Why is enthalpy a state function?

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)##.

This gives

##ΔH_(rxn)^o = ΔH_1 + Δ H_2 = ∑ΔH_f^o(pro) -∑ΔH_f^o(react)##.