In the given reaction
`CH_(3)COOH underset({:((ii)NaCN),((iii)H_(2)O //H^(o+)//Delta):})overset((i)Br_(2)//P)to[x],[x]` will be

Options

A. `CH_(3)-COOH`
B. `HOOC-CH_(2)-CH_(2)-COOH`
C.
D.

Answer

To solve the given reaction step by step, we will analyze each part of the reaction involving acetic acid (CH₃COOH) and the reagents provided.

### Step 1: Reaction with Br₂ in the presence of phosphorus
The first step involves the reaction of acetic acid (CH₃COOH) with bromine (Br₂) in the presence of phosphorus. This is a classic example of the **Hunsdiecker reaction** (or HVZ reaction) where the alpha-hydrogen of the carboxylic acid is replaced by a bromine atom.

**Reaction:**
\[ \text{CH}_3\text{COOH} + \text{Br}_2 \xrightarrow{\text{P}} \text{CH}_2\text{BrC(=O)OH} \]

**Product:**
The product formed is **2-bromoacetic acid** (CH₂BrC(=O)OH).

### Step 2: Reaction with NaCN
In the second step, sodium cyanide (NaCN) is added. Here, the bromine atom in 2-bromoacetic acid is substituted by the cyanide ion (CN⁻).

**Reaction:**
\[ \text{CH}_2\text{BrC(=O)OH} + \text{NaCN} \rightarrow \text{CH}_2\text{C(=O)OH} + \text{NaBr} \]

**Product:**
The product formed is **2-cyanoacetic acid** (CH₂C(=O)OH).

### Step 3: Hydrolysis
The next step involves hydrolysis of the cyanide group. When 2-cyanoacetic acid is hydrolyzed in the presence of water (H₂O) and an acid (H⁺), the cyanide group is converted into a carboxylic acid group.

**Reaction:**
\[ \text{CH}_2\text{C(=O)OH} + \text{H}_2\text{O} \xrightarrow{\text{H}^+} \text{CH}_2\text{C(=O)OH} \]

**Product:**
The product remains **2-carboxyacetic acid** (CH₂C(=O)OH).

### Step 4: Heating (Decarboxylation)
In the final step, heating leads to decarboxylation. Since there are two carboxylic acid groups in the molecule, one of them will be removed as carbon dioxide (CO₂).

**Reaction:**
\[ \text{CH}_2\text{C(=O)OH} \xrightarrow{\Delta} \text{CH}_3\text{C(=O)OH} + \text{CO}_2 \]

**Final Product:**
The final product is **acetic acid** (CH₃C(=O)OH).

### Summary
The final product (X) after the entire sequence of reactions is **acetic acid (CH₃C(=O)OH)**.

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