Consider all possible isomeric ketones, including stereoisomers, of MW = 100. All these isomers are independently reacted with `NaBH_(4)` (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are
Consider all possible isomeric ketones, including stereoisomers, of MW = 100. All these isomers are independently reacted with `NaBH_(4)` (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are
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The correct Answer is:
To solve the problem of determining the total number of isomeric ketones (including stereoisomers) of molecular weight 100 that give racemic products when reacted with NaBH4, we can follow these steps:
### Step 1: Determine the General Formula for Ketones
The general formula for ketones is \( C_nH_{2n}O \). Given the molecular weight (MW) is 100, we can set up the equation for the molecular weight:
\[
12n + 2n + 16 = 100
\]
### Step 2: Solve for \( n \)
Combining the terms gives us:
\[
14n + 16 = 100
\]
Subtracting 16 from both sides:
\[
14n = 84
\]
Dividing by 14:
\[
n = 6
\]
### Step 3: Write the Molecular Formula
Now that we have \( n = 6 \), we can write the molecular formula for the ketones:
\[
C_6H_{12}O
\]
### Step 4: Identify Possible Isomers
Next, we need to identify all possible structural isomers of \( C_6H_{12}O \). The structural isomers of ketones can be drawn, and we should also consider stereoisomers.
1. **Isomer A**: 2-Hexanone (no chiral centers)
2. **Isomer B**: 3-Hexanone (no chiral centers)
3. **Isomer C**: 4-Methyl-2-pentanone (no chiral centers)
4. **Isomer D**: 3-Methyl-3-pentanone (chiral center)
5. **Isomer E**: 2-Pentanone (no chiral centers)
6. **Isomer F**: 2-Methyl-3-pentanone (chiral center)
### Step 5: Analyze Chiral Centers
Now, we need to analyze which of these isomers have chiral centers. A chiral center is a carbon atom that has four different groups attached to it.
- **Isomers A, B, C, E**: No chiral centers, hence they will give racemic mixtures.
- **Isomers D, F**: Have chiral centers, hence they will give diastereomers and not racemic mixtures.
### Step 6: Count the Isomers Giving Racemic Mixtures
From our analysis:
- Isomers A, B, C, and E give racemic mixtures.
- Isomers D and F do not give racemic mixtures.
Thus, the total number of ketones that give racemic products is:
\[
\text{Total} = 4 \text{ (Isomers A, B, C, E)}
\]
### Final Answer
The total number of ketones that give racemic products is **4**.
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