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At constant pressure P, A dissociates on heating according to the equation
$A (g) ⇌ B (g) + C (g)$

The equilibrium partial pressure of A at T K is $\frac{1}{9} P$ , the equilibrium constant $K_{p}$ at T K is

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$\frac{8}{9} P$

$9 P$

$\frac{16}{9} P$

$\frac{64}{9} P$

answer is C.

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Detailed Solution

$P_{B} = P_{C}$

$P_{A} + P_{B} + P_{C} = P$

$\Rightarrow$ $P_{B} + P_{C} = P - \frac{1}{9} P = \frac{8}{9} P$

$∴$ $P_{B} = P_{C}$

$∴$ $P_{B} = P_{C} = \frac{1}{2} \times \frac{8}{9} P = \frac{4}{9} P$

$K_{p} = \frac{P_{B} \times P_{C}}{P_{A}}$

$\Rightarrow$ $K_{p} = \frac{\frac{4}{9} P \times \frac{4}{9} P}{\frac{1}{9} P} = \frac{16}{9} P$

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