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

To solve this problem,the stepwise approach required i.e,
Write the van der Waals' equation, then apply the condition that at low pressure,volume become high,i.e.V-b=V
Now calculate the value of compressibility factor (Z.)
`[Z=pV//RT]`
According to van der Waals' equation,
`(p+(a)/V^(2))(V-b)=RT`
At low pressure, `(p+(a)/V^(2))V=RTrArrpV+(a)/(V)=RT`
`pV=RT-(a)/(V)`
Divide both side by `RT,(pV)/(RT)=1-(a)/(RTV)`