Consider the equilibrium A ⇌ B in which both the forward and reverse reactions are element...

Consider the equilibrium A ⇌ B in which both the forward and reverse reactions are elementary (single-step) reactions. Assume that the only effect of a catalyst on the reaction is to lower the activation energies of the forward and reverse reactions, as shown in Figure. Using the Arrhenius equation (Section), prove that the equilibrium constant is the same for the catalyzed reaction as for the uncatalyzed one.

Figure An energy profile for the reaction A ⇌ B (left), and the change in concentration of B as a function of time (right), with and without a catalyst. Green curves show the reaction with a catalyst; black curves show the reaction without a catalyst.

What quantity dictates the speed of a reaction: (a) the energy difference between the initial state and the transition state or (b) the energy difference between the initial state and the final state?