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Q.

A gaseous phase reaction is allowed to attain equilibrium as $A (g) ⇌ B (g) + C (g)$ at constant pressure P. The partial pressure of A at equilibrium is PD. The value of equilibriurn constant K_pis:

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a

P/6

b

P/2

c

p/4

d

p/8

answer is D.

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Detailed Solution

$\underset{(a - x)}{\underset{a}{A}} ⇌ \underset{x}{\underset{0}{B}} + \underset{x}{\underset{0}{C}}$
$\begin{array}{l} P_{A}^{'} = \frac{(a - x) P}{(a + x)} = \frac{P}{2} \\ ∴ x = \frac{a}{3} \\ ∴ K_{p} = \frac{x . x}{a - x} \times {[\frac{P}{a + x}]}^{'} \\ = \frac{\frac{a}{3} \times \frac{a}{3} \times P}{a^{2} - \frac{a^{2}}{9}} = \frac{P}{8} \end{array}$

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