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

Enantiomer

In stereochemistry, 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" but opposite....

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

Enantiomeric excess is defined as the absolute

Absolute value

In mathematics, the absolute value of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3.The absolute value of a number is denoted by ....

 difference

Subtraction

Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...

 between the mole fraction

Mole fraction

In chemistry, mole fraction x is a way of expressing the composition of a mixture...

 of each enantiomer:
where
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.

The enantiomeric excess of a substance is a measure of how pure it is. In this case, the impurity is the undesired enantiomer

Enantiomer

In stereochemistry, 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" but opposite....

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

Definition

Enantiomeric excess is defined as the absolute

Absolute value

In mathematics, the absolute value of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3.The absolute value of a number is denoted by ....

 difference

Subtraction

Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...

 between the mole fraction

Mole fraction

In chemistry, mole fraction x is a way of expressing the composition of a mixture...

 of each enantiomer:
where
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:
(2)
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

Diastereomer

Diastereomers are stereoisomers that are not enantiomers . Diastereomers can have different physical properties and different reactivity...

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

Racemic

In chemistry, a racemic mixture, or racemate, is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule...

 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 or...

. It is possible to determine the specific rotation

Specific rotation

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. The specific rotation of a pure material is an...

 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, where the stationary phase is chiral instead of achiral. The enantiomers of the same compound then differ in affinity to the stationary phase, thus they exit the column at different times....

 and NMR spectroscopy

NMR spectroscopy

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is the name given to a technique which exploits the magnetic properties of certain nuclei. This phenomenon and its origins are detailed in a separate section on nuclear magnetic resonance. The most important...

 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...
  
  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).