Question

If z is a compressibility factor, van der waals' equation at low pressure can be written as

Answer 1

The van der Waals equation of state

(P+aV2m)(P+aVm2)(Vm−b)=RT(Vm−b)=RT

At low pressure, Vm−b≈VmVm−b≈Vm , the equation reduces to

(P+aV2m)(P+aVm2)(Vm)=RT(Vm)=RT

⇒PVm+aVm⇒PVm+aVm=RT=RT

Z=PVmRTZ=PVmRT=1−aVmRT=1−aVmRT

Hence (D) is the correct answer.