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Equilibrium Constant and Standard Free Energy Change

Two solids di...

Question

Two solids dissociated as follows
$A (s) ⇌ B (g) + C (g); K_{P 1} = x a t m^{2}$

$D (s) ⇌ C (g) + E (g); K_{P 2} = x a t m^{2}$
The total pressure when both the solids dissociate simultaneously is:

A

$x^{2} + y^{2}$

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B

$\sqrt{x^{2} + y^{2}}$

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C

$2 (\sqrt{x + y})$

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D

$\sqrt{x + y}$

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Solution

The correct option is C
$2 (\sqrt{x + y})$

$A (s) ⇌ B (g)_{P 1} + C (g)_{P 1}$

$D (s) ⇌ C (g)_{P 2} + E (g)_{P 2}$

$C, P_{C} = P_{1} + P_{2}$

$K_{P 1} = x = P_{B} \cdot P_{C} . . . . . . (1)$

$x = P_{1} (P_{1} + P_{2})$

$K_{P 2} = y = P_{C} \cdot P_{E} . . . . . . (2)$

$y = (P_{1} + P_{2}) (P_{2})$

$x + y = {(P_{1} + P_{2})}^{2}$

$P_{T} = P_{C} + P_{B} + P_{E}$

$= (P_{1} + P_{2}) + P_{1} + P_{2} = 2 (P_{1} + P_{2})$

$P_{T} = 2 (\sqrt{x + y)}$

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