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In the last chapter, we saw that it was possible to describe the complete
3-dimensional shape of methane by specifying its bond angles and bond lengths.
Ethane, which is comprised of two methyl groups attached to each other, has
properties very similar to those of methane. However, the complete
3-dimensional shape of ethane cannot be specified by these bond lengths and bond
angles alone because ethane can internally rotate about its C-C bond.
To understand why ethane has this extra degree of freedom, consider the
cylindrically symmetric nature of $\sigma$ bonds. The $\sigma$ bond can
maintain a full degree of overlap while its two ends rotate. Hence, the energetic
barrier to rotation about sigma bonds is generally very low. Unlike $\pi$
bonds in alkenes, the C-C sigma bond does not hold the two methyl
groups in fixed positions relative to one another. The different spatial
arrangements formed by rotations about a single bond are called
conformations or conformers.
Figure %: Free rotation about the C-C $\sigma$ bond in ethane.
Visualizing Conformations
Several methods are used by organic chemists to help them visualize the
conformations of molecules. One of these methods uses wedges to
denote bonds that are extending out from the plane of the page toward the
reader and dashes to indicate bonds that are going into the plane of
the page away from the reader. This notation is frequently used to
represent the tetrahedral geometry of $sp^3$-hydridized carbons.
A Newman projection can be used to specify the conformation of a
particular bond with clarity and detail. A Newman projection represents
the head-on look down the bond of interest. The circle in the Newman
projection represents the atom in front of the bond, and the lines radiating
from the center are the bonds of that atom. The bonds of the rear atom
emerge from the sides of the circle.
Figure %: How to draw a Newman projection.
Newman projections can be characterized by the angles formed between bonds
on the front atom and bonds on the rear atom. Such angles are called
dihedral angles. The full 3D shape of any molecule can be described by
its bond lengths, bond angles, and dihedral angles.
Conformations of Ethane
While there are an infinite number of conformations about any sigma bond,
in ethane two particular conformers are noteworthy and have special names.
In the eclipsed conformation, the C-H bonds on the front and back
carbons are aligned with each other with dihedral angles of 0 degrees. In
the staggered conformation, the C-H bonds on the rear carbon lie
between those on the front carbon with dihedral angles of 60 degrees.
