in the reaction
` 2CH_3 underset(O ) underset(||) C CH_3 underset("Catalyst ") overset("Base") to A underset("Catalyst") overset("Acid ") to B `
the product B is

Options

A. `CH_3 COH (CH_3 )CH_2 COCH_3`
B. `CH_3COH (CH_3 ) CH_2 COOH `
C. `CH_3 C (CH_3 ) =CH COCH_3`
D. `CH_3 CH=CHCH_2 COCH_3`

Explanation

To solve the problem, we need to analyze the given reaction step by step.

### Step 1: Identify the Reactants
The reactants in the reaction are two molecules of 2-butanone (CH₃C(O)CH₃). This is a ketone with the structure:

```
O
||
CH₃-C-CH₃
```

### Step 2: Understand the Reaction Conditions
The reaction is performed in the presence of a base catalyst initially. The base catalyst is typically a hydroxide ion (OH⁻), which suggests that we are likely performing an aldol condensation reaction.

### Step 3: Perform the Aldol Condensation
When two molecules of 2-butanone react under basic conditions, they undergo an aldol condensation. The base deprotonates one of the alpha-hydrogens, leading to the formation of an enolate ion. This enolate ion then attacks the carbonyl carbon of another 2-butanone molecule.

The reaction can be represented as follows:
1. Formation of the enolate ion:
```
CH₃C(O)CH₃ + OH⁻ → CH₃C(−)C(=O)CH₃
```

2. Nucleophilic attack:
```
CH₃C(−)C(=O)CH₃ + CH₃C(O)CH₃ → CH₃C(OH)(C=O)CH₂C(=O)CH₃
```

### Step 4: Dehydration to Form Product A
The product formed after the aldol condensation is a β-hydroxy ketone. This intermediate can undergo dehydration (loss of water) to form an α,β-unsaturated ketone.

### Step 5: Acid-Catalyzed Reaction
The next step involves the addition of an acid catalyst (H⁺). This step typically involves protonation of the carbonyl oxygen, making the carbonyl carbon more electrophilic, which can lead to further reactions or rearrangements.

### Step 6: Identify Product B
After the acid-catalyzed step, the final product B is likely to be mesityl oxide, which has the structure:

```
O
||
CH₃-C-CH=C-CH₃
```

Thus, the final product B is **mesityl oxide (4-methyl-3-penten-2-one)**.

### Final Answer
The product B is **mesityl oxide (4-methyl-3-penten-2-one)**.

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