Question

Draw the both chair conformations of each of the following substituted cyclohexanes. In each case, label the more stable conformation.

(a) $cis\text{-1-ethyl-2-methylcyclohexane}$

(b)$trans\text{-1,2-diethylcyclohexane}$

(c) $cis\text{-1-ethyl-4-isopropylcyclohexane}$

(d)$trans\text{-1-ethyl-4-methylcyclohexane}$

Short answer

(a)

(more stable)

(b)

(more stable)

(c)

(more stable)

(d)

(more stable)

Step-by-step solution

Drawing cis and trans isomers for cycloalkanes

In the case of cycloalkanes, if the two substituents point toward the same faces, they are known as cis isomers. Again, if the two substituents point toward the opposite faces, they are known as trans-isomers. These two geometric isomers cannot interconvert without breaking and forming the bonds again.

Axial and equatorial positions of cyclohexane

Axial bonds are directed vertically parallel to the axis of the ring, and the equatorial bonds are directed outward from the equator of the ring. As the carbon atoms are numbered in cyclohexane, it can be seen that the odd-numbered carbons have their upward bonds in theaxial position and their downward bonds in an equatorial position. The even-numbered carbons have their downward bondsin the axial position and their upward bonds in an equatorial position.

Different sizes of substituents

The substituents are of different sizes in many substituted cyclohexanes. For a larger (bulkier) group, the energy difference between axial and equatorial positions is greater than that of a smaller group (less bulky).

Identifying the most stable conformation

Larger (bulkier) substituents tend to be in an equatorial position.If both the groups cannot be in equatorial positions, the most stable conformation will have the larger (bulkier) group in an equatorial position and the smaller (less bulky) group inthe axial position.

The axial position is shown by a solid blue line, and the equatorial position is shown by a solid red line in the structures drawn.

(a)

(more stable)

(b) The more stable conformation is when the ethyl group is present in an equatorial position.

(more stable)

The more stable conformation is when both the ethyl groups are present in an equatorial position.

(c)

(more stable)

The more stable conformation is when the isopropyl group is present in an equatorial position.

(d)

The more stable conformation is when the methyl group and ethyl groupare present in anequatorial position.