Which one of the following conformation of cyclohexane is chiral?

Symmetry criterion for chirality

chiral or achiral depends on its symmetry elements.

Symmetry criterion for chirality
A molecule (or a single conformation) is achiral if it possesses any of the following improper symmetry elements:
  • a plane of symmetry (σ)
  • a center of symmetry (i)
  • an n-fold rotation-reflection axis (Sn)
If none of these is present, the conformation is chiral and can exist as a pair of enantiomers.

Case 1: Chair conformation

The chair has a C3 rotational axis and three equivalent vertical mirror planes that pass through opposite C-C bonds. Because of these σ planes, the chair is achiral.

Case 2: Boat conformation

The ideal boat possesses one plane of symmetry that bisects the ring through the two “flagpole” carbons. Presence of this σ plane renders the boat achiral.

Case 3: Rigid (half-chair) conformation

The term “rigid” usually refers to the half-chair obtained during ring inversion. This half-chair contains an improper S4 axis (a 90° rotation followed by reflection), so it is also achiral.

Case 4: Twist boat (skew boat) conformation

When the boat puckers to relieve steric repulsion, the symmetry plane is lost and only a C2 proper rotational axis remains. Because there is no mirror plane, center of symmetry, or Sn axis, the twist boat is chiral; it exists as two non-superposable mirror-image conformers.

Therefore, among the listed conformations, only the twist boat lacks any improper symmetry element and is chiral.

Option A which is: Twist boat