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id="siteNotice"></div> </div> <div class="pre-content heading-holder"> <div class="page-heading"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Spontaneous process</span></h1> <div class="tagline"></div> </div> <ul id="p-associated-pages" class="minerva__tab-container"> <li class="minerva__tab selected"> <a class="minerva__tab-text" href="/wiki/Spontaneous_process" rel="" data-event-name="tabs.subject">Article</a> </li> <li class="minerva__tab "> <a class="minerva__tab-text" href="/wiki/Talk:Spontaneous_process" rel="discussion" data-event-name="tabs.talk">Talk</a> </li> </ul> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"> <a role="button" href="#p-lang" data-mw="interface" data-event-name="menu.languages" title="Language" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet language-selector"> <span class="minerva-icon minerva-icon--language"></span> <span>Language</span> </a> </li> <li id="page-actions-watch" class="page-actions-menu__list-item"> <a role="button" id="ca-watch" href="/w/index.php?title=Special:UserLogin&returnto=Spontaneous+process" data-event-name="menu.watch" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet menu__item--page-actions-watch"> <span class="minerva-icon minerva-icon--star"></span> <span>Watch</span> </a> </li> <li id="page-actions-edit" class="page-actions-menu__list-item"> <a role="button" id="ca-edit" href="/w/index.php?title=Spontaneous_process&action=edit" data-event-name="menu.edit" data-mw="interface" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet edit-page menu__item--page-actions-edit"> <span 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"> <p>In <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, a <b>spontaneous process</b> is a <a href="/wiki/Thermodynamic_process" title="Thermodynamic process">process</a> which occurs without any external input to the system. A more technical definition is the time-evolution of a <a href="/wiki/Thermodynamic_system" title="Thermodynamic system">system</a> in which it releases <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free energy</a> and it moves to a lower, more thermodynamically stable energy state (closer to <a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">thermodynamic equilibrium</a>).<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><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> The sign convention for free energy change follows the general convention for thermodynamic measurements, in which a release of free energy from the system corresponds to a negative change in the free energy of the system and a positive change in the free energy of the <a href="/wiki/Environment_(systems)" title="Environment (systems)">surroundings</a>. </p><p>Depending on the nature of the process, the free energy is determined differently. For example, the <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> change is used when considering processes that occur under constant <a href="/wiki/Pressure" title="Pressure">pressure</a> and <a href="/wiki/Temperature" title="Temperature">temperature</a> conditions, whereas the <a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a> change is used when considering processes that occur under constant <a href="/wiki/Volume" title="Volume">volume</a> and temperature conditions. The value and even the sign of both free energy changes can depend upon the temperature and pressure or volume. </p><p>Because spontaneous processes are characterized by a decrease in the system's free energy, they do not need to be driven by an outside source of energy. </p><p>For cases involving an <a href="/wiki/Isolated_system" title="Isolated system">isolated system</a> where no energy is exchanged with the surroundings, spontaneous processes are characterized by an increase in <a href="/wiki/Entropy" title="Entropy">entropy</a>. </p><p>A <i>spontaneous reaction</i> is a <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a> which is a spontaneous process under the conditions of interest. </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="#Overview"><span class="tocnumber">1</span> <span class="toctext">Overview</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Using_free_energy_to_determine_spontaneity"><span class="tocnumber">2</span> <span class="toctext">Using free energy to determine spontaneity</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Using_entropy_to_determine_spontaneity"><span class="tocnumber">3</span> <span class="toctext">Using entropy to determine spontaneity</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#See_also"><span class="tocnumber">4</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-5"><a href="#References"><span class="tocnumber">5</span> <span class="toctext">References</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="Overview">Overview</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Spontaneous_process&action=edit&section=1" 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-1 collapsible-block" id="mf-section-1"> <p>In general, the spontaneity of a process only determines whether or not a process <i>can</i> occur and makes no indication as to whether or not the process <i>will</i> occur. In other words, spontaneity is a necessary, but not sufficient, condition for a process to actually occur. Furthermore, spontaneity makes no implication as to the speed at which the spontaneous process may occur - just because a process is spontaneous does not mean it will happen quickly (or at all). </p><p>As an example, the conversion of a <a href="/wiki/Diamond" title="Diamond">diamond</a> into <a href="/wiki/Graphite" title="Graphite">graphite</a> is a spontaneous process at room temperature and pressure. Despite being spontaneous, this process does not occur since the energy to break the strong carbon-carbon bonds is larger than the release in free energy. Another way to explain this would be that even though the conversion of diamond into graphite is thermodynamically feasible and spontaneous even at room temperature, the high <a href="/wiki/Activation_energy" title="Activation energy">activation energy</a> of this reaction renders it unspontaneous. </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="Using_free_energy_to_determine_spontaneity">Using free energy to determine spontaneity</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Spontaneous_process&action=edit&section=2" title="Edit section: Using free energy to determine spontaneity" 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>For a process that occurs at constant temperature and pressure, spontaneity can be determined using the change in <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a>, which is given by: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G=\Delta H-T\Delta S\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>G</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi mathvariant="normal">Δ</mi> <mi>S</mi> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta G=\Delta H-T\Delta S\,,}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/168a97376522e8148fa099767865425696ef39cb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.806ex; height:2.509ex;" alt="{\displaystyle \Delta G=\Delta H-T\Delta S\,,}"></noscript><span class="lazy-image-placeholder" style="width: 19.806ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/168a97376522e8148fa099767865425696ef39cb" data-alt="{\displaystyle \Delta G=\Delta H-T\Delta S\,,}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> </p><p>where the sign of Δ<i>G</i> depends on the signs of the changes in <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> (Δ<i>H</i>) and <a href="/wiki/Entropy" title="Entropy">entropy</a> (Δ<i>S</i>). If these two signs are the same (both positive or both negative), then the sign of Δ<i>G</i> will change from positive to negative (or vice versa) at the temperature <span class="nowrap"><i>T</i> = Δ<i>H</i>/Δ<i>S</i>.</span> </p><p>In cases where Δ<i>G</i> is: </p> <ul><li>negative, the process is spontaneous and may proceed in the forward direction as written.</li> <li>positive, the process is non-spontaneous as written, but it may proceed spontaneously in the <i>reverse direction</i>.</li> <li>zero, the process is at equilibrium, with no net change taking place over time.</li></ul> <p>This set of rules can be used to determine four distinct cases by examining the signs of the Δ<i>S</i> and Δ<i>H</i>. </p> <ul><li>When Δ<i>S</i> > 0 and Δ<i>H</i> < 0, the process is always spontaneous as written.</li> <li>When Δ<i>S</i> < 0 and Δ<i>H</i> > 0, the process is never spontaneous, but the reverse process is always spontaneous.</li> <li>When Δ<i>S</i> > 0 and Δ<i>H</i> > 0, the process will be spontaneous at high temperatures and non-spontaneous at low temperatures.</li> <li>When Δ<i>S</i> < 0 and Δ<i>H</i> < 0, the process will be spontaneous at low temperatures and non-spontaneous at high temperatures.</li></ul> <p>For the latter two cases, the temperature at which the spontaneity changes will be determined by the relative magnitudes of Δ<i>S</i> and Δ<i>H</i>. </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="Using_entropy_to_determine_spontaneity">Using entropy to determine spontaneity</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Spontaneous_process&action=edit&section=3" title="Edit section: Using entropy to determine spontaneity" 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"> <p>When using the entropy change of a process to assess spontaneity, it is important to carefully consider the definition of the system and surroundings. The <a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">second law of thermodynamics</a> states that a process involving an isolated system will be spontaneous if the entropy of the system increases over time. For open or closed systems, however, the statement must be modified to say that the total entropy of the <i>combined</i> system and surroundings must increase, or, <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta S_{\text{total}}=\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}\geq 0\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>total</mtext> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>system</mtext> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>surroundings</mtext> </mrow> </msub> <mo>≥</mo> <mn>0</mn> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S_{\text{total}}=\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}\geq 0\,.}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07447f181d54f3b1c81b7be7ddc8d3d717a7c5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:39.552ex; height:2.843ex;" alt="{\displaystyle \Delta S_{\text{total}}=\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}\geq 0\,.}"></noscript><span class="lazy-image-placeholder" style="width: 39.552ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07447f181d54f3b1c81b7be7ddc8d3d717a7c5" data-alt="{\displaystyle \Delta S_{\text{total}}=\Delta S_{\text{system}}+\Delta S_{\text{surroundings}}\geq 0\,.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> </p><p>This criterion can then be used to explain how it is possible for the entropy of an open or closed system to decrease during a spontaneous process. A decrease in system entropy can only occur spontaneously if the entropy change of the surroundings is both positive in sign and has a larger magnitude than the entropy change of the system: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta S_{\text{surroundings}}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>surroundings</mtext> </mrow> </msub> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S_{\text{surroundings}}>0}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1553a412cfc201d0696137bb6a0f8660f5a4ec41" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.11ex; height:2.843ex;" alt="{\displaystyle \Delta S_{\text{surroundings}}>0}"></noscript><span class="lazy-image-placeholder" style="width: 17.11ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1553a412cfc201d0696137bb6a0f8660f5a4ec41" data-alt="{\displaystyle \Delta S_{\text{surroundings}}>0}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left|\Delta S_{\text{surroundings}}\right|>\left|\Delta S_{\text{system}}\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>|</mo> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>surroundings</mtext> </mrow> </msub> </mrow> <mo>|</mo> </mrow> <mo>></mo> <mrow> <mo>|</mo> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>system</mtext> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left|\Delta S_{\text{surroundings}}\right|>\left|\Delta S_{\text{system}}\right|}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/707aca3c14b1c6239315d61718ce12cf5fa758ae" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.03ex; height:3.009ex;" alt="{\displaystyle \left|\Delta S_{\text{surroundings}}\right|>\left|\Delta S_{\text{system}}\right|}"></noscript><span class="lazy-image-placeholder" style="width: 27.03ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/707aca3c14b1c6239315d61718ce12cf5fa758ae" data-alt="{\displaystyle \left|\Delta S_{\text{surroundings}}\right|>\left|\Delta S_{\text{system}}\right|}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> </p><p>In many processes, the increase in entropy of the surroundings is accomplished via heat transfer from the system to the surroundings (i.e. an exothermic process). </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="See_also">See also</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Spontaneous_process&action=edit&section=4" 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-4 collapsible-block" id="mf-section-4"> <ul><li><a href="/wiki/Endergonic_reaction" title="Endergonic reaction">Endergonic reaction</a> reactions which are not spontaneous at standard temperature, pressure, and concentrations.</li> <li><a href="/wiki/Diffusion" title="Diffusion">Diffusion</a> spontaneous phenomenon that minimizes Gibbs free energy.</li></ul> </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="References">References</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Spontaneous_process&action=edit&section=5" 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-5 collapsible-block" id="mf-section-5"> <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="http://www.chem.purdue.edu/gchelp/gloss/sponprocess.html">Spontaneous process</a> - Purdue University</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"><a rel="nofollow" class="external text" href="http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Entropy-and-Spontaneous-Reactions-623.html">Entropy and Spontaneous Reactions</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091213190957/http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Entropy-and-Spontaneous-Reactions-623.html">Archived</a> 2009-12-13 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> - ChemEd DL</span> </li> </ol></div>    </section></div> <noscript><img src="https://login.m.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&mobile=1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Spontaneous_process&oldid=1249342488">https://en.wikipedia.org/w/index.php?title=Spontaneous_process&oldid=1249342488</a>"</div></div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"> <a class="last-modified-bar" href="/w/index.php?title=Spontaneous_process&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" 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