The specific rotation of a pure enantiomer is `+10^(@)`. The observed rotation, if it is isolated from a reaction with `30%` recemisation and `70%` inversion is

Options

A. `+10^(@)`
B. `-10^(@)`
C. `3^(@)`
D. `-7^(@)`

Answer

To solve the problem, we need to calculate the observed rotation of a mixture that has undergone 30% racemization and 70% inversion. The specific rotation of the pure enantiomer is given as +10°.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Specific Rotation**: This is the rotation of plane-polarized light by a chiral compound in a specific concentration and path length. For our pure enantiomer, it is +10°.
- **Racemization**: This process converts a pure enantiomer into a racemic mixture (equal amounts of both enantiomers), which has an observed rotation of 0°.
- **Inversion**: This process converts a portion of one enantiomer into the other, affecting the overall observed rotation.

2. **Calculate the Contribution from Racemization**:
- If 30% of the pure enantiomer undergoes racemization, then 30% of the original enantiomer will contribute to the observed rotation as follows:
- Original enantiomer = 100%
- After 30% racemization, 70% remains as the original enantiomer.
- The contribution from the racemized portion (30%) will be 0° because it forms a racemic mixture.

3. **Calculate the Contribution from Inversion**:
- The inversion affects 70% of the original enantiomer:
- The remaining 70% of the original enantiomer will still contribute to the observed rotation.
- Since the specific rotation of the pure enantiomer is +10°, the contribution from this 70% is:
\[ \text{Observed rotation from inversion} = 70\% \times +10° = 0.7 \times 10° = +7° \]

4. **Combine the Contributions**:
- The total observed rotation is the sum of the contributions from the remaining enantiomer and the racemized portion:
\[ \text{Total observed rotation} = \text{Rotation from remaining enantiomer} + \text{Rotation from racemization} \]
\[ \text{Total observed rotation} = +7° + 0° = +7° \]

### Final Answer:
The observed rotation, if it is isolated from a reaction with 30% racemization and 70% inversion, is **+7°**.