To determine the optical purity of the enantiomeric mixture, we utilize the formula for optical purity (OP):
Optical Purity (OP) = (Observed Rotation / Specific Rotation of Pure Enantiomer) × 100%
Given:
- Observed Rotation = +12.6°
- Specific Rotation of (+) isomer = +30°
We substitute these values into the formula:
OP = (+12.6° / +30°) × 100%
Calculating this gives:
OP = 0.42 × 100% = 42%
Thus, the optical purity of the mixture is 42%.
Checking against the provided range (42,42): the calculated optical purity of 42% matches exactly with the expected range.