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

Concept #1: How to calculate enantiomeric excess.

Example #1: Calculate the ee and observed rotation for the following chiral mixture where S-enantiomer has [α] = +20.

Calculate the observed rotation when given the following ratio of enantiomers in solution.

Example #2: 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.

Practice: 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.

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

Practice: 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%.

You are given a solution containing a pair of enantiomers (A and B). Careful measurements show that the solution contains 98% A and 2% B. What is the ee of this solution?

The [α] of pure S-normetanephrine is +20°. Calculate the ee of a solution with the following observed values. For each ee calculate the percent of each enantiomer.
+10°

If the ee of a certain mixture with two enantiomers is 80%. What is the ratio of the two enantiomers in the mixture?
a) 90:10
b) 80:20
c) 60:40
d) 85:15
e) none of these

The [α] of a pure chiral compound A is +30°, Calculate the ee of a solution with the value of -15°. What is the percentage of each enantiomer A and B present in the solution?

The specific rotation of (S)-carvone (at 20°C) is +61. A chemist prepared a mixture of (R)-carvone and its enantiomer, and this mixture had an observed rotation of –55°.(b) Calculate the % ee of this mixture.

The specific rotation of (S)-carvone (at 20°C) is +61. A chemist prepared a mixture of (R)-carvone and its enantiomer, and this mixture had an observed rotation of –55°.(c) What percentage of the mixture is (S)-carvone?

The specific rotation of a pure substance is -5.90°. What is the percentage of this isomer in a mixture with an observed specific rotation of -2.95°?A) 0%B) 75%C) 25%D) 50%E) 80%

Given that (S)-2-butanol has a specific rotation of +13.52 o and (R)-2-butanol has a specific rotation of -13.52o, what is % composition of a mixture whose specific rotation was found to be +6.76o? A) 75%(R) 25%(S)B) 25%(R) 75%(S)C) 50%(R) 50%(S)D) 67%(R) 33%(S)E) 33%(R) 67%(S)

If a sample contains 64.0% of the R enantiomer and 36.0% of the S enantiometer, what is the enantiomeric excess of the mixture? % enantiomeric excess =

Consider a solution that contains 74.0% R isomer and 26.0% S isomer. If the observed specific rotation of the mixture is -88.0°, what is the specific rotation of the pure R isomer?

If a pure R isomer has a specific rotation of -151.0°, and a sample contains 69.0% of the R isomer and 31.0% of its enantiomer, what is the observed specific rotation of the mixture?