# The degree of dissociation of PCl5($\alpha$) obeying the equilibrium, PCl5(g) $\leftrightarrow$PCl3(g) + Cl2(g) is approximately related to the pressure at equilibrium by   Option 1) $\alpha$ ∝ P Option 2) $\alpha$ ∝ $\frac{1}{\sqrt{p}}$ Option 3) $\alpha$ ∝$\frac{1}{p^{2}}$ Option 4) $\alpha$ ∝ $\frac{1}{p^{4}}$

Answers (1)
P Prateek Shrivastava

As we learnt in

Equilibrium constant in gaseous system -

For equilibrium involving gases, it is usually more convenient to express the equilibrium constant in terms of partial pressure.

- wherein

The ideal gas equation is written as

$PV=nRT$

Let's consider the given reaction

$PCl_{5}(g)\leftrightharpoons PCl_{5}(g)+Cl_{2}(g)$

$1-\alpha$               $\alpha$                    $\alpha$

Total pressure =P

$P_{PCl _{3}}= \frac{P\alpha }{1+\alpha}, P_{Cl _{2}}= \frac{P\alpha }{1+\alpha}$

$P_{PCl _{3}}= \frac{P(1-\alpha) }{1+\alpha}$

$K_{P}= \frac{P_{Cl_{2}}P_{PCl_3}}{P_{PCl_3}}= \frac{P\alpha ^{2}}{1-\alpha ^{2}}$

$1-\alpha ^{2}\approx 1, \alpha \angle \angle 1$

$\therefore K_{p}=P\alpha ^{2}$

$\alpha =\sqrt{\frac{K_{p}}{P}}$

$\Rightarrow \alpha\ \propto \frac{1}{\sqrt{p}}$

Option 1)

$\alpha$ ∝ P

This option is incorrect

Option 2)

$\alpha$ ∝ $\frac{1}{\sqrt{p}}$

This option is correct

Option 3)

$\alpha$ ∝$\frac{1}{p^{2}}$

This option is incorrect

Option 4)

$\alpha$ ∝ $\frac{1}{p^{4}}$

This option is incorrect

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