Ordine di reazione

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vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definizione"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Definizione</span> </div> </a> <ul id="toc-Definizione-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reazioni_dirette_di_ordine_zero" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reazioni_dirette_di_ordine_zero"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Reazioni dirette di ordine zero</span> </div> </a> <ul id="toc-Reazioni_dirette_di_ordine_zero-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reazioni_dirette_del_primo_ordine" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reazioni_dirette_del_primo_ordine"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Reazioni dirette del primo ordine</span> </div> </a> <ul id="toc-Reazioni_dirette_del_primo_ordine-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reazioni_dirette_del_secondo_ordine" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reazioni_dirette_del_secondo_ordine"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Reazioni dirette del secondo ordine</span> </div> </a> <ul id="toc-Reazioni_dirette_del_secondo_ordine-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reazioni_del_secondo_ordine_con_due_reagenti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reazioni_del_secondo_ordine_con_due_reagenti"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Reazioni del secondo ordine con due reagenti</span> </div> </a> <ul id="toc-Reazioni_del_secondo_ordine_con_due_reagenti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reazioni_dirette_di_ordine_N" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reazioni_dirette_di_ordine_N"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Reazioni dirette di ordine N</span> </div> </a> <ul id="toc-Reazioni_dirette_di_ordine_N-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-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="Indice" 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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Ordine di reazione</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="Vai a una voce in un'altra lingua. Disponibile in 16 lingue" > <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-16" 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">16 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%B1%D8%AC%D8%A9_%D8%A7%D9%84%D8%AA%D9%81%D8%A7%D8%B9%D9%84" title="درجة التفاعل - arabo" lang="ar" hreflang="ar" data-title="درجة التفاعل" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B4%D0%B0%D0%BA_%D1%80%D1%8D%D0%B0%D0%BA%D1%86%D1%8B%D1%96" title="Парадак рэакцыі - bielorusso" lang="be" hreflang="be" data-title="Парадак рэакцыі" data-language-autonym="Беларуская" data-language-local-name="bielorusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C5%98%C3%A1d_reakce" title="Řád reakce - ceco" lang="cs" hreflang="cs" data-title="Řád reakce" data-language-autonym="Čeština" data-language-local-name="ceco" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Order_of_reaction" title="Order of reaction - inglese" lang="en" hreflang="en" data-title="Order of reaction" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Reaktsiooni_j%C3%A4rk" title="Reaktsiooni järk - estone" lang="et" hreflang="et" data-title="Reaktsiooni järk" data-language-autonym="Eesti" data-language-local-name="estone" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Reaktion_kertaluku" title="Reaktion kertaluku - finlandese" lang="fi" hreflang="fi" data-title="Reaktion kertaluku" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ordre_de_r%C3%A9action" title="Ordre de réaction - francese" lang="fr" hreflang="fr" data-title="Ordre de réaction" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ord_imoibrithe" title="Ord imoibrithe - irlandese" lang="ga" hreflang="ga" data-title="Ord imoibrithe" data-language-autonym="Gaeilge" data-language-local-name="irlandese" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Orde_reaksi" title="Orde reaksi - indonesiano" lang="id" hreflang="id" data-title="Orde reaksi" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8F%8D%E5%BF%9C%E6%AC%A1%E6%95%B0" title="反応次数 - giapponese" lang="ja" hreflang="ja" data-title="反応次数" data-language-autonym="日本語" data-language-local-name="giapponese" 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/%EB%B0%98%EC%9D%91%EC%B0%A8%EC%88%98" title="반응차수 - coreano" lang="ko" hreflang="ko" data-title="반응차수" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Reactieorde" title="Reactieorde - olandese" lang="nl" hreflang="nl" data-title="Reactieorde" data-language-autonym="Nederlands" data-language-local-name="olandese" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rz%C4%85d_reakcji_chemicznej" title="Rząd reakcji chemicznej - polacco" lang="pl" hreflang="pl" data-title="Rząd reakcji chemicznej" data-language-autonym="Polski" data-language-local-name="polacco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ordem_de_rea%C3%A7%C3%A3o" title="Ordem de reação - portoghese" lang="pt" hreflang="pt" data-title="Ordem de reação" data-language-autonym="Português" data-language-local-name="portoghese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%BE%D1%80%D1%8F%D0%B4%D0%BE%D0%BA_%D1%80%D0%B5%D0%B0%D0%BA%D1%86%D1%96%D1%97" title="Порядок реакції - ucraino" lang="uk" hreflang="uk" data-title="Порядок реакції" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%8D%E5%BA%94%E7%BA%A7%E6%95%B0" title="反应级数 - cinese" lang="zh" hreflang="zh" data-title="反应级数" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2114702#sitelinks-wikipedia" title="Modifica collegamenti interlinguistici" class="wbc-editpage">Modifica collegamenti</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespace"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a 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href="/w/index.php?title=Ordine_di_reazione&action=history"><span>Cronologia</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generale </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciale:PuntanoQui/Ordine_di_reazione" title="Elenco di tutte le pagine che sono collegate a questa [j]" accesskey="j"><span>Puntano qui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciale:ModificheCorrelate/Ordine_di_reazione" rel="nofollow" title="Elenco delle ultime modifiche alle pagine collegate a questa [k]" accesskey="k"><span>Modifiche correlate</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciale:PagineSpeciali" title="Elenco di tutte le pagine speciali [q]" accesskey="q"><span>Pagine speciali</span></a></li><li id="t-permalink" class="mw-list-item"><a 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progetti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2114702" title="Collegamento all'elemento connesso dell'archivio dati [g]" accesskey="g"><span>Elemento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspetto"> <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 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id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><table class="noprint toccolours" border="0" cellspacing="0" style="margin: 0 0 10px 10px; border: 1px #aaa solid; font-size: 95%; float: right;" width="170px"> <tbody><tr style="text-align: center; background-color: #dddddd;"> <td><b><a href="/wiki/Cinetica_chimica" title="Cinetica chimica">Cinetica chimica</a></b> </td></tr> <tr> <td style="text-align: center; background-color: #eeeeee;"><b><a href="/wiki/Velocit%C3%A0_di_reazione" title="Velocità di reazione">Velocità di reazione</a></b> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Teoria_delle_collisioni" title="Teoria delle collisioni">Teoria delle collisioni</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Reazione_elementare" title="Reazione elementare">Reazione elementare</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Molecolarit%C3%A0" title="Molecolarità">Molecolarità</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Equazione_cinetica" title="Equazione cinetica">Equazione cinetica</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a class="mw-selflink selflink">Ordine di reazione</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Costante_di_velocit%C3%A0" title="Costante di velocità">Costante di velocità</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Equazione_di_Arrhenius" title="Equazione di Arrhenius">Equazione di Arrhenius</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Equazione_di_Eyring" title="Equazione di Eyring">Equazione di Eyring</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Teoria_dello_stato_di_transizione" title="Teoria dello stato di transizione">Teoria dello stato di transizione</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Stato_di_transizione" title="Stato di transizione">Stato di transizione</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Meccanismo_di_reazione" title="Meccanismo di reazione">Meccanismo di reazione</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Energia_di_attivazione" title="Energia di attivazione">Energia di attivazione</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Approssimazione_dello_stato_stazionario" title="Approssimazione dello stato stazionario">Approssimazione dello stato stazionario</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Effetto_isotopico_cinetico" title="Effetto isotopico cinetico">Effetto isotopico cinetico</a> </td></tr> <tr> <td style="text-align: center; background-color: #eeeeee;"><b><a href="/wiki/Catalisi" title="Catalisi">Catalisi</a></b> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Catalizzatore" title="Catalizzatore">Catalizzatore</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Catalisi_omogenea" title="Catalisi omogenea">Catalisi omogenea</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Catalisi_eterogenea" title="Catalisi eterogenea">Catalisi eterogenea</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Catalisi_per_trasferimento_di_fase" title="Catalisi per trasferimento di fase">Catalisi per trasferimento di fase</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Catalisi_enzimatica" title="Catalisi enzimatica">Catalisi enzimatica</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Fotocatalisi" title="Fotocatalisi">Fotocatalisi</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Autocatalisi" title="Autocatalisi">Autocatalisi</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Attivit%C3%A0_catalitica" title="Attività catalitica">Attività catalitica</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Sito_attivo" title="Sito attivo">Sito attivo</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Supporto_catalitico" title="Supporto catalitico">Supporto catalitico</a> </td></tr> <tr style="text-align: left; font-size:90%"> <td><a href="/wiki/Disattivazione_dei_catalizzatori" title="Disattivazione dei catalizzatori">Disattivazione dei catalizzatori</a> </td></tr> <tr> <td style="text-align: center; background-color: #dddddd; font-size:90%"><i><a href="/wiki/Categoria:Cinetica_chimica" title="Categoria:Cinetica chimica">Categoria:Cinetica chimica</a></i> </td></tr></tbody></table> <p>In <a href="/wiki/Chimica" title="Chimica">chimica</a>, l'<b>ordine di reazione</b> relativo ad un <a href="/wiki/Reagente" title="Reagente">reagente</a> è l'esponente al quale è elevata la <a href="/wiki/Concentrazione_(chimica)" title="Concentrazione (chimica)">concentrazione</a> del reagente nell'<a href="/wiki/Equazione_cinetica" title="Equazione cinetica">equazione cinetica</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><br /> Lo studio della <a href="/wiki/Cinetica_chimica" title="Cinetica chimica">cinetica chimica</a> di una reazione consiste principalmente nella determinazione sperimentale della sua equazione cinetica, una legge che lega la <a href="/wiki/Velocit%C3%A0_di_reazione" title="Velocità di reazione">velocità di reazione</a> alla <a href="/wiki/Molarit%C3%A0" class="mw-redirect" title="Molarità">concentrazione molare</a> di uno o più reagenti elevata a un esponente che non coincide necessariamente con il corrispondente coefficiente stechiometrico della reazione globale. </p><p>Determinare sperimentalmente l'ordine di una reazione rispetto ai suoi reagenti e prodotti può dare indicazioni per capirne il <a href="/wiki/Meccanismo_di_reazione" title="Meccanismo di reazione">meccanismo</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definizione">Definizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=1" title="Modifica la sezione Definizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=1" title="Edit section's source code: Definizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Data una generica reazione (diretta o irreversibile): </p> <dl><dd><i>aA + bB → cC + dD</i></dd></dl> <p>la legge cinetica è del tipo: </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 r=k\left[A\right]^{m}\left[B\right]^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mi>k</mi> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <msup> <mrow> <mo>[</mo> <mi>B</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=k\left[A\right]^{m}\left[B\right]^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/befb8544a8b6d648756d7e82a5fa70e0c66f305d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.346ex; height:3.009ex;" alt="{\displaystyle r=k\left[A\right]^{m}\left[B\right]^{n}}"></span></dd></dl> <p>[Attenzione in alcuni testi la velocità di reazione viene espressa con <span class="mwe-math-element"><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/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span>] </p><p><i>k</i> è una costante positiva detta <i>costante di velocità</i> della reazione, e rappresenta la velocità iniziale della reazione quando i reagenti hanno concentrazione unitaria; <i>m</i> ed <i>n</i> sono degli esponenti non necessariamente uguali ad <i>a</i> e <i>b</i>. Il valore di <i>k</i>, a discapito del nome, non è costante e varia con la temperatura del sistema. </p><p>Si definisce <i>ordine globale di reazione</i> la somma di <i>m</i> con <i>n</i>: </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 {RO} =m+n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">O</mi> </mrow> <mo>=</mo> <mi>m</mi> <mo>+</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {RO} =m+n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e7794eb7ad112294463fde8a489d4b7249467be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.893ex; height:2.343ex;" alt="{\displaystyle \mathrm {RO} =m+n}"></span></dd></dl> <p>Si definisce <i>ordine parziale di reazione</i>, riferito ad una singola specie reagente, l'esponente che accompagna la specie presa in esame nella legge cinetica: </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 {RO_{A}} =m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </msub> </mrow> <mo>=</mo> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {RO_{A}} =m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ad07b9e60e62a7f480d164fef2bbd804d20dda5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.122ex; height:2.509ex;" alt="{\displaystyle \mathrm {RO_{A}} =m}"></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 \mathrm {RO_{B}} =n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {RO_{B}} =n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1232b33c4871f2a2f6d81c4ea736e535d4c16ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.408ex; height:2.509ex;" alt="{\displaystyle \mathrm {RO_{B}} =n}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Reazioni_dirette_di_ordine_zero">Reazioni dirette di ordine zero</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=2" title="Modifica la sezione Reazioni dirette di ordine zero" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=2" title="Edit section's source code: Reazioni dirette di ordine zero"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si chiamano reazioni di ordine zero quelle reazioni la cui velocità è indipendente dalla concentrazione dei reagenti. Questo non è un comportamento raro. </p><p>La legge cinetica è: </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 r={\frac {d\left[A\right]}{dt}}=-k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {d\left[A\right]}{dt}}=-k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2c803121a66cb2c15887c11a2dc11caa484fd37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.741ex; height:5.843ex;" alt="{\displaystyle r={\frac {d\left[A\right]}{dt}}=-k}"></span></dd></dl> <p>Possiamo arrangiare ed integrare la l'equazione nel seguente modo: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[A]=-kdt\rightarrow \int _{[A]_{0}}^{[A]}d[A]=-k\int _{0}^{t}dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mi>d</mi> <mi>t</mi> <mo stretchy="false">→</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> </msubsup> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo>−</mo> <mi>k</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[A]=-kdt\rightarrow \int _{[A]_{0}}^{[A]}d[A]=-k\int _{0}^{t}dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ca9c4004c80884aa9645e50b7976212b1bca70b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:37.761ex; height:6.843ex;" alt="{\displaystyle d[A]=-kdt\rightarrow \int _{[A]_{0}}^{[A]}d[A]=-k\int _{0}^{t}dt}"></span> </p><p>Risolvendo l'integrale otteniamo l'equazione: </p><p><span class="mwe-math-element"><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]=[A]_{0}-kt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>k</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A]=[A]_{0}-kt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8b537e0312d30d6d44491dedd79923f4677228" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.118ex; height:2.843ex;" alt="{\displaystyle [A]=[A]_{0}-kt}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Reazioni_dirette_del_primo_ordine">Reazioni dirette del primo ordine</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=3" title="Modifica la sezione Reazioni dirette del primo ordine" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=3" title="Edit section's source code: Reazioni dirette del primo ordine"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ordine_1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ordine_1.png/310px-Ordine_1.png" decoding="async" width="310" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Ordine_1.png/465px-Ordine_1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/d/de/Ordine_1.png 2x" data-file-width="539" data-file-height="405" /></a><figcaption>Diagramma <a href="/w/index.php?title=Logaritmico&action=edit&redlink=1" class="new" title="Logaritmico (la pagina non esiste)">logaritmico</a> per verificare graficamente le reazioni di primo ordine. Se la reazione in questo diagramma risulta rappresentata da una retta calante, la reazione è del primo ordine. Invece, tanto più la reazione si discosta da una retta calante, tanto meno è approssimabile come reazione del primo ordine.</figcaption></figure> <p>Le reazioni del primo ordine sono quelle reazioni la cui velocità dipende dalla concentrazione di un solo reagente elevato ad un esponente pari ad 1. </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 r=-k\left[A\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=-k\left[A\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c7b904910f550eeb149d75afe1277d54067c94e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.59ex; height:2.843ex;" alt="{\displaystyle r=-k\left[A\right]}"></span></dd></dl> <p>La velocità istantanea di reazione globale coincide con la velocità istantanea di reazione di A, reagente che man mano diminuisce. Vale allora che <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=r_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=r_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0debf204568ef733bd4f97eedc5a1f35b105f96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.661ex; height:2.009ex;" alt="{\displaystyle r=r_{A}}"></span>. Quindi: </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 {\frac {d\left[A\right]}{dt}}=-k\left[A\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\left[A\right]}{dt}}=-k\left[A\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d99a1a854d8fafe83bd0a7d184c46c974480f72e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.018ex; height:5.843ex;" alt="{\displaystyle {\frac {d\left[A\right]}{dt}}=-k\left[A\right]}"></span></dd></dl> <p>Scambiamo l'ordine dei termini in modo da applicare il <a href="/wiki/Metodo_di_separazione_delle_variabili" class="mw-redirect" title="Metodo di separazione delle variabili">metodo di separazione delle variabili</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 {\frac {d\left[A\right]}{\left[A\right]}}=-kdt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\left[A\right]}{\left[A\right]}}=-kdt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad717b48d29c475014081be49e9bff97020cf393" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:13.649ex; height:6.509ex;" alt="{\displaystyle {\frac {d\left[A\right]}{\left[A\right]}}=-kdt}"></span></dd></dl> <p>integrando fra <span class="mwe-math-element"><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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.101ex; height:2.176ex;" alt="{\displaystyle t=0}"></span> e <i>t</i> generico avremo: </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 \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]}}=-k\int _{0}^{t}dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]}}=-k\int _{0}^{t}dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18a7abc57fc770db6bf467aaf58c793c3ddf9b12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:22.944ex; height:6.843ex;" alt="{\displaystyle \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]}}=-k\int _{0}^{t}dt}"></span></dd></dl> <p>e risolvendo l'integrale: </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 \left[A\right]=\left[A\right]_{0}e^{-kt}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mo>=</mo> <msub> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>k</mi> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[A\right]=\left[A\right]_{0}e^{-kt}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a505680e73f178880ded3e4e783053cad71140f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.271ex; height:3.343ex;" alt="{\displaystyle \left[A\right]=\left[A\right]_{0}e^{-kt}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Reazioni_dirette_del_secondo_ordine">Reazioni dirette del secondo ordine</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=4" title="Modifica la sezione Reazioni dirette del secondo ordine" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=4" title="Edit section's source code: Reazioni dirette del secondo ordine"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ordine_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Ordine_2.png/310px-Ordine_2.png" decoding="async" width="310" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Ordine_2.png/465px-Ordine_2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/e/ea/Ordine_2.png 2x" data-file-width="539" data-file-height="405" /></a><figcaption>Grafico caratteristico delle reazioni di secondo ordine. Si ottiene diagrammando 1/[A] in funzione del tempo</figcaption></figure> <p>Le reazioni del secondo ordine sono quelle reazioni la cui velocità dipende dalla concentrazione di uno o più reagenti in modo tale che la somma degli esponenti sia pari a 2. </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 r=-k\left[A\right]^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mo>−</mo> <mi>k</mi> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=-k\left[A\right]^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc52c3ded635787d60ce5aba997415a3e52116ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.258ex; height:3.343ex;" alt="{\displaystyle r=-k\left[A\right]^{2}}"></span></dd></dl> <p>La velocità istantanea di reazione globale coincide con la velocità istantanea di reazione di A, reagente che man mano diminuisce. Vale allora che <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=r_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=r_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0debf204568ef733bd4f97eedc5a1f35b105f96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.661ex; height:2.009ex;" alt="{\displaystyle r=r_{A}}"></span>. Quindi: </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 {\frac {d\left[A\right]}{dt}}=-k\left[A\right]^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\left[A\right]}{dt}}=-k\left[A\right]^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/097b5d35d3573f6a26f653ee09d3caf8ce96045a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.685ex; height:5.843ex;" alt="{\displaystyle {\frac {d\left[A\right]}{dt}}=-k\left[A\right]^{2}}"></span></dd></dl> <p>Scambiamo l'ordine dei termini in modo da applicare il <a href="/wiki/Metodo_di_separazione_delle_variabili" class="mw-redirect" title="Metodo di separazione delle variabili">metodo di separazione delle variabili</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 {\frac {d\left[A\right]}{\left[A\right]^{2}}}=-kdt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\left[A\right]}{\left[A\right]^{2}}}=-kdt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd3979525b137a30c668df493ccad1e54aee229d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.649ex; height:7.009ex;" alt="{\displaystyle {\frac {d\left[A\right]}{\left[A\right]^{2}}}=-kdt}"></span></dd></dl> <p>integrando fra <span class="mwe-math-element"><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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.101ex; height:2.176ex;" alt="{\displaystyle t=0}"></span> e <i>t</i> generico avremo: </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 \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]^{2}}}=-\mathrm {k} \int _{0}^{t}dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]^{2}}}=-\mathrm {k} \int _{0}^{t}dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/106c679a8107613d2ae95652969c5cdec4df6c72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:22.961ex; height:7.176ex;" alt="{\displaystyle \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]^{2}}}=-\mathrm {k} \int _{0}^{t}dt}"></span></dd></dl> <p>Risolvendo l'integrale otteniamo: </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 {\frac {1}{\left[A\right]}}-{\frac {1}{\left[A\right]_{0}}}=\mathrm {k} t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\left[A\right]}}-{\frac {1}{\left[A\right]_{0}}}=\mathrm {k} t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cea54114260d9db5864c04632cf83ff651df699" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.806ex; height:6.009ex;" alt="{\displaystyle {\frac {1}{\left[A\right]}}-{\frac {1}{\left[A\right]_{0}}}=\mathrm {k} t}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Reazioni_del_secondo_ordine_con_due_reagenti">Reazioni del secondo ordine con due reagenti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=5" title="Modifica la sezione Reazioni del secondo ordine con due reagenti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=5" title="Edit section's source code: Reazioni del secondo ordine con due reagenti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Una reazione del secondo ordine oltre ad avere la forma adottata nel paragrafo precedente, può adottare anche la seguente forma nel caso <span class="mwe-math-element"><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+B\rightarrow P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo stretchy="false">→</mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A+B\rightarrow P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40b0c04093bd090a0d19e3166b8d0a3777bf2eaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.707ex; height:2.343ex;" alt="{\displaystyle A+B\rightarrow P}"></span>, in questo caso la velocità di reazione diventa: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={d[A] \over dt}=-k_{v}[A][B]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>B</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={d[A] \over dt}=-k_{v}[A][B]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b876426d231e478a3f368320eb28dc4ca1e3c34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.478ex; height:5.843ex;" alt="{\displaystyle r={d[A] \over dt}=-k_{v}[A][B]}"></span> </p><p>In questo caso l'equazione può essere integrata per ricavare la variazione dei reagenti in funzione del tempo, prima di integrare notiamo che la concentrazione di <span class="mwe-math-element"><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> diminuisce 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 [A]_{0}-x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A]_{0}-x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afed21a3fc47dd1f49e917282bda8b10a484e1aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.261ex; height:2.843ex;" alt="{\displaystyle [A]_{0}-x}"></span>, mentre <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> diminuisce di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [B]_{0}-x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [B]_{0}-x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/347994a337b233ef047aff73f6504d99535857c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.282ex; height:2.843ex;" alt="{\displaystyle [B]_{0}-x}"></span>, a questo punto li sostituiamo nell'equazione precedente ottenendo: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={d[A] \over dt}=-k_{v}([A]_{0}-x)([B]_{0}-x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={d[A] \over dt}=-k_{v}([A]_{0}-x)([B]_{0}-x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e58d5dba1947c3f2ee73b3e6810219d16c3742b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:36.545ex; height:5.843ex;" alt="{\displaystyle r={d[A] \over dt}=-k_{v}([A]_{0}-x)([B]_{0}-x)}"></span> </p><p>Poiché <span class="mwe-math-element"><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]=[A]_{0}-x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A]=[A]_{0}-x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/946de91ec22144a79323881bdb4cd5c1deea9dde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.396ex; height:2.843ex;" alt="{\displaystyle [A]=[A]_{0}-x}"></span> ne segue che <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[A]/dt=-dx/dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mo>−</mo> <mi>d</mi> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[A]/dt=-dx/dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65fd8139f740a014c9747989d3f2e54a6211b984" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.141ex; height:2.843ex;" alt="{\displaystyle d[A]/dt=-dx/dt}"></span>, di conseguenza possiamo riscrivere la legge cinetica come: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={dx \over dt}=-k_{v}([A]_{0}-x)([B]_{0}-x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={dx \over dt}=-k_{v}([A]_{0}-x)([B]_{0}-x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/242ad92c32028de550fe2d44d8451d99db7acb28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:34.838ex; height:5.509ex;" alt="{\displaystyle r={dx \over dt}=-k_{v}([A]_{0}-x)([B]_{0}-x)}"></span> </p><p>A questo punto possiamo integrare utilizzando la condizione iniziale dove <span class="mwe-math-element"><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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/953917eaf52f2e1baad54c8c9e3d6f9bb3710cdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle x=0}"></span> quando <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {t=0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>t</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>0</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {t=0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c94e38327ee776ec4778d0d24a55834ad74fad8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.875ex; height:2.176ex;" alt="{\displaystyle {\ce {t=0}}}"></span> quindi: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{0}^{x}{dx \over ([A]_{0}-x)([B]_{0}-x)}=k_{v}\int _{0}^{t}dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{0}^{x}{dx \over ([A]_{0}-x)([B]_{0}-x)}=k_{v}\int _{0}^{t}dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe2ccbd1f9819a45fce0f886ef4e22a04f32b17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:36.481ex; height:6.509ex;" alt="{\displaystyle \int _{0}^{x}{dx \over ([A]_{0}-x)([B]_{0}-x)}=k_{v}\int _{0}^{t}dt}"></span> </p><p>L'integrale precedente viene risolto con il <a href="/w/index.php?title=Metodo_delle_frazioni_parziali&action=edit&redlink=1" class="new" title="Metodo delle frazioni parziali (la pagina non esiste)">metodo delle frazioni parziali</a>, alla fine dell'integrazione e dopo aver sistemato l'espressione, il nostro risultato finale sarà: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln {\frac {([B]/[B]_{0})}{([A]/[A]_{0})}}=k_{v}t([B]_{0}-[A]_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>B</mi> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln {\frac {([B]/[B]_{0})}{([A]/[A]_{0})}}=k_{v}t([B]_{0}-[A]_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c66a681f09dc6a26b6d491f3f6bd7329c005550" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:32.336ex; height:6.509ex;" alt="{\displaystyle \ln {\frac {([B]/[B]_{0})}{([A]/[A]_{0})}}=k_{v}t([B]_{0}-[A]_{0})}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Reazioni_dirette_di_ordine_N">Reazioni dirette di ordine N</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=6" title="Modifica la sezione Reazioni dirette di ordine N" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=6" title="Edit section's source code: Reazioni dirette di ordine N"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Si chiamano reazioni di ordine N (N non nullo positivo, intero o semi-intero e diverso da 1) quelle reazioni la cui velocità dipende dalla concentrazione di uno o più reagenti in modo tale che la somma degli esponenti sia pari a N. </p><p>La legge cinetica è: </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 r=-{k}\left[A\right]^{N}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=-{k}\left[A\right]^{N}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b6218ff775da2588a3d3aa45772a31d15767042" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.895ex; height:3.343ex;" alt="{\displaystyle r=-{k}\left[A\right]^{N}}"></span></dd></dl> <p>La velocità istantanea di reazione globale coincide con la velocità istantanea di reazione di A, reagente che man mano diminuisce. Vale allora che <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=r_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=r_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0debf204568ef733bd4f97eedc5a1f35b105f96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.661ex; height:2.009ex;" alt="{\displaystyle r=r_{A}}"></span>. Quindi: </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 {\frac {d\left[A\right]}{dt}}=-k\left[A\right]^{N}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\left[A\right]}{dt}}=-k\left[A\right]^{N}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d110e068d4efb624b959d958e3974ce05047afb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.322ex; height:5.843ex;" alt="{\displaystyle {\frac {d\left[A\right]}{dt}}=-k\left[A\right]^{N}}"></span></dd></dl> <p>Scambiamo l'ordine dei termini in modo da applicare il <a href="/wiki/Metodo_di_separazione_delle_variabili" class="mw-redirect" title="Metodo di separazione delle variabili">metodo di separazione delle variabili</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 {\frac {d\left[A\right]}{\left[A\right]^{N}}}=-\mathrm {k} dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> </mrow> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\left[A\right]}{\left[A\right]^{N}}}=-\mathrm {k} dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bab7ed7194c6ce4c40c51b3656d8c9f34d7a6f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.754ex; height:7.009ex;" alt="{\displaystyle {\frac {d\left[A\right]}{\left[A\right]^{N}}}=-\mathrm {k} dt}"></span></dd></dl> <p>integrando fra <span class="mwe-math-element"><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=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.101ex; height:2.176ex;" alt="{\displaystyle t=0}"></span> e <i>t</i> generico avremo: </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 \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]^{N}}}=-\mathrm {k} \int _{0}^{t}dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> </mrow> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]^{N}}}=-\mathrm {k} \int _{0}^{t}dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35671a2fe2daa28e38a847a17748a64b5f431173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:23.049ex; height:7.176ex;" alt="{\displaystyle \int _{\left[A\right]_{0}}^{\left[A\right]}{\frac {d\left[A\right]}{\left[A\right]^{N}}}=-\mathrm {k} \int _{0}^{t}dt}"></span></dd></dl> <p>Dall'integrazione otteniamo: </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 \left({\frac {1}{N-1}}\right)\left({\frac {1}{\left[A\right]^{N-1}}}-{\frac {1}{\left[A\right]_{0}^{N-1}}}\right)=\mathrm {k} t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msubsup> <mrow> <mo>[</mo> <mi>A</mi> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">k</mi> </mrow> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{N-1}}\right)\left({\frac {1}{\left[A\right]^{N-1}}}-{\frac {1}{\left[A\right]_{0}^{N-1}}}\right)=\mathrm {k} t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9526a249b9d8ee5af8f5c700cde88d3a950b4e6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:37.728ex; height:7.509ex;" alt="{\displaystyle \left({\frac {1}{N-1}}\right)\left({\frac {1}{\left[A\right]^{N-1}}}-{\frac {1}{\left[A\right]_{0}^{N-1}}}\right)=\mathrm {k} t}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=7" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=7" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="http://goldbook.iupac.org/O04322.html">IUPAC Gold Book, "order of reaction"</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=8" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=8" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFSilvestroni" class="citation libro" style="font-style:normal"> Paolo Silvestroni, <a rel="nofollow" class="external text" href="https://archive.org/details/fondamentidichim00silv"><span style="font-style:italic;">Fondamenti di chimica</span></a>, 10ª ed., CEA, 1996, pp. <a rel="nofollow" class="external text" href="https://archive.org/details/fondamentidichim00silv/page/n354">353</a>-355, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/88-408-0998-8" title="Speciale:RicercaISBN/88-408-0998-8">88-408-0998-8</a>.</cite></li> <li>Peter Atkins, Julio de Paula, James Keeler. <i>Chimica fisica</i>, 6ª ed.,</li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ordine_di_reazione&veaction=edit&section=9" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ordine_di_reazione&action=edit&section=9" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Molecolarit%C3%A0" title="Molecolarità">Molecolarità</a></li> <li><a href="/wiki/Velocit%C3%A0_di_reazione" title="Velocità di reazione">Velocità di reazione</a></li></ul> <div class="noprint" style="width:100%; 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Ordine di reazione - Wikipedia