The degree of dissociation of PCl_ 5 (α) obeying the equilibrium...

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 The degree of dissociation of PCl_ 5 (α) obeying the equilibrium PCl_ 5 leftharpoons PCl_ 3 +Cl_ 2 is related to the

The degree of dissociation of PCl_ 5 (α) obeying the equilibrium PCl_ 5 leftharpoons PCl_ 3 +Cl_ 2 is related to the

Options

A $\alpha \propto \frac{1}{\mathrm{P}^{4}}$
B $\alpha \propto \frac{1}{\sqrt{\mathrm{P}}}$
C $\alpha \propto \frac{1}{\mathrm{P}^{2}}$
D $\alpha \propto \mathrm{P}$

Correct answer

B. $\alpha \propto \frac{1}{\sqrt{\mathrm{P}}}$

Step-by-step 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

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