Textbook Question
Show that the [4 + 2] Diels–Alder reaction is photochemically forbidden.
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Ch. 15 - Conjugated Systems, Orbital Symmetry, and Ultraviolet Spectroscopy
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
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Wade 9th EditionCh. 15 - Conjugated Systems, Orbital Symmetry, and Ultraviolet SpectroscopyProblem 21
Wade 9th EditionCh. 15 - Conjugated Systems, Orbital Symmetry, and Ultraviolet SpectroscopyProblem 21Chapter 15, Problem 21
One milligram of a compound of molecular weight 160 is dissolved in 10 mL of ethanol, and the solution is poured into a 1-cm UV cell. The UV spectrum is taken, and there is an absorption at λmax = 247 nm. The maximum absorbance at 247 nm is 0.50. Calculate the value of e for this absorption.
Verified step by step guidance1
Step 1: Recall the Beer-Lambert Law, which is expressed as: , where A is the absorbance, ε is the molar absorptivity (in L·mol⁻¹·cm⁻¹), c is the concentration (in mol·L⁻¹), and l is the path length of the cell (in cm).
Step 2: Identify the given values from the problem: A = 0.50, l = 1 cm, and the molecular weight (MW) of the compound is 160 g/mol. The mass of the compound dissolved is 1 mg (0.001 g), and the volume of the solution is 10 mL (0.01 L).
Step 3: Calculate the concentration (c) of the solution in mol·L⁻¹. Use the formula: , where m is the mass of the compound, MW is the molecular weight, and V is the volume of the solution in liters.
Step 4: Rearrange the Beer-Lambert Law to solve for ε (molar absorptivity): . Substitute the values of A, c, and l into this equation.
Step 5: Perform the calculation to determine the value of ε. Ensure the units are consistent throughout the calculation, and the final value of ε will be in L·mol⁻¹·cm⁻¹.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Beer-Lambert Law
The Beer-Lambert Law relates the absorbance of light to the properties of the material through which the light is traveling. It states that absorbance (A) is directly proportional to the concentration (c) of the absorbing species, the path length (l) of the light through the sample, and the molar absorptivity (ε) of the substance. The equation is A = εcl, which is essential for calculating the molar absorptivity in this context.
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Molar Absorptivity (ε)
Molar absorptivity, or molar extinction coefficient (ε), is a measure of how strongly a chemical species absorbs light at a given wavelength. It is expressed in units of L/(mol·cm) and is specific to each substance at a particular wavelength. In this problem, calculating ε will provide insight into the compound's ability to absorb UV light at 247 nm.
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Concentration Calculation
To apply the Beer-Lambert Law, it is necessary to determine the concentration of the compound in the solution. Concentration (c) can be calculated using the formula c = m/MV, where m is the mass of the solute, M is the molar mass, and V is the volume of the solution in liters. In this case, the concentration will be crucial for finding the molar absorptivity.
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Related Practice
Textbook Question
Match four of the following UV absorption maxima (λmax) with the corresponding compounds: (1) 232 nm; (2) 256 nm; (3) 273 nm; (4) 292 nm; (5) 313 nm; (6) 353 nm.
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Textbook Question
Show that the [4 + 4] cycloaddition of two butadiene molecules to give cycloocta-1,5-diene is thermally forbidden but photochemically allowed.
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Textbook Question
There is a different, thermally allowed cycloaddition of two butadiene molecules. Show this reaction, and explain why it is thermally allowed. (Hint: Consider the dimerization of cyclopentadiene.)
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Textbook Question
Phenolphthalein is an acid–base indicator that is colorless below pH 8 and red above pH 8. Explain briefly why the first structure is colorless and the second structure is colored.
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Textbook Question
Classify the following dienes and polyenes as isolated, conjugated, cumulated, or some combination of these classifications.
(a) cycloocta-1,4-diene
(b) cycloocta-1,3-diene
(c) cyclodeca-1,2-diene
(d) cycloocta-1,3,5,7-tetraene
(e) cyclohexa-1,3,5-triene (benzene)
(f) penta-1,2,4-triene