The compressibility factor for a real gas at high pressure is    

At high pressure $\frac{a}{v^2}$ is neglected. So vander Waal equation is P(v-b)=RT or $\mathrm{PV}=\mathrm{RT}+\mathrm{Pb}\text{ or }\frac{Pv}{RT}=z=1+\frac{Pb}{RT}$