Question 26.5: Predicting Which Conformer of a Disubstituted Cycloalkane Is......
Predicting Which Conformer of a Disubstituted Cycloalkane Is Lowest in Energy
Draw the lowest energy conformation of cis-1,3-dimethylcyclohexane.
Analyze
First, we draw a cyclohexane ring showing both the axial and the equatorial bonds but without the substituents added to the ring. Then, we consider the placement of the substituents. A useful tip is to realize that when the carbon atoms in a cyclohexane ring are numbered, there is a relationship between the bonds on the odd- and even-numbered carbon atoms. When the odd-numbered carbons have their up bonds axial, the even-numbered carbon atoms have their down bonds axial. When the odd-numbered carbons have their up bonds equatorial, the even-numbered carbons have their down bonds equatorial. The relationship is illustrated in the diagram below:
Solve
We are dealing with a cis isomer, and so both methyl groups are adjacent to the same face of the ring. This is possible only if the two methyl groups are bonded to the two carbon atoms with both bonds up or both bonds down. The conformation of lowest energy will be the one that has the methyl groups in the equatorial positions.
Assess
If the molecule above undergoes a ring flip, the methyl groups will be in the axial positions and the resulting conformation will be higher in energy.