The number of isomeric amines corresponding to molecular formula `C_(3)H_(9)N`, which liberate `N_(2)` gas on treatment with nitrous acid is

Explanation

To solve the problem of finding the number of isomeric amines corresponding to the molecular formula \( C_3H_9N \) that liberate \( N_2 \) gas on treatment with nitrous acid, we can follow these steps:

### Step 1: Identify the possible isomeric amines
The molecular formula \( C_3H_9N \) indicates that we are dealing with amines. We can have primary, secondary, and tertiary amines.

1. **Primary amine**: The simplest primary amine is propylamine, \( CH_3CH_2CH_2NH_2 \).
2. **Secondary amines**: We can have isopropylamine, \( (CH_3)_2CHNH_2 \).
3. **Tertiary amines**: The tertiary amine can be \( (CH_3)_3CN \).

Thus, the possible isomers are:
- **1° amine**: Propylamine
- **2° amine**: Isopropylamine
- **3° amine**: Trimethylamine

### Step 2: Determine which amines liberate \( N_2 \) gas with nitrous acid
When amines react with nitrous acid (\( HNO_2 \)), primary amines produce nitrogen gas (\( N_2 \)) while secondary amines typically produce nitrous oxide (\( N_2O \)) or do not liberate nitrogen gas. Tertiary amines do not react with nitrous acid to liberate nitrogen gas.

1. **Primary amine (Propylamine)**: Reacts with nitrous acid to liberate \( N_2 \).
2. **Secondary amine (Isopropylamine)**: Does not liberate \( N_2 \) gas.
3. **Tertiary amine (Trimethylamine)**: Does not react to liberate \( N_2 \) gas.

### Step 3: Conclusion
From the analysis, only the primary amine (propylamine) liberates \( N_2 \) gas when treated with nitrous acid. Therefore, there is only **one isomeric amine** corresponding to \( C_3H_9N \) that liberates \( N_2 \) gas.

### Final Answer
The number of isomeric amines corresponding to the molecular formula \( C_3H_9N \) that liberate \( N_2 \) gas on treatment with nitrous acid is **1**.

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