Question

Draw the alternative chair conformations for the cis and trans isomers of 1,2 -dimethylcyclohexane, 1,3 -dimethylcyclohexane, and 1,4 -dimethylcyclohexane. (a) Indicate by a label whether each methyl group is axial or equatorial. (b) For which isomer(s) are the alternative chair conformations of equal stability? (c) For which isomer(s) is one chair conformation more stable than the other?

Short answer

Answer: The trans isomer of 1,4-dimethylcyclohexane has alternative chair conformations of equal stability (A1E4 and E1A4). The other isomers, cis and trans 1,2-dimethylcyclohexane, and cis and trans 1,3-dimethylcyclohexane, have one chair conformation more stable than the other.

Step-by-step solution

Draw alternative chair conformations for each isomer

To find the conformations, draw two chair isomers for each of the given cis and trans isomers and add the methyl groups at appropriate positions.

Label each methyl group as axial or equatorial

Indicate the position of the methyl group on each conformation by writing 'A' for axial and 'E' for equatorial next to the methyl group.

Determine the stability of alternative chair conformations for each isomer

Compare the conformations for each isomer and decide if they have equal stability or one chair conformation is more stable than the other. It's important to remember that equatorial positions are more stable than axial positions due to less steric hindrance. Here are the alternative chair conformations: 1,2-dimethylcyclohexane: - cis: A1A2 and E1E2 (both axial) - trans: A1E2 and E1A2 (both equatorial) 1,3-dimethylcyclohexane: - cis: A1E3 and E1A3 (alternative axial/equatorial) - trans: A1A3 and E1E3 (both equatorial) 1,4-dimethylcyclohexane: - cis: A1E4 and E1A4 (alternative axial/equatorial) - trans: A1E4 and E1A4 (alternative axial/equatorial)

Determine the isomer(s) with alternative chair conformations of equal stability

Based on the analysis in Step 3, the following isomer has alternative chair conformations of equal stability: - 1,4-dimethylcyclohexane – trans (A1E4 and E1A4)

Determine the isomer(s) with one chair conformation more stable than the other

Based on the analysis in Step 3, the following isomers have one chair conformation more stable than the other: - 1,2-dimethylcyclohexane – cis (A1A2 less stable than E1E2 due to two axial methyl groups) - 1,2-dimethylcyclohexane – trans (A1E2 more stable than E1A2 due to equatorial methyl groups) - 1,3-dimethylcyclohexane – cis (A1E3 more stable than E1A3 due to equatorial methyl groups) - 1,3-dimethylcyclohexane – trans (E1E3 more stable than A1A3 due to two equatorial methyl groups)