The ideal-gas equation can be corrected empirically by introducing the compressibility factor $Z$:

$$pv=ZR_sT,$$

where $R_s$ is the gas's specific gas constant. For an ideal gas, $Z=1$. A real gas has $Z\ne1$ because molecular attractions and finite molecular size affect its pressure-volume-temperature relation.

The size of the deviation depends strongly on state. Gases tend to behave more ideally at low density; deviations can become important near saturation and at high pressures.

For example, suppose a gas at some state has $Z=0.90$. If the ideal-gas model predicts

$$v_{ideal}=\frac{R_sT}{p}=0.40\ \mathrm{m^3/kg},$$

then the corrected estimate is

$$v=Zv_{ideal}=0.90(0.40)=0.36\ \mathrm{m^3/kg}.$$

The compressibility factor is therefore both a correction and a diagnostic: it tells you whether ideal-gas behavior is a reasonable approximation at the state of interest.