Optical activity
Chiral molecules, such as many sugars, amino acids and drugs, rotate the plane of polarized light. A polarimeter measures this rotation in degrees. The value depends on the compound, but also on how much of it the light passes through, so chemists convert it to a standard specific rotation.
The formula
[α] = α ÷ (l × c)
- α: observed rotation, in degrees;
- l: path length of the cell, in decimeters (a standard cell is 1 dm, or 10 cm);
- c: concentration, in grams per milliliter (5 g/100 mL = 0.05 g/mL). For a pure liquid, use its density.
The specific rotation is reported with the temperature and the wavelength, usually the sodium D line (589 nm), for example [α]D²⁰ = +66.5 for sucrose in water.
Example
A sample reads +2.50° in a 1 dm cell at 5 g/100 mL:
- [α] = 2.50 ÷ (1 × 0.05) = +50.0;
- the pure enantiomer has [α] = +66.5, so the optical purity is 50.0 ÷ 66.5 ≈ 75.2%;
- the mixture contains about 87.6% of the (+) enantiomer and 12.4% of the (−) enantiomer.
Enantiomeric excess
ee = (major − minor) ÷ (major + minor) × 100
When the rotation is proportional to the excess, the optical purity equals the enantiomeric excess. Then:
- major enantiomer = (100 + ee) ÷ 2;
- minor enantiomer = (100 − ee) ÷ 2.
A racemic mixture (50:50) has no rotation and an ee of 0%.
Signs and names
- Dextrorotatory (+ or d): rotates the light clockwise as seen by the observer.
- Levorotatory (− or l): rotates it counterclockwise.
The sign of rotation is not linked to the R or S configuration: it must be measured.
Limits
- Specific rotation changes with solvent, concentration, temperature and wavelength; compare only with literature values measured under the same conditions.
- Impurities that are themselves optically active distort the result.
- For precise ee values, chiral HPLC or NMR with chiral shift reagents are more reliable than polarimetry.
- Rotations above 180° are ambiguous; measuring at two concentrations resolves them.