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The reaction $AB (g) ⇌ A (g) + B (g)$ having equilibrium constant $K_{p}$ is studied at constant V and T starting from AB(g) only. If 1/3 of AB(g) dissociates at equilibrium, the ratio of $p_{total} / K_{p}$ at equilibrium will be

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answer is D.

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Detailed Solution

Let p be the initial pressure of AB(g). We will have

$\begin{array}{l} AB (g) ⇌ A (g) + B (g) \\ p (1 - 1 / 3) p / 3 p / 3 \end{array}$ $p_{total} = p (1 + \frac{1}{3}) = \frac{4}{3} p$

$K_{p} = \frac{p_{A} p_{B}}{p_{AB}} = \frac{(p / 3) (p / 3)}{p (1 - 1 / 3)} = \frac{p}{6}$ The ratio $p_{total} / K_{p} = \frac{(4 / 3) p}{(p / 6)} = 8$

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