Specific rotation

In chemistry, specific rotation ([α]) is a property of a chiral chemical compound. It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sample of a compound in solution. Compounds which rotate the plane of polarization of a beam of plane polarized light clockwise are said to be dextrorotary, and correspond with positive specific rotation values, while compounds which rotate the plane of polarization of plane polarized light counterclockwise are said to be levorotary, and correspond with negative values. If a compound is able to rotate the plane of polarization of plane-polarized light, it is said to be “optically active”.

Specific rotation is an intensive property, distinguishing it from the more general phenomenon of optical rotation. As such, the observed rotation (α) of a sample of a compound can be used to quantify the enantiomeric excess of that compound, provided that the specific rotation ([α]) for the enantiopure compound is known. 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 concentration of bulk sugar solutions is sometimes determined by comparison of the observed optical rotation with the known specific rotation.

The CRC Handbook of Chemistry and Physics defines specific rotation as:

For an optically active substance, defined by [α]^θ_λ = 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.

Values for specific rotation are reported in units of deg·mL·g⁻¹·dm⁻¹, which are typically shortened to just degrees, wherein the other components of the unit are tacitly assumed. 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. As noted above, temperature and wavelength are frequently reported as a superscript and subscript, respectively, while the solvent is reported parenthetically, or omitted if it happens to be water.

Optical rotation is measured with an instrument called a polarimeter. There is a linear relationship between the observed rotation and the concentration of optically active compound in the sample. There is a nonlinear relationship between the observed rotation and the wavelength of light used. Specific rotation is calculated using either of two equations, depending on whether the sample is a pure chemical to be tested or that chemical dissolved in solution.

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). If the wavelength of the light used is 589 nanometers (the sodium D line), the symbol “D” is used. The sign of the rotation (+ or −) is always given.