Write the formula for optical purity & enantiomeric excess.

Answer

To solve the question regarding the formulas for optical purity and enantiomeric excess, we will break down the definitions and derive the formulas step by step.

### Step 1: Understanding Optical Purity
Optical purity is a measure of the purity of an optically active compound in terms of its enantiomers. It is defined as the ratio of the observed optical rotation of a mixture to the optical rotation of a pure enantiomer.

**Formula for Optical Purity:**
\[ \text{Optical Purity} = \left( \frac{\text{Observed Optical Rotation}}{\text{Optical Rotation of Pure Enantiomer}} \right) \times 100 \]

### Step 2: Understanding Enantiomeric Excess
Enantiomeric excess (ee) is a measure of the excess of one enantiomer over the other in a mixture. It indicates the degree of asymmetry in the mixture of enantiomers.

**Formula for Enantiomeric Excess:**
\[ \text{Enantiomeric Excess} = \left( \frac{\text{Amount of one enantiomer} - \text{Amount of the other enantiomer}}{\text{Total amount of both enantiomers}} \right) \times 100 \]

Alternatively, it can also be expressed in terms of specific rotations:
\[ \text{Enantiomeric Excess} = \left( \frac{[\alpha]_{d} - [\alpha]_{l}}{[\alpha]_{d} + [\alpha]_{l}} \right) \times 100 \]
where \([\alpha]_{d}\) is the specific rotation of the dextrorotatory enantiomer and \([\alpha]_{l}\) is the specific rotation of the levorotatory enantiomer.

### Summary of Formulas
1. **Optical Purity**:
\[ \text{Optical Purity} = \left( \frac{\text{Observed Optical Rotation}}{\text{Optical Rotation of Pure Enantiomer}} \right) \times 100 \]

2. **Enantiomeric Excess**:
\[ \text{Enantiomeric Excess} = \left( \frac{\text{Amount of one enantiomer} - \text{Amount of the other enantiomer}}{\text{Total amount of both enantiomers}} \right) \times 100 \]