Physical Chemistry Third Edition

24 1 The Behavior of Gases and Liquids

Graphical Representation of Volumetric Data for Gases

Thecompression factor, denoted byZ, is sometimes used to describe the behavior of

real gases:

Z

PVm

RT

(1.3-5)

Some authors callZthecompressibility factor. We avoid this name because it might

be confused with the compressibility. The compression factor equals unity for an ideal

gas. Figure 1.3 shows a graph of the compression factor of nitrogen gas as a function

of pressure at several temperatures. At low temperatures, the value ofZis less than

unity for moderate pressures, but rises above unity for larger pressures. At higher

temperatures, the value ofZis greater than unity for all pressures. Attractions between

the molecules tend to reduce the value ofZand repulsions between the molecules tend

to increase the value ofZ. Attractions are more important at lower temperatures and

smaller pressures, and repulsions are more important at higher temperatures and higher

pressures. The temperature at which the curve has zero slope at zero pressure is called

theBoyle temperature. This is the temperature at which the gas most nearly approaches

ideality for small pressures.

For a van der Waals gas, the compression factor is given by

Z

PVm

RT



Vm

Vm−b

−

a

RTVm



1

1 −by

−

ay

RT

(1.3-6)

where we lety 1 /Vm. Sinceaandbare both positive for all gases, the first term on

the right-hand side of Eq. (1.3-6) gives a positive contribution toZ, and the second

term gives a negative contribution. The parameterbdescribes the effect of repulsive

5

0.1

0.2

0.3

0.4

0.6

0.8

1.0

2.0

10 20 50 100 200

P/bar

500

1900 K

150 K

200 K

250 K

Z

Figure 1.3 The Compression Factor of Nitrogen as a Function of Pressure at Several

Temperatures.