chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...

, specific rotation ( �'') is a property of a chiral

chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...

. It is defined as the change in orientation of

monochromatic A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, monochro ...

plane-polarized light Polarization ( also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of t ...

, 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 ( �'') for the enantiopure compound is known. The variance of specific rotation with wavelength—a phenomenon known as

optical rotatory dispersion Optical rotatory dispersion is the variation in the optical rotation of a substance with a change in the wavelength of light. Optical rotatory dispersion can be used to find the absolute configuration of metal complexes. For example, when plane-pol ...

—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.

Definition

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

For an optically active substance, defined by �sup>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.

Measurement

Optical rotation is measured with an instrument called a

polarimeter A polarimeter is a scientific instrument used to measure the angle of rotation caused by passing polarized light through an optically active substance.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.

For pure liquids

This equation is used: :

alpha Alpha (uppercase , lowercase ; grc, ἄλφα, ''álpha'', or ell, άλφα, álfa) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph , whi ...

\lambda^T = \frac 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 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...

( the sodium D line), the symbol “D” is used. The sign of the rotation (+ or −) is always given. :

D^ = +6.2°

For solutions

For solutions, a slightly different equation is used: :

\lambda^T = \frac 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. 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: :

\lambda^T = \frac 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 589

nanometer 330px, Different lengths as in respect to the molecular scale. The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re, ...

(the sodium 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: :

D^ +6.2 (''c'' 1.00, EtOH)

Dealing with large and small rotations

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.

Applications

Enantiomeric excess

If the specific rotation,

of a pure chiral compound is known, it is possible to use the observed specific rotation,

to determine the enantiomeric excess (''ee''), or "optical purity", of a sample of the compound, by using the formula: :

ee(\%) = \frac

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 R

enantiomer In chemistry, an enantiomer ( /ɪˈnænti.əmər, ɛ-, -oʊ-/ ''ih-NAN-tee-ə-mər''; from Ancient Greek ἐνάντιος ''(enántios)'' 'opposite', and μέρος ''(méros)'' 'part') – also called optical isomer, antipode, or optical anti ...

. 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%. 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 as

gas chromatography Gas chromatography (GC) is a common type of chromatography used in analytical chemistry for separating and analyzing compounds that can be vaporized without decomposition. Typical uses of GC include testing the purity of a particular substanc ...

HPLC High-performance liquid chromatography (HPLC), formerly referred to as high-pressure liquid chromatography, is a technique in analytical chemistry used to separate, identify, and quantify each component in a mixture. It relies on pumps to p ...

with a chiral column, are generally preferred.

Absolute configuration

The variation of specific rotation with wavelength is called

(ORD). ORD can be used in conjunction with computational methods to determine the absolute configuration of certain compounds.

References

{{DEFAULTSORT:Specific Rotation Chemical properties