A mixture of two enantiomers has as observed rotation of -18°. The specific rotation of the (-)
enantiomers is -27°. Find the % of the two enantiomers in the solution.
The Correct Answer and Explanation is:
To find the percentage of the two enantiomers in the mixture, we use the concept of enantiomeric excess (ee) and specific rotation.
Given:
- Observed rotation (α) = -18°
- Specific rotation of the pure (-) enantiomer = -27°
Let:
- % of (-) enantiomer = x
- % of (+) enantiomer = y = (100 – x)
Step 1: Use enantiomeric excess (ee) formula
ee=observed rotationspecific rotation of pure enantiomer×100\text{ee} = \frac{\text{observed rotation}}{\text{specific rotation of pure enantiomer}} \times 100 ee=−18−27×100=66.67%\text{ee} = \frac{-18}{-27} \times 100 = 66.67\%
Step 2: Use ee to find individual enantiomer percentages
Enantiomeric excess (ee) is also defined as the absolute difference between the two enantiomers: ee=%(−)−%(+)\text{ee} = \%(-) – \%(+)
Let %(-) = x, then: x−(100−x)=66.67⇒x−100+x=66.67⇒2x=166.67⇒x=83.33x – (100 – x) = 66.67 \Rightarrow x – 100 + x = 66.67 \Rightarrow 2x = 166.67 \Rightarrow x = 83.33 %(+)=100−83.33=16.67\%(+) = 100 – 83.33 = 16.67
Final Answer:
- % of (-) enantiomer = 83.33%
- % of (+) enantiomer = 16.67%
Explanation
Enantiomers are chiral molecules that are non-superimposable mirror images of each other. Each enantiomer rotates plane-polarized light in opposite directions: one to the left (levorotatory, denoted as “-”) and one to the right (dextrorotatory, denoted as “+”). The degree of this optical rotation is characteristic of the pure enantiomer and is expressed as specific rotation.
When a mixture contains both enantiomers, the observed optical rotation depends on the ratio of the two. The more abundant enantiomer determines the direction of the net rotation. The concept of enantiomeric excess (ee) quantifies how much one enantiomer is present in excess of the racemic (50:50) mixture.
In this problem, the observed optical rotation is -18°, and the pure (-) enantiomer has a specific rotation of -27°. The ratio of observed rotation to the specific rotation of the pure enantiomer gives us the enantiomeric excess: ee=−18−27×100=66.67%ee = \frac{-18}{-27} \times 100 = 66.67\%
This means the solution has 66.67% more of the (-) enantiomer than the (+). Using this, we determine that the mixture contains 83.33% of the (-) form and 16.67% of the (+) form.
Understanding these values is crucial in pharmaceutical and chemical industries, where one enantiomer may be biologically active and the other harmful. Thus, controlling enantiomeric purity is essential for efficacy and safety in drugs.
