Identify the compounds (X), (Y) and (Z) in the following reaction :
`CH_(3)Broverset(Mg//ether)toX overset((i)CO_(2))underset((ii)"water")to Y overset(CH_(3)OH,H^(+))underset(Delta)toZ`

Options

A. `(X)=CH_(3)MgBr, (Y)=CH_(3)COOH, (Z)=CH_(3)COOCH_(3)`
B. `(X)=CH_(3)CH_(2)Br, (Y)=CH_(3)CH_(2)OH, (Z)=CH_(3)CH_(2)CH_(2)CH_(3)`
C. `(X)=CH_(3)CH_(2)MgBr, (Y)=CH_(3)CH_(2)COOH, (Z)=CH_(3)CH_(2)COCH_(3)`
D. `(X)=CH_(3)COOH, (Y)=CH_(3)CH_(2)COCH_(3), (Z)=CH_(3)COOCH_(3)`

Explanation

To identify the compounds (X), (Y), and (Z) in the given reaction sequence, we will analyze each step of the reaction systematically.

### Step 1: Formation of Compound (X)
The reaction starts with methyl bromide (CH₃Br) reacting with magnesium (Mg) in ether. This reaction forms a Grignard reagent.

**Reaction:**
\[ \text{CH}_3\text{Br} + \text{Mg} \xrightarrow{\text{ether}} \text{X} \]

**Compound (X):**
The Grignard reagent formed is methyl magnesium bromide, represented as:
\[ \text{X} = \text{CH}_3\text{MgBr} \]

### Step 2: Reaction of Compound (X) with CO₂ and Water
Next, compound (X) reacts with carbon dioxide (CO₂) followed by water (H₂O). The Grignard reagent reacts with CO₂ to form a carboxylic acid.

**Reaction:**
\[ \text{X} + \text{CO}_2 \xrightarrow{} \text{Y} \]
After the reaction with CO₂, the product is a carboxylic acid, which upon protonation with water gives:
\[ \text{Y} = \text{CH}_3\text{COOH} \] (acetic acid)

### Step 3: Reaction of Compound (Y) with Methanol
Finally, compound (Y) (acetic acid) is heated with methanol (CH₃OH). This reaction leads to the formation of an ester.

**Reaction:**
\[ \text{Y} + \text{CH}_3\text{OH} \xrightarrow{\Delta} \text{Z} \]

**Compound (Z):**
The product formed from the reaction of acetic acid with methanol is methyl acetate:
\[ \text{Z} = \text{CH}_3\text{COOCH}_3 \]

### Summary of Compounds
- **Compound (X)**: CH₃MgBr (Methyl magnesium bromide)
- **Compound (Y)**: CH₃COOH (Acetic acid)
- **Compound (Z)**: CH₃COOCH₃ (Methyl acetate)

### Final Answer
- **X** = CH₃MgBr
- **Y** = CH₃COOH
- **Z** = CH₃COOCH₃