One of the special features of chiral molecules is that they are able to rotate plane-polarized light. Unfortunately, this means that now professors have an excuse to ask you math problems. Let’s see how this works.

- Clockwise rotation = dextrorotary (d) or (+)
- Counterclockwise rotation = levororatory (l) or (-)

These random names/signs have nothing to do with the chirality of a molecule!

Some more facts about optical activity:

- Specific rotation [α] is the rotation that 100% pure enantiomers produce.
- Opposite enantiomer = opposite rotation.
- Racemic: A perfect 1:1 ratio of enantiomers
- Scalemic: A non-1:1 ratio of enantiomers

**Example:** Calculate the ee and observed rotation for the following chiral mixture where S-enantiomer has [α] = +20.

We can also use these equations to calculate specific and observed rotation when other variables are given to us. Just plug the numbers in! Let's try a few.

**Example:** When 0.200 g of lactose is dissolved in 10.0 ml of water and placed in a sample cell 10.0 cm in length, the observed rotation is +2°. Calculate the specific rotation of lactose.

**Example:** Calculate the observed rotation of a chiral mixture that contains 65% (S)-stereoisomer where the [α] of pure (S)-stereoisomer = -118.

**Example:** An optically pure (R)-stereoisomer of a molecule has a specific rotation of – 20°. What specific rotation would be observed for a mixture of the (R) and (S) stereoisomer where there is an enantiomeric excess equal to (S) 60%.

Sometimes professors will ask us to solve for exact the percentage of each enantiomer in solution. For that we’ll need some new equations.

**Example:** The [α] of pure S-epinephrine is +50°. Calculate the ee of a solution with an observed value of +25°. Calculate percent of each enantiomer. Then sketch the approximate mixture in our sample polarimeter tube.

**Example:** The [α] of pure S-epinephrine is +50°. Calculate the ee of a solution with an observed value of -40°. Calculate percent of each enantiomer. Then sketch the approximate mixture in our sample polarimeter tube.