Examining the assumptions made in the kinetic molecular theory of gases it should be obvious that the ideal gas law (P V = n R T) should break down at some point.

If the gas is squeezed into a very small volume (or alternatively high pressure) where the volume of the molecules themselves is no longer negligible or if the gas is at a sufficiently low temperature so that the intermolecular forces become significant compared to the kinetic energy, we might expect the equation to fail. And it does.

To deal with this we must have a more complex set of gas laws called real gas equations. The simplest of these equations is the one developed by the Dutch chemist Johannes van der Waals .

All gases exhibit, to some extent, deviations from the ideal-gas laws. When these deviations are recognized, the gas is said to behave as a real, non ideal or imperfect gas.

**Compressibility factor Z: **Real and ideal gases can be compared at various pressures and various temperatures by noting the extent to which the value of PV/RT deviates from.

The quantity $\large \frac{P V}{R T}$ is given by the symbol Z and the name compressibility factor.

That is $\large Z = \frac{P V}{R T}$

Greater is the departure of Z from unity more is the deviation from ideal behaviour.

**(i)** When Z < 1, this implies that gas is more compressible.

**(ii)** When Z > 1, this means that gas is less compressible.

**(iii)** When Z = 1, the gas is ideal.

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