Question 26.4: Choosing the Most Stable Conformer of an Alkane. Draw the co......

Analyze
We must first draw a structural diagram for the molecule and identify the C2—C3 axis and then draw a Newman projection corresponding to a view along the C2—C3 bond. The lowest energy structure is the one that minimizes the repulsions among the substituents.

Solve
A structural diagram for 2,3-dimethylpentane is given here.              H—\overset{\begin{matrix} H \\ \mid \end{matrix} }{\underset{\begin{matrix} \mid \\ H \end{matrix} }{C}}—\overset{\begin{matrix} H \\ \mid \end{matrix} }{\underset{\begin{matrix} \mid \\ CH_{3} \end{matrix} }{C}}—\overset{\begin{matrix} CH_{3} \\ \mid \end{matrix} }{\underset{\begin{matrix} \mid \\ H \end{matrix} }{C}}—\overset{\begin{matrix} H \\ \mid \end{matrix} }{\underset{\begin{matrix} \mid \\ H \end{matrix} }{C}}—\overset{\begin{matrix} H \\ \mid \end{matrix} }{\underset{\begin{matrix} \mid \\ H \end{matrix} }{C}}—H

A hydrogen atom and two methyl groups are bonded to C2. Three different groups are bonded to C3: a hydrogen atom, a methyl group, and an ethyl group. The conformation of lowest energy is the one in which the alkyl groups are staggered. In addition to this, we should minimize the number of gauche interactions between the larger groups.

We must now construct a Newman projection corresponding to the view along the C2—C3 bond. First, we draw a circle to represent the rear carbon, and then we add lines for the bonds formed by the front carbon atom. Finally, we add lines for the bonds formed by the rear carbon atom.

We are now ready to attach the groups to construct 2,3-dimethylpentane. Let us add two methyl groups and a hydrogen atom to the second carbon atom. Note it does not matter where we place the groups.

We must now add a hydrogen atom, as well as ethyl and methyl groups
to the rear carbon. There are three possible staggered conformations:

Which one of these conformations is lowest in energy? Conformation (a) has two gauche interactions, but conformations (b) and (c) have three such interactions. Therefore, conformation (a) has the lowest energy.
Assess
In solving this problem, we considered rotation about a particular carbon–carbon bond. Keep in mind that rotations about other carbon carbon bonds also occur simultaneously, a complication that we will not consider.