Inchemistry,specific rotation ([α]) is a property of achiralchemical compound.^[1]: 244 It is defined as the change in orientation ofmonochromaticplane-polarized light, per unit distance–concentration product, as the light passes through a sample of a compound in solution.^{[2]: 2–65} Compounds which rotate theplane of polarization of a beam of plane polarized light clockwise are said to bedextrorotary, and correspond with positive specific rotation values, while compounds which rotate the plane of polarization of plane polarized light counterclockwise are said to belevorotary, and correspond with negative values.^[1]: 245 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 anintensive property, distinguishing it from the more general phenomenon ofoptical rotation. As such, theobserved rotation (α) of a sample of a compound can be used to quantify theenantiomeric excess of that compound, provided that thespecific rotation ([α]) for theenantiopure compound is known. The variance of specific rotation with wavelength—a phenomenon known asoptical rotatory dispersion—can be used to find theabsolute configuration of a molecule.^[3]: 124 Theconcentration 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 ofmass 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.^[2]

Values for specific rotation are reported in units of deg·mL·g⁻¹·dm⁻¹, which are typically shortened to justdegrees, wherein the other components of the unit are tacitly assumed.^[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. 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 apolarimeter. There is a linear relationship between the observed rotation and the concentration ofoptically 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:

${\displaystyle [\alpha {]}_{\lambda }^T=\frac{\alpha }{l\times \rho }}$

In this equation, α (Greek letter "alpha") is the measured rotation in degrees,l is the path length in decimeters, andρ (Greek letter "rho") is the density of the liquid in g/mL, for a sample at a temperatureT (given in degrees Celsius) and wavelengthλ (in nanometers). If the wavelength of the light used is 589nanometers (the sodium D line), the symbol “D” is used. The sign of the rotation (+ or −) is always given.

${\displaystyle [\alpha {]}_D^{20}=+6.2}$°

For solutions, a slightly different equation is used:

${\displaystyle [\alpha {]}_{\lambda }^T=\frac{\alpha }{l\times c}}$

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), andλ is the wavelength in nanometers.^[10]

For practical and historical reasons, concentrations are often reported in units of g/100mL. In this case, a correction factor in the numerator is necessary:^{[1]: 248 [3]: 123}

${\displaystyle [\alpha {]}_{\lambda }^T=\frac{100\times \alpha }{l\times c}}$

When using this equation, the concentration and the solvent may be provided in parentheses after the rotation. The rotation is reported using degrees, and no units of concentration are given (it is assumed to be g/100mL). The sign of the rotation (+ or −) is always given. If the wavelength of the light used is 589nanometer (thesodium D line), the symbol “D” is used. If the temperature is omitted, it is assumed to be at standard room temperature (20 °C).

For example, the specific rotation of a compound would be reported in the scientific literature as:^[11]

${\displaystyle [\alpha {]}_D^{20}=+6.2}$ (c 1.00, EtOH)

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°, and so 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. Another method would be to use shorter path-lengths to perform the measurements.

In cases of very small or very large angles, one can also use the variation of specific rotation with wavelength to facilitate measurement. Switching wavelength is particularly useful when the angle is small. Many polarimeters are equipped with a mercury lamp (in addition to the sodium lamp) for this purpose.

If the specific rotation,${\displaystyle [\alpha {]}_{\lambda }}$ of a pure chiral compound is known, it is possible to use the observed specific rotation,${\displaystyle [\alpha {]}_{\text{obs}}}$ to determine theenantiomeric excess (ee), or "optical purity", of a sample of the compound, by using the formula:^[3]: 124

${\displaystyle ee(\mathrm{\%})=\frac{[\alpha {]}_{\text{obs}}\times 100}{[\alpha {]}_{\lambda }}}$

For example, if a sample of bromobutane measured under standard conditions has an observed specific rotation of −9.2°, this indicates that the net effect is due to (9.2°/23.1°)(100%) = 40% of the Renantiomer. The remainder of the sample is aracemic mixture of the enantiomers (30% R and 30% S), which has no net contribution to the observed rotation. Theenantiomeric excess is 40%; the total concentration of R is 70%.

However, in practice the utility of this method is limited, as the presence of small amounts of highly rotating impurities can greatly affect the rotation of a given sample. 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 asgas chromatography orHPLC with a chiral column, are generally preferred.

The variation of specific rotation with wavelength is calledoptical rotatory dispersion (ORD). ORD can be used in conjunction with computational methods to determine the absolute configuration of certain compounds.^[12]

• Chemical properties
• Stereochemistry
• Optical phenomena

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