For a hypothetical elementary reaction [Both $K_{1}$ & $K_{2}$ are first order rate constants]

Initially 2 moles of ‘A’ is present. Then the total number of moles of A, B and C of the end of 50% completion of reaction are $1.5 x$ then the value of $\frac{x^{4}}{4}$ is

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answer is 4.

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Detailed Solution

At the end of 50% reaction [A] = 1.0 mol
$\frac{[B]}{[A]} = \frac{2 K_{1}}{K_{1} + K_{2}} = \frac{2}{3}; \frac{[C]}{[A]} = \frac{2 K_{2}}{K_{1} + K_{2}} = \frac{4}{3} [A] + [B] \times [C] = 1 + \frac{2}{3} + \frac{4}{3} = 3$

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