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The enthalpy of sublimation can be expressed as a combination of the enthalpy of fusion and the enthalpy of vaporization given that sublimation is the process of a solid vaporizing and bypassing the liquid phase and enthalpy is a state property. They are essentially both the same formula if you expand the Hsub=Hvap+Hfus into Hsub=(Hvapor-Hliquid)+(Hliquid-Hsolid) by substituting in the equations for Hvap and Hfus respectively. In this case the Hliquid terms cancel out and give you Hsub= Hvapor-Hsolid.
You can use either equation; they both work. The enthalpy of sublimation is basically a two-step process: solid -->liquid and then liquid --> vapor. The equation for deltaH(vapor)= H(vapor) - H(liquid) and the equation for deltaH(fusion)= H(liquid) - H(solid). When adding those two equations together you will be left with deltaH(sub)= H(vapor) - H(solid) because the two H(liquid)s cancel. In summary, deltaH(sub) = Hvapor - Hsolid and deltaHsub = deltaHfusion + deltaH vapor essentially mean the same thing and yield the same results.
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