Rate of an uncatalysed first-order reaction at T K is half of the rate of catalysed reaction at '0.5T' K. If the catalyst lowers the threshold energy by 20 kcal, what is the activation energy of uncat

Question

Rate of an uncatalysed first-order reaction at T K is half of the rate of catalysed reaction at '0.5T' K. If the catalyst lowers the threshold energy by 20 kcal, what is the activation energy of uncatalysed reaction? (T = 300 K, ln 2 = 0.7)

Prashant Kotian · Accepted Answer

Correct answer: A. k_uncat(T) = 0.5 k_cat(0.5T). A e^(-Ea / RT) = 0.5 A e^(-(Ea - 20) / R(0.5T)). Simplifying gives e^((Ea - 40)/RT) = 0.5, so (Ea - 40)/RT = -ln 2. Ea = 40 - RT ln 2. At 300K, RT ln 2 = (2 cal/K*mol)(300 K)(0.7) = 420 cal/mol = 0.42 kcal/mol. Ea = 40 - 0.42 = 39.58 kcal/mol. Therefore, correct answer is A.

💡 Solution & Explanation

Practice 22,000+ questions like this