Question

The specific rotation of optically pure (R)-1-phenylethylamine is +40 (neat, 20 °C). A synthetic sample of the same compound is shown to contain 4:1 mixture of (S)- and (R)-enantiomers. The specific rotation of the neat sample at 20 °C is ____________. (round off to the nearest integer)

Answer 1

Correct Answer: -24

To determine the specific rotation of the synthetic sample, we first need to calculate the ratio of the enantiomers and their contributions to specific rotation. Given is a 4:1 mixture of (S)- and (R)-enantiomers. Let's denote:
(R)-enantiomer: 20%
(S)-enantiomer: 80%
The specific rotation of optically pure (R)-enantiomer is given as +40.
For the (S)-enantiomer, the specific rotation will be of equal magnitude but opposite in sign, i.e., -40.
To find the specific rotation [α] of the mixture, use the formula:
[α] = (fraction of R) × [α]₍R₎ + (fraction of S) × [α]₍S₎
Substituting the values:
[α] = (0.2 × 40) + (0.8 × (-40))
[α] = (8) + (-32)
[α] = -24
The computed specific rotation of the sample is -24