# How to calculate enantiomeric excess & polarimetry

Written by jack brubaker
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Many organic substances exhibit optical activity; that is, they rotate plane-polarised light. Such compounds lack a plane of symmetry. More specifically, the molecule cannot be superimposed on its mirror image. This situation frequently arises when one or more carbon atoms in a molecule are bonded to four different chemical groups. The groups attached to these carbon atoms -- called "chiral centres "-- can take two possible configurations, resulting in two different compounds called "enantiomers." Chemists differentiate between enantiomers with designations of (R) and (S), (+) and (-), or D and L.

Many reactions in organic chemistry produce mixtures of enantiomers. A device known as a polarimeter measures the extent to which a solution rotates plane-polarised light. The data from such measurements allows chemists to determine the per cent of each enantiomer present in the mixture. Chemists usually state this as "enantiomeric excess," which actually represents the difference between the percentages of the two enantiomers.

Skill level:
Challenging

### Things you need

• Polarimeter or polarimetry data

## Instructions

1. 1

Calculate the specific rotation, [a], of the sample according to [a] = a / (c * l), where a represents the observed rotation, i.e., the reading from the polarimeter, c represents the concentration of the sample in grams per milliliter (g/mL) and l represents the length of the sample container in centimeters (cm). For example, if a sample prepared from 1.5 g of optical material dissolved in water to a final volume of 10 mL and measured in a 5.0-cm cell was determined to have an optical rotation of +3.5 degrees, then the concentration would be 1.5 g / 10 mL = 0.15 g/mL, and [a] = 3.5 / (0.15 * 5.0) = 4.7.

2. 2

Find the specific rotation of one of the enantiomers in the mixture in its pure form. This normally involves locating the compound in a reference work, such as "The Dictionary of Organic Compounds" or "The Merck Index," in addition to numerous online sources (see Resources). For example, if the compound under investigation is a mixture of L- and D-glutamic acid, then L-glutamic acid exhibits a specific rotation of +12 degrees.

3. 3

Calculate the enantiomeric excess (e.e.) according to

e.e. = (observed specific rotation) / (specific rotation of pure enantiomer) * 100%.

Continuing the example,

e.e. = (3.5 / 12) * 100% = 29%.

This means that the sample contains a 29 per cent excess of L-glutamic acid. Or, because the percentages of the D- and L-enantiomers must sum to 100 per cent, then the sample contains 64.5 per cent L-glutamic acid and 35.5 per cent D-glutamic acid.

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