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5. Chemical potential, simple mixtures, chemical reactions andequilibria 

(ii) Mixtures


The Gibbs-Duhem equation

Since the total free energy of a system is give by:

and hence by differentiation we get:
But, as discussed in the previous section, for a system at constant temperature and pressure we have:
and hence since G is a state function, then the two expressions must be equal, which means that:
.(Gibbs-Duhem equation)
The significance of the Gibbs-Duhem equation is that the chemical potential of a component in a mixture cannot change independently of the chemical potential of the other components. For example, in a binary mixture we have: 
i.e., if one chemical potential increases, the other must decrease.
 

Note: There is also the a similar 'Gibbs-Duhem equation for the partial molar volumes' which is given by:

where the partial molar volume, defined as:
which signifies the volume of component J in a mixture.