Ch. 6 - Stereoisomerism: Arrangement of Atoms in Space

Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition

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Mullins 1st Edition

Ch. 6 - Stereoisomerism: Arrangement of Atoms in Space

Problem 30

Chapter 5, Problem 30

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?

Verified step by step guidance

Determine the formula for specific rotation: \( [\alpha] = \frac{\alpha_{\text{obs}}}{l \cdot c} \), where \( [\alpha] \) is the specific rotation, \( \alpha_{\text{obs}} \) is the observed rotation, \( l \) is the path length in decimeters, and \( c \) is the concentration in g/mL.

Convert the path length \( l \) from centimeters to decimeters. Since 1 cm = 0.1 dm, the path length is \( l = 1.0 \times 0.1 = 0.1 \ \text{dm} \).

Calculate the concentration \( c \) of the solution. Use the formula \( c = \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \). Convert the mass of cholesterol from mg to g: \( 50 \ \text{mg} = 0.050 \ \text{g} \). Then divide by the volume of chloroform: \( c = \frac{0.050}{10} \ \text{g/mL} \).

Substitute the values into the specific rotation formula: \( [\alpha] = \frac{-1.58}{0.1 \cdot c} \), where \( c \) is the concentration calculated in the previous step.

Simplify the expression to find the specific rotation \( [\alpha] \). Ensure the units are consistent and the final value is expressed in \( \text{°} \cdot \text{dm}^{-1} \cdot \text{g}^{-1} \cdot \text{mL} \).

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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 their ability to rotate plane-polarized light. It is defined as the observed rotation of light (in degrees) divided by the path length of the sample (in decimeters) and the concentration of the solution (in grams per milliliter). The formula is [α] = α / (l × c), where [α] is the specific rotation, α is the observed rotation, l is the path length, and c is the concentration.

Chirality

Chirality refers to the geometric property of a molecule that makes it non-superimposable on its mirror image, much like left and right hands. Chiral molecules often exist as enantiomers, which are pairs of molecules that are mirror images of each other. The presence of chirality in a compound like cholesterol is crucial for its biological function and its interaction with polarized light.

Polarimetry

Polarimetry is an analytical technique used to measure the angle of rotation of polarized light as it passes through a sample. This technique is particularly useful for studying chiral substances, as the degree of rotation can provide information about the concentration and specific rotation of the compound. The polarimeter measures the observed rotation, which is essential for calculating the specific rotation of the sample.

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

Based on the absolute configuration of (S)-butan-2-ol, what can you say about the direction it rotates plane-polarized light?

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Textbook Question

A student wanted to measure the specific rotation of the following propionate derivative (density = 1.12 g/ml).

A sample of the pure compound was placed in a 10.0-cm polarimeter tube, and using the sodium D line, the observed rotation at 20°C was determined to be +46.6° . What is the specific rotation of the propionate derivative?

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

Naproxen is a commercially available anti-inflammatory sold under the name Aleve.

(b) Given that naproxen rotates plane-polarized light in the clockwise direction, should it be referred to as (d) or (l)?

(d) What direction (d or l; + or −) would you expect the enantiomer of naproxen to rotate plane-polarized light?

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Textbook Question

(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?

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