Textbook Question
Answer the following questions for the molecular orbitals (MOs) of 1,3,5,7-octatetraene:
d. Which MO is the HOMO and which is the LUMO in the ground state?
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Ch. 8 - Delocalized Electrons: Their Effect on Stability, pKa, and the Products of a Reaction • Aromaticity and Electronic Effects: An Introduction to the Reactions of Benzene
Bruice8th EditionOrganic ChemistryISBN: 9780135213711
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Table of contents
- Ch. 1 - Remembering General Chemistry: Electronic Structure and Bonding (Part 1)31
- Ch. 1 - Remembering General Chemistry: Electronic Structure and Bonding (Part 2)65
- Ch. 2 - Acids and Bases: Central to Understanding Organic Chemistry84
- Ch. 3 - An Introduction to Organic Compounds:Nomenclature, Physical Properties, and Structure183
- Ch. 4 - Isomers: The Arrangement of Atoms in Space121
- Ch. 5 - Alkenes: Structure, Nomenclature, and an Introduction to Reactivity • Thermodynamics and Kinetics83
- Ch. 6 - The Reactions of Alkenes • The Stereochemistry of Addition Reactions175
- Ch. 7 - The Reactions of Alkynes • An Introduction to Multistep Synthesis119
- Ch. 8 - Delocalized Electrons: Their Effect on Stability, pKa, and the Products of a Reaction • Aromaticity and Electronic Effects: An Introduction to the Reactions of Benzene148
- Ch. 9 - Substitution and Elimination Reactions of Alkyl Halides212
- Ch. 10 - Reactions of Alcohols, Ethers, Epoxides, Amines, and Sulfur-Containing Compounds131
- Ch. 11 - Organometallic Compounds60
- Ch. 12 - Radicals90
- Ch. 13 - Mass Spectrometry; Infrared Spectroscopy; UV/Vis Spectroscopy62
- Ch. 14 - NMR Spectroscopy95
- Ch. 15 - Reactions of Carboxylic Acids and Carboxylic Acid Derivatives123
- Ch. 16 - Reactions of Aldehydes and Ketones • More Reactions of Carboxylic Acid Derivatives141
- Ch. 17 - Reactions at the Alpha-Carbon101
- Ch. 18 - Reactions of Benzene and Substituted Benzenes144
- Ch. 19 - More About Amines • Reactions of Heterocyclic Compounds49
- Ch. 20 - The Organic Chemistry of Carbohydrates80
- Ch. 21 - Amino Acids, Peptides, and Proteins57
- Ch. 22 - Catalysis in Organic Reactions and in Enzymatic Reactions35
- Ch. 23 - The Organic Chemistry of the Coenzymes—Compounds Derived from Vitamins1
- Ch. 28 - Pericyclic Reactions58
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Bruice 8th EditionCh. 8 - Delocalized Electrons: Their Effect on Stability, pKa, and the Products of a Reaction • Aromaticity and Electronic Effects: An Introduction to the Reactions of BenzeneProblem 86g
Bruice 8th EditionCh. 8 - Delocalized Electrons: Their Effect on Stability, pKa, and the Products of a Reaction • Aromaticity and Electronic Effects: An Introduction to the Reactions of BenzeneProblem 86gChapter 9, Problem 86g
Answer the following questions for the molecular orbitals (MOs) of 1,3,5,7-octatetraene:
g. How many nodes does the highest-energy MO of 1,3,5,7-octatetraene have between the nuclei?
Verified step by step guidance1
Identify the number of π-electrons in 1,3,5,7-octatetraene. Each double bond contributes 2 π-electrons, and there are 4 double bonds, so the molecule has 8 π-electrons.
Determine the number of molecular orbitals (MOs) formed. For 8 π-electrons, there will be 8 π-MOs, labeled as Ψ₁, Ψ₂, Ψ₃, ..., Ψ₈, with Ψ₁ being the lowest-energy MO and Ψ₈ being the highest-energy MO.
Recall that the number of nodes in a molecular orbital increases as the energy of the MO increases. The number of nodes in a given MO is equal to (n - 1), where n is the MO's index (e.g., Ψ₁ has 0 nodes, Ψ₂ has 1 node, etc.).
For the highest-energy MO (Ψ₈), calculate the number of nodes using the formula (n - 1). Since n = 8 for Ψ₈, the number of nodes is (8 - 1) = 7.
Conclude that the highest-energy MO of 1,3,5,7-octatetraene has 7 nodes between the nuclei.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Molecular Orbitals (MOs)
Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO) and describe the behavior of electrons in a molecule. They can be bonding, antibonding, or non-bonding, depending on the phase relationship of the combining atomic orbitals. The energy levels of MOs are crucial for understanding the electronic structure and reactivity of molecules.
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Nodes in Molecular Orbitals
Nodes are regions in a molecular orbital where the probability of finding an electron is zero. The number of nodes in a MO is related to its energy level; higher energy MOs have more nodes. For a given molecular system, the number of nodes can be determined using the formula: number of nodes = n - 1, where n is the principal quantum number of the MO.
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Octatetraene Structure
1,3,5,7-octatetraene is a linear conjugated hydrocarbon with alternating double bonds. Its structure allows for delocalization of π electrons across the molecule, which influences the energy levels of its molecular orbitals. Understanding the arrangement of these double bonds is essential for predicting the number of nodes in the highest-energy MO, as it directly affects the electron distribution and energy states.
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Related Practice
Textbook Question
Answer the following questions for the molecular orbitals (MOs) of 1,3,5,7-octatetraene:
e. Which MO is the HOMO and which is the LUMO in the excited state?
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Textbook Question
A student obtained two products from the reaction of 1,3-cyclohexadiene with Br2 (disregarding stereoisomers). His lab partner was surprised when he obtained only one product from the reaction of 1,3-cyclohexadiene with HBr (disregarding stereoisomers). Account for these results.
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Textbook Question
How could you synthesize the following compound from starting materials containing no more than six carbons?
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Textbook Question
How could the following compounds be synthesized using a Diels–Alder reaction?
a.
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Textbook Question
Answer the following questions for the molecular orbitals (MOs) of 1,3,5,7-octatetraene:
f. What is the relationship between HOMO and LUMO and symmetric and antisymmetric orbitals?
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