The figure shows the energy profile of a reaction with and without a catalyst. Without the catalyst the activation energy is $75.0\ \text{kJ mol}^{-1}$. With it, the activation energy is $50.0\ \text{kJ mol}^{-1}$. The enthalpy change of the reaction is $-30.0\ \text{kJ mol}^{-1}$. Assume that the catalyst leaves the pre-exponential factor unchanged, and that $E_a$ and $A$ do not depend on temperature. The catalysed reaction runs at $300\ \text{K}$. To what temperature $T$ must the uncatalysed reaction be heated to go just as fast, from the same concentrations? And what is the activation energy of the reverse reaction on the catalysed path? Which choice is correct?

Fig. 1: An energy profile, not to scale, of one reaction by two paths. Both paths start at the same reactant level and end at the same product level, 30.0 kJ per mole below the reactants. The path without the catalyst has a peak 75.0 kJ per mole above the reactants; the path with the catalyst has a lower peak, 50.0 kJ per mole above the reactants.