Question

Among the following, the most stable compound is (a) Cis-1, 2-cyclohexanediol (b) Trans-1, 2-cyclohexanediol (c) Cis-1, 3 -cyclohexenediol (d) Trans-1,3-cyclohexanediol

Short answer

The most stable compound is (d) Trans-1,3-cyclohexanediol.

Step-by-step solution

Understanding Stability in Cyclohexanediol

To determine the most stable compound among the given cyclohexanediols, we need to consider the stability of cis and trans isomers. Stability in cyclohexane derivatives is often based on the ability to adopt a conformation that minimizes steric strain.

Analyzing Cis vs. Trans Isomerism

In cyclohexanediols, the stability often comes from trans isomers, particularly in cases involving small substituents like hydroxyl groups, as they can occupy equatorial positions when trans, minimizing steric hindrance compared to cis, where both groups might end up axial.

Evaluating the 1,2- Substitution

For 1,2-substituted cyclohexanediols, trans-1,2-cyclohexanediol is favored because when the hydroxyl groups are trans, they can both reside in equatorial positions, reducing steric and torsional strain, unlike the cis version where one group would need to be axial.

Evaluating the 1,3- Substitution

For 1,3-substitution, trans-1,3-cyclohexanediol can similarly place its hydroxyl groups in equatorial positions due to their relative positions, enhancing stability. However, in 1,3-cases, whether cis or trans isomers can have similar stability because of potential hydrogen bonding in the cis isomer.

Conclusion on Stability

Considering steric strain and potential energy conformations, trans-1,3-cyclohexanediol is more stable because it allows for both hydroxyl groups to adopt equatorial positions, reducing steric strain, making it generally more stable in comparison to its cis counterparts.

Key concepts

Cis vs. Trans Isomerism

In chemistry, understanding isomerism is crucial, as it can significantly affect the properties of a compound. In cyclohexanediol, isomerism refers to the distinct arrangement of the hydroxyl groups attached to the cyclohexane ring.

In particular, we focus on two types of isomers—cis and trans. *Cis isomers* have their substituents on the same side of the cyclohexane ring, while *trans isomers* have them on opposite sides.

This positioning plays a vital role in determining the compound's stability. More often, *trans isomers* are more stable due to the lesser steric strain they experience. They allow the substituent groups to position themselves further apart on the carbon ring structure, minimizing repulsion compared to *cis isomers,* which pack the groups closely together, causing destabilizing steric hindrance.

In cyclohexanediol, especially for positions like 1,2 or 1,3 substitutions, the *trans isomer* often exhibits more favorable spatial orientation by aligning the bulky substituents in a way that reduces crowding and allows for more effective molecular conformation.

Steric Strain in Cyclohexane

Steric strain is a type of strain that occurs due to the repulsion between electron clouds when atoms are situated too close to each other. In cyclohexane, this strain is particularly noteworthy due to the ring's ability to adopt different conformations to reduce such strain.

When two bulky groups are attached to the cyclohexane ring, as in cyclohexanediols, steric strain becomes significant. The cyclohexane ring's structure allows it to adopt a *chair conformation*, which helps minimize this strain by positioning substituents at predetermined distances.

In the case of 1,2-cyclohexanediol, the *trans isomer* is more stable because both hydroxyl (OH) groups can be in equatorial positions, minimizing steric strain. The *cis isomer* is less stable because one of the hydroxyl groups would need to assume an axial position, which increases repulsive interactions.

For 1,3 positions, interestingly, *cis* and *trans* isomers might sometimes demonstrate similar stability due to potential for internal hydrogen bonding in the *cis isomer*; however, generally, reducing steric strain typically favors the *trans isomer*.

Equatorial and Axial Positions

Understanding equatorial and axial positions in cyclohexane is paramount to grasping isomer stability. In the *chair conformation* of cyclohexane, which is the most stable conformation, substituents can occupy two different positions: `equatorial` and `axial`.

When a group is in the *equatorial position*, it lies roughly in the plane of the ring, extending outward, which allows more space around it and generally avoids crowding with other substituents. This positioning leads to minimized steric strain, making equatorial positioning more favorable for bulky groups like hydroxyls in cyclohexanediol.

Conversely, when in the *axial position*, the group points perpendicular to the ring plane. This position is less favorable for larger or multiple substituents due to increased steric interactions with other axial substituents on the same side of the ring, known as 1,3-diaxial interactions.

The ability of a molecule, like cyclohexanediol, to place both hydroxyl groups in the equatorial position in *trans isomers* is a key factor that leads to greater stability compared to their *cis* counterparts, where limiting crowding is more challenging.