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

Concept #1: How to solve for the percentage of each enantiomer.

Example #1: 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.

Practice: 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.

When 0.075 g of penicillamine is dissolved in 10.0 mL of pyridine and placed in a sample cell 10.0 cm in length, the observed rotation at 20°C (using the D line of sodium) is –0.47°. Calculate the specific rotation of penicillamine.

When 0.300 g of glucose is dissolved in 10.0 mL of water and placed in a sample cell 10.0 cm in length, the observed rotation is +3.1°C. Calculate the specific rotation of glucose.

Compound C has an [a] D = +28°.a) Draw the structure of compund D, which is isomer of C and features an [a] D = -28°.b) Calculate the [a] D of a 25/75 mixture of derivatives C and D, respectively.c) Draw the structure of a compound E, which is an isomer of C and D, and features an [a] D = 0°

A mixture of a pair of enantiomers has 30% ee. The observed rotation of this mixture is +15º, and it is known by experiment that the (‐)‐enantiomer has the (R) configuration. (enantiomer excess (ee) = % one enantiomer – % the other enantiomer)(a) Calculate the percentage of (R) and (S) enantiomers of the natural product.(b) What is the optical rotation of a mixture of 20% (S) and 80% (R).

An attempt at synthesizing a certain optically active compound resulted in a mixture of its enantiomers. The mixture had an observed specific rotation of +12.6°. If it is known that the specific rotation of the R enantiomer is -36.7°, determine the percentage of each isomer in the mixture.