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The equilibrium constants $K_{P_{1}}$ and $K_{P_{2}}$ for the reactions X $⇌$ 2Y and Z $⇌$ P + Q, respectively, are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal, then the ratio of total pressures at these equilibria is

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1 : 36

1 : 9

1 : 3

1 : 1

answer is A.

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Detailed Solution

X $⇌$ 2Y

1 0

(1 - x) 2x

$\Rightarrow K_{P_{1}} = \frac{{(2 x)}^{2}}{(1 - x)} {(\frac{P_{1}}{1 + x})}^{1}$

Z $⇌$ P + Q

1 0 0

(1 - x) x x

$K_{P_{2}} = \frac{x^{2}}{(1 - x)} {(\frac{P_{2}}{1 + x})}^{1}$

$\frac{K_{p_{1}}}{K_{p_{2}}} = \frac{1}{9}$

$\frac{4 \times P_{1}}{P_{2}} = \frac{1}{9} = \frac{P_{1}}{P_{2}} = \frac{1}{36}$

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