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data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Enthalpy change from diluting a substance in solution</div> <p>In <a href="/wiki/Thermochemistry" title="Thermochemistry">thermochemistry</a>, the <b>heat of dilution</b>, or <b>enthalpy of dilution</b>, refers to the <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> change associated with the dilution process of a component in a <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solution</a> at a <a href="/wiki/Isobaric_process" title="Isobaric process">constant pressure</a>. If the initial state of the component is a pure <a href="/wiki/Liquid" title="Liquid">liquid</a> (presuming the solution is liquid), the dilution process is equal to its <a href="/wiki/Dissolution_(chemistry)" class="mw-redirect" title="Dissolution (chemistry)">dissolution</a> process and the heat of dilution is the same as the <a href="/wiki/Enthalpy_change_of_solution" title="Enthalpy change of solution">heat of solution</a>. Generally, the heat of dilution is <a href="/wiki/Normalization_(statistics)" title="Normalization (statistics)">normalized</a> by the <a href="/wiki/Amount_of_substance" title="Amount of substance">amount</a> of the solution and its <a href="/wiki/Dimensional_units" class="mw-redirect" title="Dimensional units">dimensional units</a> are energy per unit mass or amount of substance, commonly expressed in the unit of <a href="/wiki/Joule" title="Joule">kJ</a>/<a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a> (or J/mol). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_of_dilution&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The heat of dilution can be defined from two perspectives: the differential heat and the integral heat. </p><p>The differential heat of dilution is viewed on a micro scale, which is associated with the process in which a small amount of solvent is added to a large quantity of solution. The <b>molar differential heat of dilution</b> is thus defined as the <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> change caused by adding a mole of solvent at a constant temperature and pressure to a very large amount of solution. Because of the small amount of addition, the concentration of dilute solution remains practically unchanged. Mathematically, the molar differential heat of dilution is denoted as:<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> </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 _{\text{dil}}^{d}H=\left({\frac {\partial \Delta _{\text{dil}}H}{\partial \Delta n_{i}}}\right)_{T,p,n_{B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dil</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msubsup> <mi>H</mi> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dil</mtext> </mrow> </msub> <mi>H</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi mathvariant="normal">Δ</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>B</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\text{dil}}^{d}H=\left({\frac {\partial \Delta _{\text{dil}}H}{\partial \Delta n_{i}}}\right)_{T,p,n_{B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14596e5e044d64765467c4eb8bbfb28ae5a31adf" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:26.089ex; height:6.509ex;" alt="{\displaystyle \Delta _{\text{dil}}^{d}H=\left({\frac {\partial \Delta _{\text{dil}}H}{\partial \Delta n_{i}}}\right)_{T,p,n_{B}}}"></span> </p><p>where ∂∆<i>n</i><sub><i>i</i></sub> is the infinitesimal change or differential of <a href="/wiki/Mole_number" class="mw-redirect" title="Mole number">mole number</a> of the dilution. </p><p>The integral heat of dilution, however, is viewed on a macro scale. With respect to the integral heat, consider a process in which a certain amount of solution diluted from an initial concentration to a final concentration. The <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> change in this process, normalized by the <a href="/wiki/Mole_number" class="mw-redirect" title="Mole number">mole number</a> of solute, is evaluated as the <b>molar integral heat of dilution</b>. Mathematically, the molar integral heat of dilution is denoted as: </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 _{\text{dil}}^{i}H={\frac {\Delta _{\text{dil}}H}{n_{B}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dil</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <mi>H</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dil</mtext> </mrow> </msub> <mi>H</mi> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{\text{dil}}^{i}H={\frac {\Delta _{\text{dil}}H}{n_{B}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da1aa4dbab3ba470c805130bd4703ad255fcd890" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.056ex; height:5.676ex;" alt="{\displaystyle \Delta _{\text{dil}}^{i}H={\frac {\Delta _{\text{dil}}H}{n_{B}}}}"></span> </p><p>If the infinite amount of solvent is added to a solution with a known concentration of solute, the corresponding change of enthalpy is called as integral heat of dilution to infinite dilution.<sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>The dilution between two concentrations of the solute is associated to an intermediary heat of dilution by mole of solute. </p> <div class="mw-heading mw-heading2"><h2 id="Dilution_and_Dissolution">Dilution and Dissolution</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_of_dilution&action=edit&section=2" title="Edit section: Dilution and Dissolution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The process of <a href="/wiki/Dissolution_(chemistry)" class="mw-redirect" title="Dissolution (chemistry)">dissolution</a> and the process of dilution are closely related to each other. In both processes, similar final statuses of solutions are reached. However, the initial statuses can be different. In a dissolution process, a solute is changed from a pure phase—solid, liquid, or gas—to a solution phase. If the pure phase of the solute is a solid or gas (presuming the solvent itself is liquid), the process can be seen in two stages: the phase change into a liquid, and the mixing of liquids. The dissolution process is generally expressed as: </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 {\textrm {solute(s,l,g)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solute(s,l,g)</mtext> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvent(l)</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solute(l)</mtext> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvent(l)</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solute(sln)</mtext> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvent(sln)</mtext> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\textrm {solute(s,l,g)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b2b7a8a7940ea835843247073489eaf7718587f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:77.689ex; height:2.843ex;" alt="{\displaystyle {\textrm {solute(s,l,g)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}}"></span> </p><p>The notation "sln" stands for "solution", which represents a status of the solvent or solute being part of the solution. </p><p>In a dilution process, on the other hand, the solution is changed from one concentration to another, illustrated as: </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 {\textrm {solute(sln}}_{1}{\textrm {)}}+{\textrm {solvent(sln}}_{1}{\textrm {)}}\rightarrow {\textrm {solute(sln}}_{2}{\textrm {)}}+{\textrm {solvent(sln}}_{2}{\textrm {)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solute(sln</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>)</mtext> </mrow> </mrow> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvent(sln</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>)</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solute(sln</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>)</mtext> </mrow> </mrow> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvent(sln</mtext> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>)</mtext> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\textrm {solute(sln}}_{1}{\textrm {)}}+{\textrm {solvent(sln}}_{1}{\textrm {)}}\rightarrow {\textrm {solute(sln}}_{2}{\textrm {)}}+{\textrm {solvent(sln}}_{2}{\textrm {)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59d3014b2b680bb1ee05f2487ac2286a689c612b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:58.447ex; height:3.009ex;" alt="{\displaystyle {\textrm {solute(sln}}_{1}{\textrm {)}}+{\textrm {solvent(sln}}_{1}{\textrm {)}}\rightarrow {\textrm {solute(sln}}_{2}{\textrm {)}}+{\textrm {solvent(sln}}_{2}{\textrm {)}}}"></span> </p><p>Consider an extreme condition for the dilution process. Let the initial status be the pure liquid. The dilution process is then described as: </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 {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solute(l)</mtext> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvent(l)</mtext> </mrow> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solute(sln)</mtext> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvent(sln)</mtext> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2da412d24e24b58a0ae45a2232a108f94f6fe5f0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:49.812ex; height:2.843ex;" alt="{\displaystyle {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}}"></span> </p><p>It is worth noting that this expression is just the second stage of the dissolution process. In other words, if both the solute to be dissolved and the initial "solution" to be diluted are liquids, the dissolution and the dilution processes are identical. </p> <div class="mw-heading mw-heading2"><h2 id="Steps_in_dilution">Steps in dilution</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_of_dilution&action=edit&section=3" title="Edit section: Steps in dilution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Viewed from a microscopic perspective, the dissolution and dilution processes involve three steps of molecular interaction: the breaking of attraction between solute molecules (<a href="/wiki/Lattice_energy" title="Lattice energy">lattice energy</a>), the breaking of attraction between solvent molecules, and the forming of attraction between a solute and a solvent molecule. If the solution is ideal, which means the solute and the solvent are identical in an interaction, then all the kinds of attraction mentioned above have the same value. As a result, the enthalpy change caused by breaking and forming attraction is canceled, and the dilution of an ideal solution causes no enthalpy change.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>However, if the solute and solvent cannot be treated identically when considered in terms of molecular attraction, which makes the solution non-ideal, the net change of enthalpy is nonzero. In other words, the heat of dilution results from the non-ideality of the solution. </p> <div class="mw-heading mw-heading2"><h2 id="Examples_for_acids">Examples for acids</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_of_dilution&action=edit&section=4" title="Edit section: Examples for acids"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The integral heats of dilution to infinite dilution of some acids in aqueous solutions are shown in the following table.<sup id="cite_ref-:0_2-1" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <td colspan="10" style="text-align:center; background:#ccf;"><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 _{m}H{\text{(dil)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <msub> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>(dil)</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\Delta _{m}H{\text{(dil)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/056958ee455c0ba399584f8f9dc24321243cab4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.878ex; height:2.843ex;" alt="{\displaystyle -\Delta _{m}H{\text{(dil)}}}"></span> in kJ/mol at 25 °C </td></tr> <tr> <td>m</td> <td>Dil. ratio</td> <td><a href="/wiki/Hydrofluoric_acid" title="Hydrofluoric acid">HF</a></td> <td><a href="/wiki/Hydrochloric_acid" title="Hydrochloric acid">HCl</a></td> <td><a href="/wiki/Perchloric_acid" title="Perchloric acid">HClO<sub>4</sub></a></td> <td><a href="/wiki/Hydrobromic_acid" title="Hydrobromic acid">HBr</a></td> <td><a href="/wiki/Hydroiodic_acid" title="Hydroiodic acid">HI</a></td> <td><a href="/wiki/Nitric_acid" title="Nitric acid">HNO<sub>3</sub></a></td> <td><a href="/wiki/Formic_acid" title="Formic acid">CH<sub>2</sub>O<sub>2</sub></a></td> <td>C<sub>2</sub>H<sub>4</sub>O<sub>4</sub> </td></tr> <tr> <td>55.506</td> <td>1.0</td> <td></td> <td>45.61</td> <td></td> <td>48.83</td> <td></td> <td>19.73</td> <td>0.046</td> <td>2.167 </td></tr> <tr> <td>5.5506</td> <td>10</td> <td>13.66</td> <td>5.841</td> <td>-0.490</td> <td>4.590</td> <td>3.577</td> <td>1.540</td> <td>0.285</td> <td>1.477 </td></tr> <tr> <td>0.5551</td> <td>100</td> <td>13.22</td> <td>1.234</td> <td>0.050</td> <td>0.983</td> <td>0.736</td> <td>0.502</td> <td>0.184</td> <td>0.423 </td></tr> <tr> <td>0.0555</td> <td>1000</td> <td>12.42</td> <td>0.427</td> <td>0.259</td> <td>0.385</td> <td>0.351</td> <td>0.318</td> <td>0.121</td> <td>0.272 </td></tr> <tr> <td>0.00555</td> <td>10000</td> <td>8.912</td> <td>0.142</td> <td>0.126</td> <td>0.130</td> <td>0.121</td> <td>0.130</td> <td>0.105</td> <td>0.243 </td></tr> <tr> <td>0.000555</td> <td>100000</td> <td>3.766</td> <td>0.042</td> <td>0.042</td> <td>0.038</td> <td>0.038</td> <td>0.046</td> <td>0.054</td> <td>0.209 </td></tr> <tr> <td>0</td> <td>∞</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heat_of_dilution&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><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">H. DeVoe, "Reactions of other chemical processes," in <i>Thermodynamics and Chemistry</i>, 2nd ed. London, UK: Pearson Education, 2001, pp. 303-366.</span> </li> <li id="cite_note-:0-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">V. B. Parker, "Heats of dilution," in <i>Thermal Properties of Aqueous Uni-Univalent Electrolytes</i>, Washington DC: U.S. Government Printing Office, 1965, pp. 10-19.</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">P. Atkins and J. D. Paula, "Simple mixtures," in <i>Physical Chemistry,</i> 8th ed. New York: W.H. Freeman and Company, 2006, pp. 137-173.</span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" 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=Heat_of_dilution&oldid=1176644734">https://en.wikipedia.org/w/index.php?title=Heat_of_dilution&oldid=1176644734</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Enthalpy" title="Category:Enthalpy">Enthalpy</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 23 September 2023, at 02:09<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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