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

PLAN To solve this problem, the stepwise approach required, i.e.
(i) Write the van der Waals’ equation, then apply the condition that at low pressure, volume become high,
i.e. `V-b, V`
(ii) 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= RT rArr pV + (a)/(V) = RT or pV = RT - (a)/(V)`
Divide both side by RT, `(pV)/(RT) = 1 - (a)/(RTV)`