Problem 31 - Chemistry: The Central Science in SI Units, Global Edition

Question

Indicate whether each statement is true or false. (a) The three isomers of dimethylbenzene are \(o\) -dimethylbenzene, \(m\) -dimethylbenzene, and \(p\) -dimethylbenzene. (b) Alkenes with at least three carbon atoms differing in the position of the \(\mathrm{C}=\mathrm{C}\) double bond are called geometric isomers. \((\mathbf{c})\) Substituted benzenes can form cis and trans isomers.

Step-by-Step Solution

Answer

(a) True: The three isomers of dimethylbenzene are indeed o-dimethylbenzene, m-dimethylbenzene, and p-dimethylbenzene. (b) False: Geometric isomers refer to the arrangement of atoms or substituents around the double bond, not to different positions of the double bond itself. (c) False: Substituted benzenes cannot form cis and trans isomers due to the planar hexagonal structure of the benzene ring.

Step 1: (a) Identifying the isomers of dimethylbenzene

Dimethylbenzene has two methyl groups attached to a benzene ring. These methyl groups can be attached to the benzene ring in three different ways. They can be attached to 1. Neighboring carbon atoms (ortho- or o-dimethylbenzene) 2. Two carbon atoms apart (meta- or m-dimethylbenzene) 3. Opposite sides of the ring (para- or p-dimethylbenzene) Thus, the statement is true.

Step 2: (b) Definition of geometric isomers in alkenes

This statement seems to mix two different concepts: the position of the double bond in alkenes and the geometric isomers (cis and trans) formed due to restricted rotation around the double bond. Alkenes with at least three carbon atoms can, indeed, have the double bond at different positions. However, geometric isomers refer to the arrangement of atoms or substituents around the double bond, not to different positions of the double bond itself. Regarding geometric isomers, compounds that differ in the arrangement of atoms or substituents around a double bond are called cis and trans isomers. So the statement is false.

Step 3: (c) Formation of cis and trans isomers in substituted benzenes

Substituted benzenes are aromatic compounds in which one or more hydrogen atoms from the benzene ring are replaced by other functional groups or atoms. Due to the planar hexagonal structure of the benzene ring, it's not possible to form cis and trans isomers in substituted benzenes like we can with alkenes, where the double bond restricts rotation. Thus, this statement about substituted benzenes is false.

Key Concepts

Isomers

Isomers are molecules that have the same molecular formula but differ in the arrangement of their atoms. In organic chemistry, this concept is crucial because the structure of a molecule determines its chemical properties and behavior. There are several types of isomers, but we will focus on the isomers of dimethylbenzene, often known as xylenes:

• **Ortho (o-dimethylbenzene):** Here, two methyl groups are adjacent to each other.
• **Meta (m-dimethylbenzene):** The methyl groups are separated by one carbon atom.
• **Para (p-dimethylbenzene):** The methyl groups are opposite each other on the benzene ring.

These differences in the position of methyl groups lead to distinct chemical and physical properties for each isomer. Recognizing these isomers helps in understanding how subtle changes in structure can influence a molecule's behavior.

Geometric Isomers

Geometric isomers, also known as cis-trans isomers, are a type of stereoisomerism where compounds have the same structural formula but differ in the spatial arrangement of groups around a double bond. This isomerism arises because a double bond restricts rotation, so different spatial arrangements can occur. Key points include:

• **Cis isomers:** Similar or identical groups are on the same side of the double bond.
• **Trans isomers:** Similar or identical groups are on opposite sides of the double bond.

It is important to note that geometric isomers are specific to compounds with restricted rotation, like double-bonded alkenes. This differs from the position of the double bond itself, which can vary in larger alkenes but isn't referred to as geometric isomerism. Understanding the arrangement of atoms helps predict the stability and reactivity of molecules.

Substituted Benzenes

Substituted benzenes are benzene rings in which one or more hydrogen atoms are replaced by other atoms or groups of atoms. This substitution can heavily influence the benzene ring's reactivity and properties. Despite these changes, substituted benzenes cannot form cis-trans isomers due to the rigidity of the benzene ring's planar structure.
Unlike alkenes, where the double bond allows for cis and trans differences, the benzene ring's symmetry and resonance prevent such isomerism. This means that, regardless of the positions of substituents around the ring, the substituents cannot switch between 'sides' as they could in an alkene with a double bond. This structural characteristic maintains benzene's classic stability but limits isomer opportunities.