Specific Rotation Formula (Optical Activity)
The specific rotation formula measures the optical activity of chiral molecules.
Used in pharmaceutical purity testing and sugar analysis.
The Formula
Specific rotation is a physical property of chiral (optically active) molecules — molecules that are non-superimposable on their mirror image. When plane-polarized light passes through a solution of such a molecule, the plane of polarization is rotated. The specific rotation is a standardized measure of this rotation, independent of concentration and path length.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| [α]DT | Specific rotation at temperature T, using sodium D line (589 nm) | deg·mL/(g·dm) or ° |
| α | Observed rotation measured by polarimeter | degrees (°) |
| l | Path length (length of sample tube) | decimeters (dm) |
| c | Concentration of the optically active compound | g/mL |
| (+) | Dextrorotatory — rotates light clockwise | — |
| (−) | Levorotatory — rotates light counterclockwise | — |
Example 1 — Sucrose Measurement
A 10 g/100 mL sucrose solution in a 1 dm tube shows α = +6.65°. Calculate specific rotation.
c = 10 g/100 mL = 0.1 g/mL
l = 1 dm
[α] = α / (l × c) = 6.65 / (1 × 0.1)
[α]D20 = +66.5° — matches the accepted value for sucrose!
Example 2 — Pharmaceutical Purity Test
A batch of pure L-glucose should have [α]D20 = −52.7°. A sample (c = 0.05 g/mL, l = 2 dm) shows α = −4.8°. Is it pure?
Calculated [α] = −4.8 / (2 × 0.05) = −4.8 / 0.1 = −48.0°
Measured [α] = −48.0° vs expected −52.7° — 8.9% deviation suggests the sample may contain the D-enantiomer or an impurity. Further testing required.
When to Use It
Use the specific rotation formula when:
- Pharmaceuticals: Many drugs are chiral; only one enantiomer is active. The FDA requires specific rotation measurements for chiral drug purity.
- Sugar industry: "Saccharimetry" uses specific rotation to determine sucrose content. Sucrose (+66.5°), glucose (+52.7°), fructose (−92.4°).
- Amino acid analysis: All natural amino acids are L-form with known specific rotations.
- Food and beverage: Honey authentication (specific rotation reveals adulteration with corn syrup).
- Essential oil analysis: Terpenes have characteristic specific rotations used for authenticity testing.