Question

For one mole of a gas, under critical conditions, the compressibility factor is:

• A. $\frac{3}{8}$
• B. $\frac{8}{3}$
• C. 1
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{3}{8}$

For 1 mole of the gas $Z=\frac{P_c{V}_c}{R{T}_c}$ (Under critical condition)

$P_c=\frac{a}{27b^2}$ ,
$V_c=3b$ ,
$T_c\frac{8a}{27Rb}$

Substituting the values of critical constants in the above equation of compressibility factor (Z), we get,

$Z=\left(\frac{a}{27b^2}\right)\times \frac{27Rb}{8a}=\frac{3}{8}$