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Question

Chemistry Question on States of matter

If Z is a compressibility factor, van der Waals equation at low pressure can be written as

A

Z=1+RTpbZ=1+\frac{RT}{pb}

B

Z=1−aVRTZ=1-\frac{a}{VRT}

C

Z=1−PbRTZ=1-\frac{Pb}{RT}

D

Z=1+PbRTZ=1+\frac{Pb}{RT}

Answer

Z=1−aVRTZ=1-\frac{a}{VRT}

Explanation

Solution

Compressibility factor (Z)=PVRT( Z )=\frac{ PV }{ RT }

(For one mole of real gas)

van der Waal equation

(P+aV2)(V−b)=RT\left( P +\frac{ a }{ V ^{2}}\right)( V - b )= RT

At low pressure

V−b≈VV - b \approx V
(P+aV2)V=RT\left( P +\frac{ a }{ V ^{2}}\right) V = RT
PV+aV=RTPV +\frac{ a }{ V }= RT
PV=RT−aVPV = RT -\frac{ a }{ V }
PVRT=1−aVRT\frac{ PV }{ RT }=1-\frac{ a }{ VRT }

So, Z=1−aVRTZ=1-\frac{a}{VRT}