*P* and *T* as state variables

First we consider *P* and *T* as the state variables. In that case *G* is the appropriate state function. *G* as a function of *P *at constant* T* is calculated by integrating Equation (4). The integration constant in Equation (7) is at the respective reference pressure *P**r* and any *T*. The usual choice of *P**r* is 0.1 MPa. For any real system we have:

(7)

Pure fluids. For the moment, the standard state of a fluid is the real pure fluid phase component. Pure phase components are generally designated by^{ o}. We will change the standard state for the fluid later, however. For such a real pure fluid *i* in its standard state, Equation (7) becomes:

(8)

Now the first rearrangement of Equation uses the ideal gas law, where *n**T* is the total number of moles (_{}),

(9)

by expanding (e.g. Gillespie 1925) the argument in the integral of Equation