Question

There are two isomers of decalin. One is of higher energy and the other is more stable. Which is the stabler form? Why?

Short answer

The more stable isomer of decalin is trans-decalin due to the absence of steric repulsion between the axial hydrogens at the junction of the rings, allowing them to maintain favorable axial positions without any strain. In contrast, cis-decalin experiences unfavorable steric interactions between the axial hydrogens, leading to a higher energy and less stable conformation.

Step-by-step solution

Identify the two isomers of decalin

Decalin (C10H18) has two isomers: cis-decalin and trans-decalin. These isomers differ in the relative orientation of the two cyclohexane rings that form the decalin structure. In cis-decalin, the two hydrogen atoms at the junction of the rings are on the same side, while in trans-decalin, they are on opposite sides.

Compare the cyclohexane rings in the isomers

In both cis-decalin and trans-decalin, the cyclohexane rings are in their most stable conformation, which is the chair conformation. However, the relative orientation of the rings in each isomer affects the overall stability of the molecule due to any potential steric strain or torsional strain when different groups on the molecule interact.

Analyze the steric interactions in cis-decalin

In cis-decalin, the two cyclohexane rings are on the same side of the molecule, leading to steric repulsion between the two axial hydrogens at the junction of the rings, forcing these hydrogens to adopt an unfavorable equatorial position. This introduces strain in the molecule, making it energetically less stable.

Analyze the steric interactions in trans-decalin

In trans-decalin, the two cyclohexane rings are on opposite sides of the molecule, avoiding any steric repulsion between the axial hydrogens at the junction of the rings. Thus, the hydrogens can maintain their favorable axial positions without any strain.

Compare the stabilities of the two isomers

Taking into account the steric interactions in both isomers, we can conclude that trans-decalin is more stable than cis-decalin. This is because there are no steric interactions between hydrogens at the junction of the rings in trans-decalin, while there are unfavorable interactions present in cis-decalin. As a result, trans-decalin is the more stable isomer of decalin.

Key concepts

Cis-decalin

Cis-decalin is one of two isomers of decalin, a compound with the molecular formula \(C_{10}H_{18}\). In the cis-decalin structure, two cyclohexane rings are connected in such a manner that the hydrogen atoms at the junction of the rings are positioned on the same face. This configuration results in certain unfavorable interactions.

The placement of these hydrogen atoms leads to steric repulsion, which is a type of strain that occurs when atoms are forced into close proximity, causing them to 'repel' each other. Because these hydrogens are close together in the cis form, there's a constraint on how the molecule can move, and this increases the overall energy of the system. Consequently, cis-decalin is considered to be the higher energy, less stable isomer when compared to its counterpart, trans-decalin.

Trans-decalin

Trans-decalin is the other isomer of decalin and showcases a configuration where the two cyclohexane rings are connected at the junction with hydrogen atoms oriented on opposite sides. This layout minimizes steric interactions, which decreases the overall strain in the molecule and makes it more stable.

Unlike cis-decalin, the hydrogens at the junction in trans-decalin can adopt a more relaxed, axial position, which is energetically favorable. With no unwanted repulsions, trans-decalin stands out as the preferred lower energy configuration. This is why, in chemical processes or natural occurrences, trans-decalin is more likely to be found due to its inherent stability.

Chair conformation

Both isomers of decalin, cis, and trans, feature cyclohexane rings in a chair conformation which is the most stable configuration for cyclohexane rings. The chair form provides an optimal arrangement where bond angles are close to 109.5° and torsional strain is minimized.

In this conformation, each carbon in the ring alternates between an axial (up or down) and an equatorial (side) position, allowing substituents on the cycle to occupy less crowded and energetically favorable positions. For decalin's stability discussion, understanding the chair conformation is essential, as it influences how effectively strains are managed between different molecules, especially concerning isomer stability.

Steric strain

Steric strain occurs when atoms in a molecule are positioned so closely that electron clouds repel each other, causing a rise in energy that destabilizes the molecule. In decalin isomers, the steric strain particularly affects the cis form.

Cis-decalin has steric repulsion between axial hydrogens that forces them into an equatorial position. This unfavorable arrangement causes the molecule to adopt higher energy states, which ultimately make it less stable.

By contrast, in trans-decalin, such repulsion is effectively avoided due to the opposite positioning of the cyclohexane rings; hence, steric strain is minimized. Reducing steric strain is vital for achieving greater molecular stability, which is a key reason why trans-decalin is favored energetically over cis-decalin.