Compression factor

The compression factor or compressibility factor measures the deviation of the behaviour a real gas from an ideal gas.

Intermolecular forces can be attractive or repulsive. Attractive forces have a longer range (several molecules in length) than repulsive forces.

At high pressures (high compression), repulsive forces between gas molecules are more significant than attractive forces, as the molecules occupy a small volume with small separations between them. The volume occupied by the gas is therefore expected to be larger than that for an ideal gas.

At low pressures (low compression), neither force is significant as the gas molecules occupy a large volume with large separations between them. The gas therefore behaves ideally (i.e. volume occupied by the gas is expected to be the same as that for an ideal gas) and can be described mathematically by the ideal gas law.

At moderate pressures, attractive forces are more significant than repulsive forces as the molecules are close enough for intermolecular attraction but not close enough for repulsive forces to be effective. The volume occupied by the gas is expected to be smaller than that for an ideal gas.

We can therefore measure the deviation of a real gas from ideality by analysing the ratio:

Z=\frac{V_m}{V_m^{\: o}}\; \; \; \; \; \; \; \; 1

where Vm is the molar volume of a gas and Vmo is the molar volume of an ideal gas at the same temperature and pressure as the gas of Vm.

We call this ratio, Z, the compression factor (or compressibility factor). The possible values of Z are as follows:






< 1


> 1


The diagram below shows the values of Z at different pressures for a few gases at the same temperature.

All gases have Z > 1 at high pressures (over 500 atm), Z < 1 at intermediate pressures (0 atm to 500 atm) and Z = 1 as p → 0. Since V_m^{\: o}=\frac{RT}{p}, eq1 becomes

pV_m=RTZ\; \; \; \; \; \; \; \; 2

Eq2 is a simple equation of state that accounts for real gases when Z deviates from 1.


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