is a state function because it is defined in terms of state functions.
U, P, and V are all state functions. Their values depend only on the state of the system and not on the paths taken to reach their values. A linear combination of state functions is also a state function.
Enthalpy is defined as H = U + PV. We see that H is a linear combination of U, P, and V. Therefore, H is a state function.
We take advantage of this when we use enthalpies of formation to calculate enthalpies of reaction that we cannot measure directly.
We first convert the reactants to their , with
##ΔH_1 = -∑ΔH_f^o(react)##.
Then we convert the elements into products with
##ΔH_2 = ∑ΔH_f^o(pro)##.
##ΔH_(rxn)^o = ΔH_1 + Δ H_2 = ∑ΔH_f^o(pro) -∑ΔH_f^o(react)##.