The activation energy of a first order reaction is 30 kJ/mol at 298K. The activation energy for

the same reaction in the presence of a catalyst is 24 kJ/mol at 298K. How many times the

reaction rate has changed in the presence of a catalyst?

K = A e^-Ea/RT

First reaction

K1 = A e^-30000/RT

Second Reaction

K2 = A e^-24000/RT

take ratio of these two equations

K1/ K2 = e^-30000/RT / e^-24000/RT

Take Ln both side

Using R = 8.314 and T = 298K

Ln(K1/K2) = -2.42

K1/K2 = 0.09

K2 = 11.24 times faster than first reaction.

Thanks.