The degree of dissociation of $\mathrm{PCl}_{5}(\alpha)$ obeying the equilibrium $\mathrm{PCl}_{5} \rightleftharpoons \mathrm{PCl}_{3}+\mathrm{Cl}_{2}$ is related to the equilibrium pressure by

• A

  $\alpha \propto \frac{1}{\mathrm{P}^{4}}$
• Correct answer
  B

  $\alpha \propto \frac{1}{\sqrt{\mathrm{P}}}$
• C

  $\alpha \propto \frac{1}{\mathrm{P}^{2}}$
• D

  $\alpha \propto \mathrm{P}$

Solution

$\therefore \mathrm{K}_{\mathrm{p}}=\frac{\frac{\alpha}{1+\alpha} \mathrm{P} \times \frac{\alpha}{1+\alpha} \mathrm{P}}{\frac{1-\alpha}{1+\alpha} \mathrm{P}}=\frac{\alpha^{2} \mathrm{P}}{1-\alpha^{2}}$ or, $\mathrm{K}_{\mathrm{p}}=\alpha^{2} \mathrm{P}$ $\therefore \alpha=\sqrt{\frac{\mathrm{K}_{\mathrm{p}}}{\mathrm{P}}}$ when $1-\alpha^{2}=1$

Hence, the correct answer is option: 'B'.