The Maxwell-Boltzmann distribution curves for a gas-phase reaction at two different temperatures, T1 T_1\,T1 and T2T_2T2, are shown below, along with the activation energy values for the uncatalysed reaction (EaE_{\text{a}}Ea) and the catalysed reaction (EcatE_{\text{cat}}Ecat).
Which of the following statements correctly explains how the reaction rate is controlled when the temperature is changed from T1 T_1\,T1 to T2 T_2\,T2 and a catalyst is added?
The temperature increase to T2T_2T2 shifts the peak of the distribution to the right, increasing the most probable energy of the molecules, while the catalyst lowers the activation energy from EaE_{\text{a}}Ea to EcatE_{\text{cat}}Ecat, greatly increasing the fraction of molecules with E≥EcatE \ge E_{\text{cat}}E≥Ecat.
The catalyst lowers the activation energy from EaE_{\text{a}}Ea to EcatE_{\text{cat}}Ecat by shifting the distribution curve from T1T_1T1 to T2T_2T2, while increasing the temperature increases the number of successful collisions by increasing the total area under the curve.
The temperature increase to T2T_2T2 lowers the activation energy from EaE_{\text{a}}Ea to EcatE_{\text{cat}}Ecat, while the catalyst increases the average kinetic energy of the molecules, shifting the distribution curve to the right.
The transition from T1T_1T1 to T2T_2T2 increases the activation energy to EaE_{\text{a}}Ea, while the catalyst increases the fraction of molecules exceeding this energy by shifting the peak of the Maxwell-Boltzmann distribution to a lower energy.