Chapter 7, Problem 7.21P

Interpretation Introduction

(a)

Interpretation:

The difficulty of that would come on models of the cis and trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ made are to be stated. The model which will form easier is to be identified. The explanation for the corresponding answer is to be stated.

Concept introduction:

The organic compounds which consist of two cyclic rings fused together are known as bicyclic compounds. Fused rings, bridged rings, and spiro rings are the examples of bicyclic compounds. The stability of bicyclic compounds depends on the ring strain.

Answer to Problem 7.21P

The cis isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ will be formed with less difficulty than the trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ as the formation of three-membered cycles in a case where methyl group are at cis position to each other are easier than the trans position.

Explanation of Solution

The structure of cis and trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ are shown below.

Figure 1

The formation of trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ is shown below.

Figure 2

In the formation of trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$, the methyl groups are in two different planes. The angle between them is large. Therefore, it is difficult to form trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$.

The formation of cis isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ is shown below.

Figure 3

In the formation of cis isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$, the methyl groups are in two same planes. The angle between them is not as large as in case of trans. Therefore, cis isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ will be form easier than the trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$.

Conclusion

It is easier to form a three-membered ring by the methyl at the cis position and the methyl groups at trans position. Therefore, cis isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ will form easier than the trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$.

Interpretation Introduction

(b)

Interpretation:

The difficulty of that would come on models of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ and $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$ make is to be stated. The model which will form easier is to be identified. The explanation for the corresponding answer is to be stated.

Concept introduction:

The organic compounds which consist of two cyclic rings fused together are known as bicyclic compounds. Fused rings, bridged rings and spiro rings are the examples of bicyclic compounds. The stability of bicyclic compounds depends on the ring strain.

Answer to Problem 7.21P

The compound $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ will form with more difficulties than the compound $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$ as the methyl groups in case of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ is movable than in case of formation $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$ but rigid in case of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$.

Explanation of Solution

The structure of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ and $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$ are shown below.

Figure 4

The formation of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ is shown below.

Figure 2

In the formation of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$, the methyl groups are in two different planes. The angle between them is large. Therefore, it is difficult to form trans isomers of $\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$.

The formation of $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$ is shown below.

Figure 5

In the formation of $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$, the distance between methyl groups is not large. The angle between them can be change by sigma bond rotation. Therefore, it is easier to form $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$ than $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$.

Conclusion

The methyl groups in case of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ is movable than in case of formation $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$ but rigid in case of $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$. Therefore, compound $trans-\text{bicyclo}\left[\text{3}\text{.1}\text{.0}\right]\text{hexane}$ will form with more difficulties than the compound $trans-\text{bicyclo}\left[\text{5}\text{.3}\text{.0}\right]\text{decane}$.