Reversible reaction

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mw-first-heading"><span class="mw-page-title-main">Reversible reaction</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="Go to an article in another language. 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href="https://zh-min-nan.wikipedia.org/wiki/Kh%C3%B3-ge%CC%8Dk_ho%C3%A1n-%C3%A8ng" title="Khó-ge̍k hoán-èng – Minnan" lang="nan" hreflang="nan" data-title="Khó-ge̍k hoán-èng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B1%D0%B0%D1%80%D0%B0%D1%87%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F_%D1%80%D1%8D%D0%B0%D0%BA%D1%86%D1%8B%D1%96" title="Абарачальныя рэакцыі – Belarusian" lang="be" hreflang="be" data-title="Абарачальныя рэакцыі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Reacci%C3%B3_reversible" title="Reacció reversible – Catalan" lang="ca" hreflang="ca" data-title="Reacció reversible" 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/Vratn%C3%A1_reakce" title="Vratná reakce – Czech" lang="cs" hreflang="cs" data-title="Vratná reakce" data-language-autonym="Čeština" data-language-local-name="Czech" 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/Reversibel_reaktion" title="Reversibel reaktion – Danish" lang="da" hreflang="da" data-title="Reversibel reaktion" data-language-autonym="Dansk" data-language-local-name="Danish" 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/Reversible_Reaktion" title="Reversible Reaktion – German" lang="de" hreflang="de" data-title="Reversible Reaktion" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/P%C3%B6%C3%B6rduv_reaktsioon" title="Pöörduv reaktsioon – Estonian" lang="et" hreflang="et" data-title="Pöörduv reaktsioon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Reacci%C3%B3n_reversible" title="Reacción reversible – Spanish" lang="es" hreflang="es" data-title="Reacción reversible" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%88%D8%A7%DA%A9%D9%86%D8%B4_%D8%A8%D8%B1%DA%AF%D8%B4%D8%AA%E2%80%8C%D9%BE%D8%B0%DB%8C%D8%B1" title="واکنش برگشت‌پذیر – Persian" lang="fa" hreflang="fa" data-title="واکنش برگشت‌پذیر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/R%C3%A9action_r%C3%A9versible" title="Réaction réversible – French" lang="fr" hreflang="fr" data-title="Réaction réversible" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B0%80%EC%97%AD_%EB%B0%98%EC%9D%91" title="가역 반응 – Korean" lang="ko" hreflang="ko" data-title="가역 반응" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%A1%D6%80%D5%B1%D5%A5%D5%AC%D5%AB_%D5%BC%D5%A5%D5%A1%D5%AF%D6%81%D5%AB%D5%A1%D5%B6%D5%A5%D6%80" title="Դարձելի ռեակցիաներ – Armenian" lang="hy" hreflang="hy" data-title="Դարձելի ռեակցիաներ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%89%E0%A4%A4%E0%A5%8D%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%A3%E0%A5%80%E0%A4%AF_%E0%A4%85%E0%A4%AD%E0%A4%BF%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%AF%E0%A4%BE" title="उत्क्रमणीय अभिक्रिया – Hindi" lang="hi" hreflang="hi" data-title="उत्क्रमणीय अभिक्रिया" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Reaksi_reversibel" title="Reaksi reversibel – Indonesian" lang="id" hreflang="id" data-title="Reaksi reversibel" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" 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/Reazione_reversibile" title="Reazione reversibile – Italian" lang="it" hreflang="it" data-title="Reazione reversibile" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D0%B0%D0%B9%D1%82%D1%8B%D0%BC%D0%B4%D1%8B_%D1%80%D0%B5%D0%B0%D0%BA%D1%86%D0%B8%D1%8F" title="Қайтымды реакция – Kazakh" lang="kk" hreflang="kk" data-title="Қайтымды реакция" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%89%E0%B4%AD%E0%B4%AF%E0%B4%A6%E0%B4%BF%E0%B4%B6%E0%B4%BE_%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%B5%E0%B5%BC%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%A8%E0%B4%82" title="ഉഭയദിശാ പ്രവർത്തനം – Malayalam" lang="ml" hreflang="ml" data-title="ഉഭയദിശാ പ്രവർത്തനം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tindak_balas_berbalik" title="Tindak balas berbalik – Malay" lang="ms" hreflang="ms" data-title="Tindak balas berbalik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8F%AF%E9%80%86%E5%8F%8D%E5%BF%9C" title="可逆反応 – Japanese" lang="ja" hreflang="ja" data-title="可逆反応" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A8%B0%E0%A8%A4%E0%A8%B5%E0%A9%80%E0%A8%86%E0%A8%82_%E0%A8%95%E0%A8%BF%E0%A8%B0%E0%A8%BF%E0%A8%86%E0%A8%B5%E0%A8%BE%E0%A8%82" title="ਪਰਤਵੀਆਂ ਕਿਰਿਆਵਾਂ – Punjabi" lang="pa" hreflang="pa" data-title="ਪਰਤਵੀਆਂ ਕਿਰਿਆਵਾਂ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Reakcja_odwracalna" title="Reakcja odwracalna – Polish" lang="pl" hreflang="pl" data-title="Reakcja odwracalna" data-language-autonym="Polski" data-language-local-name="Polish" 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/Rea%C3%A7%C3%A3o_qu%C3%ADmica_revers%C3%ADvel" title="Reação química reversível – Portuguese" lang="pt" hreflang="pt" data-title="Reação química reversível" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Reac%C8%9Bie_reversibil%C4%83" title="Reacție reversibilă – Romanian" lang="ro" hreflang="ro" data-title="Reacție reversibilă" data-language-autonym="Română" data-language-local-name="Romanian" 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%9E%D0%B1%D1%80%D0%B0%D1%82%D0%B8%D0%BC%D1%8B%D0%B5_%D1%80%D0%B5%D0%B0%D0%BA%D1%86%D0%B8%D0%B8" title="Обратимые реакции – Russian" lang="ru" hreflang="ru" data-title="Обратимые реакции" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Vratn%C3%A1_reakcia" title="Vratná reakcia – Slovak" lang="sk" hreflang="sk" data-title="Vratná reakcia" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Reverzibilna_reakcija" title="Reverzibilna reakcija – Slovenian" lang="sl" hreflang="sl" data-title="Reverzibilna reakcija" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%A9%D8%A7%D8%B1%D8%AF%D8%A7%D9%86%DB%95%D9%88%DB%95%DB%8C_%D9%BE%DB%8E%DA%86%DB%95%D9%88%D8%A7%D9%86%DB%95" title="کاردانەوەی پێچەوانە – Central Kurdish" lang="ckb" hreflang="ckb" data-title="کاردانەوەی پێچەوانە" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D0%B2%D1%80%D0%B0%D1%82%D0%BD%D0%B0_%D1%85%D0%B5%D0%BC%D0%B8%D1%98%D1%81%D0%BA%D0%B0_%D1%80%D0%B5%D0%B0%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Повратна хемијска реакција – Serbian" lang="sr" hreflang="sr" data-title="Повратна хемијска реакција" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Povratna_hemijska_reakcija" title="Povratna hemijska reakcija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Povratna hemijska reakcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Reversibel_reaktion" title="Reversibel reaktion – Swedish" lang="sv" hreflang="sv" data-title="Reversibel reaktion" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%80%E0%AE%B3%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%A9%E0%AF%88" title="மீள் வினை – Tamil" lang="ta" hreflang="ta" data-title="மீள் வினை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B1%D0%BE%D1%80%D0%BE%D1%82%D0%BD%D1%96_%D1%80%D0%B5%D0%B0%D0%BA%D1%86%D1%96%D1%97" title="Оборотні реакції – Ukrainian" lang="uk" hreflang="uk" data-title="Оборотні реакції" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%8F%AF%E9%80%86%E4%B9%8B%E5%90%88" title="可逆之合 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="可逆之合" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%AF%E9%80%86%E5%8F%8D%E6%87%89" title="可逆反應 – Chinese" lang="zh" hreflang="zh" data-title="可逆反應" data-language-autonym="中文" data-language-local-name="Chinese" 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/Q686980#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</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="Namespaces"> <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 href="/wiki/Reversible_reaction" title="View the 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</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="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Chemical reaction whose products can react together to produce the reactants again</div> <p>A <b>reversible reaction</b> is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously.<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> </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 {\ce {{\mathit {a}}A{}+{\mathit {b}}B<=>{\mathit {c}}C{}+{\mathit {d}}D}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">a</mtext> </mrow> </mrow> <mtext>A</mtext> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">b</mtext> </mrow> </mrow> <mtext>B</mtext> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded height="0" depth="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">↽</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </mpadded> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">⇀</mo> </mrow> </mrow> </mstyle> </mrow> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">c</mtext> </mrow> </mrow> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext class="MJX-tex-mathit" mathvariant="italic">d</mtext> </mrow> </mrow> <mtext>D</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {{\mathit {a}}A{}+{\mathit {b}}B<=>{\mathit {c}}C{}+{\mathit {d}}D}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c97665de25ba55d7940c882f9dffd76a63b591cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:21.686ex; height:2.843ex;" alt="{\displaystyle {\ce {{\mathit {a}}A{}+{\mathit {b}}B<=>{\mathit {c}}C{}+{\mathit {d}}D}}}"></span></dd></dl> <p>A and B can react to form C and D or, in the reverse reaction, C and D can react to form A and B. This is distinct from a <a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">reversible process</a> in <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>. </p><p>Weak <a href="/wiki/Acids" class="mw-redirect" title="Acids">acids</a> and <a href="/wiki/Base_(chemistry)" title="Base (chemistry)">bases</a> undergo reversible reactions. For example, <a href="/wiki/Carbonic_acid" title="Carbonic acid">carbonic acid</a>: </p> <dl><dd>H<sub>2</sub>CO<sub>3 (l)</sub> + H<sub>2</sub>O<sub>(l)</sub> ⇌ HCO<sub>3</sub><sup>−</sup><sub>(aq)</sub> + H<sub>3</sub>O<sup>+</sup><sub>(aq)</sub>.</dd></dl> <p>The <a href="/wiki/Concentration" title="Concentration">concentrations</a> of reactants and products in an equilibrium mixture are determined by the <a href="/wiki/Analytical_concentration" class="mw-redirect" title="Analytical concentration">analytical concentrations</a> of the reagents (A and B or C and D) and the <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a>, <i>K</i>. The magnitude of the equilibrium constant depends on the <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> change for the reaction.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> So, when the free energy change is large (more than about 30 kJ mol<sup>−1</sup>), the equilibrium constant is large (log K > 3) and the concentrations of the reactants at equilibrium are very small. Such a reaction is sometimes considered to be an irreversible reaction, although small amounts of the reactants are still expected to be present in the reacting system. A truly irreversible chemical reaction is usually achieved when one of the products exits the reacting system, for example, as does carbon dioxide (volatile) in the reaction </p> <dl><dd>CaCO<sub>3</sub> + 2HCl → CaCl<sub>2</sub> + H<sub>2</sub>O + CO<sub>2</sub>↑</dd></dl> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reversible_reaction&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concept of a reversible reaction was introduced by <a href="/wiki/Claude_Louis_Berthollet" title="Claude Louis Berthollet">Claude Louis Berthollet</a> in 1803, after he had observed the formation of <a href="/wiki/Sodium_carbonate" title="Sodium carbonate">sodium carbonate</a> crystals at the edge of a <a href="/wiki/Salt_lake" title="Salt lake">salt lake</a><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> (one of the <a href="/wiki/Natron" title="Natron">natron</a> lakes in Egypt, in <a href="/wiki/Limestone" title="Limestone">limestone</a>): </p> <dl><dd>2NaCl + CaCO<sub>3</sub> → Na<sub>2</sub>CO<sub>3</sub> + CaCl<sub>2</sub></dd></dl> <p>He recognized this as the reverse of the familiar reaction </p> <dl><dd>Na<sub>2</sub>CO<sub>3</sub> + CaCl<sub>2</sub>→ 2NaCl + CaCO<sub>3</sub></dd></dl> <p>Until then, <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> were thought to always proceed in one direction. Berthollet reasoned that the excess of <a href="/wiki/Salt" title="Salt">salt</a> in the lake helped push the "reverse" reaction towards the formation of sodium carbonate.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>In 1864, <a href="/wiki/Peter_Waage" title="Peter Waage">Peter Waage</a> and <a href="/wiki/Cato_Maximilian_Guldberg" title="Cato Maximilian Guldberg">Cato Maximilian Guldberg</a> formulated their <a href="/wiki/Law_of_mass_action" title="Law of mass action">law of mass action</a> which quantified Berthollet's observation. Between 1884 and 1888, <a href="/wiki/Henry_Louis_Le_Chatelier" title="Henry Louis Le Chatelier">Le Chatelier</a> and <a href="/wiki/Karl_Ferdinand_Braun" title="Karl Ferdinand Braun">Braun</a> formulated <a href="/wiki/Le_Chatelier%27s_principle" title="Le Chatelier's principle">Le Chatelier's principle</a>, which extended the same idea to a more general statement on the effects of factors other than concentration on the position of the equilibrium. </p> <div class="mw-heading mw-heading2"><h2 id="Reaction_kinetics">Reaction kinetics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reversible_reaction&action=edit&section=2" title="Edit section: Reaction kinetics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For the reversible reaction A⇌B, the forward step A→B has a rate 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 k_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/376315fd4983f01dada5ec2f7bebc48455b14a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{1}}"></span> and the backwards step B→A has a rate 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 k_{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c330fc841539e073ba8a335543dc8a8b0245574" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.544ex; height:2.509ex;" alt="{\displaystyle k_{-1}}"></span>. The concentration of A obeys the following differential equation: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><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[A]}{dt}}=-k_{\text{1}}[A]+k_{\text{-1}}[B]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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"> <mtext>1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>B</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d[A]}{dt}}=-k_{\text{1}}[A]+k_{\text{-1}}[B]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b829cc1998e950ea46071038b3d28687d0f878b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.009ex; height:5.843ex;" alt="{\displaystyle {\frac {d[A]}{dt}}=-k_{\text{1}}[A]+k_{\text{-1}}[B]}"></span>.</td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_1" class="reference nourlexpansion" style="font-weight:bold;">1</span>)</b></td></tr></tbody></table> <p>If we consider that the concentration of product B at anytime is equal to the concentration of reactants at time zero minus the concentration of reactants at time <span class="mwe-math-element"><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/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>, we can set up the following equation: </p> <table role="presentation" style="border-collapse:collapse; margin:0 0 0 1.6em; border:none;"><tbody><tr><td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><span class="mwe-math-element"><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]=[A]_{\text{0}}-[A]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>B</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> <mo>−</mo> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [B]=[A]_{\text{0}}-[A]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0160384d4fec5b1dff689c686e91bdb9aa34f0c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.124ex; height:2.843ex;" alt="{\displaystyle [B]=[A]_{\text{0}}-[A]}"></span>.</td> <td style="vertical-align:middle; width:99%; border:none; padding:0;"></td> <td style="vertical-align:middle; border:none; padding:0;" class="nowrap"><b>(<span id="math_2" class="reference nourlexpansion" style="font-weight:bold;">2</span>)</b></td></tr></tbody></table> <p>Combining <b><a href="#math_1">1</a></b> and <b><a href="#math_2">2</a></b>, we can write </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[A]}{dt}}=-k_{\text{1}}[A]+k_{\text{-1}}([A]_{\text{0}}-[A])}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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"> <mtext>1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> <mo>−</mo> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d[A]}{dt}}=-k_{\text{1}}[A]+k_{\text{-1}}([A]_{\text{0}}-[A])}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edd8b0ad9093979815714c89aad87eb98ad30aed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.729ex; height:5.843ex;" alt="{\displaystyle {\frac {d[A]}{dt}}=-k_{\text{1}}[A]+k_{\text{-1}}([A]_{\text{0}}-[A])}"></span>.</dd></dl> <p>Separation of variables is possible and using an initial value <span class="mwe-math-element"><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](t=0)=[A]_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo>=</mo> <mn>0</mn> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A](t=0)=[A]_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7091d40392dcd39a4791ff940043b521ea14d96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.136ex; height:2.843ex;" alt="{\displaystyle [A](t=0)=[A]_{0}}"></span>, we obtain: </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 C={\frac {{-\ln }(-k_{\text{1}}[A]_{\text{0}})}{k_{\text{1}}+k_{\text{-1}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>ln</mi> </mrow> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {{-\ln }(-k_{\text{1}}[A]_{\text{0}})}{k_{\text{1}}+k_{\text{-1}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e68a01fa14373f62142b54a523bc64926a27cfe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.809ex; height:6.176ex;" alt="{\displaystyle C={\frac {{-\ln }(-k_{\text{1}}[A]_{\text{0}})}{k_{\text{1}}+k_{\text{-1}}}}}"></span></dd></dl> <p>and after some algebra we arrive at the final kinetic expression: </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 [A]={\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}+{\frac {k_{\text{1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}\exp {{(-k_{\text{1}}+k_{\text{-1}}})t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mi>exp</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mi>t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A]={\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}+{\frac {k_{\text{1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}\exp {{(-k_{\text{1}}+k_{\text{-1}}})t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e066314d0c5c6518785e38b10b1e5c3acf7e8039" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:43.189ex; height:6.176ex;" alt="{\displaystyle [A]={\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}+{\frac {k_{\text{1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}\exp {{(-k_{\text{1}}+k_{\text{-1}}})t}}"></span>.</dd></dl> <p>The concentration of A and B at infinite time has a behavior as follows: </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 [A]_{\infty }={\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}}"> <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"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A]_{\infty }={\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7a472057e6969083895bf550e3839f7b9bbb7b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.766ex; height:6.176ex;" alt="{\displaystyle [A]_{\infty }={\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}}"></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 [B]_{\infty }=[A]_{\text{0}}-[A]_{\infty }=[A]_{\text{0}}-{\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}}"> <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"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> <mo>−</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [B]_{\infty }=[A]_{\text{0}}-[A]_{\infty }=[A]_{\text{0}}-{\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a6b5bb52715c8cda6b30e16abd1f76f3cd8d382" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:38.66ex; height:6.176ex;" alt="{\displaystyle [B]_{\infty }=[A]_{\text{0}}-[A]_{\infty }=[A]_{\text{0}}-{\frac {k_{\text{-1}}[A]_{\text{0}}}{k_{\text{1}}+k_{\text{-1}}}}}"></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 {\frac {[B]_{\infty }}{[A]_{\infty }}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}=K_{\text{eq}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {[B]_{\infty }}{[A]_{\infty }}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}=K_{\text{eq}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a7839fbfff514aaa89d68e38c8dd91bfe152822" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:19.419ex; height:6.509ex;" alt="{\displaystyle {\frac {[B]_{\infty }}{[A]_{\infty }}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}=K_{\text{eq}}}"></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 [A]=[A]_{\infty }+([A]_{\text{0}}-[A]_{\infty })\exp(-k_{\text{1}}+k_{\text{-1}})t}"> <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"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> <mo>−</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>exp</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A]=[A]_{\infty }+([A]_{\text{0}}-[A]_{\infty })\exp(-k_{\text{1}}+k_{\text{-1}})t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/352bf5b4cdbd18de47726b79e4a037623f78d8ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.856ex; height:2.843ex;" alt="{\displaystyle [A]=[A]_{\infty }+([A]_{\text{0}}-[A]_{\infty })\exp(-k_{\text{1}}+k_{\text{-1}})t}"></span></dd></dl> <p>Thus, the formula can be linearized in order to determine <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{1}+k_{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{1}+k_{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8506630c9ff4c83e3da8a338139a380f3b9758ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.65ex; height:2.509ex;" alt="{\displaystyle k_{1}+k_{-1}}"></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 \ln([A]-[A]_{\infty })=\ln([A]_{\text{0}}-[A]_{\infty })-(k_{\text{1}}+k_{\text{-1}})t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <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"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> <mo>−</mo> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln([A]-[A]_{\infty })=\ln([A]_{\text{0}}-[A]_{\infty })-(k_{\text{1}}+k_{\text{-1}})t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1224f5264515a79cd10322a680f25b43c1b4e0a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:46.637ex; height:2.843ex;" alt="{\displaystyle \ln([A]-[A]_{\infty })=\ln([A]_{\text{0}}-[A]_{\infty })-(k_{\text{1}}+k_{\text{-1}})t}"></span></dd></dl> <p>To find the individual constants <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/376315fd4983f01dada5ec2f7bebc48455b14a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{1}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c330fc841539e073ba8a335543dc8a8b0245574" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.544ex; height:2.509ex;" alt="{\displaystyle k_{-1}}"></span>, the following formula is required: </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 K_{\text{eq}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}={\frac {[B]_{\infty }}{[A]_{\infty }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>eq</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1</mtext> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>-1</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mi>B</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mrow> <mrow> <mo stretchy="false">[</mo> <mi>A</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{\text{eq}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}={\frac {[B]_{\infty }}{[A]_{\infty }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b62cb0b9b9cddee6c68ca99417c8101a1e43d78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:19.419ex; height:6.509ex;" alt="{\displaystyle K_{\text{eq}}={\frac {k_{\text{1}}}{k_{\text{-1}}}}={\frac {[B]_{\infty }}{[A]_{\infty }}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reversible_reaction&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Dynamic_equilibrium" title="Dynamic equilibrium">Dynamic equilibrium</a></li> <li><a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">Chemical equilibrium</a></li> <li><a href="/wiki/Irreversibility" class="mw-redirect" title="Irreversibility">Irreversibility</a></li> <li><a href="/wiki/Microscopic_reversibility" title="Microscopic reversibility">Microscopic reversibility</a></li> <li><a href="/wiki/Static_equilibrium" class="mw-redirect" title="Static equilibrium">Static equilibrium</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reversible_reaction&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://courses.lumenlearning.com/cheminter/chapter/reversible-reaction/">"Reversible Reaction"</a>. <i>lumenlearning.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-01-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=lumenlearning.com&rft.atitle=Reversible+Reaction&rft_id=https%3A%2F%2Fcourses.lumenlearning.com%2Fcheminter%2Fchapter%2Freversible-reaction%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReversible+reaction" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">at constant pressure.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.chem1.com/acad/webtext/chemeq/Eq-01.html#NAP">How did Napoleon Bonaparte help discover reversible reactions?</a>. Chem<sub>1</sub> General Chemistry Virtual Textbook: Chemical Equilibrium Introduction: reactions that go both ways.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Claude-Louis Berthollet,"Essai de statique chimique", Paris, 1803. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cKU5AAAAcAAJ&q=berthollet+essai">(Google books)</a></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Reversible_reaction&oldid=1245812898">https://en.wikipedia.org/w/index.php?title=Reversible_reaction&oldid=1245812898</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Equilibrium_chemistry" title="Category:Equilibrium chemistry">Equilibrium chemistry</a></li><li><a href="/wiki/Category:Physical_chemistry" title="Category:Physical chemistry">Physical chemistry</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Pages_that_use_a_deprecated_format_of_the_chem_tags" title="Category:Pages that use a deprecated format of the chem tags">Pages that use a deprecated format of the chem tags</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 15 September 2024, at 07:59<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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