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Enthalpy of vaporization
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<h2 id="units">Units</h2> <p>Values are usually quoted in <a href="/facts/Joule/9ndq9jD2">J</a>/<a href="/facts/Mole_(unit)/kCMFwCc0">mol</a>, or kJ/mol (molar enthalpy of vaporization), although kJ/kg, or J/g (specific heat of vaporization), and older units like <a href="/facts/Calorie/ntNMPx65">kcal</a>/mol, cal/g and <a href="/facts/British_thermal_unit/GwIjRAPz">Btu</a>/lb are sometimes still used among others. </p> <h2 id="enthalpy-of-condensation">Enthalpy of condensation</h2> <p>The enthalpy of condensation (or heat of condensation) is by definition equal to the enthalpy of vaporization with the opposite sign: enthalpy changes of vaporization are always positive (heat is absorbed by the substance), whereas enthalpy changes of condensation are always negative (heat is released by the substance). </p> <h2 id="thermodynamic-background">Thermodynamic background</h2> <p>The enthalpy of vaporization can be written as </p> Δ H vap = Δ U vap + p Δ V {\displaystyle \Delta H_{\text{vap}}=\Delta U_{\text{vap}}+p\,\Delta V} <p>It is equal to the increased <a href="/facts/Internal_energy/IYdsoxhR">internal energy</a> of the vapor phase compared with the liquid phase, plus the work done against ambient pressure. The increase in the internal energy can be viewed as the energy required to overcome the <a href="/facts/Chemical_bond/ArNUMnIB">intermolecular interactions</a> in the liquid (or solid, in the case of <a href="/facts/Sublimation_(chemistry)/KDoKokMn">sublimation</a>). Hence <a href="/facts/Helium/yRul93TG">helium</a> has a particularly low enthalpy of vaporization, 0.0845 kJ/mol, as the <a href="/facts/Van_der_Waals_force/jyGU8Vh9">van der Waals forces</a> between helium <a href="/facts/Atom/FoQ4kGN5">atoms</a> are particularly weak. On the other hand, the <a href="/facts/Molecule/N9ljSfFq">molecules</a> in liquid <a href="/facts/Water_(molecule)/FFsl65l1">water</a> are held together by relatively strong <a href="/facts/Hydrogen_bond/85V86IIg">hydrogen bonds</a>, and its enthalpy of vaporization, 40.65 kJ/mol, is more than five times the energy required to heat the same quantity of water from 0 °C to 100 °C (<a href="/facts/Heat_capacity/I63nzSyp"><i>c</i>p</a> = 75.3 J/K·mol). Care must be taken, however, when using enthalpies of vaporization to <i>measure</i> the strength of intermolecular forces, as these forces may persist to an extent in the gas phase (as is the case with <a href="/facts/Hydrogen_fluoride/XfQxlqR6">hydrogen fluoride</a>), and so the calculated value of the <a href="/facts/Bond_strength/q4be3EeR">bond strength</a> will be too low. This is particularly true of metals, which often form <a href="/facts/Covalent_bond/EzMLf3Pz">covalently bonded</a> molecules in the gas phase: in these cases, the <a href="/facts/Enthalpy_of_atomization/2etA4muz">enthalpy of atomization</a> must be used to obtain a true value of the <a href="/facts/Bond_energy/q4be3EeR">bond energy</a>. </p><p>An alternative description is to view the enthalpy of condensation as the heat which must be released to the surroundings to compensate for the drop in <a href="/facts/Entropy/s52IXeFz">entropy</a> when a gas condenses to a liquid. As the liquid and gas are in <a href="/facts/Chemical_equilibrium/y8ToYXHp">equilibrium</a> at the boiling point (<i>T</i>b), <a href="/facts/Gibbs_free_energy/bvenDuzh">Δv<i>G</i></a> = 0, which leads to: </p> Δ v S = S gas − S liquid = Δ v H T b {\displaystyle \Delta _{\text{v}}S=S_{\text{gas}}-S_{\text{liquid}}={\frac {\Delta _{\text{v}}H}{T_{\text{b}}}}} <p>As neither entropy nor <a href="/facts/Enthalpy/bBou8lCE">enthalpy</a> vary greatly with temperature, it is normal to use the tabulated standard values without any correction for the difference in temperature from 298 K. A correction must be made if the <a href="/facts/Pressure/eyc37GRG">pressure</a> is different from 100 <a href="/facts/Pascal_(unit)/Am1To2Qm">kPa</a>, as the entropy of an <a href="/facts/Ideal_gas/80EfYGFj">ideal gas</a> is proportional to the logarithm of its pressure. The entropies of liquids vary little with pressure, as the <a href="/facts/Thermal_expansion/BP2vjX0N">coefficient of thermal expansion</a> of a liquid is small.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> </p><p>These two definitions are equivalent: the boiling point is the temperature at which the increased entropy of the gas phase overcomes the intermolecular forces. As a given quantity of matter always has a higher entropy in the gas phase than in a condensed phase ( Δ v S {\displaystyle \Delta _{\text{v}}S} is always positive), and from </p> Δ G = Δ H − T Δ S {\displaystyle \Delta G=\Delta H-T\Delta S} , <p>the <a href="/facts/Gibbs_free_energy/bvenDuzh">Gibbs free energy</a> change falls with increasing temperature: gases are favored at higher temperatures, as is observed in practice. </p> <h2 id="vaporization-enthalpy-of-electrolyte-solutions">Vaporization enthalpy of electrolyte solutions</h2> <p>Estimation of the enthalpy of vaporization of electrolyte solutions can be simply carried out using equations based on the chemical thermodynamic models, such as Pitzer model<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> or TCPC model.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> </p> <h2 id="selected-values">Selected values</h2> <h3>Elements</h3> <table><tbody><tr><th colspan="20">Enthalpies of vaporization of the elements</th></tr><tr><th></th><th><a href="/facts/Alkali_metal/IkWbCLk2">1</a></th><th><a href="/facts/Alkaline_earth_metal/Ts4U5zIe">2</a></th><th></th><th><a href="/facts/Group_3_element/q60AHJ7U">3</a></th><th><a href="/facts/Group_4_element/QGKs7lMz">4</a></th><th><a href="/facts/Group_5_element/C08aMlur">5</a></th><th><a href="/facts/Group_6_element/s8cA1Rwd">6</a></th><th><a href="/facts/Group_7_element/C1kHt0oD">7</a></th><th><a href="/facts/Group_8_element/VtbLeVpY">8</a></th><th><a href="/facts/Group_9_element/YsFjV4Ey">9</a></th><th><a href="/facts/Group_10_element/oIUwy5mC">10</a></th><th><a href="/facts/Group_11_element/phumzNJU">11</a></th><th><a href="/facts/Group_12_element/z8aB00Ih">12</a></th><th><a href="/facts/Boron_group/RXnvqnNk">13</a></th><th><a href="/facts/Carbon_group/PkWCV3Vx">14</a></th><th><a href="/facts/Nitrogen_group/jX4hvCkK">15</a></th><th><a href="/facts/Chalcogen/nXLGmnqL">16</a></th><th><a href="/facts/Halogen/YeFgWHeA">17</a></th><th><a href="/facts/Noble_gas/j0yHMEAE">18</a></th></tr><tr><th colspan="3"><a href="/facts/Group_(periodic_table)/YGBcUabv">Group</a> →</th></tr><tr><th colspan="3">↓ <a href="/facts/Periodic_table_period/WpGUFh5V">Period</a></th></tr><tr><th><a href="/facts/Period_1_element/bRg5LCQF">1</a></th><td><a href="/facts/Hydrogen/BoYHjl0J">H</a>0.90</td><td colspan="17"></td><td><a href="/facts/Helium/yRul93TG">He</a>0.08</td></tr><tr><th><a href="/facts/Period_2_element/1ajRWfrb">2</a></th><td><a href="/facts/Lithium/7vXX6BWA">Li</a>136</td><td><a href="/facts/Beryllium/dv295voP">Be</a>292</td><td colspan="11"></td><td><a href="/facts/Boron/Pmwgd7Mf">B</a>508</td><td><a href="/facts/Carbon/ukrgQexo">C</a>715</td><td><a href="/facts/Nitrogen/Nf1QpGDz">N</a>5.57</td><td><a href="/facts/Oxygen/acyn6o8r">O</a>6.82</td><td><a href="/facts/Fluorine/YUV0Fb8m">F</a>6.62</td><td><a href="/facts/Neon/5bF1FwGL">Ne</a>1.71</td></tr><tr><th><a href="/facts/Period_3_element/1BE0Nc0K">3</a></th><td><a href="/facts/Sodium/eYuSPu2V">Na</a>97.4</td><td><a href="/facts/Magnesium/XyIhd2FG">Mg</a>128</td><td colspan="11"></td><td><a href="/facts/Aluminium/7wmR8jYE">Al</a>284</td><td><a href="/facts/Silicon/cgWx0hdr">Si</a>359</td><td><a href="/facts/Phosphorus/27xCeIqs">P</a>12.4</td><td><a href="/facts/Sulfur/IK0amTfM">S</a>45</td><td><a href="/facts/Chlorine/y27UwYBM">Cl</a>20.4</td><td><a href="/facts/Argon/QX6NRH6d">Ar</a>6.53</td></tr><tr><th><a href="/facts/Period_4_element/BgDFfE26">4</a></th><td><a href="/facts/Potassium/FWPwS7Rj">K</a>76.9</td><td><a href="/facts/Calcium/hf252CC0">Ca</a>155</td><td></td><td><a href="/facts/Scandium/TJRt1chg">Sc</a>333</td><td><a href="/facts/Titanium/53ArnDoy">Ti</a>425</td><td><a href="/facts/Vanadium/UvKkKTSm">V</a>444</td><td><a href="/facts/Chromium/6sVk6Uu7">Cr</a>339</td><td><a href="/facts/Manganese/j9ELd1TL">Mn</a>221</td><td><a href="/facts/Iron/QK1JYy8E">Fe</a>340</td><td><a href="/facts/Cobalt/gqhScEw4">Co</a>377</td><td><a href="/facts/Nickel/KwMCHYRP">Ni</a>379</td><td><a href="/facts/Copper/I8PEE8oX">Cu</a>300</td><td><a href="/facts/Zinc/80b1qgk3">Zn</a>115</td><td><a href="/facts/Gallium/EucevDs9">Ga</a>256</td><td><a href="/facts/Germanium/wtoALHGs">Ge</a>334</td><td><a href="/facts/Arsenic/k1c4f44D">As</a>32.4</td><td><a href="/facts/Selenium/k975NApC">Se</a>95.5</td><td><a href="/facts/Bromine/oLfj3C7D">Br</a>30.0</td><td><a href="/facts/Krypton/llkNlCke">Kr</a>9.08</td></tr><tr><th><a href="/facts/Period_5_element/xLJUWWDS">5</a></th><td><a href="/facts/Rubidium/KDHSe2HM">Rb</a>75.8</td><td><a href="/facts/Strontium/ABaA5qQK">Sr</a>141</td><td></td><td><a href="/facts/Yttrium/BlX6rj99">Y</a>390</td><td><a href="/facts/Zirconium/y7gsoQFz">Zr</a>573</td><td><a href="/facts/Niobium/3zNI8AKp">Nb</a>690</td><td><a href="/facts/Molybdenum/RX6vp2bF">Mo</a>617</td><td><a href="/facts/Technetium/MGYWNI5d">Tc</a>585</td><td><a href="/facts/Ruthenium/uzCm4ufn">Ru</a>619</td><td><a href="/facts/Rhodium/xmBd9aFG">Rh</a>494</td><td><a href="/facts/Palladium/AXMwDFxs">Pd</a>358</td><td><a href="/facts/Silver/xXe41BGg">Ag</a>254</td><td><a href="/facts/Cadmium/wXkV2eIX">Cd</a>99.9</td><td><a href="/facts/Indium/zRq3stVb">In</a>232</td><td><a href="/facts/Tin/obW9mqc3">Sn</a>296</td><td><a href="/facts/Antimony/YsA7lVgT">Sb</a>193</td><td><a href="/facts/Tellurium/v7QvfIvS">Te</a>114</td><td><a href="/facts/Iodine/JlfMecMf">I</a>41.6</td><td><a href="/facts/Xenon/9E3XR69R">Xe</a>12.6</td></tr><tr><th><a href="/facts/Period_6_element/9YleCXwf">6</a></th><td><a href="/facts/Caesium/dXKN1S5k">Cs</a>63.9</td><td><a href="/facts/Barium/IkL09XHQ">Ba</a>140</td><td></td><td><a href="/facts/Lutetium/URlmnYG8">Lu</a>414</td><td><a href="/facts/Hafnium/rBNnlxDS">Hf</a>648</td><td><a href="/facts/Tantalum/VwaxMm33">Ta</a>733</td><td><a href="/facts/Tungsten/WYwbNDYX">W</a>807</td><td><a href="/facts/Rhenium/TzyqJYEn">Re</a>704</td><td><a href="/facts/Osmium/1TjXD69n">Os</a>678</td><td><a href="/facts/Iridium/TFQutoj1">Ir</a>564</td><td><a href="/facts/Platinum/qJC6lQf7">Pt</a>510</td><td><a href="/facts/Gold/1znknojp">Au</a>342</td><td><a href="/facts/Mercury_(element)/WlxfoHva">Hg</a>59.1</td><td><a href="/facts/Thallium/v35pGMJB">Tl</a>165</td><td><a href="/facts/Lead/EYljasJN">Pb</a>179</td><td><a href="/facts/Bismuth/75FLjkoX">Bi</a>179</td><td><a href="/facts/Polonium/G4rzsyjP">Po</a>103</td><td><a href="/facts/Astatine/AlbHPBK5">At</a>54.4</td><td><a href="/facts/Radon/0V9arWKl">Rn</a>18.1</td></tr><tr><th><a href="/facts/Period_7_element/H5QuVHGQ">7</a></th><td><a href="/facts/Francium/P3Rz4gDP">Fr</a>65</td><td><a href="/facts/Radium/VWo5gkzn">Ra</a>113</td><td></td><td><a href="/facts/Lawrencium/HVw2LVlx">Lr</a><i>n/a</i></td><td><a href="/facts/Rutherfordium/44LSnv9p">Rf</a><i>n/a</i></td><td><a href="/facts/Dubnium/3CHC1lEt">Db</a><i>n/a</i></td><td><a href="/facts/Seaborgium/ejs0Ap6P">Sg</a><i>n/a</i></td><td><a href="/facts/Bohrium/epvp3GWM">Bh</a><i>n/a</i></td><td><a href="/facts/Hassium/t0bgGzwt">Hs</a><i>n/a</i></td><td><a href="/facts/Meitnerium/pKaD3sRY">Mt</a><i>n/a</i></td><td><a href="/facts/Darmstadtium/etmwTLmP">Ds</a><i>n/a</i></td><td><a href="/facts/Roentgenium/LEhvJaJQ">Rg</a><i>n/a</i></td><td><a href="/facts/Copernicium/EhgyBkg0">Cn</a><i>n/a</i></td><td><a href="/facts/Nihonium/sb09p5dv">Nh</a><i>n/a</i></td><td><a href="/facts/Flerovium/Aa7uGMuG">Fl</a><i>n/a</i></td><td><a href="/facts/Moscovium/QhSEr0H5">Mc</a><i>n/a</i></td><td><a href="/facts/Livermorium/nQc1FE6E">Lv</a><i>n/a</i></td><td><a href="/facts/Tennessine/eGCBDvEr">Ts</a><i>n/a</i></td><td><a href="/facts/Oganesson/zs5MQDjV">Og</a><i>n/a</i></td></tr><tr><td></td></tr><tr><td colspan="4"></td><td><a href="/facts/Lanthanum/Uhmmy1sB">La</a>400</td><td><a href="/facts/Cerium/a7UjMBQ6">Ce</a>398</td><td><a href="/facts/Praseodymium/2lnRJ9dH">Pr</a>331</td><td><a href="/facts/Neodymium/GzDkTIoI">Nd</a>289</td><td><a href="/facts/Promethium/8xvCz9Rg">Pm</a>289</td><td><a href="/facts/Samarium/09K3kl93">Sm</a>172</td><td><a href="/facts/Europium/dqmBm1vr">Eu</a>176</td><td><a href="/facts/Gadolinium/eLYUeScu">Gd</a>301</td><td><a href="/facts/Terbium/ICF3PMED">Tb</a>391</td><td><a href="/facts/Dysprosium/eMev6zGS">Dy</a>280</td><td><a href="/facts/Holmium/C73kJVtp">Ho</a>251</td><td><a href="/facts/Erbium/XEJlgJcx">Er</a>280</td><td><a href="/facts/Thulium/G2905xhd">Tm</a>191</td><td><a href="/facts/Ytterbium/3lerM9uf">Yb</a>129</td></tr><tr><td colspan="4"></td><td><a href="/facts/Actinium/GMQtJ4Gm">Ac</a>400</td><td><a href="/facts/Thorium/ysdWH470">Th</a>514</td><td><a href="/facts/Protactinium/v87VqTPf">Pa</a>481</td><td><a href="/facts/Uranium/n2sGWBzU">U</a>417</td><td><a href="/facts/Neptunium/pwp7Yvds">Np</a>336</td><td><a href="/facts/Plutonium/4bUw9zH3">Pu</a>333</td><td><a href="/facts/Americium/rxL9Yc64">Am</a><i>n/a</i></td><td><a href="/facts/Curium/LMyWXg8l">Cm</a><i>n/a</i></td><td><a href="/facts/Berkelium/ePryEYy3">Bk</a><i>n/a</i></td><td><a href="/facts/Californium/AJVjoVut">Cf</a><i>n/a</i></td><td><a href="/facts/Einsteinium/RePoIVN9">Es</a><i>n/a</i></td><td><a href="/facts/Fermium/Us3rnvG5">Fm</a><i>n/a</i></td><td><a href="/facts/Mendelevium/bEHBu18F">Md</a><i>n/a</i></td><td><a href="/facts/Nobelium/syRkloSw">No</a><i>n/a</i></td></tr><tr><td> </td></tr><tr><td></td><td colspan="20">Enthalpy in kJ/mol, measured at their respective normal boiling points</td></tr><tr><td></td><td colspan="3">0–10 kJ/mol</td><td colspan="3">10–100 kJ/mol</td><td colspan="3">100–300 kJ/mol</td><td colspan="3">>300 kJ/mol</td></tr></tbody></table> <p>The vaporization of metals is a key step in <a href="/facts/Metal_vapor_synthesis/dGzRfp2Q">metal vapor synthesis</a>, which exploits the increased reactivity of metal atoms or small particles relative to the bulk elements. </p> <h3>Other common substances</h3> <p>Enthalpies of vaporization of common substances, measured at their respective standard boiling points: </p> <table><tbody><tr><th rowspan="2">Compound</th><th colspan="3">Boiling point, at normal pressure</th><th colspan="2">Heat of vaporization</th></tr><tr><th>(K)</th><th>(°C)</th><th>(°F)</th><th>(<a href="/facts/Kilojoule_per_mole/MCWSGtRG">kJ/mol</a>)</th><th>(J/g)</th></tr><tr><td><a href="/facts/Acetone/cVyJxKqw">Acetone</a></td><td>329</td><td>56</td><td>133</td><td>31.300</td><td>538.9</td></tr><tr><td><a href="/facts/Aluminium/7wmR8jYE">Aluminium</a></td><td>2792</td><td>2519</td><td>4566</td><td>294.0</td><td>10500</td></tr><tr><td><a href="/facts/Ammonia/MtLtJFtz">Ammonia</a></td><td>240</td><td>−33.34</td><td>−28</td><td>23.35</td><td>1371</td></tr><tr><td><a href="/facts/Butane/InIHpYlY">Butane</a></td><td>272–274</td><td>−1</td><td>30–34</td><td>21.0</td><td>320</td></tr><tr><td><a href="/facts/Diethyl_ether/Ep20vEdj">Diethyl ether</a></td><td>307.8</td><td>34.6</td><td>94.3</td><td>26.17</td><td>353.1</td></tr><tr><td><a href="/facts/Ethanol/3lCLfBSP">Ethanol</a></td><td>352</td><td>78.37</td><td>173</td><td>38.6</td><td>841</td></tr><tr><td><a href="/facts/Hydrogen/BoYHjl0J">Hydrogen</a> (<a href="/facts/Parahydrogen/zhN4qBMQ">parahydrogen</a>)</td><td>20.271</td><td>−252.879</td><td>−423.182</td><td>0.8992</td><td>446.1</td></tr><tr><td><a href="/facts/Iron/QK1JYy8E">Iron</a></td><td>3134</td><td>2862</td><td>5182</td><td>340</td><td>6090</td></tr><tr><td><a href="/facts/Isopropyl_alcohol/7KqgIkUd">Isopropyl alcohol</a></td><td>356</td><td>82.6</td><td>181</td><td>44</td><td>732.2</td></tr><tr><td><a href="/facts/Methane/kBHneYnh">Methane</a></td><td>112</td><td>−161</td><td>−259</td><td>8.170</td><td>480.6</td></tr><tr><td><a href="/facts/Methanol/EIfpoNCg">Methanol</a></td><td>338</td><td>64.7</td><td>148</td><td>35.2<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></td><td>1104</td></tr><tr><td><a href="/facts/Propane/E0b23KGh">Propane</a></td><td>231</td><td>−42</td><td>−44</td><td>15.7</td><td>356</td></tr><tr><td><a href="/facts/Phosphine/aYysn5TS">Phosphine</a></td><td>185</td><td>−87.7</td><td>−126</td><td>14.6</td><td>429.4</td></tr><tr><td><a href="/facts/Properties_of_water/FFsl65l1">Water</a></td><td>373.15</td><td>100</td><td>212</td><td>40.66</td><td>2257</td></tr></tbody></table> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Clausius%E2%80%93Clapeyron_relation/Lo9SfNqM">Clausius–Clapeyron relation</a></li> <li><a href="/facts/Shimansky_equation/sVQjsTPR">Shimansky equation</a>, describes the temperature dependence of the heat of vaporization</li> <li><a href="/facts/Enthalpy_of_fusion/eLJIURcp">Enthalpy of fusion</a>, specific heat of melting</li> <li><a href="/facts/Enthalpy_of_sublimation/fAsEUnh5">Enthalpy of sublimation</a></li> <li><a href="/facts/Joback_method/ooIpgSHL">Joback method</a>, estimation of the heat of vaporization at the normal boiling point from molecular structures</li> <li><a href="/facts/Latent_heat/QCIWSGln">Latent heat</a></li></ul> <ul><li><a href="http://www.codata.info/resources/databases/key1.html">CODATA Key Values for Thermodynamics</a></li> <li>Gmelin, Leopold (1985). <i>Gmelin-Handbuch der anorganischen Chemie / 08 a</i> (8., völlig neu bearb. Aufl. ed.). Berlin [u.a.]: Springer. pp. 116–117. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-540-93516-2.</li> <li><a href="http://webbook.nist.gov/chemistry/">NIST Chemistry WebBook</a></li> <li>Young, Francis W. Sears, Mark W. Zemansky, Hugh D. (1982). <i>University physics</i> (6th ed.). Reading, Mass.: Addison-Wesley. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-201-07199-3.{{cite book}}: CS1 maint: multiple names: authors list (link)</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Note that the rate of change of entropy with pressure and the rate of thermal expansion are related by the Maxwell Relation: ( ∂ S ∂ P ) T = ( ∂ V ∂ T ) P . {\displaystyle \left({\frac {\partial S}{\partial P}}\right)_{T}=\left({\frac {\partial V}{\partial T}}\right)_{P}.} <a href="/wiki/Maxwell_Relations" target="_blank">/wiki/Maxwell_Relations</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Ge, Xinlei; Wang, Xidong (20 May 2009). "Estimation of Freezing Point Depression, Boiling Point Elevation, and Vaporization Enthalpies of Electrolyte Solutions". Industrial & Engineering Chemistry Research. 48 (10): 5123. doi:10.1021/ie900434h. <a href="https://doi.org/10.1021%2Fie900434h" target="_blank">https://doi.org/10.1021%2Fie900434h</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Ge, Xinlei; Wang, Xidong (2009). "Calculations of Freezing Point Depression, Boiling Point Elevation, Vapor Pressure and Enthalpies of Vaporization of Electrolyte Solutions by a Modified Three-Characteristic Parameter Correlation Model". Journal of Solution Chemistry. 38 (9): 1097–1117. doi:10.1007/s10953-009-9433-0. ISSN 0095-9782. S2CID 96186176. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>NIST <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> </ol>