Well, it is usually zero, but this requires that we specify which one...
The Gibbs' free energy, GG, is a function of the temperature TT and pressure PP, i.e. G = G(T,P)G=G(T,P). So, if the temperature and TOTAL pressure are constant, as they are in a chemical equilibrium in a closed system, DeltaG = 0.
The Helmholtz free energy, A, is a function of the temperature T and volume V, i.e. A = A(T,V). So, if the temperature and volume are constant, as they (sometimes) are in a chemical equilibrium in a closed system, DeltaA = 0. (This is less often considered because if different mols of gas are formed than was started with, DeltaV ne 0 and thus DeltaA ne 0.)
