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Ch. 6 - Stereoisomerism: Arrangement of Atoms in Space
Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition
Mullins1st EditionOrganic Chemistry: A Learner Centered ApproachISBN: 9780137566471Not the one you use?Change textbook
All textbooksMullins 1st EditionCh. 6 - Stereoisomerism: Arrangement of Atoms in SpaceProblem 33
Chapter 5, Problem 33

(S)-Propranolol, a drug used for the treatment of anxiety, has a specific rotation of -25.5° . Attempting to prepare it in enantiopure form, a chemist produced a compound that gave a specific rotation of -18.3° . What is the ratio of (S)- to (R)-propranolol produced by the chemist?
Chemical structure of (S)-propranolol, a drug for anxiety treatment, labeled with its name.

Verified step by step guidance
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Step 1: Understand the concept of enantiomeric excess (ee). Enantiomeric excess is a measure of the purity of one enantiomer in a mixture. It is calculated using the formula: ee = (observed specific rotation / specific rotation of pure enantiomer) × 100%.
Step 2: Calculate the enantiomeric excess (ee) using the given values. The observed specific rotation is -18.3°, and the specific rotation of pure (S)-propranolol is -25.5°. Substitute these values into the formula: ee = (-18.3 / -25.5) × 100%.
Step 3: Relate the enantiomeric excess to the ratio of (S)- to (R)-propranolol. The enantiomeric excess represents the percentage of the excess enantiomer (in this case, (S)-propranolol) over the racemic mixture. Use the formula: % (S) = (ee + 100) / 2 and % (R) = 100 - % (S).
Step 4: Calculate the percentage of (S)-propranolol and (R)-propranolol in the mixture using the formulas derived in Step 3. This will give the proportions of each enantiomer in the mixture.
Step 5: Express the ratio of (S)- to (R)-propranolol as a fraction or ratio based on the percentages calculated in Step 4. This ratio represents the relative amounts of the two enantiomers in the mixture.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Specific Rotation

Specific rotation is a property of chiral compounds that quantifies the degree to which they rotate plane-polarized light. It is expressed in degrees and is influenced by the concentration of the solution and the path length of the light. The specific rotation can help determine the purity and composition of enantiomers in a mixture.
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Specific rotation vs. observed rotation.

Enantiomers

Enantiomers are a pair of molecules that are non-superimposable mirror images of each other, often differing in their optical activity. In the case of (S)- and (R)-propranolol, they exhibit different specific rotations. Understanding the relationship between enantiomers is crucial for determining the composition of a racemic mixture and calculating the ratio of each enantiomer present.
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How to solve for the percentage of each enantiomer.

Optical Purity

Optical purity is a measure of the proportion of one enantiomer in a mixture relative to the total amount of both enantiomers. It can be calculated using the specific rotation of the mixture compared to that of the pure enantiomer. This concept is essential for determining the ratio of (S)- to (R)-propranolol produced by the chemist, as it provides insight into the effectiveness of the synthesis process.
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Mutorotation and Optical Activity
Related Practice
Textbook Question

Using a 1.0-cm polarimeter cell and a solution prepared by dissolving 2.54 g of glucose in 1 L of H₂O, the specific rotation of d-glucose was calculated to be +52.7° at 20 °C using the sodium D line as the source of light. What was the observed rotation of the solution?

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Textbook Question

For the molecules shown,

(i) count the number of stereocenters present and

(ii) draw all possible stereoisomers.

(iii) Identify the relationships between stereoisomers as enantiomers or diastereomers.

(b)

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Textbook Question

Imagine a sample that is enriched in the R enantiomer. If the % ee of the sample is 83%,

(a) what percent of the mixture is racemic?

(b) What is the ratio of R to S?

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Textbook Question

(R)-Selegiline, a monoamine oxidase (MAO) inactivator, was approved by the FDA in 1989 for the treatment of Parkinson's disease. In pure form, it has a specific rotation, [α]²⁰D = - 11.0°. What is the expected specific rotation of a mixture containing 64% S and 36% R?

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Textbook Question

Cholesterol (50 mg) was dissolved in 10 mL of chloroform and placed in a 1.0-cm polarimeter cell. This solution produced an observed rotation (using the sodium D line at 20°C ) of - 1.58° . What is the specific rotation of cholesterol?

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Textbook Question

For the molecules shown,

(i) count the number of stereocenters present and

(ii) draw all possible stereoisomers.

(iii) Identify the relationships between stereoisomers as enantiomers or diastereomers.

(a)

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