Real Gases

Thus far we have concentrated on perfect gases. It is important to appreciate that no gas actually is perfect - they all deviate from ideal behaviour to some degree:

One of our assumptions about ideal gases was that the molecules didn't interact except when they collided with each other. However, in real gases there is a potential energy between two molecules;

The attractions at medium distances are the result of coulombic forces. These arise due to uneven distribution of the electrons in the molecules, which may induce dipoles in neighbouring molecules resulting in an attraction. The repulsions are due to the two molecules being compressed together (the mutual short-range repulsion between the negatively charged electrons of the two molecules).

These attractions and repulsions make the gas more compressible at low pressures and less compressible at high pressures than a perfect gas would be.

Note that at large separations, the potential energy tends to zero, ie at large separations the interactions between particles in a gas are effectively zero. Hence low pressure gases (in which the average separation of particles is large) behave more like perfect gases than do high pressure gas samples.

The perfect gas equation pV_m/RT = 1 predicts that the ratio pV_m/RT is constant at 1. However, we find that in fact it is a function of pressure.

We say that pV_m/RT = Z. Z is the compressibility factor. For a perfect gas it equals 1 always. However, due to the molecular interactions in real gases, Z changes with pressure.

These deviations suggest that in fact pV_m/RT = 1 is just the first term of a series of powers

Z = pV_m/RT = 1 + B'p + C'p² + ......

The temperature at which Z ® 1 is called the Boyle Temperature. We could also consider that dZ/dp ® 0. In either case,
B' ® 0. At the Boyle Temperature real gases behave ideally over a slightly larger pressure range than at other temperatures. See graph opposite

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