Textbook Question
Draw the enantiomer, if any, for each structure.
(e)
(f)
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Ch.5 - Stereochemistry
Wade9th EditionOrganic ChemistryISBN: 9780135213728
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Table of contents
- Ch.1 - Structure and Bonding107
- Ch. 2 - Acids and Bases; Functional Groups115
- Ch.3 - Structure and Stereochemistry of Alkanes100
- Ch.4 - The Study of Chemical Reactions99
- Ch.5 - Stereochemistry93
- Ch.6 - Alkyl Halides; Nucleophilic Substitution118
- Ch. 7 - Structure and Synthesis of Alkenes; Elimination158
- Ch.8 - Reactions of Alkenes171
- Ch.9 - Alkynes91
- Ch.10 - Structure and Synthesis of Alcohols143
- Ch.11 - Reactions of Alcohols104
- Ch. 12 - Infrared Spectroscopy and Mass Spectrometry22
- Ch. 13 - Nuclear Magnetic Resonance Spectroscopy45
- Ch. 14 - Ethers, Epoxides, and Thioethers72
- Ch. 15 - Conjugated Systems, Orbital Symmetry, and Ultraviolet Spectroscopy89
- Ch. 16 - Aromatic Compounds74
- Ch. 17 - Reactions of Aromatic Compounds126
- Ch. 18 - Ketones and Aldehydes193
- Ch. 19 - Amines129
- Ch. 20 - Carboxylic Acids77
- Ch. 21 - Carboxylic Acid Derivatives141
- Ch. 22 - Condensations and Alpha Substitutions of Carbonyl Compounds175
- Ch. 23 - Carbohydrates and Nucleic Acids93
- Ch. 24 - Amino Acids, Peptides, and Proteins54
Chapter 5, Problem 32b
Calculate the specific rotations of the following samples taken at 25 °C using the sodium D line.
b. 0.050 g of sample is dissolved in 2.0 mL of ethanol, and this solution is placed in a 2.0-cm polarimeter tube. The observed rotation is clockwise 0.043°.
Verified step by step guidance1
Understand 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 (dm), and \( c \) is the concentration in grams per milliliter (g/mL).
Convert the path length \( l \) from centimeters to decimeters. Since 1 dm = 10 cm, divide the given path length (2.0 cm) by 10 to get \( l \) in dm.
Calculate the concentration \( c \) of the solution. Use the formula \( c = \frac{\text{mass of sample}}{\text{volume of solution}} \). The mass of the sample is 0.050 g, and the volume of the solution is 2.0 mL.
Substitute the values for \( \alpha_{\text{obs}} \) (0.043°), \( l \) (in dm), and \( c \) (in g/mL) into the specific rotation formula \( [\alpha] = \frac{\alpha_{\text{obs}}}{l \cdot c} \).
Simplify the expression to calculate the specific rotation \( [\alpha] \). Ensure the units are consistent throughout the calculation.
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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). This value is temperature and wavelength dependent, typically measured at 20 °C or 25 °C using the sodium D line (589 nm).
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Specific rotation vs. observed rotation.
Polarimetry
Polarimetry is an analytical technique used to measure the optical activity of chiral substances. A polarimeter consists of a light source, a polarizer, a sample tube, and an analyzer. When plane-polarized light passes through a sample, the rotation of the light is measured, allowing for the determination of the specific rotation of the compound. This technique is crucial in characterizing and quantifying chiral molecules.
Concentration and Path Length
In the context of specific rotation, concentration refers to the amount of solute (in grams) per unit volume of solvent (in milliliters), while path length is the distance the light travels through the sample (in decimeters). Both factors are essential for calculating specific rotation, as they directly influence the observed rotation. The formula for specific rotation incorporates these variables, emphasizing their importance in polarimetric measurements.
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Related Practice
Textbook Question
The specific rotation of (S)-2-iodobutane is +15.90°.
a. Draw the structure of (S)-2-iodobutane.
b. Predict the specific rotation of (R)-2-iodobutane.
c. Determine the percentage composition of a mixture of (R)- and (S)-2-iodobutane with a specific rotation of –7.95°.
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Textbook Question
Draw the enantiomer, if any, for each structure.
(g)
(h)
Textbook Question
For each structure,
1. draw all the stereoisomers.
2. label each structure as chiral or achiral.
3. give the relationships between the stereoisomers (enantiomers, diastereomers).
(a)
Textbook Question
Calculate the specific rotations of the following samples taken at 25 °C using the sodium D line.
a. 1.00 g of sample is dissolved in 20.0 mL of ethanol. Then 5.00 mL of this solution is placed in a 20.0-cm polarimeter tube. The observed rotation is 1.25° counterclockwise.
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Textbook Question
(+)-Tartaric acid has a specific rotation Of +12.0°. Calculate the specific rotation of a mixture of 68% (+)-tartaric acid and 32% (–)-tartaric acid.
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