Optical Activity

If the specific rotation of (S)-aspartic acid is +24.5, what is the specific rotation of (R)-aspartic acid?

A solution of enantiomerically pure (S)-2-methyl-1,2-butanediol, shown below, was prepared by dissolving 0.800 g in 10.0 mL of ethanol. The solution was added to a 10.0 cm sample cell and the optical activity was determined to be −0.74. What is the specific rotation of (R)-2-methyl-1,2-butanediol?

A mixture of enantiomers of a newly-developed drug candidate is composed of 64.0% of the dextrorotatory isomer and 36.0% of the levorotatory isomer. What is the percent enantiomeric excess of this mixture?

You find a vial labeled only as “epinephrine enantiomers”. You measure the optical activity of the sample and find it has an observed rotation of +22.3°. What is the percent enantiomeric excess (% ee) of the sample? Biologically-active epinephrine, shown below has a specific rotation of −50.0.

CHALLENGE

The two cyclic forms of glucose are α-D-glucopyranose and β-D-glucopyranose. In solutions of glucose, these two forms exist in equilibrium. The specific rotation of α-D-glucopyranose is +112, while that of β-D-glucopyranose is +18.7. If the specific rotation of an equilibrium mixture of these two diastereomers is +52.7, what percent of the mixture exists as β-D-glucopyranose?