Question

Assume you had access to all possible physical properties of each isomeric alkene. Can you think of a way to establish the ration of isomers in the mixture?

Answer 1

Let's assume a problem,A mixture of enantiomers has an observed specific rotation of +11.2⁰; The specific rotation of the R enantiomer is -39.839⁰, We have to determine the percentage of each isomer and their ratio in the mixture.

The rotations of the two enantiomers cancel each other, so the rotation of the mixture will be that of the excess enantiomer.

As the mixture has a positive sign of rotation, so there is S isomer is in excess.

Formula for enantiomeric excess is: $ee = \frac{observed specific rotation}{maximum specific rotation}*100$ %

Now, %

11.2° ee * 100 = 28 39.8390

Here we have a mixture of (+) and (-) isomers and (+) is in excess,

%(+)=(ee/2)+50%

∴ %(+)=(28/2)%+50%=(14+50)%=64%

So, the mixture contains 64 % (S) and 36 % (R).

$\therefore$ Ratio of R & S isomer = 64 : 36 = 16 : 9.