A disubstituted cycloalkane can have two distinct stereoisomers — cis and trans — depending on the relative spatial orientation of the two substituents.
While the cis isomer has both substituents on the same side of the ring, the trans isomer has its substituents on the opposite sides.
The isomers have different physical properties and are not interconvertible by rotation about the C-C bond. As such, they are never in equilibrium.
Consider the stereoisomers of 1,4-dimethylcyclohexane.
The two chair conformations of the cis isomer have equal energies and equilibrate in equal proportions.
Both conformations of the cis isomer have one axial methyl group and one equatorial methyl group, and their positions switch when the ring flips.
In contrast, trans-1,4-dimethylcyclohexane exists in two non-equivalent chair forms with the methyl groups facing opposite directions.
One chair conformer has both methyl groups in the axial position, whereas the alternative conformer has the methyl groups equatorially arranged.
Due to strong steric repulsions, the trans-diaxial form has higher energy than the trans-diequatorial form, making the latter more stable and abundant at equilibrium.
Now consider the two energetically non-equivalent chair forms of cis-1,3-dimethylcyclohexane.
While one cis form has two axial methyl groups with strong, unfavorable 1,3-diaxial interactions, the other cis form has two equatorial methyl groups and is devoid of any 1,3-diaxial interactions.
The absence of steric repulsion makes the cis-diequatorial conformer more stable and abundant than the cis-diaxial conformer.
In comparison, the trans isomer of 1,3-dimethylcyclohexane equilibrates in equal proportions between two equivalent chair forms. Each trans conformer has one axial and one equatorial methyl group.
If the substituents of trans 1,3-disubstituted cycloalkane have different sizes, the two conformers no longer stay equivalent. This is because the bulky substituent at the axial position encounters strong steric repulsions, making the bulky group preferentially occupy the equatorial position.
