GATE 2024 CY – Question 26
The correct statement(s) for decalin is (are)
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Correct answer: (A) cis-Decalin is thermodynamically less stable than trans-decalin.; (D) trans-Decalin belongs to the point group of C2h.
Explanation
Check each statement about decalin (bicyclo[4.4.0]decane).
- **A. cis-Decalin is less stable than trans-decalin.** True. The cis isomer has three more gauche butane interactions, so it is about 2.7 kcal/mol (11 kJ/mol) less stable. ✓
- **B. cis-Decalin contains a plane of symmetry.** False. A single chair-chair conformation of cis-decalin has a $C_2$ axis only (the two enantiomeric conformers interconvert by ring flip, so the compound as a whole is achiral, but a given conformer has no mirror plane).
- **C. trans-Decalin undergoes ring inversion.** False. The trans ring fusion locks both rings in chair forms; a ring flip would require impossible strain.
- **D. trans-Decalin belongs to the point group $C_{2h}$.** True: it has a $C_2$ axis, a perpendicular mirror plane $\sigma_h$ and an inversion centre. ✓
Answer **A and D**.