The presence and number of planes of symmetry in butane depend entirely on its specific conformational arrangement. Butane, as an alkane, can rotate around its carbon-carbon single bonds, leading to various three-dimensional structures known as conformations.
Understanding Planes of Symmetry
A plane of symmetry (often denoted by the symbol σ) is an imaginary plane that divides a molecule into two halves that are mirror images of each other. If a molecule possesses at least one plane of symmetry, it is considered achiral, meaning it is superimposable on its mirror image and will not exhibit optical activity.
Symmetry in Butane Conformations
Butane (specifically n-butane, CH₃CH₂CH₂CH₃) exists primarily in two broad categories of conformations: staggered and eclipsed. Each of these categories includes specific conformers with distinct symmetry elements.
Staggered Butane Conformations
The provided reference states that "Staggered Butane has one plane of symmetry and one axis of symmetry." This statement primarily refers to the most stable anti-staggered conformation.
Anti-Staggered Butane
- Description: This is the most stable and lowest-energy staggered conformation. Here, the two terminal methyl (CH₃) groups are positioned as far apart as possible, approximately 180 degrees from each other across the central C2-C3 bond.
- Plane of Symmetry: Anti-staggered butane possesses one plane of symmetry. This plane passes through the central C2-C3 bond and precisely bisects both terminal methyl groups, dividing the entire molecule into two perfectly identical mirror halves.
- Axis of Symmetry: It also exhibits a C₂ axis of symmetry that passes through the midpoint of the C2-C3 bond.
Gauche-Staggered Butane
- Description: In this staggered conformation, the methyl groups are approximately 60 degrees apart from each other. This arrangement leads to slight steric hindrance, making it less stable than the anti-staggered form.
- Plane of Symmetry: Gauche-butane, despite being a staggered form, does not possess a plane of symmetry. Due to this lack of a plane of symmetry, it is a chiral molecule and exists as a pair of enantiomers (non-superimposable mirror images). However, these enantiomers rapidly interconvert at room temperature.
Eclipsed Butane Conformations
The reference indicates that "Eclipsed Butane has two planes of symmetry and one axis of symmetry." This specifically describes the totally eclipsed conformation.
Totally Eclipsed Butane
- Description: This is the least stable and highest-energy eclipsed conformation. In this arrangement, the two methyl groups are directly aligned (eclipsing each other), resulting in significant steric strain.
- Planes of Symmetry: Totally eclipsed butane exhibits two distinct planes of symmetry:
- One plane passes through the central C2-C3 bond and contains both of the eclipsing methyl groups, as well as their directly opposing hydrogen atoms.
- A second plane also passes through the central C2-C3 bond but is perpendicular to the first, bisecting the other two pairs of eclipsing hydrogen atoms.
- Axis of Symmetry: It also contains a C₂ axis of symmetry, coincident with the C2-C3 bond.
Other Eclipsed Butane Conformations (Methyl-Hydrogen Eclipsed)
- Description: These intermediate eclipsed forms occur when a methyl group eclipses a hydrogen atom.
- Plane of Symmetry: These conformations typically possess one plane of symmetry. This plane contains the central C-C bond and the methyl group and hydrogen atom that are directly eclipsing each other.
Summary of Butane's Symmetry Elements
The table below summarizes the symmetry elements for the key conformations of butane:
| Butane Conformation | Planes of Symmetry (σ) | Axes of Symmetry (Cn) |
|---|---|---|
| Anti-Staggered | 1 | 1 (C2) |
| Gauche-Staggered | 0 | 1 (C2) |
| Totally Eclipsed | 2 | 1 (C2) |
| Methyl-Hydrogen Eclipsed | 1 | 1 (C2) |
It is important to note that the general statements from the reference, "Staggered Butane has one plane of symmetry" and "Eclipsed Butane has two planes of symmetry," refer to the highest symmetry forms typically found within those conformational categories (i.e., anti-staggered and totally eclipsed, respectively).
Practical Implications
The presence or absence of a plane of symmetry is crucial in determining a molecule's chirality. Only conformations that lack a plane of symmetry, such as gauche-butane, can be chiral. However, because butane molecules are constantly interconverting between these conformations at room temperature, an overall sample of butane is considered achiral and will not exhibit optical activity.
