Question

The activation energy of a certain uncatalyzed reaction is 64 kJ/mol. In the presence of a catalyst, the Ea 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.

Answer 1

The rate of the reaction is proportional to the exp(-Ea/RT), where Ea- activation energy in Joules, R-gas constant and T -temperature in K.
So, the ratio of rate constants of catalyzed and uncatalyzed reactions will be equal to exp(-Ea1/RT) / exp(-Ea2/RT) = exp((Ea2-Ea1)/RT), where Ea1 - activation energy of catalyzed reaction and Ea1 - activation energy of not catalyzed reaction.
ratio = exp((64000-55000)/8.314/673.15)=5
Catalyzed reaction will be 5 times faster than uncatalyzed reaction.