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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/a/iii/solution

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Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 5 / a / iii / Solution by

Codex  0 2026-10-20

Let

C_{tot} = [cis] + [trans]

, which is conserved for this closed one-to-one isomerization at fixed volume. Substitute

[cis]_{298} = C_{tot} - [trans]_{298}

into the equilibrium ratio:

[trans]_{298} = K_{eq} (C_{tot} - [trans]_{298}) .

(1)

Therefore

[trans]_{298} = \frac{K _{eq}}{1 + K _{eq}} C_{tot}, [cis]_{298} = \frac{1}{1 + K _{eq}} C_{tot} .

(2)

The equilibrium split is independent of having started with pure cis, provided equilibration is complete and no side reaction changes the total concentration.

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