The specific rotation of a pure enantiomer is `+16^@`. The observed rotation, if it is isolated from a reaction with 25% racemisation and 75% inversion is

Options

A. `+12^@`
B. `-12^@`
C. `4^@`
D. `-4^@`

Answer

To solve the problem, we need to calculate the observed rotation of a pure enantiomer that has undergone a reaction resulting in 25% racemization and 75% inversion. The specific rotation of the pure enantiomer is given as +16°.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Specific rotation of the pure enantiomer (\[ \alpha_{pure} \]) = +16°
- Percentage of racemization = 25%
- Percentage of inversion (or retention) = 75%

2. **Calculate the Contribution from Inversion:**
- The observed rotation due to the retained enantiomer (inversion) can be calculated using the formula:
\[ \text{Observed Rotation} = \text{Specific Rotation} \times \text{Percentage Retention} \]
- Here, the percentage retention is 75%, which means:
\[ \text{Observed Rotation from Inversion} = +16° \times \frac{75}{100} = +12° \]

3. **Calculate the Contribution from Racemization:**
- The racemization results in the formation of the opposite enantiomer. Since 25% of the original enantiomer is converted to the opposite enantiomer, the contribution from this racemization will be:
\[ \text{Observed Rotation from Racemization} = -\text{Specific Rotation} \times \text{Percentage Racemization} \]
- Thus:
\[ \text{Observed Rotation from Racemization} = -16° \times \frac{25}{100} = -4° \]

4. **Combine the Contributions:**
- Now, we can find the total observed rotation by adding the contributions from inversion and racemization:
\[ \text{Total Observed Rotation} = \text{Observed Rotation from Inversion} + \text{Observed Rotation from Racemization} \]
- Therefore:
\[ \text{Total Observed Rotation} = +12° + (-4°) = +8° \]

### Final Answer:
The observed rotation, if it is isolated from a reaction with 25% racemization and 75% inversion, is **+8°**.