GATE 2026 CY – Question 29

Organic Chemistry · Stereochemistry: Chirality and symmetry of organic molecules with or without chiral centres and determination of their absolute configurations and optical purity. Relative stereochemistry in compounds having more than one stereogenic centre. Homotopic, enantiotopic and diastereotopic atoms, groups and faces. Conformational analysis of acyclic and cyclic compounds. Geometrical isomerism and optical isomerism. Configurational and conformational effects, atropisomerism, and neighbouring group participation on reactivity and selectivity/specificity. Stereoselective and stereospecific synthesis. Enantiomeric excess. · 1 mark · Numerical answer

The difference in the number of gauche interactions present in diaxial and diequatorial chair conformations of trans-1,2-dimethylcyclohexane is ______ (in integer).

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Correct answer: 3

Explanation

**Gauche interactions in trans-1,2-dimethylcyclohexane.**

**Diequatorial conformer.** Both methyl groups are equatorial. The two adjacent equatorial methyls are gauche to each other: **1 gauche interaction** (Me/Me).

**Diaxial conformer.** Each axial methyl has two gauche interactions with the ring carbons, C3 and C5 for one methyl (1,3-diaxial interactions with the axial hydrogens) and the equivalent ones for the other. Counting methyl-ring gauche interactions, there are $2\times2=4$ gauche interactions. The two axial methyls are anti to each other, so there is no Me/Me gauche interaction.

**Difference:**
$$4-1=\mathbf{3}.$$

(Each gauche interaction costs about 3.8 kJ/mol, so the diequatorial form is favoured by about 11 kJ/mol.)