# Enantiomeric Excess: Definition, Calculation & Examples

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

Sometimes we need to know how pure a mixture of two enantiomers is. In this lesson we will learn how to do this by calculating the enantiomeric excess.

## Enantiomeric Excess

Pick your favorite and least favorite Skittles color. Let's say red is your favorite and green is your least favorite. You want to know how many more red skittles are in a bag of Skittles than green (or vice versa), you would count the number of each and then determine the excess.

You could also calculate this as a percentage of excess. Enantiomeric excess is doing this same thing, only with enantiomers instead of Skittles colors.

Enantiomeric excess is a way of describing how optically pure a mixture is by calculating the purity of the major enantiomer. It can range from 0%-100%.

Now, 0% does not mean that there is none of the major enantiomer, it just means that it is 0% pure, which is actually a 50-50 mixture of both enantiomers, making a racemic mixture. But 100% does mean that it is 100% pure, that is, the mixture is 100% the major enantiomer.

Now, you may stop and ask ''But how would the mixture be described if this 'major enantiomer' had less than 50%? What if it had 45%?'' Well, it is no longer the major enantiomer, because this means that the other enantiomer is 55% of the mixture, making it the major enantiomer.

## Enantiomeric Excess Calculation

The formula for calculating the enantiomeric excess is actually pretty straightforward. We calculate the optical purity by dividing the observed rotation of the mixture by the specific rotation of the pure enantiomer.

Now remember, this optical purity does not describe the percentage of the major enantiomer in the mixture, it is simply telling you what percentage the major enantiomer is found in EXCESS to the minor enantiomer.

We can see how this works if we look at the extreme ends of the spectrum. In order to get a 0% optically pure mixture, then we need to have a racemic mixture, which means that the observed rotation will be equal to 0, and 0 divided by anything is equal to 0%. So a racemic mixture will have an optical purity of 0%.

Or, if we look at a 100% pure mixture, then the observed rotation will be equal to the specific rotation. When we divide something by itself, it is equal to 1 or 100%, so a pure mixture will have an optical purity of 100%.

## Example Calculation

Let's look at a sugar mixture made up of glucose. You are trying to make L-glucose, and want to know how pure your mixture is. You know that pure L-glucose should have a specific rotation of -18o. When you measure your mixture you get a specific rotation of -15o.

The optical purity is equal to -15 / -18 = 0.8333

Now, remember 0.8333 does NOT mean that our mixture is 83% L-glucose and 17% R-glucose. It means that 83% of the excess is our L-glucose. We can calculate this using a couple of simple algebra equations:

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