 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/5/b/ii/solution

The equal Arrhenius prefactors cancel in the ratio:

K_{298} = \frac{A e ^{- E_{a, 1} / RT}}{A e ^{- E_{a, - 1} / RT}} = exp (\frac{E _{a, - 1} - E _{a, 1}}{RT}) = exp (\frac{2230}{8.3145 \times 298}) .

Hence $K_{298} = 2.46$ , favouring trans, with trans fraction

K / (1 + K) = 0.71095

. The factor 1000 converting the barrier difference from kilojoules to joules is essential.

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