For a certain endothermic reaction in the gas phase, molecules must possess at least 300 kJ mol−1 of kinetic energy to undergo a successful collision. The fraction of molecules with energies at or above this threshold is measured at several temperatures and reported in the table below.
Temperature (K) Fraction ≥ 300 kJ mol−1
640 0.90 %
660 1.15 %
680 1.47 %
Ideal‐gas behaviour may be assumed.
(a) Using the data, determine whether the relationship between the high‐energy fraction and temperature in this range is better described as linear with T or exponential with 1/T. Support your choice with an appropriate calculation or plot description.
(b) Interpolate (or extrapolate, if necessary) to estimate the temperature at which 2.0 % of the molecules will possess at least 300 kJ mol−1 of kinetic energy. Show all reasoning.
(c) Using your temperature estimate from part (b), compute the factor by which the reaction rate is expected to increase relative to 640 K if the rate is directly proportional to the fraction of molecules above the threshold energy.