In the previous post, we talked about optical rotation which is caused by chiral compounds when plane-polarized light passes through their samples. An interesting feature about optical rotation was the discovery that enantiomers rotate the plane-polarized light to an equal extent but in the opposite direction.

For example, the specific rotation of (R)-2-butanol and (S)-2-butanol are -13.52 ^o and +13.52^o respectively.

So, one question that comes to mind is what happens to the plane of a polarized light when it passes through a mixture contains equal amounts of enantiomers. A mixture containing equal amounts of two enantiomers is called a racemic mixture or a racemate.

What happens is that as the light passes through the sample, each enantiomer rotates the plane-polarized light to an equal extent but in opposite directions and the overall rotation levels up to zero. In other words, each molecule of one enantiomer cancels the rotation caused by a molecule of other enantiomer and therefore, no net rotation is observed. And thus, we know that racemic mixtures are optically inactive and therefore they are achiral.

Because each enantiomer rotates the plane of the light clockwise (+) or counterclockwise (-), the racemic mixture of a sample is often labeled as being (±). For example, a racemic mixture of (R)-(−)-2-butanol and (S)-(+)-2-butanol can be designated as (±)-2-butanol.

To highlight the most important peace of information about racemic mixture, remember that racemic mixtures are optically inactive and therefore they are achiral.

Enantiomeric Excess and Optical Activity 

Another possibility for a mixture of enantiomers is when they are present in different quantities. In this case, the extent and the direction of the rotation is determined by the enantiomer with the greater amount.

For example, if the mixture contains 60% of the R enantiomer and 40% of the S enantiomer, the degree and direction will be based on the specific rotation of the R enantiomer because it is in excess. If it is (+), then the rotation is going to be clockwise and if it is an R-(-) enantiomer, then the rotation will be counterclockwise.

The degree of the rotation is calculated by using the excess amount of the enantiomer. It this case, the enantiomeric excess is 60-40=20%. This means that the specific rotation of this sample will 20% of the specific rotation of the R enantiomer.

For example, if the specific rotation of the R enantiomer is +8.40^o, then the mixture containing 60% R will have a specific rotation of +8.4^o x 0.20 = +1.68^o (sorry about the significant figures).

There is more to the enantiomeric excess and its relation to optical activity and we will cover this in the next article.

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