Specific rotation

The variance of specific rotation with wavelength—a phenomenon known as optical rotatory dispersion—can be used to find the absolute configuration of a molecule.

The CRC Handbook of Chemistry and Physics defines specific rotation as: For an optically active substance, defined by [α]θλ = α/γl, where α is the angle through which plane polarized light is rotated by a solution of mass concentration γ and path length l. Here θ is the Celsius temperature and λ the wavelength of the light at which the measurement is carried out.

[4] These values should always be accompanied by information about the temperature, solvent and wavelength of light used, as all of these variables can affect the specific rotation.

There is a linear relationship between the observed rotation and the concentration of optically active compound in the sample.

This equation is used: In this equation, α (Greek letter "alpha") is the measured rotation in degrees, l is the path length in decimeters, and ρ (Greek letter "rho") is the density of the liquid in g/mL, for a sample at a temperature T (given in degrees Celsius) and wavelength λ (in nanometers).

For solutions, a slightly different equation is used: In this equation, α (Greek letter "alpha") is the measured rotation in degrees, l is the path length in decimeters, c is the concentration in g/mL, T is the temperature at which the measurement was taken (in degrees Celsius), and λ is the wavelength in nanometers.

In this case, a correction factor in the numerator is necessary:[1]: 248 [3]: 123 When using this equation, the concentration and the solvent may be provided in parentheses after the rotation.

In cases of very small or very large angles, one can also use the variation of specific rotation with wavelength to facilitate measurement.

Moreover, the optical rotation of a compound may be non-linearly dependent on its enantiomeric excess because of aggregation in solution.

For these reasons other methods of determining the enantiomeric ratio, such as gas chromatography or HPLC with a chiral column, are generally preferred.