Problem 31 - Chemistry The Central Science In Si Units

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, (b) False, (c) False.

Step 1: Identify Isomers - Statement (a)

The three isomers of dimethylbenzene are based on the positions of the methyl groups on the benzene ring. These positions can be ortho (o-), meta (m-), and para (p-), where the numbers assigned to the carbon atoms on the benzene ring determine the isomer. - Ortho (o-) refers to positions 1,2. - Meta (m-) refers to positions 1,3. - Para (p-) refers to positions 1,4. These correspond to the only structural isomers for dimethylbenzene.

Step 2: Evaluate Definition of Geometric Isomers - Statement (b)

Alkenes can potentially have geometric isomers (cis and trans) if there is restricted rotation around the carbon-carbon double bond, and each carbon in that bond has different groups attached. However, geometric isomers specifically deal with the spatial arrangement of groups around the double bond, not just different positions of the double bond in the carbon chain. Hence, alkenes with different positions of a C=C double bond are classified as structural isomers instead of geometric isomers.

Step 3: Check for Cis-Trans Isomerism - Statement (c)

Cis and trans isomerism occurs in alkenes that have two different groups attached to the carbon atoms in the double bond, leading to two distinct spatial arrangements (cis or trans) of these groups. Benzene rings with substituents cannot exhibit cis-trans isomerism since they contain no such double bond and are planar structures, where substituents have free rotation. Thus, substituted benzenes do not form cis and trans isomers.

Key Concepts

Dimethylbenzene

Dimethylbenzene, also known by the common name xylene, is an aromatic hydrocarbon that consists of a benzene ring with two methyl groups attached. These methyl groups can be situated at different positions around the benzene ring, leading to the formation of three distinct structural isomers: ortho (o-), meta (m-), and para (p-). This type of isomerism specifically involves the arrangement of the methyl groups at these different positions.

• Ortho dimethylbenzene: Here, the methyl groups are positioned on adjacent carbon atoms, defined as 1,2-positions.
• Meta dimethylbenzene: In this configuration, the methyl groups are separated by one carbon atom, occupying the 1,3-positions.
• Para dimethylbenzene: This isomer involves the methyl groups being opposite each other on the benzene ring, located at the 1,4-positions.

These are the only forms dimethylbenzene can take, thanks to the rigid structure of the benzene molecule, which influences the spatial arrangement of any substituents attached to it.

Geometric Isomers

Geometric isomers, a subtype of stereoisomers, occur when there is restricted rotation around a bond, most commonly seen in alkenes (compounds with carbon-carbon double bonds). For an alkene to exhibit geometric isomerism, each carbon atom of the double bond must have two different groups attached. This restriction in rotation allows for distinct spatial arrangements of these groups, primarily classified as cis or trans.

• Cis isomers have similar or identical groups on the same side of the double bond.
• Trans isomers have similar or identical groups on opposite sides of the double bond.

It's important to note that the existence of geometric isomers isn't merely about changes in position of the double bond itself, but specifically the arrangement of different groups around that bond. Thus, alkenes varying in the position of a double bond alone are considered structural isomers, not geometric.

Cis-Trans Isomerism

Cis-trans isomerism is frequently associated with alkenes due to their carbon-carbon double bonds which provide fixed spatial arrangements for substituents. This type of isomerism refers to how the substituents are oriented around the double bond.

• "Cis" implies the substituents are on the same side, causing potential stereo hindrance.
• "Trans" indicates the substituents are on opposite sides, often resulting in a more stable, lower-energy configuration.

However, substituted benzenes don't fit into this classification. The benzene ring itself is a planar structure with delocalized electrons and lacks the fixed double bonds necessary for cis-trans variations. As such, any substituents placed on a benzene ring have free rotation around the ring's plane, negating the possibility of forming cis or trans isomers. This key difference emphasizes why cis-trans isomerism is not applicable to aromatic compounds such as dimethylbenzene.