Final answer:
The heat of sublimation is equal to the sum of the enthalpy of fusion and vaporization because it represents the energy required to transition directly from a solid to a gas, encompassing the energy needed for both phase changes as per Hess's Law.
Step-by-step explanation:
The heat of sublimation, ∆H_subl, is equal to the sum of the enthalpy of fusion, ∆H_fus, and the enthalpy of vaporization, ∆H_vap, at the same temperature because sublimation is the direct transition from a solid phase to a gas phase without passing through a liquid phase.
To undergo sublimation, a substance must first absorb the energy equivalent to its enthalpy of fusion to change from solid to liquid, and then absorb the energy equivalent to its enthalpy of vaporization to change from liquid to gas.
These two energy changes combined equal the energy required for the direct solid to gas transition, which is the enthalpy of sublimation.
This is in accordance with Hess's Law, which states that the total enthalpy change for a reaction is the same, regardless of the number of steps in the process.