Question

Using what you know about the conformational energetics of substituted cyclohexanes, predict which of the two $\text{9-methyldecalin}$isomers is more stable. Explain your reasoning.

Short answer

Trans isomer of$\text{9-methyldecalin}$ is more stable than cis isomer of $\text{9-methyldecalin}$.

Step-by-step solution

Decalin

The most common example of a fused ring system is decalin. There are two geometric isomers of decalin. The isomer in which the rings are fused using two cis bonds is the $cis\text{-decalin}$and the isomer in which the rings are fused using two trans bonds is the$trans\text{-decalin}$ .

Drawing cis-decalinand trans-decalin

While drawing $cis\text{-decalin}$, if the left ring is considered, the bonds to the right ring are both directed in downward direction, where the attached hydrogens are directed upward. These bonds are cis, and this can be called a cis ring fusion. One of the bonds to the right ring must be in anaxial position, and the other is in an equatorial position.While drawing , one of the bonds to the right ring must be directed upward and the other in downward direction. These bonds are trans, and this can be called a trans ring fusion. Both of the bonds to the right ring are equatorial.

Identifying the stable isomer

The conformation of$cis\text{-decalin}$ is flexible while that of $trans\text{-decalin}$is quite rigid.

Cis isomer of $\text{9-methyldecalin}$will be less stable than trans isomer of $\text{9-methyldecalin}$because ofa larger number of gauche interactions.