*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 *µ**i*. 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)