Question

The number of isomers possible for \(\mathrm{C}_{7} \mathrm{H}_{8} \mathrm{O}\) are (a) 3 (b) 4 (c) 5 (d) 6

Short answer

The correct number of isomers is 4.

Step-by-step solution

Understand the Molecular Formula

The molecular formula is \( \text{C}_7\text{H}_8\text{O} \). This indicates there are 7 carbon atoms, 8 hydrogen atoms, and 1 oxygen atom in each isomer.

Determine the Degree of Unsaturation

Calculate the degree of unsaturation using the formula: \[ U = C + 1 - \frac{H}{2} + \frac{N}{2} - \frac{X}{2} \] For \( \text{C}_7\text{H}_8\text{O} \), where \( C = 7 \), \( H = 8 \), and \( O = 1 \), we have:\[ U = 7 + 1 - \frac{8}{2} = 5\]This tells us that the molecule has 5 degrees of unsaturation, suggestive of five rings and/or double bonds.

Identify Possible Ring Structures

Given the 5 degrees of unsaturation, benzene ring structures are a likely option:- **Phenol**: A hydroxyl group \( (-OH) \) attached to a benzene ring.- **Toluene derivatives**: Toluene with different positions for \( -OH \), like ortho, meta, and para isomers.

List Possible Isomers

- **Phenol**: Benzene with \( -OH \) on one carbon.- **Toluene with \(-OH\)** : - **Ortho-cresol**: \( -OH \) and \( -CH_3 \) adjacent on benzene. - **Meta-cresol**: \( -OH \) and \( -CH_3 \) separated by one carbon on benzene. - **Para-cresol**: \( -OH \) and \( -CH_3 \) on opposite sides of benzene.

Count the Unique Structures

The unique structures we identified are: 1. Phenol 2. Ortho-cresol 3. Meta-cresol 4. Para-cresol Thus, there are 4 total unique isomers.

Key concepts

Molecular Formula

The molecular formula provides essential information about a compound, indicating the precise number and type of atoms involved. For the compound with the formula \( \text{C}_7\text{H}_8\text{O} \), it consists of 7 carbon atoms, 8 hydrogen atoms, and 1 oxygen atom. This formula does not show the particular structure or arrangement of the atoms, but it does suggest the potential for different structural possibilities, known as isomers.
In organic chemistry, structural variations can offer different physical and chemical properties, even when the molecular formula remains unchanged. Therefore, understanding the molecular formula is the first step in discovering potential isomers that might exist for a given compound.

Degree of Unsaturation

The degree of unsaturation, often symbolized as \( U \), tells us how many rings or double bonds a compound may have. The formula used to calculate the degree of unsaturation is:

• \[ U = C + 1 - \frac{H}{2} + \frac{N}{2} - \frac{X}{2} \]

where

• \( C \) is the number of carbon atoms,
• \( H \) is the number of hydrogen atoms,
• \( N \) is the number of nitrogen atoms, and
• \( X \) is the number of halogens.

For \( \text{C}_7\text{H}_8\text{O} \), since there are no nitrogen atoms or halogens, it simplifies to \( U = 7 + 1 - \frac{8}{2} = 5 \).
This tells us there are 5 unsaturations, which could be a combination of rings and double bonds. This is a critical clue in determining the likely structure of the isomers that the molecular formula might represent.

Phenol and Cresols

Phenol and the isomers of cresol (ortho-cresol, meta-cresol, and para-cresol) are classic examples of isomerism in aromatic compounds. Phenol is characterized by having a hydroxyl group \( (-OH) \) directly attached to a benzene ring. This setup is significant because the aromatic ring can significantly influence the chemical behavior of phenol.
Cresols are methylphenols where a methyl group \( (-CH_3) \) is attached alongside the hydroxyl group but in different positions on the benzene ring. In ortho-cresol, the methyl group is adjacent to the hydroxyl group. In meta-cresol, there is one carbon group separating the two, while in para-cresol, they are directly opposite each other on the benzene ring. These differences in position result in significant variations in the properties and uses of these compounds.

Benzene Ring Isomers

Benzene, with its six-carbon ring bonded by alternating single and double bonds, is a fundamental structure in organic chemistry. Its ability to support substitutions at various positions leads to different isomers. The isomer count, for a given molecular formula, depends on how the substituents (like \( -OH \) or \( -CH_3 \)) arrange themselves on the ring.
For \( \text{C}_7\text{H}_8\text{O} \), we recognize classic isomers like phenol and cresols. These represent different ways that functional groups can be attached to the benzene ring, resulting in distinct structural isomers. The ring's arrangement affects the chemical properties and potential applications in industries or research, demonstrating the benzene ring's versatility as a structural unit in chemistry.