Mixtures of Real Gases

Now that we have obtained expressions for the fugacity of a real gas and its temperature and pressure coefficients, let us consider the application of the concept of fugacity to components of a mixture of real gases. 

---

In mixtures of real gases the ideal gas law does not hold. The chemical potential of A of a mixture of real gases is defined in terms of the fugacity of the gas, fA. The fugacity is, as discussed in Chapter 2, the thermodynamic term used to relate the chemical potential of the real gas to that of the (hypothetical) standard state of the gas at 1 bar where the gas is ideal ... 

In this chapter we will apply the concepts developed in Chapter 11 to gaseous systems, first to mixtures of ideal gases, then to pure real gases, and finally to mixtures of real gases. 

Since the petroleum engineer primarily is concerned with gas mixtures, the laws governing the behavior of mixtures of ideal gases will now be introduced. This will later lead to an understanding of the behavior of mixtures of real gases. 

Two further crude approximations have been used for the virial equation of state. The first is that the virial coefficients combine linearly. This combination of constants results in an equation of state that is additive in the properties of the pure components. In such a mixture Dalton s and Amagat s laws still hold, and the mixture may be called an ideal mixture of real gases. The assumption is probably the crudest that can be used and is... 

Similarly we can write for any component, i, in a mixture of real gases ... 

What has been discussed is valid if it is assumed that a mixture of real gases is ideal ... 

The definition of tlie fugacity of a species in solution is parallel to the definition of tire pure-speciesfugacity. For species i m a mixture of real gases or in a solution of liquids, the equation analogous to Eq. (11.28), tire ideal-gas expression, is ... 

Activities and Activity Coefficients in a Mixture of Real Gases. 

Sj. Mixtures of Real Gases Additive Pressure Law.—The rule that the total pressure of a mixture of gases is equal to the sum of the pressures exerted by each gas if it alone occupied the whole of the available volume ( 5b) does not apply to real gases. The total pressure is thus not equal to the sum of the partial pressures defined in the usual manner. However, for some purposes it is convenient to define the partial pressure of a gas in a mixture by means of equation (5.8), i.e., p == n P, where p is the partial pressure and n is the mole fraction of any constituent of the mixture of gases of total pressure P. 

A simple modification of the law of partial pressures as applied to ideal gases has been proposed for mixtures of real gases (E. P. Bartlett, 1928). If PJ is the pressure which would be exerted by a constituent of a gas mixture when its molar volume is the same as that of the mixture, then it is suggested that the total pressure P is given by... 

Sk. Additive Volume Law.— The additive pressure law, as given by equation (5.26), is useful for the calculation of the approximate pressure exerted by each gas, and the total pressure, in a mixture of real gases, when the volume is known. If the total pressure is given, however, the evaluation of the volume is somewhat more complicated, involving a series of trial solutions. An alternative approxi-... 

Gas mixtures Ideal perfect mixture, p= bar. Mixture of real gases,yj=l bar. 

J. A. Beattie The Computation of the Thermodynamic Properties of Real Gases and Mixtures of Real Gases, Chem. Rev., 44 141 (1949). 

The problem of finding effectively the equation of state of a mixture of hard spheres of different diameters, incidentally, is of considerable interest in a number of applications, e.g., for finding the high temperature equation of state of mixtures of real gases and the surface tension of mixtures, amoi other things. While a number of the theories of fluids mentioned in Section IV of this chapter can also be reformulated " formally for mixtures,... 

In this section we shall extend some of the results of the previous section to mixtures of real gases. 

The entropy of a mixture of real gases is readily determined by making use of Eq. (7-167) and the relation... 

In this chapter we apply the general criteria for equilibrium developed in Chap. 6 to systems in which chemical reactions may occur. In Sec. 8-1, we present a general discussion of chemical equilibrium in homogeneous and heterogeneous systems. The concept of a progress variable is introduced, and the conditions for chemical equilibrium are derived. The equilibrium constant is defined, and some of its properties are developed. A discussion of the Le Chatelier-Braun principle applied to chemical reactions is presented. In Sec. 8-2, the results of Sec. 8-1 are applied to chemical reactions in mixtures of real gases. 

---