Identify the final product (Z) in the following sequence of reactions :
` Me_2 CO + HCN to X overset(H_3 O^+) to Y underset("Heat ") overset( H_2 SO_4) to Z `

Options

A. `(CH_3)_2 C (OH) COOH `
B. `CH_2=C (CH_3)COOH`
C. `HOCCH_2 CH (CH_3)COOH`
D. `CH_3CH = CHCOOH `

Explanation

To identify the final product (Z) in the given sequence of reactions, let's break down the steps systematically:

### Step 1: Reaction of Acetone with HCN
The starting compound is acetone (Me₂CO), which is CH₃C(=O)CH₃. When acetone reacts with HCN, the cyanide ion (CN⁻) acts as a nucleophile and attacks the carbonyl carbon of acetone.

**Reaction:**
\[ \text{CH}_3C(=O)\text{CH}_3 + \text{HCN} \rightarrow \text{CH}_3C(OH)(CN)\text{CH}_3 \]

**Product (X):**
The product formed is a cyanohydrin, specifically:
\[ \text{X} = \text{CH}_3C(OH)(CN)\text{CH}_3 \]

### Step 2: Hydrolysis of the Cyanohydrin
Next, we treat the cyanohydrin (X) with an acid (H₃O⁺) to hydrolyze the CN group into a carboxylic acid.

**Reaction:**
\[ \text{CH}_3C(OH)(CN)\text{CH}_3 + \text{H}_2O \rightarrow \text{CH}_3C(OH)(COOH)\text{CH}_3 \]

**Product (Y):**
The product after hydrolysis is:
\[ \text{Y} = \text{CH}_3C(OH)(COOH)\text{CH}_3 \]

### Step 3: Dehydration of the Hydroxy Acid
Now, we heat the hydroxy acid (Y) in the presence of sulfuric acid (H₂SO₄). This step involves dehydration, where water is eliminated.

**Reaction:**
When heated, the hydroxyl group (OH) can be removed, leading to the formation of an alkene:
\[ \text{CH}_3C(OH)(COOH)\text{CH}_3 \overset{\text{Heat}}{\rightarrow} \text{CH}_3C(COOH)=C\text{CH}_3 + \text{H}_2O \]

**Product (Z):**
The final product (Z) formed is:
\[ \text{Z} = \text{CH}_3C(COOH)=C\text{CH}_3 \]

### Final Product
Thus, the final product (Z) is a compound with a double bond and a carboxylic acid group:
\[ \text{Z} = \text{CH}_2=CH\text{COOH} \]

### Conclusion
The final product (Z) is:
\[ \text{Z} = \text{CH}_2=CH\text{COOH} \]