Stoichiometry - Wikipedia

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<span>Definition</span> </div> </a> <ul id="toc-Definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Converting_grams_to_moles" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Converting_grams_to_moles"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Converting grams to moles</span> </div> </a> <ul id="toc-Converting_grams_to_moles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Molar_proportion" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Molar_proportion"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Molar proportion</span> </div> </a> <ul id="toc-Molar_proportion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Determining_amount_of_product" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Determining_amount_of_product"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Determining amount of product</span> </div> </a> <button aria-controls="toc-Determining_amount_of_product-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 Determining amount of product subsection</span> </button> <ul id="toc-Determining_amount_of_product-sublist" class="vector-toc-list"> <li id="toc-Further_examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Further_examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Further examples</span> </div> </a> <ul id="toc-Further_examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Stoichiometric_ratio" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stoichiometric_ratio"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Stoichiometric ratio</span> </div> </a> <ul id="toc-Stoichiometric_ratio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limiting_reagent_and_percent_yield" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limiting_reagent_and_percent_yield"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Limiting reagent and percent yield</span> </div> </a> <button aria-controls="toc-Limiting_reagent_and_percent_yield-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 Limiting reagent and percent yield subsection</span> </button> <ul id="toc-Limiting_reagent_and_percent_yield-sublist" class="vector-toc-list"> <li id="toc-Example" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Example</span> </div> </a> <ul id="toc-Example-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Different_stoichiometries_in_competing_reactions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Different_stoichiometries_in_competing_reactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Different stoichiometries in competing reactions</span> </div> </a> <ul id="toc-Different_stoichiometries_in_competing_reactions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stoichiometric_coefficient_and_stoichiometric_number" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stoichiometric_coefficient_and_stoichiometric_number"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Stoichiometric coefficient and stoichiometric number</span> </div> </a> <ul id="toc-Stoichiometric_coefficient_and_stoichiometric_number-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stoichiometry_matrix" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stoichiometry_matrix"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Stoichiometry matrix</span> </div> </a> <ul id="toc-Stoichiometry_matrix-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gas_stoichiometry" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gas_stoichiometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Gas stoichiometry</span> </div> </a> <ul id="toc-Gas_stoichiometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stoichiometric_air-to-fuel_ratios_of_common_fuels" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stoichiometric_air-to-fuel_ratios_of_common_fuels"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Stoichiometric air-to-fuel ratios of common fuels</span> </div> </a> <ul id="toc-Stoichiometric_air-to-fuel_ratios_of_common_fuels-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</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">14</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">15</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" > <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">Stoichiometry</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 54 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-54" 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">54 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/Stoigiometrie" title="Stoigiometrie – Afrikaans" lang="af" hreflang="af" data-title="Stoigiometrie" 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%AA%D9%83%D8%A7%D9%81%D8%A4_%D8%AA%D8%B1%D8%A7%D8%A8%D8%B7_%D8%A7%D9%84%D8%B9%D9%86%D8%A7%D8%B5%D8%B1" title="تكافؤ ترابط العناصر – Arabic" lang="ar" hreflang="ar" data-title="تكافؤ ترابط العناصر" 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/Estequiometr%C3%ADa" title="Estequiometría – Asturian" lang="ast" hreflang="ast" data-title="Estequiometría" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D1%8D%D1%85%D1%96%D1%8F%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Стэхіяметрыя – Belarusian" lang="be" hreflang="be" data-title="Стэхіяметрыя" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%85%D0%B8%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стехиометрия – Bulgarian" lang="bg" hreflang="bg" data-title="Стехиометрия" 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/Stehiometrija" title="Stehiometrija – Bosnian" lang="bs" hreflang="bs" data-title="Stehiometrija" 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/Estequiometria" title="Estequiometria – Catalan" lang="ca" hreflang="ca" data-title="Estequiometria" 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/Stechiometrie" title="Stechiometrie – Czech" lang="cs" hreflang="cs" data-title="Stechiometrie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/St%C3%B8kiometri" title="Støkiometri – Danish" lang="da" hreflang="da" data-title="Støkiometri" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/St%C3%B6chiometrie" title="Stöchiometrie – German" lang="de" hreflang="de" data-title="Stöchiometrie" 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/St%C3%B6hhiomeetria" title="Stöhhiomeetria – Estonian" lang="et" hreflang="et" data-title="Stöhhiomeetria" 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%A3%CF%84%CE%BF%CE%B9%CF%87%CE%B5%CE%B9%CE%BF%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Στοιχειομετρία – Greek" lang="el" hreflang="el" data-title="Στοιχειομετρία" 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/Estequiometr%C3%ADa" title="Estequiometría – Spanish" lang="es" hreflang="es" data-title="Estequiometría" 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/Stekiometrio" title="Stekiometrio – Esperanto" lang="eo" hreflang="eo" data-title="Stekiometrio" 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/Estekiometria" title="Estekiometria – Basque" lang="eu" hreflang="eu" data-title="Estekiometria" 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%A7%D8%B3%D8%AA%D9%88%DA%A9%DB%8C%D9%88%D9%85%D8%AA%D8%B1%DB%8C" title="استوکیومتری – Persian" lang="fa" hreflang="fa" data-title="استوکیومتری" 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/St%C5%93chiom%C3%A9trie" title="Stœchiométrie – French" lang="fr" hreflang="fr" data-title="Stœchiométrie" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/St%C3%B3caim%C3%A9adracht" title="Stócaiméadracht – Irish" lang="ga" hreflang="ga" data-title="Stócaiméadracht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</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%9F%89%EB%A1%A0" title="화학량론 – Korean" lang="ko" hreflang="ko" data-title="화학량론" 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%8D%D5%BF%D5%A5%D5%AD%D5%AB%D5%B8%D5%B4%D5%A5%D5%BF%D6%80%D5%AB%D5%A1" title="Ստեխիոմետրիա – Armenian" lang="hy" hreflang="hy" data-title="Ստեխիոմետրիա" 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%B8%E0%A4%B8%E0%A4%AE%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="रससमीकरणमिति – Hindi" lang="hi" hreflang="hi" data-title="रससमीकरणमिति" 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/Stehiometrija" title="Stehiometrija – Croatian" lang="hr" hreflang="hr" data-title="Stehiometrija" 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/Stoikiometri" title="Stoikiometri – Indonesian" lang="id" hreflang="id" data-title="Stoikiometri" 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/Stechiometria" title="Stechiometria – Italian" lang="it" hreflang="it" data-title="Stechiometria" 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%A1%D7%98%D7%95%D7%99%D7%9B%D7%99%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="סטויכיומטריה – Hebrew" lang="he" hreflang="he" data-title="סטויכיומטריה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%85%D0%B8%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стехиометрия – Kazakh" lang="kk" hreflang="kk" data-title="Стехиометрия" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Estekyometri" title="Estekyometri – Haitian Creole" lang="ht" hreflang="ht" data-title="Estekyometri" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%85%D0%B8%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стехиометрия – Kyrgyz" lang="ky" hreflang="ky" data-title="Стехиометрия" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Stehiometrija" title="Stehiometrija – Latvian" lang="lv" hreflang="lv" data-title="Stehiometrija" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Szt%C3%B6chiometria" title="Sztöchiometria – Hungarian" lang="hu" hreflang="hu" data-title="Sztöchiometria" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B5%8D%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%8B%E0%B4%AF%E0%B5%8D%E0%B4%95%E0%B5%8D%E0%B4%AF%E0%B5%8B%E0%B4%AE%E0%B5%86%E0%B4%9F%E0%B5%8D%E0%B4%B0%E0%B4%BF" title="സ്റ്റോയ്ക്യോമെട്രി – Malayalam" lang="ml" hreflang="ml" data-title="സ്റ്റോയ്ക്യോമെട്രി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Stoikiometri" title="Stoikiometri – Malay" lang="ms" hreflang="ms" data-title="Stoikiometri" 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%A1%D1%82%D0%B5%D1%85%D0%B8%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Стехиометр – Mongolian" lang="mn" hreflang="mn" data-title="Стехиометр" 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/Stoichiometrie" title="Stoichiometrie – Dutch" lang="nl" hreflang="nl" data-title="Stoichiometrie" 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%8C%96%E5%AD%A6%E9%87%8F%E8%AB%96" title="化学量論 – Japanese" lang="ja" hreflang="ja" data-title="化学量論" 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/St%C3%B8kiometri" title="Støkiometri – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Støkiometri" 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-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B3%D9%B9%D9%88%D8%A6%DB%8C%DA%A9%DB%8C%D9%88%D9%85%DB%8C%D9%B9%D8%B1%DB%8C" title="سٹوئیکیومیٹری – Western Punjabi" lang="pnb" hreflang="pnb" data-title="سٹوئیکیومیٹری" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Stechiometria" title="Stechiometria – Polish" lang="pl" hreflang="pl" data-title="Stechiometria" 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/Estequiometria" title="Estequiometria – Portuguese" lang="pt" hreflang="pt" data-title="Estequiometria" 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/Stoechiometrie" title="Stoechiometrie – Romanian" lang="ro" hreflang="ro" data-title="Stoechiometrie" 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%A1%D1%82%D0%B5%D1%85%D0%B8%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стехиометрия – Russian" lang="ru" hreflang="ru" data-title="Стехиометрия" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Stekiometria" title="Stekiometria – Albanian" lang="sq" hreflang="sq" data-title="Stekiometria" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Stoichiometry" title="Stoichiometry – Simple English" lang="en-simple" hreflang="en-simple" data-title="Stoichiometry" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Stehiometrija" title="Stehiometrija – Slovenian" lang="sl" hreflang="sl" data-title="Stehiometrija" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%85%D0%B8%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Стехиометрија – Serbian" lang="sr" hreflang="sr" data-title="Стехиометрија" 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/Stehiometrija" title="Stehiometrija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Stehiometrija" 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/Stoikiometria" title="Stoikiometria – Finnish" lang="fi" hreflang="fi" data-title="Stoikiometria" 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/St%C3%B6kiometri" title="Stökiometri – Swedish" lang="sv" hreflang="sv" data-title="Stökiometri" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B8%E0%B1%8D%E0%B0%9F%E0%B0%BE%E0%B0%AF%E0%B0%BF%E0%B0%95%E0%B0%BF%E0%B0%AF%E0%B1%8B%E0%B0%AE%E0%B1%86%E0%B0%9F%E0%B1%8D%E0%B0%B0%E0%B1%80" title="స్టాయికియోమెట్రీ – Telugu" lang="te" hreflang="te" data-title="స్టాయికియోమెట్రీ" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Stokiyometri" title="Stokiyometri – Turkish" lang="tr" hreflang="tr" data-title="Stokiyometri" 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%A1%D1%82%D0%B5%D1%85%D1%96%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Стехіометрія – Ukrainian" lang="uk" hreflang="uk" data-title="Стехіометрія" 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/%D8%B9%D9%86%D8%B5%D8%B1_%D9%BE%DB%8C%D9%85%D8%A7%D8%A6%DB%8C" title="عنصر پیمائی – Urdu" lang="ur" hreflang="ur" data-title="عنصر پیمائی" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</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%E8%A8%88%E9%87%8F%E6%95%B8" title="化學計量數 – Cantonese" lang="yue" hreflang="yue" data-title="化學計量數" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8C%96%E5%AD%A6%E8%AE%A1%E9%87%8F" title="化学计量 – Chinese" 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Calculation of relative weights of reactants and products in chemical reactions</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Combustion_reaction_of_methane.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Combustion_reaction_of_methane.jpg/400px-Combustion_reaction_of_methane.jpg" decoding="async" width="400" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Combustion_reaction_of_methane.jpg/600px-Combustion_reaction_of_methane.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Combustion_reaction_of_methane.jpg/800px-Combustion_reaction_of_methane.jpg 2x" data-file-width="1009" data-file-height="451" /></a><figcaption>A stoichiometric diagram of the <a href="/wiki/Combustion" title="Combustion">combustion</a> reaction of <a href="/wiki/Methane" title="Methane">methane</a></figcaption></figure> <p><b>Stoichiometry</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˌ/: secondary stress follows">ˌ</span><span title="'s' in 'sigh'">s</span><span title="'t' in 'tie'">t</span><span title="/ɔɪ/: 'oi' in 'choice'">ɔɪ</span><span title="'k' in 'kind'">k</span><span title="/i/: 'y' in 'happy'">i</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ɒ/: 'o' in 'body'">ɒ</span><span title="'m' in 'my'">m</span><span title="/ɪ/: 'i' in 'kit'">ɪ</span><span title="'t' in 'tie'">t</span><span title="'r' in 'rye'">r</span><span title="/i/: 'y' in 'happy'">i</span></span>/</a></span></span>) is the relationships among the weights of <a href="/wiki/Reactant" class="mw-redirect" title="Reactant">reactants</a> and <a href="/wiki/Product_(chemistry)" title="Product (chemistry)">products</a> before, during, and following <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a>. </p><p>Stoichiometry is founded on the <a href="/wiki/Law_of_conservation_of_mass" class="mw-redirect" title="Law of conservation of mass">law of conservation of mass</a> where the total mass of the reactants equals the total mass of the products, leading to the insight that the relations among quantities of reactants and products typically form a ratio of positive integers. This means that if the amounts of the separate reactants are known, then the amount of the product can be calculated. Conversely, if one reactant has a known quantity and the quantity of the products can be empirically determined, then the amount of the other reactants can also be calculated. </p><p>This is illustrated in the image here, where the balanced equation is: </p> <dl><dd><style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style><span class="chemf nowrap">CH<sub class="template-chem2-sub">4</sub> + 2 O<sub class="template-chem2-sub">2</sub> → CO<sub class="template-chem2-sub">2</sub> + 2 H<sub class="template-chem2-sub">2</sub>O</span></dd></dl> <p>Here, one <a href="/wiki/Molecule" title="Molecule">molecule</a> of <a href="/wiki/Methane" title="Methane">methane</a> reacts with two molecules of <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> gas to yield one molecule of <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a> and two molecules of <a href="/wiki/Properties_of_water" title="Properties of water">water</a>. This particular chemical equation is an example of <a href="/wiki/Combustion#Complete" title="Combustion">complete combustion</a>. Stoichiometry measures these quantitative relationships, and is used to determine the amount of products and reactants that are produced or needed in a given reaction. Describing the quantitative relationships among substances as they participate in chemical reactions is known as <i>reaction stoichiometry</i>. In the example above, reaction stoichiometry measures the relationship between the quantities of methane and oxygen that react to form carbon dioxide and water. </p><p>Because of the well known relationship of <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a> to <a href="/wiki/Relative_atomic_mass" title="Relative atomic mass">atomic weights</a>, the ratios that are arrived at by stoichiometry can be used to determine quantities by weight in a reaction described by a balanced equation. This is called <i>composition stoichiometry</i>. </p><p><i>Gas stoichiometry</i> deals with reactions involving gases, where the gases are at a known temperature, pressure, and volume and can be assumed to be <a href="/wiki/Ideal_gas" title="Ideal gas">ideal gases</a>. For gases, the volume ratio is ideally the same by the <a href="/wiki/Ideal_gas_law" title="Ideal gas law">ideal gas law</a>, but the mass ratio of a single reaction has to be calculated from the <a href="/wiki/Molecular_mass" title="Molecular mass">molecular masses</a> of the reactants and products. In practice, because of the existence of <a href="/wiki/Isotope" title="Isotope">isotopes</a>, <a href="/wiki/Molar_mass" title="Molar mass">molar masses</a> are used instead in calculating the mass ratio. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=1" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term <i>stoichiometry</i> was first used by <a href="/wiki/Jeremias_Benjamin_Richter" title="Jeremias Benjamin Richter">Jeremias Benjamin Richter</a> in 1792 when the first volume of Richter's <span title="German-language text"><i lang="de">Anfangsgründe der Stöchyometrie oder Meßkunst chymischer Elemente</i></span> (<i>Fundamentals of Stoichiometry, or the Art of Measuring the Chemical Elements</i>) was published.<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> The term is derived from the <a href="/wiki/Ancient_Greek" title="Ancient Greek">Ancient Greek</a> words <span lang="grc"><a href="https://en.wiktionary.org/wiki/%CF%83%CF%84%CE%BF%CE%B9%CF%87%CE%B5%E1%BF%96%CE%BF%CE%BD#Ancient_Greek" class="extiw" title="wikt:στοιχεῖον">στοιχεῖον</a></span> <span title="Ancient Greek (to 1453)-language romanization"><i lang="grc-Latn">stoikheîon</i></span> "element"<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and <span lang="grc"><a href="https://en.wiktionary.org/wiki/%CE%BC%CE%AD%CF%84%CF%81%CE%BF%CE%BD#Ancient_Greek" class="extiw" title="wikt:μέτρον">μέτρον</a></span> <span title="Ancient Greek (to 1453)-language romanization"><i lang="grc-Latn">métron</i></span> "measure". L. Darmstaedter and <a href="/wiki/Ralph_E._Oesper" title="Ralph E. Oesper">Ralph E. Oesper</a> has written a useful account on this.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=2" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Amount_of_substance" title="Amount of substance">Amount of substance</a></div> <p>A <b>stoichiometric amount</b><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> or <b>stoichiometric ratio</b> of a <a href="/wiki/Reagent" title="Reagent">reagent</a> is the optimum amount or ratio where, assuming that the reaction proceeds to completion: </p> <ol><li>All of the reagent is consumed</li> <li>There is no deficiency of the reagent</li> <li>There is no excess of the reagent.</li></ol> <p>Stoichiometry rests upon the very basic laws that help to understand it better, i.e., <a href="/wiki/Law_of_conservation_of_mass" class="mw-redirect" title="Law of conservation of mass">law of conservation of mass</a>, the <a href="/wiki/Law_of_definite_proportions" title="Law of definite proportions">law of definite proportions</a> (i.e., the <a href="/wiki/Law_of_constant_composition" class="mw-redirect" title="Law of constant composition">law of constant composition</a>), the <a href="/wiki/Law_of_multiple_proportions" title="Law of multiple proportions">law of multiple proportions</a> and the <a href="/wiki/Law_of_reciprocal_proportions" title="Law of reciprocal proportions">law of reciprocal proportions</a>. In general, chemical reactions combine in definite ratios of chemicals. Since chemical reactions can neither create nor destroy matter, nor <a href="/wiki/Nuclear_transmutation" title="Nuclear transmutation">transmute</a> one element into another, the amount of each element must be the same throughout the overall reaction. For example, the number of atoms of a given element X on the reactant side must equal the number of atoms of that element on the product side, whether or not all of those atoms are actually involved in a reaction.<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> </p><p>Chemical reactions, as macroscopic unit operations, consist of simply a very large number of <a href="/wiki/Elementary_reaction" title="Elementary reaction">elementary reactions</a>, where a single molecule reacts with another molecule. As the reacting molecules (or moieties) consist of a definite set of atoms in an integer ratio, the ratio between reactants in a complete reaction is also in integer ratio. A reaction may consume more than one molecule, and the <b>stoichiometric number</b> counts this number, defined as positive for products (added) and negative for reactants (removed).<sup id="cite_ref-GoldBookS06025_6-0" class="reference"><a href="#cite_note-GoldBookS06025-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The unsigned coefficients are generally referred to as the <b>stoichiometric coefficients</b>.<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> </p><p>Each element has an <a href="/wiki/Atomic_mass" title="Atomic mass">atomic mass</a>, and considering molecules as collections of atoms, compounds have a definite <a href="/wiki/Molecular_mass" title="Molecular mass">molecular mass</a>, which when expressed in daltons is numerically equal to the <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a> in <a href="/wiki/Gram" title="Gram">g</a>/<a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>. By definition, the atomic mass of <a href="/wiki/Carbon-12" title="Carbon-12">carbon-12</a> is 12 <a href="/wiki/Dalton_(unit)" title="Dalton (unit)">Da</a>, giving a molar mass of 12 g/mol. The number of molecules per mole in a substance is given by the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>, exactly <span class="nowrap"><span data-sort-value="7023602214076000000♠"></span>6.022<span style="margin-left:.25em;">140</span><span style="margin-left:.25em;">76</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>23</sup> mol<sup>−1</sup></span> since the <a href="/wiki/2019_revision_of_the_SI" title="2019 revision of the SI">2019 revision of the SI</a>. Thus, to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction. The mass ratios can be calculated by dividing each by the total in the whole reaction. </p><p>Elements in their natural state are mixtures of <a href="/wiki/Isotope" title="Isotope">isotopes</a> of differing mass; thus, <a href="/wiki/Atomic_mass" title="Atomic mass">atomic masses</a> and thus molar masses are not exactly integers. For instance, instead of an exact 14:3 proportion, 17.04 g of ammonia consists of 14.01 g of nitrogen and 3 × 1.01 g of hydrogen, because natural nitrogen includes a small amount of nitrogen-15, and natural hydrogen includes hydrogen-2 (<a href="/wiki/Deuterium" title="Deuterium">deuterium</a>). </p><p>A <b>stoichiometric reactant</b> is a reactant that is consumed in a reaction, as opposed to a <a href="/wiki/Catalysis" title="Catalysis">catalytic reactant</a>, which is not consumed in the overall reaction because it reacts in one step and is regenerated in another step. </p> <div class="mw-heading mw-heading2"><h2 id="Converting_grams_to_moles">Converting grams to moles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=3" title="Edit section: Converting grams to moles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Stoichiometry is not only used to balance chemical equations but also used in conversions, i.e., converting from grams to moles using <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a> as the conversion factor, or from grams to milliliters using <a href="/wiki/Density" title="Density">density</a>. For example, to find the <a href="/wiki/Amount_of_substance" title="Amount of substance">amount</a> of NaCl (sodium chloride) in 2.00 g, one would do the following: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {2.00{\mbox{ g NaCl}}}{58.44{\mbox{ g NaCl mol}}^{-1}}}=0.0342\ {\text{mol}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2.00</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g NaCl</mtext> </mstyle> </mrow> </mrow> <mrow> <mn>58.44</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g NaCl mol</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0.0342</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>mol</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2.00{\mbox{ g NaCl}}}{58.44{\mbox{ g NaCl mol}}^{-1}}}=0.0342\ {\text{mol}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4e84333c745aeeda76409b73a38f8f09aea7f5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:34.229ex; height:6.343ex;" alt="{\displaystyle {\frac {2.00{\mbox{ g NaCl}}}{58.44{\mbox{ g NaCl mol}}^{-1}}}=0.0342\ {\text{mol}}}"></span></dd></dl> <p>In the above example, when written out in fraction form, the units of grams form a multiplicative identity, which is equivalent to one (g/g = 1), with the resulting amount in moles (the unit that was needed), as shown in the following equation, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {2.00{\mbox{ g NaCl}}}{1}}\right)\left({\frac {1{\mbox{ mol NaCl}}}{58.44{\mbox{ g NaCl}}}}\right)=0.0342\ {\text{mol}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2.00</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g NaCl</mtext> </mstyle> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol NaCl</mtext> </mstyle> </mrow> </mrow> <mrow> <mn>58.44</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g NaCl</mtext> </mstyle> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.0342</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>mol</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {2.00{\mbox{ g NaCl}}}{1}}\right)\left({\frac {1{\mbox{ mol NaCl}}}{58.44{\mbox{ g NaCl}}}}\right)=0.0342\ {\text{mol}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f737136d2070c7da1847bcbaa8823f913bb0a9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:47.324ex; height:6.176ex;" alt="{\displaystyle \left({\frac {2.00{\mbox{ g NaCl}}}{1}}\right)\left({\frac {1{\mbox{ mol NaCl}}}{58.44{\mbox{ g NaCl}}}}\right)=0.0342\ {\text{mol}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Molar_proportion">Molar proportion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=4" title="Edit section: Molar proportion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Stoichiometry is often used to balance chemical equations (reaction stoichiometry). For example, the two <a href="/wiki/Diatomic_molecule" title="Diatomic molecule">diatomic</a> gases, <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> and <a href="/wiki/Oxygen" title="Oxygen">oxygen</a>, can combine to form a liquid, water, in an <a href="/wiki/Exothermic_reaction" title="Exothermic reaction">exothermic reaction</a>, as described by the following equation: </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 H<sub class="template-chem2-sub">2</sub> + O<sub class="template-chem2-sub">2</sub> → 2 H<sub class="template-chem2-sub">2</sub>O</span></dd></dl> <p>Reaction stoichiometry describes the 2:1:2 ratio of hydrogen, oxygen, and water molecules in the above equation. </p><p>The molar ratio allows for conversion between moles of one substance and moles of another. For example, in the reaction </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 CH<sub class="template-chem2-sub">3</sub>OH + 3 O<sub class="template-chem2-sub">2</sub> → 2 CO<sub class="template-chem2-sub">2</sub> + 4 H<sub class="template-chem2-sub">2</sub>O</span></dd></dl> <p>the amount of water that will be produced by the combustion of 0.27 moles of <span class="chemf nowrap">CH<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span>OH</span> is obtained using the molar ratio between <span class="chemf nowrap">CH<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span>OH</span> and <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> of 2 to 4. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {0.27{\mbox{ mol }}\mathrm {CH_{3}OH} }{1}}\right)\left({\frac {4{\mbox{ mol }}\mathrm {H_{2}O} }{2{\mbox{ mol }}\mathrm {CH_{3}OH} }}\right)=0.54\ {\text{mol }}\mathrm {H_{2}O} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.27</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> <mi mathvariant="normal">H</mi> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> <mi mathvariant="normal">H</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.54</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>mol </mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {0.27{\mbox{ mol }}\mathrm {CH_{3}OH} }{1}}\right)\left({\frac {4{\mbox{ mol }}\mathrm {H_{2}O} }{2{\mbox{ mol }}\mathrm {CH_{3}OH} }}\right)=0.54\ {\text{mol }}\mathrm {H_{2}O} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b59824ae1352347e5e870e1566d49f3ac8d26f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:56.809ex; height:6.176ex;" alt="{\displaystyle \left({\frac {0.27{\mbox{ mol }}\mathrm {CH_{3}OH} }{1}}\right)\left({\frac {4{\mbox{ mol }}\mathrm {H_{2}O} }{2{\mbox{ mol }}\mathrm {CH_{3}OH} }}\right)=0.54\ {\text{mol }}\mathrm {H_{2}O} }"></span></dd></dl> <p>The term stoichiometry is also often used for the <a href="/wiki/Mole_(unit)" title="Mole (unit)">molar</a> proportions of elements in stoichiometric compounds (composition stoichiometry). For example, the stoichiometry of hydrogen and oxygen in <span class="chemf nowrap">H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>O</span> is 2:1. In stoichiometric compounds, the molar proportions are whole numbers. </p> <div class="mw-heading mw-heading2"><h2 id="Determining_amount_of_product">Determining amount of product</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=5" title="Edit section: Determining amount of product"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Stoichiometry can also be used to find the quantity of a product yielded by a reaction. If a piece of solid <a href="/wiki/Copper" title="Copper">copper</a> (Cu) were added to an aqueous solution of <a href="/wiki/Silver_nitrate" title="Silver nitrate">silver nitrate</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">AgNO<sub class="template-chem2-sub">3</sub></span>), the <a href="/wiki/Silver" title="Silver">silver</a> (Ag) would be replaced in a <a href="/wiki/Single_displacement_reaction" title="Single displacement reaction">single displacement reaction</a> forming aqueous <a href="/wiki/Copper(II)_nitrate" title="Copper(II) nitrate">copper(II) nitrate</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Cu(NO<sub class="template-chem2-sub">3</sub>)<sub class="template-chem2-sub">2</sub></span>) and solid silver. How much silver is produced if 16.00 grams of Cu is added to the solution of excess silver nitrate? </p><p>The following steps would be used: </p> <ol><li>Write and balance the equation</li> <li>Mass to moles: Convert grams of Cu to moles of Cu</li> <li>Mole ratio: Convert moles of Cu to moles of Ag produced</li> <li>Mole to mass: Convert moles of Ag to grams of Ag produced</li></ol> <p>The complete balanced equation would be: </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Cu + 2 AgNO<sub class="template-chem2-sub">3</sub> → Cu(NO<sub class="template-chem2-sub">3</sub>)<sub class="template-chem2-sub">2</sub> + 2 Ag</span></dd></dl> <p>For the mass to mole step, the mass of copper (16.00 g) would be converted to moles of copper by dividing the mass of copper by its <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a>: 63.55 g/mol. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {16.00{\mbox{ g Cu}}}{1}}\right)\left({\frac {1{\mbox{ mol Cu}}}{63.55{\mbox{ g Cu}}}}\right)=0.2518\ {\text{mol Cu}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>16.00</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g Cu</mtext> </mstyle> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Cu</mtext> </mstyle> </mrow> </mrow> <mrow> <mn>63.55</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g Cu</mtext> </mstyle> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.2518</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>mol Cu</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {16.00{\mbox{ g Cu}}}{1}}\right)\left({\frac {1{\mbox{ mol Cu}}}{63.55{\mbox{ g Cu}}}}\right)=0.2518\ {\text{mol Cu}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9ce4a29b4b1dbfab4012ba02048c3ba918df8c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:47.518ex; height:6.176ex;" alt="{\displaystyle \left({\frac {16.00{\mbox{ g Cu}}}{1}}\right)\left({\frac {1{\mbox{ mol Cu}}}{63.55{\mbox{ g Cu}}}}\right)=0.2518\ {\text{mol Cu}}}"></span></dd></dl> <p>Now that the amount of Cu in moles (0.2518) is found, we can set up the mole ratio. This is found by looking at the coefficients in the balanced equation: Cu and Ag are in a 1:2 ratio. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {0.2518{\mbox{ mol Cu}}}{1}}\right)\left({\frac {2{\mbox{ mol Ag}}}{1{\mbox{ mol Cu}}}}\right)=0.5036\ {\text{mol Ag}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.2518</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Cu</mtext> </mstyle> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Ag</mtext> </mstyle> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Cu</mtext> </mstyle> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.5036</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>mol Ag</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {0.2518{\mbox{ mol Cu}}}{1}}\right)\left({\frac {2{\mbox{ mol Ag}}}{1{\mbox{ mol Cu}}}}\right)=0.5036\ {\text{mol Ag}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7627d279b9b04ca258e0874b8e392ce1e708de3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:49.647ex; height:6.176ex;" alt="{\displaystyle \left({\frac {0.2518{\mbox{ mol Cu}}}{1}}\right)\left({\frac {2{\mbox{ mol Ag}}}{1{\mbox{ mol Cu}}}}\right)=0.5036\ {\text{mol Ag}}}"></span></dd></dl> <p>Now that the moles of Ag produced is known to be 0.5036 mol, we convert this amount to grams of Ag produced to come to the final answer: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {0.5036{\mbox{ mol Ag}}}{1}}\right)\left({\frac {107.87{\mbox{ g Ag}}}{1{\mbox{ mol Ag}}}}\right)=54.32\ {\text{g Ag}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.5036</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Ag</mtext> </mstyle> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>107.87</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g Ag</mtext> </mstyle> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Ag</mtext> </mstyle> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>54.32</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>g Ag</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {0.5036{\mbox{ mol Ag}}}{1}}\right)\left({\frac {107.87{\mbox{ g Ag}}}{1{\mbox{ mol Ag}}}}\right)=54.32\ {\text{g Ag}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c15290aebadc62848f54dd495688682bd24a54c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:48.486ex; height:6.176ex;" alt="{\displaystyle \left({\frac {0.5036{\mbox{ mol Ag}}}{1}}\right)\left({\frac {107.87{\mbox{ g Ag}}}{1{\mbox{ mol Ag}}}}\right)=54.32\ {\text{g Ag}}}"></span></dd></dl> <p>This set of calculations can be further condensed into a single step: </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 m_{\mathrm {Ag} }=\left({\frac {16.00{\mbox{ g }}\mathrm {Cu} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {Cu} }{63.55{\mbox{ g }}\mathrm {Cu} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {Ag} }{1{\mbox{ mol }}\mathrm {Cu} }}\right)\left({\frac {107.87{\mbox{ g }}\mathrm {Ag} }{1{\mbox{ mol Ag}}}}\right)=54.32{\mbox{ g}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>16.00</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> <mrow> <mn>63.55</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">g</mi> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>107.87</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">g</mi> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Ag</mtext> </mstyle> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>54.32</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\mathrm {Ag} }=\left({\frac {16.00{\mbox{ g }}\mathrm {Cu} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {Cu} }{63.55{\mbox{ g }}\mathrm {Cu} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {Ag} }{1{\mbox{ mol }}\mathrm {Cu} }}\right)\left({\frac {107.87{\mbox{ g }}\mathrm {Ag} }{1{\mbox{ mol Ag}}}}\right)=54.32{\mbox{ g}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49fadeaf1a58585b4a5ae81d127ac44d9d5b733d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:77.664ex; height:6.176ex;" alt="{\displaystyle m_{\mathrm {Ag} }=\left({\frac {16.00{\mbox{ g }}\mathrm {Cu} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {Cu} }{63.55{\mbox{ g }}\mathrm {Cu} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {Ag} }{1{\mbox{ mol }}\mathrm {Cu} }}\right)\left({\frac {107.87{\mbox{ g }}\mathrm {Ag} }{1{\mbox{ mol Ag}}}}\right)=54.32{\mbox{ g}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Further_examples">Further examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=6" title="Edit section: Further examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For <a href="/wiki/Propane" title="Propane">propane</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">3</sub>H<sub class="template-chem2-sub">8</sub></span>) reacting with <a href="/wiki/Oxygen" title="Oxygen">oxygen gas</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">O<sub class="template-chem2-sub">2</sub></span>), the balanced chemical equation is: </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">3</sub>H<sub class="template-chem2-sub">8</sub> + 5 O<sub class="template-chem2-sub">2</sub> → 3 CO<sub class="template-chem2-sub">2</sub> + 4 H<sub class="template-chem2-sub">2</sub>O</span></dd></dl> <p>The mass of water formed if 120 g of propane (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">3</sub>H<sub class="template-chem2-sub">8</sub></span>) is burned in excess oxygen is then </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 m_{\mathrm {H_{2}O} }=\left({\frac {120.{\mbox{ g }}\mathrm {C_{3}H_{8}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {C_{3}H_{8}} }{44.09{\mbox{ g }}\mathrm {C_{3}H_{8}} }}\right)\left({\frac {4{\mbox{ mol }}\mathrm {H_{2}O} }{1{\mbox{ mol }}\mathrm {C_{3}H_{8}} }}\right)\left({\frac {18.02{\mbox{ g }}\mathrm {H_{2}O} }{1{\mbox{ mol }}\mathrm {H_{2}O} }}\right)=196{\mbox{ g}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>120.</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>44.09</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>18.02</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>196</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\mathrm {H_{2}O} }=\left({\frac {120.{\mbox{ g }}\mathrm {C_{3}H_{8}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {C_{3}H_{8}} }{44.09{\mbox{ g }}\mathrm {C_{3}H_{8}} }}\right)\left({\frac {4{\mbox{ mol }}\mathrm {H_{2}O} }{1{\mbox{ mol }}\mathrm {C_{3}H_{8}} }}\right)\left({\frac {18.02{\mbox{ g }}\mathrm {H_{2}O} }{1{\mbox{ mol }}\mathrm {H_{2}O} }}\right)=196{\mbox{ g}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7068b8687e71f17d98a133a28d777ecbe6ad97f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:84.195ex; height:6.176ex;" alt="{\displaystyle m_{\mathrm {H_{2}O} }=\left({\frac {120.{\mbox{ g }}\mathrm {C_{3}H_{8}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {C_{3}H_{8}} }{44.09{\mbox{ g }}\mathrm {C_{3}H_{8}} }}\right)\left({\frac {4{\mbox{ mol }}\mathrm {H_{2}O} }{1{\mbox{ mol }}\mathrm {C_{3}H_{8}} }}\right)\left({\frac {18.02{\mbox{ g }}\mathrm {H_{2}O} }{1{\mbox{ mol }}\mathrm {H_{2}O} }}\right)=196{\mbox{ g}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Stoichiometric_ratio">Stoichiometric ratio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=7" title="Edit section: Stoichiometric ratio"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Stoichiometry is also used to find the right amount of one <a href="/wiki/Reactant" class="mw-redirect" title="Reactant">reactant</a> to "completely" react with the other reactant in a <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a> – that is, the stoichiometric amounts that would result in no leftover reactants when the reaction takes place. An example is shown below using the <a href="/wiki/Thermite_reaction" class="mw-redirect" title="Thermite reaction">thermite reaction</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. (February 2024)">citation needed</span></a></i>]</sup> </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Fe<sub class="template-chem2-sub">2</sub>O<sub class="template-chem2-sub">3</sub> + 2 Al → Al<sub class="template-chem2-sub">2</sub>O<sub class="template-chem2-sub">3</sub> + 2 Fe</span></dd></dl> <p>This equation shows that 1 mole of <span class="nowrap"><a href="/wiki/Iron(III)_oxide" title="Iron(III) oxide">iron(III) oxide</a></span> and 2 moles of <a href="/wiki/Aluminum" class="mw-redirect" title="Aluminum">aluminum</a> will produce 1 mole of <a href="/wiki/Aluminium_oxide" title="Aluminium oxide">aluminium oxide</a> and 2 moles of <a href="/wiki/Iron" title="Iron">iron</a>. So, to completely react with 85.0 g of <span class="nowrap">iron(III) oxide</span> (0.532 mol), 28.7 g (1.06 mol) of aluminium are needed. </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 m_{\mathrm {Al} }=\left({\frac {85.0{\mbox{ g }}\mathrm {Fe_{2}O_{3}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {Fe_{2}O_{3}} }{159.7{\mbox{ g }}\mathrm {Fe_{2}O_{3}} }}\right)\left({\frac {2{\mbox{ mol Al}}}{1{\mbox{ mol }}\mathrm {Fe_{2}O_{3}} }}\right)\left({\frac {26.98{\mbox{ g Al}}}{1{\mbox{ mol Al}}}}\right)=28.7{\mbox{ g}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>85.0</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <msub> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <msub> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>159.7</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <msub> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Al</mtext> </mstyle> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <msub> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>26.98</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g Al</mtext> </mstyle> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol Al</mtext> </mstyle> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>28.7</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\mathrm {Al} }=\left({\frac {85.0{\mbox{ g }}\mathrm {Fe_{2}O_{3}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {Fe_{2}O_{3}} }{159.7{\mbox{ g }}\mathrm {Fe_{2}O_{3}} }}\right)\left({\frac {2{\mbox{ mol Al}}}{1{\mbox{ mol }}\mathrm {Fe_{2}O_{3}} }}\right)\left({\frac {26.98{\mbox{ g Al}}}{1{\mbox{ mol Al}}}}\right)=28.7{\mbox{ g}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a495811d42a905af5ff2be8296e94071e2e4cced" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:83.785ex; height:6.176ex;" alt="{\displaystyle m_{\mathrm {Al} }=\left({\frac {85.0{\mbox{ g }}\mathrm {Fe_{2}O_{3}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {Fe_{2}O_{3}} }{159.7{\mbox{ g }}\mathrm {Fe_{2}O_{3}} }}\right)\left({\frac {2{\mbox{ mol Al}}}{1{\mbox{ mol }}\mathrm {Fe_{2}O_{3}} }}\right)\left({\frac {26.98{\mbox{ g Al}}}{1{\mbox{ mol Al}}}}\right)=28.7{\mbox{ g}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Limiting_reagent_and_percent_yield">Limiting reagent and percent yield</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=8" title="Edit section: Limiting reagent and percent yield"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Limiting_reagent" title="Limiting reagent">Limiting reagent</a> and <a href="/wiki/Yield_(chemistry)" title="Yield (chemistry)">Yield (chemistry)</a></div> <p>The limiting reagent is the reagent that limits the amount of product that can be formed and is completely consumed when the reaction is complete. An excess reactant is a reactant that is left over once the reaction has stopped due to the limiting reactant being exhausted. </p><p>Consider the equation of roasting <a href="/wiki/Lead(II)_sulfide" title="Lead(II) sulfide">lead(II) sulfide</a> (PbS) in oxygen (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">O<sub class="template-chem2-sub">2</sub></span>) to produce <a href="/wiki/Lead(II)_oxide" title="Lead(II) oxide">lead(II) oxide</a> (PbO) and <a href="/wiki/Sulfur_dioxide" title="Sulfur dioxide">sulfur dioxide</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">SO<sub class="template-chem2-sub">2</sub></span>): </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 PbS + 3 O<sub class="template-chem2-sub">2</sub> → 2 PbO + 2 SO<sub class="template-chem2-sub">2</sub></span></dd></dl> <p>To determine the theoretical yield of lead(II) oxide if 200.0 g of lead(II) sulfide and 200.0 g of oxygen are heated in an open container: </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 m_{\mathrm {PbO} }=\left({\frac {200.0{\mbox{ g }}\mathrm {PbS} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {PbS} }{239.27{\mbox{ g }}\mathrm {PbS} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {PbO} }{2{\mbox{ mol }}\mathrm {PbS} }}\right)\left({\frac {223.2{\mbox{ g }}\mathrm {PbO} }{1{\mbox{ mol }}\mathrm {PbO} }}\right)=186.6{\mbox{ g}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>200.0</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mrow> <mn>239.27</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">S</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">S</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>223.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>186.6</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\mathrm {PbO} }=\left({\frac {200.0{\mbox{ g }}\mathrm {PbS} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {PbS} }{239.27{\mbox{ g }}\mathrm {PbS} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {PbO} }{2{\mbox{ mol }}\mathrm {PbS} }}\right)\left({\frac {223.2{\mbox{ g }}\mathrm {PbO} }{1{\mbox{ mol }}\mathrm {PbO} }}\right)=186.6{\mbox{ g}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4615f1a1a6656df74b8558a41a223db31284b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:84.807ex; height:6.176ex;" alt="{\displaystyle m_{\mathrm {PbO} }=\left({\frac {200.0{\mbox{ g }}\mathrm {PbS} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {PbS} }{239.27{\mbox{ g }}\mathrm {PbS} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {PbO} }{2{\mbox{ mol }}\mathrm {PbS} }}\right)\left({\frac {223.2{\mbox{ g }}\mathrm {PbO} }{1{\mbox{ mol }}\mathrm {PbO} }}\right)=186.6{\mbox{ g}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{\mathrm {PbO} }=\left({\frac {200.0{\mbox{ g }}\mathrm {O_{2}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {O_{2}} }{32.00{\mbox{ g }}\mathrm {O_{2}} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {PbO} }{3{\mbox{ mol }}\mathrm {O_{2}} }}\right)\left({\frac {223.2{\mbox{ g }}\mathrm {PbO} }{1{\mbox{ mol }}\mathrm {PbO} }}\right)=930.0{\mbox{ g}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>200.0</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>32.00</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> <mrow> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>223.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> mol </mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">O</mi> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>930.0</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> g</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\mathrm {PbO} }=\left({\frac {200.0{\mbox{ g }}\mathrm {O_{2}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {O_{2}} }{32.00{\mbox{ g }}\mathrm {O_{2}} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {PbO} }{3{\mbox{ mol }}\mathrm {O_{2}} }}\right)\left({\frac {223.2{\mbox{ g }}\mathrm {PbO} }{1{\mbox{ mol }}\mathrm {PbO} }}\right)=930.0{\mbox{ g}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93590304ea8845c40f888a9de46fa1124ab7bbcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:81.034ex; height:6.176ex;" alt="{\displaystyle m_{\mathrm {PbO} }=\left({\frac {200.0{\mbox{ g }}\mathrm {O_{2}} }{1}}\right)\left({\frac {1{\mbox{ mol }}\mathrm {O_{2}} }{32.00{\mbox{ g }}\mathrm {O_{2}} }}\right)\left({\frac {2{\mbox{ mol }}\mathrm {PbO} }{3{\mbox{ mol }}\mathrm {O_{2}} }}\right)\left({\frac {223.2{\mbox{ g }}\mathrm {PbO} }{1{\mbox{ mol }}\mathrm {PbO} }}\right)=930.0{\mbox{ g}}}"></span></dd></dl> <p>Because a lesser amount of PbO is produced for the 200.0 g of PbS, it is clear that PbS is the limiting reagent. </p><p>In reality, the actual yield is not the same as the stoichiometrically-calculated theoretical yield. Percent yield, then, is expressed in the following equation: </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 {\mbox{percent yield}}={\frac {\mbox{actual yield}}{\mbox{theoretical yield}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>percent yield</mtext> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="false" scriptlevel="0"> <mtext>actual yield</mtext> </mstyle> <mstyle displaystyle="false" scriptlevel="0"> <mtext>theoretical yield</mtext> </mstyle> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{percent yield}}={\frac {\mbox{actual yield}}{\mbox{theoretical yield}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e1ede9d684f4f1f9258d3f51d68b63d3b7d086e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.016ex; height:5.843ex;" alt="{\displaystyle {\mbox{percent yield}}={\frac {\mbox{actual yield}}{\mbox{theoretical yield}}}}"></span></dd></dl> <p>If 170.0 g of lead(II) oxide is obtained, then the percent yield would be calculated as follows: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{percent yield}}={\frac {\mbox{170.0 g PbO}}{\mbox{186.6 g PbO}}}=91.12\%}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>percent yield</mtext> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="false" scriptlevel="0"> <mtext>170.0 g PbO</mtext> </mstyle> <mstyle displaystyle="false" scriptlevel="0"> <mtext>186.6 g PbO</mtext> </mstyle> </mfrac> </mrow> <mo>=</mo> <mn>91.12</mn> <mi mathvariant="normal">%</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{percent yield}}={\frac {\mbox{170.0 g PbO}}{\mbox{186.6 g PbO}}}=91.12\%}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b873224b3d8f84f5824aae2b4d0b4e0bb11defc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:39.495ex; height:5.843ex;" alt="{\displaystyle {\mbox{percent yield}}={\frac {\mbox{170.0 g PbO}}{\mbox{186.6 g PbO}}}=91.12\%}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Example">Example</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=9" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider the following reaction, in which <a href="/wiki/Iron(III)_chloride" title="Iron(III) chloride">iron(III) chloride</a> reacts with <a href="/wiki/Hydrogen_sulfide" title="Hydrogen sulfide">hydrogen sulfide</a> to produce <a href="/wiki/Iron(III)_sulfide" title="Iron(III) sulfide">iron(III) sulfide</a> and <a href="/wiki/Hydrogen_chloride" title="Hydrogen chloride">hydrogen chloride</a>: </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 FeCl<sub class="template-chem2-sub">3</sub> + 3 H<sub class="template-chem2-sub">2</sub>S → Fe<sub class="template-chem2-sub">2</sub>S<sub class="template-chem2-sub">3</sub> + 6 HCl</span></dd></dl> <p>The stoichiometric masses for this reaction are: </p> <dl><dd>324.41 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">FeCl<sub class="template-chem2-sub">3</sub></span>, 102.25 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>S</span>, 207.89 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Fe<sub class="template-chem2-sub">2</sub>S<sub class="template-chem2-sub">3</sub></span>, 218.77 g HCl</dd></dl> <p>Suppose 90.0 g of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">FeCl<sub class="template-chem2-sub">3</sub></span> reacts with 52.0 g of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>S</span>. To find the limiting reagent and the mass of HCl produced by the reaction, we change the above amounts by a factor of 90/324.41 and obtain the following amounts: </p> <dl><dd>90.00 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">FeCl<sub class="template-chem2-sub">3</sub></span>, 28.37 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>S</span>, 57.67 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Fe<sub class="template-chem2-sub">2</sub>S<sub class="template-chem2-sub">3</sub></span>, 60.69 g HCl</dd></dl> <p>The limiting reactant (or reagent) is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">FeCl<sub class="template-chem2-sub">3</sub></span>, since all 90.00 g of it is used up while only 28.37 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>S</span> are consumed. Thus, 52.0 − 28.4 = 23.6 g <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>S</span> left in excess. The mass of HCl produced is 60.7 g. </p><p>By looking at the stoichiometry of the reaction, one might have guessed <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">FeCl<sub class="template-chem2-sub">3</sub></span> being the limiting reactant; three times more <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">FeCl<sub class="template-chem2-sub">3</sub></span> is used compared to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>S</span> (324 g vs 102 g). </p> <div class="mw-heading mw-heading2"><h2 id="Different_stoichiometries_in_competing_reactions">Different stoichiometries in competing reactions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=10" title="Edit section: Different stoichiometries in competing reactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Often, more than one reaction is possible given the same starting materials. The reactions may differ in their stoichiometry. For example, the <a href="/wiki/Methylation" title="Methylation">methylation</a> of <a href="/wiki/Benzene" title="Benzene">benzene</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">6</sub></span>), through a <a href="/wiki/Friedel%E2%80%93Crafts_reaction" title="Friedel–Crafts reaction">Friedel–Crafts reaction</a> using <a href="/wiki/Aluminium_chloride" title="Aluminium chloride"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">AlCl<sub class="template-chem2-sub">3</sub></span></a> as a catalyst, may produce singly methylated (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">5</sub>CH<sub class="template-chem2-sub">3</sub></span>), doubly methylated (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">4</sub>(CH<sub class="template-chem2-sub">3</sub>)<sub class="template-chem2-sub">2</sub></span>), or still more highly methylated (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">6−<i>n</i></sub>(CH<sub class="template-chem2-sub">3</sub>)<sub class="template-chem2-sub"><i>n</i></sub></span>) products, as shown in the following example, </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">6</sub> + CH<sub class="template-chem2-sub">3</sub>Cl → C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">5</sub>CH<sub class="template-chem2-sub">3</sub> + HCl</span></dd> <dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">6</sub> + 2 CH<sub class="template-chem2-sub">3</sub>Cl → C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">4</sub>(CH<sub class="template-chem2-sub">3</sub>)<sub class="template-chem2-sub">2</sub> + 2 HCl</span></dd> <dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">6</sub> + <i>n</i> CH<sub class="template-chem2-sub">3</sub>Cl → C<sub class="template-chem2-sub">6</sub>H<sub class="template-chem2-sub">6−<i>n</i></sub>(CH<sub class="template-chem2-sub">3</sub>)<sub class="template-chem2-sub"><i>n</i></sub> + <i>n</i> HCl</span></dd></dl> <p>In this example, which reaction takes place is controlled in part by the relative <a href="/wiki/Concentration" title="Concentration">concentrations</a> of the reactants. </p> <div class="mw-heading mw-heading2"><h2 id="Stoichiometric_coefficient_and_stoichiometric_number">Stoichiometric coefficient and stoichiometric number</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=11" title="Edit section: Stoichiometric coefficient and stoichiometric number"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In lay terms, the <i>stoichiometric coefficient</i> of any given component is the number of molecules and/or <a href="/wiki/Formula_units" class="mw-redirect" title="Formula units">formula units</a> that participate in the reaction as written. A related concept is the <i>stoichiometric number</i> (using IUPAC nomenclature), wherein the stoichiometric coefficient is multiplied by +1 for all products and by −1 for all reactants. </p><p>For example, in the reaction <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">CH<sub class="template-chem2-sub">4</sub> + 2 O<sub class="template-chem2-sub">2</sub> → <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">CO<sub class="template-chem2-sub">2</sub></a> + 2 H<sub class="template-chem2-sub">2</sub>O</span>, the stoichiometric number of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">CH<sub class="template-chem2-sub">4</sub></span> is −1, the stoichiometric number of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">O<sub class="template-chem2-sub">2</sub></span> is −2, for CO<sub style="font-size: 80%;vertical-align: -0.35em">2</sub> it would be +1 and for <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">H<sub class="template-chem2-sub">2</sub>O</span> it is +2. </p><p>In more technically precise terms, the stoichiometric number in a <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a> <a href="/wiki/System" title="System">system</a> of the <i>i</i>-th component is defined as </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 \nu _{i}={\frac {\Delta N_{i}}{\Delta \xi }}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}={\frac {\Delta N_{i}}{\Delta \xi }}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64062b4edd78064ba6b6464a0e28b8ea7474df4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:10.872ex; height:6.009ex;" alt="{\displaystyle \nu _{i}={\frac {\Delta N_{i}}{\Delta \xi }}\,}"></span></dd></dl> <p>or </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta N_{i}=\nu _{i}\,\Delta \xi \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi mathvariant="normal">Δ</mi> <mi>ξ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta N_{i}=\nu _{i}\,\Delta \xi \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bd1b2989ee6dc2d86202c22a17c3e8bfa92e694" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.389ex; height:2.509ex;" alt="{\displaystyle \Delta N_{i}=\nu _{i}\,\Delta \xi \,}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fef58cebf23adff9199f17325aefb5515fdca99d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.666ex; height:2.509ex;" alt="{\displaystyle N_{i}}"></span> is the number of <a href="/wiki/Molecule" title="Molecule">molecules</a> of <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 \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span> is the progress variable or <a href="/wiki/Extent_of_reaction" title="Extent of reaction">extent of reaction</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><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The stoichiometric number <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcb0577728049599bceabd5ed148f426e9d44308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.948ex; height:2.009ex;" alt="{\displaystyle \nu _{i}}"></span> represents the degree to which a chemical species participates in a reaction. The convention is to assign negative numbers to <i>reactants</i> (which are consumed) and positive ones to <i>products</i>, consistent with the convention that increasing the extent of reaction will correspond to shifting the composition from reactants towards products. However, any reaction may be viewed as going in the reverse direction, and in that point of view, would change in the negative direction in order to lower the system's Gibbs free energy. Whether a reaction actually <i>will</i> go in the arbitrarily selected forward direction or not depends on the amounts of the <a href="/wiki/Chemical_substance" title="Chemical substance">substances</a> present at any given time, which determines the <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">kinetics</a> and <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamics</a>, i.e., whether <a href="/wiki/Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a> lies to the <i>right</i> or the <i>left</i> of the initial state, </p><p>In <a href="/wiki/Reaction_mechanism" title="Reaction mechanism">reaction mechanisms</a>, stoichiometric coefficients for each step are always <a href="/wiki/Integer" title="Integer">integers</a>, since elementary reactions always involve whole molecules. If one uses a composite representation of an overall reaction, some may be <a href="/wiki/Rational_number" title="Rational number">rational</a> <a href="/wiki/Fraction_(mathematics)" class="mw-redirect" title="Fraction (mathematics)">fractions</a>. There are often chemical species present that do not participate in a reaction; their stoichiometric coefficients are therefore zero. Any chemical species that is regenerated, such as a <a href="/wiki/Catalyst" class="mw-redirect" title="Catalyst">catalyst</a>, also has a stoichiometric coefficient of zero. </p><p>The simplest possible case is an <a href="/wiki/Isomerization" title="Isomerization">isomerization</a> </p> <dl><dd>A → B</dd></dl> <p>in which <span class="texhtml"><i>ν</i><sub>B</sub> = 1</span> since one molecule of B is produced each time the reaction occurs, while <span class="texhtml"><i>ν</i><sub>A</sub> = −1</span> since one molecule of A is necessarily consumed. In any chemical reaction, not only is the total <a href="/wiki/Conservation_of_mass" title="Conservation of mass">mass conserved</a> but also the numbers of <a href="/wiki/Atom" title="Atom">atoms</a> of each <a href="/wiki/Periodic_table" title="Periodic table">kind</a> are conserved, and this imposes corresponding constraints on possible values for the stoichiometric coefficients. </p><p>There are usually multiple reactions proceeding simultaneously in any <a href="/wiki/Nature" title="Nature">natural</a> reaction system, including those in <a href="/wiki/Biology" title="Biology">biology</a>. Since any chemical component can participate in several reactions simultaneously, the stoichiometric number of the <i>i</i>-th component in the <i>k</i>-th reaction is defined as </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 \nu _{ik}={\frac {\partial N_{i}}{\partial \xi _{k}}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{ik}={\frac {\partial N_{i}}{\partial \xi _{k}}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85e04d6f0ada596043b39f69bb7ee253917077be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:11.11ex; height:6.009ex;" alt="{\displaystyle \nu _{ik}={\frac {\partial N_{i}}{\partial \xi _{k}}}\,}"></span></dd></dl> <p>so that the total (differential) change in the amount of the <i>i</i>-th component is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dN_{i}=\sum _{k}\nu _{ik}\,d\xi _{k}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munder> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dN_{i}=\sum _{k}\nu _{ik}\,d\xi _{k}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f3e565e86536244d154c272572b31f612f95fce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.271ex; height:5.509ex;" alt="{\displaystyle dN_{i}=\sum _{k}\nu _{ik}\,d\xi _{k}.\,}"></span></dd></dl> <p>Extents of reaction provide the clearest and most explicit way of representing compositional change, although they are not yet widely used. </p><p>With complex reaction systems, it is often useful to consider both the representation of a reaction system in terms of the amounts of the chemicals present <span class="texhtml">{ <i>N<sub>i</sub></i> }</span> (<a href="/wiki/Thermodynamic_variable" class="mw-redirect" title="Thermodynamic variable">state variables</a>), and the representation in terms of the actual compositional <a href="/wiki/Degrees_of_freedom_(physics_and_chemistry)" title="Degrees of freedom (physics and chemistry)">degrees of freedom</a>, as expressed by the extents of reaction <span class="texhtml">{ <i>ξ<sub>k</sub></i> }</span>. The transformation from a <a href="/wiki/Vector_space" title="Vector space">vector</a> expressing the extents to a vector expressing the amounts uses a rectangular <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a> whose elements are the stoichiometric numbers <span class="texhtml">[ <i>ν<sub>i k</sub></i> ]</span>. </p><p>The <a href="/wiki/Extreme_value" class="mw-redirect" title="Extreme value">maximum and minimum</a> for any <i>ξ<sub>k</sub></i> occur whenever the first of the reactants is depleted for the forward reaction; or the first of the "products" is depleted if the reaction as viewed as being pushed in the reverse direction. This is a purely <a href="/wiki/Kinematics" title="Kinematics">kinematic</a> restriction on the reaction <a href="/wiki/Simplex" title="Simplex">simplex</a>, a <a href="/wiki/Hyperplane" title="Hyperplane">hyperplane</a> in composition space, or <i>N</i>‑space, whose <a href="/wiki/Dimension" title="Dimension">dimensionality</a> equals the number of <i><a href="/wiki/Linear_independence" title="Linear independence">linearly-independent</a></i> chemical reactions. This is necessarily less than the number of chemical components, since each reaction manifests a relation between at least two chemicals. The accessible region of the hyperplane depends on the amounts of each chemical species actually present, a contingent fact. Different such amounts can even generate different hyperplanes, all sharing the same algebraic stoichiometry. </p><p>In accord with the principles of <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">chemical kinetics</a> and <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>, every chemical reaction is <i>reversible</i>, at least to some degree, so that each equilibrium point must be an <a href="/wiki/Interior_(topology)" title="Interior (topology)">interior point</a> of the simplex. As a consequence, extrema for the <i>ξ</i>s will not occur unless an experimental system is prepared with zero initial amounts of some products. </p><p>The number of <i>physically</i>-independent reactions can be even greater than the number of chemical components, and depends on the various reaction mechanisms. For example, there may be two (or more) reaction <i>paths</i> for the isomerism above. The reaction may occur by itself, but faster and with different intermediates, in the presence of a catalyst. </p><p>The (dimensionless) "units" may be taken to be <a href="/wiki/Molecule" title="Molecule">molecules</a> or <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a>. Moles are most commonly used, but it is more suggestive to picture incremental chemical reactions in terms of molecules. The <i>N</i>s and <i>ξ</i>s are reduced to molar units by dividing by the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>. While dimensional <a href="/wiki/Mass" title="Mass">mass</a> units may be used, the comments about integers are then no longer applicable. </p> <div class="mw-heading mw-heading2"><h2 id="Stoichiometry_matrix">Stoichiometry matrix</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=12" title="Edit section: Stoichiometry matrix"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Chemical_reaction_network_theory" title="Chemical reaction network theory">Chemical reaction network theory</a></div> <p>In complex reactions, stoichiometries are often represented in a more compact form called the stoichiometry matrix. The stoichiometry matrix is denoted by the symbol <b>N</b>.<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-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<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> </p><p>If a reaction network has <i>n</i> reactions and <i>m</i> participating molecular species, then the stoichiometry matrix will have correspondingly <i>m</i> rows and <i>n</i> columns. </p><p>For example, consider the system of reactions shown below: </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">S<sub class="template-chem2-sub">1</sub> → S<sub class="template-chem2-sub">2</sub></span></dd> <dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">5 S<sub class="template-chem2-sub">3</sub> + S<sub class="template-chem2-sub">2</sub> → 4 S<sub class="template-chem2-sub">3</sub> + 2 S<sub class="template-chem2-sub">2</sub></span></dd> <dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">S<sub class="template-chem2-sub">3</sub> → S<sub class="template-chem2-sub">4</sub></span></dd> <dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">S<sub class="template-chem2-sub">4</sub> → S<sub class="template-chem2-sub">5</sub></span></dd></dl> <p>This system comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as: </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 \mathbf {N} ={\begin{bmatrix}-1&0&0&0\\1&1&0&0\\0&-1&-1&0\\0&0&1&-1\\0&0&0&1\\\end{bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mo>−</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {N} ={\begin{bmatrix}-1&0&0&0\\1&1&0&0\\0&-1&-1&0\\0&0&1&-1\\0&0&0&1\\\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fa55fcd89837b018d7349dbece93ca9ed0348e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:27.892ex; height:15.843ex;" alt="{\displaystyle \mathbf {N} ={\begin{bmatrix}-1&0&0&0\\1&1&0&0\\0&-1&-1&0\\0&0&1&-1\\0&0&0&1\\\end{bmatrix}}}"></span></dd></dl> <p>where the rows correspond to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">S<sub class="template-chem2-sub">1</sub>, S<sub class="template-chem2-sub">2</sub>, S<sub class="template-chem2-sub">3</sub>, S<sub class="template-chem2-sub">4</sub> and S<sub class="template-chem2-sub">5</sub>,</span> respectively. The process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation: for example, the stoichiometries in the second reaction simplify when included in the matrix. This means that it is not always possible to recover the original reaction scheme from a stoichiometry matrix. </p><p>Often the stoichiometry matrix is combined with the rate vector, <b>v</b>, and the species vector, <b>x</b> to form a compact equation, the <a href="/wiki/Biochemical_systems_equation" title="Biochemical systems equation">biochemical systems equation</a>, describing the rates of change of the molecular species: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d\mathbf {x} }{dt}}=\mathbf {N} \cdot \mathbf {v} .}"> <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"> <mi mathvariant="bold">x</mi> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">N</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\mathbf {x} }{dt}}=\mathbf {N} \cdot \mathbf {v} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b957b5f7dfa9c56338dc59d1e1bcb94c55055a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.39ex; height:5.509ex;" alt="{\displaystyle {\frac {d\mathbf {x} }{dt}}=\mathbf {N} \cdot \mathbf {v} .}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Gas_stoichiometry">Gas stoichiometry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=13" title="Edit section: Gas stoichiometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Gas stoichiometry</i> is the quantitative relationship (ratio) between reactants and products in a <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a> with reactions that produce <a href="/wiki/Gases" class="mw-redirect" title="Gases">gases</a>. Gas stoichiometry applies when the gases produced are assumed to be <a href="/wiki/Ideal_gas" title="Ideal gas">ideal</a>, and the temperature, pressure, and volume of the gases are all known. The ideal gas law is used for these calculations. Often, but not always, the <a href="/wiki/Standard_temperature_and_pressure" title="Standard temperature and pressure">standard temperature and pressure</a> (STP) are taken as 0 °C and 1 bar and used as the conditions for gas stoichiometric calculations. </p><p>Gas stoichiometry calculations solve for the unknown <a href="/wiki/Volume" title="Volume">volume</a> or <a href="/wiki/Mass" title="Mass">mass</a> of a gaseous product or reactant. For example, if we wanted to calculate the volume of gaseous <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> produced from the combustion of 100 g of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NH<sub class="template-chem2-sub">3</sub></span>, by the reaction: </p> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">4 NH<sub class="template-chem2-sub">3</sub> (g) + 7 O<sub class="template-chem2-sub">2</sub> (g) → 4 NO<sub class="template-chem2-sub">2</sub> (g) + 6 H<sub class="template-chem2-sub">2</sub>O (l)</span></dd></dl> <p>we would carry out the following calculations: </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 100\,\mathrm {g\,NH_{3}} \cdot {\frac {1\,\mathrm {mol\,NH_{3}} }{17.034\,\mathrm {g\,NH_{3}} }}=5.871\,\mathrm {mol\,NH_{3}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>100</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">l</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>17.034</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>5.871</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">l</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 100\,\mathrm {g\,NH_{3}} \cdot {\frac {1\,\mathrm {mol\,NH_{3}} }{17.034\,\mathrm {g\,NH_{3}} }}=5.871\,\mathrm {mol\,NH_{3}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/590924c18d29b8d0ee368cfd6b3738ee9492cd72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:42.871ex; height:5.843ex;" alt="{\displaystyle 100\,\mathrm {g\,NH_{3}} \cdot {\frac {1\,\mathrm {mol\,NH_{3}} }{17.034\,\mathrm {g\,NH_{3}} }}=5.871\,\mathrm {mol\,NH_{3}} }"></span></dd></dl> <p>There is a 1:1 molar ratio of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NH<sub class="template-chem2-sub">3</sub></span> to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> in the above balanced combustion reaction, so 5.871 mol of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">NO<sub class="template-chem2-sub">2</sub></span> will be formed. We will employ the <a href="/wiki/Ideal_gas_law" title="Ideal gas law">ideal gas law</a> to solve for the volume at 0 °C (273.15 K) and 1 atmosphere using the <a href="/wiki/Gas_constant" title="Gas constant">gas law constant</a> of <i>R</i> = 0.08206 L·atm·K<sup>−1</sup>·mol<sup>−1</sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}PV&=nRT\\V&={\frac {nRT}{P}}\\&={\frac {5.871{\text{ mol}}\cdot 0.08206\,{\frac {\mathrm {L\cdot atm} }{\mathrm {mol\cdot K} }}\cdot 273.15{\text{ K}}}{1{\text{ atm}}}}\\&=131.597\,\mathrm {L\,NO_{2}} \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>P</mi> <mi>V</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> </mtd> </mtr> <mtr> <mtd> <mi>V</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mi>R</mi> <mi>T</mi> </mrow> <mi>P</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>5.871</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> mol</mtext> </mrow> <mo>⋅</mo> <mn>0.08206</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mo>⋅</mo> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">m</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">l</mi> <mo>⋅</mo> <mi mathvariant="normal">K</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mn>273.15</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> K</mtext> </mrow> </mrow> <mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> atm</mtext> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>131.597</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> <mspace width="thinmathspace" /> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}PV&=nRT\\V&={\frac {nRT}{P}}\\&={\frac {5.871{\text{ mol}}\cdot 0.08206\,{\frac {\mathrm {L\cdot atm} }{\mathrm {mol\cdot K} }}\cdot 273.15{\text{ K}}}{1{\text{ atm}}}}\\&=131.597\,\mathrm {L\,NO_{2}} \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5c4b3ce9d67a58746c634932e5ada87b39fa6aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.505ex; width:43.276ex; height:18.176ex;" alt="{\displaystyle {\begin{aligned}PV&=nRT\\V&={\frac {nRT}{P}}\\&={\frac {5.871{\text{ mol}}\cdot 0.08206\,{\frac {\mathrm {L\cdot atm} }{\mathrm {mol\cdot K} }}\cdot 273.15{\text{ K}}}{1{\text{ atm}}}}\\&=131.597\,\mathrm {L\,NO_{2}} \end{aligned}}}"></span></dd></dl> <p>Gas stoichiometry often involves having to know the <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a> of a gas, given the <a href="/wiki/Density" title="Density">density</a> of that gas. The ideal gas law can be re-arranged to obtain a relation between the <a href="/wiki/Density" title="Density">density</a> and the <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a> of an ideal gas: </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 \rho ={\frac {m}{V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>m</mi> <mi>V</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {m}{V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f63465553e3f944d6ef79f90f992a02cf29c7f38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.177ex; height:4.843ex;" alt="{\displaystyle \rho ={\frac {m}{V}}}"></span>    and    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n={\frac {m}{M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>m</mi> <mi>M</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n={\frac {m}{M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a24b521a5398f08280966f24dcead66c0b93a625" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.772ex; height:4.676ex;" alt="{\displaystyle n={\frac {m}{M}}}"></span></dd></dl> <p>and thus: </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 \rho ={\frac {MP}{R\,T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>M</mi> <mi>P</mi> </mrow> <mrow> <mi>R</mi> <mspace width="thinmathspace" /> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {MP}{R\,T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e62ee5f79d039ac692af594f32973ce37d7b23f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.324ex; height:5.343ex;" alt="{\displaystyle \rho ={\frac {MP}{R\,T}}}"></span></dd></dl> <p>where: </p> <ul><li><i>P</i> = absolute gas <a href="/wiki/Pressure" title="Pressure">pressure</a></li> <li><i>V</i> = gas <a href="/wiki/Volume" title="Volume">volume</a></li> <li><i>n</i> = amount (measured in <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a>)</li> <li><i>R</i> = universal ideal gas law constant</li> <li><i>T</i> = absolute gas <a href="/wiki/Temperature" title="Temperature">temperature</a></li> <li><i>ρ</i> = gas density at <i>T</i> and <i>P</i></li> <li><i>m</i> = mass of gas</li> <li><i>M</i> = molar mass of gas</li></ul> <div class="mw-heading mw-heading2"><h2 id="Stoichiometric_air-to-fuel_ratios_of_common_fuels">Stoichiometric air-to-fuel ratios of common fuels</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=14" title="Edit section: Stoichiometric air-to-fuel ratios of common fuels"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Air%E2%80%93fuel_ratio" title="Air–fuel ratio">Air–fuel ratio</a> and <a href="/wiki/Combustion" title="Combustion">Combustion</a></div> <p>In the <a href="/wiki/Combustion" title="Combustion">combustion</a> reaction, oxygen reacts with the fuel, and the point where exactly all oxygen is consumed and all fuel burned is defined as the stoichiometric point. With more oxygen (overstoichiometric combustion), some of it stays unreacted. Likewise, if the combustion is incomplete due to lack of sufficient oxygen, fuel remains unreacted. (Unreacted fuel may also remain because of slow combustion or insufficient mixing of fuel and oxygen – this is not due to stoichiometry.) Different hydrocarbon fuels have different contents of carbon, hydrogen and other elements, thus their stoichiometry varies. </p><p>Oxygen makes up only 20.95% of the volume of air, and only 23.20% of its mass.<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> The air-fuel ratios listed below are much higher than the equivalent oxygen-fuel ratios, due to the high proportion of inert gasses in the air. </p> <table class="wikitable sortable" style="text-align:right;"> <tbody><tr> <th>Fuel </th> <th data-sort-type="number">Ratio by mass <sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </th> <th data-sort-type="number">Ratio by volume <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> </th> <th data-sort-type="number">Percent fuel by mass </th> <th>Main reaction </th></tr> <tr> <td><a href="/wiki/Gasoline" title="Gasoline">Gasoline</a> </td> <td>14.7 : 1 </td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">— </td> <td>6.8% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 C<sub class="template-chem2-sub">8</sub>H<sub class="template-chem2-sub">18</sub> + 25 O<sub class="template-chem2-sub">2</sub> → 16 CO<sub class="template-chem2-sub">2</sub> + 18 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Natural_gas" title="Natural gas">Natural gas</a> </td> <td>17.2 : 1 </td> <td>9.7  : 1 </td> <td>5.8% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">CH<sub class="template-chem2-sub">4</sub> + 2 O<sub class="template-chem2-sub">2</sub> → CO<sub class="template-chem2-sub">2</sub> + 2 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Propane" title="Propane">Propane</a> (<a href="/wiki/Liquid_propane" class="mw-redirect" title="Liquid propane">LP</a>) </td> <td>15.67 : 1 </td> <td>23.9 : 1 </td> <td>6.45% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">3</sub>H<sub class="template-chem2-sub">8</sub> + 5 O<sub class="template-chem2-sub">2</sub> → 3 CO<sub class="template-chem2-sub">2</sub> + 4 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Ethanol" title="Ethanol">Ethanol</a> </td> <td>9 : 1 </td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">— </td> <td>11.1% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">2</sub>H<sub class="template-chem2-sub">6</sub>O + 3 O<sub class="template-chem2-sub">2</sub> → 2 CO<sub class="template-chem2-sub">2</sub> + 3 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Methanol" title="Methanol">Methanol</a> </td> <td>6.47 : 1 </td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">— </td> <td>15.6% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 CH<sub class="template-chem2-sub">4</sub>O + 3 O<sub class="template-chem2-sub">2</sub> → 2 CO<sub class="template-chem2-sub">2</sub> + 4 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/N-Butanol" class="mw-redirect" title="N-Butanol"><i>n</i>-Butanol</a> </td> <td>11.2 : 1 </td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">— </td> <td>8.2% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">4</sub>H<sub class="template-chem2-sub">10</sub>O + 6 O<sub class="template-chem2-sub">2</sub> → 4 CO<sub class="template-chem2-sub">2</sub> + 5 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Hydrogen" title="Hydrogen">Hydrogen</a> </td> <td>34.3 : 1 </td> <td>2.39 : 1 </td> <td>2.9% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 H<sub class="template-chem2-sub">2</sub> + O<sub class="template-chem2-sub">2</sub> → 2 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Diesel_fuel" title="Diesel fuel">Diesel</a> </td> <td>14.5 : 1 </td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">— </td> <td>6.8% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 C<sub class="template-chem2-sub">12</sub>H<sub class="template-chem2-sub">26</sub> + 37 O<sub class="template-chem2-sub">2</sub> → 24 CO<sub class="template-chem2-sub">2</sub> + 26 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Methane" title="Methane">Methane</a> </td> <td>17.19 : 1 </td> <td>9.52 : 1 </td> <td>5.5% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">CH<sub class="template-chem2-sub">4</sub> + 2 O<sub class="template-chem2-sub">2</sub> → CO<sub class="template-chem2-sub">2</sub> + 2 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Acetylene" title="Acetylene">Acetylene</a> </td> <td>13.26 : 1 </td> <td>11.92 : 1 </td> <td>7.0% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 C<sub class="template-chem2-sub">2</sub>H<sub class="template-chem2-sub">2</sub> + 5 O<sub class="template-chem2-sub">2</sub> → 4 CO<sub class="template-chem2-sub">2</sub> + 2 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Ethane" title="Ethane">Ethane</a> </td> <td>16.07 : 1 </td> <td>16.68 : 1 </td> <td>5.9% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 C<sub class="template-chem2-sub">2</sub>H<sub class="template-chem2-sub">6</sub> + 7 O<sub class="template-chem2-sub">2</sub> → 4 CO<sub class="template-chem2-sub">2</sub> + 6 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Butane" title="Butane">Butane</a> </td> <td>15.44 : 1 </td> <td>30.98 : 1 </td> <td>6.1% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">2 C<sub class="template-chem2-sub">4</sub>H<sub class="template-chem2-sub">10</sub> + 13 O<sub class="template-chem2-sub">2</sub> → 8 CO<sub class="template-chem2-sub">2</sub> + 10 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr> <tr> <td><a href="/wiki/Pentane" title="Pentane">Pentane</a> </td> <td>15.31 : 1 </td> <td>38.13 : 1 </td> <td>6.1% </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">C<sub class="template-chem2-sub">5</sub>H<sub class="template-chem2-sub">12</sub> + 8 O<sub class="template-chem2-sub">2</sub> → 5 CO<sub class="template-chem2-sub">2</sub> + 6 H<sub class="template-chem2-sub">2</sub>O</span> </td></tr></tbody></table> <p>Gasoline engines can run at stoichiometric air-to-fuel ratio, because gasoline is quite volatile and is mixed (sprayed or carburetted) with the air prior to ignition. Diesel engines, in contrast, run lean, with more air available than simple stoichiometry would require. Diesel fuel is less volatile and is effectively burned as it is injected.<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> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Non-stoichiometric_compound" title="Non-stoichiometric compound">Non-stoichiometric compound</a></li> <li><a href="/wiki/Biochemical_systems_equation" title="Biochemical systems equation">Biochemical systems equation</a></li> <li><a href="/wiki/Chemical_reaction" title="Chemical reaction">Chemical reaction</a></li> <li><a href="/wiki/Chemical_equation" title="Chemical equation">Chemical equation</a></li> <li><a href="/wiki/Molecule" title="Molecule">Molecule</a></li> <li><a href="/wiki/Molar_mass" title="Molar mass">Molar mass</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap 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"><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="CITEREFRichter1792" class="citation book cs1 cs1-prop-foreign-lang-source">Richter, J.B. (1792). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NhFQAAAAcAAJ&pg=RA1-PA121"><i>Anfangsgründe der Stöchyometrie ... (in 3 vol.s)</i></a> [<i>Rudiments of Stoichiometry ...</i>] (in German). Vol. 1. Breslau and Hirschberg, (Germany): Johann Friedrich Korn der Aeltere. p. 121.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Anfangsgr%C3%BCnde+der+St%C3%B6chyometrie+...+%28in+3+vol.s%29&rft.place=Breslau+and+Hirschberg%2C+%28Germany%29&rft.pages=121&rft.pub=Johann+Friedrich+Korn+der+Aeltere&rft.date=1792&rft.aulast=Richter&rft.aufirst=J.B.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNhFQAAAAcAAJ%26pg%3DRA1-PA121&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStoichiometry" class="Z3988"></span> From p. 121: <i>"Die Stöchyometrie (</i>Stöchyometria<i>) ist die Wissenschaft die quantitativen oder Massenverhältnisse ... zu messen, in welchen die chemischen Elemente ... gegen einander stehen."</i> (Stoichiometry (<i>stoichiometria</i>) is the science of measuring the quantitative or mass relations in which the chemical "elements" exist in relation to each other.) [On pp. 3–7, Richter explains that an "element" is a pure substance, and that a "chemical element" (<i>chymisches Element (Elementum chymicum)</i>) is a substance that cannot be resolved into dissimilar substances by known physical or chemical means. Thus, for example, <a href="/wiki/Aluminium_oxide" title="Aluminium oxide">aluminium oxide</a> was a "chemical element" because in Richter's time, it couldn't be resolved further into its component elements.]</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSinnott2005" class="citation book cs1">Sinnott, R. K. (2005). <i>Coulson and Richardson's Chemical Engineering</i> (4th ed.). 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"Metabolic control theory: A structural approach". <i>Journal of Theoretical Biology</i>. <b>135</b> (2): 175–201. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988JThBi.135..175R">1988JThBi.135..175R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fs0022-5193%2888%2980073-0">10.1016/s0022-5193(88)80073-0</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/3267767">3267767</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Theoretical+Biology&rft.atitle=Metabolic+control+theory%3A+A+structural+approach&rft.volume=135&rft.issue=2&rft.pages=175-201&rft.date=1988-11-21&rft_id=info%3Apmid%2F3267767&rft_id=info%3Adoi%2F10.1016%2Fs0022-5193%2888%2980073-0&rft_id=info%3Abibcode%2F1988JThBi.135..175R&rft.aulast=Reder&rft.aufirst=Christine&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStoichiometry" class="Z3988"></span></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"><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.uigi.com/air.html">"Universal Industrial Gases, Inc: Composition of Air - Components & Properties of Air - Answers to "What is air?" - "What is air made up of?" -" What are air products and what are they used for?"<span class="cs1-kern-right"></span>"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Universal+Industrial+Gases%2C+Inc%3A+Composition+of+Air+-+Components+%26+Properties+of+Air+-+Answers+to+%22What+is+air%3F%22+-+%22What+is+air+made+up+of%3F%22+-%22+What+are+air+products+and+what+are+they+used+for%3F%22&rft_id=http%3A%2F%2Fwww.uigi.com%2Fair.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStoichiometry" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">John B. Heywood: "Internal Combustion Engine Fundamentals page 915", 1988</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">North American Mfg. Co.: "North American Combustion Handbook", 1952</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://x-engineer.org/automotive-engineering/internal-combustion-engines/performance/air-fuel-ratio-lambda-engine-performance/">"Air-fuel ratio, lambda and engine performance"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-05-31</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Air-fuel+ratio%2C+lambda+and+engine+performance&rft_id=https%3A%2F%2Fx-engineer.org%2Fautomotive-engineering%2Finternal-combustion-engines%2Fperformance%2Fair-fuel-ratio-lambda-engine-performance%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStoichiometry" class="Z3988"></span></span> </li> </ol></div></div> <ul><li>Zumdahl, Steven S. <i>Chemical Principles</i>. Houghton Mifflin, New York, 2005, pp 148–150.</li> <li>Internal Combustion Engine Fundamentals, John B. Heywood</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Stoichiometry&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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 .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/stoichiometry" class="extiw" title="wiktionary:Special:Search/stoichiometry">stoichiometry</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><div class="side-box metadata side-box-right"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-abovebelow"> <a href="/wiki/Wikipedia:The_Wikipedia_Library" title="Wikipedia:The Wikipedia Library">Library resources</a> about <br /> <b>Stoichiometry</b> <hr /></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><a class="external text" href="https://ftl.toolforge.org/cgi-bin/ftl?st=wp&su=Stoichiometry">Resources in your library</a></li> </ul></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070206060439/http://www.tech.plym.ac.uk/sme/ther305-web/Combust1.PDF">Engine Combustion primer</a> from the University of Plymouth</li> <li><a rel="nofollow" class="external text" href="https://chemcollective.org/tutorials.php">Free Stoichiometry Tutorials</a> from Carnegie Mellon's ChemCollective</li> <li><a rel="nofollow" class="external text" href="http://chemistry-in-excel.jimdo.com/">Stoichiometry Add-In for Microsoft Excel</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110511073820/http://chemistry-in-excel.jimdo.com/">Archived</a> 2011-05-11 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> for calculation of molecular weights, reaction coëfficients and stoichiometry.</li> <li><a rel="nofollow" class="external text" href="http://www.thermobook.net/stoichiometry/">Reaction Stoichiometry Calculator</a> a comprehensive free online reaction stoichiometry calculator.</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 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Stoichiometry - Wikipedia