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class="vector-toc-numb">2</span> <span>Factors affecting reaction rate</span> </div> </a> <button aria-controls="toc-Factors_affecting_reaction_rate-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Factors affecting reaction rate subsection</span> </button> <ul id="toc-Factors_affecting_reaction_rate-sublist" class="vector-toc-list"> <li id="toc-Nature_of_the_reactants" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nature_of_the_reactants"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Nature of the reactants</span> </div> </a> <ul id="toc-Nature_of_the_reactants-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physical_state" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physical_state"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Physical state</span> </div> </a> <ul id="toc-Physical_state-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surface_area_of_solid_state" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surface_area_of_solid_state"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Surface area of solid state</span> </div> </a> <ul id="toc-Surface_area_of_solid_state-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Concentration" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Concentration"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Concentration</span> </div> </a> <ul id="toc-Concentration-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Temperature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Temperature"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Temperature</span> </div> </a> <ul id="toc-Temperature-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Catalysts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Catalysts"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Catalysts</span> </div> </a> <ul id="toc-Catalysts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pressure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Pressure</span> </div> </a> <ul id="toc-Pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Absorption_of_light" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Absorption_of_light"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>Absorption of light</span> </div> </a> <ul id="toc-Absorption_of_light-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Experimental_methods" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Experimental_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Experimental methods</span> </div> </a> <button aria-controls="toc-Experimental_methods-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Experimental methods subsection</span> </button> <ul id="toc-Experimental_methods-sublist" class="vector-toc-list"> <li id="toc-Fast_reactions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fast_reactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Fast reactions</span> </div> </a> <ul id="toc-Fast_reactions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Equilibrium" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Equilibrium"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Equilibrium</span> </div> </a> <ul id="toc-Equilibrium-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Free_energy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Free_energy"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Free energy</span> </div> </a> <ul id="toc-Free_energy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_and_models" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications_and_models"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Applications and models</span> </div> </a> <button aria-controls="toc-Applications_and_models-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications and models subsection</span> </button> <ul id="toc-Applications_and_models-sublist" class="vector-toc-list"> <li id="toc-Numerical_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Numerical_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Numerical methods</span> </div> </a> <ul id="toc-Numerical_methods-sublist" class="vector-toc-list"> </ul> </li> </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> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Chemical kinetics</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. Available in 62 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-62" 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">62 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Chemiese_kinetika" title="Chemiese kinetika – Afrikaans" lang="af" hreflang="af" data-title="Chemiese kinetika" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B1%D9%83%D9%8A%D8%A9_%D8%AA%D9%81%D8%A7%D8%B9%D9%84" title="حركية تفاعل – Arabic" lang="ar" hreflang="ar" data-title="حركية تفاعل" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Cin%C3%A9tica_qu%C3%ADmica" title="Cinética química – Asturian" lang="ast" hreflang="ast" data-title="Cinética química" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kimy%C9%99vi_kinetika" title="Kimyəvi kinetika – Azerbaijani" lang="az" hreflang="az" data-title="Kimyəvi kinetika" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B0%E0%A6%BE%E0%A6%B8%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%A8%E0%A6%BF%E0%A6%95_%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="রাসায়নিক গতিবিদ্যা – Bangla" lang="bn" hreflang="bn" data-title="রাসায়নিক গতিবিদ্যা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/H%C3%B2a-ha%CC%8Dk_t%C5%8Dng-le%CC%8Dk-ha%CC%8Dk" title="Hòa-ha̍k tōng-le̍k-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Hòa-ha̍k tōng-le̍k-ha̍k" 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%A5%D1%96%D0%BC%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D0%BA%D1%96%D0%BD%D0%B5%D1%82%D1%8B%D0%BA%D0%B0" title="Хімічная кінетыка – Belarusian" lang="be" hreflang="be" data-title="Хімічная кінетыка" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A5%D1%96%D0%BC%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D0%BA%D1%96%D0%BD%D1%8D%D1%82%D1%8B%D0%BA%D0%B0" title="Хімічная кінэтыка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Хімічная кінэтыка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D1%87%D0%BD%D0%B0_%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Химична кинетика – Bulgarian" lang="bg" hreflang="bg" data-title="Химична кинетика" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Hemijska_kinetika" title="Hemijska kinetika – Bosnian" lang="bs" hreflang="bs" data-title="Hemijska kinetika" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cin%C3%A8tica_qu%C3%ADmica" title="Cinètica química – Catalan" lang="ca" hreflang="ca" data-title="Cinètica química" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Chemick%C3%A1_kinetika" title="Chemická kinetika – Czech" lang="cs" hreflang="cs" data-title="Chemická kinetika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Kinetik_(Chemie)" title="Kinetik (Chemie) – German" lang="de" hreflang="de" data-title="Kinetik (Chemie)" 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/Keemiline_kineetika" title="Keemiline kineetika – Estonian" lang="et" hreflang="et" data-title="Keemiline kineetika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CE%B7%CE%BC%CE%B9%CE%BA%CE%AE_%CE%BA%CE%B9%CE%BD%CE%B7%CF%84%CE%B9%CE%BA%CE%AE" title="Χημική κινητική – Greek" lang="el" hreflang="el" data-title="Χημική κινητική" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cin%C3%A9tica_qu%C3%ADmica" title="Cinética química – Spanish" lang="es" hreflang="es" data-title="Cinética química" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kemia_kinetiko" title="Kemia kinetiko – Esperanto" lang="eo" hreflang="eo" data-title="Kemia kinetiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zinetika_kimiko" title="Zinetika kimiko – Basque" lang="eu" hreflang="eu" data-title="Zinetika kimiko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%DB%8C%D9%86%D8%AA%DB%8C%DA%A9_%D8%B4%DB%8C%D9%85%DB%8C%D8%A7%DB%8C%DB%8C" title="سینتیک شیمیایی – Persian" lang="fa" hreflang="fa" data-title="سینتیک شیمیایی" 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/Cin%C3%A9tique_chimique" title="Cinétique chimique – French" lang="fr" hreflang="fr" data-title="Cinétique chimique" 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/%ED%99%94%ED%95%99_%EB%B0%98%EC%9D%91%EC%86%8D%EB%8F%84%EB%A1%A0" title="화학 반응속도론 – Korean" lang="ko" hreflang="ko" data-title="화학 반응속도론" 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/%D5%94%D5%AB%D5%B4%D5%AB%D5%A1%D5%AF%D5%A1%D5%B6_%D5%AF%D5%AB%D5%B6%D5%A5%D5%BF%D5%AB%D5%AF%D5%A1" title="Քիմիական կինետիկա – Armenian" lang="hy" hreflang="hy" data-title="Քիմիական կինետիկա" 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%B0%E0%A4%BE%E0%A4%B8%E0%A4%BE%E0%A4%AF%E0%A4%A8%E0%A4%BF%E0%A4%95_%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="रासायनिक गतिकी – Hindi" lang="hi" hreflang="hi" data-title="रासायनिक गतिकी" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kemijska_kinetika" title="Kemijska kinetika – Croatian" lang="hr" hreflang="hr" data-title="Kemijska kinetika" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kinetika_kimia" title="Kinetika kimia – Indonesian" lang="id" hreflang="id" data-title="Kinetika kimia" 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/Cinetica_chimica" title="Cinetica chimica – Italian" lang="it" hreflang="it" data-title="Cinetica chimica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%99%D7%A0%D7%98%D7%99%D7%A7%D7%94_%D7%9B%D7%99%D7%9E%D7%99%D7%AA" title="קינטיקה כימית – Hebrew" lang="he" hreflang="he" data-title="קינטיקה כימית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A5%E1%83%98%E1%83%9B%E1%83%98%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%99%E1%83%98%E1%83%9C%E1%83%94%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="ქიმიური კინეტიკა – Georgian" lang="ka" hreflang="ka" data-title="ქიმიური კინეტიკა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Химиялық кинетика – Kazakh" lang="kk" hreflang="kk" data-title="Химиялық кинетика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Kinetiek" title="Kinetiek – Limburgish" lang="li" hreflang="li" data-title="Kinetiek" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Cinetica_chimica" title="Cinetica chimica – Lombard" lang="lmo" hreflang="lmo" data-title="Cinetica chimica" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Reakci%C3%B3kinetika" title="Reakciókinetika – Hungarian" lang="hu" hreflang="hu" data-title="Reakciókinetika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A5%D0%B5%D0%BC%D0%B8%D1%81%D0%BA%D0%B0_%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Хемиска кинетика – Macedonian" lang="mk" hreflang="mk" data-title="Хемиска кинетика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kinetik_kimia" title="Kinetik kimia – Malay" lang="ms" hreflang="ms" data-title="Kinetik kimia" 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-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D0%B9%D0%BD_%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D0%BA" title="Химийн кинетик – Mongolian" lang="mn" hreflang="mn" data-title="Химийн кинетик" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Chemische_kinetiek" title="Chemische kinetiek – Dutch" lang="nl" hreflang="nl" data-title="Chemische kinetiek" 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%E8%AB%96" title="反応速度論 – Japanese" lang="ja" hreflang="ja" data-title="反応速度論" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kjemisk_kinetikk" title="Kjemisk kinetikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kjemisk kinetikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kimyoviy_kinetika" title="Kimyoviy kinetika – Uzbek" lang="uz" hreflang="uz" data-title="Kimyoviy kinetika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kinetyka_chemiczna" title="Kinetyka chemiczna – Polish" lang="pl" hreflang="pl" data-title="Kinetyka chemiczna" 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/Cin%C3%A9tica_qu%C3%ADmica" title="Cinética química – Portuguese" lang="pt" hreflang="pt" data-title="Cinética química" 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/Cinetic%C4%83_chimic%C4%83" title="Cinetică chimică – Romanian" lang="ro" hreflang="ro" data-title="Cinetică chimică" 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%A5%D0%B8%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Химическая кинетика – Russian" lang="ru" hreflang="ru" data-title="Химическая кинетика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Cin%C3%A8tica_ch%C3%ACmica" title="Cinètica chìmica – Sicilian" lang="scn" hreflang="scn" data-title="Cinètica chìmica" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%AD%E0%B7%92%E0%B6%9A%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%93%E0%B6%BA%E0%B6%9A%E0%B6%BA%E0%B7%9A_%E0%B7%83%E0%B7%8A%E0%B7%80%E0%B6%B7%E0%B7%8F%E0%B7%80%E0%B6%BA" title="ප්‍රතික්‍රීයකයේ ස්වභාවය – Sinhala" lang="si" hreflang="si" data-title="ප්‍රතික්‍රීයකයේ ස්වභාවය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Chemical_kinetics" title="Chemical kinetics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Chemical kinetics" 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/Chemick%C3%A1_kinetika" title="Chemická kinetika – Slovak" lang="sk" hreflang="sk" data-title="Chemická kinetika" 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/Kemijska_kinetika" title="Kemijska kinetika – Slovenian" lang="sl" hreflang="sl" data-title="Kemijska kinetika" 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%DB%8C%D9%85%DB%8C%D8%A7%DB%8C_%D8%AC%D9%88%D9%88%DA%B5%DB%95%DB%8C%DB%8C" title="کیمیای جووڵەیی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="کیمیای جووڵەیی" 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%A5%D0%B5%D0%BC%D0%B8%D1%98%D1%81%D0%BA%D0%B0_%D0%BA%D0%B8%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Хемијска кинетика – Serbian" lang="sr" hreflang="sr" data-title="Хемијска кинетика" 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/Hemijska_kinetika" title="Hemijska kinetika – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Hemijska kinetika" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Reaktiokinetiikka" title="Reaktiokinetiikka – Finnish" lang="fi" hreflang="fi" data-title="Reaktiokinetiikka" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kinetik_(kemi)" title="Kinetik (kemi) – Swedish" lang="sv" hreflang="sv" data-title="Kinetik (kemi)" 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%B5%E0%AF%87%E0%AE%A4%E0%AE%BF_%E0%AE%B5%E0%AE%BF%E0%AE%A9%E0%AF%88%E0%AE%B5%E0%AF%87%E0%AE%95%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="வேதி வினைவேகவியல் – Tamil" lang="ta" hreflang="ta" data-title="வேதி வினைவேகவியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B0%E0%B0%B8%E0%B0%BE%E0%B0%AF%E0%B0%A8_%E0%B0%97%E0%B0%A4%E0%B0%BF_%E0%B0%B6%E0%B0%BE%E0%B0%B8%E0%B1%8D%E0%B0%A4%E0%B1%8D%E0%B0%B0%E0%B0%82" title="రసాయన గతి శాస్త్రం – Telugu" lang="te" hreflang="te" data-title="రసాయన గతి శాస్త్రం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%A5%E0%B8%99%E0%B8%9E%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B9%80%E0%B8%84%E0%B8%A1%E0%B8%B5" title="จลนพลศาสตร์เคมี – Thai" lang="th" hreflang="th" data-title="จลนพลศาสตร์เคมี" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kimyasal_kinetik" title="Kimyasal kinetik – Turkish" lang="tr" hreflang="tr" data-title="Kimyasal kinetik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A5%D1%96%D0%BC%D1%96%D1%87%D0%BD%D0%B0_%D0%BA%D1%96%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Хімічна кінетика – Ukrainian" lang="uk" hreflang="uk" data-title="Хімічна кінетика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DA%A9%DB%8C%D9%85%DB%8C%D8%A7%D8%A6%DB%8C_%D8%AD%D8%B1%DA%A9%DB%8C%D8%A7%D8%AA" title="کیمیائی حرکیات – Urdu" lang="ur" hreflang="ur" data-title="کیمیائی حرکیات" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%99ng_h%E1%BB%8Dc_h%C3%B3a_h%E1%BB%8Dc" title="Động học hóa học – Vietnamese" lang="vi" hreflang="vi" data-title="Động học hóa học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8C%96%E5%AD%B8%E5%8B%95%E5%8A%9B%E5%AD%B8" title="化學動力學 – Cantonese" lang="yue" hreflang="yue" data-title="化學動力學" data-language-autonym="粵語" data-language-local-name="Cantonese" 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Study of the rates of chemical reactions</div> <p class="mw-empty-elt"> </p><p><b>Chemical kinetics</b>, also known as <b>reaction kinetics</b>, is the branch of <a href="/wiki/Physical_chemistry" title="Physical chemistry">physical chemistry</a> that is concerned with understanding the rates of chemical reactions. It is different from <a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">chemical thermodynamics</a>, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a> and yield information about the <a href="/wiki/Reaction_mechanism" title="Reaction mechanism">reaction's mechanism</a> and <a href="/wiki/Transition_state" title="Transition state">transition states</a>, as well as the construction of <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical models</a> that also can describe the characteristics of a chemical reaction. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2></div> <p>The pioneering work of chemical kinetics was done by German chemist <a href="/wiki/Ludwig_Wilhelmy" title="Ludwig Wilhelmy">Ludwig Wilhelmy</a> in 1850.<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> He experimentally studied the rate of <a href="/wiki/Inversion_of_sucrose" class="mw-redirect" title="Inversion of sucrose">inversion of sucrose</a> and he used <a href="/wiki/Rate_equation#Integral_method" title="Rate equation">integrated rate law</a> for the determination of the reaction kinetics of this reaction. His work was noticed 34 years later by <a href="/wiki/Wilhelm_Ostwald" title="Wilhelm Ostwald">Wilhelm Ostwald</a>. In 1864, <a href="/wiki/Peter_Waage" title="Peter Waage">Peter Waage</a> and <a href="/wiki/Cato_Guldberg" class="mw-redirect" title="Cato Guldberg">Cato Guldberg</a> published the <a href="/wiki/Law_of_mass_action" title="Law of mass action">law of mass action</a>, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.<sup id="cite_ref-GW1_2-0" class="reference"><a href="#cite_note-GW1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-GW2_3-0" class="reference"><a href="#cite_note-GW2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-GW3_4-0" class="reference"><a href="#cite_note-GW3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Jacobus_Henricus_van_%27t_Hoff" title="Jacobus Henricus van 't Hoff">Van 't Hoff</a> studied chemical dynamics and in 1884 published his famous "Études de dynamique chimique".<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> In 1901 he was awarded the first Nobel Prize in Chemistry "in recognition of the extraordinary services he has rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions".<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> After van 't Hoff, chemical kinetics dealt with the experimental determination of <a href="/wiki/Reaction_rate" title="Reaction rate">reaction rates</a> from which <a href="/wiki/Rate_law" class="mw-redirect" title="Rate law">rate laws</a> and <a href="/wiki/Reaction_rate_constant" title="Reaction rate constant">rate constants</a> are derived. Relatively simple <a href="/wiki/Rate_law" class="mw-redirect" title="Rate law">rate laws</a> exist for <a href="/wiki/Rate_law#Zero-order_reactions" class="mw-redirect" title="Rate law">zero order reactions</a> (for which reaction rates are independent of concentration), <a href="/wiki/Rate_equation#First-order_reactions" title="Rate equation">first order reactions</a>, and <a href="/wiki/Second-order_reaction" class="mw-redirect" title="Second-order reaction">second order reactions</a>, and can be derived for others. <a href="/wiki/Elementary_reaction" title="Elementary reaction">Elementary reactions</a> follow the <a href="/wiki/Law_of_mass_action" title="Law of mass action">law of mass action</a>, but the rate law of <a href="/wiki/Stepwise_reaction" class="mw-redirect" title="Stepwise reaction">stepwise reactions</a> has to be derived by combining the rate laws of the various elementary steps, and can become rather complex. In consecutive reactions, the <a href="/wiki/Rate-determining_step" title="Rate-determining step">rate-determining step</a> often determines the kinetics. In consecutive first order reactions, a <a href="/wiki/Steady_state_(chemistry)" title="Steady state (chemistry)">steady state</a> approximation can simplify the <a href="/wiki/Rate_law" class="mw-redirect" title="Rate law">rate law</a>. The <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a> for a reaction is experimentally determined through the <a href="/wiki/Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a> and the <a href="/wiki/Eyring_equation" title="Eyring equation">Eyring equation</a>. The main factors that influence the <a href="/wiki/Reaction_rate" title="Reaction rate">reaction rate</a> include: the <a href="/wiki/Physical_state" class="mw-redirect" title="Physical state">physical state</a> of the reactants, the <a href="/wiki/Concentrations" class="mw-redirect" title="Concentrations">concentrations</a> of the reactants, the <a href="/wiki/Temperature" title="Temperature">temperature</a> at which the reaction occurs, and whether or not any <a href="/wiki/Catalysts" class="mw-redirect" title="Catalysts">catalysts</a> are present in the reaction. </p><p><a href="/wiki/Alexander_Nikolaevich_Gorban" class="mw-redirect" title="Alexander Nikolaevich Gorban">Gorban</a> and Yablonsky have suggested that the history of chemical dynamics can be divided into three eras.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The first is the van 't Hoff wave searching for the general laws of chemical reactions and relating kinetics to thermodynamics. The second may be called the <a href="/wiki/Nikolay_Semyonov" title="Nikolay Semyonov">Semenov</a>-<a href="/wiki/Cyril_Norman_Hinshelwood" class="mw-redirect" title="Cyril Norman Hinshelwood">Hinshelwood</a> wave with emphasis on reaction mechanisms, especially for <a href="/wiki/Chain_reaction#chemical_chain_reactions" title="Chain reaction">chain reactions</a>. The third is associated with <a href="/wiki/Rutherford_Aris" title="Rutherford Aris">Aris</a> and the detailed mathematical description of chemical reaction networks. </p> <div class="mw-heading mw-heading2"><h2 id="Factors_affecting_reaction_rate">Factors affecting reaction rate</h2></div> <div class="mw-heading mw-heading3"><h3 id="Nature_of_the_reactants">Nature of the reactants</h3></div> <p>The reaction rate varies depending upon what substances are reacting. Acid/base reactions, the formation of <a href="/wiki/Salts" class="mw-redirect" title="Salts">salts</a>, and <a href="/wiki/Ion_exchange" title="Ion exchange">ion exchange</a> are usually fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be slower. </p><p>The nature and strength of bonds in reactant molecules greatly influence the rate of their transformation into products. </p> <div class="mw-heading mw-heading3"><h3 id="Physical_state">Physical state</h3></div> <p>The <a href="/wiki/Physical_state" class="mw-redirect" title="Physical state">physical state</a> (<a href="/wiki/Solid" title="Solid">solid</a>, <a href="/wiki/Liquid" title="Liquid">liquid</a>, or <a href="/wiki/Gas" title="Gas">gas</a>) of a reactant is also an important factor of the rate of change. When reactants are in the same <a href="/wiki/Phase_(matter)" title="Phase (matter)">phase</a>, as in <a href="/wiki/Aqueous_solution" title="Aqueous solution">aqueous solution</a>, thermal motion brings them into contact. However, when they are in separate phases, the reaction is limited to the interface between the reactants. Reaction can occur only at their area of contact; in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant the greater its <a href="/wiki/Surface_area" title="Surface area">surface area</a> per unit <a href="/wiki/Volume" title="Volume">volume</a> and the more contact it with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches — one does not start with large logs right away. In organic chemistry, <a href="/wiki/On_water_reaction" class="mw-redirect" title="On water reaction">on water reactions</a> are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions (those in which solute and solvent are not mixed properly). </p> <div class="mw-heading mw-heading3"><h3 id="Surface_area_of_solid_state">Surface area of solid state</h3></div> <p>In a solid, only those particles that are at the surface can be involved in a reaction. Crushing a solid into smaller parts means that more particles are present at the surface, and the frequency of collisions between these and reactant particles increases, and so reaction occurs more rapidly. For example, <a href="/wiki/Sherbet_(powder)" title="Sherbet (powder)">Sherbet (powder)</a> is a mixture of very fine powder of <a href="/wiki/Malic_acid" title="Malic acid">malic acid</a> (a weak organic acid) and <a href="/wiki/Sodium_hydrogen_carbonate" class="mw-redirect" title="Sodium hydrogen carbonate">sodium hydrogen carbonate</a>. On contact with the <a href="/wiki/Saliva" title="Saliva">saliva</a> in the mouth, these chemicals quickly dissolve and react, releasing <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a> and providing for the fizzy sensation. Also, <a href="/wiki/Fireworks" title="Fireworks">fireworks</a> manufacturers modify the surface area of solid reactants to control the rate at which the fuels in fireworks are oxidised, using this to create diverse effects. For example, finely divided <a href="/wiki/Aluminium" title="Aluminium">aluminium</a> confined in a shell explodes violently. If larger pieces of aluminium are used, the reaction is slower and sparks are seen as pieces of burning metal are ejected. </p> <div class="mw-heading mw-heading3"><h3 id="Concentration">Concentration</h3></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rate_equation" title="Rate equation">Rate equation</a></div> <p>The reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depends upon their <a href="/wiki/Concentration" title="Concentration">concentrations</a>. The more crowded the molecules are, the more likely they are to collide and react with one another. Thus, an increase in the concentrations of the reactants will usually result in the corresponding increase in the reaction rate, while a decrease in the concentrations will usually have a reverse effect. For example, <a href="/wiki/Combustion" title="Combustion">combustion</a> will occur more rapidly in pure oxygen than in air (21% oxygen). </p><p>The <a href="/wiki/Rate_equation" title="Rate equation">rate equation</a> shows the detailed dependence of the reaction rate on the concentrations of reactants and other species present. The mathematical forms depend on the <a href="/wiki/Reaction_mechanism" title="Reaction mechanism">reaction mechanism</a>. The actual rate equation for a given reaction is determined experimentally and provides information about the reaction mechanism. The mathematical expression of the rate equation is often given by </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={\frac {\mathrm {d} c}{\mathrm {d} t}}=k\prod _{i}c_{i}^{m_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>c</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>k</mi> <munder> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msubsup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {\mathrm {d} c}{\mathrm {d} t}}=k\prod _{i}c_{i}^{m_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51929446492781f4f543dfbf1ec336aa2812ca9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.722ex; height:6.509ex;" alt="{\displaystyle v={\frac {\mathrm {d} c}{\mathrm {d} t}}=k\prod _{i}c_{i}^{m_{i}}}"></span></dd></dl> <p>Here <span class="mwe-math-element"><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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> is the <a href="/wiki/Reaction_rate_constant" title="Reaction rate constant">reaction rate constant</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01acb7953ba52c2aa44264b5d0f8fd223aa178a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.807ex; height:2.009ex;" alt="{\displaystyle c_{i}}"></span> is the molar concentration of reactant <i>i</i> 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 m_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.84ex; height:2.009ex;" alt="{\displaystyle m_{i}}"></span> is the partial order of reaction for this reactant. The <a href="/wiki/Rate_equation" title="Rate equation">partial order</a> for a reactant can only be determined experimentally and is often not indicated by its <a href="/wiki/Stoichiometry#Stoichiometric_coefficient" title="Stoichiometry">stoichiometric coefficient</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Temperature">Temperature</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a></div> <p><a href="/wiki/Temperature" title="Temperature">Temperature</a> usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more <a href="/wiki/Thermal_energy" title="Thermal energy">thermal energy</a>. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in rate of reaction. Much more important is the fact that the proportion of reactant molecules with sufficient energy to react (energy greater than <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a>: <i>E</i> > <i>E</i><sub><i>a</i></sub>) is significantly higher and is explained in detail by the <a href="/wiki/Maxwell%E2%80%93Boltzmann_distribution" title="Maxwell–Boltzmann distribution">Maxwell–Boltzmann distribution</a> of molecular energies. </p><p>The effect of temperature on the reaction rate constant usually obeys the <a href="/wiki/Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k=Ae^{-E_{\rm {a}}/(RT)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mo>=</mo> <mi>A</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k=Ae^{-E_{\rm {a}}/(RT)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b337ccc0120d6275d50ad726036a01be7bcfd79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.197ex; height:2.843ex;" alt="{\displaystyle k=Ae^{-E_{\rm {a}}/(RT)}}"></span>, where A is the <a href="/wiki/Pre-exponential_factor" title="Pre-exponential factor">pre-exponential factor</a> or A-factor, E<sub>a</sub> is the activation energy, R is the <a href="/wiki/Molar_gas_constant" class="mw-redirect" title="Molar gas constant">molar gas constant</a> and T is the <a href="/wiki/Absolute_temperature" class="mw-redirect" title="Absolute temperature">absolute temperature</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>At a given temperature, the chemical rate of a reaction depends on the value of the A-factor, the magnitude of the activation energy, and the concentrations of the reactants. Usually, rapid reactions require relatively small activation energies. </p><p>The 'rule of thumb' that the rate of chemical reactions doubles for every 10 °C temperature rise is a common misconception. This may have been generalized from the special case of biological systems, where the <a href="/wiki/Q10_(temperature_coefficient)" title="Q10 (temperature coefficient)"><i>α</i> (temperature coefficient)</a> is often between 1.5 and 2.5. </p><p>The kinetics of rapid reactions can be studied with the <a href="/wiki/Temperature_jump" title="Temperature jump">temperature jump</a> method. This involves using a sharp rise in temperature and observing the <a href="/wiki/Relaxation_time" class="mw-redirect" title="Relaxation time">relaxation time</a> of the return to equilibrium. A particularly useful form of temperature jump apparatus is a <a href="/wiki/Shock_tube" title="Shock tube">shock tube</a>, which can rapidly increase a gas's temperature by more than 1000 degrees. </p> <div class="mw-heading mw-heading3"><h3 id="Catalysts">Catalysts</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Catalysis" title="Catalysis">Catalysis</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Activation_energy.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Activation_energy.svg/220px-Activation_energy.svg.png" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Activation_energy.svg/330px-Activation_energy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Activation_energy.svg/440px-Activation_energy.svg.png 2x" data-file-width="929" data-file-height="743" /></a><figcaption>Generic potential energy diagram showing the effect of a catalyst in a hypothetical endothermic chemical reaction. The presence of the catalyst opens a new reaction pathway (shown in red) with a lower activation energy. The final result and the overall thermodynamics are the same.</figcaption></figure> <p>A <a href="/wiki/Catalyst" class="mw-redirect" title="Catalyst">catalyst</a> is a substance that alters the rate of a chemical reaction but it remains <a href="/wiki/Chemically" class="mw-redirect" title="Chemically">chemically</a> unchanged afterwards. The catalyst increases the rate of the reaction by providing a new <a href="/wiki/Reaction_mechanism" title="Reaction mechanism">reaction mechanism</a> to occur with in a lower <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a>. In <a href="/wiki/Autocatalysis" title="Autocatalysis">autocatalysis</a> a reaction product is itself a catalyst for that reaction leading to <a href="/wiki/Positive_feedback" title="Positive feedback">positive feedback</a>. Proteins that act as catalysts in biochemical reactions are called <a href="/wiki/Enzyme" title="Enzyme">enzymes</a>. <a href="/wiki/Michaelis%E2%80%93Menten_kinetics" title="Michaelis–Menten kinetics">Michaelis–Menten kinetics</a> describe the <a href="/wiki/Enzyme_kinetics" title="Enzyme kinetics">rate of enzyme mediated reactions</a>. A catalyst does not affect the position of the equilibrium, as the catalyst speeds up the backward and forward reactions equally. </p><p>In certain organic molecules, specific substituents can have an influence on reaction rate in <a href="/wiki/Neighbouring_group_participation" title="Neighbouring group participation">neighbouring group participation</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2014)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pressure">Pressure</h3></div> <p>Increasing the pressure in a gaseous reaction will increase the number of collisions between reactants, increasing the rate of reaction. This is because the <a href="/wiki/Activity_(chemistry)" class="mw-redirect" title="Activity (chemistry)">activity</a> of a gas is directly proportional to the partial pressure of the gas. This is similar to the effect of increasing the concentration of a solution. </p><p>In addition to this straightforward mass-action effect, the rate coefficients themselves can change due to pressure. The rate coefficients and products of many high-temperature gas-phase reactions change if an inert gas is added to the mixture; variations on this effect are called <b>fall-off</b> and <b>chemical activation</b>. These phenomena are due to exothermic or endothermic reactions occurring faster than heat transfer, causing the reacting molecules to have non-thermal energy distributions (<b>non-<a href="/wiki/Boltzmann_distribution" title="Boltzmann distribution">Boltzmann distribution</a></b>). Increasing the pressure increases the heat transfer rate between the reacting molecules and the rest of the system, reducing this effect. </p><p>Condensed-phase rate coefficients can also be affected by pressure, although rather high pressures are required for a measurable effect because ions and molecules are not very compressible. This effect is often studied using <a href="/wiki/Diamond_anvil" class="mw-redirect" title="Diamond anvil">diamond anvils</a>. </p><p>A reaction's kinetics can also be studied with a <a href="/wiki/Pressure_jump" title="Pressure jump">pressure jump</a> approach. This involves making fast changes in pressure and observing the <a href="/wiki/Relaxation_time" class="mw-redirect" title="Relaxation time">relaxation time</a> of the return to equilibrium. </p> <div class="mw-heading mw-heading3"><h3 id="Absorption_of_light">Absorption of light</h3></div> <p>The activation energy for a chemical reaction can be provided when one reactant molecule absorbs light of suitable <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> and is promoted to an <a href="/wiki/Excited_state" title="Excited state">excited state</a>. The study of reactions initiated by light is <a href="/wiki/Photochemistry" title="Photochemistry">photochemistry</a>, one prominent example being <a href="/wiki/Photosynthesis" title="Photosynthesis">photosynthesis</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Experimental_methods">Experimental methods</h2></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Reaction_kinetics_system_nz805z932.tiff" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Reaction_kinetics_system_nz805z932.tiff/lossy-page1-220px-Reaction_kinetics_system_nz805z932.tiff.jpg" decoding="async" width="220" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Reaction_kinetics_system_nz805z932.tiff/lossy-page1-330px-Reaction_kinetics_system_nz805z932.tiff.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Reaction_kinetics_system_nz805z932.tiff/lossy-page1-440px-Reaction_kinetics_system_nz805z932.tiff.jpg 2x" data-file-width="1594" data-file-height="2177" /></a><figcaption> The Spinco Division Model 260 Reaction Kinetics System measured the precise rate constants of molecular reactions.</figcaption></figure> <p>The experimental determination of reaction rates involves measuring how the concentrations of reactants or products change over time. For example, the concentration of a reactant can be measured by <a href="/wiki/Spectrophotometry" title="Spectrophotometry">spectrophotometry</a> at a wavelength where no other reactant or product in the system absorbs light. </p><p>For reactions which take at least several minutes, it is possible to start the observations after the reactants have been mixed at the temperature of interest. </p> <div class="mw-heading mw-heading3"><h3 id="Fast_reactions">Fast reactions</h3></div> <p>For faster reactions, the time required to mix the reactants and bring them to a specified temperature may be comparable or longer than the <a href="/wiki/Half-life" title="Half-life">half-life</a> of the reaction.<sup id="cite_ref-Laidler_9-0" class="reference"><a href="#cite_note-Laidler-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Special methods to start fast reactions without slow mixing step include </p> <ul><li><a href="/wiki/Stopped_flow" class="mw-redirect" title="Stopped flow">Stopped flow</a> methods, which can reduce the mixing time to the order of a millisecond<sup id="cite_ref-Laidler_9-1" class="reference"><a href="#cite_note-Laidler-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Atkins793_11-0" class="reference"><a href="#cite_note-Atkins793-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The stopped flow methods have limitation, for example, we need to consider the time it takes to mix gases or solutions and are not suitable if the half-life is less than about a hundredth of a second.</li> <li><a href="/wiki/Relaxation_(physics)" title="Relaxation (physics)">Chemical relaxation</a> methods such as <a href="/wiki/Temperature_jump" title="Temperature jump">temperature jump</a> and <a href="/wiki/Pressure_jump" title="Pressure jump">pressure jump</a>, in which a pre-mixed system initially at equilibrium is perturbed by rapid heating or depressurization so that it is no longer at equilibrium, and the relaxation back to equilibrium is observed.<sup id="cite_ref-Laidler_9-2" class="reference"><a href="#cite_note-Laidler-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Atkins805_14-0" class="reference"><a href="#cite_note-Atkins805-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> For example, this method has been used to study the <a href="/wiki/Neutralization_(chemistry)" title="Neutralization (chemistry)">neutralization</a> H<sub>3</sub>O<sup>+</sup> + OH<sup>−</sup> with a half-life of 1 μs or less under ordinary conditions.<sup id="cite_ref-Laidler_9-3" class="reference"><a href="#cite_note-Laidler-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Atkins805_14-1" class="reference"><a href="#cite_note-Atkins805-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Flash_photolysis" title="Flash photolysis">Flash photolysis</a>, in which a laser pulse produces highly excited species such as <a href="/wiki/Radical_(chemistry)" title="Radical (chemistry)">free radicals</a>, whose reactions are then studied.<sup id="cite_ref-Atkins793_11-1" class="reference"><a href="#cite_note-Atkins793-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Equilibrium">Equilibrium</h2></div> <p>While chemical kinetics is concerned with the rate of a chemical reaction, <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a> determines the extent to which reactions occur. In a <a href="/wiki/Reversible_reaction" title="Reversible reaction">reversible reaction</a>, chemical equilibrium is reached when the rates of the forward and reverse reactions are equal (the principle of <a href="/wiki/Dynamic_equilibrium" title="Dynamic equilibrium">dynamic equilibrium</a>) and the concentrations of the reactants and products no longer change. This is demonstrated by, for example, the <a href="/wiki/Haber%E2%80%93Bosch_process" class="mw-redirect" title="Haber–Bosch process">Haber–Bosch process</a> for combining nitrogen and hydrogen to produce ammonia. <a href="/wiki/Chemical_clock" title="Chemical clock">Chemical clock</a> reactions such as the <a href="/wiki/Belousov%E2%80%93Zhabotinsky_reaction" title="Belousov–Zhabotinsky reaction">Belousov–Zhabotinsky reaction</a> demonstrate that component concentrations can oscillate for a long time before finally attaining the equilibrium. </p> <div class="mw-heading mw-heading2"><h2 id="Free_energy">Free energy</h2></div> <p>In general terms, the <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free energy change (ΔG)</a> of a reaction determines whether a chemical change will take place, but kinetics describes how fast the reaction is. A reaction can be very <a href="/wiki/Exothermic" class="mw-redirect" title="Exothermic">exothermic</a> and have a very positive <a href="/wiki/Entropy" title="Entropy">entropy</a> change but will not happen in practice if the reaction is too slow. If a reactant can produce two products, the thermodynamically most stable one will form in general, except in special circumstances when the reaction is said to be under <a href="/wiki/Kinetic_reaction_control" class="mw-redirect" title="Kinetic reaction control">kinetic reaction control</a>. The <a href="/wiki/Curtin%E2%80%93Hammett_principle" title="Curtin–Hammett principle">Curtin–Hammett principle</a> applies when determining the product ratio for two reactants interconverting rapidly, each going to a distinct product. It is possible to make predictions about reaction rate constants for a reaction from <a href="/wiki/Free-energy_relationship" title="Free-energy relationship">free-energy relationships</a>. </p><p>The <a href="/wiki/Kinetic_isotope_effect" title="Kinetic isotope effect">kinetic isotope effect</a> is the difference in the rate of a chemical reaction when an atom in one of the reactants is replaced by one of its <a href="/wiki/Isotope" title="Isotope">isotopes</a>. </p><p>Chemical kinetics provides information on <a href="/wiki/Residence_time_distribution" class="mw-redirect" title="Residence time distribution">residence time</a> and <a href="/wiki/Heat_transfer" title="Heat transfer">heat transfer</a> in a <a href="/wiki/Chemical_reactor" title="Chemical reactor">chemical reactor</a> in <a href="/wiki/Chemical_engineering" title="Chemical engineering">chemical engineering</a> and the <a href="/wiki/Molar_mass_distribution" title="Molar mass distribution">molar mass distribution</a> in <a href="/wiki/Polymer_chemistry" title="Polymer chemistry">polymer chemistry</a>. It is also provides information in <a href="/wiki/Corrosion_engineering" title="Corrosion engineering">corrosion engineering</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Applications_and_models">Applications and models</h2></div> <p>The mathematical models that describe chemical reaction kinetics provide chemists and chemical engineers with tools to better understand and describe chemical processes such as food decomposition, microorganism growth, stratospheric ozone decomposition, and the chemistry of biological systems. These models can also be used in the design or modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful by-products. When performing <a href="/wiki/Catalytic_cracking" class="mw-redirect" title="Catalytic cracking">catalytic cracking</a> of heavy hydrocarbons into gasoline and light gas, for example, kinetic models can be used to find the temperature and pressure at which the highest yield of heavy hydrocarbons into gasoline will occur. </p><p>Chemical Kinetics is frequently validated and explored through modeling in specialized packages as a function of <a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">ordinary differential equation</a>-solving (ODE-solving) and <a href="/wiki/Curve-fitting" class="mw-redirect" title="Curve-fitting">curve-fitting</a>.<sup id="cite_ref-ChemicalKinetics_18-0" class="reference"><a href="#cite_note-ChemicalKinetics-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Numerical_methods">Numerical methods</h3></div> <p>In some cases, equations are unsolvable analytically, but can be solved using numerical methods if data values are given. There are two different ways to do this, by either using software programmes or mathematical methods such as the <a href="/wiki/Euler_method" title="Euler method">Euler method</a>. Examples of software for chemical kinetics are i) Tenua, a <a href="/wiki/Java_(programming_language)" title="Java (programming language)">Java</a> app which simulates chemical reactions numerically and allows comparison of the simulation to real data, ii) <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> coding for calculations and estimates and iii) the Kintecus software compiler to model, regress, fit and optimize reactions. </p><p>-Numerical integration: for a 1st order reaction A → B </p><p>The differential equation of the reactant A is: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d{\ce {[A]}}}{dt}}=-k{\ce {[A]}}}"> <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> <mtext>A</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>A</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d{\ce {[A]}}}{dt}}=-k{\ce {[A]}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5afc7459a6c89649f2aa0176e075cf709c88a8cb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.243ex; height:5.843ex;" alt="{\displaystyle {\frac {d{\ce {[A]}}}{dt}}=-k{\ce {[A]}}}"></span> </p><p>It can also be expressed as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d{\ce {[A]}}}{dt}}=f(t,{\ce {[A]}})}"> <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> <mtext>A</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mtext>A</mtext> <mo stretchy="false">]</mo> </mrow> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d{\ce {[A]}}}{dt}}=f(t,{\ce {[A]}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cbbece9164c4f458325c33774da32a5f87c1588" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.185ex; height:5.843ex;" alt="{\displaystyle {\frac {d{\ce {[A]}}}{dt}}=f(t,{\ce {[A]}})}"></span> which is the same as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y'=f(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y'=f(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8855ed828ac868d6c7e8b4e06c420306ba0dec0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.551ex; height:3.009ex;" alt="{\displaystyle y'=f(x,y)}"></span> </p><p>To solve the differential equations with Euler and Runge-Kutta methods we need to have the initial values. </p> <div><ul><li><a href="/wiki/Euler_method" title="Euler method">Euler method</a> → simple but inaccurate. <div class="paragraphbreak" style="margin-top:0.5em"></div> <p>At any point <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y'=f(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y'=f(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8855ed828ac868d6c7e8b4e06c420306ba0dec0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.551ex; height:3.009ex;" alt="{\displaystyle y'=f(x,y)}"></span> is the same as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y'={\frac {dy}{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y'={\frac {dy}{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3178da3dbb34c2da08d26fa0847ce4bd60ae43cb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.325ex; height:5.509ex;" alt="{\displaystyle y'={\frac {dy}{dx}}}"></span> </p><p>We can approximate the differentials as discrete increases: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y'={\frac {dy}{dx}}\approx {\frac {\Delta y}{\Delta x}}={\frac {y(x+\Delta x)-y(x)}{\Delta x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>y</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>y</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y'={\frac {dy}{dx}}\approx {\frac {\Delta y}{\Delta x}}={\frac {y(x+\Delta x)-y(x)}{\Delta x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a07bf970f8936f9be3e8906a7390b3cc31b02587" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:36.995ex; height:5.843ex;" alt="{\displaystyle y'={\frac {dy}{dx}}\approx {\frac {\Delta y}{\Delta x}}={\frac {y(x+\Delta x)-y(x)}{\Delta x}}}"></span> </p> The unknown part of the equation is <span class="texhtml"><i>y</i>(<i>x</i>+Δ<i>x</i>)</span>, which can be found if we have the data for the initial values.</li><li><a href="/wiki/Runge-Kutta_methods" class="mw-redirect" title="Runge-Kutta methods">Runge-Kutta methods</a> → it is more accurate than the Euler method. In this method, an initial condition is required: <span class="texhtml"><i>y</i> = <i>y</i><sub>0</sub></span> at <span class="texhtml"><i>x</i> = <i>x</i><sub>0</sub></span>. The problem is to find the value of <i>y</i> when <span class="texhtml"><i>x</i> = <i>x</i><sub>0</sub> + <i>h</i></span>, where <span class="texhtml"><i>h</i></span> is a given constant. <div class="paragraphbreak" style="margin-top:0.5em"></div> <p>It can be shown analytically that the ordinate at that moment to the curve through <span class="texhtml">(<i>x</i><sub>0</sub>, <i>y</i><sub>0</sub>)</span> is given by the third-order Runge-Kutta formula. </p> <div class="paragraphbreak" style="margin-top:0.5em"></div> In first-order ordinary equations, the Runge-Kutta method uses a mathematical model that represents the relationship between the temperature and the rate of reaction. It is worth it to calculate the rate of reaction at different temperatures for different concentrations. The equation obtained is: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dr/dt=R/T+r\Delta H^{\circ }/RT^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo>+</mo> <mi>r</mi> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>R</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dr/dt=R/T+r\Delta H^{\circ }/RT^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c7cd132238dbfbaa54747192debac3586f98a61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.827ex; height:3.176ex;" alt="{\displaystyle dr/dt=R/T+r\Delta H^{\circ }/RT^{2}}"></span></li><li><a href="/wiki/Stochastic_methods" class="mw-redirect" title="Stochastic methods">Stochastic methods</a> → probabilities of the differential rate laws and the kinetic constants. In an equilibrioum reaction with direct and inverse rate constants, it is easier to transform from A to B rather than B to A. <div class="paragraphbreak" style="margin-top:0.5em"></div> As for probability computations, at each time it choose a random number to be compared with a threshold to know if the reaction runs from A to B or the other way around.</li></ul></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <ul><li><a href="/wiki/Autocatalytic_reactions_and_order_creation" class="mw-redirect" title="Autocatalytic reactions and order creation">Autocatalytic reactions and order creation</a></li> <li><a href="/wiki/Corrosion_engineering" title="Corrosion engineering">Corrosion engineering</a></li> <li><a href="/wiki/Detonation" title="Detonation">Detonation</a></li> <li><a href="/wiki/Electrochemical_kinetics" title="Electrochemical kinetics">Electrochemical kinetics</a></li> <li><a href="/wiki/Flame_speed" title="Flame speed">Flame speed</a></li> <li><a href="/wiki/Heterogenous_catalysis" class="mw-redirect" title="Heterogenous catalysis">Heterogenous catalysis</a></li> <li><a href="/wiki/Intrinsic_low-dimensional_manifold" title="Intrinsic low-dimensional manifold">Intrinsic low-dimensional manifold</a></li> <li><a href="/wiki/MLAB" title="MLAB">MLAB</a> chemical kinetics modeling package</li> <li><a href="/wiki/Nonthermal_surface_reaction" title="Nonthermal surface reaction">Nonthermal surface reaction</a></li> <li><a href="/wiki/PottersWheel" title="PottersWheel">PottersWheel</a> Matlab toolbox to fit chemical rate constants to experimental data</li> <li><a href="/wiki/Reaction_progress_kinetic_analysis" title="Reaction progress kinetic analysis">Reaction progress kinetic analysis</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></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 mw-references-columns"><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">L. Wilhelmy, "Ann. Phys. Chem. (Poggendorf)" Vol 81, (1850) 413</span> </li> <li id="cite_note-GW1-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-GW1_2-0">^</a></b></span> <span class="reference-text">C.M. Guldberg and P. Waage,"Studies Concerning Affinity" <i>Forhandlinger i Videnskabs-Selskabet i Christiania</i> (1864), 35</span> </li> <li id="cite_note-GW2-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-GW2_3-0">^</a></b></span> <span class="reference-text">P. Waage, "Experiments for Determining the Affinity Law" ,<i>Forhandlinger i Videnskabs-Selskabet i Christiania</i>, (1864) 92.</span> </li> <li id="cite_note-GW3-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-GW3_4-0">^</a></b></span> <span class="reference-text">C.M. Guldberg, "Concerning the Laws of Chemical Affinity", <i>Forhandlinger i Videnskabs-Selskabet i Christiania</i> (1864) 111</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"><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="CITEREFHoffCohenEwan1896" class="citation book cs1">Hoff, J. H. van't (Jacobus Henricus van't); Cohen, Ernst; Ewan, Thomas (1896-01-01). <a rel="nofollow" class="external text" href="https://archive.org/details/studiesinchemica00hoffrich"><i>Studies in chemical dynamics</i></a>. Amsterdam : F. Muller; London : Williams & Norgate.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Studies+in+chemical+dynamics&rft.pub=Amsterdam+%3A+F.+Muller%3B+London+%3A+Williams+%26+Norgate&rft.date=1896-01-01&rft.aulast=Hoff&rft.aufirst=J.+H.+van%27t+%28Jacobus+Henricus+van%27t%29&rft.au=Cohen%2C+Ernst&rft.au=Ewan%2C+Thomas&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fstudiesinchemica00hoffrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+kinetics" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1901/">The Nobel Prize in Chemistry 1901</a>, Nobel Prizes and Laureates, official website.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">A.N. Gorban, G.S. Yablonsky <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/281411623_Three_Waves_of_Chemical_Dynamics">Three Waves of Chemical Dynamics</a>, <i>Mathematical Modelling of Natural Phenomena</i> 10(5) (2015), p. 1–5.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="/wiki/Keith_J._Laidler" title="Keith J. Laidler">Laidler, K. J.</a> <i>Chemical Kinetics</i> (3rd ed., Harper and Row 1987) p.42 <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-Laidler-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Laidler_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Laidler_9-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Laidler_9-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Laidler_9-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Keith_J._Laidler" title="Keith J. Laidler">Laidler, K. J.</a> <i>Chemical Kinetics</i> (3rd ed., Harper and Row 1987) p.33-39 <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-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Espenson, J.H. <i>Chemical Kinetics and Reaction Mechanisms</i> (2nd ed., McGraw-Hill 2002), p.254-256 <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/0-07-288362-6" title="Special:BookSources/0-07-288362-6">0-07-288362-6</a></span> </li> <li id="cite_note-Atkins793-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Atkins793_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Atkins793_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Atkins P. and de Paula J., <i>Physical Chemistry</i> (8th ed., W.H. Freeman 2006) p.793 <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-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Espenson, J.H. <i>Chemical Kinetics and Reaction Mechanisms</i> (2nd ed., McGraw-Hill 2002), p.256-8 <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/0-07-288362-6" title="Special:BookSources/0-07-288362-6">0-07-288362-6</a></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Steinfeld J.I., Francisco J.S. and Hase W.L. <i>Chemical Kinetics and Dynamics</i> (2nd ed., Prentice-Hall 1999) p.140-3 <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/0-13-737123-3" title="Special:BookSources/0-13-737123-3">0-13-737123-3</a></span> </li> <li id="cite_note-Atkins805-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Atkins805_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Atkins805_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Atkins P. and de Paula J., <i>Physical Chemistry</i> (8th ed., W.H. Freeman 2006) pp.805-7 <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-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Laidler, K.J. <i>Chemical Kinetics</i> (3rd ed., Harper and Row 1987) p.359-360 <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-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Espenson, J.H. <i>Chemical Kinetics and Reaction Mechanisms</i> (2nd ed., McGraw-Hill 2002), p.264-6 <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/0-07-288362-6" title="Special:BookSources/0-07-288362-6">0-07-288362-6</a></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Steinfeld J.I., Francisco J.S. and Hase W.L. <i>Chemical Kinetics and Dynamics</i> (2nd ed., Prentice-Hall 1999) p.94-97 <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/0-13-737123-3" title="Special:BookSources/0-13-737123-3">0-13-737123-3</a></span> </li> <li id="cite_note-ChemicalKinetics-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-ChemicalKinetics_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.civilized.com/files/sobnew.pdf">"Chemical Kinetics: Simple Binding: F + G ⇋ B"</a> <span class="cs1-format">(PDF)</span>. Civilized Software, Inc<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-09-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Chemical+Kinetics%3A+Simple+Binding%3A+F+%2B+G+%E2%87%8B+B&rft.pub=Civilized+Software%2C+Inc.&rft_id=http%3A%2F%2Fwww.civilized.com%2Ffiles%2Fsobnew.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+kinetics" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output 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class="external text" href="https://ftl.toolforge.org/cgi-bin/ftl?st=wp&su=Chemical+kinetics">Resources in your library</a></li> </ul></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.chm.davidson.edu/ChemistryApplets/kinetics/">Chemistry applets</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090604052110/http://www.chm.davidson.edu/ChemistryApplets/kinetics/">Archived</a> 2009-06-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051124110717/http://www.science.uwaterloo.ca/~cchieh/cact/c123/chmkntcs.html">University of Waterloo</a></li> <li><a rel="nofollow" class="external text" href="http://www.Chemked.com/">Chemical Kinetics of Gas Phase Reactions</a></li> <li><a rel="nofollow" class="external text" href="https://code.google.com/p/kinpy/">Kinpy: Python code generator for solving kinetic equations</a></li> <li><a rel="nofollow" class="external text" href="https://av.tib.eu/media/34661?pag=1">Reaction rate law and reaction profile - a question of temperature, concentration, solvent and catalyst - how fast will a reaction proceed</a> (Video by SciFox on TIB AV-Portal)</li></ul> <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 .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul 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title="Special:EditPage/Template:Reaction mechanisms"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Basic_reaction_mechanisms264" 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 class="mw-selflink selflink">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 href="/wiki/Rate-determining_step" title="Rate-determining step">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 class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Branches_of_chemistry854" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Branches_of_chemistry" title="Template:Branches of chemistry"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Branches_of_chemistry" title="Template talk:Branches of chemistry"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Branches_of_chemistry" title="Special:EditPage/Template:Branches of chemistry"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Branches_of_chemistry854" style="font-size:114%;margin:0 4em">Branches of <a href="/wiki/Chemistry" title="Chemistry">chemistry</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Glossary_of_chemical_formulae" title="Glossary of chemical formulae">Glossary of chemical formulae</a></li> <li><a href="/wiki/List_of_biomolecules" title="List of biomolecules">List of biomolecules</a></li> <li><a href="/wiki/List_of_inorganic_compounds" title="List of inorganic compounds">List of inorganic compounds</a></li> <li><a href="/wiki/Periodic_table" title="Periodic table">Periodic table</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Analytical_chemistry" title="Analytical chemistry">Analytical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Instrumental_chemistry" title="Instrumental chemistry">Instrumental chemistry</a></li> <li><a href="/wiki/Electroanalytical_methods" title="Electroanalytical methods">Electroanalytical methods</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a> <ul><li><a href="/wiki/Infrared_spectroscopy" title="Infrared spectroscopy">IR</a></li> <li><a href="/wiki/Raman_spectroscopy" title="Raman spectroscopy">Raman</a></li> <li><a href="/wiki/Ultraviolet%E2%80%93visible_spectroscopy" title="Ultraviolet–visible spectroscopy">UV-Vis</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance_spectroscopy" title="Nuclear magnetic resonance spectroscopy">NMR</a></li></ul></li> <li><a href="/wiki/Mass_spectrometry" title="Mass spectrometry">Mass spectrometry</a> <ul><li><a href="/wiki/Electron_ionization" title="Electron ionization">EI</a></li> <li><a href="/wiki/Inductively_coupled_plasma_mass_spectrometry" title="Inductively coupled plasma mass spectrometry">ICP</a></li> <li><a href="/wiki/Matrix-assisted_laser_desorption/ionization" title="Matrix-assisted laser desorption/ionization">MALDI</a></li></ul></li> <li><a href="/wiki/Separation_process" title="Separation process">Separation process</a></li> <li><a href="/wiki/Chromatography" title="Chromatography">Chromatography</a> <ul><li><a href="/wiki/Gas_chromatography" title="Gas chromatography">GC</a></li> <li><a href="/wiki/High-performance_liquid_chromatography" title="High-performance liquid chromatography">HPLC</a></li></ul></li> <li><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></li> <li><a href="/wiki/Characterization_(materials_science)" title="Characterization (materials science)">Characterization</a></li> <li><a href="/wiki/Titration" title="Titration">Titration</a></li> <li><a href="/wiki/Wet_chemistry" title="Wet chemistry">Wet chemistry</a></li> <li><a href="/wiki/Calorimetry" title="Calorimetry">Calorimetry</a></li> <li><a href="/wiki/Elemental_analysis" title="Elemental analysis">Elemental analysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Theoretical_chemistry" title="Theoretical chemistry">Theoretical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Computational_chemistry" title="Computational chemistry">Computational chemistry</a> <ul><li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Mathematical chemistry</a></li></ul></li> <li><a href="/wiki/Molecular_modelling" title="Molecular modelling">Molecular modelling</a></li> <li><a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a></li> <li><a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></li> <li><a href="/wiki/Molecular_geometry" title="Molecular geometry">Molecular geometry</a> <ul><li><a href="/wiki/VSEPR_theory" title="VSEPR theory">VSEPR theory</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Physical_chemistry" title="Physical chemistry">Physical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electrochemistry" title="Electrochemistry">Electrochemistry</a> <ul><li><a href="/wiki/Spectroelectrochemistry" title="Spectroelectrochemistry">Spectroelectrochemistry</a></li> <li><a href="/wiki/Photoelectrochemistry" title="Photoelectrochemistry">Photoelectrochemistry</a></li></ul></li> <li><a href="/wiki/Thermochemistry" title="Thermochemistry">Thermochemistry</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical thermodynamics</a></li> <li><a href="/wiki/Surface_science" title="Surface science">Surface science</a></li> <li><a href="/wiki/Interface_and_colloid_science" title="Interface and colloid science">Interface and colloid science</a> <ul><li><a href="/wiki/Micromeritics" title="Micromeritics">Micromeritics</a></li></ul></li> <li><a href="/wiki/Cryochemistry" title="Cryochemistry">Cryochemistry</a></li> <li><a href="/wiki/Sonochemistry" title="Sonochemistry">Sonochemistry</a></li> <li><a href="/wiki/Structural_chemistry" title="Structural chemistry">Structural chemistry</a></li> <li><a href="/wiki/Chemical_physics" title="Chemical physics">Chemical physics</a> <ul><li><a href="/wiki/Molecular_physics" title="Molecular physics">Molecular physics</a></li></ul></li> <li><a href="/wiki/Femtochemistry" title="Femtochemistry">Femtochemistry</a></li> <li><a class="mw-selflink selflink">Chemical kinetics</a></li> <li><a href="/wiki/Spectroscopy" title="Spectroscopy">Spectroscopy</a></li> <li><a href="/wiki/Photochemistry" title="Photochemistry">Photochemistry</a></li> <li><a href="/wiki/Spin_chemistry" title="Spin chemistry">Spin chemistry</a></li> <li><a href="/wiki/Microwave_chemistry" title="Microwave chemistry">Microwave chemistry</a></li> <li><a href="/wiki/Equilibrium_chemistry" title="Equilibrium chemistry">Equilibrium chemistry</a></li> <li><a href="/wiki/Mechanochemistry" title="Mechanochemistry">Mechanochemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Inorganic_chemistry" title="Inorganic chemistry">Inorganic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coordination_complex" title="Coordination complex">Coordination chemistry</a></li> <li><a href="/wiki/Magnetochemistry" title="Magnetochemistry">Magnetochemistry</a></li> <li><a href="/wiki/Organometallic_chemistry" title="Organometallic chemistry">Organometallic chemistry</a> <ul><li><a href="/wiki/Organolanthanide_chemistry" title="Organolanthanide chemistry">Organolanthanide chemistry</a></li></ul></li> <li><a href="/wiki/Atom_cluster" class="mw-redirect" title="Atom cluster">Cluster chemistry</a></li> <li><a href="/wiki/Solid-state_chemistry" title="Solid-state chemistry">Solid-state chemistry</a></li> <li><a href="/wiki/Ceramic_chemistry" class="mw-redirect" title="Ceramic chemistry">Ceramic chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Organic_chemistry" title="Organic chemistry">Organic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stereochemistry" title="Stereochemistry">Stereochemistry</a> <ul><li><a href="/wiki/Alkane_stereochemistry" class="mw-redirect" title="Alkane stereochemistry">Alkane stereochemistry</a></li></ul></li> <li><a href="/wiki/Physical_organic_chemistry" title="Physical organic chemistry">Physical organic chemistry</a></li> <li><a href="/wiki/Organic_reactions" class="mw-redirect" title="Organic reactions">Organic reactions</a></li> <li><a href="/wiki/Organic_synthesis" title="Organic synthesis">Organic synthesis</a></li> <li><a href="/wiki/Retrosynthetic_analysis" title="Retrosynthetic analysis">Retrosynthetic analysis</a></li> <li><a href="/wiki/Enantioselective_synthesis" title="Enantioselective synthesis">Enantioselective synthesis</a></li> <li><a href="/wiki/Total_synthesis" title="Total synthesis">Total synthesis</a> / <a href="/wiki/Semisynthesis" title="Semisynthesis">Semisynthesis</a></li> <li><a href="/wiki/Fullerene_chemistry" title="Fullerene chemistry">Fullerene chemistry</a></li> <li><a href="/wiki/Polymer_chemistry" title="Polymer chemistry">Polymer chemistry</a></li> <li><a href="/wiki/Petrochemistry" class="mw-redirect" title="Petrochemistry">Petrochemistry</a></li> <li><a href="/wiki/Dynamic_covalent_chemistry" title="Dynamic covalent chemistry">Dynamic covalent chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Biochemistry" title="Biochemistry">Biological</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biochemistry" title="Biochemistry">Biochemistry</a> <ul><li><a href="/wiki/Molecular_biology" title="Molecular biology">Molecular biology</a></li> <li><a href="/wiki/Cell_biology" title="Cell biology">Cell biology</a></li></ul></li> <li><a href="/wiki/Chemical_biology" title="Chemical biology">Chemical biology</a> <ul><li><a href="/wiki/Bioorthogonal_chemistry" title="Bioorthogonal chemistry">Bioorthogonal chemistry</a></li></ul></li> <li><a href="/wiki/Medicinal_chemistry" title="Medicinal chemistry">Medicinal chemistry</a> <ul><li><a href="/wiki/Pharmacology" title="Pharmacology">Pharmacology</a></li></ul></li> <li><a href="/wiki/Clinical_chemistry" title="Clinical chemistry">Clinical chemistry</a></li> <li><a href="/wiki/Neurochemistry" title="Neurochemistry">Neurochemistry</a></li> <li><a href="/wiki/Bioorganic_chemistry" title="Bioorganic chemistry">Bioorganic chemistry</a></li> <li><a href="/wiki/Bioorganometallic_chemistry" title="Bioorganometallic chemistry">Bioorganometallic chemistry</a></li> <li><a href="/wiki/Bioinorganic_chemistry" title="Bioinorganic chemistry">Bioinorganic chemistry</a></li> <li><a href="/wiki/Biophysical_chemistry" title="Biophysical chemistry">Biophysical chemistry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interdisciplinarity" title="Interdisciplinarity">Interdisciplinarity</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nuclear_chemistry" title="Nuclear chemistry">Nuclear chemistry</a> <ul><li><a href="/wiki/Radiochemistry" title="Radiochemistry">Radiochemistry</a></li> <li><a href="/wiki/Radiation_chemistry" title="Radiation chemistry">Radiation chemistry</a></li> <li><a href="/wiki/Actinide_chemistry" title="Actinide chemistry">Actinide chemistry</a></li></ul></li> <li><a href="/wiki/Cosmochemistry" title="Cosmochemistry">Cosmochemistry</a> / <a href="/wiki/Astrochemistry" title="Astrochemistry">Astrochemistry</a> / <a href="/wiki/Stellar_chemistry" title="Stellar chemistry">Stellar chemistry</a></li> <li><a href="/wiki/Geochemistry" title="Geochemistry">Geochemistry</a> <ul><li><a href="/wiki/Biogeochemistry" title="Biogeochemistry">Biogeochemistry</a></li> <li><a href="/wiki/Photogeochemistry" title="Photogeochemistry">Photogeochemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Environmental_chemistry" title="Environmental chemistry">Environmental chemistry</a> <ul><li><a href="/wiki/Atmospheric_chemistry" title="Atmospheric chemistry">Atmospheric chemistry</a></li> <li><a href="/wiki/Ocean_chemistry" class="mw-redirect" title="Ocean chemistry">Ocean chemistry</a></li></ul></li> <li><a href="/wiki/Clay_chemistry" title="Clay chemistry">Clay chemistry</a></li> <li><a href="/wiki/Carbochemistry" title="Carbochemistry">Carbochemistry</a></li> <li><a href="/wiki/Food_chemistry" title="Food chemistry">Food chemistry</a> <ul><li><a href="/wiki/Carbohydrate_chemistry" class="mw-redirect" title="Carbohydrate chemistry">Carbohydrate chemistry</a></li> <li><a href="/wiki/Food_physical_chemistry" title="Food physical chemistry">Food physical chemistry</a></li></ul></li> <li><a href="/wiki/Agricultural_chemistry" title="Agricultural chemistry">Agricultural chemistry</a> <ul><li><a href="/wiki/Soil_chemistry" title="Soil chemistry">Soil chemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Chemistry_education" title="Chemistry education">Chemistry education</a> <ul><li><a href="/wiki/Amateur_chemistry" title="Amateur chemistry">Amateur chemistry</a></li> <li><a href="/wiki/General_chemistry" title="General chemistry">General chemistry</a></li></ul></li> <li><a href="/wiki/Clandestine_chemistry" title="Clandestine chemistry">Clandestine chemistry</a></li> <li><a href="/wiki/Forensic_chemistry" title="Forensic chemistry">Forensic chemistry</a> <ul><li><a href="/wiki/Forensic_toxicology" title="Forensic toxicology">Forensic toxicology</a></li> <li><a href="/wiki/Post-mortem_chemistry" title="Post-mortem chemistry">Post-mortem chemistry</a></li></ul></li></ul> <ul><li><a href="/wiki/Nanochemistry" title="Nanochemistry">Nanochemistry</a> <ul><li><a href="/wiki/Supramolecular_chemistry" title="Supramolecular chemistry">Supramolecular chemistry</a></li></ul></li> <li><a href="/wiki/Chemical_synthesis" title="Chemical synthesis">Chemical synthesis</a> <ul><li><a href="/wiki/Green_chemistry" title="Green chemistry">Green chemistry</a></li> <li><a href="/wiki/Click_chemistry" title="Click chemistry">Click chemistry</a></li> <li><a href="/wiki/Combinatorial_chemistry" title="Combinatorial chemistry">Combinatorial chemistry</a></li> <li><a href="/wiki/Biosynthesis" title="Biosynthesis">Biosynthesis</a></li></ul></li> <li><a href="/wiki/Chemical_engineering" title="Chemical engineering">Chemical engineering</a> <ul><li><a href="/wiki/Stoichiometry" title="Stoichiometry">Stoichiometry</a></li></ul></li> <li><a href="/wiki/Materials_science" title="Materials science">Materials science</a> <ul><li><a href="/wiki/Metallurgy" title="Metallurgy">Metallurgy</a></li> <li><a href="/wiki/Ceramic_engineering" title="Ceramic engineering">Ceramic engineering</a></li> <li><a href="/wiki/Polymer_science" title="Polymer science">Polymer science</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_chemistry" title="History of chemistry">History of chemistry</a></li> <li><a href="/wiki/Nobel_Prize_in_Chemistry" title="Nobel Prize in Chemistry">Nobel Prize in Chemistry</a></li> <li><a href="/wiki/Timeline_of_chemistry" title="Timeline of chemistry">Timeline of chemistry</a> <ul><li><a href="/wiki/Discovery_of_chemical_elements" title="Discovery of chemical elements">of element discoveries</a></li></ul></li> <li>"<a href="/wiki/The_central_science" title="The central science">The central science</a>"</li> <li><a href="/wiki/Chemical_reaction" title="Chemical reaction">Chemical reaction</a> <ul><li><a href="/wiki/Catalysis" title="Catalysis">Catalysis</a></li></ul></li> <li><a href="/wiki/Chemical_element" title="Chemical element">Chemical element</a></li> <li><a href="/wiki/Chemical_compound" title="Chemical compound">Chemical compound</a></li> <li><a href="/wiki/Atom" title="Atom">Atom</a></li> <li><a href="/wiki/Molecule" title="Molecule">Molecule</a></li> <li><a href="/wiki/Ion" title="Ion">Ion</a></li> <li><a href="/wiki/Chemical_substance" title="Chemical substance">Chemical substance</a></li> <li><a href="/wiki/Chemical_bond" title="Chemical bond">Chemical bond</a></li> <li><a href="/wiki/Alchemy" title="Alchemy">Alchemy</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Chemistry" title="Category:Chemistry">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Chemistry" class="extiw" title="commons:Category:Chemistry">Commons</a></b></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span> <b><a href="/wiki/Portal:Chemistry" title="Portal:Chemistry">Portal</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span> <b><a href="/wiki/Wikipedia:WikiProject_Chemistry" title="Wikipedia:WikiProject Chemistry">WikiProject</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Chemical_engineering_topics321" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" 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topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">History</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_chemical_engineering" title="History of chemical engineering">History of chemical engineering</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:TASNEE_001.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/TASNEE_001.jpg/170px-TASNEE_001.jpg" decoding="async" width="170" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/TASNEE_001.jpg/255px-TASNEE_001.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/TASNEE_001.jpg/340px-TASNEE_001.jpg 2x" data-file-width="2000" data-file-height="1333" /></a></span></div></td></tr><tr><th scope="row" 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