The degree of dissociation of PC l _ 5 ( α ) obeying the...

The degree of dissociation of

PC{l}_{5} ( \alpha )

obeying the equilibrium,

PC{l}_{5} ( g ) ⇌ PC{l}_{3} ( g ) + C{l}_{2} ( g )

, is approximately related to the pressure at equilibrium by The degree of dissociation of PC l _ 5 ( α ) obeying the equilibrium, PC l _ 5 ( g ) ⇌ PC l _ 3 ( g ) + C l _ 2 ( g ) ,

Options

A $\alpha ∝ P$
B $\alpha ∝ \dfrac{1}{\sqrt{P}}$
C $\alpha ∝ \dfrac{1}{P^{2}}$
D $\alpha ∝ \dfrac{1}{P^{4}}$

Correct answer

B. $\alpha ∝ \dfrac{1}{\sqrt{P}}$

Step-by-step solution

So,

{K}_{p} = \dfrac{{\alpha}^{2}}{( 1 - \alpha )}\left[\dfrac{P}{1 + \alpha}\right] = \dfrac{{\alpha}^{2}P}{1 - {\alpha}^{2}}

\alpha = \sqrt{\dfrac{{K}_{P}}{P}}

(if

1 - {\alpha}^{2} = 1

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