Properties of partial molar variables

Let us recap the following relations which are found in all basic publications of chemical thermodynamics  

This last relation is known as the generalized Gibbs-Duhem lelatioa If we keep constant all the intensive variables 7, this relation can be simplified 

We can then use this relation using the molar fractions x,  

We are going to assess some properties of the chemical potential and how it can be extended to generalized chemical potentials. 

Chemical potential and partial molar free enthalpy We are going to prove the following theorem  

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