In chemistry, specific rotation 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 light clockwise are said to be dextrorotary, and correspond with
positive specific rotation values, while compounds which rotate light
counterclockwise are said to be levorotary, and correspond with negative
values. If a compound is able to rotate 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 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—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 [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. Although the unit for specific rotation
is deg·mL·g−1·dm−1, values for specific rotation are typically reported in units
of 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. 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.
= For pure liquids= This equation is used:
In this equation, α is the measured rotation in degrees, l is the path
length in decimeters, and ρ is the density of the liquid in g/mL, for a
sample at a temperature T and wavelength λ. If the wavelength of the light used
is 589 nanometers, the symbol “D” is used. The sign of the rotation is always
given. = For solutions=
For solutions, a slightly different equation is used:
In this equation, α 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, 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:
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. The sign of the rotation is
always given. If the wavelength of the light used is 589 nanometer, the symbol
“D” is used. If the temperature is omitted, it is assumed to be at standard
room temperature. For example, the specific rotation of a
compound would be reported in the scientific literature as:
= 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. 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 for
this purpose. Applications
= Enantiomeric excess= If the specific rotation of a pure
chiral compound is known, it is possible to use the observed rotation to
determine the enantiomeric excess, or "optical purity", of a sample of the
compound, by using the formula: 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%) = 40% of the R enantiomer. The
remainder of the sample is a racemic mixture of the enantiomers, 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 or HPLC with a chiral
column, are generally preferred. = Absolute configuration=
The variation of specific rotation with wavelength is called optical rotatory
dispersion. ORD can be used in conjunction with computational methods
to determine the absolute configuration of certain compounds.
References External links
Specific rotation calculator