilibre l'entropie atteint un maximum et ne varie plus, alors <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a329d47ed2422fe6ccdbd49143b01cada3cf80a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =0}"></span>. Deux cas sont possibles : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf57ca6b08f69f3fdcfeac4642cc7c339f229735" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.164ex; height:2.843ex;" alt="{\displaystyle {\mathcal {A}}\neq 0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0026e072e7c4c928c7378f74bcb0119c1c61341b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi =0}"></span>, la réaction pourrait avoir lieu car le potentiel de réaction est non nul, mais l'avancement de réaction ne varie pas ; les causes de ce défaut de réaction peuvent être une <a href="/wiki/Cin%C3%A9tique_chimique" title="Cinétique chimique">cinétique</a> extrêmement lente (l'équilibre est dit <b>instable</b>) ou l'absence d'un facteur déclenchant (l'équilibre est dit <b>métastable</b>)<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite_crochet">[</span>13<span class="cite_crochet">]</span></a></sup> ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e910693c11b298e27340bac2bc9d8ed8faac016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.164ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}=0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi \neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi \neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79a61dcd0fdae7f91cdd3765a18f1d0cff9010d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.584ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} \xi \neq 0}"></span>, la réaction a eu lieu, le potentiel de réaction est désormais nul ; l'équilibre est dit <b>stable</b>.</li></ul> <p>Lorsqu'une réaction est équilibrée, cela ne signifie pas qu'il n'y a plus de transformation chimique dans le milieu : des réactifs continuent à se transformer en produits (réaction directe), et des produits à se transformer en réactifs (réaction inverse), cependant les deux réactions ont lieu à la même vitesse. L'état d'équilibre obtenu dans ce cas peut être qualifié de <b>dynamique</b> ou <b>stationnaire</b> : globalement les effets des deux réactions s'annulent ; par exemple l'une consomme les réactifs aussi vite que l'autre les recrée, d'où une composition stable dans le temps ; ou encore l'une absorbe totalement la chaleur dégagée par l'autre, d'où un bilan énergétique globalement nul. En conséquence, à l'équilibre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi \neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi \neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79a61dcd0fdae7f91cdd3765a18f1d0cff9010d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.584ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} \xi \neq 0}"></span>, d'où : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>À l'équilibre :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e910693c11b298e27340bac2bc9d8ed8faac016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.164ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}=0}"></span> </td></tr></tbody></table> </center> <p>Ceci est vrai quelle que soit la façon dont la réaction chimique est écrite. Pour reprendre l'exemple précédent, à l'équilibre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{1}={\mathcal {A}}_{2}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{1}={\mathcal {A}}_{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94ac855fb6b308694be13e7c5820f5c4f873812e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.177ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{1}={\mathcal {A}}_{2}=0}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Formulations_avec_les_potentiels_thermodynamiques">Formulations avec les potentiels thermodynamiques</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=10" title="Modifier la section : Formulations avec les potentiels thermodynamiques" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=10" title="Modifier le code source de la section : Formulations avec les potentiels thermodynamiques"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Cas_général"><span id="Cas_g.C3.A9n.C3.A9ral"></span>Cas général</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=11" title="Modifier la section : Cas général" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=11" title="Modifier le code source de la section : Cas général"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Comme vu précédemment, l'affinité chimique peut être définie par la <a href="/wiki/D%C3%A9riv%C3%A9e_partielle" title="Dérivée partielle">dérivée partielle</a> d'un <a href="/wiki/Potentiel_thermodynamique" title="Potentiel thermodynamique">potentiel thermodynamique</a> par rapport à l'avancement de la réaction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span> : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=-\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=-\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=-\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=-\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=-\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00075579dde11aa06d7c3c0fe8afa07dadf505a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:63.434ex; height:6.509ex;" alt="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=-\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=-\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}}"></span></dd></dl> <p>Notons de façon générique <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> un potentiel thermodynamique, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> les deux variables gardées constantes dans la dérivation : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=-\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2548f58562fe129c158158d7391114274a216c25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:17.407ex; height:6.509ex;" alt="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}}"></span></dd></dl> <p>Nous avons la <a href="/wiki/Diff%C3%A9rentielle" title="Différentielle">différentielle</a> du potentiel thermodynamique : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial X}}\right)_{Y,\xi }\,\mathrm {d} X+\left({\frac {\partial \Phi }{\partial Y}}\right)_{X,\xi }\,\mathrm {d} Y+\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>X</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> <mo>,</mo> <mi>ξ</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>X</mi> <mo>+</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>Y</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>ξ</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Y</mi> <mo>+</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial X}}\right)_{Y,\xi }\,\mathrm {d} X+\left({\frac {\partial \Phi }{\partial Y}}\right)_{X,\xi }\,\mathrm {d} Y+\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbda50480693370ce35a8e820861078a685fcc7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:52.563ex; height:6.509ex;" alt="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial X}}\right)_{Y,\xi }\,\mathrm {d} X+\left({\frac {\partial \Phi }{\partial Y}}\right)_{X,\xi }\,\mathrm {d} Y+\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi }"></span></dd></dl> <p>et par conséquent pour toute réaction effectuée à <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> constantes on a, selon la condition d'évolution spontanée d'une réaction chimique : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi =-{\mathcal {A}}\,\mathrm {d} \xi \leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi =-{\mathcal {A}}\,\mathrm {d} \xi \leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7dc1f0908684231aed1d7a8f3cd7a9e8dbccdca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:33.156ex; height:6.509ex;" alt="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi =-{\mathcal {A}}\,\mathrm {d} \xi \leq 0}"></span></dd></dl> <p>Autrement dit, au cours de la réaction l'entropie globale <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{\text{sys}}+S_{\text{ext}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{\text{sys}}+S_{\text{ext}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6c8b52437e9d52283b042b30ba8ab183101d02a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.556ex; height:2.843ex;" alt="{\displaystyle S_{\text{sys}}+S_{\text{ext}}}"></span> augmente selon le <a href="/wiki/Deuxi%C3%A8me_principe_de_la_thermodynamique" title="Deuxième principe de la thermodynamique">deuxième principe de la thermodynamique</a>, ce qui implique une diminution du potentiel thermodynamique <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span>, d'où une autre formulation de la <b>condition d'évolution spontanée</b> d'une réaction chimique effectuée à <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> constantes : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Condition d'évolution spontanée à <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> constantes :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi \leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi \leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67b4514e36152391ff854d531bbe45779f50234a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:23.637ex; height:6.509ex;" alt="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi \leq 0}"></span> </td></tr></tbody></table> </center> <p>Ceci implique que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f37867c157495f9f8368000a46dc05265bdfe35d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:10.597ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89dad203ae5bdf94199adc19c338525861e04e86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.323ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi }"></span> ne peuvent être que de signes contraires : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/694235e6a0468aee6a1875e76842f9d20d3c9f62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.858ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}<0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c18566664fa065930257ba762160b7c7aafd9ad4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi >0}"></span>, <b>la réaction progresse</b> : l'équilibre se déplace de la gauche vers la droite, des réactifs sont consommés et des produits apparaissent ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f829bbad7c7772f9b38fd7420ea72940033011a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.858ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31903c372b25d62f311cde0c68ac07c738eeea90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi <0}"></span>, <b>la réaction régresse</b> : l'équilibre se déplace de la droite vers la gauche, des produits sont consommés et des réactifs apparaissent.</li></ul> <p>À l'équilibre l'entropie ne varie plus, soit : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ext</mtext> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e9c4964e4431653b5bd69153f269e26aa609eba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.402ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} S_{\text{sys}}+\mathrm {d} S_{\text{ext}}=0}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi =-{\mathcal {A}}\,\mathrm {d} \xi =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi =-{\mathcal {A}}\,\mathrm {d} \xi =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c69cda41a9819a89916ad03a2941e593be2d3cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:33.156ex; height:6.509ex;" alt="{\displaystyle \mathrm {d} \Phi =\left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}\,\mathrm {d} \xi =-{\mathcal {A}}\,\mathrm {d} \xi =0}"></span></dd></dl> <p>d'où à l'équilibre : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>À l'équilibre :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f360aaa439f5b51f6f382743b6482891718627d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.858ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}=0}"></span> </td></tr></tbody></table> </center> <div class="mw-heading mw-heading4"><h4 id="Cas_d'une_réaction_à_volume_et_température_constants"><span id="Cas_d.27une_r.C3.A9action_.C3.A0_volume_et_temp.C3.A9rature_constants"></span>Cas d'une réaction à volume et température constants</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=12" title="Modifier la section : Cas d'une réaction à volume et température constants" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=12" title="Modifier le code source de la section : Cas d'une réaction à volume et température constants"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dans le cas d'une réaction à volume constant, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q_{\text{sys}}=\mathrm {d} U_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{\text{sys}}=\mathrm {d} U_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a485f2c194749e8474bfb620114aa0a17bdc80ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.657ex; height:3.009ex;" alt="{\displaystyle \delta Q_{\text{sys}}=\mathrm {d} U_{\text{sys}}}"></span>. Si la réaction se fait également à température constante, on a : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\mathrm {d} U_{\text{sys}}=-\mathrm {d} \left(U_{\text{sys}}-TS_{\text{sys}}\right)=-\mathrm {d} F_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <mi>T</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\mathrm {d} U_{\text{sys}}=-\mathrm {d} \left(U_{\text{sys}}-TS_{\text{sys}}\right)=-\mathrm {d} F_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04dc01aa0f2caa6fb51fcc1afc22b759dba0b78a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:53.731ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\mathrm {d} U_{\text{sys}}=-\mathrm {d} \left(U_{\text{sys}}-TS_{\text{sys}}\right)=-\mathrm {d} F_{\text{sys}}}"></span></dd></dl> <p>avec : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fa1c5ce59c589a5df63722738f280d64ded5b27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.984ex; height:2.843ex;" alt="{\displaystyle U_{\text{sys}}}"></span> l'<a href="/wiki/%C3%89nergie_interne" title="Énergie interne">énergie interne</a> du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c78fee9a6b8695313c220fab5330f29eb834aa6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.891ex; height:2.843ex;" alt="{\displaystyle F_{\text{sys}}}"></span> l'<a href="/wiki/%C3%89nergie_libre" title="Énergie libre">énergie libre</a> du système.</li></ul> <p>D'où, puisque <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e884df098d1c5068f1cba8c0346d3cb141fa401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"></span> : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Condition d'évolution spontanée à volume et température constants :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} F_{\text{sys}}\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} F_{\text{sys}}\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/986bb50ec816ed265a540fa80d54bd11ef3d2cef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.444ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} F_{\text{sys}}\leq 0}"></span> </td></tr></tbody></table> </center> <div class="mw-heading mw-heading4"><h4 id="Cas_d'une_réaction_à_pression_et_température_constantes"><span id="Cas_d.27une_r.C3.A9action_.C3.A0_pression_et_temp.C3.A9rature_constantes"></span>Cas d'une réaction à pression et température constantes</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=13" title="Modifier la section : Cas d'une réaction à pression et température constantes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=13" title="Modifier le code source de la section : Cas d'une réaction à pression et température constantes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/%C3%89quilibre_chimique" title="Équilibre chimique">Équilibre chimique</a>.</div></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fichier:D%C3%A9placement_d%27%C3%A9quilibre.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/D%C3%A9placement_d%27%C3%A9quilibre.GIF/250px-D%C3%A9placement_d%27%C3%A9quilibre.GIF" decoding="async" width="250" height="202" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/D%C3%A9placement_d%27%C3%A9quilibre.GIF/375px-D%C3%A9placement_d%27%C3%A9quilibre.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/D%C3%A9placement_d%27%C3%A9quilibre.GIF/500px-D%C3%A9placement_d%27%C3%A9quilibre.GIF 2x" data-file-width="839" data-file-height="679" /></a><figcaption><b>Évolution d'un équilibre chimique à pression et température constantes selon le signe de l'enthalpie libre de réaction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e919b96ce80f74b08fe25f63787bb4008572a60c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.639ex; height:2.509ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G}"></span></b> <br /> La réaction progresse lorsque <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b2cdba509fee0de117178ea19dbe77d9212fa62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.9ex; height:2.509ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G<0}"></span>. La réaction régresse lorsque <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06f95c1ee756afc31552b88b944fd8229499e171" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.9ex; height:2.509ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G>0}"></span>. L'équilibre est atteint lorsque <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3432c020ccf84ea7f2fec9667c010690a68063c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.9ex; height:2.509ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G=0}"></span>.</figcaption></figure> <p>Dans le cas d'une réaction à pression constante, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta Q_{\text{sys}}=\mathrm {d} H_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta Q_{\text{sys}}=\mathrm {d} H_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b96dc77d581dacb7eab96bf5ea5efd145d1f3d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.001ex; height:3.009ex;" alt="{\displaystyle \delta Q_{\text{sys}}=\mathrm {d} H_{\text{sys}}}"></span>. Si la réaction se fait également à température constante, on a : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\mathrm {d} H_{\text{sys}}=-\mathrm {d} \left(H_{\text{sys}}-TS_{\text{sys}}\right)=-\mathrm {d} G_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>=</mo> <mi>T</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>−</mo> <mi>T</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\mathrm {d} H_{\text{sys}}=-\mathrm {d} \left(H_{\text{sys}}-TS_{\text{sys}}\right)=-\mathrm {d} G_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0dbeadb77af1afce3e126d5ac50668b531cb67c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:54.751ex; height:3.009ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi =T\,\mathrm {d} S_{\text{sys}}-\mathrm {d} H_{\text{sys}}=-\mathrm {d} \left(H_{\text{sys}}-TS_{\text{sys}}\right)=-\mathrm {d} G_{\text{sys}}}"></span></dd></dl> <p>avec : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3521bea16d21afdd22daac5fd9ebdcc9490f983" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.327ex; height:2.843ex;" alt="{\displaystyle H_{\text{sys}}}"></span> l'<a href="/wiki/Enthalpie" title="Enthalpie">enthalpie</a> du système ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\text{sys}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\text{sys}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3626a55adf418a220404c466dff0ec2fcf01676b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.223ex; height:2.843ex;" alt="{\displaystyle G_{\text{sys}}}"></span> l'<a href="/wiki/Enthalpie_libre" title="Enthalpie libre">enthalpie libre</a> du système.</li></ul> <p>D'où, puisque <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e884df098d1c5068f1cba8c0346d3cb141fa401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"></span> : </p> <center> <table border="1" cellpadding="5" style="text-align:center;"> <tbody><tr> <td><b>Condition d'évolution spontanée à pression et température constantes :</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} G_{\text{sys}}\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G_{\text{sys}}\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed3c514b5cacc63cdfa8b8b43aa48e9232154800" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.776ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} G_{\text{sys}}\leq 0}"></span> </td></tr></tbody></table> </center> <p>Nous avons vu dans les relations définissant l'affinité chimique que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=-\Delta _{\mathrm {r} }G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=-\Delta _{\mathrm {r} }G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dad36d181c5b65b8c7d2ebe5756aa69707466b03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:26.839ex; height:6.509ex;" alt="{\displaystyle {\mathcal {A}}=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=-\Delta _{\mathrm {r} }G}"></span>. Cette dernière expression est l'<a href="/wiki/Grandeur_de_r%C3%A9action" title="Grandeur de réaction">enthalpie libre de réaction</a> ; ainsi, à pression et température constantes : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} G_{\text{sys}}=\Delta _{\mathrm {r} }G\cdot \mathrm {d} \xi \leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>sys</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G_{\text{sys}}=\Delta _{\mathrm {r} }G\cdot \mathrm {d} \xi \leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef755db4935bfb92b1a6d382b8c97d84f44cb775" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.516ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} G_{\text{sys}}=\Delta _{\mathrm {r} }G\cdot \mathrm {d} \xi \leq 0}"></span>. Cette relation est centrale dans l'étude des <a href="/wiki/%C3%89quilibre_chimique" title="Équilibre chimique">équilibres chimiques</a> à pression et température constantes : </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b2cdba509fee0de117178ea19dbe77d9212fa62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.9ex; height:2.509ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G<0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c18566664fa065930257ba762160b7c7aafd9ad4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi >0}"></span>, <b>la réaction progresse</b> : des réactifs sont consommés et des produits apparaissent ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06f95c1ee756afc31552b88b944fd8229499e171" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.9ex; height:2.509ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G>0}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \xi <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \xi <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31903c372b25d62f311cde0c68ac07c738eeea90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.584ex; height:2.509ex;" alt="{\displaystyle \mathrm {d} \xi <0}"></span>, <b>la réaction régresse</b> : des produits sont consommés et des réactifs apparaissent ;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3432c020ccf84ea7f2fec9667c010690a68063c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.9ex; height:2.509ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G=0}"></span> <b>à l'équilibre</b>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Condition_de_stabilité_de_l'équilibre"><span id="Condition_de_stabilit.C3.A9_de_l.27.C3.A9quilibre"></span>Condition de stabilité de l'équilibre</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=14" title="Modifier la section : Condition de stabilité de l'équilibre" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=14" title="Modifier le code source de la section : Condition de stabilité de l'équilibre"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fichier:Stabilit%C3%A9_d%27un_%C3%A9quilibre_chimique.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Stabilit%C3%A9_d%27un_%C3%A9quilibre_chimique.gif/250px-Stabilit%C3%A9_d%27un_%C3%A9quilibre_chimique.gif" decoding="async" width="250" height="351" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Stabilit%C3%A9_d%27un_%C3%A9quilibre_chimique.gif/375px-Stabilit%C3%A9_d%27un_%C3%A9quilibre_chimique.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Stabilit%C3%A9_d%27un_%C3%A9quilibre_chimique.gif/500px-Stabilit%C3%A9_d%27un_%C3%A9quilibre_chimique.gif 2x" data-file-width="547" data-file-height="769" /></a><figcaption><b>Condition de stabilité d'un équilibre chimique en fonction du signe de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\partial ^{2}G \over \partial \xi ^{2}}\right)_{P,T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\partial ^{2}G \over \partial \xi ^{2}}\right)_{P,T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4260e1eb36219435b85f6f5a8c1019fc6b40fa9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:11.562ex; height:6.843ex;" alt="{\displaystyle \left({\partial ^{2}G \over \partial \xi ^{2}}\right)_{P,T}}"></span></b> <br /> L'équilibre n'est stable que lorsque <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\partial ^{2}G \over \partial \xi ^{2}}\right)_{P,T}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\partial ^{2}G \over \partial \xi ^{2}}\right)_{P,T}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52eb4ffc920c2462182985aa9cdbb54de22f22f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.823ex; height:6.843ex;" alt="{\displaystyle \left({\partial ^{2}G \over \partial \xi ^{2}}\right)_{P,T}>0}"></span>. De plus l'équilibre réel est celui pour lequel l'enthalpie libre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> a atteint le minimum global sur l'ensemble des valeurs possibles de l'avancement de réaction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span>.</figcaption></figure> <p>L'entropie croît pendant la réaction ; lorsque l'équilibre est atteint l'entropie a atteint un maximum. Par conséquent, le potentiel <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> qui décroît pendant la réaction atteint un minimum à l'équilibre. D'un point de vue mathématique, un <a href="/wiki/Extremum" title="Extremum">minimum</a> de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> est atteint si, en plus de l'annulation de sa dérivée première, sa <a href="/wiki/D%C3%A9riv%C3%A9e_seconde" title="Dérivée seconde">dérivée seconde</a> est positive <i>strictement</i>, soit, à l'équilibre : </p> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}=-{\mathcal {A}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}=-{\mathcal {A}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f856f10651b0821dab661f83e0f9ae3e1d04025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:21.668ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial \Phi }{\partial \xi }}\right)_{X,Y}=-{\mathcal {A}}=0}"></span>, <b>condition d'équilibre</b></center> <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}=-\left({\frac {\partial {\mathcal {A}}}{\partial \xi }}\right)_{X,Y}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}=-\left({\frac {\partial {\mathcal {A}}}{\partial \xi }}\right)_{X,Y}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/852bb7d48cff935a5d52a50d5af7c0e79c81bc1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:31.666ex; height:6.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}=-\left({\frac {\partial {\mathcal {A}}}{\partial \xi }}\right)_{X,Y}>0}"></span>, <b>condition de stabilité</b></center> <p>C'est à cette seconde condition seulement que l'équilibre pourra être qualifié de stable. </p><p>Il est impossible que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b824842abee37560d9ca872570be90f50d767e3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.937ex; height:6.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}<0}"></span> à l'équilibre, ce qui supposerait un maximum de la fonction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span>, et donc que <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> a crû. Si cette solution est mathématiquement possible, elle est irréaliste du point de vue de la thermodynamique et doit donc être écartée, cet équilibre est un <b>équilibre instable</b>. </p><p>Il est possible en revanche qu'à l'équilibre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">Φ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b9bb014910c55d0907f6927c2f9cc4c7fb3156c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.937ex; height:6.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}\Phi }{\partial \xi ^{2}}}\right)_{X,Y}=0}"></span>, c'est-à-dire que l'équilibre ait atteint un <a href="/wiki/Point_d%27inflexion" title="Point d'inflexion">point d'inflexion</a> : dans ce cas l'équilibre atteint est un <b>équilibre métastable</b>, et la moindre perturbation relancera la réaction jusqu'à ce qu'elle atteigne un équilibre stable. La situation est possible du point de vue de la thermodynamique. </p><p>L'équilibre peut également atteindre un <b>minimum local</b> de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span>, c'est-à-dire un minimum auquel la réaction revient si elle subit de petites perturbations, mais dont la réaction s'éloigne définitivement sous des perturbations plus importantes, conduisant à un autre minimum de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span>, plus bas. L'équilibre est atteint lorsque la réaction atteint le <b>minimum global</b>, c'est-à-dire parmi tous les minimums locaux possibles celui auquel le potentiel thermodynamique a sa valeur la plus basse. </p><p>Les situations d'équilibre métastable ou de minimum local ne sont que rarement observées expérimentalement, mais elles peuvent être obtenues lors de simulations numériques d'équilibres : les dérivées première et seconde de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> ainsi que la possibilité d'un minimum local doivent être impérativement vérifiées pour en garantir le résultat. </p> <div class="mw-heading mw-heading2"><h2 id="Récapitulatif"><span id="R.C3.A9capitulatif"></span>Récapitulatif</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=15" title="Modifier la section : Récapitulatif" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=15" title="Modifier le code source de la section : Récapitulatif"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le tableau suivant récapitule les conditions d'évolution d'une réaction chimique, les conditions d'équilibre et de stabilité selon les paramètres fixés pour effectuer l'étude de la réaction. L'ensemble des grandeurs de ce tableau sont les grandeurs du système réactionnel seul, y compris l'entropie. </p><p>On entend par <i>progression de la réaction</i> le déplacement de la réaction dans le sens de la consommation des réactifs et de l'apparition des produits (<i>sens direct</i>, soit <i>réactifs</i> → <i>produits</i>). Au contraire, on entend par <i>régression de la réaction</i> le déplacement de la réaction dans le sens de la consommation des produits et de l'apparition des réactifs (<i>sens inverse</i>, soit <i>produits</i> → <i>réactifs</i>). Un équilibre chimique se caractérise par la présence simultanée d'une réaction en sens direct et d'une réaction en sens inverse qui se compensent, d'où un état stationnaire <i>réactifs</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightleftarrows }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇄</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightleftarrows }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdbaea31afa0894aa82079b04d6a5e7566da7195" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle \rightleftarrows }"></span> <i>produits</i>. </p> <table class="wikitable centre"> <caption>Évolution des réactions chimiques </caption> <tbody><tr> <th scope="col">Paramètres constants<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> </th> <th scope="col">Potentiel thermodynamique<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> </th> <th scope="col">Condition d'évolution spontanée<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e884df098d1c5068f1cba8c0346d3cb141fa401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.874ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}\,\mathrm {d} \xi \geq 0}"></span> </th> <th scope="col">Progression de la réaction<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba3c2b0a70538e75f9cbe69c1a29647fc296369f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.164ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}>0}"></span> </th> <th scope="col">Régression de la réaction<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beca201aa44ce1453cdddb777517834c09727227" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.164ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}<0}"></span> </th> <th scope="col">Condition d'équilibre<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e910693c11b298e27340bac2bc9d8ed8faac016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.164ex; height:2.343ex;" alt="{\displaystyle {\mathcal {A}}=0}"></span> </th> <th scope="col">Condition de stabilité<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}\Phi }{{\partial \xi }^{2}}}\right)_{X,Y}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">Φ</mi> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}\Phi }{{\partial \xi }^{2}}}\right)_{X,Y}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60669c46e2338d27440af5c0675d70fba5c6ddaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:16.198ex; height:7.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}\Phi }{{\partial \xi }^{2}}}\right)_{X,Y}>0}"></span> </th></tr> <tr> <th scope="col"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> volume<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> entropie </th> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="{\displaystyle U}"></span><br />Énergie interne </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} U\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>U</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} U\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44bab54cea63a6dff247f628e1f198ec108a8b3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.336ex; height:2.343ex;" alt="{\displaystyle \mathrm {d} U\leq 0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b01024d3fbe5634aed77d4b43d678adb8059f87c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.632ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}<0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c2737d4f0e114e3b27f76ac2f1ca34fbb5a11a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.632ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}>0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1666ecdf039ed4f2a31aa8158fa82570c5993f9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.632ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}U}{\partial \xi ^{2}}}\right)_{V,S}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}U}{\partial \xi ^{2}}}\right)_{V,S}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18acbf9f0bf64bd004372367d9498769afdadac9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.712ex; height:6.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}U}{\partial \xi ^{2}}}\right)_{V,S}>0}"></span> </td></tr> <tr> <th scope="col"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> pression<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> entropie </th> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle H}"></span><br />Enthalpie </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} H\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>H</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} H\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8aa72551e2bab1d6c6f087d927c8936f7d5eac58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.617ex; height:2.343ex;" alt="{\displaystyle \mathrm {d} H\leq 0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/395cb8befc556b2caffef1ad383a06603374dbea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.884ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}<0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/457669d3fe20f23c9ebd6bd51f8f88b0946ada52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.884ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}>0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c43b789520ad5d56166ca5330155a6a9258e67a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.884ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}H}{\partial \xi ^{2}}}\right)_{P,S}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}H}{\partial \xi ^{2}}}\right)_{P,S}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbac2eb97d4c58609ac3f20645e20ae8b950951a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.963ex; height:6.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}H}{\partial \xi ^{2}}}\right)_{P,S}>0}"></span> </td></tr> <tr> <th scope="col"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> volume<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> température </th> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span><br />Énergie libre </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} F\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>F</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} F\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b063642dfa80f3cbffad0e78f172c8297d1af08a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.294ex; height:2.343ex;" alt="{\displaystyle \mathrm {d} F\leq 0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1333d57777d24480d2e26c57ac5cc9d3b94b4eb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.687ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}<0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38518dead6405f36943ab6686d6488586654650c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.687ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}>0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78ce9c1a2a01e25d3f29dac799093fcdc824ae48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.687ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}F}{\partial \xi ^{2}}}\right)_{V,T}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}F}{\partial \xi ^{2}}}\right)_{V,T}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57952b00c97b0c2a38d6c69a5e1ea5b25e4b5a04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.767ex; height:6.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}F}{\partial \xi ^{2}}}\right)_{V,T}>0}"></span> </td></tr> <tr> <th scope="col"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> pression<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> température </th> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span><br />Enthalpie libre </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} G\leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G\leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07cf2f5029d76e4527669996e53fe0e22bc08407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.38ex; height:2.343ex;" alt="{\displaystyle \mathrm {d} G\leq 0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3ec679d70892dd6b32effe7c98325bb0c7c7281" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.744ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}<0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/716de1d0c16f900494c7226048b8013b460523c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.744ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}>0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96ba9d01d74e9dc92d8a43b788d6a8d425eb7828" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.744ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=0}"></span> </td> <td style="text-align:center;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial ^{2}G}{\partial \xi ^{2}}}\right)_{P,T}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial ^{2}G}{\partial \xi ^{2}}}\right)_{P,T}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feaae89815b22c2ef3b24a8ad232889e391dbbd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.823ex; height:6.843ex;" alt="{\displaystyle \left({\frac {\partial ^{2}G}{\partial \xi ^{2}}}\right)_{P,T}>0}"></span> </td></tr></tbody></table> <dl><dt>Notes</dt></dl> <ul><li>À <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> constants, on a pour condition d'évolution spontanée la variation du potentiel chimique correspondant : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} \Phi =-{\mathcal {A}}\,\mathrm {d} \xi \leq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi mathvariant="normal">Φ</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>≤</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \Phi =-{\mathcal {A}}\,\mathrm {d} \xi \leq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8924ce2f081cfa43de32776d609dc943be87581b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.751ex; height:2.676ex;" alt="{\displaystyle \mathrm {d} \Phi =-{\mathcal {A}}\,\mathrm {d} \xi \leq 0}"></span>.</li> <li>L'<a href="/wiki/Grandeur_de_r%C3%A9action" title="Grandeur de réaction">enthalpie libre de réaction</a> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\mathrm {r} }G=\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=\sum _{i}\nu _{i}\mu _{i}=-{\mathcal {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mi>G</mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>U</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> <mo>,</mo> <mi>S</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>F</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo>,</mo> <mi>T</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\mathrm {r} }G=\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=\sum _{i}\nu _{i}\mu _{i}=-{\mathcal {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/102eda35ce9541280aeb9cce467b02337827c321" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:76.737ex; height:6.676ex;" alt="{\displaystyle \Delta _{\mathrm {r} }G=\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}=\left({\frac {\partial U}{\partial \xi }}\right)_{V,S}=\left({\frac {\partial H}{\partial \xi }}\right)_{P,S}=\left({\frac {\partial F}{\partial \xi }}\right)_{V,T}=\sum _{i}\nu _{i}\mu _{i}=-{\mathcal {A}}}"></span>, l'affinité chimique<sup id="cite_ref-IUPACnotation_10-1" class="reference"><a href="#cite_note-IUPACnotation-10"><span class="cite_crochet">[</span>10<span class="cite_crochet">]</span></a></sup>.</li> <li>Tout équilibre chimique doit vérifier la condition de stabilité qui est une inégalité <i>stricte</i>, sans quoi l'équilibre est instable ou métastable et la réaction repart à la moindre perturbation. Vérifier aussi que l'équilibre atteint correspond au minimum global du potentiel thermodynamique (dans le cas où existent plusieurs minimum locaux, rechercher celui où le potentiel <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> a sa valeur la plus basse).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=16" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=16" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=17" title="Modifier la section : Notes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=17" title="Modifier le code source de la section : Notes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink noprint"><a href="#cite_ref-1">↑</a> </span><span class="reference-text">Charles Brunold, <a rel="nofollow" class="external text" href="http://pcbu-iris.univ-lille1.fr/bitstream/handle/1908/2432/CH0125.pdf?...4">Le problème de l'affinité chimique et de l'atomistique</a> - Étude du rapprochement actuel de la physique et de la chimie,  <abbr class="abbr" title="édition">éd.</abbr> Masson & Cie (1930).</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text">La notion chimique d'<i>affinité élective</i>, selon la dénomination de l'époque, inspira à Goethe son roman paru en 1809, <i>Les affinités électives</i>, dans lequel les rapports humains sont assimilés à des attractions et répulsions comme dans des réactions chimiques. Bernard Joly, Revue Méthodos, savoirs et textes, numéro 6, 2006, <a rel="nofollow" class="external text" href="http://methodos.revues.org/482">Les Affinités électives de Goethe : entre science et littérature</a>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink noprint"><a href="#cite_ref-3">↑</a> </span><span class="reference-text">SABIX - Société des amis de la bibliothèque et de l'histoire de l'École polytechnique - <a rel="nofollow" class="external text" href="http://www.sabix.org/bulletin/b23/berthollet.html">Bulletin <abbr class="abbr" title="numéro">n<sup>o</sup></abbr> 23 (avril 2000) - Biographie de Berthollet</a>.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink noprint"><a href="#cite_ref-4">↑</a> </span><span class="reference-text">SABIX - Société des amis de la bibliothèque et de l'histoire de l'École polytechnique - <a rel="nofollow" class="external text" href="http://www.sabix.org/bulletin/b24/affinites.html">Bulletin <abbr class="abbr" title="numéro">n<sup>o</sup></abbr> 24 (août 2000) - Berthollet et la théorie des affinités</a>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink noprint"><a href="#cite_ref-5">↑</a> </span><span class="reference-text">J. J. Berzelius, « Traité de chimie », minérale, végétale et animale, traduit par A. J. L. Jourdan,  <abbr class="abbr" title="édition">éd.</abbr> Firmin Didot frères, libraires, Paris, 1829.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink noprint"><a href="#cite_ref-6">↑</a> </span><span class="reference-text"><a rel="nofollow" class="external text" href="http://culture.univ-lille1.fr/fileadmin/lna/lna65/lna65p14.pdf">Prévoir les réactions chimiques : un problème controversé au <abbr class="abbr" title="19ᵉ siècle"><span class="romain">XIX</span><sup style="font-size:72%">e</sup></abbr> siècle</a> par Vangelis Antzoulatos, Laboratoire SCité, Université Lille 1.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink noprint"><a href="#cite_ref-7">↑</a> </span><span class="reference-text">Encyclopædia universalis - <a rel="nofollow" class="external text" href="http://www.universalis.fr/encyclopedie/affinite-chimique/">affinité chimique</a>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink noprint"><a href="#cite_ref-8">↑</a> </span><span class="reference-text"><span class="ouvrage" id="Hertz2004"><span class="ouvrage" id="Jean_Hertz2004">Jean Hertz, « <cite style="font-style:normal">Historique en grandes enjambées de la thermodynamique de l’équilibre</cite> », <i>J. Phys. IV France</i>, <abbr class="abbr" title="volume">vol.</abbr> 122,‎ <time>2004</time>, <abbr class="abbr" title="pages">p.</abbr> <span class="nowrap">3-20</span> <small style="line-height:1em;">(<a href="/wiki/Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <span class="plainlinks noarchive nowrap"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1051/jp4%3A2004122001">10.1051/jp4:2004122001</a></span>, <a rel="nofollow" class="external text" href="https://jp4.journaldephysique.org/articles/jp4/pdf/2004/10/jp4122001.pdf">lire en ligne</a> <abbr class="abbr indicateur-format format-pdf" title="Document au format Portable Document Format (PDF) d'Adobe">[PDF]</abbr>, consulté le <time class="nowrap" datetime="2020-07-24" data-sort-value="2020-07-24">24 juillet 2020</time>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Historique+en+grandes+enjamb%C3%A9es+de+la+thermodynamique+de+l%E2%80%99%C3%A9quilibre&rft.jtitle=J.+Phys.+IV+France&rft.aulast=Hertz&rft.aufirst=Jean&rft.date=2004&rft.volume=122&rft.pages=3-20&rft_id=info%3Adoi%2F10.1051%2Fjp4%3A2004122001&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAffinit%C3%A9+chimique"></span></span></span>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink noprint"><a href="#cite_ref-9">↑</a> </span><span class="reference-text"><span class="ouvrage" id="TrambouzeEuzen2002"><span class="ouvrage" id="Pierre_TrambouzeJean-Paul_Euzen2002">Pierre Trambouze et Jean-Paul Euzen, <cite class="italique">Les réacteurs chimiques : De la conception à la mise en œuvre</cite>, Éditions OPHRYS, <abbr class="abbr" title="collection">coll.</abbr> « Publications de l'Institut français du pétrole », <time>2002</time> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/2710811219" title="Spécial:Ouvrages de référence/2710811219"><span class="nowrap">2710811219</span></a>, <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=JzJlW3_nS-8C&pg=PA1#v=onepage&q&f=false">lire en ligne</a>)</small>, <abbr class="abbr" title="page">p.</abbr> 1<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Les+r%C3%A9acteurs+chimiques&rft.pub=%C3%89ditions+OPHRYS&rft.stitle=De+la+conception+%C3%A0+la+mise+en+%C5%93uvre&rft.aulast=Trambouze&rft.aufirst=Pierre&rft.au=Jean-Paul+Euzen&rft.date=2002&rft.pages=1&rft.isbn=2710811219&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAffinit%C3%A9+chimique"></span></span></span>.</span> </li> <li id="cite_note-IUPACnotation-10"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-IUPACnotation_10-0">a</a> et <a href="#cite_ref-IUPACnotation_10-1">b</a></sup> </span><span class="reference-text"><i>Green Book</i> (<a href="/wiki/Union_internationale_de_chimie_pure_et_appliqu%C3%A9e" title="Union internationale de chimie pure et appliquée">IUPAC</a>), <a href="/wiki/Quantities,_Units_and_Symbols_in_Physical_Chemistry" title="Quantities, Units and Symbols in Physical Chemistry">Quantities, Units and Symbols in Physical Chemistry</a>, page 58, édition 2007.</span> </li> <li id="cite_note-R2-11"><span class="mw-cite-backlink noprint"><a href="#cite_ref-R2_11-0">↑</a> </span><span class="reference-text"><span class="ouvrage" id="Schwartzentruber">Jacques Schwartzentruber, <a href="/wiki/%C3%89cole_nationale_sup%C3%A9rieure_des_mines_d%27Albi-Carmaux" title="École nationale supérieure des mines d'Albi-Carmaux">École nationale supérieure des mines d'Albi-Carmaux</a>, « <a rel="nofollow" class="external text" href="http://nte.mines-albi.fr/Thermo/fr/co/uc_Affinite.html"><cite style="font-style:normal;">Affinité chimique</cite></a> », sur <span class="italique">nte.mines-albi.fr</span>, <time class="nowrap" datetime="2021-03-11" data-sort-value="2021-03-11">11 mars 2021</time> <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2022-01-12" data-sort-value="2022-01-12">12 janvier 2022</time>)</small></span>.</span> </li> <li id="cite_note-Mesplède-45-12"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-Mesplède-45_12-0">a</a> et <a href="#cite_ref-Mesplède-45_12-1">b</a></sup> </span><span class="reference-text"><a href="#Mesplède">Mesplède 2004</a>, <abbr class="abbr" title="page(s)">p.</abbr> 45.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink noprint"><a href="#cite_ref-13">↑</a> </span><span class="reference-text">Un équilibre <b>instable</b> est défini par des vitesses de réaction extrêmement faibles, conduisant à une variation de l'avancement de réaction quasi nulle, non mesurable, comme pour la transformation du <a href="/wiki/Diamant" title="Diamant">diamant</a> en <a href="/wiki/Graphite" title="Graphite">graphite</a>. Un équilibre <b>métastable</b> est un équilibre dans lequel les réactions n'ont pas lieu faute d'un facteur déclenchant ; par exemple un mélange d'hydrogène et d'oxygène est métastable, il peut être conservé dans le temps sans variation de composition, mais une simple étincelle déclenche une réaction violente produisant de l'eau. Ce terme s'emploie également dans l'état de <a href="/wiki/Surfusion" title="Surfusion">surfusion</a> de l'eau.</span> </li> </ol></div> </div> <div class="mw-heading mw-heading3"><h3 id="Bibliographie">Bibliographie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=18" title="Modifier la section : Bibliographie" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=18" title="Modifier le code source de la section : Bibliographie"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="ouvrage" id="Corriou1985"><span class="ouvrage" id="Jean-Pierre_Corriou1985">Jean-Pierre Corriou, <cite class="italique">Thermodynamique chimique : Équilibres thermodynamiques</cite>, <abbr class="abbr" title="volume">vol.</abbr> J 1028, <a href="/wiki/%C3%89ditions_techniques_de_l%27ing%C3%A9nieur" title="Éditions techniques de l'ingénieur">Techniques de l'ingénieur</a>, <abbr class="abbr" title="collection">coll.</abbr> « base documentaire <i>Thermodynamique et cinétique chimique</i>, pack <i>Opérations unitaires. Génie de la réaction chimique</i>, univers <i>Procédés chimie - bio - agro</i> », <time>1985</time> <small style="line-height:1em;">(<a rel="nofollow" class="external text" href="https://books.google.fr/books?id=OXYfQZ8Vc84C&pg=PA1">lire en ligne</a>)</small>, <abbr class="abbr" title="pages">p.</abbr> <span class="nowrap">1-31</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamique+chimique&rft.pub=Techniques+de+l%27ing%C3%A9nieur&rft.stitle=%C3%89quilibres+thermodynamiques&rft.aulast=Corriou&rft.aufirst=Jean-Pierre&rft.date=1985&rft.volume=J+1028&rft.pages=1-31&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAffinit%C3%A9+chimique"></span></span></span>.</li> <li><span class="ouvrage" id="Mesplède">J. <span class="nom_auteur">Mesplède</span>, <cite class="italique">Chimie PSI - Cours - Méthodes - Exercices résolus</cite>, Bréal, <abbr class="abbr" title="collection">coll.</abbr> « Les nouveaux précis Bréal », <time>2004</time>, 350 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/978-2-7495-2063-6" title="Spécial:Ouvrages de référence/978-2-7495-2063-6"><span class="nowrap">978-2-7495-2063-6</span></a>, <a rel="nofollow" class="external text" href="https://books.google.fr/books?id=L5ko1vwPxeEC&pg=PA37">lire en ligne</a>)</small>, partie I - Thermodynamique ; Chapitre 2 - Équilibres chimiques <abbr class="abbr" title="pages">pp.</abbr> 37-80 ; Chapitre 3 - Déplacement des équilibres <abbr class="abbr" title="pages">pp.</abbr> 81-116<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chimie+PSI+-+Cours+-+M%C3%A9thodes+-+Exercices+r%C3%A9solus&rft.pub=Br%C3%A9al&rft.aulast=Mespl%C3%A8de&rft.aufirst=J.&rft.date=2004&rft.pages=partie+I+-+Thermodynamique+%3B+Chapitre+2+-+%C3%89quilibres+chimiques+%3Cabbr+class%3D%22abbr+%22+title%3D%22pages%22+%3Epp.%3C%2Fabbr%3E%26nbsp%3B37-80+%3B+Chapitre+3+-+D%C3%A9placement+des+%C3%A9quilibres+%3Cabbr+class%3D%22abbr+%22+title%3D%22pages%22+%3Epp.%3C%2Fabbr%3E%26nbsp%3B81-116&rft.tpages=350&rft.isbn=978-2-7495-2063-6&rft_id=https%3A%2F%2Fbooks.google.fr%2Fbooks%3Fid%3DL5ko1vwPxeEC%26pg%3DPA37&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAffinit%C3%A9+chimique"></span></span>.</li> <li><span class="ouvrage" id="Soustelle">Michel Soustelle, <cite class="italique">Équilibres chimiques</cite>, <abbr class="abbr" title="volume">vol.</abbr> 4, ISTE Group, <abbr class="abbr" title="collection">coll.</abbr> « Génie des procédés / Thermodynamique chimique approfondie », <time>2015</time>, 196 <abbr class="abbr" title="pages">p.</abbr> <small style="line-height:1em;">(<a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Sp%C3%A9cial:Ouvrages_de_r%C3%A9f%C3%A9rence/9781784051037" title="Spécial:Ouvrages de référence/9781784051037"><span class="nowrap">9781784051037</span></a>, <a rel="nofollow" class="external text" href="https://books.google.be/books?id=NQtjDwAAQBAJ">lire en ligne</a>)</small><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%C3%89quilibres+chimiques&rft.pub=ISTE+Group&rft.au=Michel+Soustelle&rft.date=2015&rft.volume=4&rft.tpages=196&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AAffinit%C3%A9+chimique"></span></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Articles_connexes">Articles connexes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Affinit%C3%A9_chimique&veaction=edit&section=19" title="Modifier la section : Articles connexes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Affinit%C3%A9_chimique&action=edit&section=19" title="Modifier le code source de la section : Articles connexes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Avancement_de_r%C3%A9action" title="Avancement de réaction">Avancement de réaction</a></li> <li><a href="/wiki/Deuxi%C3%A8me_principe_de_la_thermodynamique" title="Deuxième principe de la thermodynamique">Deuxième principe de la thermodynamique</a></li> <li><a href="/wiki/Entropie_(thermodynamique)" title="Entropie (thermodynamique)">Entropie (thermodynamique)</a></li> <li><a href="/wiki/%C3%89quilibre_chimique" title="Équilibre chimique">Équilibre chimique</a></li> <li><a href="/wiki/Potentiel_chimique" title="Potentiel chimique">Potentiel chimique</a></li> <li><a href="/wiki/R%C3%A9action_chimique" title="Réaction chimique">Réaction chimique</a></li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_R%C3%A9actions_chimiques" title="Modèle:Palette Réactions chimiques"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_R%C3%A9actions_chimiques&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a href="/wiki/R%C3%A9action_chimique" title="Réaction chimique">Réactions chimiques</a></div></th> </tr> <tr> <td class="navbox-list" style="text-align:center;" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Milieu_r%C3%A9actionnel" title="Milieu réactionnel">Milieu réactionnel</a></li> <li><a href="/wiki/R%C3%A9actif_(chimie)" title="Réactif (chimie)">Réactif</a></li> <li><a href="/wiki/R%C3%A9actif_limitant" title="Réactif limitant">Réactif limitant</a></li> <li><a href="/wiki/Interm%C3%A9diaire_r%C3%A9actionnel" title="Intermédiaire réactionnel">Intermédiaire réactionnel</a></li> <li><a href="/wiki/Produit_de_r%C3%A9action" title="Produit de réaction">Produit de réaction</a></li> <li><a href="/wiki/Catalyse" title="Catalyse">Catalyse</a></li> <li><a href="/wiki/Inerte_(chimie)" title="Inerte (chimie)">Inerte</a></li></ul> </div></td> </tr> <tr> <td class="navbox-list navbox-even" style="text-align:center;" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Chimie_min%C3%A9rale" title="Chimie minérale">Chimie minérale</a> / <a href="/wiki/R%C3%A9action_organique" title="Réaction organique">Réaction organique</a></li> <li><a href="/wiki/R%C3%A9action_endergonique" title="Réaction endergonique">Réaction endergonique</a> / <a href="/wiki/R%C3%A9action_exergonique" title="Réaction exergonique">Réaction exergonique</a></li> <li><a href="/wiki/R%C3%A9action_endothermique" title="Réaction endothermique">Réaction endothermique</a> / <a href="/wiki/R%C3%A9action_exothermique" title="Réaction exothermique">Réaction exothermique</a></li> <li><a href="/wiki/R%C3%A9action_intermol%C3%A9culaire" title="Réaction intermoléculaire">Réaction intermoléculaire</a> / <a href="/wiki/R%C3%A9action_intramol%C3%A9culaire" title="Réaction intramoléculaire">Réaction intramoléculaire</a></li> <li><a href="/wiki/R%C3%A9action_par_%C3%A9tapes" title="Réaction par étapes">Réaction par étapes</a> / <a href="/wiki/R%C3%A9action_chimique_en_cha%C3%AEne" title="Réaction chimique en chaîne">Réaction en chaîne</a></li></ul> </div></td> </tr> <tr> <td class="navbox-list" style="text-align:center;" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Rendement_chimique" title="Rendement chimique">Rendement</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/505a4ceef454c69dffd23792c84b90f488543743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.307ex; margin-bottom: -0.478ex; width:1.808ex; height:1.343ex;" alt="{\displaystyle =}"></span> <a href="/wiki/S%C3%A9lectivit%C3%A9_(chimie)" title="Sélectivité (chimie)">Sélectivité</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span> <a href="/wiki/Taux_de_conversion" title="Taux de conversion">Conversion</a></li></ul> </div></td> </tr> <tr> <td class="navbox-list navbox-even" style="text-align:center;" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/St%C5%93chiom%C3%A9trie" title="Stœchiométrie">Stœchiométrie</a></li> <li><a href="/wiki/Cin%C3%A9tique_chimique" title="Cinétique chimique">Cinétique chimique</a></li> <li><a href="/wiki/Avancement_de_r%C3%A9action" title="Avancement de réaction">Avancement de réaction</a></li> <li><a class="mw-selflink selflink">Affinité chimique</a></li> <li><a href="/wiki/%C3%89quilibre_chimique" title="Équilibre chimique">Équilibre chimique</a></li></ul> </div></td> </tr> </tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer" typeof="mw:File"><a href="/wiki/Portail:Physique" title="Portail de la physique"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Circle-icons-physics-logo.svg/24px-Circle-icons-physics-logo.svg.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Circle-icons-physics-logo.svg/36px-Circle-icons-physics-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Circle-icons-physics-logo.svg/48px-Circle-icons-physics-logo.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Physique" title="Portail:Physique">Portail de la physique</a></span> </span></li> <li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer" typeof="mw:File"><a href="/wiki/Portail:Chimie" title="Portail de la chimie"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Nuvola_apps_edu_science.svg/24px-Nuvola_apps_edu_science.svg.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Nuvola_apps_edu_science.svg/36px-Nuvola_apps_edu_science.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Nuvola_apps_edu_science.svg/48px-Nuvola_apps_edu_science.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Chimie" title="Portail:Chimie">Portail de la chimie</a></span> </span></li> </ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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