A solid XY kept in an evacuated sealed container undergoes decomposition to form a mixture of gases X and Y at temperature T. The equilibrium pressure is 10 bar in this vessel. Kp for this reaction is :

Chemical Equilibrium PYQ — JEE Main 2016 · 10 Apr · Shift 1 · Q15 with Solution

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Correct answer: C

A solid $XY$ decomposes as:

XY(s) \rightleftharpoons X(g) + Y(g)

Since $XY$ is a solid, it does not appear in the expression for $K_p$ .

For the reaction,

K_p = P_X \cdot P_Y

Initially, the container is evacuated, so only the gases formed by decomposition are present.

From the stoichiometry,

XY(s) \to X(g) + Y(g)

$x$ moles of $X$ and $x$ moles of $Y$ are formed.

Hence at equilibrium, partial pressures of $X$ and $Y$ are equal:

P_X = P_Y

Given total pressure is $10$ bar,

P_X + P_Y = 10

So,

P_X = P_Y = 5 \text{ bar}

K_p = P_X \cdot P_Y = 5 \times 5 = 25

\boxed{K_p = 25}

So the correct option is C.