Chapter 5, Problem 5.1E

(a)

Interpretation Introduction

Interpretation:The isomeric relationship between cyclopropylcyclopentane and cyclobutylcyclobutane should beidentified.

Concept introduction:Chiral carbon is any stereocenter attached to four different alkyl substituents. If any two of the substituent happen to be similar the center is regarded as achiral.

The enantiomers are identical chemical compounds that have a mirror-image relationship to each other while diastereomers do not hold similar mirror image relationships.

The molecular models of $\text{n-butane}$ and $\text{2-methylpropane}$ are illustrated below.

  

The two compounds constitute a pair of constitutional isomers. These kinds of isomers are formed by cleavage and replacement of bonds, unlike the conformational isomers that result due to rotation around the bond.

Explanation of Solution

Structures of cyclopropylcyclopentane and cyclobutylcyclobutane are illustrated as follows:

  

The molecular formula for both cyclopropylcyclopentane and cyclobutylcyclobutane is ${\text{C}}_{\text{8}}{\text{H}}_{\text{14}}$ . Since the isomers are formed by bond cleavage from cyclopentane and cyclopropane moietiesfollowed by attachment at other ring to form cyclobutylcyclobutane,so these represent constitutional isomers.

(b)

Interpretation Introduction

Interpretation: The isomeric relationship among $\text{cis-1,2-dimethylcyclopentane}$ and $\text{trans-1,2-dimethylcyclopentane}$ as well as $\text{1,3-dimethylcyclopentane}$ should be identified.

Concept introduction: Chiral carbon is any stereocenter attached to four different alkyl substituents. If any two of the substituent happen to be similar the center is regarded as achiral.

The enantiomers are identical chemical compounds that have a mirror-image relationship to each other while diastereomers do not hold similar mirror image relationships.

The molecular models of $\text{n-butane}$ and $\text{2-methylpropane}$ are illustrated below.

  

The two compounds constitute a pair of constitutional isomers. These kinds of isomers are formed by cleavage and replacement of bonds, unlike the conformational isomers that result due to rotation around the bond.

Explanation of Solution

Structures of $\text{cis-1,2-dimethylcyclopentane}$ and $\text{trans-1,2-dimethylcyclopentane}$

are illustrated as follows:

  

  $\text{cis-1,2-dimethylcyclopentane}$ and $\text{trans-1,2-dimethylcyclopentane}$ are constitutional isomers of $\text{1,3-dimethylcyclopentane}$ because they are formed when bond at second carbon broken down to form new bond at third carbon.

Since cis and trans form represent diastereoisomers therefore $\text{cis-1,2-dimethylcyclopentane}$ and $\text{trans-1,2-dimethylcyclopentane}$ have diastereoisomeric relationship.