Question

The value of $Z_c$ at $T_c,P_c$ and $V_c$ is :

• A. 3/8
• B. 4/8
• C. 1
• D. 0

Answer 1

The correct option is A 3/8

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

Therefore, the value of critical compressibility factor in terms of Van der Waals constants is given by :

$Z_c=\frac{P_c{V}_c}{R{T}_c}$

$=\frac{\frac{a}{27b^2}\times 3b}{R\times \frac{8b}{27Rb}}=\frac{\frac{a}{9b}}{\frac{8Ra}{27Rb}}$

$=\frac{\frac{8a}{9b}}{\frac{8a}{27b}}$

$Z=\frac{P_c{V}_c}{R{T}_c}=\frac{a}{9b}\times \frac{27b}{8a}$

$Z=\frac{3}{8}$

Hence, option $\left(A\right)$ is correct.