A compound 'X' on treatment with `Br_(2)//NaOH`, provided `C_(3)H_(9)N`, which gives positive carbylamine test. Compound 'X' is :

Options

A. `CH_(3) CH_(2) CH_(2) CONH_(2)`
B. `CH_(3) CON(CH_(3)) _(2)`
C. `CH_(3) COCH_(2), NHCH_(3)`
D. `CH_(3) CH_(2) COCH_(2) NH_(2)`

Explanation

To solve the problem, we need to identify the compound 'X' that, when treated with `Br2/NaOH`, produces `C3H9N`, which gives a positive carbylamine test. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Reaction
The reaction mentioned is a type of reaction known as the Hofmann bromamide reaction. In this reaction, a primary amide reacts with bromine and sodium hydroxide to yield a primary amine.

### Step 2: Analyze the Product
The product given is `C3H9N`, which indicates that it is a primary amine. The positive carbylamine test confirms that this amine is a primary amine since only primary amines give a positive result in this test.

### Step 3: Determine the Structure of the Amine
Since `C3H9N` is a primary amine, we can deduce that it has the structure of R-NH2, where R is an alkyl group. Given that the molecular formula has three carbons, we can represent it as:
- Propylamine: `CH3-CH2-CH2-NH2` (3 carbons)

### Step 4: Relate the Amine to Compound 'X'
Since the reaction produces a primary amine from a primary amide, we can conclude that the compound 'X' must be a primary amide with one more carbon than the amine. Therefore, if the amine has three carbons, the amide must have four carbons:
- The structure of the amide would be R-CO-NH2, where R has three carbons.

### Step 5: Identify the Correct Compound 'X'
Now, we need to find a suitable primary amide with four carbons. The options provided are:
1. `CH3-CH2-CH2-CO-NH2` (butyric amide)
2. `CH3-CO-NH-CH3` (acetamide, not primary)
3. `CH3-CO-CH2-NH-CH3` (not primary)
4. `CH3-CH2-CO-CH2-NH2` (butyric amide, but not the correct structure)

The correct compound 'X' is the first option: `CH3-CH2-CH2-CO-NH2`.

### Final Answer
The compound 'X' is `CH3-CH2-CH2-CO-NH2` (butyric amide).

---