Fugacities with the Virial Equation

We restrict our discussion to the virial equation truncated after the second term, because third or higher virial coefficients are rarely available. Use of the volume series with Eq. 11.9.3 yields  

and B are the molar volume, compressibility factor, and second virial coefficient of the mixture respectively, By is the second virial coefficient of the pair i-j, and the summation is over all the components of the mixture. Thus, for a binary mixture, Eq. 11.9.5 becomes  

No comparison between Eqs 11.9.4 and 11.9.5 is available but we saw in Chapter 8 that, for pure compounds, Eq. 11.9.5 performs at least as well as Eq.l 1.9.4. In addition, it is more convenient to use since it does not require the calculation of the molar volume. It is, therefore, recommended for mixtures as well. 

The virial equation is, of course, applicable to the vtqwr phase only and, when truncated after B, should not be used outside the pressure range of Eq.l 1.7.9. 

Finally, because of its rigorous mixing rules, and the success of the empiric correlations for the estimation of Bjf and By, the virial equation finds extensive use in the estimation of vapor fugacities for low pressure vapor-liquid equilibrium calculations, especially in systems containing polar components. The liquid phase fugacities, in such cases, are calculated using the standard state fugacity approach that will be discussed in Section 11.10. 

---