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

Options

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

Answer

D

Explanation

For one mol gas
`[P + (a)/(V^(2)) [V - b] = RT`
At low pressure, volume will be high `:. (V - b) ~~ V`
`PV + (a)/(V) = RT`
`(PV)/(RT) = 1 - (a)/(VRT)`
`Z = 1 - (a)/(VRT)`