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=-(Rb)/(RT)`
D. `Z=1+(Pb)/(RT)`

Answer

B

Explanation

(b) 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)`