Enthalpy of fusion 2360383 225855132 2008-07-15T18:39:01Z WilfriedC 2780956 Joback method [[Image:Heat_Content_of_Zn(c,l,g).PNG|thumb|right|350px|'''Molar heat content of zinc''' above 298.15 K and at 1 atm pressure, showing discontinuities at the melting and boiling points. The enthalpy of melting (Δ''H''°m) of zinc is 7323 J/mol, and the enthalpy of vaporization (Δ''H''°v) is 115 330 J/mol.]] The '''standard [[enthalpy]] of fusion''' (symbol: <math>\Delta{}H_{fus}</math>), also known as the '''heat of fusion''' or '''specific melting heat''', is the amount of [[thermal energy]] which must be absorbed or evolved for 1 [[Mole (unit)|mole]] of a substance to change states from a [[solid]] to a [[liquid]] or vice versa. It is also called the '''latent heat of fusion''' or the '''enthalpy change of fusion''', and the [[temperature]] at which it occurs is called the [[melting point]]. When you withdraw [[thermal energy]] from a liquid or solid, the [[temperature]] falls. When you add heat energy the temperature rises. However, at the transition point between solid and liquid (the [[melting point]]), extra energy is required (the heat of fusion). To go from liquid to solid, the [[molecule]]s of a substance must become more ordered. For them to maintain the order of a solid, extra heat must be withdrawn. In the other direction, to create the disorder from the solid crystal to liquid, extra heat must be added. The heat of fusion can be observed if you measure the temperature of water as it freezes. If you plunge a closed container of room temperature water into a very cold environment (say &minus;20 °C), you will see the temperature fall steadily until it drops just below the freezing point (0 °C). The temperature then rebounds and holds steady while the water crystallizes. Once completely frozen, the temperature will fall steadily again. The temperature stops falling at (or just below) the freezing point due to the heat of fusion. The energy of the heat of fusion must be withdrawn (the liquid must turn to solid) before the temperature can continue to fall. The units of heat of fusion are usually expressed as: #[[joule]]s per [[Mole (unit)|mole]] (the [[SI]] units) #[[calorie]]s per gram (old metric units now little used, except for a different, larger calorie used in nutritional contexts) #[[British thermal unit]]s per pound or Btu per [[pound-mole]] *Note: These are not the [[calories]] found in food. The calories found in food are more properly known as kilocalories—equal to 1000 calories. 1000 [[calories]] = 1 kilocalorie = 1 food calorie. Food calories are sometimes abbreviated as kcal as if small calories were being used, while calories are abbreviated as cal. Another distinguishing method, though often confusing, uses capitalisation. A Calorie is a food calorie, or 1000 calories. So 1 Cal = 1000 cal or 1 kcal == Reference values of common substances == [[Image:Enthalpy_of_Fusion_period_three.PNG|thumb|right|150px|Standard enthalpy change of fusion of period three.]][[Image:Molar_heat_of_fusion_period_two.png|thumb|right|150px|Standard enthalpy change of fusion of period two of the [[periodic table of elements]].]] <table class="wikitable sortable"> <tr><th>Substance</th><th>Heat of fusion<br> (cal/g) </th><th>Heat of fusion<br> (J/g) </th></tr> <tr><td>water</td><td> 79.72</td><td>333.55</td></tr> <tr><td>methane</td><td> 13.96</td><td>58.41</td></tr> <tr><td>ethane</td><td> 22.73</td><td>95.10</td></tr> <tr><td>propane</td><td> 19.11</td><td>79.96</td></tr> <tr><td>methanol</td><td> 23.70</td><td>99.16</td></tr> <tr><td>ethanol</td><td> 26.05</td><td>108.99</td></tr> <tr><td>glycerol</td><td> 47.95</td><td>200.62</td></tr> <tr><td>formic acid</td><td> 66.05</td><td>276.35</td></tr> <tr><td>acetic acid</td><td> 45.91</td><td>192.09</td></tr> <tr><td>acetone</td><td> 23.42</td><td>97.99</td></tr> <tr><td>benzene</td><td> 30.45</td><td>127.40</td></tr> <tr><td>myristic acid</td><td> 47.49</td><td>198.70</td></tr> <tr><td>palmitic acid</td><td> 39.18</td><td>163.93</td></tr> <tr><td>stearic acid</td><td> 47.54</td><td>198.91</td></tr> </table> These values are from the [[CRC Press|CRC]] '''Handbook of Chemistry and Physics''', 62nd edition. The conversion between cal/g and kJ/kg in the above table uses the thermochemical [[calorie]] (cal<sub>th</sub>) = 4.184 joules rather than the International Steam Table calorie (cal<sub>INT</sub>) = 4.1868 joules. == Applications == To heat one kilogram (about 1 litre) of water from 10 °C to 30 °C requires 20 kcal. <br> However, to melt ice and raise the resulting water temperature 20 °C requires extra energy. To heat ice from 0 °C to water at 20 °C requires: :(1) 80 cal/g (heat of fusion of ice) = 80 kcal for 1 kg :PLUS :(2) 1 cal/(g·°C) = 20 kcal for 1 kg to go up 20 °C := 100 kcal ==Solubility prediction== The heat of fusion can also be used to predict [[solubility]] for solids in liquids. Provided an [[ideal solution]] is obtained the [[mole fraction]] <math>(x_2)</math> of solute at saturation is a function of the heat of fusion, the [[melting point]] of the solid <math>(T_{fus})</math> and the [[temperature]] (T) of the solution: :<math> \ln x_2 = - \frac {\Delta H^\circ_{fus}}{R} \left(\frac{1}{T}- \frac{1}{T_{fus}}\right)</math> Here, R is the [[gas constant]]. For example the solubility of [[paracetamol]] in water at 298 [[Kelvin (unit)|K]] is predicted to be: :<math> \ln x_2 = - \frac {28100 \mbox{ J mol}^{-1}} {8.314 \mbox{ J K}^{-1} \mbox{ mol}^{-1}}\left(\frac{1}{298}- \frac{1}{442}\right) = 0.0248 </math> This equals to a solubility in grams per liter of: <math> \frac{0.0248*\frac{1000 \mbox{ g}}{18.053 \mbox{ mol}^{-1}}}{1-0.0248}*151.17 \mbox{ mol}^{-1} = 213.4</math> which is a deviation from the real solubility (240 g/L) of 11%. This error can be reduced when an additional [[heat capacity]] parameter is taken into account <ref>''Measurement and Prediction of Solubility of Paracetamol in Water-Isopropanol Solution. Part 2. Prediction'' H. Hojjati and S. Rohani Org. Process Res. Dev.; '''2006'''; 10(6) pp 1110 - 1118; (Article) {{DOI|10.1021/op060074g}}</ref> ===Proof=== At [[Chemical equilibrium|equilibrium]] the [[chemical potential]]s for the pure solvent and pure solid are identical: :<math>\mu^\circ_{solid} = \mu^\circ_{solution}\,</math> or :<math>\mu^\circ_{solid} = \mu^\circ_{liquid} + RT\ln X_2\,</math> with <math>R\,</math> the [[gas constant]] and <math>T\,</math> the [[temperature]]. Rearranging gives: :<math>RT\ln X_2 = - (\mu^\circ_{liquid} - \mu^\circ_{solid})\,</math> and since :<math> \Delta G^\circ_{fus} = - (\mu^\circ_{liquid} - \mu^\circ_{solid})\,</math> the heat of fusion being the difference in chemical potential between the pure liquid and the pure solid, it follows that :<math>RT\ln X_2 = - ( \Delta G^\circ_{fus})\,</math> Application of the [[Gibbs-Helmholtz equation]]: :<math>\left( \frac{\partial ( \frac{\Delta G^\circ_{fus} } {T} ) } {\partial T} \right)_{p\,} = \frac {\Delta H^\circ_{fus}} {T^2}</math> ultimately gives: :<math>\left( \frac{\partial ( \ln X_2 ) } {\partial T} \right) = \frac {\Delta H^\circ_{fus}} {RT^2}</math> or: :<math> \partial \ln X_2 = \frac {\Delta H^\circ_{fus}} {RT^2}*\delta T</math> and with [[Integral|integration]]: :<math> \int^{x_2=x_2}_{x_2 = 1} \delta \ln X_2 = \ln x_2 = \int_{T_fus}^T \frac {\Delta H^\circ_{fus}} {RT^2}*\Delta T</math> the end result is obtained: :<math> \ln x_2 = - \frac {\Delta H^\circ_{fus}} {R}\left(\frac{1}{T}- \frac{1}{T_{fus}}\right)</math> == See also == *[[Heat of vaporization]] *[[Heat capacity]] *[[Specific heat capacity]] *[[Thermodynamic databases for pure substances]] *[[Joback method]] (Estimation of the heat of fusion from molecular structure) ==References== <div class="references-small"><references/></div> [[Category:Thermodynamic properties]] [[af:Smeltingswarmte]] [[ar:حرارة الانصهار]] [[ast:Entalpía de fusión]] [[bn:ফিউশনের এনথালপি]] [[bs:Toplota topljenja]] [[ca:Calor de fusió]] [[cs:Měrné skupenské teplo tání]] [[da:Smeltevarme]] [[de:Schmelzwärme]] [[es:Entalpía de fusión]] [[eu:Urtze-entalpia]] [[fr:Énergie de fusion]] [[ko:융해열]] [[it:Entalpia di fusione]] [[lt:Lydymosi šiluma]] [[jbo:manri dujbi'o nejni]] [[hu:Olvadáshő]] [[nl:Smeltwarmte]] [[pl:Ciepło topnienia]] [[pt:Calor de fusão]] [[sk:Merné skupenské teplo topenia]] [[sl:Talilna toplota]] [[sr:Топлота топљења]] [[sh:Toplota topljenja]] [[fi:Sulamislämpö]] [[sv:Smältvärme]] [[th:ความร้อนแฝงของการหลอมเหลว]] [[vi:Nhiệt nóng chảy]] [[uk:Питома теплота плавлення]] [[ur:سخانۂ ائتلاف]] [[zh:熔化热]]