Acetone `overset( HCN) ( rarr) ( A) overset( H_(3) O^(+))(rarr) ( B ) `. In the above sequence of reaction A and B are `:`

Options

A. `( CH_(3))_(2) C( OH ) CN, ( CH_(3))_(2)C( OH ) COOH`
B. `( CH_(3))_(2)C(OH) CN, ( CH_(3))_(2)C ( OH)_(2)`
C. `( CH_(3))_(2)C(OH)CN,(CH_(3))_(2)CHCOOH`
D. `(CH_(3))_(2)C(OH)CN, ( CH_(3))_(2)C=O`

Answer

To solve the problem, we need to identify the products A and B from the given reaction sequence involving acetone and HCN followed by hydrolysis.

### Step-by-Step Solution:

1. **Identify the Reactants**:
The starting compound is acetone, which has the structure CH₃COCH₃.

2. **Reaction with HCN**:
When acetone reacts with HCN, the cyanide ion (CN⁻) acts as a nucleophile and attacks the carbonyl carbon of acetone. This leads to the formation of a cyanohydrin.

**Product A**: The product formed after the reaction with HCN is 2-hydroxy-2-methylpropanenitrile (or simply acetone cyanohydrin), which can be represented as:
\[ \text{A: } CH_3C(OH)(CN)CH_3 \]

3. **Hydrolysis of Product A**:
The next step involves the hydrolysis of the cyanohydrin (Product A) in the presence of an acid (H₃O⁺). During hydrolysis, the nitrile group (CN) is converted to a carboxylic acid (COOH).

The hydrolysis mechanism involves:
- Protonation of the hydroxyl group.
- Nucleophilic attack by water on the carbon atom.
- Rearrangement leading to the formation of a carboxylic acid.

**Product B**: The final product after hydrolysis is 2-hydroxy-2-methylpropanoic acid (or simply lactic acid), which can be represented as:
\[ \text{B: } CH_3C(OH)COOH \]

### Final Answer:
- **A**: Acetone cyanohydrin (CH₃C(OH)(CN)CH₃)
- **B**: Lactic acid (CH₃C(OH)COOH)

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