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<p><b>Chemical thermodynamics</b> is the study of the interrelation of <a href="/wiki/Heat" title="Heat">heat</a> and <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a> with <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> or with physical changes of <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">state</a> within the confines of the <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a>. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the <i>spontaneity</i> of processes. </p><p>The structure of chemical thermodynamics is based on the first two <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a>. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">thermodynamic system</a> can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.<sup id="cite_ref-Book1_1-0" class="reference"><a href="#cite_note-Book1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <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="#History"><span class="tocnumber">1</span> <span class="toctext">History</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Overview"><span class="tocnumber">2</span> <span class="toctext">Overview</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Chemical_energy"><span class="tocnumber">3</span> <span class="toctext">Chemical energy</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#Chemical_reactions"><span class="tocnumber">4</span> <span class="toctext">Chemical reactions</span></a> <ul> <li class="toclevel-2 tocsection-5"><a href="#Gibbs_function_or_Gibbs_Energy"><span class="tocnumber">4.1</span> <span class="toctext">Gibbs function or Gibbs Energy</span></a></li> <li class="toclevel-2 tocsection-6"><a href="#Chemical_affinity"><span class="tocnumber">4.2</span> <span class="toctext">Chemical affinity</span></a></li> <li class="toclevel-2 tocsection-7"><a href="#Solutions"><span class="tocnumber">4.3</span> <span class="toctext">Solutions</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-8"><a href="#Non-equilibrium"><span class="tocnumber">5</span> <span class="toctext">Non-equilibrium</span></a> <ul> <li class="toclevel-2 tocsection-9"><a href="#System_constraints"><span class="tocnumber">5.1</span> <span class="toctext">System constraints</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-10"><a href="#See_also"><span class="tocnumber">6</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-11"><a href="#References"><span class="tocnumber">7</span> <span class="toctext">References</span></a></li> <li class="toclevel-1 tocsection-12"><a href="#Further_reading"><span class="tocnumber">8</span> <span class="toctext">Further reading</span></a></li> <li class="toclevel-1 tocsection-13"><a href="#External_links"><span class="tocnumber">9</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="History">History</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=1" title="Edit section: History" 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"> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Willard_Gibbs.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Willard_Gibbs.jpg/170px-Willard_Gibbs.jpg" decoding="async" width="170" height="207" class="mw-file-element" data-file-width="200" data-file-height="243"></noscript><span class="lazy-image-placeholder" style="width: 170px;height: 207px;" data-mw-src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Willard_Gibbs.jpg/170px-Willard_Gibbs.jpg" data-width="170" data-height="207" data-srcset="//upload.wikimedia.org/wikipedia/commons/8/8b/Willard_Gibbs.jpg 1.5x" data-class="mw-file-element"> </span></a><figcaption><a href="/wiki/J._Willard_Gibbs" class="mw-redirect" title="J. Willard Gibbs">J. Willard Gibbs</a> - founder of <i>chemical thermodynamics</i></figcaption></figure> <p>In 1865, the German physicist <a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a>, in his <i>Mechanical Theory of Heat</i>, suggested that the principles of <a href="/wiki/Thermochemistry" title="Thermochemistry">thermochemistry</a>, e.g. the <a href="/wiki/Heat" title="Heat">heat</a> evolved in <a href="/wiki/Combustion" title="Combustion">combustion reactions</a>, could be applied to the principles of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</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> Building on the work of Clausius, between the years 1873-76 the American mathematical physicist <a href="/wiki/Willard_Gibbs" class="mw-redirect" title="Willard Gibbs">Willard Gibbs</a> published a series of three papers, the most famous one being the paper <i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of Heterogeneous Substances</a></i>. In these papers, Gibbs showed how the first two laws of thermodynamics could be measured graphically and mathematically to determine both the <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a> of chemical reactions as well as their tendencies to occur or proceed. Gibbs’ collection of papers provided the first unified body of thermodynamic theorems from the principles developed by others, such as Clausius and <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a>. </p><p>During the early 20th century, two major publications successfully applied the principles developed by Gibbs to chemical processes and thus established the foundation of the science of chemical thermodynamics. The first was the 1923 textbook <i>Thermodynamics and the Free Energy of Chemical Substances</i> by <a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Gilbert N. Lewis</a> and <a href="/wiki/Merle_Randall" title="Merle Randall">Merle Randall</a>. This book was responsible for supplanting the <a href="/wiki/Chemical_affinity" title="Chemical affinity">chemical affinity</a> with the term <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free energy</a> in the English-speaking world. The second was the 1933 book <i>Modern Thermodynamics by the methods of Willard Gibbs</i> written by <a href="/wiki/E._A._Guggenheim" class="mw-redirect" title="E. A. Guggenheim">E. A. Guggenheim</a>. In this manner, Lewis, Randall, and Guggenheim are considered as the founders of modern chemical thermodynamics because of the major contribution of these two books in unifying the application of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a> to <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>.<sup id="cite_ref-Book1_1-1" class="reference"><a href="#cite_note-Book1-1"><span class="cite-bracket">[</span>1<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="Overview">Overview</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=2" title="Edit section: Overview" 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>The primary objective of chemical thermodynamics is the establishment of a criterion for determination of the feasibility or <a href="/wiki/Spontaneous_process" title="Spontaneous process">spontaneity</a> of a given transformation.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In this manner, chemical thermodynamics is typically used to predict the <a href="/wiki/Energy" title="Energy">energy</a> exchanges that occur in the following processes: </p> <ol><li><a href="/wiki/Chemical_reaction" title="Chemical reaction">Chemical reactions</a></li> <li><a href="/wiki/Phase_changes" class="mw-redirect" title="Phase changes">Phase changes</a></li> <li>The formation of <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solutions</a></li></ol> <p>The following <a href="/wiki/State_function" title="State function">state functions</a> are of primary concern in chemical thermodynamics: </p> <ul><li><a href="/wiki/Internal_energy" title="Internal energy">Internal energy</a> (<i>U</i>)</li> <li><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a> (<i>H</i>)</li> <li><a href="/wiki/Entropy" title="Entropy">Entropy</a> (<i>S</i>)</li> <li><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> (<i>G</i>)</li></ul> <p>Most <a href="/wiki/Identity_(mathematics)" title="Identity (mathematics)">identities</a> in chemical thermodynamics arise from application of the first and second laws of thermodynamics, particularly the <a href="/wiki/Conservation_of_energy" title="Conservation of energy">law of conservation of energy</a>, to these state functions. </p><p><b>The three <a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</a></b> (global, unspecific forms): </p><p>1. The energy of the universe is constant. </p><p>2. In any spontaneous process, there is always an increase in entropy of the universe. </p><p>3. The entropy of a perfect crystal (well ordered) at 0 Kelvin is zero. </p> </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="Chemical_energy">Chemical energy</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=3" title="Edit section: Chemical energy" 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"> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chemical_energy" title="Chemical energy">Chemical energy</a></div> <p><b>Chemical energy</b> is the energy that can be released when <a href="/wiki/Chemical_substance" title="Chemical substance">chemical substances</a> undergo a transformation through a <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a>. Breaking and making chemical bonds involves <a href="/wiki/Energy" title="Energy">energy</a> release or uptake, often as heat that may be either absorbed by or evolved from the chemical system. </p><p>Energy released (or absorbed) because of a reaction between chemical substances ("reactants") is equal to the difference between the energy content of the products and the reactants. This change in energy is called the change in <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> of a chemical system. It can be calculated from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <msubsup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cea488ab6a33c0b022b2091d68eb168a452f343" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.189ex; height:2.676ex;" alt="{\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}}"></noscript><span class="lazy-image-placeholder" style="width: 11.189ex;height: 2.676ex;vertical-align: -0.838ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cea488ab6a33c0b022b2091d68eb168a452f343" data-alt="{\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, the <a href="/wiki/Internal_energy" title="Internal energy">internal energy</a> of formation of the reactant molecules related to the <a href="/wiki/Bond_energy" title="Bond energy">bond energies</a> of the molecules under consideration, 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 \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <msubsup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffa73811316dd412591efd19724bf9a010805967" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:10.826ex; height:3.176ex;" alt="{\displaystyle \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}}"></noscript><span class="lazy-image-placeholder" style="width: 10.826ex;height: 3.176ex;vertical-align: -1.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffa73811316dd412591efd19724bf9a010805967" data-alt="{\displaystyle \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, the internal energy of formation of the product molecules. The change in internal energy is equal to the heat change if it is measured under conditions of constant volume (at STP condition), as in a closed rigid container such as a <a href="/wiki/Calorimeter#Bomb_calorimeters" title="Calorimeter">bomb calorimeter</a>. However, at constant pressure, as in reactions in vessels open to the atmosphere, the measured heat is usually not equal to the internal energy change, because pressure-volume work also releases or absorbs energy. (The heat change at constant pressure is called the <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> change; in this case the widely tabulated <a href="/wiki/Standard_enthalpy_change_of_formation" class="mw-redirect" title="Standard enthalpy change of formation">enthalpies of formation</a> are used.) </p><p>A related term is the <a href="/wiki/Heat_of_combustion" title="Heat of combustion">heat of combustion</a>, which is the chemical energy released due to a <a href="/wiki/Combustion" title="Combustion">combustion</a> reaction and of interest in the study of <a href="/wiki/Fuels" class="mw-redirect" title="Fuels">fuels</a>. Food is similar to hydrocarbon and carbohydrate fuels, and when it is oxidized, its energy release is similar (though assessed differently than for a hydrocarbon fuel — see <a href="/wiki/Food_energy" title="Food energy">food energy</a>). </p><p>In chemical thermodynamics, the term used for the chemical potential energy is <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a>, and sometimes the <a href="/wiki/Gibbs-Duhem_equation" class="mw-redirect" title="Gibbs-Duhem equation">Gibbs-Duhem equation</a> is used. </p> </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="Chemical_reactions">Chemical reactions</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=4" title="Edit section: Chemical reactions" 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"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chemical_reaction" title="Chemical reaction">Chemical reaction</a></div> <p>In most cases of interest in chemical thermodynamics there are internal <a href="/wiki/Degrees_of_freedom_(physics_and_chemistry)" title="Degrees of freedom (physics and chemistry)">degrees of freedom</a> and processes, such as <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> and <a href="/wiki/Phase_transition" title="Phase transition">phase transitions</a>, which create <a href="/wiki/Entropy" title="Entropy">entropy</a> in the universe unless they are at equilibrium or are maintained at a "running equilibrium" through "quasi-static" changes by being coupled to constraining devices, such as <a href="/wiki/Piston" title="Piston">pistons</a> or <a href="/wiki/Electrode" title="Electrode">electrodes</a>, to deliver and receive external work. Even for homogeneous "bulk" systems, the free-energy functions depend on the <a href="/wiki/Chemical_compound" title="Chemical compound">composition</a>, as do all the <a href="/wiki/Extensive_quantity" class="mw-redirect" title="Extensive quantity">extensive</a> <a href="/wiki/Thermodynamic_potentials" class="mw-redirect" title="Thermodynamic potentials">thermodynamic potentials</a>, including the internal energy. If the quantities { <i>N</i><sub><i>i</i></sub> }, the number of <a href="/wiki/Chemical_species" title="Chemical species">chemical species</a>, are omitted from the formulae, it is impossible to describe compositional changes. </p> <div class="mw-heading mw-heading3"><h3 id="Gibbs_function_or_Gibbs_Energy">Gibbs function or Gibbs Energy</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=5" title="Edit section: Gibbs function or Gibbs Energy" 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 an unstructured, homogeneous "bulk" system, there are still various <i>extensive</i> compositional variables { <i>N</i><sub><i>i</i></sub> } that <i>G</i> depends on, which specify the composition (the amounts of each <a href="/wiki/Chemical_substance" title="Chemical substance">chemical substance</a>, expressed as the numbers of molecules present or the numbers of <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a>). Explicitly, </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 G=G(T,P,\{N_{i}\})\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <mi>G</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo>,</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G=G(T,P,\{N_{i}\})\,.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95e8fd8a3b056ed79f31140cc8da46f18ca0d6e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.035ex; height:2.843ex;" alt="{\displaystyle G=G(T,P,\{N_{i}\})\,.}"></noscript><span class="lazy-image-placeholder" style="width: 20.035ex;height: 2.843ex;vertical-align: -0.838ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95e8fd8a3b056ed79f31140cc8da46f18ca0d6e6" data-alt="{\displaystyle G=G(T,P,\{N_{i}\})\,.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>For the case where only <i>PV</i> work is possible, </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 \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <mi>V</mi> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbaa515a5f77662e05d49a0c7eec2789c790d05f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:34.41ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}"></noscript><span class="lazy-image-placeholder" style="width: 34.41ex;height: 5.509ex;vertical-align: -3.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbaa515a5f77662e05d49a0c7eec2789c790d05f" data-alt="{\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>a restatement of the <a href="/wiki/Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">fundamental thermodynamic relation</a>, in which <i>μ<sub>i</sub></i> is the <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potential</a> for the <i>i</i>-th <a href="/wiki/Component_(thermodynamics)" title="Component (thermodynamics)">component</a> in the system </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 \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i},etc.}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo>,</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>≠</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>e</mi> <mi>t</mi> <mi>c</mi> <mo>.</mo> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i},etc.}\,.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1db1e5238bbb4e070c586d134c657960ea25ae92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:24.632ex; height:6.843ex;" alt="{\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i},etc.}\,.}"></noscript><span class="lazy-image-placeholder" style="width: 24.632ex;height: 6.843ex;vertical-align: -3.171ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1db1e5238bbb4e070c586d134c657960ea25ae92" data-alt="{\displaystyle \mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i},etc.}\,.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>The expression for d<i>G</i> is especially useful at constant <i>T</i> and <i>P</i>, conditions, which are easy to achieve experimentally and which approximate the conditions in <a href="/wiki/Life" title="Life">living</a> creatures </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 (\mathrm {d} G)_{T,P}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathrm {d} G)_{T,P}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbe26a3e023b5ed0c7490727a726df032c36d15e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:22.431ex; height:5.509ex;" alt="{\displaystyle (\mathrm {d} G)_{T,P}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,.}"></noscript><span class="lazy-image-placeholder" style="width: 22.431ex;height: 5.509ex;vertical-align: -3.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbe26a3e023b5ed0c7490727a726df032c36d15e" data-alt="{\displaystyle (\mathrm {d} G)_{T,P}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Chemical_affinity">Chemical affinity</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=6" title="Edit section: Chemical affinity" 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> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chemical_affinity" title="Chemical affinity">Chemical affinity</a></div> <p>While this formulation is mathematically defensible, it is not particularly transparent since one does not simply add or remove molecules from a system. There is always a <i>process</i> involved in changing the composition; e.g., a chemical reaction (or many), or movement of molecules from one phase (liquid) to another (gas or solid). We should find a notation which does not seem to imply that the amounts of the components ( <i>N</i><sub><i>i</i></sub> ) can be changed independently. All real processes obey <a href="/wiki/Conservation_of_mass" title="Conservation of mass">conservation of mass</a>, and in addition, conservation of the numbers of <a href="/wiki/Atom" title="Atom">atoms</a> of each kind. </p><p>Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progress <a href="/wiki/Variable_(mathematics)" title="Variable (mathematics)">variable</a> <i>ξ</i> for the <i><a href="/wiki/Extent_of_reaction" title="Extent of reaction">extent of reaction</a></i> (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37.62), and to the use of the <a href="/wiki/Partial_derivative" title="Partial derivative">partial derivative</a> ∂<i>G</i>/∂<i>ξ</i> (in place of the widely used "Δ<i>G</i>", since the quantity at issue is not a finite change). The result is an understandable <a href="/wiki/Expression_(mathematics)" title="Expression (mathematics)">expression</a> for the dependence of d<i>G</i> on <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> (or other processes). If there is just one reaction </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 (\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ξ</mi> <mo>.</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fdc41876a803702dc9fc96027e2c6e03b831b57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:25.334ex; height:6.509ex;" alt="{\displaystyle (\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,}"></noscript><span class="lazy-image-placeholder" style="width: 25.334ex;height: 6.509ex;vertical-align: -2.838ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fdc41876a803702dc9fc96027e2c6e03b831b57" data-alt="{\displaystyle (\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>If we introduce the <i><a href="/wiki/Stoichiometric_coefficient" class="mw-redirect" title="Stoichiometric coefficient">stoichiometric coefficient</a></i> for the <i>i-th</i> component in the reaction </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu _{i}=\partial N_{i}/\partial \xi \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">∂</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{i}=\partial N_{i}/\partial \xi \,}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36184241e01adcbda2d534723a689cb8bf487773" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.928ex; height:2.843ex;" alt="{\displaystyle \nu _{i}=\partial N_{i}/\partial \xi \,}"></noscript><span class="lazy-image-placeholder" style="width: 12.928ex;height: 2.843ex;vertical-align: -0.838ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36184241e01adcbda2d534723a689cb8bf487773" data-alt="{\displaystyle \nu _{i}=\partial N_{i}/\partial \xi \,}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl></dd></dl> <p>(negative for reactants), which tells how many molecules of <i>i</i> are produced or consumed, we obtain an algebraic expression for the partial derivative </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=\sum _{i}\mu _{i}\nu _{i}=-\mathbb {A} \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>G</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=\sum _{i}\mu _{i}\nu _{i}=-\mathbb {A} \,}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96fc939418560fb9ed460757b0db8d5b2e4423b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:28.445ex; height:6.676ex;" alt="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=\sum _{i}\mu _{i}\nu _{i}=-\mathbb {A} \,}"></noscript><span class="lazy-image-placeholder" style="width: 28.445ex;height: 6.676ex;vertical-align: -3.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96fc939418560fb9ed460757b0db8d5b2e4423b1" data-alt="{\displaystyle \left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=\sum _{i}\mu _{i}\nu _{i}=-\mathbb {A} \,}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>where we introduce a concise and historical name for this quantity, the "<a href="/wiki/Chemical_affinity" title="Chemical affinity">affinity</a>", symbolized by <b>A</b>, as introduced by <a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">Théophile de Donder</a> in 1923.(De Donder; Progogine & Defay, p. 69; Guggenheim, pp. 37, 240) The minus sign ensures that in a spontaneous change, when the change in the Gibbs free energy of the process is negative, the chemical species have a positive affinity for each other. The differential of <i>G</i> takes on a simple form that displays its dependence on composition change </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 (\mathrm {d} G)_{T,P}=-\mathbb {A} \,d\xi \,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>ξ</mi> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathrm {d} G)_{T,P}=-\mathbb {A} \,d\xi \,.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06ed096ca5f31bc54a65aeb9a0ad899a48d09aae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.261ex; height:3.009ex;" alt="{\displaystyle (\mathrm {d} G)_{T,P}=-\mathbb {A} \,d\xi \,.}"></noscript><span class="lazy-image-placeholder" style="width: 18.261ex;height: 3.009ex;vertical-align: -1.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06ed096ca5f31bc54a65aeb9a0ad899a48d09aae" data-alt="{\displaystyle (\mathrm {d} G)_{T,P}=-\mathbb {A} \,d\xi \,.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>If there are a number of chemical reactions going on simultaneously, as is usually the case, </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 (\mathrm {d} G)_{T,P}=-\sum _{k}\mathbb {A} _{k}\,d\xi _{k}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mi>d</mi> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\mathrm {d} G)_{T,P}=-\sum _{k}\mathbb {A} _{k}\,d\xi _{k}\,.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9345cd4fd2e800b8a0700450595527056351a4b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:24.556ex; height:5.509ex;" alt="{\displaystyle (\mathrm {d} G)_{T,P}=-\sum _{k}\mathbb {A} _{k}\,d\xi _{k}\,.}"></noscript><span class="lazy-image-placeholder" style="width: 24.556ex;height: 5.509ex;vertical-align: -3.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9345cd4fd2e800b8a0700450595527056351a4b0" data-alt="{\displaystyle (\mathrm {d} G)_{T,P}=-\sum _{k}\mathbb {A} _{k}\,d\xi _{k}\,.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>with a set of reaction coordinates { ξ<sub><i>j</i></sub> }, avoiding the notion that the amounts of the components ( <i>N</i><sub><i>i</i></sub> ) can be changed independently. The expressions above are equal to zero at <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>, while they are negative when chemical reactions proceed at a finite rate, producing entropy. This can be made even more explicit by introducing the reaction <i>rates</i> d<i>ξ</i><sub><i>j</i></sub>/d<i>t</i>. For every <span style="color:maroon;"><i>physically independent</i></span> <i>process</i> (Prigogine & Defay, p. 38; Prigogine, p. 24) </p> <dl><dd><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 \mathbb {A} \ {\dot {\xi }}\leq 0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ξ</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mo>≤</mo> <mn>0</mn> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {A} \ {\dot {\xi }}\leq 0\,.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fa9452853d4e8980984b0f096ed9b6e18b40dcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.981ex; height:3.176ex;" alt="{\displaystyle \mathbb {A} \ {\dot {\xi }}\leq 0\,.}"></noscript><span class="lazy-image-placeholder" style="width: 8.981ex;height: 3.176ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fa9452853d4e8980984b0f096ed9b6e18b40dcb" data-alt="{\displaystyle \mathbb {A} \ {\dot {\xi }}\leq 0\,.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl></dd></dl> <p>This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether temperature and pressure (or any other system variables) are going to be held constant over time. It is a purely local criterion and must hold regardless of any such constraints. Of course, it could have been obtained by taking partial derivatives of any of the other fundamental state functions, but nonetheless is a general criterion for (−<i>T</i> times) the entropy production from that spontaneous process; or at least any part of it that is not captured as external work. (See <i>Constraints</i> below.) </p><p>We now relax the requirement of a homogeneous "bulk" system by letting the <a href="/wiki/Chemical_potential" title="Chemical potential">chemical potentials</a> and the affinity apply to any locality in which a chemical reaction (or any other process) is occurring. By accounting for the <a href="/wiki/Entropy_production" title="Entropy production">entropy production</a> due to irreversible processes, the equality for d<i>G</i> is now replaced 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 \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>G</mi> <mo>=</mo> <mo>−</mo> <mi>S</mi> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>T</mi> <mo>+</mo> <mi>V</mi> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>P</mi> <mo>−</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> </mrow> <msup> <mi>W</mi> <mo>′</mo> </msup> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'\,}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a79845e873e54c56f0bfcd5a94e31936e584ee1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:41.498ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'\,}"></noscript><span class="lazy-image-placeholder" style="width: 41.498ex;height: 5.509ex;vertical-align: -3.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a79845e873e54c56f0bfcd5a94e31936e584ee1" data-alt="{\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'\,}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>or </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {d} G_{T,P}=-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>ξ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> </mrow> <msup> <mi>W</mi> <mo>′</mo> </msup> <mo>.</mo> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} G_{T,P}=-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'.\,}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e74e0f979d448db209b6c39ae7fa9f6bef05c57b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:29.905ex; height:5.509ex;" alt="{\displaystyle \mathrm {d} G_{T,P}=-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'.\,}"></noscript><span class="lazy-image-placeholder" style="width: 29.905ex;height: 5.509ex;vertical-align: -3.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e74e0f979d448db209b6c39ae7fa9f6bef05c57b" data-alt="{\displaystyle \mathrm {d} G_{T,P}=-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'.\,}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>Any decrease in the <a href="/wiki/Gibbs_function" class="mw-redirect" title="Gibbs function">Gibbs function</a> of a system is the upper limit for any <a href="/wiki/Isothermal_process" title="Isothermal process">isothermal</a>, <a href="/wiki/Isobaric_process" title="Isobaric process">isobaric</a> work that can be captured in the <a href="/wiki/Surroundings" title="Surroundings">surroundings</a>, or it may simply be <a href="/wiki/Dissipation" title="Dissipation">dissipated</a>, appearing as <i>T</i> times a corresponding increase in the entropy of the system and its surrounding. Or it may go partly toward doing external work and partly toward creating entropy. The important point is that the <i><a href="/wiki/Extent_of_reaction" title="Extent of reaction">extent of reaction</a></i> for a chemical reaction may be coupled to the displacement of some external mechanical or electrical quantity in such a way that one can advance only if the other also does. The coupling may occasionally be <i>rigid</i>, but it is often flexible and variable. </p> <div class="mw-heading mw-heading3"><h3 id="Solutions">Solutions</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=7" title="Edit section: Solutions" 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>In solution <a href="/wiki/Chemistry" title="Chemistry">chemistry</a> and <a href="/wiki/Biochemistry" title="Biochemistry">biochemistry</a>, the <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> decrease (∂<i>G</i>/∂<i>ξ</i>, in molar units, denoted cryptically by Δ<i>G</i>) is commonly used as a surrogate for (−<i>T</i> times) the global entropy produced by spontaneous <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> in situations where no work is being done; or at least no "useful" work; i.e., other than perhaps ± <i>P</i> d<i>V</i>. The assertion that all <i>spontaneous reactions have a negative ΔG</i> is merely a restatement of the <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a>, giving it the <a href="/wiki/Dimensional_analysis" title="Dimensional analysis">physical dimensions</a> of energy and somewhat obscuring its significance in terms of entropy. When no useful work is being done, it would be less misleading to use the <a href="/wiki/Legendre_transformation" title="Legendre transformation">Legendre transforms</a> of the entropy appropriate for constant <i>T</i>, or for constant <i>T</i> and <i>P</i>, the Massieu functions −<i>F/T</i> and −<i>G/T</i>, respectively. </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="Non-equilibrium">Non-equilibrium</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=8" title="Edit section: Non-equilibrium" 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"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">non-equilibrium thermodynamics</a></div> <p>Generally the systems treated with the conventional chemical thermodynamics are either at equilibrium or near equilibrium. <a href="/wiki/Ilya_Prigogine" title="Ilya Prigogine">Ilya Prigogine</a> developed the thermodynamic treatment of <a href="/wiki/Open_system_(systems_theory)" title="Open system (systems theory)">open systems</a> that are far from equilibrium. In doing so he has discovered phenomena and structures of completely new and completely unexpected types. His generalized, nonlinear and irreversible thermodynamics has found surprising applications in a wide variety of fields. </p><p>The non-equilibrium thermodynamics has been applied for explaining how ordered structures e.g. the biological systems, can develop from disorder. Even if Onsager's relations are utilized, the classical principles of equilibrium in thermodynamics still show that linear systems close to equilibrium always develop into states of disorder which are stable to perturbations and cannot explain the occurrence of ordered structures. </p><p>Prigogine called these systems <a href="/wiki/Dissipative_systems" class="mw-redirect" title="Dissipative systems">dissipative systems</a>, because they are formed and maintained by the dissipative processes which take place because of the exchange of energy between the system and its environment and because they disappear if that exchange ceases. They may be said to live in <a href="/wiki/Symbiosis" title="Symbiosis">symbiosis</a> with their environment. </p><p>The method which Prigogine used to study the stability of the dissipative structures to perturbations is of very great general interest. It makes it possible to study the most varied problems, such as city traffic problems, the stability of insect communities, the development of ordered biological structures and the growth of cancer cells to mention but a few examples. </p> <div class="mw-heading mw-heading3"><h3 id="System_constraints">System constraints</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=9" title="Edit section: System constraints" 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>In this regard, it is crucial to understand the role of walls and other <i>constraints</i>, and the distinction between <i>independent</i> processes and <i>coupling</i>. Contrary to the clear implications of many reference sources, the previous analysis is not restricted to <a href="https://en.wiktionary.org/wiki/homogeneous" class="extiw" title="wiktionary:homogeneous">homogeneous</a>, <a href="/wiki/Isotropy" title="Isotropy">isotropic</a> bulk systems which can deliver only <i>P</i>d<i>V</i> work to the outside world, but applies even to the most structured systems. There are complex systems with many chemical "reactions" going on at the same time, some of which are really only parts of the same, overall process. An <i>independent</i> process is one that <i>could</i> proceed even if all others were unaccountably stopped in their tracks. Understanding this is perhaps a "<a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a>" in <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">chemical kinetics</a>, but actual examples exist. </p><p>A gas-phase reaction at constant temperature and pressure which results in an increase in the number of molecules will lead to an increase in volume. Inside a cylinder closed with a piston, it can proceed only by doing work on the piston. The extent variable for the reaction can increase only if the piston moves out, and conversely if the piston is pushed inward, the reaction is driven backwards. </p><p>Similarly, a <a href="/wiki/Redox" title="Redox">redox</a> reaction might occur in an <a href="/wiki/Electrochemistry" title="Electrochemistry">electrochemical</a> cell with the passage of <a href="/wiki/Electric_current" title="Electric current">current</a> through a <a href="/wiki/Wire" title="Wire">wire</a> connecting the <a href="/wiki/Electrode" title="Electrode">electrodes</a>. The half-cell reactions at the <a href="/wiki/Electrode" title="Electrode">electrodes</a> are constrained if no current is allowed to flow. The current might be dissipated as <a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a>, or it might in turn run an electrical device like a <a href="/wiki/Electric_motor" title="Electric motor">motor</a> doing <a href="/wiki/Mechanical_work" class="mw-redirect" title="Mechanical work">mechanical work</a>. An <a href="/wiki/Automobile" class="mw-redirect" title="Automobile">automobile</a> <a href="/wiki/Lead" title="Lead">lead</a>-<a href="/wiki/Acid" title="Acid">acid</a> <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">battery</a> can be recharged, driving the chemical reaction backwards. In this case as well, the reaction is not an independent process. Some, perhaps most, of the Gibbs free energy of reaction may be delivered as external work. </p><p>The <a href="/wiki/Hydrolysis" title="Hydrolysis">hydrolysis</a> of <a href="/wiki/Adenosine_triphosphate" title="Adenosine triphosphate">ATP</a> to <a href="/wiki/Adenosine_diphosphate" title="Adenosine diphosphate">ADP</a> and <a href="/wiki/Phosphate" title="Phosphate">phosphate</a> can drive the <a href="/wiki/Force" title="Force">force</a>-times-<a href="/wiki/Distance" title="Distance">distance</a> work delivered by living <a href="/wiki/Muscle" title="Muscle">muscles</a>, and synthesis of ATP is in turn driven by a redox chain in <a href="/wiki/Mitochondrion" title="Mitochondrion">mitochondria</a> and <a href="/wiki/Chloroplast" title="Chloroplast">chloroplasts</a>, which involves the transport of <a href="/wiki/Ion" title="Ion">ions</a> across the membranes of these <a href="/wiki/Cell_(biology)" title="Cell (biology)">cellular</a> <a href="/wiki/Organelle" title="Organelle">organelles</a>. The coupling of processes here, and in the previous examples, is often not complete. Gas can leak slowly past a piston, just as it can slowly leak out of a <a href="/wiki/Rubber" class="mw-redirect" title="Rubber">rubber</a> <a href="/wiki/Balloon" title="Balloon">balloon</a>. Some reaction may occur in a battery even if no external current is flowing. There is usually a coupling <a href="/wiki/Coefficient" title="Coefficient">coefficient</a>, which may depend on relative rates, which determines what percentage of the driving free energy is turned into external work, or captured as "chemical work", a misnomer for the free energy of another chemical process. </p> </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=Chemical_thermodynamics&action=edit&section=10" 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/Thermodynamic_databases_for_pure_substances" title="Thermodynamic databases for pure substances">Thermodynamic databases for pure substances</a></li> <li><a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">laws of thermodynamics</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=Chemical_thermodynamics&action=edit&section=11" 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-Book1-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Book1_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Book1_1-1"><sup><i><b>b</b></i></sup></a></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="CITEREFOttBoerio-Goates,_Juliana2000" class="citation book cs1">Ott, Bevan J.; Boerio-Goates, Juliana (2000). <i>Chemical Thermodynamics – Principles and Applications</i>. Academic Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-12-530990-2" title="Special:BookSources/0-12-530990-2"><bdi>0-12-530990-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Thermodynamics+%E2%80%93+Principles+and+Applications&rft.pub=Academic+Press&rft.date=2000&rft.isbn=0-12-530990-2&rft.aulast=Ott&rft.aufirst=Bevan+J.&rft.au=Boerio-Goates%2C+Juliana&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+thermodynamics" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Clausius, R. (1865). <i>The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies.</i> London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Klotz, I. (1950). <i>Chemical Thermodynamics.</i> New York: Prentice-Hall, Inc.</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="Further_reading">Further reading</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Chemical_thermodynamics&action=edit&section=12" title="Edit section: Further reading" 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-8 collapsible-block" id="mf-section-8"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHerbert_B._Callen1960" class="citation book cs1">Herbert B. Callen (1960). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/thermodynamicsin00call"><i>Thermodynamics</i></a></span>. Wiley & Sons. The clearest account of the logical foundations of the subject. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-13035-4" title="Special:BookSources/0-471-13035-4"><bdi>0-471-13035-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics&rft.pub=Wiley+%26+Sons.+The+clearest+account+of+the+logical+foundations+of+the+subject&rft.date=1960&rft.isbn=0-471-13035-4&rft.au=Herbert+B.+Callen&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fthermodynamicsin00call&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+thermodynamics" class="Z3988"></span> Library of Congress Catalog No. 60-5597</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIlya_Prigogine_&_R._Defay,_translated_by_D.H._Everett;_Chapter_IV1954" class="citation book cs1">Ilya Prigogine & R. Defay, translated by D.H. Everett; Chapter IV (1954). <i>Chemical Thermodynamics</i>. Longmans, Green & Co. Exceptionally clear on the logical foundations as applied to chemistry; includes <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">non-equilibrium thermodynamics</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Thermodynamics&rft.pub=Longmans%2C+Green+%26+Co.+Exceptionally+clear+on+the+logical+foundations+as+applied+to+chemistry%3B+includes+non-equilibrium+thermodynamics&rft.date=1954&rft.au=Ilya+Prigogine+%26+R.+Defay%2C+translated+by+D.H.+Everett%3B+Chapter+IV&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+thermodynamics" 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: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIlya_Prigogine1967" class="citation book cs1">Ilya Prigogine (1967). <i>Thermodynamics of Irreversible Processes, 3rd ed</i>. Interscience: John Wiley & Sons. A simple, concise monograph explaining all the basic ideas.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics+of+Irreversible+Processes%2C+3rd+ed.&rft.pub=Interscience%3A+John+Wiley+%26+Sons.+A+simple%2C+concise+monograph+explaining+all+the+basic+ideas&rft.date=1967&rft.au=Ilya+Prigogine&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+thermodynamics" class="Z3988"></span> Library of Congress Catalog No. 67-29540</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFE.A._Guggenheim1967" class="citation book cs1">E.A. Guggenheim (1967). <i>Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th ed</i>. North Holland; John Wiley & Sons (Interscience). A remarkably astute treatise.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics%3A+An+Advanced+Treatment+for+Chemists+and+Physicists%2C+5th+ed.&rft.pub=North+Holland%3B+John+Wiley+%26+Sons+%28Interscience%29.+A+remarkably+astute+treatise&rft.date=1967&rft.au=E.A.+Guggenheim&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+thermodynamics" class="Z3988"></span> Library of Congress Catalog No. 67-20003</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTh._De_Donder1922" class="citation journal cs1">Th. De Donder (1922). "L'affinite. Applications aux gaz parfaits". <i>Bulletin de la Classe des Sciences, Académie Royale de Belgique</i>. Series 5. <b>8</b>: <span class="nowrap">197–</span>205.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+de+la+Classe+des+Sciences%2C+Acad%C3%A9mie+Royale+de+Belgique&rft.atitle=L%27affinite.+Applications+aux+gaz+parfaits&rft.volume=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E197-%3C%2Fspan%3E205&rft.date=1922&rft.au=Th.+De+Donder&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+thermodynamics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTh._De_Donder1922" class="citation journal cs1">Th. De Donder (1922). "Sur le theoreme de Nernst". <i>Bulletin de la Classe des Sciences, Académie Royale de Belgique</i>. Series 5. <b>8</b>: <span class="nowrap">205–</span>210.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+de+la+Classe+des+Sciences%2C+Acad%C3%A9mie+Royale+de+Belgique&rft.atitle=Sur+le+theoreme+de+Nernst&rft.volume=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E205-%3C%2Fspan%3E210&rft.date=1922&rft.au=Th.+De+Donder&rfr_id=info%3Asid%2Fen.wikipedia.org%3AChemical+thermodynamics" class="Z3988"></span></li></ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(9)"><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=Chemical_thermodynamics&action=edit&section=13" title="Edit section: External links" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> 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lang="ar" hreflang="ar" data-title="ترموديناميكا كيميائية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kimy%C9%99vi_termodinamika" title="Kimyəvi termodinamika – Azerbaijani" lang="az" hreflang="az" data-title="Kimyəvi termodinamika" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/H%C3%B2a-ha%CC%8Dk_jia%CC%8Dt-le%CC%8Dk-ha%CC%8Dk" title="Hòa-ha̍k jia̍t-le̍k-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Hòa-ha̍k jia̍t-le̍k-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A5%D1%96%D0%BC%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D1%82%D1%8D%D1%80%D0%BC%D0%B0%D0%B4%D1%8B%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Хімічная тэрмадынаміка – Belarusian" lang="be" hreflang="be" data-title="Хімічная тэрмадынаміка" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Химическа термодинамика – Bulgarian" lang="bg" hreflang="bg" data-title="Химическа термодинамика" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Termodin%C3%A0mica_qu%C3%ADmica" title="Termodinàmica química – Catalan" lang="ca" hreflang="ca" data-title="Termodinàmica química" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CE%B7%CE%BC%CE%B9%CE%BA%CE%AE_%CE%B8%CE%B5%CF%81%CE%BC%CE%BF%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%AE" title="Χημική θερμοδυναμική – Greek" lang="el" hreflang="el" data-title="Χημική θερμοδυναμική" 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/Termodin%C3%A1mica_qu%C3%ADmica" title="Termodinámica química – Spanish" lang="es" hreflang="es" data-title="Termodinámica química" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kemia_termodinamiko" title="Kemia termodinamiko – Esperanto" lang="eo" hreflang="eo" data-title="Kemia termodinamiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%B1%D9%85%D9%88%D8%AF%DB%8C%D9%86%D8%A7%D9%85%DB%8C%DA%A9_%D8%B4%DB%8C%D9%85%DB%8C%D8%A7%DB%8C%DB%8C" title="ترمودینامیک شیمیایی – Persian" lang="fa" hreflang="fa" data-title="ترمودینامیک شیمیایی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Termodin%C3%A1mica_qu%C3%ADmica" title="Termodinámica química – Galician" lang="gl" hreflang="gl" data-title="Termodinámica química" 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/%ED%99%94%ED%95%99%EC%97%B4%EC%97%AD%ED%95%99" title="화학열역학 – Korean" lang="ko" hreflang="ko" data-title="화학열역학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%94%D5%AB%D5%B4%D5%AB%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A9%D5%A5%D6%80%D5%B4%D5%B8%D5%A4%D5%AB%D5%B6%D5%A1%D5%B4%D5%AB%D5%AF%D5%A1" title="Քիմիական թերմոդինամիկա – Armenian" lang="hy" hreflang="hy" data-title="Քիմիական թերմոդինամիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A4%BE%E0%A4%B8%E0%A4%BE%E0%A4%AF%E0%A4%A8%E0%A4%BF%E0%A4%95_%E0%A4%8A%E0%A4%B7%E0%A5%8D%E0%A4%AE%E0%A4%BE%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="रासायनिक ऊष्मागतिकी – Hindi" lang="hi" hreflang="hi" data-title="रासायनिक ऊष्मागतिकी" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kemijska_termodinamika" title="Kemijska termodinamika – Croatian" lang="hr" hreflang="hr" data-title="Kemijska termodinamika" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Termodinamika_kimia" title="Termodinamika kimia – Indonesian" lang="id" hreflang="id" data-title="Termodinamika kimia" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A5%E1%83%98%E1%83%9B%E1%83%98%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%97%E1%83%94%E1%83%A0%E1%83%9B%E1%83%9D%E1%83%93%E1%83%98%E1%83%9C%E1%83%90%E1%83%9B%E1%83%98%E1%83%99%E1%83%90" title="ქიმიური თერმოდინამიკა – Georgian" lang="ka" hreflang="ka" data-title="ქიმიური თერმოდინამიკა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Химиялық термодинамика – Kazakh" lang="kk" hreflang="kk" data-title="Химиялық термодинамика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Chemin%C4%97_termodinamika" title="Cheminė termodinamika – Lithuanian" lang="lt" hreflang="lt" data-title="Cheminė termodinamika" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Termodinamik_kimia" title="Termodinamik kimia – Malay" lang="ms" hreflang="ms" data-title="Termodinamik kimia" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Chemische_thermodynamica" title="Chemische thermodynamica – Dutch" lang="nl" hreflang="nl" data-title="Chemische thermodynamica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8C%96%E5%AD%A6%E7%86%B1%E5%8A%9B%E5%AD%A6" title="化学熱力学 – Japanese" lang="ja" hreflang="ja" data-title="化学熱力学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kjemisk_termodynamikk" title="Kjemisk termodynamikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kjemisk termodynamikk" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Termodynamika_chemiczna" title="Termodynamika chemiczna – Polish" lang="pl" hreflang="pl" data-title="Termodynamika chemiczna" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Termodinamic%C4%83_chimic%C4%83" title="Termodinamică chimică – Romanian" lang="ro" hreflang="ro" data-title="Termodinamică chimică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA%D0%B0" title="Химическая термодинамика – Russian" lang="ru" hreflang="ru" data-title="Химическая термодинамика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Hemijska_termodinamika" title="Hemijska termodinamika – Serbian" lang="sr" hreflang="sr" data-title="Hemijska termodinamika" 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 mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kemisk_termodynamik" title="Kemisk termodynamik – Swedish" lang="sv" hreflang="sv" data-title="Kemisk termodynamik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kimyasal_termodinamik" title="Kimyasal termodinamik – Turkish" lang="tr" hreflang="tr" data-title="Kimyasal termodinamik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A5%D1%96%D0%BC%D1%96%D1%87%D0%BD%D0%B0_%D1%82%D0%B5%D1%80%D0%BC%D0%BE%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D1%96%D0%BA%D0%B0" title="Хімічна термодинаміка – Ukrainian" lang="uk" hreflang="uk" data-title="Хімічна термодинаміка" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Nhi%E1%BB%87t_%C4%91%E1%BB%99ng_h%C3%B3a_h%E1%BB%8Dc" title="Nhiệt động hóa học – Vietnamese" lang="vi" hreflang="vi" data-title="Nhiệt động hóa học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8C%96%E5%AD%B8%E7%86%B1%E5%8A%9B%E5%AD%B8" title="化學熱力學 – Cantonese" lang="yue" hreflang="yue" data-title="化學熱力學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8C%96%E5%AD%A6%E7%83%AD%E5%8A%9B%E5%AD%A6" title="化学热力学 – Chinese" lang="zh" hreflang="zh" data-title="化学热力学" data-language-autonym="中文" data-language-local-name="Chinese" 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