At 600K, a gas-phase elementary reaction has an activation energy of 180kJ mol−1. A catalyst provides an alternative pathway with an activation energy that is 25kJ mol−1 lower. A researcher has tabulated the cumulative area under the Maxwell–Boltzmann curve for the reactant gas at 600K as a function of kinetic energy:
E (kJ mol−1) | 120kJ mol−1 | 140kJ mol−1 | 160kJ mol−1 | 180kJ mol−1 | 200kJ mol−1 | 220kJ mol−1 | 240kJ mol−1
Cumulative area (fraction of molecules with energy ≤E) | 0.52 | 0.68 | 0.80 | 0.88 | 0.93 | 0.96 | 0.98
Assume that the total area under the distribution is 1.00 and that molecular orientation is always favourable.
(1) Part 1: (a) Determine the fraction of molecules that possess at least 180kJ mol−1 of kinetic energy at 600K.
(2) Part 2: (b) Using the same data table, determine the fraction of molecules that possess at least 155kJ mol−1 of kinetic energy (i.e., the activation energy for the catalysed pathway).
(3) Part 3: (c) Calculate the ratio of the fractions obtained in parts (b) and (a). Interpret this ratio in terms of the expected change in the reaction rate when the catalyst is introduced at 600K.
(4) Part 4: (d) Besides lowering the activation energy, cite one other way in which a catalyst could influence the rate of an elementary reaction, and briefly explain whether that effect is reflected in a Maxwell–Boltzmann energy distribution.