Question

Draw the two chair conformations of cis-1-chloro-2-methylcyclohexane. Which is more stable, and by how much?

Short answer

The conformation with both substituents equatorial is more stable by about 2.3 kcal/mol.

Step-by-step solution

Understanding Cyclohexane Chair Conformations

Cyclohexane can exist in two main chair conformations, which can interconvert through ring-flipping. Each conformation has alternative axial and equatorial positions for substituents.

Identify the Substituents on Cyclohexane

In cis-1-chloro-2-methylcyclohexane, the chloro group and methyl group are on adjacent carbons and point in the same direction (either both up or both down) due to the 'cis' configuration.

Draw the First Chair Conformation

Draw a cyclohexane chair structure. Place the chlorine atom and the methyl group both in the axial positions, keeping them on adjacent carbons, ensuring they are both pointing in the same direction (either both as wedges or dashes).

Draw the Second Chair Conformation

Draw the flipped chair conformation where the previous axial positions become equatorial and vice versa. Place the chlorine and methyl groups in equatorial positions, keeping them cis to each other.

Analyze Stability of Each Conformation

Equatorial positions are generally more stable due to less steric hindrance. In this case, the second conformation where both substituents are equatorial is more stable.

Calculate Stability Difference

The axial conformations are destabilized by steric interactions, particularly 1,3-diaxial interactions. A methyl substituent has an energy cost of about 1.8 kcal/mol while a chloro substituent is smaller with about 0.5 kcal/mol. The difference in energy for both groups being axial vs. equatorial is approximately the sum of these costs, or about 2.3 kcal/mol.

Key concepts

Cis-1-Chloro-2-Methylcyclohexane

In chemistry, understanding the structure of molecules is crucial for predicting their properties and behavior. Cis-1-chloro-2-methylcyclohexane is a compound derived from cyclohexane—this simply means that the main ring of the structure is cyclohexane with some added groups. In this case, a chlorine (chloro) group and a methyl group.
Cis indicates that these substituents are on the same side of the cyclohexane ring, either both pointing upwards or both downwards at the same time. This positioning significantly influences how the compound behaves and which conformations are more stable.

Axial and Equatorial Positions

Cyclohexane chair conformation features two types of positions for groups attached to the ring: axial and equatorial. Axial positions stick out vertically, either above or below the plane of the ring. Equatorial positions, on the other hand, are more out towards the sides, around the equator of the ring.
Axial and equatorial positions are vital for determining stability because groups in equatorial positions experience less steric hindrance and generally have lower energy. Thus, it is often more favorable for larger groups to occupy equatorial sites.

Stability Analysis

Analyzing which conformation of a molecule is more stable involves understanding both steric factors and electronic effects. For cis-1-chloro-2-methylcyclohexane, we compare two chair conformations — one where both substituents are axial and one where they are both equatorial.
It turns out that the equatorial conformation is more stable. This is mainly because substituents in equatorial positions have more space and encounter fewer steric clashes, resulting in a lower overall energy state for the molecule. Stability differences translate to energy differences, making equatorial arrangements more energetically favorable.

Steric Hindrance

Steric hindrance occurs when atoms or groups in a molecule are too close to each other, leading to physical interference. This phenomenon is common in cyclohexane chair structures when substituents are crowded in axial positions.
In our example of cis-1-chloro-2-methylcyclohexane, placing both groups in axial positions can lead to clashes with hydrogen atoms on axial positions of adjacent carbons in the ring. The result is a less stable conformation due to increased repulsive interactions between atoms.

1,3-Diaxial Interactions

1,3-diaxial interactions refer to repulsive interactions that occur when axial substituents on cyclohexane are positioned three carbons apart. This spatial conflict is a specific type of steric hindrance.
For instance, the axial methyl group in cis-1-chloro-2-methylcyclohexane faces these interactions with axial hydrogens on the same side of the ring, contributing to instability. The energy penalty for such interactions can be quantified, with methyl groups introducing around 1.8 kcal/mol of destabilization. The cumulative effect makes equatorial conformations more preferable due to the lack of such repulsive forces.