Cholesterol, when isolated from natural sources, is obtained as a single enantiomer. The observed rotation `alpha` of a 0.3 g sample of cholesterol in 5mL of chloroform solution contained in a 10 cm polarimeter tube is `-0.78^(@)`. Calculate the specific rotation of cholesterol. A sample of synthetic cholesterol was prepared consisting entirely of (+)-cholesterol. This synthetic (+)-cholesterol was mixed with some natural (-)-cholesterol. The mixture had a specific rotation `[alpha]_(D)^(20) " of " -13^(@).` What fraction of the mixture was (+)-cholesterol ?

Explanation

Specific rotation `=[alpha]_(t)^(lambda) = (theta)/(t xx c) = -(0.78)/(1 xx (0.3)/(15)) - 39^(@)`
Enantiomeric excess `=("observed optical rotation")/("optical rotation of pure enantionmer") xx 100 = (-13)/(-39) xx 100 = 33.3%.`
Therefore (+)-cholesterol is of 33.3% and (-)-cholesterol is of 66.6% in the mixture.