The enthalpy of fusion is the amount of energy required to convert one mole of solid into liquid. For example, whenmelting 1 kg of ice (at 0 °C under awide range of pressures), 333.55 kJ of energy is absorbed with notemperature change. Theheat of solidification (when a substancechanges from liquid to solid) is equal and opposite.
This energy includes the contribution required to make room for any associated change in volume by displacing its environment against ambient pressure. The temperature at which thephase transition occurs is themelting point or the freezing point, according to context. By convention, the pressure is assumed to be 1 atm (101.325 kPa) unless otherwise specified.
The enthalpy of fusion is alatent heat, because, while melting, the heat energy needed to change the substance from solid to liquid does not cause any increase in temperature. Temperature remains constant during the freezing or melting process, and only begins to change again (assuming the energy input or removal (cooling) continues) after the phase change is complete. The latent heat of fusion is the enthalpy change of any amount of substance when it melts. When the heat of fusion is referenced to a unit of mass, it is usually called thespecific heat of fusion, while themolar heat of fusion refers to the enthalpy change peramount of substance inmoles.
The liquid phase has a higher internal energy than the solid phase. This means energy must be supplied to a solid in order to melt it and energy is released from a liquid when it freezes, because themolecules in the liquid experience weakerintermolecular forces and so have a higher potential energy (a kind ofbond-dissociation energy for intermolecular forces).
When liquid water is cooled, its temperature falls steadily until it drops just below the line of freezing point at 0 °C. The temperature then remains constant at the freezing point while the water crystallizes. Once the water is completely frozen, its temperature resumes a colder trend.
The enthalpy of fusion is almost always a positive quantity;helium is the only known exception.[1]Helium-3 has a negative enthalpy of fusion at temperatures below 0.3 K.Helium-4 also has a very slightly negative enthalpy of fusion below 0.77 K (−272.380 °C). This means that, at appropriate constant pressures, these substances freeze with the addition of heat.[2] In the case of4He, this pressure range is between 24.992 and 25.00 atm (2,533 kPa).[3]
Standard enthalpy change of fusion of period threeStandard enthalpy change of fusion of period two of theperiodic table of elements
These values are mostly from theCRCHandbook of Chemistry and Physics, 62nd edition. The conversion between cal/g and J/g in the above table uses the thermochemicalcalorie (calth) = 4.184 joules rather than the International Steam Table calorie (calINT) = 4.1868 joules.
To heat 1 kg of liquid water from 0 °C to 20 °C requires 83.6 kJ (see below). However, heating 0 °C ice to 20 °C requires additional energy to melt the ice. We can treat these two processes independently and using the specific heat capacity of water to be 4.18 J/(g⋅K); thus, to heat 1 kg of ice from 273.15 K to water at 293.15 K (0 °C to 20 °C) requires:
(1) 333.55 J/g (heat of fusion of ice) = 333.55 kJ/kg = 333.55 kJ for 1 kg of ice to melt, plus
(2) 4.18 J/(g⋅°C) × 20 °C = 4.18 kJ/(kg⋅°C) × 20 °C = 83.6 kJ for 1 kg of water to increase in temperature by 20 °C
(1 + 2) 333.55 kJ + 83.6 kJ = 417.15 kJ for 1 kg of ice to increase in temperature by 20 °C
Silicon has a heat of fusion of 50.21 kJ/mol. 50 kW of power can supply the energy required to melt about 100 kg of silicon in one hour:
The heat of fusion can also be used to predictsolubility for solids in liquids. Provided anideal solution is obtained themole fraction of solute at saturation is a function of the heat of fusion, themelting point of the solid and thetemperature of the solution:
Here, is thegas constant. For example, the solubility ofparacetamol in water at 298K is predicted to be:
Since the molar mass of water and paracetamol are18.0153gmol−1 and151.17gmol−1 and the density of the solution is1000gL−1, an estimate of the solubility in grams per liter is:
1000 g/L * (mol/18.0153g) is an estimate of the number of moles of molecules in 1L solution, using water density as a reference;
0.0248 * (1000 g/L * (mol/18.0153g)) is the molar fraction of substance in saturated solution with a unit of mol/L;
0.0248 * (1000 g/L * (mol/18.0153g)) * 151.17g/mol is the solute's molar fraction equivalent mass conversion;
1-0.0248 will be the fraction of the solution that is solvent.
which is a deviation from the real solubility (240 g/L) of 11%. This error can be reduced when an additionalheat capacity parameter is taken into account.[6]
^Hojjati, H.; Rohani, S. (November 2006). "Measurement and Prediction of Solubility of Paracetamol in Water−Isopropanol Solution. Part 2. Prediction".Organic Process Research & Development.10 (6):1110–1118.doi:10.1021/op060074g.
