`C_(7)H_(9)N` has how many isomeric forms that contain a benzene ring?

Options

A. 4
B. 5
C. 6
D. 7

Answer

To determine the number of isomeric forms of the compound with the molecular formula \( C_7H_9N \) that contain a benzene ring, we can follow these steps:

### Step 1: Analyze the Molecular Formula
The molecular formula \( C_7H_9N \) indicates that we have a total of 7 carbon atoms, 9 hydrogen atoms, and 1 nitrogen atom. Since we need to include a benzene ring in our structure, we know that the benzene ring contributes 6 carbon atoms and 5 hydrogen atoms.

### Step 2: Determine Remaining Atoms
After accounting for the benzene ring, we have:
- Remaining Carbons: \( 7 - 6 = 1 \)
- Remaining Hydrogens: \( 9 - 5 = 4 \)
- Remaining Nitrogens: \( 1 \)

This means we need to arrange 1 carbon, 4 hydrogens, and 1 nitrogen as substituents on the benzene ring.

### Step 3: Identify Possible Substituents
The remaining atoms can be arranged in several ways:
1. The nitrogen can be part of an amino group (\(-NH_2\)).
2. The carbon can be part of a methyl group (\(-CH_3\)).
3. The carbon can also be part of a methylene group (\(-CH_2-\)).

### Step 4: Create Isomers
Now we can create isomers by placing the substituents in different positions relative to the benzene ring:
1. **Amino Group at the ortho position**:
- \( C_6H_4(NH_2)(CH_3) \) (ortho)
2. **Amino Group at the meta position**:
- \( C_6H_4(NH_2)(CH_3) \) (meta)
3. **Amino Group at the para position**:
- \( C_6H_4(NH_2)(CH_3) \) (para)
4. **N-Methyl Amino Group**:
- \( C_6H_4(N(CH_3)_2) \)

### Step 5: Count the Isomers
From the above arrangements, we can summarize the isomeric forms:
1. Ortho isomer with \( NH_2 \) and \( CH_3 \)
2. Meta isomer with \( NH_2 \) and \( CH_3 \)
3. Para isomer with \( NH_2 \) and \( CH_3 \)
4. N-Methyl isomer

In total, we find **5 distinct isomeric forms** that contain a benzene ring.

### Final Answer
The total number of isomeric forms of \( C_7H_9N \) that contain a benzene ring is **5**.

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