State Functions for Systems of Variable Composition

For a closed system of fixed composition, the extensive thermodynamic properties such as y, U, S, A, Y, and G are functions of any pair of convenient independent variables. For example. Equation (7.38) suggests that G is a natural function of T and P. That is G =f(T, P). The total differential of G would be 

Chemical Thermodynamics Basic Concepts and Methods, Seventh Edition. By Irving M. Klotz and Robert M. Rosenberg 

When the composition of a system varies, the mole numbers of the components are additional independent variables and we have 

The partial derivative (dG/dm)T,p,nj in which i j, represents the rate of increase in the Gibbs function of the system per mole of component i added to the system when T, P, and the other mole numbers are held constant. [Equation (9.3) is based on the assumption that surface effects can be neglected.] The summation is over all components of the system. 

If the composition is constant, so the dm terms are zero. Equation (9.3) becomes Equation (9.1), and we can write 

---