Relations Among Partial Molar Quantities

Partial molar properties can be related to each other, further extending the thermodynamic web. For example, consider the total solution enthalpy  

Note the similarity between Equation (6.31), which applies to the partial molar enthalpy, 

It is straightforward to show that the similar derived property relations described in Chapter 5 likewise hold  

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In a similar fashion a large collection of relations among the partial molar quantities can be developed. For example, since dCj cT)p M — —S- for a pure fluid, one can easily show that (8G /dT)pj j. — —5j for a mixture. In fact, by extending this argument to other mixture properties, one finds that for each relationship among the thermodynamic variables in a pure fluid, there exists an identical relationship for the partial molar thermodynamic properties in a mixture ... 

For isothermal-isobaric processes (3.4.10) reduces to a relation among the partial molar quantities themselves. 

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