The cumulative percentage of molecules with energies greater than or equal to a specified value is reported for a gas sample at two temperatures.
Energy ≥ 80 kJ mol⁻¹ 290 K: 2.0 × 10⁻⁵ % 310 K: 8.0 × 10⁻⁵ %
An elementary decomposition reaction occurring in this gas has an activation energy of 80 kJ mol⁻¹. Assume that the collision frequency of the molecules does not change appreciably between 290 K and 310 K.
(a) Calculate the factor by which the fraction of collisions possessing at least the activation energy changes when the temperature rises from 290 K to 310 K.
(b) Assuming the collision frequency is constant, determine by what factor the overall reaction rate is expected to change over the same temperature interval.
(c) At 290 K the reaction mixture reaches 50 % completion in 4.0 h. Estimate the time required to reach the same extent of reaction at 310 K and state any assumption you make.