# Why is enthalpy a state function?

Feb 16, 2014

Enthalpy 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 elements, 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).