Question

A) assume you synthesized a molecule with a single chiral center. The known specific rotation for the pure R enentiomer of this compound is +20 degrees. After you synthesis, you measure a specific rotation of +4 degrees. What is the ee of your compound ? Answer is 20% ee of R

B) the S of a certain alcohol has a specific rotation (of a plane polarized light) of +8 degrees. What is the specific rotation of a solution of this alcohol if it is composed of 75% R enantiomer and 25% S enantiomer? Answer is -4 degrees.

Please show how to find answers

Answer 1

[α]_l^T = α/lc

α = observed rotation in degrees.

l = cell path length in decimeters. (1 decimeter = 1 dm = 10 cm. A standard polarimeter tube is 1.00 dm in length.)

c = concentration in g ml^-1 for a pure liquid compound (i.e., the liquid's density), or g 100 ml^-1 for a solution.

Optical purity, % = 100 [a]_mixture / [a]_{pure sample}

Optical purity, % = 100 x 4 / 20 = 20 % enantiomeric excess

The 80% leftover, which is optically inactive, must be equal amounts of both (R)- and (S)- each 40%

Question B

Use the same formula

Optical purity, % = 100 [a]_mixture / [a]_{pure sample}

[a]_mixture = Optical purity, % x  [a]_{pure sample} / 100

[a]_mixture =    = 50 x 8 / 100 = -4

-4 is represents R enantiomer is presents over S enantiomer