A chemist analyses a gaseous reaction mixture at 500 K and sketches the Maxwell–Boltzmann energy distribution for the reacting molecules. The curve is unimodal, peaks at 60 kJ mol⁻¹, and approaches the x-axis at 200 kJ mol⁻¹. The activation energy for the elementary step is 150 kJ mol⁻¹, shown on the sketch as a vertical mark.
For parts (b)–(d), assume that the total area under the curve is 1.00 and that the orientation factor for this reaction is 0.12.
(a) On your own copy of the graph, clearly label the activation energy, Ea, and shade the region that represents molecules possessing sufficient energy to react.
(b) Describe in words the physical meaning of the shaded area you produced in part (a).
(c) When the temperature is raised to 550 K, the shaded area increases from 0.048 to 0.080. Calculate the factor by which the frequency of successful collisions changes, assuming the orientation factor remains constant.
(d) Explain why even a modest increase in the shaded area can lead to a substantially larger rate constant for the reaction.