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Two solid compounds X and Y dissociate at a certain temperature in a closed container as follows :
$X (s) ⇌ A (g) + 2 B (g); K_{p_{1}} = 9 \times 10^{- 3} {atm}^{3}$
$Y (s) ⇌ 2 B (g) + C (g); K_{p_{2}} = 4.5 \times 10^{- 3} {atm}^{3}$
The total pressure of gases over a mixture of X and Y at equilibrium is :

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none of these

4.5 atm

0.45 atm

0.6 atm

answer is B.

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Detailed Solution

$X (s) ⇌ A (g) + 2 B (g)$

$P_{1}$ $2 P_{1} + 2 P_{2}$

$Y (s) ⇌ 2 B (g) + C (g)$

$2 P_{2} + 2 P_{1}$ $P_{2}$

$Total pressure = P_{1} + 2 P_{1} + 2 P_{2} + P_{2} = 3 P_{1} + 3 P_{2}$

$K_{P_{1}} = 4 P_{1} {(P_{1} + P_{2})}^{2}; K_{P_{2}} = 4 P_{2} {(P_{1} + P_{2})}^{2}$

$K_{P_{1}} + K_{P_{2}} = 4 {(P_{1} + P_{2})}^{3}$

$P_{1} + P_{2} = 1.5 \times 10^{- 1}$

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