Catalysts are substances that increase the rate of a chemical reaction without being consumed in the process. They do this by lowering the activation energy of the reaction, which is the minimum energy required for the reactants to form products. By lowering the activation energy, catalysts allow more reactant molecules to have enough energy to overcome the energy barrier and react, thus increasing the reaction rate.The Arrhenius equation is used to describe the relationship between the rate constant k of a reaction, the activation energy Ea , and the temperature T at which the reaction occurs. The equation is as follows:k = Ae^-Ea/RT where:k = rate constantA = pre-exponential factor frequency factor Ea = activation energyR = gas constant 8.314 J/molK T = temperature in KelvinTo compare the activation energy for the catalyzed and non-catalyzed reactions, we need to know the rate constants k for both reactions at the same temperature. Let's assume we have the following data:- For the non-catalyzed reaction: k1 = 1.0 x 10^3 s^-1- For the catalyzed reaction: k2 = 1.0 x 10^5 s^-1- Temperature T = 298 K 25C We can rearrange the Arrhenius equation to solve for Ea:Ea = -RT * ln k/A Since we don't have the pre-exponential factor A , we can compare the activation energies by taking the ratio of the rate constants for the catalyzed and non-catalyzed reactions:k2/k1 = e^ Ea1 - Ea2 /RT Now, we can solve for the difference in activation energies Ea1 - Ea2 : Ea1 - Ea2 = RT * ln k2/k1 Using the given data: Ea1 - Ea2 = 8.314 J/molK * 298 K * ln 1.0 x 10^5 s^-1 / 1.0 x 10^3 s^-1 Ea1 - Ea2 40,700 J/molThis result indicates that the activation energy for the catalyzed reaction Ea2 is approximately 40,700 J/mol lower than the activation energy for the non-catalyzed reaction Ea1 . This lower activation energy allows the catalyzed reaction to proceed at a faster rate.