Effect of liquid composition on gas fugacities

Consider system 1 in Fig. 9.5 on page 246. A binary liquid mixture of two volatile components, A and B, is equilibrated with a gas mixture containing A, B, and a third gaseous component C of negligible solubility used to control the total pressure. In order for A and B to be in transfer equilibrium, their chemical potentials must be the same in both phases  

Suppose we make an infinitesimal change in the liquid composition at constant T and 

By inserting these expressions in the Gibbs-Duhem equation xa d/XA = —d/XR (Eq. 9.2.43), we obtain 

This equation is a relation between changes in gas-phase fugacities caused by a change in the liquid-phase composition. It shows that a composition change at constant T and p that increases the fugacity of A in the equilibrated gas phase must decrease the fugacity of B. 

Now let us treat the liquid mixture as a binary solution with component B as the solute. In the ideal-dilute region, at constant T and p, the solute obeys Henry s law for fugacity  

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