How many isomer of `C_(4)H_(8)O` when reacts with `CH_(3)MgBr` followed by acidification to give `2^(@)` alcohol (only consider carbonyl isomers) ?
(including stereoisomer)

Answer

To determine how many isomers of C₄H₈O can react with CH₃MgBr followed by acidification to yield a secondary alcohol, we will follow these steps:

### Step 1: Identify the possible carbonyl isomers of C₄H₈O.
The molecular formula C₄H₈O indicates that we are dealing with either aldehydes or ketones, as these are the carbonyl compounds. The possible carbonyl isomers of C₄H₈O include:
1. Butanal (an aldehyde)
2. 2-Butanone (a ketone)
3. 3-Butanone (a ketone)
4. Cyclobutanone (a cyclic ketone)

### Step 2: Determine which of these isomers can yield a secondary alcohol upon reaction with CH₃MgBr.
A secondary alcohol is formed when the carbon atom bonded to the hydroxyl group (OH) is attached to two other carbon atoms. Let's analyze each isomer:

1. **Butanal**:
- Reaction: Butanal (C₃H₇CHO) reacts with CH₃MgBr to form a secondary alcohol.
- Product: Butanol (C₄H₉OH) - This is a primary alcohol, so it does not count.

2. **2-Butanone**:
- Reaction: 2-Butanone (C₄H₈O) reacts with CH₃MgBr.
- Product: 2-Butanol (C₄H₉OH) - This is a secondary alcohol, so it counts.

3. **3-Butanone**:
- Reaction: 3-Butanone (C₄H₈O) reacts with CH₃MgBr.
- Product: 3-Butanol (C₄H₉OH) - This is also a secondary alcohol, so it counts.

4. **Cyclobutanone**:
- Reaction: Cyclobutanone (C₄H₈O) reacts with CH₃MgBr.
- Product: A secondary alcohol is formed, as the carbonyl carbon is bonded to two other carbons in the ring.

### Step 3: Count the isomers that yield secondary alcohols.
From our analysis:
- 2-Butanone yields 2-Butanol (secondary alcohol).
- 3-Butanone yields 3-Butanol (secondary alcohol).
- Cyclobutanone yields a secondary alcohol.

### Step 4: Consider stereoisomers.
For both 2-Butanol and 3-Butanol, we can have stereoisomers due to the presence of chiral centers:
- 2-Butanol has one chiral center, leading to two stereoisomers (R and S).
- 3-Butanol also has one chiral center, leading to two stereoisomers (R and S).
- Cyclobutanone does not have any stereocenters.

### Final Count:
- 2-Butanol: 2 stereoisomers
- 3-Butanol: 2 stereoisomers
- Cyclobutanone: 1 isomer (no stereoisomers)

Thus, the total number of isomers that yield secondary alcohols is:
- 2 (from 2-Butanol) + 2 (from 3-Butanol) + 1 (from Cyclobutanone) = 5 isomers.

### Conclusion:
The total number of isomers of C₄H₈O that can react with CH₃MgBr followed by acidification to give a secondary alcohol is **5**.

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