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Chemistry Question on Van Der Waals equation

At low pressure, the van der Waal's equation is reduced to

A

Z=PVmRT=1−aVRTZ=\frac{PV_{m}}{RT}=1-\frac{a}{VRT}

B

Z=PVmRT=1+bRTPZ=\frac{PV_{m}}{RT}=1+\frac{b}{RT}P

C

PVm=RTPV_{m}=RT

D

Z=PVmRT=1−aRTZ=\frac{PV_{m}}{RT}=1-\frac{a}{RT}

Answer

Z=PVmRT=1−aVRTZ=\frac{PV_{m}}{RT}=1-\frac{a}{VRT}

Explanation

Solution

When pressure is low
[P+aV2](V−b)=RT\left[P+\frac{a}{V^{2}}\right]\left(V-b\right)=RT
or PV=RT+Pb−aV+abV2PV=RT+Pb-\frac{a}{V}+\frac{ab}{V^{2}}
or PVRT=1−aVRT\frac{PV}{RT}=1-\frac{a}{VRT}
Z=−aVRTZ=-\frac{a}{VRT}
(∵PVRT−Z)\left(\because\frac{PV}{RT}-Z\right)