Specific rotation

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The specific rotation of a chemical compound [α]_D is defined as the observed angle of optical rotation α when light of 589 nanometer wavelength (the sodium D line) is passed through a sample with a path length of 0.1 meter and a sample concentration of 1 gram per deciliter. The specific rotation of a pure material is an intrinsic property of that material at a given wavelength and temperature. Values should always be accompanied by the temperature at which the measurement was performed and the solvent in which the material was dissolved (though water is often implied). The formal unit for specific rotation values is deg cm² g^-1 but scientific literature usually uses just degrees. A negative value means levorotatory rotation and a positive value means dextrorotatory rotation. Some examples:

Sucrose +66.47°
cholesterol −31.5°
Camphor +44.26°
Penicillin V +223°
taxol −49°
(S)-bromobutane +23.1°
(R)-bromobutane −23.1°
(+)-cavicularin +168.2°

Optical rotation is measured with an instrument called a polarimeter. There is a linear relationship between the observed rotation and the amount of optically active compound in the sample:

[[alpha]_\lambda^T = \frac]

where l is the path length and c is the concentration, for a sample at a temperature T and wavelength λ. If a compound has a very large specific rotation or a sample is very concentrated, the actual rotation of the sample may be larger than 180°. However, a single polarimeter measurement cannot detect when this has happened (for example, the values +270° and –90° are not distinguishable, nor are the values 361° and 1°). In these cases, measuring the rotation at several different concentrations allows one to determine the true value.

Measuring optical rotation provides a way to assess optical purity of a sample containing a mixture of enantiomers. For example, if a sample of bromobutane measured under standard conditions has an observed rotation of −9.2°, this indicates that the net effect is due to (100%)(9.2°/23.1°)=40% of the R enantiomer. The remainder of the sample is a racemic mixture of the enantiomers (30% R and 30% S), which has no net contribution to the observed rotation. The enantiomeric excess is 40%; the total concentration of R is 70%.

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