V and T as state variables
Because most EOS are explicit in P instead of V, the Helmholtz free energy has to be used to calculate µi. The line of arguments is, however, identical to the one given for the Gibbs free energy. The dependence of A on V is given by integrating (3):
(34)
Pure fluids. Expanding Equation (34) using the ideal gas law for a pure phase component we get:
(35)
Splitting the first integral by expanding the upper integration boundary to infinity (the lower and the higher integration boundaries are switched; therefore, the sign changes) and solving the second we get:
(36)
