The ratio PVmRTfor a gas is known as the compressibility factor. What is the value of this ratio for one mole of a vanderwaal’s gas at it’s Boyle’s temperature?

P+aV2V-b=RT⇒PV+aVV-bV=RT⇒PVRT+aVRT=VV-b⇒PVRT=VV-b-aVRT                                                    ∴T=aRb⇒PVRT=VV-b-bV⇒V2-bV+b2V(V-b)=V(V-b)+b2V(V-b)=1+b2V(V-b)