The specific rotation of a pure enantiomers is `+12^(@)`. What will be its observed rotation if it is isolated form a reaction with `20%` racemization and `80%` retention.

Options

A. `+9.6^(@)`
B. `-9.6^(@)`
C. `+2.4^(@)`
D. `-2.4^(@)`

Explanation

To solve the problem, we need to determine the observed rotation of a sample that has undergone racemization and retention of a specific enantiomer. Here's the step-by-step solution:

### Step 1: Understand the Given Information
- The specific rotation of the pure enantiomer is \( +12^\circ \).
- There is a 20% racemization, which means that 20% of the original enantiomer has converted to its enantiomer.
- 80% of the original enantiomer remains unchanged.

### Step 2: Calculate the Amount of Each Enantiomer
- If we assume we start with 100 parts of the pure enantiomer:
- 80% retention means \( 80 \) parts remain as the original enantiomer (let's call it \( [\alpha] \)).
- 20% racemization means \( 20 \) parts have converted to the opposite enantiomer (let's call it \( [\beta] \)).

### Step 3: Determine the Contribution to Optical Activity
- The contribution to optical activity from the retained enantiomer \( [\alpha] \):
\[ \text{Rotation from } [\alpha] = 80 \times +12^\circ = +960^\circ \]

- The contribution to optical activity from the formed enantiomer \( [\beta] \) (which has a specific rotation of \( -12^\circ \)):
\[ \text{Rotation from } [\beta] = 20 \times -12^\circ = -240^\circ \]

### Step 4: Calculate the Total Observed Rotation
- Now, we add the contributions from both enantiomers:
\[ \text{Total Rotation} = +960^\circ + (-240^\circ) = +720^\circ \]

### Step 5: Calculate the Specific Rotation
- The total amount of the sample is \( 100 \) parts (80 parts of \( [\alpha] \) and 20 parts of \( [\beta] \)).
- The specific rotation \( [\alpha]_{obs} \) can be calculated as:
\[ [\alpha]_{obs} = \frac{\text{Total Rotation}}{\text{Total Amount}} = \frac{720^\circ}{100} = +7.2^\circ \]

### Conclusion
The observed rotation of the sample after 20% racemization and 80% retention is \( +7.2^\circ \).

---