The procedures described in Chapter 15 are well suited to solid and liquid solutions and could also be applied to gases, but in fact, other approaches are generally used. The main reason for this is partly historical; much work was done early in the history of physical chemistry on the behavior of gases, and these methods have continued to evolve to the present day. We have also just seen that the Margules equations become very unwieldy with multi-component systems. Because true gases are completely miscible, natural gases often contain many different components, so the Margules approach is not very suitable. Unfortunately, the most successful alternative methods described in this section are also quite unwieldy; however, they do not become much more complicated for multi-component gases than they are for the pure gases themselves, and this is a definite advantage. We have seen that with real, non-ideal gases, all the thermodynamic properties are described if we know the T, P, and the fugacity coefficient. For gaseous solutions, the fugacity coefficient for each component generally depends on the concentrations and types of other gaseous species in the same mixture. All gases, whether pure or multi-component, should approach ideality at higher T and lower P; conversely, non-ideality is most pronounced in dense, low-temperature gases where intermolecular forces are strongest. The challenge here is to find an equation of state that can adequately cover this range of conditions for gases of many different constituents. In the following discussion we first briefly outline some of the equations of state used to describe pure gases. We will introduce these from the molecular point of view since this helps understand the physical basis (and limitations) of each model. Each of these equations of state can then be applied to mixtures of gases using a set of rules which we describe at the end of this section.
Precise Numerical Differentiation of Thermodynamic Functions with
Multicomplex Variables
