The compressibility factor of $H_2\left(g\right)$ at its critical condition if it follows van der Waals' equation is given by:

As we already know, Z=RT PV is the formula for the compression factor (Z). While P equals pressure
V = gas's molar volume
R is the global gas constant.
Temperature is T.
At a turning point- $\mathrm{P}=\frac{\mathrm{a}}{27{\mathrm{b}}^2}$ $\mathrm{V}=3\mathrm{b}$, $\mathrm{T}=\frac{8\mathrm{a}}{27\mathrm{Rb}}$, $\therefore Z=\frac{\left(\frac{\mathrm{a}}{27{\mathrm{b}}^2}\right)3\mathrm{b}}{\mathrm{R}\left(\frac{8\mathrm{a}}{27\mathrm{Rb}}\right)}$ $\Rightarrow Z=\frac{3}{8}$Consequently, the critical point's compression factor for a van der Waals gas is $Z_C=3/8$