For the first-order reaction: A(g) - 2B(g) + C(g), the total pressure, after time t from the start of reaction with A, is P and after infinite time, it is P_inf. Then the rate constant of the reactio

Question

For the first-order reaction: A(g) -> 2B(g) + C(g), the total pressure, after time t from the start of reaction with A, is P and after infinite time, it is P_inf. Then the rate constant of the reaction is

Prashant Kotian · Accepted Answer

Correct answer: B. Let the initial pressure of A be P_0. At time t, P_A = P_0 - x, P_B = 2x, P_C = x. Total pressure P = P_0 - x + 2x + x = P_0 + 2x => x = (P - P_0)/2. At t = inf, P_inf = 3P_0 => P_0 = P_inf/3. The remaining reactant pressure at time t is P_A = P_0 - x = (3P_0 - P)/2 = (P_inf - P)/2. The rate constant is K = 1/t * ln(P_0/P_A) = 1/t * ln((P_inf/3) / ((P_inf - P)/2)) = 1/t * ln(2*P_inf / 3(P_inf - P)).

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