How many gauche butane interactions are present in this chair conformation

How many gauche butane interactions are present in this chair conformation? 01 04 00 03 02

The Correct Answer and Explanation is:

The correct answer is 4.

Here is a step-by-step explanation:

A gauche butane interaction is a type of steric strain that occurs when two methyl groups (or other non-hydrogen groups) in a butane-like fragment are positioned with a 60° dihedral angle. In cyclohexane chair conformations, these interactions are a key factor in determining the stability of different conformers. We count these interactions to estimate the overall steric strain introduced by substituents.

1. Identify the Substituents and Their Positions:
   First, let’s analyze the provided chair conformation. It is a substituted cyclohexane with three methyl groups.
   • One methyl group is in an axial position (pointing straight up).
   • A second methyl group is also in an axial position (pointing straight down).
   • The third methyl group is in an equatorial position (pointing out to the side, and slightly down).
2. Apply the Rules for Counting Gauche Butane Interactions:
   The standard method for counting these interactions in a substituted cyclohexane is as follows:
   • Axial Substituents: Each axial substituent (like a methyl group) creates two gauche butane interactions with the carbon-carbon bonds of the ring. This is because the axial substituent is gauche to the ring bonds located two carbons away (at the C-3 and C-5 positions relative to the substituent).
   • Equatorial Substituents: An equatorial substituent is in an anti conformation relative to these same ring bonds. An anti conformation has a 180° dihedral angle and introduces no steric strain. Therefore, an equatorial substituent contributes zero gauche butane interactions with the ring.
3. Calculate the Total Interactions for This Molecule:
   Using the rules above, we can count the interactions for each substituent in the given molecule:
   • First axial methyl group: Contributes 2 gauche butane interactions.
   • Second axial methyl group: Contributes 2 gauche butane interactions.
   • Equatorial methyl group: Contributes 0 gauche butane interactions.
   The total number of gauche butane interactions is the sum of the contributions from each substituent:
   Total = 2 + 2 + 0 = 4

Therefore, there are a total of 4 gauche butane interactions present in this chair conformation. It is important to note that the very severe steric clash between the two axial methyl groups (a 1,3-diaxial interaction) is a different and more significant type of strain, not typically counted under the “gauche butane” label in this context.