Chirality in Cyclohexane Conformations

Chirality refers to the property of a molecule or object that is non-superimposable on its mirror image. In other words, a chiral molecule or object cannot be rotated or flipped in any way to match its mirror image.

Cyclohexane is a six-membered carbon ring that can exist in several conformations, including the chair, boat, and twist boat conformations.

Out of these conformations, only the twist boat conformation is chiral.

Explanation of each conformation:

1. Chair Conformation
The chair conformation is the most stable conformation of cyclohexane. It has all carbon atoms in the ring in a staggered conformation. The chair conformation is not chiral because it possesses an internal plane of symmetry that can divide the molecule into two identical halves.

2. Boat Conformation
The boat conformation is a higher energy conformation of cyclohexane that occurs when two neighboring carbons adopt a planar conformation. The boat conformation is not chiral because it has a plane of symmetry that bisects the molecule into two identical halves.

3. Twist Boat Conformation
The twist boat conformation is a higher energy conformation of cyclohexane that is a combination of the chair and boat conformations. It has two sets of non-equivalent carbon atoms, and the molecule cannot be superimposed on its mirror image. Therefore, the twist boat conformation is chiral.

4. Rigid Conformation
There is no conformation of cyclohexane that is specifically called the rigid conformation. Therefore, option (c) is not a valid answer.

Conclusion:
In summary, the only chiral conformation of cyclohexane is the twist boat conformation. The chair conformation and boat conformation are achiral because they possess internal planes of symmetry.