At very high pressure, the compressibility factor of one mole of a gas is given by

The van der Waals equation of state is $\left(p+\frac{a}{V_{\mathrm{m}}^2}\right)\left(V_{\mathrm{m}}-b\right)=RT$

At high pressure, the term $a/V_{\mathrm{m}}^2$ may be ignored in comparison top to get

$p\left(V_{\mathrm{m}}-b\right)=RT$

This gives $Z=\frac{p{V}_{\mathrm{m}}}{RT}=1+\frac{pb}{RT}$