Limits on Activity Coefficient Correlations, the Gibbs-Duhem Equation

2 LIMITS ON ACTIVITY COEFFICIENT CORRELATIONS, THE GIBBS-DUHEM EQUATION 

It is shown in Chapter 6 that for any partial molar property (for example, q where Q is any extensive property) of any mixture with any number of species in one phase the partial molar equation requires that 

If we let q be the partial molar Gibbs energy, then Eq. 6.22 becomes the Gibbs-Duhem equation  

If we consider a binary mixture for which ( c = nj = =0), then a little algebra converts this to 

Intuitively, the reason for the Gibbs-Duhem equation is that for each species -y, depends on the fraction of the molecules with which a molecule interacts that are of the same kind and the fraction that are of the other kind. Thus, as we change the ratio of one kind of molecule to the other (change the mol fractions), we would expect both -y,s to change the Gibbs-Duhem equation shows how those changes relate to each other. 

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