Equilibrium constant Gibbs-Duhem relation

We study the consequences of applying the Gibbs-Duhem relation to a two-component system at constant T and P. This should make that relationship appear much less abstract it imposes important restrictions on components in equilibrium. We proceed as follows Divide the relation - - U2dfi2 = 0 by (ni + 2) to obtain x dfii + (1 x )dfi2 = 0. With dx2 = —dx we find that... 

If we vary the composition of a liquid mixture over all possible composition values at constant temperature, the equilibrium pressure does not remain constant. Therefore, if integrated forms of the Gibbs-Duhem equation [Equation (16)] are used to correlate isothermal activity coefficient data, it is necessary that all activity coefficients be evaluated at the same pressure. Unfortunately, however, experimentally obtained isothermal activity coefficients are not all at the same pressure and therefore they must be corrected from the experimental total pressure P to the same (arbitrary) reference pressure designated P. This may be done by the rigorous thermodynamic relation at constant temperature and composition ... 

---