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# Mixtures of Stereoisomers

Samples containing only a single stereoisomer are described as enantiomerically pure. However, many processes give mixtures of stereoisomers, at least to some extent.

### Racemic Mixtures

A racemic mixture contains two enantiomers in equal amounts. As a result, a racemic mixture has no net optical activity.

### Enantiomeric Excess

For non-racemic mixtures of enantiomers, one enantiomer is more abundant than the other. The composition of these mixtures is described by the enantiomeric excess, which is the difference between the relative abundance of the two enantiomers. Therefore, if a mixture contains 75% of the R enantiomer and 25% S, the enantiomeric excess if 50%. Similarly, a mixture that is 95% of one enantiomer, the enantiomeric excess is 90%, etc.

Enantiomeric excess is useful because it reflects the optical activity of the mixture. The standard optical rotation by the mixture ($$[\alpha]_{mix}$$) is equal to the product of the standard optical rotation of the major isomer ($$[\alpha]_{major}$$) and the enantiomeric excess ($$EE$$):

$[\alpha]_{mix} = EE \times [\alpha]_{major}$

In the same way, the enantiomeric excess in a mixture can be measured if the optical rotation of the pure enantiomer is known.

### Diastereomeric Excess

A similar approach can be used to describe mixtures of diastereomers, resulting in the diastereomeric excess.