Fugacities from an EOS for Gas Mixtures

We have experimental PvT data of this quality for only a few mixtures, so the procedure in Example 7.5, while theoretically the most reliable, is seldom used. However, if we have an EOS that we believe accurately reproduces or estimates the PvT data of a mixture, we can repeat the above calculation using it. When working with experimental PvT data as in Example 7.5 it is generally most convenient to work with the first form of Eq. 7.18  

A plot of Zjnix vs. according to Eq. 7.X is a straight line, like 

All the EOSs in Chapter 2 are for one single pure species and can be written in the form z =f(T, P, and various constants). In the corresponding-states formulation, they are mostly written as z=f (Tf, Pr, (o). Most EOSs for mixtures begin with the EOSs for the individual pure species, and then use empirical or semitheoretical mixing rules to fill in the region between the pure species. 

If we have a mixture of a and b, at some T and P then we will have two pure species zs, z, and z. Any mixing rule must be of the form 

The mixing rules must give back the pure species values as the concentration approaches either pure species, so only some mathematical forms are possible. Many of the empirical, data-fitting mles are of the form 

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