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<span>Toggle Example reaction: <span>NO<sub>2</sub></span> + CO subsection</span> </button> <ul id="toc-Example_reaction:_NO2_+_CO-sublist" class="vector-toc-list"> <li id="toc-First_step_rate-determining" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#First_step_rate-determining"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>First step rate-determining</span> </div> </a> <ul id="toc-First_step_rate-determining-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pre-equilibrium:_if_the_second_step_were_rate-determining" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pre-equilibrium:_if_the_second_step_were_rate-determining"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Pre-equilibrium: if the second step were rate-determining</span> </div> </a> <ul id="toc-Pre-equilibrium:_if_the_second_step_were_rate-determining-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Nucleophilic_substitution" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nucleophilic_substitution"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Nucleophilic substitution</span> </div> </a> <ul id="toc-Nucleophilic_substitution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Composition_of_the_transition_state" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Composition_of_the_transition_state"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Composition of the transition state</span> </div> </a> <ul id="toc-Composition_of_the_transition_state-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reaction_coordinate_diagram" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reaction_coordinate_diagram"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Reaction coordinate diagram</span> </div> </a> <ul id="toc-Reaction_coordinate_diagram-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chain_reactions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Chain_reactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Chain reactions</span> </div> </a> <ul id="toc-Chain_reactions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diffusion_control" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Diffusion_control"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Diffusion control</span> </div> </a> <ul id="toc-Diffusion_control-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-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="Contents" 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" 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Available in 22 languages" > <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-22" 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">22 languages</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%AE%D8%B7%D9%88%D8%A9_%D9%85%D8%AD%D8%AF%D8%AF%D8%A9_%D9%84%D8%B3%D8%B1%D8%B9%D8%A9_%D8%A7%D9%84%D8%AA%D9%81%D8%A7%D8%B9%D9%84" title="خطوة محددة لسرعة التفاعل – Arabic" lang="ar" hreflang="ar" data-title="خطوة محددة لسرعة التفاعل" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Etapa_limitant" title="Etapa limitant – Catalan" lang="ca" hreflang="ca" data-title="Etapa limitant" 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/Krok_ur%C4%8Duj%C3%ADc%C3%AD_rychlost" title="Krok určující rychlost – Czech" lang="cs" hreflang="cs" data-title="Krok určující rychlost" 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/Hastighedsbestemmende_trin" title="Hastighedsbestemmende trin – Danish" lang="da" hreflang="da" data-title="Hastighedsbestemmende trin" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kiirust_limiteeriv_staadium" title="Kiirust limiteeriv staadium – Estonian" lang="et" hreflang="et" data-title="Kiirust limiteeriv staadium" 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/Paso_limitante_de_la_velocidad" title="Paso limitante de la velocidad – Spanish" lang="es" hreflang="es" data-title="Paso limitante de la velocidad" 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%85%D8%B1%D8%AD%D9%84%D9%87_%D8%AA%D8%B9%DB%8C%DB%8C%D9%86%E2%80%8C%DA%A9%D9%86%D9%86%D8%AF%D9%87_%D8%B3%D8%B1%D8%B9%D8%AA" title="مرحله تعیین‌کننده سرعت – Persian" lang="fa" hreflang="fa" data-title="مرحله تعیین‌کننده سرعت" 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/%C3%89tape_cin%C3%A9tiquement_d%C3%A9terminante" title="Étape cinétiquement déterminante – French" lang="fr" hreflang="fr" data-title="Étape cinétiquement déterminante" 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/%EC%86%8D%EB%8F%84_%EA%B2%B0%EC%A0%95_%EB%8B%A8%EA%B3%84" title="속도 결정 단계 – Korean" lang="ko" hreflang="ko" data-title="속도 결정 단계" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tahap_penentu_laju" title="Tahap penentu laju – Indonesian" lang="id" hreflang="id" data-title="Tahap penentu laju" 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/Stadio_cineticamente_determinante" title="Stadio cineticamente determinante – Italian" lang="it" hreflang="it" data-title="Stadio cineticamente determinante" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sebess%C3%A9gmeghat%C3%A1roz%C3%B3_l%C3%A9p%C3%A9s" title="Sebességmeghatározó lépés – Hungarian" lang="hu" hreflang="hu" data-title="Sebességmeghatározó lépés" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Snelheidsbepalende_stap" title="Snelheidsbepalende stap – Dutch" lang="nl" hreflang="nl" data-title="Snelheidsbepalende stap" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</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%E9%80%9F%E5%BA%A6#律速段階" title="反応速度 – Japanese" lang="ja" hreflang="ja" data-title="反応速度" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Passo_determinante_de_taxa" title="Passo determinante de taxa – Portuguese" lang="pt" hreflang="pt" data-title="Passo determinante de taxa" 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/Etap%C4%83_determinant%C4%83_de_vitez%C4%83" title="Etapă determinantă de viteză – Romanian" lang="ro" hreflang="ro" data-title="Etapă determinantă de viteză" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Rate-determining_step" title="Rate-determining step – Simple English" lang="en-simple" hreflang="en-simple" data-title="Rate-determining step" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/R%C3%BDchlos%C5%A5_ur%C4%8Duj%C3%BAci_krok" title="Rýchlosť určujúci krok – Slovak" lang="sk" hreflang="sk" data-title="Rýchlosť určujúci krok" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%BE%DB%95%D9%86%DA%AF%D8%A7%D9%88%DB%8C_%D8%AE%DB%8E%D8%B1%D8%A7%DB%8C%DB%8C_%D8%AF%DB%8C%D8%A7%D8%B1%DB%8C%DA%A9%DB%95%D8%B1" title="ھەنگاوی خێرایی دیاریکەر – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ھەنگاوی خێرایی دیاریکەر" data-language-autonym="کوردی" 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data-mw-ve-target-container> <div class="vector-body-before-content"> <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">Slowest step of a chemical reaction</div> <p>In <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">chemical kinetics</a>, the overall rate of a reaction is often approximately determined by the slowest step, known as the <b>rate-determining step</b> (<b>RDS</b> or <b>RD-step</b><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> or <b>r/d step</b><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><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>) or <b>rate-limiting step</b>. For a given reaction mechanism, the prediction of the corresponding <a href="/wiki/Rate_equation" title="Rate equation">rate equation</a> (for comparison with the experimental rate law) is often simplified by using this approximation of the rate-determining step. </p><p>In principle, the time evolution of the reactant and product concentrations can be determined from the set of simultaneous rate equations for the individual steps of the mechanism, one for each step. However, the analytical solution of these <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a> is not always easy, and in some cases <a href="/wiki/Numerical_methods_for_ordinary_differential_equations" title="Numerical methods for ordinary differential equations">numerical integration</a> may even be required.<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> The hypothesis of a single rate-determining step can greatly simplify the mathematics. In the simplest case the initial step is the slowest, and the overall rate is just the rate of the first step. </p><p>Also, the rate equations for mechanisms with a single rate-determining step are usually in a simple mathematical form, whose relation to the mechanism and choice of rate-determining step is clear. The correct rate-determining step can be identified by predicting the rate law for each possible choice and comparing the different predictions with the experimental law, as for the example of <style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> and CO below. </p><p>The concept of the rate-determining step is very important to the optimization and understanding of many chemical processes such as <a href="/wiki/Catalysis" title="Catalysis">catalysis</a> and <a href="/wiki/Combustion" title="Combustion">combustion</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Example_reaction:_NO2_+_CO"><span id="Example_reaction:_NO2_.2B_CO"></span>Example reaction: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> + CO</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=1" title="Edit section: Example reaction: NO2 + CO"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As an example, consider the gas-phase reaction <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> + CO → NO + CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub>. If this reaction occurred in a single step, its <a href="/wiki/Reaction_rate" title="Reaction rate">reaction rate</a> (<i>r</i>) would be proportional to the rate of <a href="/wiki/Collision_theory" title="Collision theory">collisions</a> between <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> and CO molecules: <i>r</i> = <i>k</i>[<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span>][CO], where <i>k</i> is the reaction <a href="/wiki/Rate_constant" class="mw-redirect" title="Rate constant">rate constant</a>, and square brackets indicate a <a href="/wiki/Molar_concentration" title="Molar concentration">molar concentration</a>. Another typical example is the <a href="/wiki/Zel%27dovich_mechanism" class="mw-redirect" title="Zel'dovich mechanism">Zel'dovich mechanism</a>. </p> <div class="mw-heading mw-heading3"><h3 id="First_step_rate-determining">First step rate-determining</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=2" title="Edit section: First step rate-determining"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In fact, however, the observed reaction rate is <a href="/wiki/Order_of_reaction" class="mw-redirect" title="Order of reaction">second-order</a> in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> and zero-order in CO,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> with rate equation <i>r</i> = <i>k</i>[<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span>]<sup>2</sup>. This suggests that the rate is determined by a step in which two <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> molecules react, with the CO molecule entering at another, faster, step. A possible mechanism in two elementary steps that explains the rate equation is: </p> <ol><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> → NO + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> <i>(slow step, rate-determining)</i></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> + CO → <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> + CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub> <i>(fast step)</i></li></ol> <p>In this mechanism the <a href="/wiki/Reactive_intermediate" title="Reactive intermediate">reactive intermediate</a> species <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> is formed in the first step with rate <i>r</i><sub>1</sub> and reacts with CO in the second step with rate <i>r</i><sub>2</sub>. However, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> can also react with NO if the first step occurs in the <i>reverse direction</i> (NO + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> → 2 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span>) with rate <i>r</i><sub>−1</sub>, where the minus sign indicates the rate of a reverse reaction. </p><p>The concentration of a reactive intermediate such as [<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span>] remains low and almost constant. It may therefore be estimated by the <a href="/wiki/Steady_state_(chemistry)" title="Steady state (chemistry)">steady-state</a> approximation, which specifies that the rate at which it is formed equals the (total) rate at which it is consumed. In this example <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> is formed in one step and reacts in two, so that </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{\ce {[NO3]}}}{dt}}=r_{1}-r_{2}-r_{-1}\approx 0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>≈</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d{\ce {[NO3]}}}{dt}}=r_{1}-r_{2}-r_{-1}\approx 0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ecf92288f5a82cd3e1109f4bcf95c175b0304d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:29.225ex; height:6.009ex;" alt="{\displaystyle {\frac {d{\ce {[NO3]}}}{dt}}=r_{1}-r_{2}-r_{-1}\approx 0.}"></span></dd></dl> <p>The statement that the first step is the slow step actually means that the first step <i>in the reverse direction</i> is slower than the second step in the forward direction, so that almost all <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> is consumed by reaction with CO and not with NO. That is, <i>r</i><sub>−1</sub> ≪ <i>r</i><sub>2</sub>, so that <i>r</i><sub>1</sub> − <i>r</i><sub>2</sub> ≈ 0. But the overall rate of reaction is the rate of formation of final product (here CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub>), so that <i>r</i> = <i>r</i><sub>2</sub> ≈ <i>r</i><sub>1</sub>. That is, the overall rate is determined by the rate of the first step, and (almost) all molecules that react at the first step continue to the fast second step. </p> <div class="mw-heading mw-heading3"><h3 id="Pre-equilibrium:_if_the_second_step_were_rate-determining">Pre-equilibrium: if the second step were rate-determining</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=3" title="Edit section: Pre-equilibrium: if the second step were rate-determining"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The other possible case would be that the second step is slow and rate-determining, meaning that it is slower than the first step in the reverse direction: <i>r</i><sub>2</sub> ≪ <i>r</i><sub>−1</sub>. In this hypothesis, <i>r</i><sub>1</sub> − r<sub>−1</sub> ≈ 0, so that the first step is (almost) at <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a>. The overall rate is determined by the second step: <i>r</i> = <i>r</i><sub>2</sub> ≪ <i>r</i><sub>1</sub>, as very few molecules that react at the first step continue to the second step, which is much slower. Such a situation in which an intermediate (here <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span>) forms an equilibrium with reactants <i>prior</i> to the rate-determining step is described as a <i>pre-equilibrium</i><sup id="cite_ref-Atkins_6-0" class="reference"><a href="#cite_note-Atkins-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> For the reaction of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> and CO, this hypothesis can be rejected, since it implies a rate equation that disagrees with experiment. </p> <ol><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> → NO + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> <i>(fast step)</i></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> + CO → <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> + CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub> <i>(slow step, rate-determining)</i></li></ol> <p>If the first step were at equilibrium, then its <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> expression permits calculation of the concentration of the intermediate <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">3</sub></span> in terms of more stable (and more easily measured) reactant and product species: </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_{1}={\frac {{\ce {[NO][NO3]}}}{{\ce {[NO2]^2}}}},}"> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>NO</mtext> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{1}={\frac {{\ce {[NO][NO3]}}}{{\ce {[NO2]^2}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80999e5d22d393cfb0b436e351a14dbcc7ea1ffe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.353ex; height:7.176ex;" alt="{\displaystyle K_{1}={\frac {{\ce {[NO][NO3]}}}{{\ce {[NO2]^2}}}},}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [{\ce {NO3}}]=K_{1}{\frac {{\ce {[NO2]^2}}}{{\ce {[NO]}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> <mo stretchy="false">]</mo> <mo>=</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>NO</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [{\ce {NO3}}]=K_{1}{\frac {{\ce {[NO2]^2}}}{{\ce {[NO]}}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/657b6abb8fc1acb20fbcda4fd85dd5d01cc84657" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:20.461ex; height:7.009ex;" alt="{\displaystyle [{\ce {NO3}}]=K_{1}{\frac {{\ce {[NO2]^2}}}{{\ce {[NO]}}}}.}"></span></dd></dl> <p>The overall reaction rate would then be </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=r_{2}=k_{2}{\ce {[NO3][CO]}}=k_{2}K_{1}{\frac {{\ce {[NO2]^2 [CO]}}}{{\ce {[NO]}}}},}"> <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"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>CO</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>NO</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>CO</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>NO</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=r_{2}=k_{2}{\ce {[NO3][CO]}}=k_{2}K_{1}{\frac {{\ce {[NO2]^2 [CO]}}}{{\ce {[NO]}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469e8efed24cec0fda01438c293b926abf7ea94d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:43.9ex; height:7.009ex;" alt="{\displaystyle r=r_{2}=k_{2}{\ce {[NO3][CO]}}=k_{2}K_{1}{\frac {{\ce {[NO2]^2 [CO]}}}{{\ce {[NO]}}}},}"></span></dd></dl> <p>which disagrees with the experimental rate law given above, and so disproves the hypothesis that the second step is rate-determining for this reaction. However, some other reactions are believed to involve rapid pre-equilibria prior to the rate-determining step, <a href="#Composition_of_the_transition_state">as shown below</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Nucleophilic_substitution">Nucleophilic substitution</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=4" title="Edit section: Nucleophilic substitution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Another example is the <a href="/wiki/Unimolecular_nucleophilic_substitution" class="mw-redirect" title="Unimolecular nucleophilic substitution">unimolecular nucleophilic substitution</a> (S<sub>N</sub>1) reaction in organic chemistry, where it is the first, rate-determining step that is <a href="/wiki/Molecularity" title="Molecularity">unimolecular</a>. A specific case is the <a href="/wiki/Base_(chemistry)" title="Base (chemistry)">basic</a> <a href="/wiki/Hydrolysis" title="Hydrolysis">hydrolysis</a> of <a href="/wiki/Tert-butyl_bromide" class="mw-redirect" title="Tert-butyl bromide">tert-butyl bromide</a> (<span class="chemf nowrap">t-C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">9</sub></span></span>Br</span>) by aqueous <a href="/wiki/Sodium_hydroxide" title="Sodium hydroxide">sodium hydroxide</a>. The mechanism has two steps (where R denotes the tert-butyl radical <span class="chemf nowrap">t-C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">9</sub></span></span></span>): </p> <ol><li>Formation of a <a href="/wiki/Carbocation" title="Carbocation">carbocation</a> R−Br → <span class="chemf nowrap">R<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span class="chemf nowrap">Br<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>.</li> <li><a href="/wiki/Nucleophile" title="Nucleophile">Nucleophilic</a> attack by hydroxide ion <span class="chemf nowrap">R<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span class="chemf nowrap">OH<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> → ROH.</li></ol> <p>This reaction is found to be <a href="/wiki/Rate_equation#First-order_reactions" title="Rate equation">first-order</a> with <i>r</i> = <i>k</i>[R−Br], which indicates that the first step is slow and determines the rate. The second step with OH<sup>−</sup> is much faster, so the overall rate is independent of the concentration of OH<sup>−</sup>. </p><p>In contrast, the alkaline hydrolysis of <a href="/wiki/Methyl_bromide" class="mw-redirect" title="Methyl bromide">methyl bromide</a> (<span class="chemf nowrap">CH<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span>Br</span>) is a <a href="/wiki/Bimolecular_nucleophilic_substitution" class="mw-redirect" title="Bimolecular nucleophilic substitution">bimolecular nucleophilic substitution</a> (S<sub>N</sub>2) reaction in a single <a href="/wiki/Molecularity" title="Molecularity">bimolecular</a> step. Its rate law is <a href="/wiki/Rate_equation#Second-order_reactions" title="Rate equation">second-order</a>: <i>r</i> = <i>k</i>[R−Br][<span class="chemf nowrap">OH<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>]. </p> <div class="mw-heading mw-heading2"><h2 id="Composition_of_the_transition_state">Composition of the transition state</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=5" title="Edit section: Composition of the transition state"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A useful rule in the determination of mechanism is that the concentration factors in the rate law indicate the composition and charge of the <a href="/wiki/Activated_complex" title="Activated complex">activated complex</a> or <a href="/wiki/Transition_state" title="Transition state">transition state</a>.<sup id="cite_ref-Espenson_7-0" class="reference"><a href="#cite_note-Espenson-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> For the <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span>–CO reaction above, the rate depends on [<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span>]<sup>2</sup>, so that the activated complex has composition <span class="chemf nowrap">N<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span>, with 2 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> entering the reaction before the transition state, and CO reacting after the transition state. </p><p>A multistep example is the reaction between <a href="/wiki/Oxalic_acid" title="Oxalic acid">oxalic acid</a> and chlorine in aqueous solution: <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span> + <span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> → 2 CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub> + 2 <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + 2 <span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>.<sup id="cite_ref-Espenson_7-1" class="reference"><a href="#cite_note-Espenson-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The observed rate law is </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 v=k{\frac {{\ce {[Cl2][H2C2O4]}}}{[{\ce {H+}}]^{2}[{\ce {Cl^-}}]}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>Cl</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <mo stretchy="false">]</mo> </mrow> </mrow> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mtext>Cl</mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=k{\frac {{\ce {[Cl2][H2C2O4]}}}{[{\ce {H+}}]^{2}[{\ce {Cl^-}}]}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f393df90aea1ad148e41b5c616546f5204a71e28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:21.279ex; height:6.843ex;" alt="{\displaystyle v=k{\frac {{\ce {[Cl2][H2C2O4]}}}{[{\ce {H+}}]^{2}[{\ce {Cl^-}}]}},}"></span></dd></dl> <p>which implies an activated complex in which the reactants lose 2<span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> before the rate-determining step. The formula of the activated complex is <span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> + <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span> − 2 <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> − <span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span class="texhtml mvar" style="font-style:italic;">x</span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><a href="/wiki/Water" title="Water">H<sub class="template-chem2-sub">2</sub>O</a></span>, or <span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span>Cl(H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O)<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">–</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"><span class="texhtml mvar" style="font-style:italic;">x</span></sub></span></span></span> (an unknown number of water molecules are added because the possible dependence of the reaction rate on <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><a href="/wiki/Water" title="Water">H<sub class="template-chem2-sub">2</sub>O</a></span> was not studied, since the data were obtained in water solvent at a large and essentially unvarying concentration). </p><p>One possible mechanism in which the preliminary steps are assumed to be rapid pre-equilibria occurring prior to the transition state is<sup id="cite_ref-Espenson_7-2" class="reference"><a href="#cite_note-Espenson-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><a href="/wiki/Water" title="Water">H<sub class="template-chem2-sub">2</sub>O</a></span> ⇌ HOCl + <span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span></dd> <dd><span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span> ⇌ <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + <span class="chemf nowrap">HC<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span></dd> <dd>HOCl + <span class="chemf nowrap">HC<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span> → <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><a href="/wiki/Water" title="Water">H<sub class="template-chem2-sub">2</sub>O</a></span> + <span class="chemf nowrap">Cl<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> + 2 CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Reaction_coordinate_diagram">Reaction coordinate diagram</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=6" title="Edit section: Reaction coordinate diagram"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a multistep reaction, the rate-determining step does not necessarily correspond to the highest <a href="/wiki/Gibbs_energy" class="mw-redirect" title="Gibbs energy">Gibbs energy</a> on the <a href="/wiki/Reaction_coordinate" title="Reaction coordinate">reaction coordinate</a> diagram.<sup id="cite_ref-Laidler_8-0" class="reference"><a href="#cite_note-Laidler-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Atkins_6-1" class="reference"><a href="#cite_note-Atkins-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> If there is a <a href="/wiki/Reaction_intermediate" title="Reaction intermediate">reaction intermediate</a> whose energy is lower than the initial reactants, then the activation energy needed to pass through any subsequent <a href="/wiki/Transition_state" title="Transition state">transition state</a> depends on the Gibbs energy of that state relative to the lower-energy intermediate. The rate-determining step is then the step with the largest Gibbs energy difference relative either to the starting material or to any previous intermediate on the diagram.<sup id="cite_ref-Laidler_8-1" class="reference"><a href="#cite_note-Laidler-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Also, for reaction steps that are not first-order, concentration terms must be considered in choosing the rate-determining step.<sup id="cite_ref-Laidler_8-2" class="reference"><a href="#cite_note-Laidler-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Atkins_6-2" class="reference"><a href="#cite_note-Atkins-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Chain_reactions">Chain reactions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=7" title="Edit section: Chain reactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Not all reactions have a single rate-determining step. In particular, the rate of a <a href="/wiki/Chain_reaction#Chemical_chain_reactions" title="Chain reaction">chain reaction</a> is usually not controlled by any single step.<sup id="cite_ref-Laidler_8-3" class="reference"><a href="#cite_note-Laidler-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Diffusion_control">Diffusion control</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rate-determining_step&action=edit&section=8" title="Edit section: Diffusion control"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the previous examples the rate determining step was one of the sequential chemical reactions leading to a product. The rate-determining step can also be the transport of reactants to where they can interact and form the product. This case is referred to as <a href="/wiki/Diffusion_control" class="mw-redirect" title="Diffusion control">diffusion control</a> and, in general, occurs when the formation of product from the activated complex is very rapid and thus the provision of the supply of reactants is rate-determining. </p> <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=Rate-determining_step&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Product-determining_step" title="Product-determining step">Product-determining step</a></li> <li><a href="/wiki/Rate-limiting_step_(biochemistry)" title="Rate-limiting step (biochemistry)">Rate-limiting step (biochemistry)</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=Rate-determining_step&action=edit&section=10" 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 id="CITEREFKozuchMartin2011" class="citation journal cs1">Kozuch, Sebastian; Martin, Jan (June 2011). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/51080585">"The Rate-Determining Step is Dead. Long Live the Rate-Determining State!"</a>. <i>ChemPhysChem</i>. <b>12</b> (8): 1413–1418. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcphc.201100137">10.1002/cphc.201100137</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/21523880">21523880</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ChemPhysChem&rft.atitle=The+Rate-Determining+Step+is+Dead.+Long+Live+the+Rate-Determining+State%21&rft.volume=12&rft.issue=8&rft.pages=1413-1418&rft.date=2011-06&rft_id=info%3Adoi%2F10.1002%2Fcphc.201100137&rft_id=info%3Apmid%2F21523880&rft.aulast=Kozuch&rft.aufirst=Sebastian&rft.au=Martin%2C+Jan&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F51080585&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARate-determining+step" 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">{{Organic Chemistry, Volume 1, 6/E By Finar}}</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">{{Aliphatic Organic Chemistry By Amit Arora}}</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">Steinfeld J. I., Francisco J. S., Hase W. L. <i>Chemical Kinetics and Dynamics</i> (2nd ed., Prentice-Hall 1999) ch. 2.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Whitten K. W., Galley K. D., Davis R. E. <i>General Chemistry</i> (4th edition, Saunders 1992), p. 638–639.</span> </li> <li id="cite_note-Atkins-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Atkins_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Atkins_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Atkins_6-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Peter_Atkins" title="Peter Atkins">Peter Atkins</a> and Julio de Paula, <i>Physical Chemistry</i> (8th ed., W. H. Freeman 2006) p. 814–815. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-8759-8" title="Special:BookSources/0-7167-8759-8">0-7167-8759-8</a>.</span> </li> <li id="cite_note-Espenson-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Espenson_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Espenson_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Espenson_7-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEspenson2002" class="citation book cs1">Espenson, J. H. (2002). <i>Chemical Kinetics and Reaction Mechanisms</i> (2nd ed.). McGraw-Hill. pp. 127–132. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0072883626" title="Special:BookSources/0072883626"><bdi>0072883626</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Kinetics+and+Reaction+Mechanisms&rft.pages=127-132&rft.edition=2nd&rft.pub=McGraw-Hill&rft.date=2002&rft.isbn=0072883626&rft.aulast=Espenson&rft.aufirst=J.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARate-determining+step" class="Z3988"></span></span> </li> <li id="cite_note-Laidler-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Laidler_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Laidler_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Laidler_8-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Laidler_8-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Keith_J._Laidler" title="Keith J. Laidler">Keith J. Laidler</a>. <i>Chemical Kinetics</i> (3rd ed., Harper and Row 1987) p. 283–285. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-06-043862-2" title="Special:BookSources/0-06-043862-2">0-06-043862-2</a>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMurdoch1981" class="citation journal cs1">Murdoch, Joseph R. (1981). "What is the rate-limiting step of a multistep reaction?". <i>Journal of Chemical Education</i>. <b>58</b> (1): 32–36. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1981JChEd..58...32M">1981JChEd..58...32M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fed058p32">10.1021/ed058p32</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Chemical+Education&rft.atitle=What+is+the+rate-limiting+step+of+a+multistep+reaction%3F&rft.volume=58&rft.issue=1&rft.pages=32-36&rft.date=1981&rft_id=info%3Adoi%2F10.1021%2Fed058p32&rft_id=info%3Abibcode%2F1981JChEd..58...32M&rft.aulast=Murdoch&rft.aufirst=Joseph+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARate-determining+step" class="Z3988"></span></span> </li> </ol></div></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZumdahl2005" class="citation book cs1">Zumdahl, Steven S. (2005). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/chemicalprincipl00zumd/page/727"><i>Chemical Principles</i></a></span> (5th ed.). Houghton Mifflin. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/chemicalprincipl00zumd/page/727">727–8</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0618372067" title="Special:BookSources/0618372067"><bdi>0618372067</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Principles&rft.pages=727-8&rft.edition=5th&rft.pub=Houghton+Mifflin&rft.date=2005&rft.isbn=0618372067&rft.aulast=Zumdahl&rft.aufirst=Steven+S.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fchemicalprincipl00zumd%2Fpage%2F727&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARate-determining+step" class="Z3988"></span></li></ul> <p><br /> </p> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output 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href="/wiki/Template:Reaction_mechanisms" title="Template:Reaction mechanisms"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Reaction_mechanisms" title="Template talk:Reaction mechanisms"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Reaction_mechanisms" title="Special:EditPage/Template:Reaction mechanisms"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Basic_reaction_mechanisms" style="font-size:114%;margin:0 4em">Basic <a href="/wiki/Reaction_mechanism" title="Reaction mechanism">reaction mechanisms</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Nucleophilic_substitution" title="Nucleophilic substitution">Nucleophilic substitutions</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/SN1_reaction" title="SN1 reaction">Unimolecular nucleophilic substitution</a> (S<sub>N</sub>1)</li> <li><a href="/wiki/SN2_reaction" title="SN2 reaction">Bimolecular nucleophilic substitution</a> (S<sub>N</sub>2)</li> <li><a href="/wiki/Nucleophilic_aromatic_substitution" title="Nucleophilic aromatic substitution">Nucleophilic aromatic substitution</a> (S<sub>N</sub>Ar)</li> <li><a href="/wiki/SNi" title="SNi">Nucleophilic internal substitution</a> (S<sub>N</sub>i)</li> <li><a href="/wiki/Nucleophilic_acyl_substitution" class="mw-redirect" title="Nucleophilic acyl substitution">Nucleophilic acyl substitution</a> (S<sub>N</sub>Acyl)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Electrophilic_substitution" title="Electrophilic substitution">Electrophilic substitutions</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electrophilic_aromatic_substitution" title="Electrophilic aromatic substitution">Electrophilic aromatic substitution</a> (S<sub>E</sub>Ar)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Elimination_reaction" title="Elimination reaction">Elimination reactions</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/E1_elimination" class="mw-redirect" title="E1 elimination">Unimolecular elimination</a> (E1)</li> <li><a href="/wiki/E1cB-elimination_reaction" title="E1cB-elimination reaction">E1cB-elimination</a></li> <li><a href="/wiki/E2_elimination" class="mw-redirect" title="E2 elimination">Bimolecular elimination</a> (E2)</li> <li><a href="/wiki/Ei_mechanism" title="Ei mechanism">E<sub>i</sub> elimination</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Addition_reaction" title="Addition reaction">Addition reactions</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electrophilic_addition" title="Electrophilic addition">Electrophilic addition</a> (A<sub>E</sub>)</li> <li><a href="/wiki/Nucleophilic_addition" title="Nucleophilic addition">Nucleophilic addition</a> (A<sub>N</sub>)</li> <li><a href="/wiki/Free-radical_addition" title="Free-radical addition">Free-radical addition</a></li> <li><a href="/wiki/Cycloaddition" title="Cycloaddition">Cycloaddition</a></li> <li><a href="/wiki/Oxidative_addition" title="Oxidative addition">Oxidative addition</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Unimolecular reactions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Intramolecular_reaction" title="Intramolecular reaction">Intramolecular reaction</a></li> <li><a href="/wiki/Isomerization" title="Isomerization">Isomerization</a></li> <li><a href="/wiki/Photodissociation" title="Photodissociation">Photodissociation</a></li> <li><a href="/wiki/Lindemann%E2%80%93Hinshelwood_mechanism" class="mw-redirect" title="Lindemann–Hinshelwood mechanism">Lindemann–Hinshelwood mechanism</a></li> <li><a href="/wiki/RRKM_theory" title="RRKM theory">RRKM theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Electron_transfer" title="Electron transfer">Electron/Proton transfer</a> reactions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Redox" title="Redox">Redox</a></li> <li><a href="/wiki/Harpoon_reaction" title="Harpoon reaction">Harpoon reaction</a></li> <li><a href="/wiki/Grotthuss_mechanism" title="Grotthuss mechanism">Grotthuss mechanism</a></li> <li><a href="/wiki/Marcus_theory" title="Marcus theory">Marcus theory</a></li> <li><a href="/wiki/Inner_sphere_electron_transfer" title="Inner sphere electron transfer">Inner sphere electron transfer</a></li> <li><a href="/wiki/Outer_sphere_electron_transfer" title="Outer sphere electron transfer">Outer sphere electron transfer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Medium effects</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Solvent_effects" title="Solvent effects">Solvent effects</a></li> <li><a href="/wiki/Cage_effect" title="Cage effect">Cage effect</a></li> <li><a href="/wiki/Matrix_isolation" title="Matrix isolation">Matrix isolation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Elementary_reaction" title="Elementary reaction">Elementary reaction</a></li> <li><a href="/wiki/Reaction_dynamics" title="Reaction dynamics">Reaction dynamics</a></li> <li><a href="/wiki/Reactive_intermediate" title="Reactive intermediate">Reactive intermediate</a></li> <li><a href="/wiki/Radical_(chemistry)" title="Radical (chemistry)">Radical (chemistry)</a></li> <li><a href="/wiki/Molecularity" title="Molecularity">Molecularity</a></li> <li><a href="/wiki/Stereochemistry" title="Stereochemistry">Stereochemistry</a></li> <li><a href="/wiki/Catalysis" title="Catalysis">Catalysis</a></li> <li><a href="/wiki/Collision_theory" title="Collision theory">Collision theory</a></li> <li><a href="/wiki/Arrow_pushing" title="Arrow pushing">Arrow pushing</a></li> <li><a href="/wiki/Potential_energy_surface" title="Potential energy surface">Potential energy surface</a></li> <li><a href="/wiki/More_O%27Ferrall%E2%80%93Jencks_plot" title="More O'Ferrall–Jencks plot">More O'Ferrall–Jencks plot</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chemical_kinetics" title="Chemical kinetics">Chemical kinetics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Rate_equation" title="Rate equation">Rate equation</a></li> <li><a href="/wiki/Equilibrium_constant" title="Equilibrium constant">Equilibrium constant</a></li> <li><a class="mw-selflink selflink">Rate-determining step</a></li> <li><a href="/wiki/Reaction_coordinate" title="Reaction coordinate">Reaction coordinate</a></li> <li><a href="/wiki/Energy_profile_(chemistry)" title="Energy profile (chemistry)">Energy profile (chemistry)</a></li> <li><a href="/wiki/Transition_state_theory" title="Transition state theory">Transition state theory</a></li> <li><a href="/wiki/Activation_energy" title="Activation energy">Activation energy</a></li> <li><a href="/wiki/Activated_complex" title="Activated complex">Activated complex</a></li> <li><a href="/wiki/Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a></li> <li><a href="/wiki/Eyring_equation" title="Eyring equation">Eyring equation</a></li> <li><a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Michaelis–Menten kinetics</a></li> <li><a href="/wiki/Diffusion-controlled_reaction" title="Diffusion-controlled reaction">Diffusion-controlled reaction</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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