First-order deviations from ideal-gas mixtures

1 First-order deviations from ideal-gas mixtures 

We choose a two-component system for which the pressure (or the total density) is sufficiently low such that the pair correlation function for each pair of species has the form (see section 2.5) 

For simplicity, we have assumed that all the pair potentials are spherically symmetrical, and that all the internal partition functions are unity. The general expression for the chemical potential of, say, A in this system is obtained by a simple extension of the one-component expression given in chapter 3. 

We now analyze equation (6.50) with respect to the various kinds of ideality. For the purpose of this section, it is preferable to transform (6.50) so that pA is expressed as a function of T, P, and xA. To do this, we use the analog of the virial expansion for mixtures, which reads 

The factor in the square brackets can be viewed as an average virial coefficient for the mixture of two components. We now invert this relation by assuming an expansion of the total density p = pT in the form 

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