An example state functions of a mixture

Thermodynamics and Chemistry, second edition,version 3 by Howard DeVoe. Latest version www.chem.umd.edu/themobook 

We could make other choices of the independent variables for the aqueous sucrose system. For instance, we could choose the set T, p, V, and vr, or the set p, V, p, and xr-If there are no imposed conditions, the number of independent variables of this system is always four. (Note that we could not arbitrarily choose just any four variables. For instance, there are only three independent variables in the set p, V,m, and p because of the relation p = mlV) 

If the system has imposed conditions, there will be fewer independent variables. Suppose the sucrose solution is in a closed system with fixed, known values of a and r then there are only two independent variables and we could describe the state by the values of just T and p. 

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