In 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 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. 

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. 

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 ... 

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. 

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-... 

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. 

But, following the discussion given at the end of iii. above and similarly as for the first pure interpretation of (4.417), we can interpret (4.422) as a limiting property of each real gas mixture of fixed composition, i.e. property (A.3) is valid also for mixtures of real gases which therefore in the limit of zero pressures behaves as an ideal gas mixture with state equation (4.421). 

The fugacity coefficient of the i-th constituent in an ideal mixture of real gases can be calculated as follows ... 

Operations of most fuel cell power systems involve a mixture of gases. Therefore, we need to perform thermodynamic analysis and transport phenomena analysis with a mixture of gases. The gas mixture may be a mixture of ideal gases or a mixture of real gases. In this book, the presentation of fuel cell analysis is restricted to the mixture of ideal gases only. 

The real atmosphere is more than a dry mixture of permanent gases. It has other constituents—vapor of both water and organic liquids, and particulate matter held in suspension. Above their temperature of condensation, vapor molecules act just like permanent gas molecules in the air. The predominant vapor in the air is water vapor. Below its condensation temperature, if the air is saturated, water changes from vapor to liquid. We are all familiar with this phenomenon because it appears as fog or mist in the air and as condensed liquid water on windows and other cold surfaces exposed to air. The quantity of water vapor in the air varies greatly from almost complete dryness to supersaturation, i.e., between 0% and 4% by weight. If Table 2-1 is compiled on a wet air basis at a time when the water vapor concentration is 31,200 parts by volume per million parts by volume of wet air (Table 2-2), the concentration of condensable organic vapors is seen to be so low compared to that of water vapor that for all practical purposes the difference between wet air and dry air is its water vapor content. 

Gas sensors are of importance for a variety of environmental, industrial, medical, scientific and even domestic applications. The gas may be, for example, hazardous to human health, an atmospheric pollutant, or important, in terms of its concentration, for an industrial or medical process. Apart from systems merely providing an alarm signal, it is frequently required to obtain accurate real-time measurements of the concentration of a particular target gas, often in a mixture of other gases. 

Supermolecular spectra could perhaps be studied with state-selection using adequate molecular beam techniques. That would not be easy, however, because of the smallness of the dipole moments induced by in-termolecular interactions. For the purpose of this book, we will mostly deal with bulk spectra, or interaction-induced absorption of pure and mixed gases. A great variety of excellent measurements of such spectra exists for a broad range of temperatures, while state-selected supermolecular absorption beam data are virtually non-existent at this time. Furthermore, important applications in astrophysics, etc., are concerned precisely with the optical bulk properties of real gases and mixtures. 

The thermodynamic functions for the gas phase are more easily developed than for the liquid or solid phases, because the temperature-pressure-volume relations can be expressed, at least for low pressures, by an algebraic equation of state. For this reason the thermodynamic functions for the gas phase are developed in this chapter before discussing those for the liquid and solid phases in Chapter 8. First the equation of state for pure ideal gases and for mixtures of ideal gases is discussed. Then various equations of state for real gases, both pure and mixed, are outlined. Finally, the more general thermodynamic functions for the gas phase are developed in terms of the experimentally observable quantities the pressure, the volume, the temperature, and the mole numbers. Emphasis is placed on the virial equation of state accurate to the second virial coefficient. However, the methods used are applicable to any equation of state, and the development of the thermodynamic functions for any given equation of state should present no difficulty. 

The rationalizations of signs for HE of binary liquid mixtures presented in Sec. 16.7 apply approximately to the signs of S 2 for binary gas mixtures. Thus, positive Su is the norm for NP/NP, NA/NP, and AS/NP mixtures, whereas is usually negative for NA/NA mixtures comprising solvating species. One expects < 12 to be essentially zero for ideal solutions of real gases, e.g., for binary gas mixtures of the isomeric xylenes. 

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