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.

Short Answer

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(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 by step solution

01

(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.
02

(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.
03

(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.

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