91Ó°ÊÓ

The specific rotation of a mixture can be calculated from the ee value. The term ee refers to the enantiomeric excess. The following is the relation between the enantiomeric excess and the specific rotation:

$\text{ee=}\frac{\left[\text{α}\right]\text{mixture}}{\left[\text{α}\right]\text{pure}}\text{×100\%}$

$\left[\text{α}\right]$refers to the specific rotation of the pure enantiomer.

(a)

The $\left[\text{α}\right]$for the solution can be calculated by the following relationship:

$$\begin{gathered} \text{ee=}\frac{\left[\text{α}\right]\text{mixture}}{\left[\text{α}\right]\text{pure}}\text{×100\%} \\ \frac{\left[\text{α}\right]\text{mixture}}{+3.8}×100\%=60\%\text{ee} \\ \left[\text{α}\right]\text{mixture=+2.3} \end{gathered}$$

(b)

The percentage of the dextrorotatory and the levorotatory isomers can be calculated by using the following relationship:

Enantiomeric excess (ee) = percentage of one isomer – the percentage of another isomer

$\text{80\%-20\%=60\%ee}$

Therefore, there is 80% dextrorotatory (+) isomer and 20% levorotatory (-) isomer.