No, chiral molecules lack certain symmetry elements; specifically, they are not superimposable on their mirror images. While they may possess some symmetry, they cannot possess a plane of symmetry (σ), a center of symmetry (i), or an alternating axis of symmetry (Sn).
Understanding Chirality and Symmetry
Chirality, in the context of molecules, refers to the property of being non-superimposable on its mirror image. Think of your hands: they are mirror images, but you can't perfectly overlay one on the other. A chiral molecule behaves the same way.
Symmetry, on the other hand, describes the presence of symmetry elements within a molecule. The key symmetry elements to consider in relation to chirality are:
- Plane of Symmetry (σ): An imaginary plane that bisects a molecule into two halves that are mirror images of each other.
- Center of Symmetry (i): A point in the center of a molecule such that for any atom, an identical atom exists on the opposite side of that point, equidistant from it.
- Alternating Axis of Symmetry (Sn): An axis about which a rotation by 360°/n, followed by reflection through a plane perpendicular to the axis, leaves the molecule indistinguishable from the original.
Chirality and Symmetry Elements
A molecule is chiral if it lacks a plane of symmetry (σ), a center of symmetry (i), and an alternating axis of symmetry (Sn). The presence of any of these elements generally makes a molecule achiral (non-chiral).
It's important to note that a chiral molecule can possess other symmetry elements, such as a simple axis of rotation (Cn). However, the absence of σ, i, and Sn is what fundamentally defines chirality.
Asymmetry vs. Dissymmetry
It is also important to differentiate between asymmetry and dissymmetry.
-
Asymmetric: A molecule lacking all symmetry elements except the identity (E). All asymmetric molecules are chiral.
-
Dissymmetric: A molecule lacking Sn elements, but which may have Cn axes. Dissymmetric molecules are chiral.
Therefore, a chiral molecule must be dissymmetric, but is not necessarily asymmetric.
Examples
Here are some examples illustrating the relationship between symmetry and chirality:
| Molecule | Chirality | Symmetry Elements |
|---|---|---|
| Lactic acid (CH3CH(OH)COOH) | Chiral | None (asymmetric) |
| trans-1,2-dimethylcyclohexane | Chiral | C2 axis |
| Achiral molecule with plane of symmetry | Achiral | σ |
| Achiral molecule with center of symmetry | Achiral | i |
Conclusion
Chiral molecules lack specific symmetry elements (σ, i, and Sn), making them non-superimposable on their mirror images. While they might possess other types of symmetry, the absence of these key elements is what defines their chiral nature.
