Compression factors

Compression factors

For an ideal gas, PV = nRT. If PV and nRT are the same, and you divide one by the other, then the answer will, of course, be 1. For real gases, PV doesn't equal nRT, and so the value will be something different.
The term PV / nRT is called the compression factor. 

• Different gases deviate from ideal behaviour in different ways
•  Deviation can be positive (Z>1) or negative (Z<1)
• Deviation always positive at sufficiently high pressure

The graphs below show how this varies for nitrogen as you change the temperature and the pressure.

If nitrogen was an ideal gas under all conditions of temperature and pressure, every one of these curves would be a horizontal straight line showing a compression factor of 1. That's obviously not true!

Things to notice

• At low pressures of about 1 bar (100 kPa - just a bit less than 1 atmosphere), the compression factor is close to 1. Nitrogen approximates to ideal behaviour at ordinary pressures.
• The non-ideal behaviour gets worse at lower temperatures. For temperatures of 300 or 400 K, the compression factor is close to 1 over quite a large pressure range. The nitrogen becomes more ideal over a greater pressure range as the temperature rises.
• The non-ideal behaviour gets worse at higher pressures.
• There must be at least two different effects causing these deviations. There must be at least one effect causing the pV / nRT ratio to be too low, especially at low temperatures. And there must be at least one effect causing it to get too high as pressure increases. We will explore those effects in a while.