Consider a one-step gas-phase reaction that occurs at 298 K. The activation energy for the uncatalyzed pathway is 120 kJ mol⁻¹, whereas the activation energy in the presence of a catalyst is 75 kJ mol⁻¹. Assume the pre-exponential factor (frequency factor) is the same for both pathways. The universal gas constant is R=8.314J mol−1K−1.
(a) Calculate the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at 298 K.
(b) Interpret quantitatively what this ratio means for the speed of the reaction.
(c) If the uncatalyzed reaction takes 2.0 h to reach 95 % completion under the stated conditions, estimate how long the catalyzed reaction would take to reach the same extent of reaction. State any assumptions you make.