The diagram below shows the Maxwell-Boltzmann distribution of molecular kinetic energies for a gas-phase reaction at two different temperatures, T1 T_1\,T1 and T2T_2T2, along with the activation energy thresholds for both the catalysed and uncatalysed pathways.
Which of the following statements correctly describes how reaction conditions can be controlled to alter the rate of reaction?
Increasing the temperature from T1T_1T1 to T2T_2T2 increases the rate of reaction because the higher thermal energy physically lowers the activation energy barrier, Ea (without catalyst)E_{\text{a}} \text{ (without catalyst)}Ea (without catalyst).
At either temperature, adding a catalyst increases the rate of reaction by providing an alternative reaction pathway that has a lower activation energy, Ea (with catalyst)E_{\text{a}} \text{ (with catalyst)}Ea (with catalyst).
Increasing the pressure or concentration of the reactants shifts the Maxwell-Boltzmann distribution curve to the right, which lowers the activation energy from Ea (without catalyst)E_{\text{a}} \text{ (without catalyst)}Ea (without catalyst) to Ea (with catalyst)E_{\text{a}} \text{ (with catalyst)}Ea (with catalyst).
At the higher temperature T2T_2T2, the fraction of molecules with energy greater than or equal to Ea (with catalyst)E_{\text{a}} \text{ (with catalyst)}Ea (with catalyst) is lower than at T1T_1T1 because the peak of the curve is lower.