Two reactions: (I) A → Products, and (II) B → Products, follow first-order kinetics. The rate of reaction-I is doubled when temperature is raised from 300 to 310 K. The half-life for this reaction at

Question

Two reactions: (I) A → Products, and (II) B → Products, follow first-order kinetics. The rate of reaction-I is doubled when temperature is raised from 300 to 310 K. The half-life for this reaction at 310 K is 30 min. At the same temperature, B decomposes twice as fast as A. If the energy of activation for the reaction-II is half that of reaction-I, the rate constant of reaction-II at 300 K is

Prashant Kotian · Accepted Answer

Correct answer: B. For I at 310K, k_I = ln 2 / 30 = 0.0231 min^-1. For II at 310K, k_II = 2 k_I = 0.0462 min^-1. Since Ea_II = 0.5 Ea_I, the temperature effect is halved in the exponent. k_II(310)/k_II(300) = (k_I(310)/k_I(300))^0.5 = 2^0.5 ≈ 1.414. Thus, k_II(300) = 0.0462 / 1.414 = 0.0327 min^-1. Therefore, correct answer is B.

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