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ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2024/paper-1/a4/a/i/solution

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Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 1 / A4 / a / i / Solution by

Codex  0 2026-10-20

The molecular symmetry operations must be closed under composition. Write the proposed nonidentity operations as

R = C_{2}

and

S = σ

. Their product

RS

cannot equal any proposed member:

RS = E \Rightarrow R = S^{- 1} = S, RS = R \Rightarrow S = E, RS = S \Rightarrow R = E .

(1)

Each conclusion contradicts the distinct operations stipulated. Therefore at least a fourth symmetry operation must exist. For a mirror plane containing the twofold axis, the product generates another mirror plane; for a plane perpendicular to it, the product is inversion. A tilted plane may generate still more operations, but cannot evade group closure.

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