Please identify the number of gauche butane (GB) interactions in each chair conformation. * Me* Me Me H H H H H Gauche Butane -0.9 kcal/mol Axial methyl (CH3) -1.8 kcal/mol (2 gauche butane interactions) Me H Me H G.B Me G.B Me H H Me A H Me H G.B H G.B H H G.B
The Correct Answer and Explanation is :
In the chair conformation of substituted cyclohexanes, the number of gauche butane (GB) interactions—steric interactions between adjacent substituents at a 60° dihedral angle—depends on the positions of the substituents. Each GB interaction contributes approximately 0.9 kcal/mol to the molecule’s strain energy.
Axial Methyl Group (CH₃):
When a methyl group occupies an axial position on a cyclohexane ring, it can engage in two GB interactions:
- First GB Interaction: The axial CH₃ group is at a 60° angle to the axial hydrogen on the same carbon, resulting in a GB interaction.
- Second GB Interaction: The axial CH₃ group is also at a 60° angle to the axial hydrogen on the adjacent carbon, leading to another GB interaction.
Therefore, a cyclohexane conformation with an axial methyl group experiences two GB interactions, contributing a total of 1.8 kcal/mol to the strain energy.
Equatorial Methyl Group (CH₃):
In contrast, when a methyl group is in an equatorial position, it does not engage in any GB interactions because it is not at a 60° angle to any adjacent substituent.
Consequently, the conformation with an equatorial methyl group is free from GB interactions, resulting in a more stable structure.
Summary:
- Axial Methyl Group: 2 GB interactions (1.8 kcal/mol strain energy)
- Equatorial Methyl Group: 0 GB interactions (no additional strain energy)
This analysis underscores the preference for larger substituents to occupy equatorial positions in cyclohexane rings, as this orientation minimizes steric strain and enhances molecular stability.
For a visual explanation of gauche interactions, you might find the following video helpful:
videoGauche-butane interaction in cis- and trans-methyldecalinsturn0search5