Enantiomeric excess
The enantiomeric excess of a substance is a measure of how pure it is. In this case, the impurity is the undesired enantiomer
In chemistry, an enantiomer is one of two stereoisomers that are mirror images of each other that are non-superposable , much as one's left and right hands are the same except for opposite orientation. It can be clearly understood if you try to place your hands one over the other without...

 (the "opposite-handed" mirror image of a chiral compound).


Enantiomeric excess is defined as the absolute difference
Absolute difference
The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y...

 between the mole fraction of each enantiomer:


In practice, it is most often expressed as a percent enantiomeric excess. (1)

The enantiomeric excess can be determined in another way if we know the amount of each enantiomer produced. If one knows the moles of each enantiomer produced then:
and are the respective fractions of enantiomers in a mixture such that

Enantiomeric excess is used as one of the indicators of the success of an asymmetric synthesis. For mixtures of diastereomer
Diastereomers are stereoisomers that are not enantiomers.Diastereomerism occurs when two or more stereoisomers of a compound have different configurations at one or more of the equivalent stereocenters and are not mirror images of each other.When two diastereoisomers differ from each other at...

s, there are analogous definitions and uses for diastereomeric excess and percent diastereomeric excess.

As an example, a sample with 70% of R isomer and 30% of S will have an enantiomeric excess of 40%. This can also be thought of as a mixture of 40% pure R with 60% of a racemic mixture (which contributes 30% R and 30% S to the overall composition).

A non-racemic
In chemistry, a racemic mixture, or racemate , is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule. The first known racemic mixture was "racemic acid", which Louis Pasteur found to be a mixture of the two enantiomeric isomers of tartaric acid.- Nomenclature :A...

 mixture of two enantiomers will have a net optical rotation
Optical rotation
Optical rotation is the turning of the plane of linearly polarized light about the direction of motion as the light travels through certain materials. It occurs in solutions of chiral molecules such as sucrose , solids with rotated crystal planes such as quartz, and spin-polarized gases of atoms...

. It is possible to determine the specific rotation
Specific rotation
In stereochemistry, the specific rotation of a chemical compound [α] is defined as the observed angle of optical rotation α when plane-polarized light is passed through a sample with a path length of 1 decimeter and a sample concentration of 1 gram per 1 millilitre. It is the main property used to...

 of the mixture and, with knowledge of the specific rotation of the pure enantiomer, the optical purity can be determined.

Ideally, the contribution of each component of the mixture to the total optical rotation is directly proportional to its mole fraction, and as a result the numerical value of the optical purity is identical to the enantiomeric excess. This has led to informal use the two terms as interchangeable, especially because optical purity was the traditional way of measuring enantiomeric excess. However, other methods such as chiral column chromatography
Chiral column chromatography
Chiral column chromatography is a variant of column chromatography in which the stationary phase contains a single enantiomer of a chiral compound rather than being achiral...

 and NMR spectroscopy
NMR spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a research technique that exploits the magnetic properties of certain atomic nuclei to determine physical and chemical properties of atoms or the molecules in which they are contained...

 can now be used for measuring the amount of each enantiomer individually.

The ideal equivalence between enantiomeric excess and optical purity does not always hold. For example,
  • the specific rotation of (S)-2-ethyl-2-methyl succinic acid is found to be dependent on concentration
  • in what is known as the Horeau effect the relationship between mole based ee and optical rotation based ee can be non-linear i.d. in the succinic acid
    Succinic acid
    Succinic acid is a dicarboxylic acid. Succinate plays a biochemical role in the citric acid cycle. The name derives from Latin succinum, meaning amber, from which the acid may be obtained....

    example the optical activity at 50% ee is lower than expected.
  • the specific rotation of enantiopure 1-phenylethanol can be enhanced by the addition of achiral acetophenone as an impurity.

The term enantiomeric excess was introduced in 1971 by Morrison and Mosher in their publication Asymmetric Organic Reactions. The use of enantiomeric excess has established itself because of its historic ties with optical rotation. It has been suggested that the concept of ee should be replaced by that of er which stands for enantiomeric ratio or er (S:R) or q (S/R) because determination of optical purity has been replaced by other techniques which directly measure R and S and because it simplifies mathematical treatments such as the calculation of equilibrium constants and relative reaction rates. The same arguments are valid for changing diastereomeric excess (de) to diastereomeric ratio (dr).
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