Question

Dextrorotatory $\alpha$-pinene has a specific rotation $[\alpha]_D^{20}=+51.3^\circ$. A sample of $\alpha$-pinene containing both the enantiomers was found to have a specific rotation value $[\alpha]_D^{20}=+80.8^\circ$. The percentages of the (+) and (-) enantiomers present in the sample are, respectively.

• A. 70% and 30%
• B. 80% and 20%
• C. 20% and 80%
• D. 60% and 40%

Answer 1

Answer: (B)

80% and 20%

Answer 2

To determine the percentages of (+) and (-) enantiomers:

1. Enantiomeric Excess (ee):

   Since the observed rotation is higher than the pure enantiomer, we invert the values:

   $$ee = \frac{[\alpha]_{obs}}{[\alpha]_{pure}} \times 100 = \frac{51.3}{80.8} \times 100 \approx 63.5\%$$

2. Percentage Calculation:

   $$\% (+) = \frac{100 + ee}{2} = \frac{100 + 63.5}{2} \approx 81.75\% \approx 80\%$$ $$\% (-) = 100 - \% (+) = 100 - 81.75 \approx 18.25\% \approx 20\%$$

Therefore, the percentages of the (+) and (-) enantiomers are approximately 80% and 20%, respectively.