a. The specific rotation of a pure enantiomer is `+10^(@)`. What will be its observed rotation if its is isolated from a reaction with
i. `30%` racemisation and `70%` retention.
ii. `70%` racemisation and `30%` inversion.
b. What is the percentage composition of a mixtrue of two enantiomers whose rotation is `-10^(@)`? The specific rotation of pure enantiomers is `-20^(@)`.
c. What is the optical purity of a sample having an `[alpha]_(obs.)=+9.0^(@)` if `[alpha]_(D)=+12^(@)`.

Explanation

a. i. `[alpha]_(obs.)= 0.70xx(+10^(@))= +7.0^(@)`
ii. `30%` inversion, with inversion specific rotation is `(-10^(@))`.
`:. [alpha]_(obs.)=0.30 xx (-10^(@)) = -3.0^(@)`
b. Optical purity `(OP)` of sample `=([alpha]_(obs.))/([alpha]_(D))`
`= (-10^(@)xx100)/(-20^(@))=50%`
So, `50%` of the mixtrue consists of `(-)` enantiomer and `50%` is the racemate [i.e., `25% (+)` and `25%(-)` form]
Total percentage of `(-)` form `= 50%+25%=75%`
Total percentage of `(+)` form `=25%`
c. Optical purity `(OP)` of sample `=(+9^(@))/(+12^(@))xx100= 75%`
The mixtrue has `75% (+)` and `25%` racemic mixtrue [i.e., `12.5%(+)` and `12.5%(-)` form]
Total percentage of `(+)` form `=75%+(25%)/(2)= 87.5%`
Total percentage of `(-)` form `=12.5%`