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Dalton's Law of Partial Pressures

For the react...

Question

For the reaction $A (g) ⇌ B (g) + C (g)$ at equilibrium, the partial pressure of the species are $P_{A} = 0.15 a t m, P_{C} = P_{B} = 0.30 a t m$ . If the capacity of reaction vessel is reduced, the equilibrium is re-established in the new situation, partial pressure $A$ and $B$ become twice. What is the partial pressure of $C$ ?

A

0.3 a t m

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B

0.6 a t m

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C

1.2 a t m

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D

1.8 a t m

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Solution

The correct option is A $0.3 a t m$
For the given equilibrium:
$A ⇌ B + C$
Equilibrium constant is:
$K_{p} = \frac{p_{B} \times p_{C}}{p_{A}}$
where $p_{A}, p_{B} a n d p_{C}$ are the
partial pressure of $A, B, C$ at equilibrium.
$K_{p} = \frac{0.3 \times 0.3}{0.15}$
At new equilibrium $p_{A} = 0.3$ and $p_{B} = o .6$
Since equilibrium constant will be same:
$∴ K_{p} = \frac{0.3 \times 0.3}{0.15} = \frac{0.6 \times x}{0.3}$
Or, $x = 0.3$
Hence, at new equilibrium partial pressure of $C$ is $0.3 a t m$ .
Option A is correct.

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