Question

Which one of the following conformations of cyclohexane is chiral? (a) rigid (b) chair (c) boat (d) twist boat

Short answer

The twist boat conformation is chiral.

Step-by-step solution

Understanding Chirality

Chirality refers to a property of a molecule that is not superimposable on its mirror image. As applied to cyclohexane, we need to identify which conformation lacks a plane of symmetry and has a chiral center.

Rigid Conformation

The term 'rigid' for cyclohexane usually refers to conformations like chair, boat, etc. Each of these are rigid in structure, but 'rigid' itself doesn't define a single, specific chiral or achiral conformation. Thus, it is not directly applicable.

Chair Conformation

The chair conformation is the most stable and symmetric conformation of cyclohexane. It usually possesses a plane of symmetry and its mirror image is superimposable, making it achiral.

Boat Conformation

Boat conformation of cyclohexane is less stable than the chair but does possess symmetry along a plane that divides the molecule, making it usually achiral.

Twist Boat Conformation

The twist boat conformation distorts slightly from the boat to relieve some steric strain. This conformation lacks mirror symmetry and becomes chiral as the twist allows it to exist in two non-superimposable mirror images.

Conclusion

Among the options given, the twist boat conformation of cyclohexane is the only conformation that is chiral due to its lack of a plane of symmetry and ability to exist as enantiomers.

Key concepts

Cyclohexane Conformations

Cyclohexane is a six-carbon ring and can adopt several different conformations to minimize steric strain. These conformations primarily include:

• Chair
• Boat
• Twist Boat
• Half-Chair

Changing their angles helps cyclohexane achieve a more relaxed state. Among these, chair and boat are the most well-known. The chair conformation is particularly stable due to minimized torsional strain, achieved as all carbon-carbon bonds are staggered. In contrast, the boat conformation is not as stable due to steric interactions between hydrogen atoms on adjacent carbons, which are known as flagpole interactions. The twist boat conformation slightly relieves this strain by twisting, making it somewhat more stable than the boat, but not as stable as the chair.

Chiral Molecules

Chirality is a fascinating property of some molecules. A molecule is chiral if it cannot be superimposed onto its mirror image. This is comparable to how our left and right hands are mirror images but are not identical. For cyclohexane conformations, chirality arises due to the absence of a plane of symmetry.
To determine chirality in molecules:

• Check for a chiral center, usually a carbon atom bonded to four different substituents.
• Look for the absence of a plane of symmetry, which means the molecule cannot be divided into two identical halves.

Chiral molecules can exhibit optical activity and exist as enantiomers—two molecules that are mirror images of each other but can interact differently in biological systems.

Twist Boat Conformation

The twist boat conformation of cyclohexane offers an interesting look into conformational isomerism. It is derived from the basic boat form but includes a twisting motion that alleviates some steric hindrance present in the usual boat conformation.
In the twist boat:

• The hydrogens at the so-called 'flagpole' positions are twisted away from each other, reducing repulsive interactions.
• This conformation lacks a plane of symmetry, thereby making it chiral.
• It is less stable than the chair conformation but more stable than the pure boat conformation.

This twist allows the twist boat to become chiral, and capable of existing as two distinct, non-superimposable mirror images, known as enantiomers.

Plane of Symmetry

A plane of symmetry in a molecule is an imaginary plane that divides the molecule into two identical halves. The presence or absence of such a plane is crucial in determining the chirality of a molecule.
For example:

• Molecules with a plane of symmetry are usually achiral as the two halves are mirror images that can be superimposed on each other.
• Conversely, molecules lacking a plane of symmetry, like the twist boat conformation of cyclohexane, might exhibit chirality.

Understanding symmetry is important not just for identifying chirality but also for discerning a molecule's physical and chemical properties, such as its optical activity and interaction with other chiral substances, like enzymes.