The activation energy of a certain uncatalyzed reaction is 64 kJ/mol.In the presence of a catalyst, the E_a is 55 kJ/mol.How many times faster is the catalyzed than the uncatalyzed reaction at 400°C? Assume that the frequency factor remains the same.

Question

Quizplus · Accepted Answer

The rate constant for a reaction is given by the Arrhenius equation:k = Ae^(-Ea/RT)where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature.If the frequency factor remains the same, then the ratio of the rate constants for the catalyzed and uncatalyzed reactions is:k_cat/k_uncat = e^(-(Ea,uncat - Ea,cat)/RT)Substituting the given values, we get:k_cat/k_uncat = e^(-(64 kJ/mol - 55 kJ/mol)/(8.314 J/mol*K * 673 K)) = 5.0Therefore, the catalyzed reaction is 5.0 times faster than the uncatalyzed reaction at 400°C.

The Activation Energy of a Certain Uncatalyzed Reaction Is 64