Pure real gases

the volume of a mixture of ideal gases is the sum of the volumes of the individual gases when measured at the same pressure and temperature. 

Many equations have been suggested to express the behavior of real gases. In general, there are those equations that express the pressure as a function of the volume and temperature, and those that express the volume as a function of the pressure and temperature. These cannot usually be converted from one into the other without obtaining an infinite series. The most convenient thermodynamic function to use for those in which the volume and temperature are the independent variables is the Helmholtz energy. The 

Gibbs energy is the most convenient function to use for those in which the pressure and temperature are the independent variables. 

The virial equation of state, first suggested by Kammerlingh-Ohnes, is probably one of the most convenient equations to use, and is used in this chapter to illustrate the development of the thermodynamic equations that are consistent with the given equation of state. The methods used here can be applied to any equation of state. 

The virial equation gives the pressure as a power series of the molar density, so that either 

In this chapter, we will focus on a system with two variables, either V and T or P and T. We know that to describe a pure compound we must know either a characteristic function (For G), or three thermodynamic coefficients two diagonal terms of a characteristic matrix and a third term the fourth is deduced from the symmetiy of the characteristic matrix. 

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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. 

The van der Waals equation applies strictly to pure real gases, not to mixtures. For a mixture like the one resulting from the reaction of part (a), it may still be possible to define effective a and b parameters to relate total pressure, volume, temperature, and total number of moles. Suppose the gas mixture has a = 4.00 atm moU and b = 0.0330 L moU. Recalculate the pressure of the gas... 

RELATIONS BETWEEN HEAT CAPACITIES IN PURE REAL GASES... 

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