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

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$α \propto \frac{1}{P^{4}}$

$α \propto \frac{1}{\sqrt{P}}$

$α \propto \frac{1}{P^{2}}$

$α \propto P$

answer is B.

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Detailed Solution

${PCl}_{5} ⇌ {PCl}_{3} + {Cl}_{2} 1 - α α α ∴ K_{p} = \frac{\frac{α}{1 + α} P \times \frac{α}{1 + α} P}{\frac{1 - α}{1 + α} P} = \frac{α^{2} P}{1 - α^{2}} or, K_{p} = α^{2} P ∴ α = \sqrt{\frac{K_{p}}{P}} when 1 - α^{2} = 1$

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