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The molar enthalpy of fusion , sometimes also called the molar heat of fusion, is the enthalpy change of phase change from solid to liquid of one mole of substance at its melting point . Since the enthalpy change is equivalent to the heat of a process carried out at constant pressure, we can also define the molar enthalpy of fusion as the amount of heat required to pass one mole of substance from the solid state to the liquid state in its melting point and constant pressure.
This enthalpy is an intensive property of matter, so it depends solely on its composition, and not on the quantity of the sample with which one is working, nor on the extension or size of the system. In other words, it is a characteristic property of each material and generally refers to pure substances.
For example, the enthalpy of fusion of water at a pressure of 1 atm is 6.02 kJ/mol, which means that it takes 6.02 kJ to melt or melt 18 g of solid water or ice (mass corresponding to one mole of water) that are at 0°C and thus convert them into 18 g of liquid water, also at 0°C.
Symbol for molar enthalpy of fusion
Different ways of representing molar enthalpies have existed over time, including the molar enthalpy of fusion. The universally accepted symbol for enthalpy is H. It is a state function defined by the difference between the internal energy of a system and the PV product; in other words, H = U – PV. However, when we talk about the enthalpy of a process such as fusion, and not of a substance, then we are really referring to a change in enthalpy of the system as a consequence of said process. For this reason, in these cases the symbol for enthalpy is actually ΔH.
Since it is the enthalpy of the fusion process, fo “fus” is added as a subscript, that is ΔH fus (although f is rarely used as it can be confused with the enthalpy of formation, which is a different concept). Finally, there are two ways in which it is usually indicated that an enthalpy is molar. Formerly it was customary to place a bar above the symbol. However, for various reasons, this way of representing molar thermodynamic quantities is inadequate, so the letter m (for molar) was replaced by the addition as a subscript, separated from the subscript of the process by a comma. This means that the currently accepted symbol for the molar enthalpy of fusion is:
The standard molar enthalpy of fusion
When the pressure at which the molar enthalpy is measured is the standard pressure of 1 atm (or 1 bar, depending on the convention used) and the phase change process occurs at the normal melting point (which corresponds to the melting point at standard pressure), then it is called the standard molar enthalpy of fusion, which is indicated by adding a 0 as an exponent to the enthalpy symbol.
Units of molar enthalpy of fusion
The units of the molar enthalpy of fusion are [energy]/[mol] or, what is the same, [energy].[mol] -1 . These units depend on the unit system in which you are working. Here are some examples of units commonly used in different fields:
- SI units are J/mol or J.mol -1 .
- kJ/mol or kJ.mol -1 (these units are very common given the order of magnitude of most molar enthalpies of fusion).
- cal/mol or cal.mol -1 .
- kcal/mol or kcal.mol -1 or, what is the same Cal/mol or Cal.mol -1 (these units are very common given the order of magnitude of most molar enthalpies of fusion).
- BTU/mol or BTU.mol -1 (often used in engineering).
The molar enthalpy of fusion versus the latent heat of fusion
It is a relatively common mistake to confuse the molar enthalpy of fusion with the latent heat of fusion. The reason is simple: both refer to the amount of heat needed to melt or melt a solid substance, in both cases the phase change occurs at constant pressure and temperature, in both cases it occurs at the melting point of the solid, and both are intensive properties of matter. However, they are not the same.
To begin with, the latent heat of fusion is represented by the symbol L fus or L f . However, there is a more important conceptual difference related to the amount of substance each term refers to. While the molar heat of fusion refers to 1 mole of substance , the latent heat of fusion represents the amount of heat required to melt one unit mass of the substance, not one mole. That is to say that the latent heat is, in reality, a specific heat of fusion, whose units in the SI are J/kg.
Determination of the molar enthalpy of fusion
experimental determination
There are different ways to determine the molar enthalpy of fusion of a substance. It is measured experimentally using a calorimeter . For example, if we want to measure the molar heat of fusion of water, we can introduce a known mass of solid water (ice) into a calorimeter of known heat capacity and then let the ice melt while controlling the temperature. Then, the amount of heat absorbed by the ice to melt can be determined from the change in temperature of the calorimeter, which gives us the amount of heat released by it. If we are using an isobaric calorimeter, that is, one with constant pressure, this heat directly represents the enthalpy of fusion of the sample (note: it is the enthalpy of fusion ΔH fus, not the molar enthalpy ΔH m,fus ).
Finally, using the mass of water and its molar mass (18.02 g/mol), the number of moles that were present in the sample is determined and the melting molar mass is calculated using the following equation:
Determination from the latent heat of fusion
As mentioned before, the latent heat of fusion is the heat per unit mass, rather than per mole. For this reason, the latent heat of fusion can be transformed into the molar heat of fusion simply by multiplying it by the molar mass of the substance:
Before carrying out the calculation, the consistency of the units must be checked and any necessary transformations carried out.
theoretical determination
The molar enthalpy of fusion can also be calculated theoretically from other thermodynamic quantities. For example, if we know the values of the standard enthalpies of formation of the solid and the liquid, as well as their respective heat capacities at constant pressure (C p,m, s and C P, m, l , respectively).
In these cases, Hess’ Law is used to establish two different ways of calculating the enthalpy variation of fusion under standard conditions of temperature and pressure, one directly and the other by taking the solid to its normal melting point, carrying out the melting at said temperature and then bringing the liquid to the standard temperature at which the standard enthalpies of formation are reported.
That is, the enthalpy of the following processes is calculated:
The above represents the one-step process in which a certain amount of A passes from the solid state at the standard temperature and pressure of T 0 and P 0 , respectively, to the liquid state at the same temperature and pressure. The enthalpy of this process can be calculated directly from the standard enthalpies of formation of A in both states.
This is the same process, only carried out in a different way, bringing the solid to the melting point (T fus ), melting it at that temperature, and then bringing the liquid to the standard temperature T 0 .
Since both processes start and end in the same states, then Hess’s Law indicates that the total enthalpy changes must be equal, therefore:
From here, we solve the equation to find the molar enthalpy of fusion, which gives us:
References
Atkins, P., & dePaula, J. (2010). Atkins. Physical Chemistry (8th ed .). Panamerican Medical Editorial.
Latent heat of fusion . (nd). Physics with computer. http://www.sc.ehu.es/sbweb/fisica/estadistica/otros/fusion/fusion.htm
Chang, R. (2002). Physicochemistry (1st ed .). MCGRAW HILL EDUCATION.
Fusion enthalpy. Educaplus (2021). http://www.educaplus.org/elementos-quimicos/propiedades/entalpia-fusion.html
Heat of Fusion. (2020, August 15). https://chem.libretexts.org/@go/page/1936
LearnChemE. (2020, October 13). Calculate Heat of Reaction at an Elevated Temperature [Video]. Youtube. https://www.youtube.com/watch?v=dxBD0j2gzjo&t=252s
Molar heat of fusion of ice . (2018, April 5). nanopdf. https://nanopdf.com/download/molar-heat-of-fusion-of-ice-5aec35580aeb3_pdf
