The figure shows how the kinetic energies of the molecules of a gas are spread out at $300\ \text{K}$ and at $310\ \text{K}$, for the same sample in a closed vessel. The activation energy $E_a = 50.0\ \text{kJ mol}^{-1}$ is marked on the energy axis. Each curve gives the share of the molecules that have each kinetic energy. The gas reacts when two of its molecules collide, and its concentration stays fixed because the vessel is rigid. In collision theory, the fraction of collisions with at least the energy $E_a$ is $e^{-E_a/RT}$. Take $R = 8.314\ \text{J K}^{-1}\ \text{mol}^{-1}$. Which of the following statements are correct?

Fig. 1: Two panels showing how the kinetic energies of the molecules are spread out at 300 K and at 310 K. In the left panel both curves rise to a peak at a few kJ per mole and fall away; the 310 K curve has a slightly lower peak and spreads a little further to the right. The right panel magnifies the far tail near the activation energy, 50.0 kJ per mole, marked by a dashed line; there the 310 K curve lies above the 300 K curve, and the area beyond the activation energy is shaded.