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Q.

The values of K_c for the reactions,
$\begin{array}{l} X ⇌ Y + Z . . . (i) \\ A ⇌ 2 B . . . (ii) \end{array}$
are in the ratio 9 :1. If degree of dissociation of X and, A be equal, then total pressure at equilibrium (i) and (ii) are in the ratio :

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a

36: 1

b

1:1

c

3: 1

d

1:9

answer is A.

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Detailed Solution

$\underset{1 - α}{X} ⇌ \underset{α}{Y} + \underset{α}{Z}; K_{c_{1}} = \frac{[Y] [Z]}{[X]} = \frac{α^{2}}{(1 - α)} \cdot {[\frac{P_{1}}{1 + α}]}^{1}$
$\underset{1 - α}{A} ⇌ \underset{2 α}{2} B; K_{c_{2}} = \frac{[B]^{2}}{[A]} = \frac{4 α^{2}}{(1 - α)} \cdot {[\frac{P_{2}}{1 + α}]}^{1}$
$\begin{array}{l} ∴ \frac{K_{c_{1}}}{K_{c_{2}}} = \frac{9}{1} = \frac{α^{2} \times (1 - α)}{(1 - α) \times 4 α^{2}} \times \frac{P_{1}}{P_{2}} \\ ∴ \frac{P_{1}}{P_{2}} = \frac{36}{1} \end{array}$

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