Concise Physical Chemistry

c02 JWBS043-Rogers September 13, 2010 11:23 Printer Name: Yet to Come

THE COMPRESSIBILITY FACTOR 23

2.3.1 Corresponding States

An interesting comparison from amongZfactors is shown schematically in Figs. 2.3

and 2.4 which might beZ=f(p) for two different gases orZ=f(p)forthe same

gas at two different temperatures. Simply by choosing the right two temperatures,

one can make any two gases identical to each other in their degree of nonideality,

that is, theirZfactors. When different gases at different temperatures behave in the

same way, they are said to be incorresponding states. To define thestateof a real

gas, we must describe it in such detail that a colleague can reproduce it inallof its

physical properties from the description. Because of the essentially infinite number

of physical properties one can measure, this would seem to be a tall order; but, if it is

pure, the number of degrees of freedom for one mole of a real gas is 2 regardless of

its degree of nonideality, so specifying any two properties is equivalent to specifying

all of them. The equation of state is written with two independent variables, but it

doesn’t matter which two.

To summarize up to this point: We are left with a van der Waals qualitative picture

of nonideal gas behavior that is quite reasonable but gives an equation that doesn’t

work very well outside of common laboratory conditions. Our alternative is to rely

upon empirical equations that work quite well in most cases but are hard to interpret.

The term “empirical” as applied to the virial equation in this context has become

somewhat of a misnomer over the years, however, because considerable progress has

been made in theoretical interpretation of the virial equation and Fig. 2.3. Indeed, the

statistical mechanics of these curves and others like them is an active research topic.

p (bar)

0 100 200 300 400 500 600 700

Z

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

FIGURE 2.3 TheZ=f(p) curve for two different gases or for the same gas at two different

temperatures. The unit—bar—is approximately one atmosphere.