Answer
Symmetry Concepts – Detailed Explanation
1. Symmetry Operations Generated by the S5 Improper Rotation Axis
The S5 operation involves a 72° rotation followed by a reflection through a plane perpendicular to the rotation axis.
| Operation | Description |
|---|---|
| S51 | 72° rotation + reflection |
| S52 | 144° rotation + reflection |
| S53 | 216° rotation + reflection |
| S54 | 288° rotation + reflection |
| S55 | 360° rotation + reflection = Identity (E) |
Conclusion: These five operations are distinct for a general molecule.
2. Symmetry in Trans-Planar H2O2
- S2: Equivalent to inversion (i), as a 180° rotation + perpendicular reflection passes every atom through the center.
- S1: Equivalent to mirror reflection (σ), since a full 360° rotation is identity followed by a reflection.
3. S6 Symmetry in Staggered Ethane
The staggered conformation of ethane (D3d symmetry) exhibits S6 symmetry:
- Step 1: 60° rotation about the C–C axis.
- Step 2: Reflection through a horizontal plane perpendicular to the axis.
✅ The molecule maps onto itself → S6 is a valid symmetry operation.
4. Principal Axes of Rotation
(a) Para-aminophenol: NH2 and OH are at para positions on a benzene ring.
➤ Has a vertical C2 axis through the center of the ring.
(b) Pyridine: Six-membered ring with one nitrogen atom.
➤ Possesses a C2 axis passing through N and the opposite carbon.
(c) Cyclohexane (Chair Form): Non-planar conformation.
➤ Has a C3 axis through opposite carbon atoms (C1 and C4), with 120° rotational symmetry.