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

Options

A. `Z=1+(RT)/(pb)`
B. `Z=1-a/(VRT)`
C. `Z=1-(Pb)/(RT)`
D. `Z=1+(Pb)/(RT)`

Answer

B

Explanation

Compressibility factor (Z) `=(PV)/(RT)`
(For one mole of real gas)
van der Waals equation
`(P+a/(V^(2)))(V-b)=RT`
At low pressure, volume is very large and hence correction term b can be neglected in comparison to very large volume of V.
i.e. `V-b~~V`
`(P+a/(V^(2)))V=RT,PV+a/V=RT`
`PV=RT-a/V,(PV)/(RT)=1-a/(VRT)`
Hence, `Z=1-a/(VRT)`