How many isomers of molecular formula `C_(3)H_(9)N` will liberate `N_(2)` gas on treatment with `HNO_(2)`?

Options

A. One
B. Three
C. Two
D. Five

Answer

To determine how many isomers of the molecular formula \( C_3H_9N \) will liberate \( N_2 \) gas on treatment with \( HNO_2 \), we need to analyze the types of amines present in this molecular formula and their reactions with nitrous acid (\( HNO_2 \)).

### Step-by-Step Solution:

1. **Identify the Types of Amines**:
The molecular formula \( C_3H_9N \) can correspond to primary, secondary, or tertiary amines.
- Primary amines: \( RNH_2 \)
- Secondary amines: \( R_2NH \)
- Tertiary amines: \( R_3N \)

2. **Determine Which Amines Liberate \( N_2 \)**:
- **Primary Amines**: When primary amines react with \( HNO_2 \), they form an unstable diazonium salt which decomposes to liberate \( N_2 \) gas.
- **Secondary Amines**: Secondary amines do not liberate \( N_2 \) gas upon reaction with \( HNO_2 \).
- **Tertiary Amines**: Tertiary amines do not react with \( HNO_2 \) to liberate \( N_2 \) gas.

3. **Identify Possible Isomers**:
We need to find the structural isomers of \( C_3H_9N \) that are primary amines:
- **Isomer 1**: Propylamine (\( CH_3CH_2CH_2NH_2 \))
- **Isomer 2**: Isopropylamine (\( (CH_3)_2CHNH_2 \))

4. **Count the Primary Amines**:
From the isomers identified, both propylamine and isopropylamine are primary amines and will liberate \( N_2 \) gas when treated with \( HNO_2 \).

5. **Conclusion**:
Therefore, there are **2 isomers** of \( C_3H_9N \) that will liberate \( N_2 \) gas on treatment with \( HNO_2 \).

### Final Answer:
The number of isomers of molecular formula \( C_3H_9N \) that liberate \( N_2 \) gas on treatment with \( HNO_2 \) is **2**.

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