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The degree of dissociation of ${PCl}_{5}$ $(α)$ obeying the equilibrium, ${PCl}_{5} ⇌ {PCl}_{3} + {Cl}_{2},$ is approximately related to the pressure at equilibrium by (given $α$ << 1)

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$α \propto \frac{1}{P^{2}}$

$α \propto \frac{1}{P^{4}}$

$α \propto \frac{1}{\sqrt{P}}$

$α \propto P$

answer is B.

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Detailed Solution

$\underset{1 - α}{{PCl}_{5}^{}} ⇋ \underset{α}{{PCl}_{3}^{}} + \underset{α}{{Cl}_{2}^{}}$

$∴ K_{p} = \frac{\frac{α}{1 + α} P \times \frac{α}{1 + α} P}{\frac{1 - α}{1 + α} P} = \frac{α^{2} P}{1 - α^{2}}$

$K_{p} = α^{2} P$
( $∵ 1 - α^{2} = 1$ )
$∴ α = \sqrt{\frac{K_{p}}{P}}$
$α \infty \frac{1}{\sqrt{p}}$

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