Question

The specific rotation of enantiomer 1 of alanine (L-alanine) in water is +2.8. A mixture of both enantiomers gave a rotation of +1.78. What is the % of enantiomer 1 of alanine in the mixture?

Answer 1

let fraction of L enantiomer be x

then fraction of D enantiomer will be 1-x

specific rotation of L enantiomer = 2.8

specific rotation of D enantiomer = -2.8

net rotation = fraction of L enantiomer * specific rotation of L enantiomer + fraction of D enantiomer * specific rotation of D enantiomer

1.78 = x * 2.8 + (1-x) * ( -2.8)

1.78 = x * 2.8 - 2.8 + x * 2.8

5.6*x = 4.58

x = 0.8179

so,

fraction of L enantiomer = 0.8179

fraction of D enantiomer = 0.1821

percentage of L enantiomer = 81.7857 %

percentage of D enantiomer = 18.2143 %

Answer: 81.8 %