Isomerisation of cyclopropane to propene in the gas phase has an activation energy of 270kJmol−1. A researcher measures the fraction of cyclopropane molecules whose kinetic energies exceed 270kJmol−1 at two different temperatures and obtains the following data:
Temperature (K) Fraction above 270kJmol−1700K 2.0 %
T2 (unknown) 3.8 %
Assume the gas behaves ideally throughout the experiment.
(a) Calculate the ratio of the high‐energy fraction at temperature T2 to that at 700K.
(b) The researcher observes empirically that, over small temperature intervals in this range, the fraction of particles in the high‐energy tail changes approximately exponentially with the reciprocal of the absolute temperature. Using this observation together with the data above, estimate the value of T2 to the nearest 10 K.
(c) Discuss two potential sources of uncertainty in the estimate you obtained in part (b). For each source, explain whether it would tend to make the calculated T2 too high, too low, or indeterminate.