Partial molar quantities and additivity rules

Equations (11.76), (11.77), (11.78), and (11.79) are the fundamental equations for systems of variable composition, and they imply that pi may be interpreted in f our different ways  

Therefore, corresponding to any extensive property U, V, 5, H, A, G, there are partial molar properties, Ui, Vi, Si, Hi, Ai, G. The partial molar quantities are defined by 

Equations (11.83) show that the partial molar quantities are related to each other in the same way as the total quantities. (The use of rather than Gj for the partial molar Gibbs energy is customary.) 

The total differential of any extensive property then takes a form analogous to Eq. (11.7). Choosing 5, F, and H as examples, 

Since and Hi are intensive properties they must have the same value everywhere 

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