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href="#Molar_masses_of_compounds"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Molar masses of compounds</span> </div> </a> <ul id="toc-Molar_masses_of_compounds-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Average_molar_mass_of_mixtures" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Average_molar_mass_of_mixtures"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Average molar mass of mixtures</span> </div> </a> <ul id="toc-Average_molar_mass_of_mixtures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Related_quantities" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_quantities"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Related quantities</span> </div> </a> <button aria-controls="toc-Related_quantities-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 Related quantities subsection</span> </button> <ul id="toc-Related_quantities-sublist" class="vector-toc-list"> <li id="toc-Molecular_mass" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Molecular_mass"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Molecular mass</span> </div> </a> <ul id="toc-Molecular_mass-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-DNA_synthesis_usage" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#DNA_synthesis_usage"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>DNA synthesis usage</span> </div> </a> <ul id="toc-DNA_synthesis_usage-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Precision_and_uncertainties" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Precision_and_uncertainties"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Precision and uncertainties</span> </div> </a> <ul id="toc-Precision_and_uncertainties-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Measurement" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Measurement</span> </div> </a> <button aria-controls="toc-Measurement-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 Measurement subsection</span> </button> <ul id="toc-Measurement-sublist" class="vector-toc-list"> <li id="toc-Vapour_density" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vapour_density"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Vapour density</span> </div> </a> <ul id="toc-Vapour_density-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Freezing-point_depression" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Freezing-point_depression"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Freezing-point depression</span> </div> </a> <ul id="toc-Freezing-point_depression-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Boiling-point_elevation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Boiling-point_elevation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Boiling-point elevation</span> </div> </a> <ul id="toc-Boiling-point_elevation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <button aria-controls="toc-References-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 References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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">Molar mass</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 73 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-73" 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">73 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/Mol%C3%AAre_massa" title="Molêre massa – Afrikaans" lang="af" hreflang="af" data-title="Molêre massa" 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/%D9%83%D8%AA%D9%84%D8%A9_%D9%85%D9%88%D9%84%D9%8A%D8%A9" title="كتلة مولية – Arabic" lang="ar" hreflang="ar" data-title="كتلة مولية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Masa_molar" title="Masa molar – Aragonese" lang="an" hreflang="an" data-title="Masa molar" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Molyar_k%C3%BCtl%C9%99" title="Molyar kütlə – Azerbaijani" lang="az" hreflang="az" data-title="Molyar kütlə" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D9%88%D9%84_%D8%AC%D8%B1%D9%85%DB%8C" title="مول جرمی – South Azerbaijani" lang="azb" hreflang="azb" data-title="مول جرمی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%81%D0%B0" title="Малярная маса – Belarusian" lang="be" hreflang="be" data-title="Малярная маса" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%81%D0%B0" title="Малярная маса – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Малярная маса" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B0%D1%80%D0%BD%D0%B0_%D0%BC%D0%B0%D1%81%D0%B0" title="Моларна маса – Bulgarian" lang="bg" hreflang="bg" data-title="Моларна маса" 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/Molarna_masa" title="Molarna masa – Bosnian" lang="bs" hreflang="bs" data-title="Molarna masa" 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/Massa_molar" title="Massa molar – Catalan" lang="ca" hreflang="ca" data-title="Massa molar" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D1%8C_%D0%BC%D0%B0%D1%81%D1%81%D0%B8" title="Моль масси – Chuvash" lang="cv" hreflang="cv" data-title="Моль масси" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Mol%C3%A1rn%C3%AD_hmotnost" title="Molární hmotnost – Czech" lang="cs" hreflang="cs" data-title="Molární hmotnost" 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/Molmasse" title="Molmasse – Danish" lang="da" hreflang="da" data-title="Molmasse" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-se mw-list-item"><a href="https://se.wikipedia.org/wiki/Mol%C3%A1ra_m%C3%A1ss%C3%A1" title="Molára mássá – Northern Sami" lang="se" hreflang="se" data-title="Molára mássá" data-language-autonym="Davvisámegiella" data-language-local-name="Northern Sami" class="interlanguage-link-target"><span>Davvisámegiella</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Molare_Masse" title="Molare Masse – German" lang="de" hreflang="de" data-title="Molare Masse" 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/Molaarmass" title="Molaarmass – Estonian" lang="et" hreflang="et" data-title="Molaarmass" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Masa_molar" title="Masa molar – Spanish" lang="es" hreflang="es" data-title="Masa molar" 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/Molmaso" title="Molmaso – Esperanto" lang="eo" hreflang="eo" data-title="Molmaso" 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/Masa_molar" title="Masa molar – Basque" lang="eu" hreflang="eu" data-title="Masa molar" 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%AC%D8%B1%D9%85_%D9%85%D9%88%D9%84%DB%8C" title="جرم مولی – Persian" lang="fa" hreflang="fa" data-title="جرم مولی" 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/Masse_molaire" title="Masse molaire – French" lang="fr" hreflang="fr" data-title="Masse molaire" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Masa_molar" title="Masa molar – Galician" lang="gl" hreflang="gl" data-title="Masa molar" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AA%B0_%EC%A7%88%EB%9F%89" title="몰 질량 – Korean" lang="ko" hreflang="ko" data-title="몰 질량" 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%84%D5%B8%D5%AC%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A6%D5%A1%D5%B6%D5%A3%D5%BE%D5%A1%D5%AE" title="Մոլային զանգված – Armenian" lang="hy" hreflang="hy" data-title="Մոլային զանգված" 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%AE%E0%A5%8B%E0%A4%B2%E0%A4%B0_%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%B5%E0%A5%8D%E0%A4%AF%E0%A4%AE%E0%A4%BE%E0%A4%A8" title="मोलर द्रव्यमान – Hindi" lang="hi" hreflang="hi" data-title="मोलर द्रव्यमान" 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/Molna_masa" title="Molna masa – Croatian" lang="hr" hreflang="hr" data-title="Molna masa" 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/Massa_molar" title="Massa molar – Indonesian" lang="id" hreflang="id" data-title="Massa molar" 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-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Massa_molar" title="Massa molar – Interlingua" lang="ia" hreflang="ia" data-title="Massa molar" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Massa_molare" title="Massa molare – Italian" lang="it" hreflang="it" data-title="Massa molare" 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%9E%D7%A1%D7%94_%D7%9E%D7%95%D7%9C%D7%A8%D7%99%D7%AA" title="מסה מולרית – Hebrew" lang="he" hreflang="he" data-title="מסה מולרית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%9D%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%9B%E1%83%90%E1%83%A1%E1%83%90" title="მოლური მასა – Georgian" lang="ka" hreflang="ka" data-title="მოლური მასა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D1%8C%D0%B4%D1%96%D0%BA_%D0%BC%D0%B0%D1%81%D1%81%D0%B0" title="Мольдік масса – Kazakh" lang="kk" hreflang="kk" data-title="Мольдік масса" 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/Mas_mol%C3%A8" title="Mas molè – Haitian Creole" lang="ht" hreflang="ht" data-title="Mas molè" 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%9C%D0%BE%D0%BB%D1%8F%D1%80%D0%B4%D1%8B%D0%BA_%D0%BC%D0%B0%D1%81%D1%81%D0%B0" title="Молярдык масса – Kyrgyz" lang="ky" hreflang="ky" data-title="Молярдык масса" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Massa_molaris" title="Massa molaris – Latin" lang="la" hreflang="la" data-title="Massa molaris" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Molmasa" title="Molmasa – Latvian" lang="lv" hreflang="lv" data-title="Molmasa" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Molio_mas%C4%97" title="Molio masė – Lithuanian" lang="lt" hreflang="lt" data-title="Molio masė" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Mol%C3%A1ris_t%C3%B6meg" title="Moláris tömeg – Hungarian" lang="hu" hreflang="hu" data-title="Moláris tömeg" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B0%D1%80%D0%BD%D0%B0_%D0%BC%D0%B0%D1%81%D0%B0" title="Моларна маса – Macedonian" lang="mk" hreflang="mk" data-title="Моларна маса" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AE%E0%B5%8B%E0%B4%B3%E0%B4%BE%E0%B5%BC_%E0%B4%AE%E0%B4%BE%E0%B4%B8%E0%B5%8D" title="മോളാർ മാസ് – Malayalam" lang="ml" hreflang="ml" data-title="മോളാർ മാസ്" 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/Jisim_molar" title="Jisim molar – Malay" lang="ms" hreflang="ms" data-title="Jisim molar" 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-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D1%8F%D1%80%D0%BE%D0%BD%D1%8C_%D1%81%D1%82%D0%B0%D0%BB%D0%BC%D0%BE%D1%81%D1%8C" title="Моляронь сталмось – Moksha" lang="mdf" hreflang="mdf" data-title="Моляронь сталмось" data-language-autonym="Мокшень" data-language-local-name="Moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B8%D0%B9%D0%BD_%D0%BC%D0%B0%D1%81%D1%81" title="Молийн масс – Mongolian" lang="mn" hreflang="mn" data-title="Молийн масс" 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/Molaire_massa" title="Molaire massa – Dutch" lang="nl" hreflang="nl" data-title="Molaire massa" 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/%E3%83%A2%E3%83%AB%E8%B3%AA%E9%87%8F" title="モル質量 – Japanese" lang="ja" hreflang="ja" data-title="モル質量" 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/Molar_masse" title="Molar masse – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Molar masse" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Molmasse" title="Molmasse – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Molmasse" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Massa_molara" title="Massa molara – Occitan" lang="oc" hreflang="oc" data-title="Massa molara" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz badge-Q70893996 mw-list-item" title=""><a href="https://uz.wikipedia.org/wiki/Molyar_massa" title="Molyar massa – Uzbek" lang="uz" hreflang="uz" data-title="Molyar massa" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AE%E0%A9%8B%E0%A8%B2%E0%A8%B0_%E0%A8%AA%E0%A9%81%E0%A9%B0%E0%A8%9C" title="ਮੋਲਰ ਪੁੰਜ – Punjabi" lang="pa" hreflang="pa" data-title="ਮੋਲਰ ਪੁੰਜ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Masa_molowa" title="Masa molowa – Polish" lang="pl" hreflang="pl" data-title="Masa molowa" 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/Massa_molar" title="Massa molar – Portuguese" lang="pt" hreflang="pt" data-title="Massa molar" 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/Mas%C4%83_molar%C4%83" title="Masă molară – Romanian" lang="ro" hreflang="ro" data-title="Masă molară" 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%9C%D0%BE%D0%BB%D1%8F%D1%80%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%81%D1%81%D0%B0" title="Молярная масса – Russian" lang="ru" hreflang="ru" data-title="Молярная масса" 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/Masa_molare" title="Masa molare – Albanian" lang="sq" hreflang="sq" data-title="Masa molare" 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/Molar_mass" title="Molar mass – Simple English" lang="en-simple" hreflang="en-simple" data-title="Molar mass" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Mol%C3%A1rna_hmotnos%C5%A5" title="Molárna hmotnosť – Slovak" lang="sk" hreflang="sk" data-title="Molárna hmotnosť" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Molska_masa" title="Molska masa – Slovenian" lang="sl" hreflang="sl" data-title="Molska masa" 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%9C%D0%BE%D0%BB%D0%B0%D1%80%D0%BD%D0%B0_%D0%BC%D0%B0%D1%81%D0%B0" title="Моларна маса – Serbian" lang="sr" hreflang="sr" data-title="Моларна маса" 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/Molarna_masa" title="Molarna masa – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Molarna masa" 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/Moolimassa" title="Moolimassa – Finnish" lang="fi" hreflang="fi" data-title="Moolimassa" 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/Molmassa" title="Molmassa – Swedish" lang="sv" hreflang="sv" data-title="Molmassa" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Bigat_ng_molar" title="Bigat ng molar – Tagalog" lang="tl" hreflang="tl" data-title="Bigat ng molar" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BE%E0%AE%AF%E0%AF%8D%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%81_%E0%AE%8E%E0%AE%9F%E0%AF%88" title="வாய்ப்பாட்டு எடை – Tamil" lang="ta" hreflang="ta" data-title="வாய்ப்பாட்டு எடை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AE%E0%B1%8B%E0%B0%B2%E0%B0%BE%E0%B0%B0%E0%B1%8D_%E0%B0%A6%E0%B1%8D%E0%B0%B0%E0%B0%B5%E0%B1%8D%E0%B0%AF%E0%B0%B0%E0%B0%BE%E0%B0%B6%E0%B0%BF" title="మోలార్ ద్రవ్యరాశి – Telugu" lang="te" hreflang="te" data-title="మోలార్ ద్రవ్యరాశి" 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/Mol_k%C3%BCtlesi" title="Mol kütlesi – Turkish" lang="tr" hreflang="tr" data-title="Mol kütlesi" 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%9C%D0%BE%D0%BB%D1%8F%D1%80%D0%BD%D0%B0_%D0%BC%D0%B0%D1%81%D0%B0" title="Молярна маса – Ukrainian" lang="uk" hreflang="uk" data-title="Молярна маса" 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/%D9%85%D9%88%D9%84%D8%B1_%DA%A9%D9%85%DB%8C%D8%AA" title="مولر کمیت – Urdu" lang="ur" hreflang="ur" data-title="مولر کمیت" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Kh%E1%BB%91i_l%C6%B0%E1%BB%A3ng_mol" title="Khối lượng mol – Vietnamese" lang="vi" hreflang="vi" data-title="Khối lượng mol" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%91%A9%E7%88%BE%E8%B3%AA%E9%87%8F" title="摩爾質量 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="摩爾質量" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%91%A9%E5%B0%94%E8%B4%A8%E9%87%8F" title="摩尔质量 – Wu" lang="wuu" hreflang="wuu" data-title="摩尔质量" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li 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.hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Molecular_mass" title="Molecular mass">Molecular mass</a> or <a href="/wiki/Mass_number" title="Mass number">Mass number</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Molar mass</th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Mass_versus_moles_of_iron_vs_gold.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Mass_versus_moles_of_iron_vs_gold.svg/220px-Mass_versus_moles_of_iron_vs_gold.svg.png" decoding="async" width="220" height="299" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Mass_versus_moles_of_iron_vs_gold.svg/330px-Mass_versus_moles_of_iron_vs_gold.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Mass_versus_moles_of_iron_vs_gold.svg/440px-Mass_versus_moles_of_iron_vs_gold.svg.png 2x" data-file-width="443" data-file-height="602" /></a></span><div class="infobox-caption">A diagram comparing <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a> and molar masses of <a href="/wiki/Iron" title="Iron">iron</a> and <a href="/wiki/Gold" title="Gold">gold</a> samples that have equal <a href="/wiki/Mass" title="Mass">masses</a></div></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Common symbols</div></th><td class="infobox-data"><span class="texhtml mvar" style="font-style:italic;">M</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI unit</a></th><td class="infobox-data"><a href="/wiki/Kilogram" title="Kilogram">kg</a>/<a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Other units</div></th><td class="infobox-data"><a href="/wiki/Gram" title="Gram">g</a>/<a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dimensional_analysis#Formulation" title="Dimensional analysis">Dimension</a></th><td class="infobox-data"><b>M</b> <b>N</b><sup>−1</sup></td></tr></tbody></table> <p>In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, the <b>molar mass</b> (<span class="texhtml mvar" style="font-style:italic;">M</span>) (sometimes called <b>molecular weight</b> or <b>formula weight</b>, but see <a class="mw-selflink-fragment" href="#Related_quantities">related quantities</a> for usage) of a <a href="/wiki/Chemical_compound" title="Chemical compound">chemical compound</a> is defined as the ratio between the <a href="/wiki/Mass" title="Mass">mass</a> and the <a href="/wiki/Amount_of_substance" title="Amount of substance">amount of substance</a> (measured in <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a>) of any sample of the compound.<sup id="cite_ref-GreenBook_1-0" class="reference"><a href="#cite_note-GreenBook-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The molar mass is a bulk, not molecular, <a href="/wiki/Physical_property" title="Physical property">property</a> of a substance. The molar mass is an <i><a href="/wiki/Average" title="Average">average</a></i> of many instances of the compound, which often vary in mass due to the presence of <a href="/wiki/Isotope" title="Isotope">isotopes</a>. Most commonly, the molar mass is computed from the <a href="/wiki/Standard_atomic_weight" title="Standard atomic weight">standard atomic weights</a> and is thus a terrestrial average and a function of the relative abundance of the <a href="/wiki/Isotope" title="Isotope">isotopes</a> of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities. </p><p>The <a href="/wiki/Molecular_mass" title="Molecular mass">molecular mass</a> (for molecular compounds) and formula mass (for non-molecular compounds, such as <a href="/wiki/Ionic_salt" class="mw-redirect" title="Ionic salt">ionic salts</a>) are commonly used as synonyms of molar mass, differing only in units (<a href="/wiki/Dalton_(unit)" title="Dalton (unit)">daltons</a> vs g/mol); however, the most authoritative sources define it differently. The difference is that molecular mass is the mass of one specific particle or molecule, while the molar mass is an average over many particles or molecules. </p><p>The molar mass is an <a href="/wiki/Intensive_property" class="mw-redirect" title="Intensive property">intensive property</a> of the substance, that does not depend on the size of the sample. In the <a href="/wiki/International_System_of_Units" title="International System of Units">International System of Units</a> (SI), the <a href="/wiki/Coherent_unit" class="mw-redirect" title="Coherent unit">coherent unit</a> of molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol. </p><p>The mole was defined in such a way that the molar mass of a compound, in g/mol, is numerically equal to the average mass of one molecule or formula unit, in daltons. It was exactly equal before the <a href="/wiki/2019_revision_of_the_SI#Mole" title="2019 revision of the SI">redefinition of the mole in 2019</a>, and is now only approximately equal, but the difference is negligible for all practical purposes. Thus, for example, the average mass of a molecule of <a href="/wiki/Properties_of_water" title="Properties of water">water</a> is about 18.0153 daltons, and the molar mass of water is about 18.0153 g/mol. </p><p>For chemical elements without isolated molecules, such as <a href="/wiki/Carbon" title="Carbon">carbon</a> and metals, the molar mass is computed dividing by the number of moles of atoms instead. Thus, for example, the molar mass of <a href="/wiki/Iron" title="Iron">iron</a> is about 55.845 g/mol. </p><p>Since 1971, SI defined the "amount of substance" as a separate <a href="/wiki/Dimensional_analysis" title="Dimensional analysis">dimension of measurement</a>. Until 2019, the mole was defined as the amount of substance that has as many constituent particles as there are atoms in 12 grams of <a href="/wiki/Carbon-12" title="Carbon-12">carbon-12</a>. During that period, the molar mass of carbon-12 was thus <i>exactly</i> 12 g/mol, by definition. Since 2019, a mole of any substance has been <a href="/wiki/2019_revision_of_the_SI" title="2019 revision of the SI">redefined in the SI</a> as the amount of that substance containing an exactly defined number of particles, <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></span>. The molar mass of a compound in g/mol thus is equal to the mass of this number of molecules of the compound in grams. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Molar_masses_of_elements">Molar masses of elements</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=1" title="Edit section: Molar masses of elements"><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/Relative_atomic_mass" title="Relative atomic mass">Relative atomic mass</a> and <a href="/wiki/Standard_atomic_weight" title="Standard atomic weight">Standard atomic weight</a></div> <p>The molar mass of <a href="/wiki/Atom" title="Atom">atoms</a> of an <a href="/wiki/Chemical_element" title="Chemical element">element</a> is given by the relative atomic mass of the element multiplied by the <a href="/wiki/Molar_mass_constant" title="Molar mass constant">molar mass constant</a>, <i>M</i><sub>u</sub> ≈ <span class="nowrap"><span data-sort-value="6997100000000000000♠"></span>1.000<span style="margin-left:.25em;">000</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−3</sup></span> kg/mol = 1 g/mol. For normal samples from earth with typical isotope composition, the atomic weight can be approximated by the standard atomic weight<sup id="cite_ref-AtWt_2-0" class="reference"><a href="#cite_note-AtWt-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> or the conventional atomic weight. </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{array}{lll}M({\ce {H}})&=1.00797(7)\times M_{\mathrm {u} }&=1.00797(7){\text{ g/mol}}\\M({\ce {S}})&=32.065(5)\times M_{\mathrm {u} }&=32.065(5){\text{ g/mol}}\\M({\ce {Cl}})&=35.453(2)\times M_{\mathrm {u} }&=35.453(2){\text{ g/mol}}\\M({\ce {Fe}})&=55.845(2)\times M_{\mathrm {u} }&=55.845(2){\text{ g/mol}}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left left left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>1.00797</mn> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mo>=</mo> <mn>1.00797</mn> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>32.065</mn> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mo>=</mo> <mn>32.065</mn> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Cl</mtext> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>35.453</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mo>=</mo> <mn>35.453</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Fe</mtext> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>55.845</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mo>=</mo> <mn>55.845</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lll}M({\ce {H}})&=1.00797(7)\times M_{\mathrm {u} }&=1.00797(7){\text{ g/mol}}\\M({\ce {S}})&=32.065(5)\times M_{\mathrm {u} }&=32.065(5){\text{ g/mol}}\\M({\ce {Cl}})&=35.453(2)\times M_{\mathrm {u} }&=35.453(2){\text{ g/mol}}\\M({\ce {Fe}})&=55.845(2)\times M_{\mathrm {u} }&=55.845(2){\text{ g/mol}}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c7a73569b99da97b37325fa9749befd8da8b2cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:51.183ex; height:13.176ex;" alt="{\displaystyle {\begin{array}{lll}M({\ce {H}})&=1.00797(7)\times M_{\mathrm {u} }&=1.00797(7){\text{ g/mol}}\\M({\ce {S}})&=32.065(5)\times M_{\mathrm {u} }&=32.065(5){\text{ g/mol}}\\M({\ce {Cl}})&=35.453(2)\times M_{\mathrm {u} }&=35.453(2){\text{ g/mol}}\\M({\ce {Fe}})&=55.845(2)\times M_{\mathrm {u} }&=55.845(2){\text{ g/mol}}\end{array}}}"></span></dd></dl> <p>Multiplying by the molar mass constant ensures that the calculation is <a href="/wiki/Dimension" title="Dimension">dimensionally</a> correct: standard relative atomic masses are dimensionless quantities (i.e., pure numbers) whereas molar masses have units (in this case, grams per mole). </p><p>Some elements are usually encountered as <a href="/wiki/Molecule" title="Molecule">molecules</a>, e.g. <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> (<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">H<sub class="template-chem2-sub">2</sub></span>), <a href="/wiki/Sulfur" title="Sulfur">sulfur</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">S<sub class="template-chem2-sub">8</sub></span>), <a href="/wiki/Chlorine" title="Chlorine">chlorine</a> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Cl<sub class="template-chem2-sub">2</sub></span>). The molar mass of molecules of these elements is the molar mass of the atoms multiplied by the number of atoms in each molecule: </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{array}{lll}M({\ce {H2}})&=2\times 1.00797(7)\times M_{\mathrm {u} }&=2.01595(4){\text{ g/mol}}\\M({\ce {S8}})&=8\times 32.065(5)\times M_{\mathrm {u} }&=256.52(4){\text{ g/mol}}\\M({\ce {Cl2}})&=2\times 35.453(2)\times M_{\mathrm {u} }&=70.906(4){\text{ g/mol}}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left left left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>2</mn> <mo>×</mo> <mn>1.00797</mn> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mo>=</mo> <mn>2.01595</mn> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>S</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>8</mn> <mo>×</mo> <mn>32.065</mn> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mo>=</mo> <mn>256.52</mn> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>Cl</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mn>2</mn> <mo>×</mo> <mn>35.453</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mo>=</mo> <mn>70.906</mn> <mo stretchy="false">(</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{lll}M({\ce {H2}})&=2\times 1.00797(7)\times M_{\mathrm {u} }&=2.01595(4){\text{ g/mol}}\\M({\ce {S8}})&=8\times 32.065(5)\times M_{\mathrm {u} }&=256.52(4){\text{ g/mol}}\\M({\ce {Cl2}})&=2\times 35.453(2)\times M_{\mathrm {u} }&=70.906(4){\text{ g/mol}}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d9b8999793e8c80559a2aaf4b9dfc6b18f76a4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.226ex; margin-bottom: -0.278ex; width:56.015ex; height:10.176ex;" alt="{\displaystyle {\begin{array}{lll}M({\ce {H2}})&=2\times 1.00797(7)\times M_{\mathrm {u} }&=2.01595(4){\text{ g/mol}}\\M({\ce {S8}})&=8\times 32.065(5)\times M_{\mathrm {u} }&=256.52(4){\text{ g/mol}}\\M({\ce {Cl2}})&=2\times 35.453(2)\times M_{\mathrm {u} }&=70.906(4){\text{ g/mol}}\end{array}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Molar_masses_of_compounds">Molar masses of compounds</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=2" title="Edit section: Molar masses of compounds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The molar mass of a <a href="/wiki/Chemical_compound" title="Chemical compound">compound</a> is given by the sum of the <a href="/wiki/Relative_atomic_mass" title="Relative atomic mass">relative atomic mass</a> <span class="texhtml"><i>A</i><sub>r</sub></span> of the <a href="/wiki/Atom" title="Atom">atoms</a> which form the compound multiplied by the <a href="/wiki/Molar_mass_constant" title="Molar mass constant">molar mass constant</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M_{u}\approx 1{\text{ g/mol}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> <mo>≈</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{u}\approx 1{\text{ g/mol}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5e45db83dc524f0f9377797e1bfa7f00b96ffda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.338ex; height:2.843ex;" alt="{\displaystyle M_{u}\approx 1{\text{ g/mol}}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M=M_{\rm {u}}M_{\rm {r}}=M_{\rm {u}}\sum _{i}{A_{\rm {r}}}_{i}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=M_{\rm {u}}M_{\rm {r}}=M_{\rm {u}}\sum _{i}{A_{\rm {r}}}_{i}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71b91b04e33acf17a0372e8f9be650702b1e67d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:26.766ex; height:5.509ex;" alt="{\displaystyle M=M_{\rm {u}}M_{\rm {r}}=M_{\rm {u}}\sum _{i}{A_{\rm {r}}}_{i}.}"></span></dd></dl> <p>Here, <span class="texhtml"><i>M</i><sub>r</sub></span> is the relative molar mass, also called formula weight. For normal samples from earth with typical isotope composition, the <a href="/wiki/Standard_atomic_weight" title="Standard atomic weight">standard atomic weight</a> or the conventional atomic weight can be used as an approximation of the relative atomic mass of the sample. Examples are: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{ll}M({\ce {NaCl}})&={\bigl [}22.98976928(2)+35.453(2){\bigr ]}\times 1{\text{ g/mol}}\\&=58.443(2){\text{ g/mol}}\\[4pt]M({\ce {C12H22O11}})&={\bigl [}12\times 12.0107(8)+22\times 1.00794(7)+11\times 15.9994(3){\bigr ]}\times 1{\text{ g/mol}}\\&=342.297(14){\text{ g/mol}}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="left left" rowspacing="4pt 0.8em 0.4em 0.4em" columnspacing="1em"> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>NaCl</mtext> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">[</mo> </mrow> </mrow> <mn>22.98976928</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>35.453</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">]</mo> </mrow> </mrow> <mo>×</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mo>=</mo> <mn>58.443</mn> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>22</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">[</mo> </mrow> </mrow> <mn>12</mn> <mo>×</mo> <mn>12.0107</mn> <mo stretchy="false">(</mo> <mn>8</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>22</mn> <mo>×</mo> <mn>1.00794</mn> <mo stretchy="false">(</mo> <mn>7</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>11</mn> <mo>×</mo> <mn>15.9994</mn> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="1.2em" minsize="1.2em">]</mo> </mrow> </mrow> <mo>×</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mo>=</mo> <mn>342.297</mn> <mo stretchy="false">(</mo> <mn>14</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> g/mol</mtext> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{ll}M({\ce {NaCl}})&={\bigl [}22.98976928(2)+35.453(2){\bigr ]}\times 1{\text{ g/mol}}\\&=58.443(2){\text{ g/mol}}\\[4pt]M({\ce {C12H22O11}})&={\bigl [}12\times 12.0107(8)+22\times 1.00794(7)+11\times 15.9994(3){\bigr ]}\times 1{\text{ g/mol}}\\&=342.297(14){\text{ g/mol}}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39cb9ce805e77e7e7fe54b58cc23d3f34dad22c2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.838ex; width:86.186ex; height:14.843ex;" alt="{\displaystyle {\begin{array}{ll}M({\ce {NaCl}})&={\bigl [}22.98976928(2)+35.453(2){\bigr ]}\times 1{\text{ g/mol}}\\&=58.443(2){\text{ g/mol}}\\[4pt]M({\ce {C12H22O11}})&={\bigl [}12\times 12.0107(8)+22\times 1.00794(7)+11\times 15.9994(3){\bigr ]}\times 1{\text{ g/mol}}\\&=342.297(14){\text{ g/mol}}\end{array}}}"></span> </p><p>An average molar mass may be defined for mixtures of compounds.<sup id="cite_ref-GreenBook_1-1" class="reference"><a href="#cite_note-GreenBook-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> This is particularly important in <a href="/wiki/Polymer_science" title="Polymer science">polymer science</a>, where there is usually a <a href="/wiki/Molar_mass_distribution" title="Molar mass distribution">molar mass distribution</a> of non-uniform polymers so that different polymer molecules contain different numbers of <a href="/wiki/Monomer" title="Monomer">monomer</a> units.<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><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Average_molar_mass_of_mixtures">Average molar mass of mixtures</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=3" title="Edit section: Average molar mass of mixtures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The average molar mass of mixtures <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 {\overline {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0e2d2cef85c7247cc507120eb8980b6f2714591" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.68ex; height:3.009ex;" alt="{\displaystyle {\overline {M}}}"></span> can be calculated from the <a href="/wiki/Mole_fraction" title="Mole fraction">mole fractions</a> <span class="texhtml mvar" style="font-style:italic;">x<sub>i</sub></span> of the components and their molar masses <span class="texhtml mvar" style="font-style:italic;">M<sub>i</sub></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {M}}=\sum _{i}x_{i}M_{i}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>M</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {M}}=\sum _{i}x_{i}M_{i}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f14a5fbe3ff5ea33d848a09bdb6ca1282ab1d322" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.35ex; height:5.676ex;" alt="{\displaystyle {\overline {M}}=\sum _{i}x_{i}M_{i}.}"></span></dd></dl> <p>It can also be calculated from the <a href="/wiki/Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">mass fractions</a> <span class="texhtml mvar" style="font-style:italic;">w<sub>i</sub></span> of the components: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\overline {M}}}=\sum _{i}{\frac {w_{i}}{M_{i}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mover> <mi>M</mi> <mo accent="false">¯</mo> </mover> </mfrac> </mrow> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\overline {M}}}=\sum _{i}{\frac {w_{i}}{M_{i}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c1285b6385c2e1fcf9c3edf6d3da7cf844c903f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.893ex; height:6.343ex;" alt="{\displaystyle {\frac {1}{\overline {M}}}=\sum _{i}{\frac {w_{i}}{M_{i}}}.}"></span></dd></dl> <p>As an example, the average molar mass of dry air is 28.96 g/mol.<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> <div class="mw-heading mw-heading2"><h2 id="Related_quantities">Related quantities</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=4" title="Edit section: Related quantities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Molar mass is closely related to the <b>relative molar mass</b> (<span class="texhtml"><i>M</i><sub>r</sub></span>) of a compound and to the <a href="/wiki/Standard_atomic_weight" title="Standard atomic weight">standard atomic weights</a> of its constituent elements. However, it should be distinguished from the <a href="/wiki/Molecular_mass" title="Molecular mass">molecular mass</a> (which is confusingly <i>also</i> sometimes known as molecular weight), which is the mass of <i>one</i> molecule (of any <i>single</i> isotopic composition), and to the <a href="/wiki/Atomic_mass" title="Atomic mass">atomic mass</a>, which is the mass of <i>one</i> atom (of any <i>single</i> isotope). The <a href="/wiki/Dalton_(unit)" title="Dalton (unit)">dalton</a>, symbol Da, is also sometimes used as a unit of molar mass, especially in <a href="/wiki/Biochemistry" title="Biochemistry">biochemistry</a>, with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u = <span class="nowrap"><span data-sort-value="6973166053906892000♠"></span>1.660<span style="margin-left:.25em;">539</span><span style="margin-left:.25em;">068</span><span style="margin-left:.25em;">92</span>(52)<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−27</sup> kg</span>, as of 2022 CODATA recommended values).<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Obsolete terms for molar mass include <b>gram atomic mass</b> for the mass, in grams, of one mole of atoms of an element, and <b>gram molecular mass</b> for the mass, in grams, of one mole of molecules of a compound. The <b>gram-atom</b> is a former term for a mole of atoms, and <b>gram-molecule</b> for a mole of molecules.<sup id="cite_ref-SI_7-0" class="reference"><a href="#cite_note-SI-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p><b>Molecular weight</b> (M.W.) (for molecular compounds) and <b>formula weight</b> (F.W.) (for non-molecular compounds), are older terms for what is now more correctly called the <b>relative molar mass</b> (<span class="texhtml"><i>M</i><sub>r</sub></span>).<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> This is a <a href="/wiki/Dimension" title="Dimension">dimensionless</a> quantity (i.e., a pure number, without units) equal to the molar mass divided by the <a href="/wiki/Molar_mass_constant" title="Molar mass constant">molar mass constant</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>notes 1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Molecular_mass">Molecular mass</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=5" title="Edit section: Molecular mass"><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/Molecular_mass" title="Molecular mass">Molecular mass</a></div> <p>The molecular mass (<span class="texhtml mvar" style="font-style:italic;">m</span>) is the mass of a given molecule: it is usually measured in <a href="/wiki/Dalton_(unit)" title="Dalton (unit)">daltons</a> (Da or u).<sup id="cite_ref-SI_7-1" class="reference"><a href="#cite_note-SI-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Different molecules of the same compound may have different molecular masses because they contain different <a href="/wiki/Isotope" title="Isotope">isotopes</a> of an element. This is distinct but related to the molar mass, which is a measure of the average molecular mass of all the molecules in a sample and is usually the more appropriate measure when dealing with macroscopic (weigh-able) quantities of a substance. </p><p>Molecular masses are calculated from the <a href="/wiki/Atomic_mass" title="Atomic mass">atomic masses</a> of each <a href="/wiki/Nuclide" title="Nuclide">nuclide</a>, while molar masses are calculated from the <a href="/wiki/Standard_atomic_weight" title="Standard atomic weight">standard atomic weights</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> of each <a href="/wiki/Chemical_element" title="Chemical element">element</a>. The standard atomic weight takes into account the <a href="/wiki/Isotope" title="Isotope">isotopic distribution</a> of the element in a given sample (usually assumed to be "normal"). For example, <a href="/wiki/Water_(molecule)" class="mw-redirect" title="Water (molecule)">water</a> has a molar mass of <span class="nowrap"><span data-sort-value="6998180153000000000♠"></span>18.0153(3) g/mol</span>, but individual water molecules have molecular masses which range between <span class="nowrap"><span data-sort-value="7001180105646863000♠"></span>18.010<span style="margin-left:.25em;">564</span><span style="margin-left:.25em;">6863</span>(15) Da</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><sup class="template-chem2-sup">1</sup>H<sub class="template-chem2-sub">2</sub><sup class="template-chem2-sup">16</sup>O</span>) and <span class="nowrap"><span data-sort-value="7001220277364000000♠"></span>22.027<span style="margin-left:.25em;">7364</span>(9) Da</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap"><sup class="template-chem2-sup">2</sup>H<sub class="template-chem2-sub">2</sub><sup class="template-chem2-sup">18</sup>O</span>). </p><p>The distinction between molar mass and molecular mass is important because relative molecular masses can be measured directly by <a href="/wiki/Mass_spectrometry" title="Mass spectrometry">mass spectrometry</a>, often to a precision of a few <a href="/wiki/Part_per_million" class="mw-redirect" title="Part per million">parts per million</a>. This is accurate enough to directly determine the <a href="/wiki/Chemical_formula" title="Chemical formula">chemical formula</a> of a molecule.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="DNA_synthesis_usage">DNA synthesis usage</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=6" title="Edit section: DNA synthesis usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term <b>formula weight</b> has a specific meaning when used in the context of DNA synthesis: whereas an individual <a href="/wiki/Phosphoramidite" title="Phosphoramidite">phosphoramidite</a> nucleobase to be added to a DNA polymer has protecting groups and has its <i>molecular weight</i> quoted including these groups, the amount of molecular weight that is ultimately added by this nucleobase to a DNA polymer is referred to as the nucleobase's <i>formula weight</i> (i.e., the molecular weight of this nucleobase within the DNA polymer, minus protecting groups).<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. (August 2022)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Precision_and_uncertainties">Precision and uncertainties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=7" title="Edit section: Precision and uncertainties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The precision to which a molar mass is known depends on the precision of the <a href="/wiki/Atomic_mass" title="Atomic mass">atomic masses</a> from which it was calculated (and very slightly on the value of the <a href="/wiki/Molar_mass_constant" title="Molar mass constant">molar mass constant</a>, which depends on the measured value of the <a href="/wiki/Dalton_(unit)" title="Dalton (unit)">dalton</a>). Most atomic masses are known to a precision of at least one part in ten-thousand, often much better<sup id="cite_ref-AtWt_2-1" class="reference"><a href="#cite_note-AtWt-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> (the atomic mass of <a href="/wiki/Lithium" title="Lithium">lithium</a> is a notable, and serious,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> exception). This is adequate for almost all normal uses in chemistry: it is more precise than most <a href="/wiki/Chemical_analysis" class="mw-redirect" title="Chemical analysis">chemical analyses</a>, and exceeds the purity of most laboratory reagents. </p><p>The precision of atomic masses, and hence of molar masses, is limited by the knowledge of the <a href="/wiki/Isotope" title="Isotope">isotopic distribution</a> of the element. If a more accurate value of the molar mass is required, it is necessary to determine the isotopic distribution of the sample in question, which may be different from the standard distribution used to calculate the standard atomic mass. The isotopic distributions of the different elements in a sample are not necessarily independent of one another: for example, a sample which has been <a href="/wiki/Distillation" title="Distillation">distilled</a> will be <a href="/wiki/Isotopic_enrichment" class="mw-redirect" title="Isotopic enrichment">enriched</a> in the lighter <a href="/wiki/Isotope" title="Isotope">isotopes</a> of all the elements present. This complicates the calculation of the <a href="/wiki/Standard_uncertainty" class="mw-redirect" title="Standard uncertainty">standard uncertainty</a> in the molar mass. </p><p>A useful convention for normal laboratory work is to quote molar masses to two <a href="/wiki/Decimal_place" class="mw-redirect" title="Decimal place">decimal places</a> for all calculations. This is more accurate than is usually required, but avoids <a href="/wiki/Rounding_error" class="mw-redirect" title="Rounding error">rounding errors</a> during calculations. When the molar mass is greater than 1000 g/mol, it is rarely appropriate to use more than one decimal place. These conventions are followed in most tabulated values of molar masses.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Measurement">Measurement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=8" title="Edit section: Measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Molar masses are almost never measured directly. They may be calculated from standard atomic masses, and are often listed in chemical catalogues and on <a href="/wiki/Safety_data_sheet" title="Safety data sheet">safety data sheets</a> (SDS). Molar masses typically vary between: </p> <dl><dd>1–238 g/mol for atoms of naturally occurring elements;</dd> <dd><span class="nowrap"><span data-sort-value="6998100000000000000♠"></span>10–1000 g/mol</span> for <a href="/wiki/Small_molecule" title="Small molecule">simple chemical compounds</a>;</dd> <dd><span class="nowrap"><span data-sort-value="7000100000000000000♠"></span>1000–5<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span> g/mol</span> for <a href="/wiki/Polymer" title="Polymer">polymers</a>, <a href="/wiki/Protein" title="Protein">proteins</a>, <a href="/wiki/DNA" title="DNA">DNA</a> fragments, etc.</dd></dl> <p>While molar masses are almost always, in practice, calculated from atomic weights, they can also be measured in certain cases. Such measurements are much less precise than modern <a href="/wiki/Mass_spectrometry" title="Mass spectrometry">mass spectrometric</a> measurements of atomic weights and molecular masses, and are of mostly historical interest. All of the procedures rely on <a href="/wiki/Colligative_property" class="mw-redirect" title="Colligative property">colligative properties</a>, and any <a href="/wiki/Dissociation_(chemistry)" title="Dissociation (chemistry)">dissociation</a> of the compound must be taken into account. </p> <div class="mw-heading mw-heading3"><h3 id="Vapour_density">Vapour density</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=9" title="Edit section: Vapour density"><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/Vapour_density" title="Vapour density">Vapour density</a></div> <p>The measurement of molar mass by vapour density relies on the principle, first enunciated by <a href="/wiki/Amedeo_Avogadro" title="Amedeo Avogadro">Amedeo Avogadro</a>, that equal volumes of gases under identical conditions contain equal numbers of particles. This principle is included in the <a href="/wiki/Ideal_gas_equation" class="mw-redirect" title="Ideal gas equation">ideal gas equation</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle pV=nRT,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mi>V</mi> <mo>=</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle pV=nRT,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2c5d5a7aae3733049c52bad27008bf7d60e17c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:11.586ex; height:2.509ex;" alt="{\displaystyle pV=nRT,}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">n</span> is the <a href="/wiki/Amount_of_substance" title="Amount of substance">amount of substance</a>. The vapour density (<span class="texhtml mvar" style="font-style:italic;">ρ</span>) is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho ={{nM} \over {V}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>M</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho ={{nM} \over {V}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf9c7fe3f4c8d7138b5ebb06de2537c20c823b74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.62ex; height:5.343ex;" alt="{\displaystyle \rho ={{nM} \over {V}}.}"></span></dd></dl> <p>Combining these two equations gives an expression for the molar mass in terms of the vapour density for conditions of known <a href="/wiki/Pressure" title="Pressure">pressure</a> and <a href="/wiki/Temperature" title="Temperature">temperature</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M={{RT\rho } \over {p}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>T</mi> <mi>ρ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M={{RT\rho } \over {p}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b5a388149e7accc4e8ef40518186a5dd0e480c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.626ex; height:5.843ex;" alt="{\displaystyle M={{RT\rho } \over {p}}.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Freezing-point_depression">Freezing-point depression</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=10" title="Edit section: Freezing-point depression"><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/Freezing-point_depression" title="Freezing-point depression">Freezing-point depression</a></div> <p>The <a href="/wiki/Freezing_point" class="mw-redirect" title="Freezing point">freezing point</a> of a <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solution</a> is lower than that of the pure <a href="/wiki/Solvent" title="Solvent">solvent</a>, and the freezing-point depression (<span class="texhtml">Δ<i>T</i></span>) is directly proportional to the <a href="/wiki/Amount_concentration" class="mw-redirect" title="Amount concentration">amount concentration</a> for dilute solutions. When the composition is expressed as a <a href="/wiki/Molality" title="Molality">molality</a>, the proportionality constant is known as the <a href="/wiki/Cryoscopic_constant" title="Cryoscopic constant">cryoscopic constant</a> (<span class="texhtml"><i>K</i><sub>f</sub></span>) and is characteristic for each solvent. If <span class="texhtml mvar" style="font-style:italic;">w</span> represents the <a href="/wiki/Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">mass fraction</a> of the <a href="/wiki/Solute" class="mw-redirect" title="Solute">solute</a> in solution, and assuming no dissociation of the solute, the molar mass is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M={{wK_{\text{f}}} \over {\Delta T}}.\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>.</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M={{wK_{\text{f}}} \over {\Delta T}}.\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b514fa61f96d0ba989ac684a73846972eeec97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.473ex; height:5.343ex;" alt="{\displaystyle M={{wK_{\text{f}}} \over {\Delta T}}.\ }"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Boiling-point_elevation">Boiling-point elevation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=11" title="Edit section: Boiling-point elevation"><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/Boiling-point_elevation" title="Boiling-point elevation">Boiling-point elevation</a></div> <p>The <a href="/wiki/Boiling_point" title="Boiling point">boiling point</a> of a <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solution</a> of an involatile <a href="/wiki/Solute" class="mw-redirect" title="Solute">solute</a> is higher than that of the pure <a href="/wiki/Solvent" title="Solvent">solvent</a>, and the boiling-point elevation (<span class="texhtml">Δ<i>T</i></span>) is directly proportional to the <a href="/wiki/Amount_concentration" class="mw-redirect" title="Amount concentration">amount concentration</a> for dilute solutions. When the composition is expressed as a <a href="/wiki/Molality" title="Molality">molality</a>, the proportionality constant is known as the <a href="/wiki/Ebullioscopic_constant" title="Ebullioscopic constant">ebullioscopic constant</a> (<span class="texhtml"><i>K</i><sub>b</sub></span>) and is characteristic for each solvent. If <span class="texhtml mvar" style="font-style:italic;">w</span> represents the <a href="/wiki/Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">mass fraction</a> of the solute in solution, and assuming no dissociation of the solute, the molar mass is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M={{wK_{\text{b}}} \over {\Delta T}}.\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>b</mtext> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>.</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M={{wK_{\text{b}}} \over {\Delta T}}.\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bc3d87fbd00f58bfec0994383748c5264a176fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.775ex; height:5.343ex;" alt="{\displaystyle M={{wK_{\text{b}}} \over {\Delta T}}.\ }"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Mole_map_(chemistry)" title="Mole map (chemistry)">Mole map (chemistry)</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=Molar_mass&action=edit&section=13" 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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-GreenBook-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-GreenBook_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-GreenBook_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">International Union of Pure and Applied Chemistry</a> (1993). <i><a href="/wiki/Quantities,_Units_and_Symbols_in_Physical_Chemistry" title="Quantities, Units and Symbols in Physical Chemistry">Quantities, Units and Symbols in Physical Chemistry</a></i>, 2nd edition, Oxford: Blackwell Science. <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-632-03583-8" title="Special:BookSources/0-632-03583-8">0-632-03583-8</a>. p. 41. <a rel="nofollow" class="external text" href="https://old.iupac.org/publications/books/gbook/green_book_2ed.pdf">Electronic version.</a></span> </li> <li id="cite_note-AtWt-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-AtWt_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-AtWt_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWieser2006" class="citation cs2">Wieser, M. E. (2006), <a rel="nofollow" class="external text" href="http://www.iupac.org/publications/pac/2006/pdf/7811x2051.pdf">"Atomic Weights of the Elements 2005"</a> <span class="cs1-format">(PDF)</span>, <i><a href="/wiki/Pure_and_Applied_Chemistry" title="Pure and Applied Chemistry">Pure and Applied Chemistry</a></i>, <b>78</b> (11): 2051–66, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fpac200678112051">10.1351/pac200678112051</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pure+and+Applied+Chemistry&rft.atitle=Atomic+Weights+of+the+Elements+2005&rft.volume=78&rft.issue=11&rft.pages=2051-66&rft.date=2006&rft_id=info%3Adoi%2F10.1351%2Fpac200678112051&rft.aulast=Wieser&rft.aufirst=M.+E.&rft_id=http%3A%2F%2Fwww.iupac.org%2Fpublications%2Fpac%2F2006%2Fpdf%2F7811x2051.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">"International union of pure and applied chemistry, commission on macromolecular nomenclature, note on the terminology for molar masses in polymer science". <i>Journal of Polymer Science: Polymer Letters Edition</i>. <b>22</b> (1): 57. 1984. <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/1984JPoSL..22...57.">1984JPoSL..22...57.</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fpol.1984.130220116">10.1002/pol.1984.130220116</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+Polymer+Science%3A+Polymer+Letters+Edition&rft.atitle=International+union+of+pure+and+applied+chemistry%2C+commission+on+macromolecular+nomenclature%2C+note+on+the+terminology+for+molar+masses+in+polymer+science&rft.volume=22&rft.issue=1&rft.pages=57&rft.date=1984&rft_id=info%3Adoi%2F10.1002%2Fpol.1984.130220116&rft_id=info%3Abibcode%2F1984JPoSL..22...57.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMetanomski1991" class="citation book cs1">Metanomski, W. V. (1991). <i>Compendium of Macromolecular Nomenclature</i>. Oxford: <a href="/wiki/Blackwell_Science" class="mw-redirect" title="Blackwell Science">Blackwell Science</a>. pp. 47–73. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-632-02847-5" title="Special:BookSources/0-632-02847-5"><bdi>0-632-02847-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Compendium+of+Macromolecular+Nomenclature&rft.place=Oxford&rft.pages=47-73&rft.pub=Blackwell+Science&rft.date=1991&rft.isbn=0-632-02847-5&rft.aulast=Metanomski&rft.aufirst=W.+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">The Engineering ToolBox <a rel="nofollow" class="external text" href="http://www.engineeringtoolbox.com/molecular-mass-air-d_679.html">Molecular Mass of Air</a></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physics.nist.gov/cgi-bin/cuu/Value?u">"CODATA Value: atomic mass constant"</a>. <i>physics.nist.gov</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-06-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=physics.nist.gov&rft.atitle=CODATA+Value%3A+atomic+mass+constant&rft_id=https%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2Fcuu%2FValue%3Fu&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> <li id="cite_note-SI-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-SI_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-SI_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFInternational_Bureau_of_Weights_and_Measures2006" class="citation cs2"><a href="/wiki/International_Bureau_of_Weights_and_Measures" title="International Bureau of Weights and Measures">International Bureau of Weights and Measures</a> (2006), <a rel="nofollow" class="external text" href="https://www.bipm.org/documents/20126/41483022/si_brochure_8.pdf"><i>The International System of Units (SI)</i></a> <span class="cs1-format">(PDF)</span> (8th ed.), p. 126, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/92-822-2213-6" title="Special:BookSources/92-822-2213-6"><bdi>92-822-2213-6</bdi></a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210604163219/https://www.bipm.org/documents/20126/41483022/si_brochure_8.pdf">archived</a> <span class="cs1-format">(PDF)</span> from the original on 2021-06-04<span class="reference-accessdate">, retrieved <span class="nowrap">2021-12-16</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+International+System+of+Units+%28SI%29&rft.pages=126&rft.edition=8th&rft.date=2006&rft.isbn=92-822-2213-6&rft.au=International+Bureau+of+Weights+and+Measures&rft_id=https%3A%2F%2Fwww.bipm.org%2Fdocuments%2F20126%2F41483022%2Fsi_brochure_8.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <i><a href="/wiki/IUPAC_books#Gold_Book" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a></i>, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/R05270.html">relative molar mass</a>". <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.R05270">10.1351/goldbook.R05270</a></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=html&isotype=some">"Atomic Weights and Isotopic Compositions for All Elements"</a>. <a href="/wiki/NIST" class="mw-redirect" title="NIST">NIST</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2007-10-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Atomic+Weights+and+Isotopic+Compositions+for+All+Elements&rft.pub=NIST&rft_id=http%3A%2F%2Fphysics.nist.gov%2Fcgi-bin%2FCompositions%2Fstand_alone.pl%3Fele%3D%26all%3Dall%26ascii%3Dhtml%26isotype%3Dsome&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</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.rsc.org/Publishing/ReSourCe/AuthorGuidelines/ArticleLayout/sect3.asp">"Author Guidelines – Article Layout"</a>. <a href="/wiki/Royal_Society_of_Chemistry" title="Royal Society of Chemistry">RSC Publishing</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2007-10-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Author+Guidelines+%E2%80%93+Article+Layout&rft.pub=RSC+Publishing&rft_id=http%3A%2F%2Fwww.rsc.org%2FPublishing%2FReSourCe%2FAuthorGuidelines%2FArticleLayout%2Fsect3.asp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenwoodEarnshaw1997" class="citation book cs1"><a href="/wiki/Norman_Greenwood" title="Norman Greenwood">Greenwood, Norman N.</a>; Earnshaw, Alan (1997). <i>Chemistry of the Elements</i> (2nd ed.). <a href="/wiki/Butterworth-Heinemann" title="Butterworth-Heinemann">Butterworth-Heinemann</a>. p. 21. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-037941-8" title="Special:BookSources/978-0-08-037941-8"><bdi>978-0-08-037941-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry+of+the+Elements&rft.pages=21&rft.edition=2nd&rft.pub=Butterworth-Heinemann&rft.date=1997&rft.isbn=978-0-08-037941-8&rft.aulast=Greenwood&rft.aufirst=Norman+N.&rft.au=Earnshaw%2C+Alan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" 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">See, e.g., <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeast,_R._C.1972" class="citation book cs1">Weast, R. C., ed. (1972). <i>Handbook of Chemistry and Physics</i> (53rd ed.). Cleveland, OH: Chemical Rubber Co.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Chemistry+and+Physics&rft.place=Cleveland%2C+OH&rft.edition=53rd&rft.pub=Chemical+Rubber+Co.&rft.date=1972&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" 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"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPossolovan_der_VeenMeijaHibbert2018" class="citation journal cs1">Possolo, Antonio; van der Veen, Adriaan M. H.; Meija, Juris; Hibbert, D. Brynn (2018-01-04). <a rel="nofollow" class="external text" href="https://nrc-publications.canada.ca/eng/view/fulltext/?id=f1f2ca7f-9b5f-4da0-bbba-d196cc190911">"Interpreting and propagating the uncertainty of the standard atomic weights (IUPAC Technical Report)"</a>. <i>Pure and Applied Chemistry</i>. <b>90</b> (2): 395–424. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fpac-2016-0402">10.1515/pac-2016-0402</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:145931362">145931362</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pure+and+Applied+Chemistry&rft.atitle=Interpreting+and+propagating+the+uncertainty+of+the+standard+atomic+weights+%28IUPAC+Technical+Report%29&rft.volume=90&rft.issue=2&rft.pages=395-424&rft.date=2018-01-04&rft_id=info%3Adoi%2F10.1515%2Fpac-2016-0402&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A145931362%23id-name%3DS2CID&rft.aulast=Possolo&rft.aufirst=Antonio&rft.au=van+der+Veen%2C+Adriaan+M.+H.&rft.au=Meija%2C+Juris&rft.au=Hibbert%2C+D.+Brynn&rft_id=https%3A%2F%2Fnrc-publications.canada.ca%2Feng%2Fview%2Ffulltext%2F%3Fid%3Df1f2ca7f-9b5f-4da0-bbba-d196cc190911&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+mass" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Molar_mass&action=edit&section=14" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">The technical definition is that the relative molar mass is the molar mass measured on a scale where the molar mass of unbound <a href="/wiki/Carbon_12" class="mw-redirect" title="Carbon 12">carbon 12</a> atoms, at rest and in their electronic ground state, is 12. The simpler definition given here is equivalent to the full definition because of the way the <a href="/wiki/Molar_mass_constant" title="Molar mass constant">molar mass constant</a> is itself defined.</span> </li> </ol></div></div> <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=Molar_mass&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://hox.io/molcalc">HTML5 Molar Mass Calculator</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170425114833/http://hox.io/molcalc/">Archived</a> 2017-04-25 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> web and mobile application.</li> <li><a rel="nofollow" class="external text" href="http://www.chem4free.info/calculators/molarmass.htm">Online Molar Mass Calculator</a> with the uncertainty of <i>M</i> and all the calculations shown</li> <li><a rel="nofollow" class="external text" href="http://www.webqc.org/mmcalc.php">Molar Mass Calculator</a> Online Molar Mass and Elemental Composition Calculator</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 coefficients and stoichiometry. It includes both average atomic weights and isotopic weights.</li> <li><a rel="nofollow" class="external text" href="http://www.physics-chemistry-class.com/chemistry/molar-mass.html">Molar mass: chemistry second-level course</a>.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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.navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Mole_concepts" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse 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4em"><a href="/wiki/Mole_(unit)" title="Mole (unit)">Mole</a> concepts</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constants</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a></li> <li><a href="/wiki/Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a></li> <li><a href="/wiki/Gas_constant" title="Gas constant">Gas constant</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical quantities</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mass_concentration_(chemistry)" title="Mass concentration (chemistry)">Mass concentration</a></li> <li><a href="/wiki/Molar_concentration" title="Molar concentration">Molar concentration</a></li> <li><a href="/wiki/Molality" title="Molality">Molality</a></li> <li><a href="/wiki/Mass" title="Mass">Mass</a></li> <li><a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></li> <li><a href="/wiki/Density" title="Density">Density</a></li> <li><a href="/wiki/Mole_fraction" title="Mole fraction">Mole fraction</a></li> <li><a href="/wiki/Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">Mass fraction</a></li> <li><a href="/wiki/Amount_of_substance" title="Amount of substance">Amount of substance</a></li> <li><a class="mw-selflink selflink">Molar mass</a></li> <li><a href="/wiki/Atomic_mass" title="Atomic mass">Atomic mass</a></li> <li><a href="/wiki/Particle_number" title="Particle number">Particle number</a></li> <li><a href="/wiki/Pressure" title="Pressure">Pressure</a></li> <li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Thermodynamic temperature</a></li> <li><a href="/wiki/Molar_volume" title="Molar volume">Molar volume</a></li> <li><a href="/wiki/Specific_volume" title="Specific volume">Specific volume</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Laws</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Avogadro%27s_law" title="Avogadro's law">Avogadro's law</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link 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