Enthalpy of Sublimation

The relationship [latex]\Delta H_{\text{sub}} = \Delta H_{\text{fus}} + \Delta H_{\text{vap}}[/latex] is a direct application of Hess’s Law of Constant Heat Summation, a fundamental principle in thermochemistry. This law states that the total enthalpy change during a chemical or physical process is the same regardless of the pathway taken, as long as the initial and final states are the same. In this context, the initial state is the solid phase and the final state is the gas phase. One can imagine two pathways to get from solid to gas: a direct one-step path (sublimation) or a two-step path (melting the solid to a liquid, then vaporizing the liquid to a gas).

The enthalpy change for the direct path is the enthalpy of sublimation, [latex]\Delta H_{\text{sub}}[/latex]. The enthalpy change for the two-step path is the sum of the enthalpy of fusion ([latex]\Delta H_{\text{fus}}[/latex], for the solid-to-liquid transition) and the enthalpy of vaporization ([latex]\Delta H_{\text{vap}}[/latex], for the liquid-to-gas transition). Since the initial and final states are identical for both pathways, Hess’s Law dictates that their total enthalpy changes must be equal. This principle is incredibly useful because it allows for the calculation of an unknown enthalpy change from known values. For instance, if the enthalpies of fusion and vaporization are experimentally easier to measure than the enthalpy of sublimation, the latter can be calculated accurately. This data is crucial for chemical engineers and physicists in designing processes and modeling physical phenomena where sublimation is a key factor, such as in material deposition, cryogenics, and astrophysics.