What is the percentage of the S enantiomer in a sample of carvone that has a specific rotation of 30, given that the specific rotation of (R)-carvone is −61?

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Quizplus · Accepted Answer

The specific rotation of a mixture of enantiomers can be used to determine the composition of the mixture. The formula for calculating the percentage of each enantiomer in a mixture is: $$ \text{observed rotation} = [\alpha]_D \times \frac{\text{percentage of S enantiomer} - \text{percentage of R enantiomer}}{100} $$ Given that the specific rotation of (R)-carvone is -61, and assuming the specific rotation of (S)-carvone is +61 (since enantiomers have equal but opposite specific rotations), and the observed rotation is +30, we can set up the equation: $$ 30 = \frac{(+61) \times \text{percentage of S} + (-61) \times \text{percentage of R}}{100} $$ Since the percentages of S and R enantiomers must add up to 100%, we can substitute $\text{percentage of R}$ with $100 - \text{percentage of S}$ and solve for the percentage of S. Doing so, we find that the percentage of the S enantiomer is 74.5%.

What Is the Percentage of the S Enantiomer in a Sample