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class="minerva-icon minerva-icon--edit"></span> <span>Edit</span> </a> </li> </ul> </nav>  <div id="mw-content-subtitle"></div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"><script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><section class="mf-section-0" id="mf-section-0"> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Molarity" redirects here. Not to be confused with <a href="/wiki/Molality" title="Molality">Molality</a> or <a href="/wiki/Morality" title="Morality">Morality</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><p><b>Molar concentration</b> (also called <b>molarity</b>, <b>amount concentration</b> or <b>substance concentration</b>) is a measure of the <a href="/wiki/Concentration" title="Concentration">concentration</a> of a <a href="/wiki/Chemical_species" title="Chemical species">chemical species</a>, in particular, of a <a href="/wiki/Solute" class="mw-redirect" title="Solute">solute</a> in a <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solution</a>, in terms of <a href="/wiki/Amount_of_substance" title="Amount of substance">amount of substance</a> per unit <a href="/wiki/Volume" title="Volume">volume</a> of solution. In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, the most commonly used unit for molarity is the number of <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a> per <a href="/wiki/Liter" class="mw-redirect" title="Liter">liter</a>, having the unit symbol mol/L or <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>/<a href="/wiki/Decimetre" title="Decimetre">dm</a><sup>3</sup> in SI units. A solution with a concentration of 1 mol/L is said to be 1 <b>molar</b>, commonly designated as 1 M or 1 <u>M</u>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as [H<sup>+</sup>]. </p><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Molar concentration</th></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;">c</span>, <span class="nowrap">[chemical symbol or formula]</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">mol/m<sup>3</sup></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">mol/L</td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Derivations from<br>other quantities</div></th><td class="infobox-data"><span class="texhtml"><i>c</i> = <i>n</i>/<i>V</i></span></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"><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 {\mathsf {L}}^{-3}{\mathsf {N}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">N</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {L}}^{-3}{\mathsf {N}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0c049e7c3cf001fbe67f32331f692f9de048300" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.238ex; height:2.676ex;" alt="{\displaystyle {\mathsf {L}}^{-3}{\mathsf {N}}}"></span></td></tr></tbody></table> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Definition"><span class="tocnumber">1</span> <span class="toctext">Definition</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="#Formality_or_analytical_concentration"><span class="tocnumber">1.1</span> <span class="toctext">Formality or analytical concentration</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-3"><a href="#Units"><span class="tocnumber">2</span> <span class="toctext">Units</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#Related_quantities"><span class="tocnumber">3</span> <span class="toctext">Related quantities</span></a> <ul> <li class="toclevel-2 tocsection-5"><a href="#Number_concentration"><span class="tocnumber">3.1</span> <span class="toctext">Number concentration</span></a></li> <li class="toclevel-2 tocsection-6"><a href="#Mass_concentration"><span class="tocnumber">3.2</span> <span class="toctext">Mass concentration</span></a></li> <li class="toclevel-2 tocsection-7"><a href="#Mole_fraction"><span class="tocnumber">3.3</span> <span class="toctext">Mole fraction</span></a></li> <li class="toclevel-2 tocsection-8"><a href="#Mass_fraction"><span class="tocnumber">3.4</span> <span class="toctext">Mass fraction</span></a></li> <li class="toclevel-2 tocsection-9"><a href="#Molality"><span class="tocnumber">3.5</span> <span class="toctext">Molality</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-10"><a href="#Properties"><span class="tocnumber">4</span> <span class="toctext">Properties</span></a> <ul> <li class="toclevel-2 tocsection-11"><a href="#Sum_of_molar_concentrations_%E2%80%93_normalizing_relations"><span class="tocnumber">4.1</span> <span class="toctext">Sum of molar concentrations – normalizing relations</span></a></li> <li class="toclevel-2 tocsection-12"><a href="#Sum_of_products_of_molar_concentrations_and_partial_molar_volumes"><span class="tocnumber">4.2</span> <span class="toctext">Sum of products of molar concentrations and partial molar volumes</span></a></li> <li class="toclevel-2 tocsection-13"><a href="#Dependence_on_volume"><span class="tocnumber">4.3</span> <span class="toctext">Dependence on volume</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-14"><a href="#Examples"><span class="tocnumber">5</span> <span class="toctext">Examples</span></a></li> <li class="toclevel-1 tocsection-15"><a href="#See_also"><span class="tocnumber">6</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-16"><a href="#References"><span class="tocnumber">7</span> <span class="toctext">References</span></a></li> <li class="toclevel-1 tocsection-17"><a href="#External_links"><span class="tocnumber">8</span> <span class="toctext">External links</span></a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Definition">Definition</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=1" title="Edit section: Definition" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>Molar concentration or molarity is most commonly expressed in units of moles of <a href="/wiki/Solute" class="mw-redirect" title="Solute">solute</a> per litre of <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solution</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> For use in broader applications, it is defined as <a href="/wiki/Amount_of_substance" title="Amount of substance">amount of substance</a> of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></noscript><span class="lazy-image-placeholder" style="width: 1.007ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" data-alt="{\displaystyle c}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>:<sup id="cite_ref-GoldBook_3-0" class="reference"><a href="#cite_note-GoldBook-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c={\frac {n}{V}}={\frac {N}{N_{\text{A}}\,V}}={\frac {C}{N_{\text{A}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mi>V</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>N</mi> <mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mi>V</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>C</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </msub> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c={\frac {n}{V}}={\frac {N}{N_{\text{A}}\,V}}={\frac {C}{N_{\text{A}}}}.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d67a4efd0627465b007b944d388a18ada05ec12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.081ex; height:5.843ex;" alt="{\displaystyle c={\frac {n}{V}}={\frac {N}{N_{\text{A}}\,V}}={\frac {C}{N_{\text{A}}}}.}"></noscript><span class="lazy-image-placeholder" style="width: 24.081ex;height: 5.843ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d67a4efd0627465b007b944d388a18ada05ec12" data-alt="{\displaystyle c={\frac {n}{V}}={\frac {N}{N_{\text{A}}\,V}}={\frac {C}{N_{\text{A}}}}.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>Here, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></noscript><span class="lazy-image-placeholder" style="width: 1.395ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" data-alt="{\displaystyle n}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the amount of the solute in moles,<sup id="cite_ref-kaufman_4-0" class="reference"><a href="#cite_note-kaufman-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></noscript><span class="lazy-image-placeholder" style="width: 2.064ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" data-alt="{\displaystyle N}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the number of <a href="/wiki/Particle_number" title="Particle number">constituent particles</a> present in volume <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></noscript><span class="lazy-image-placeholder" style="width: 1.787ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" data-alt="{\displaystyle V}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> (in litres) of the solution, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{\text{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{\text{A}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/037f8d054f445451d8fee1b440cddba989e66ea1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.331ex; height:2.509ex;" alt="{\displaystyle N_{\text{A}}}"></noscript><span class="lazy-image-placeholder" style="width: 3.331ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/037f8d054f445451d8fee1b440cddba989e66ea1" data-alt="{\displaystyle N_{\text{A}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>, since 2019 defined as exactly <span class="nowrap"><span data-sort-value="7023602214076000000♠"></span>6.022<span style="margin-left:.25em;">140</span><span style="margin-left:.25em;">76</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>23</sup> mol<sup>−1</sup></span>. The ratio <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 {N}{V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>N</mi> <mi>V</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {N}{V}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efb0e2c09f237284b86f9fae654270de0ba1d310" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:2.9ex; height:5.343ex;" alt="{\displaystyle {\frac {N}{V}}}"></noscript><span class="lazy-image-placeholder" style="width: 2.9ex;height: 5.343ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efb0e2c09f237284b86f9fae654270de0ba1d310" data-alt="{\displaystyle {\frac {N}{V}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the <a href="/wiki/Number_density" title="Number density">number density</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></noscript><span class="lazy-image-placeholder" style="width: 1.766ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" data-alt="{\displaystyle C}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. </p><p>In <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, the use of molar concentration is often not convenient because the volume of most solutions slightly depends on <a href="/wiki/Temperature" title="Temperature">temperature</a> due to <a href="/wiki/Thermal_expansion" title="Thermal expansion">thermal expansion</a>. This problem is usually resolved by introducing temperature correction <a href="/wiki/Coefficient" title="Coefficient">factors</a>, or by using a temperature-independent measure of concentration such as <a href="/wiki/Molality" title="Molality">molality</a>.<sup id="cite_ref-kaufman_4-1" class="reference"><a href="#cite_note-kaufman-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="https://en.wiktionary.org/wiki/reciprocal" class="extiw" title="wikt:reciprocal">reciprocal</a> quantity represents the dilution (volume) which can appear in Ostwald's <a href="/wiki/Law_of_dilution" title="Law of dilution">law of dilution</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Formality_or_analytical_concentration">Formality or analytical concentration</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=2" title="Edit section: Formality or analytical concentration" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p><span class="anchor" id="Formal"></span> If a molecule or salt dissociates in solution, the concentration refers to the original chemical formula in solution, the molar concentration is sometimes called <b>formal concentration</b> or <b>formality</b> (<i>F</i><sub>A</sub>) or <b>analytical concentration</b> (<i>c</i><sub>A</sub>). For example, if a sodium carbonate solution (<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">Na<sub class="template-chem2-sub">2</sub>CO<sub class="template-chem2-sub">3</sub></span>) has a formal concentration of <i>c</i>(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Na<sub class="template-chem2-sub">2</sub>CO<sub class="template-chem2-sub">3</sub></span>) = 1 mol/L, the molar concentrations are <i>c</i>(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">Na<sup class="template-chem2-sup">+</sup></span>) = 2 mol/L and <i>c</i>(<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410"><span class="chemf nowrap">CO<span class="template-chem2-su"><span>2−</span><span>3</span></span></span>) = 1 mol/L because the salt dissociates into these ions.<sup id="cite_ref-Harvey_2020_5-0" class="reference"><a href="#cite_note-Harvey_2020-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Units">Units</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=3" title="Edit section: Units" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> <p>In the <a href="/wiki/International_System_of_Units" title="International System of Units">International System of Units</a> (SI), the <a href="/wiki/Coherence_(units_of_measurement)" title="Coherence (units of measurement)">coherent unit</a> for molar concentration is <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>/<a href="/wiki/Metre" title="Metre">m</a><sup>3</sup>. However, most chemical literature traditionally uses <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>/<a href="/wiki/Decimetre" title="Decimetre">dm</a><sup>3</sup>, which is the same as <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>/<a href="/wiki/Litre" title="Litre">L</a>. This traditional unit is often called a <b>molar</b> and denoted by the letter M, for example: </p> <dl><dd>1 <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>/<a href="/wiki/Metre" title="Metre">m</a><sup>3</sup> = 10<sup>−3</sup> <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>/<a href="/wiki/Decimetre" title="Decimetre">dm</a><sup>3</sup> = 10<sup>−3</sup> <a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a>/<a href="/wiki/Litre" title="Litre">L</a> = 10<sup>−3</sup> M = 1 mM = 1 mmol/L.</dd></dl> <p>The <a href="/wiki/SI_prefix" class="mw-redirect" title="SI prefix">SI prefix</a> "<a href="/wiki/Mega-" title="Mega-">mega</a>" (symbol M) has the same symbol. However, the prefix is never used alone, so "M" unambiguously denotes molar. Sub-multiples, such as "millimolar" (mM) and "nanomolar" (nM), consist of the unit preceded by an <a href="/wiki/SI_prefix" class="mw-redirect" title="SI prefix">SI prefix</a>: </p> <table class="wikitable" style="text-align:center;" border="0"> <tbody><tr> <th rowspan="2">Name </th> <th rowspan="2">Abbreviation </th> <th colspan="2">Concentration </th></tr> <tr> <th>(mol/L) </th> <th>(mol/m<sup>3</sup>) </th></tr> <tr> <td><span class="anchor" id="millimolar"></span>millimolar </td> <td>mM </td> <td>10<sup>−3</sup> </td> <td>10<sup>0</sup>=1 </td></tr> <tr> <td>micromolar </td> <td>μM </td> <td>10<sup>−6</sup> </td> <td>10<sup>−3</sup> </td></tr> <tr> <td>nanomolar </td> <td>nM </td> <td>10<sup>−9</sup> </td> <td>10<sup>−6</sup> </td></tr> <tr> <td>picomolar </td> <td>pM </td> <td>10<sup>−12</sup> </td> <td>10<sup>−9</sup> </td></tr> <tr> <td>femtomolar </td> <td>fM </td> <td>10<sup>−15</sup> </td> <td>10<sup>−12</sup> </td></tr> <tr> <td>attomolar </td> <td>aM </td> <td>10<sup>−18</sup> </td> <td>10<sup>−15</sup> </td></tr> <tr> <td>zeptomolar </td> <td>zM </td> <td>10<sup>−21</sup> </td> <td>10<sup>−18</sup> </td></tr> <tr> <td>yoctomolar </td> <td>yM </td> <td>10<sup>−24</sup><br>(6 particles per 10 L) </td> <td>10<sup>−21</sup> </td></tr> <tr> <td>rontomolar </td> <td>rM </td> <td>10<sup>−27</sup> </td> <td>10<sup>−24</sup> </td></tr> <tr> <td>quectomolar </td> <td>qM </td> <td>10<sup>−30</sup> </td> <td>10<sup>−27</sup> </td></tr></tbody></table> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Related_quantities">Related quantities</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=4" title="Edit section: Related quantities" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> <div class="mw-heading mw-heading3"><h3 id="Number_concentration">Number concentration</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=5" title="Edit section: Number concentration" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The conversion to <a href="/wiki/Number_concentration" class="mw-redirect" title="Number concentration">number concentration</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{i}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc49dc02c0ec8c86b67e7d10518ac791eda0bf22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.461ex; height:2.509ex;" alt="{\displaystyle C_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.461ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc49dc02c0ec8c86b67e7d10518ac791eda0bf22" data-alt="{\displaystyle C_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></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 C_{i}=c_{i}N_{\text{A}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{i}=c_{i}N_{\text{A}},}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f3c6ba085d8142eac47ca6e479537d69b007143" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.344ex; height:2.509ex;" alt="{\displaystyle C_{i}=c_{i}N_{\text{A}},}"></noscript><span class="lazy-image-placeholder" style="width: 11.344ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f3c6ba085d8142eac47ca6e479537d69b007143" data-alt="{\displaystyle C_{i}=c_{i}N_{\text{A}},}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{\text{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{\text{A}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/037f8d054f445451d8fee1b440cddba989e66ea1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.331ex; height:2.509ex;" alt="{\displaystyle N_{\text{A}}}"></noscript><span class="lazy-image-placeholder" style="width: 3.331ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/037f8d054f445451d8fee1b440cddba989e66ea1" data-alt="{\displaystyle N_{\text{A}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Mass_concentration">Mass concentration</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=6" title="Edit section: Mass concentration" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The conversion to <a href="/wiki/Mass_concentration_(chemistry)" title="Mass concentration (chemistry)">mass concentration</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 \rho _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{i}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f9e51d2ad9cab8f8a5d962502ddf4189b713f7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.002ex; height:2.176ex;" alt="{\displaystyle \rho _{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.002ex;height: 2.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f9e51d2ad9cab8f8a5d962502ddf4189b713f7a" data-alt="{\displaystyle \rho _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></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 _{i}=c_{i}M_{i},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>c</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 \rho _{i}=c_{i}M_{i},}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1eaaa0cd8ea1bfceb5f559affaf5efda04b5d827" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.607ex; height:2.676ex;" alt="{\displaystyle \rho _{i}=c_{i}M_{i},}"></noscript><span class="lazy-image-placeholder" style="width: 10.607ex;height: 2.676ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1eaaa0cd8ea1bfceb5f559affaf5efda04b5d827" data-alt="{\displaystyle \rho _{i}=c_{i}M_{i},}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{i}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eda8fd06f1cd5de22ed07385a0f8aa19773b2de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.054ex; height:2.509ex;" alt="{\displaystyle M_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 3.054ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eda8fd06f1cd5de22ed07385a0f8aa19773b2de9" data-alt="{\displaystyle M_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a> of constituent <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 i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Mole_fraction">Mole fraction</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=7" title="Edit section: Mole fraction" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The conversion to <a href="/wiki/Mole_fraction" title="Mole fraction">mole fraction</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 x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.129ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158" data-alt="{\displaystyle x_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></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 x_{i}=c_{i}{\frac {\overline {M}}{\rho }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mover> <mi>M</mi> <mo accent="false">¯</mo> </mover> <mi>ρ</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}=c_{i}{\frac {\overline {M}}{\rho }},}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c98493905528f473957f0d84aa8c7f0f72b8332" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.197ex; height:6.509ex;" alt="{\displaystyle x_{i}=c_{i}{\frac {\overline {M}}{\rho }},}"></noscript><span class="lazy-image-placeholder" style="width: 11.197ex;height: 6.509ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c98493905528f473957f0d84aa8c7f0f72b8332" data-alt="{\displaystyle x_{i}=c_{i}{\frac {\overline {M}}{\rho }},}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\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><noscript><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}}}"></noscript><span class="lazy-image-placeholder" style="width: 2.68ex;height: 3.009ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0e2d2cef85c7247cc507120eb8980b6f2714591" data-alt="{\displaystyle {\overline {M}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the average molar mass of the solution, <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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></noscript><span class="lazy-image-placeholder" style="width: 1.202ex;height: 2.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" data-alt="{\displaystyle \rho }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the <a href="/wiki/Density" title="Density">density</a> of the solution. </p><p>A simpler relation can be obtained by considering the total molar concentration, namely, the sum of molar concentrations of all the components of the mixture: </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 x_{i}={\frac {c_{i}}{c}}={\frac {c_{i}}{\sum _{j}c_{j}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}={\frac {c_{i}}{c}}={\frac {c_{i}}{\sum _{j}c_{j}}}.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac62a43ae1bf16ccabb3db3d56e456f2d5eb68a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.119ex; height:5.843ex;" alt="{\displaystyle x_{i}={\frac {c_{i}}{c}}={\frac {c_{i}}{\sum _{j}c_{j}}}.}"></noscript><span class="lazy-image-placeholder" style="width: 18.119ex;height: 5.843ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac62a43ae1bf16ccabb3db3d56e456f2d5eb68a9" data-alt="{\displaystyle x_{i}={\frac {c_{i}}{c}}={\frac {c_{i}}{\sum _{j}c_{j}}}.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Mass_fraction">Mass fraction</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=8" title="Edit section: Mass fraction" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The conversion to <a href="/wiki/Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">mass fraction</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 w_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{i}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe22f0329d3ecb2e1880d44d191aba0e5475db68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.464ex; height:2.009ex;" alt="{\displaystyle w_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.464ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe22f0329d3ecb2e1880d44d191aba0e5475db68" data-alt="{\displaystyle w_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></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 w_{i}=c_{i}{\frac {M_{i}}{\rho }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>ρ</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{i}=c_{i}{\frac {M_{i}}{\rho }}.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64b1414007fdfd0166fbead8dbf199a67bafb2c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.906ex; height:5.676ex;" alt="{\displaystyle w_{i}=c_{i}{\frac {M_{i}}{\rho }}.}"></noscript><span class="lazy-image-placeholder" style="width: 11.906ex;height: 5.676ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64b1414007fdfd0166fbead8dbf199a67bafb2c5" data-alt="{\displaystyle w_{i}=c_{i}{\frac {M_{i}}{\rho }}.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Molality">Molality</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=9" title="Edit section: Molality" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>For binary mixtures, the conversion to <a href="/wiki/Molality" title="Molality">molality</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 b_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{2}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2530a260ad35bf21ee61f1f4d6493ae0474f6068" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.052ex; height:2.509ex;" alt="{\displaystyle b_{2}}"></noscript><span class="lazy-image-placeholder" style="width: 2.052ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2530a260ad35bf21ee61f1f4d6493ae0474f6068" data-alt="{\displaystyle b_{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{2}={\frac {c_{2}}{\rho -c_{1}M_{1}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mi>ρ</mi> <mo>−</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{2}={\frac {c_{2}}{\rho -c_{1}M_{1}}},}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d52281bbc84065528f88e8955740ea5e4dbf4be7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.045ex; height:5.176ex;" alt="{\displaystyle b_{2}={\frac {c_{2}}{\rho -c_{1}M_{1}}},}"></noscript><span class="lazy-image-placeholder" style="width: 16.045ex;height: 5.176ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d52281bbc84065528f88e8955740ea5e4dbf4be7" data-alt="{\displaystyle b_{2}={\frac {c_{2}}{\rho -c_{1}M_{1}}},}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>where the solvent is substance 1, and the solute is substance 2. </p><p>For solutions with more than one solute, the conversion is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{i}={\frac {c_{i}}{\rho -\sum _{j\neq i}c_{j}M_{j}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mi>ρ</mi> <mo>−</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>≠</mo> <mi>i</mi> </mrow> </munder> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{i}={\frac {c_{i}}{\rho -\sum _{j\neq i}c_{j}M_{j}}}.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbdc322925b265a4b14da5ba8df529514ad68c6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.098ex; height:5.843ex;" alt="{\displaystyle b_{i}={\frac {c_{i}}{\rho -\sum _{j\neq i}c_{j}M_{j}}}.}"></noscript><span class="lazy-image-placeholder" style="width: 21.098ex;height: 5.843ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbdc322925b265a4b14da5ba8df529514ad68c6f" data-alt="{\displaystyle b_{i}={\frac {c_{i}}{\rho -\sum _{j\neq i}c_{j}M_{j}}}.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Properties">Properties</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=10" title="Edit section: Properties" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> <div class="mw-heading mw-heading3"><h3 id="Sum_of_molar_concentrations_–_normalizing_relations"><span id="Sum_of_molar_concentrations_.E2.80.93_normalizing_relations"></span>Sum of molar concentrations – normalizing relations</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=11" title="Edit section: Sum of molar concentrations – normalizing relations" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The sum of molar concentrations gives the total molar concentration, namely the density of the mixture divided by the molar mass of the mixture or by another name the reciprocal of the molar volume of the mixture. In an ionic solution, ionic strength is proportional to the sum of the molar concentration of salts. </p> <div class="mw-heading mw-heading3"><h3 id="Sum_of_products_of_molar_concentrations_and_partial_molar_volumes">Sum of products of molar concentrations and partial molar volumes</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=12" title="Edit section: Sum of products of molar concentrations and partial molar volumes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The sum of products between these quantities equals one: </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 \sum _{i}c_{i}{\overline {V_{i}}}=1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i}c_{i}{\overline {V_{i}}}=1.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/757798d18d18ee016119cc0c164220a47c0b9e6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:12.726ex; height:5.676ex;" alt="{\displaystyle \sum _{i}c_{i}{\overline {V_{i}}}=1.}"></noscript><span class="lazy-image-placeholder" style="width: 12.726ex;height: 5.676ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/757798d18d18ee016119cc0c164220a47c0b9e6e" data-alt="{\displaystyle \sum _{i}c_{i}{\overline {V_{i}}}=1.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Dependence_on_volume">Dependence on volume</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=13" title="Edit section: Dependence on volume" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The molar concentration depends on the variation of the volume of the solution due mainly to thermal expansion. On small intervals of temperature, the dependence is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{i}={\frac {c_{i,T_{0}}}{1+\alpha \Delta T}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> <mrow> <mn>1</mn> <mo>+</mo> <mi>α</mi> <mi mathvariant="normal">Δ</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{i}={\frac {c_{i,T_{0}}}{1+\alpha \Delta T}},}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3bdfa5a5c93276e8b6214d1bb3ebedc3c1d3ee9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.451ex; height:5.343ex;" alt="{\displaystyle c_{i}={\frac {c_{i,T_{0}}}{1+\alpha \Delta T}},}"></noscript><span class="lazy-image-placeholder" style="width: 15.451ex;height: 5.343ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3bdfa5a5c93276e8b6214d1bb3ebedc3c1d3ee9" data-alt="{\displaystyle c_{i}={\frac {c_{i,T_{0}}}{1+\alpha \Delta T}},}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{i,T_{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{i,T_{0}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5a9f07e11ba94247c24b3223f9f6f6ecd2d7174" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.055ex; height:2.343ex;" alt="{\displaystyle c_{i,T_{0}}}"></noscript><span class="lazy-image-placeholder" style="width: 4.055ex;height: 2.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5a9f07e11ba94247c24b3223f9f6f6ecd2d7174" data-alt="{\displaystyle c_{i,T_{0}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the molar concentration at a reference temperature, <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></noscript><span class="lazy-image-placeholder" style="width: 1.488ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" data-alt="{\displaystyle \alpha }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the <a href="/wiki/Thermal_expansion_coefficient" class="mw-redirect" title="Thermal expansion coefficient">thermal expansion coefficient</a> of the mixture. </p> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Examples">Examples</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=14" title="Edit section: Examples" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <div><ul><li>11.6 g of <a href="/wiki/NaCl" class="mw-redirect" title="NaCl">NaCl</a> is dissolved in 100 g of water. The final mass concentration <i>ρ</i>(NaCl) is <dl><dd><i>ρ</i>(NaCl) = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">11.6 g</span><span class="sr-only">/</span><span class="den">11.6 g + 100 g</span></span>⁠</span> = 0.104 g/g = 10.4 %.</dd></dl> <p>The volume of such a solution is 104.3mL (volume is directly observable); its density is calculated to be 1.07 (111.6g/104.3mL) </p><p>The molar concentration of NaCl in the solution is therefore </p> <dl><dd><i>c</i>(NaCl) = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">11.6 g</span><span class="sr-only">/</span><span class="den">58 g/mol</span></span>⁠</span> / 104.3 mL = 0.00192 mol/mL = 1.92 mol/L.</dd></dl> Here, 58 g/mol is the <a href="/wiki/Molar_mass" title="Molar mass">molar mass</a> of NaCl.</li><li>A typical task in chemistry is the preparation of 100 mL (= 0.1 L) of a 2 mol/L solution of NaCl in water. The mass of salt needed is <dl><dd><i>m</i>(NaCl) = 2 mol/L × 0.1 L × 58 g/mol = 11.6 g.</dd></dl> To create the solution, 11.6 g NaCl is placed in a <a href="/wiki/Volumetric_flask" title="Volumetric flask">volumetric flask</a>, dissolved in some water, then followed by the addition of more water until the total volume reaches 100 mL.</li><li>The density of <a href="/wiki/Water" title="Water">water</a> is approximately 1000 g/L and its molar mass is 18.02 g/mol (or 1/18.02 = 0.055 mol/g). Therefore, the molar concentration of water is <dl><dd><i>c</i>(H<sub>2</sub>O) = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1000 g/L</span><span class="sr-only">/</span><span class="den">18.02 g/mol</span></span>⁠</span> ≈ 55.5 mol/L.</dd></dl> Likewise, the concentration of <a href="/wiki/Solid_hydrogen" title="Solid hydrogen">solid hydrogen</a> (molar mass = 2.02 g/mol) is <dl><dd><i>c</i>(H<sub>2</sub>) = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">88 g/L</span><span class="sr-only">/</span><span class="den">2.02 g/mol</span></span>⁠</span> = 43.7 mol/L.</dd></dl> The concentration of pure <a href="/wiki/Osmium_tetroxide" title="Osmium tetroxide">osmium tetroxide</a> (molar mass = 254.23 g/mol) is <dl><dd><i>c</i>(OsO<sub>4</sub>) = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">5.1 kg/L</span><span class="sr-only">/</span><span class="den">254.23 g/mol</span></span>⁠</span> = 20.1 mol/L.</dd></dl></li><li>A typical protein in <a href="/wiki/Bacterium" class="mw-redirect" title="Bacterium">bacteria</a>, such as <i><a href="/wiki/Escherichia_coli" title="Escherichia coli">E. coli</a></i>, may have about 60 copies, and the volume of a bacterium is about 10<sup>−15</sup> L. Thus, the number concentration <i>C</i> is <dd><i>C</i> = 60 / (10<sup>−15</sup> L) = 6<span style="margin:0 .15em 0 .25em">×</span>10<sup><span class="nowrap"><span data-sort-value="7001160000000000000♠"></span>16</span></sup> L<sup>−1</sup>.</dd> The molar concentration is <dl><dd><i>c</i> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>C</i></span><span class="sr-only">/</span><span class="den"><i>N</i><sub>A</sub></span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">6<span style="margin:0 .15em 0 .25em">×</span>10<sup><span class="nowrap"><span data-sort-value="7001160000000000000♠"></span>16</span></sup> L<sup>−1</sup></span><span class="sr-only">/</span><span class="den">6<span style="margin:0 .15em 0 .25em">×</span>10<sup><span class="nowrap"><span data-sort-value="7001230000000000000♠"></span>23</span></sup> mol<sup>−1</sup></span></span>⁠</span> = 10<sup>−7</sup> mol/L = 100 nmol/L.</dd></dl></li><li><a href="/wiki/Reference_ranges_for_blood_tests" title="Reference ranges for blood tests">Reference ranges for blood tests</a>, sorted by molar concentration: <div class="thumb tnone" style="margin-left:auto;margin-right:auto;overflow:hidden;width:auto;max-width:3008px"><div class="thumbinner"><div class="noresize" style="overflow:auto"><span typeof="mw:File"><a href="/wiki/File:Reference_ranges_for_blood_tests_-_by_molarity.png" class="mw-file-description"><noscript><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Reference_ranges_for_blood_tests_-_by_molarity.png/3000px-Reference_ranges_for_blood_tests_-_by_molarity.png" decoding="async" width="3000" height="174" class="mw-file-element" data-file-width="6576" data-file-height="382"></noscript><span class="lazy-image-placeholder" style="width: 3000px;height: 174px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Reference_ranges_for_blood_tests_-_by_molarity.png/3000px-Reference_ranges_for_blood_tests_-_by_molarity.png" data-alt="" data-width="3000" data-height="174" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Reference_ranges_for_blood_tests_-_by_molarity.png/4500px-Reference_ranges_for_blood_tests_-_by_molarity.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Reference_ranges_for_blood_tests_-_by_molarity.png/6000px-Reference_ranges_for_blood_tests_-_by_molarity.png 2x" data-class="mw-file-element"> </span></a></span></div></div></div></li></ul></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="See_also">See also</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=15" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-6 collapsible-block" id="mf-section-6"> <ul><li><a href="/wiki/Molality" title="Molality">Molality</a></li> <li><a href="/wiki/Orders_of_magnitude_(molar_concentration)" title="Orders of magnitude (molar concentration)">Orders of magnitude (molar concentration)</a></li></ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="References">References</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=16" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-7 collapsible-block" id="mf-section-7"> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://molaritycalc.com/">Molar Concentration calculation</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFTro,_Nivaldo_J.2014" class="citation book cs1">Tro, Nivaldo J. (6 January 2014). <i>Introductory chemistry essentials</i> (Fifth ed.). Boston. p. 457. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780321919052" title="Special:BookSources/9780321919052"><bdi>9780321919052</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/857356651">857356651</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+chemistry+essentials&rft.place=Boston&rft.pages=457&rft.edition=Fifth&rft.date=2014-01-06&rft_id=info%3Aoclcnum%2F857356651&rft.isbn=9780321919052&rft.au=Tro%2C+Nivaldo+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+concentration" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-GoldBook-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-GoldBook_3-0">^</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/A00295.html">amount concentration, <i>c</i></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.A00295">10.1351/goldbook.A00295</a></span> </li> <li id="cite_note-kaufman-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-kaufman_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-kaufman_4-1"><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="CITEREFKaufman,_Myron2002" class="citation book cs1">Kaufman, Myron (2002). <i>Principles of thermodynamics</i>. CRC Press. p. 213. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-0692-7" title="Special:BookSources/0-8247-0692-7"><bdi>0-8247-0692-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+thermodynamics&rft.pages=213&rft.pub=CRC+Press&rft.date=2002&rft.isbn=0-8247-0692-7&rft.au=Kaufman%2C+Myron&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+concentration" class="Z3988"></span></span> </li> <li id="cite_note-Harvey_2020-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Harvey_2020_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarvey2020" class="citation web cs1">Harvey, David (2020-06-15). <a rel="nofollow" class="external text" href="https://chem.libretexts.org/Courses/BethuneCookman_University/B-CU%3A_CH-345_Quantitative_Analysis/Book%3A_Analytical_Chemistry_2.1_(Harvey)/02%3A_Basic_Tools_of_Analytical_Chemistry/2.02%3A_Concentration">"2.2: Concentration"</a>. <i>Chemistry LibreTexts</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-12-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Chemistry+LibreTexts&rft.atitle=2.2%3A+Concentration&rft.date=2020-06-15&rft.aulast=Harvey&rft.aufirst=David&rft_id=https%3A%2F%2Fchem.libretexts.org%2FCourses%2FBethuneCookman_University%2FB-CU%253A_CH-345_Quantitative_Analysis%2FBook%253A_Analytical_Chemistry_2.1_%28Harvey%29%2F02%253A_Basic_Tools_of_Analytical_Chemistry%2F2.02%253A_Concentration&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMolar+concentration" class="Z3988"></span></span> </li> </ol></div></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="External_links">External links</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Molar_concentration&action=edit&section=17" title="Edit section: External links" 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id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"> <a class="last-modified-bar" href="/w/index.php?title=Molar_concentration&action=history"> <div class="post-content last-modified-bar__content"> <span class="minerva-icon minerva-icon-size-medium minerva-icon--modified-history"></span> <span class="last-modified-bar__text modified-enhancement" data-user-name="Denmosa" data-user-gender="unknown" data-timestamp="1729632749"> <span>Last edited on 22 October 2024, at 21:32</span> </span> <span class="minerva-icon minerva-icon-size-small minerva-icon--expand"></span> </div> </a> <div class="post-content footer-content"> <div id='mw-data-after-content'> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Languages</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B1%D9%83%D9%8A%D8%B2_%D9%85%D9%88%D9%84%D9%8A" title="تركيز مولي – Arabic" lang="ar" hreflang="ar" data-title="تركيز مولي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A7%8B%E0%A6%B2%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%98%E0%A6%A8%E0%A6%AE%E0%A6%BE%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BE" title="মোলীয় ঘনমাত্রা – Bangla" lang="bn" hreflang="bn" data-title="মোলীয় ঘনমাত্রা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Molaridad" title="Molaridad – Central Bikol" lang="bcl" hreflang="bcl" data-title="Molaridad" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Concentraci%C3%B3_en_quantitat_de_subst%C3%A0ncia" title="Concentració en quantitat de substància – Catalan" lang="ca" hreflang="ca" data-title="Concentració en quantitat de substància" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Mol%C3%A1rn%C3%AD_koncentrace" title="Molární koncentrace – Czech" lang="cs" hreflang="cs" data-title="Molární koncentrace" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Molaredd" title="Molaredd – Welsh" lang="cy" hreflang="cy" data-title="Molaredd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Stofm%C3%A6ngdekoncentration" title="Stofmængdekoncentration – Danish" lang="da" hreflang="da" data-title="Stofmængdekoncentration" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Stoffmengenkonzentration" title="Stoffmengenkonzentration – German" lang="de" hreflang="de" data-title="Stoffmengenkonzentration" 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/Molaarne_kontsentratsioon" title="Molaarne kontsentratsioon – Estonian" lang="et" hreflang="et" data-title="Molaarne kontsentratsioon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CF%81%CE%B1%CE%BC%CE%BC%CE%BF%CE%BC%CE%BF%CF%81%CE%B9%CE%B1%CE%BA%CF%8C%CF%84%CE%B7%CF%84%CE%B1_%CE%BA%CE%B1%CF%84%CE%84_%CF%8C%CE%B3%CE%BA%CE%BF" title="Γραμμομοριακότητα κατ΄ όγκο – Greek" lang="el" hreflang="el" data-title="Γραμμομοριακότητα κατ΄ όγκο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Molaridad" title="Molaridad – Spanish" lang="es" hreflang="es" data-title="Molaridad" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%BA%D9%84%D8%B8%D8%AA_%D9%85%D9%88%D9%84%D8%A7%D8%B1" title="غلظت مولار – Persian" lang="fa" hreflang="fa" data-title="غلظت مولار" 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/Concentration_molaire" title="Concentration molaire – French" lang="fr" hreflang="fr" data-title="Concentration 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/Molaridade" title="Molaridade – Galician" lang="gl" hreflang="gl" data-title="Molaridade" 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_%EB%86%8D%EB%8F%84" title="몰 농도 – Korean" lang="ko" hreflang="ko" data-title="몰 농도" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</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%B8%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BE" title="मोलर सान्द्रता – Hindi" lang="hi" hreflang="hi" data-title="मोलर सान्द्रता" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Molaritas" title="Molaritas – Indonesian" lang="id" hreflang="id" data-title="Molaritas" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Concentrazione_di_quantit%C3%A0_di_sostanza" title="Concentrazione di quantità di sostanza – Italian" lang="it" hreflang="it" data-title="Concentrazione di quantità di sostanza" 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%A8%D7%99%D7%9B%D7%95%D7%96_%D7%9E%D7%95%D7%9C%D7%A8%D7%99" title="ריכוז מולרי – Hebrew" lang="he" hreflang="he" data-title="ריכוז מולרי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Molarite" title="Molarite – Haitian Creole" lang="ht" hreflang="ht" data-title="Molarite" 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-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kemolaran" title="Kemolaran – Malay" lang="ms" hreflang="ms" data-title="Kemolaran" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Molaire_concentratie" title="Molaire concentratie – Dutch" lang="nl" hreflang="nl" data-title="Molaire concentratie" 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%E6%BF%83%E5%BA%A6" title="モル濃度 – Japanese" lang="ja" hreflang="ja" data-title="モル濃度" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Molar_(enhet)" title="Molar (enhet) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Molar (enhet)" 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-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Cunqooma_buroo" title="Cunqooma buroo – Oromo" lang="om" hreflang="om" data-title="Cunqooma buroo" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</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%A9%88%E0%A8%B0%E0%A8%BF%E0%A8%9F%E0%A9%80" title="ਮੋਲੈਰਿਟੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਮੋਲੈਰਿਟੀ" 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/St%C4%99%C5%BCenie_molowe" title="Stężenie molowe – Polish" lang="pl" hreflang="pl" data-title="Stężenie molowe" 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/Molaridade" title="Molaridade – Portuguese" lang="pt" hreflang="pt" data-title="Molaridade" 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/Concentra%C8%9Bie_molar%C4%83" title="Concentrație molară – Romanian" lang="ro" hreflang="ro" data-title="Concentrație molară" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/P%C3%ABrqendrimi_molar" title="Përqendrimi molar – Albanian" lang="sq" hreflang="sq" data-title="Përqendrimi molar" 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_concentration" title="Molar concentration – Simple English" lang="en-simple" hreflang="en-simple" data-title="Molar concentration" 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/Molarita" title="Molarita – Slovak" lang="sk" hreflang="sk" data-title="Molarita" 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/Molarna_koncentracija" title="Molarna koncentracija – Slovenian" lang="sl" hreflang="sl" data-title="Molarna koncentracija" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AE%DB%95%D8%B3%D8%AA%DB%8C%DB%8C_%D9%85%DB%86%D9%84%D8%A7%D8%B1" title="خەستیی مۆلار – Central Kurdish" lang="ckb" hreflang="ckb" data-title="خەستیی مۆلار" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Molarna_koncentracija" title="Molarna koncentracija – Serbian" lang="sr" hreflang="sr" data-title="Molarna koncentracija" 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-sv badge-Q70893996 mw-list-item" title=""><a href="https://sv.wikipedia.org/wiki/Molar_(enhet)" title="Molar (enhet) – Swedish" lang="sv" hreflang="sv" data-title="Molar (enhet)" 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/Molar_concentration" title="Molar concentration – Tagalog" lang="tl" hreflang="tl" data-title="Molar concentration" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Molarite" title="Molarite – Turkish" lang="tr" hreflang="tr" data-title="Molarite" 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%BA%D0%BE%D0%BD%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B0%D1%86%D1%96%D1%8F" title="Молярна концентрація – Ukrainian" lang="uk" hreflang="uk" data-title="Молярна концентрація" 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%DB%8C_%D8%A7%D8%B1%D8%AA%DA%A9%D8%A7%D8%B2" title="مولی ارتکاز – Urdu" lang="ur" hreflang="ur" data-title="مولی ارتکاز" 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/N%E1%BB%93ng_%C4%91%E1%BB%99_mol" title="Nồng độ mol – Vietnamese" lang="vi" hreflang="vi" data-title="Nồng độ 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 mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%AB%94%E7%A9%8D%E8%8E%AB%E8%80%B3%E6%BF%83%E5%BA%A6" title="體積莫耳濃度 – Chinese" lang="zh" hreflang="zh" data-title="體積莫耳濃度" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li></ul> </section> </div> <div class="minerva-footer-logo"><img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 1.125em;"/> </div> <ul id="footer-info" class="footer-info hlist hlist-separated"> <li id="footer-info-lastmod"> This page was last edited on 22 October 2024, at 21:32<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Content is available under <a class="external" rel="nofollow" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">CC BY-SA 4.0</a> unless otherwise noted.</li> </ul> <ul id="footer-places" class="footer-places hlist hlist-separated"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a 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