Question

Among the dimethylcyclohexanes, which one can be obtained in enantiopure form? 

• A. (A)
• B. (B)
• C. (C)
• D. (D)

Hint:

For a compound to be enantiopure, it must have a chiral center and must not have any symmetry that would lead to a racemic mixture.

Answer 1

The Correct Option is A

A compound can be obtained in enantiopure form if and only if its molecules are chiral (non-superimposable on their mirror image).

For an organic molecule, the key test for chirality is the absence of an improper axis of rotation ($S_n$), which includes the absence of a center of inversion ($i$) or a plane of symmetry ($\sigma$).

Analysis of options:

A. cis-1,2-Dimethylcyclohexane

• Structure: Both methyl groups are on the same side of the ring (cis) and are attached to C1 and C2.
• Chirality: The molecule has two chiral centers (C1 and C2).
• Symmetry Analysis (Chair Conformer):
• The molecule exists as a pair of rapidly interconverting chair conformers (diaxial and diequatorial).
• The cis-1,2-dimethylcyclohexane molecule lacks a plane of symmetry ($\sigma$) and a center of inversion ($i$) in both chair conformations.
• The entire molecule (as an average structure, or in its individual conformers) is chiral.
• Result: Since the molecule is chiral, it exists as a pair of enantiomers that are non-superimposable mirror images. Therefore, it can be resolved and obtained in enantiopure form.

B. trans-1,2-Dimethylcyclohexane

• Structure: The methyl groups are on opposite sides (trans) at C1 and C2.
• Chirality: The molecule has two chiral centers (C1 and C2).
• Symmetry Analysis (Chair Conformer): The trans-1,2-dimethylcyclohexane exists as a pair of enantiomers, similar to the cis isomer.
• Result: It can be obtained in enantiopure form. However, Option (B) in the image shows trans-1,3-dimethylcyclohexane (based on the way the methyl groups are drawn on adjacent carbons that are not C1 and C2, but if C1 is the top right, then they are at C1 and C2—this drawing is ambiguous, but let's assume it represents trans-1,2-dimethylcyclohexane for simplicity or cis-1,3-dimethylcyclohexane if based on the connectivity).
• If B is trans-1,2: It is chiral, and can be resolved.
• If B is cis-1,3: It is achiral (a meso compound) due to a plane of symmetry that bisects the C2 and C5 bonds and passes through C1 and C4. It cannot be resolved.

C. cis-1,3-Dimethylcyclohexane (Meso)

• Structure: Methyl groups are on the same side (cis) at C1 and C3.
• Chirality: The molecule has two chiral centers (C1 and C3).
• Symmetry Analysis: This molecule is a meso compound. It possesses an internal plane of symmetry ($\sigma$) that passes through C2 and C5 and bisects the C1-C6 and C3-C4 bonds (or passes through C1 and C4, depending on the conformation).
• Result: Due to the plane of symmetry, the molecule is achiral and cannot be obtained in enantiopure form.

D. trans-1,4-Dimethylcyclohexane

• Structure: Methyl groups are on opposite sides (trans) at C1 and C4.
• Chirality: The molecule has no chiral centers.
• Symmetry Analysis: It possesses a center of inversion ($i$) and a plane of symmetry ($\sigma$) in its most stable chair conformation.
• Result: The molecule is achiral and cannot be obtained in enantiopure form.

Answer: (A)