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

Answer

C

Explanation

`(p+(a)/(V^(2)))(V-b)=RT`
At low pressure, the volume is sufficiently large and therefore, b can be neglected in comparison to V so that
`(p+(a)/(V^(2)))V=RT`
`pV+(a)/(V)=RT`
`"or "pV=RT-(a)/(V)`
`(pV)/(RT)=1-sqrt((3RT)/(M))or Z=1-(a)/(RTV)`