Compressibility Factor and Ideal Gas Deviations

As a first step toward improved description of real gases, we define the compressibility factor Z by the equation 

Here (Vm)ideai = RT/P is the molar volume of an ideal gas and (Vm)0bs =V/n is the actual ( observed ) molar volume with these substitutions, Z can be defined equivalently as 

Although Z is identically one for an ideal gas, its value generally deviates from this ideal limit for real gases. Like other measurable properties, Z is expected to depend on two degrees of freedom (for fixed n = 1), which can be taken, for example, as P and T, 

Let us first examine the pressure dependence of the compressibility factor under isothermal conditions. Table 2.2 and Fig. 2.2 exhibit some representative P-dependent values of Z for gaseous C02 (at fixed temperature 40°C = 313K) in tabular and graphical form. 

The graph of Z versus P in Fig. 2.2 is rather typical, showing the following general features that should be noted  

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