See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Concept: The lowest energy conformer/isomer among dimethylcyclohexanes is the one that can place both methyl substituents in equatorial positions simultaneously, minimizing 1,3-diaxial interactions. Step 2 - Identify each structure: (a) cis-1,3-dimethylcyclohexane: In the most stable chair, cis-1,3 means both methyls are either both axial or both equatorial. Both equatorial is possible, so this is relatively stable. (b) 1,1-dimethylcyclohexane (gem-dimethyl): One methyl must always be axial; cannot avoid axial methyl strain entirely, but there is no 1,3-diaxial interaction between the two gem methyls with ring substituents — however one methyl is always axial. (c) trans-1,4-dimethylcyclohexane: In the chair conformation, trans-1,4 substitution allows BOTH methyl groups to be equatorial simultaneously (diequatorial). This is the most stable arrangement. (d) cis-1,4-dimethylcyclohexane: One methyl must be axial and one equatorial; cannot achieve diequatorial arrangement. (e) Another depiction similar to trans-1,4 or a different isomer — examining the wedge/dash pattern suggests one axial and one equatorial arrangement. Step 3 - Reasoning: trans-1,4-dimethylcyclohexane (option c) can adopt a chair conformation with both methyl groups equatorial. This diequatorial arrangement has the lowest steric strain (no 1,3-diaxial interactions from either methyl group), giving it the lowest potential energy among the listed isomers. Step 4 - Why other options fail: - (a) cis-1,3: both equatorial is achievable but the ring geometry still introduces some strain compared to 1,4-trans. - (b) 1,1-dimethyl: always has one axial methyl, higher energy. - (d) cis-1,4: one axial methyl always present, higher energy. - (e) appears to be a mono-substituted or different stereoisomer that cannot achieve diequatorial. The diequatorial trans-1,4-dimethylcyclohexane has the lowest energy. Therefore, the correct answer is C.