Partial molar variables and thermodynamic coefficients

Theorem 5.- The partial molar variables are elements of the characteristic matrix associated with the intensive variables. 

We will attempt to prove this theorem for a phase with two components and four variables, its extension to a phase with more variable couples is direct Let us choose the ensemble of variables e = (f, -P, rt, n-. The corresponding characteristic matrix is written  

We obtain expression [2.28] in which the following derivatives arise  

We have seen that to define a thermodynamic phase, one must know a certain number of thermodynamic coefficients. There is no table or ensemble of data that directly provide us with the thermodynamic coefficients. These must be deduced from other data. We will now focus on some data from tables which allow the desires thermodynamic coefficients to be obtained. 

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