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

Trans-1,3-cyclohexanediol is the most stable due to optimal equatorial positioning of both OH groups.

Step-by-step solution

Understanding the Options

We have four options to consider: (a) cis-1,2-cyclohexanediol, (b) trans-1,2-cyclohexanediol, (c) cis-1,3-cyclohexanediol, and (d) trans-1,3-cyclohexanediol. Each involves cyclohexane rings with different hydroxyl (-OH) group arrangements.

Assessing Stability in Cyclohexane

Cis and trans isomerism influences stability. Cyclohexane prefers the chair conformation, and in this conformation, substituents can occupy equatorial or axial positions. Equatorial positions offer more stability due to reduced steric hindrance.

Cis vs. Trans Analysis

For 1,2 positions: In cis-1,2-cyclohexanediol, both hydroxyl groups might prefer equatorial, but must adopt one equatorial, one axial due to steric effects. In trans-1,2-cyclohexanediol, both OH groups can be axial or equatorial, but equatorial positions are preferable for stability.

Consider 1,3-Substitution

In cis-1,3-cyclohexanediol, one OH group is axial and the other equatorial, causing more steric hindrance. In trans-1,3-cyclohexanediol, both hydroxyl groups can adopt equatorial positions, minimizing steric hindrance—hence more stable.

Compare and Choose the Most Stable

Trans-1,3-cyclohexanediol allows both OH groups to stabilize in equatorial positions, the optimal configuration. Among the options, this configuration provides fewer steric interactions.

Key concepts

Cis-Trans Isomerism

Cis-trans isomerism is a type of stereochemistry related to the arrangement of groups around a double bond or a ring structure. In cyclic compounds like cyclohexane, this is observed due to the fixed position of substituents. The term "cis" refers to the arrangement where two similar or identical substituents are on the same side of the ring, while "trans" means they are on opposite sides.
For example, in cyclohexanediol isomers, the cis version will have both hydroxyl (-OH) groups on the same side of the cyclohexane ring. In contrast, the trans version positions them on opposite sides of the ring.
This arrangement directly affects the stability and reactivity of the molecules, making understanding this concept vital for predicting physical and chemical properties of isomers.

Chair Conformation of Cyclohexane

Cyclohexane primarily exists in a chair conformation, which is the most stable form due to its ability to minimize torsional strain and steric hindrance. In this conformation, each carbon atom in the ring alternates between an upward and downward position, resembling a chair.
Each carbon atom has two types of positions available for substituents: axial and equatorial.

• Axial positions are perpendicular to the plane of the ring, creating potential interactions with neighboring axial groups.
• Equatorial positions are roughly parallel to the plane and offer more space, reducing steric hindrance.

The preference for equatorial positions is due to their lower energy, contributing to the overall stability of the molecule, particularly when bulky groups are involved, such as hydroxyl groups in diols.

Steric Hindrance in Cyclic Compounds

Steric hindrance occurs when atoms or groups within a molecule are positioned in a way that causes them to physically interfere with each other. This is a common feature in cyclic compounds like cyclohexane because of their fixed structure.
In cyclic compounds, substituents can crowd each other, especially if they are large or if the ring forces them into proximity. This crowding can increase molecular instability and affect how the molecule interacts with other chemicals.
In cyclohexanediol isomers, arranging both hydroxyl groups in equatorial positions becomes crucial to minimize steric hindrance. When both groups are equatorial, they avoid clashing with axial hydrogens and other substituents, leading to more stable structures.

Organic Chemistry Reactions

Understanding the stability of isomers like those of cyclohexanediol is essential in predicting their behavior in organic chemistry reactions. Stable isomers are generally more favorable in reactions due to their lower energy states.
Reactions involving cyclohexane derivatives often depend on the ability of the compound to maintain or achieve an energetically favorable conformation. For example, trans-1,3-cyclohexanediol, with its equatorial positioning of hydroxyl groups, will undergo different reactions and pathways compared to its cis counterpart due to its greater stability.
This stability affects how the molecule might interact in reactions such as substitution, elimination, and even some oxidation or reduction processes. Understanding these interactions is key to manipulating organic reactions for desired outcomes.