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 32a
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.
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, and \( c \) is the concentration in g/mL.
Convert the path length \( l \) from cm to dm. Since 1 dm = 10 cm, divide the given path length (20.0 cm) by 10 to get \( l \) in dm.
Calculate the concentration \( c \) of the solution. First, determine the amount of sample in the 5.00 mL solution. Since 1.00 g of sample is dissolved in 20.0 mL of ethanol, the concentration of the stock solution is \( \frac{1.00}{20.0} \) g/mL. Multiply this by the volume of the solution used (5.00 mL) to find the mass of the sample in the polarimeter tube. Then divide this mass by the total volume of the solution in the polarimeter tube (5.00 mL) to get \( c \).
Substitute the observed rotation \( \alpha_{\text{obs}} = -1.25^{\circ} \) (negative because it is counterclockwise), the calculated path length \( l \), and the calculated concentration \( c \) into the specific rotation formula.
Simplify the expression to find the specific rotation \( [\alpha] \). Ensure the units are consistent and the final value is expressed with the correct sign and units (degrees·mL·g⁻¹·dm⁻¹).
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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 using the sodium D line (589 nm).
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05:43
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 sample holder, and a detector. 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 for characterizing enantiomers and assessing purity.
Concentration and Dilution
Concentration refers to the amount of solute present in a given volume of solution, typically expressed in grams per milliliter (g/mL). In the context of the question, a specific volume of a diluted solution is used to measure optical rotation. Understanding how to calculate concentration from mass and volume, as well as how dilution affects concentration, is essential for accurately determining specific rotation in polarimetry.
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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
Draw the enantiomer, if any, for each structure.
(a)
(b)
2
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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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Textbook Question
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°.
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