Textbook Question
We have studied a number of pericyclic reactions previously. Draw the mechanism of the steps shown. The section number where this material was first studied is given for your review.
(a)
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Ch. 22 - Conjugated Systems II: Pericyclic Reactions
Mullins1st EditionOrganic Chemistry: A Learner Centered ApproachISBN: 9780137566471
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Table of contents
- Ch. 2 - General Chemistry Translated: Finding the Electrons114
- Ch. 3 - Alkanes and Cycloalkanes: Properties and Conformational Analysis109
- Ch. 4 - Acids and Bases: Electron Flow144
- Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics118
- Ch. 6 - Stereoisomerism: Arrangement of Atoms in Space112
- Ch. 7 - Principles of Green (Organic) Chemistry3
- Ch. 8 - Alkenes I: Properties and Electrophilic Additions158
- Ch. 9 - Alkenes II: Oxidation and Reduction150
- Ch. 10 - Alkynes: Electrophilic Addition and Redox Reactions101
- Ch. 11 - Properties and Synthesis of Alkyl Halides: Radical Reactions108
- Ch. 12 - Substitution and Elimination: Reactions of Haloalkanes172
- Ch. 13 - Alcohols, Ethers and Related Compounds: Substitution and Elimination239
- Ch. 14 - Structural Identification I: Infrared Spectroscopy and Mass Spectrometry54
- Ch. 15 - Structural Identification II: Nuclear Magnetic Resonance Spectroscopy93
- Ch. 16 - Metals in Organic Chemistry48
- Ch. 17 - Carbonyl Addition Reactions: Aldehydes and Ketones45
- Ch. 18 - Nucleophilic Acyl Substitution I: Carboxylic Acids18
- Ch. 19 - Nucleophilic Acyl Substitution II: Carboxylic Acid Derivatives39
- Ch. 20 - Enolates: Carbonyl Addition and Substitution13
- Ch. 21 - Conjugated Systems I: Stability and Addition Reactions56
- Ch. 22 - Conjugated Systems II: Pericyclic Reactions54
- Ch. 23 - Benzene I: Aromatic Stability and Substitution Reactions64
- Ch. 24 - Benzene II: Reactions Influenced by the Aromatic Ring62
- Ch. 25 - Amines: Structure, Reactions, and Synthesis27
- Ch. 26 - Amino Acids, Proteins, and Peptide Synthesis9
- Ch. 27 - Carbohydrates, Nucleic Acids, and Lipids54
Mullins1st EditionOrganic Chemistry: A Learner Centered ApproachISBN: 9780137566471Not the one you use?Change textbook
Chapter 21, Problem 4
What frequency of light would be required to excite an electron if the HOMO–LUMO energy gap was 33.9 kcal/mol (142 kJ/mol)?
Verified step by step guidance1
Step 1: Understand the relationship between energy and frequency. The energy of a photon is related to its frequency by the equation E = hν, where E is the energy, h is Planck's constant (6.626 × 10⁻³⁴ J·s), and ν is the frequency of the light.
Step 2: Convert the given energy from kcal/mol or kJ/mol to joules per molecule. Use the conversion factors: 1 kcal = 4184 J and 1 mol = 6.022 × 10²³ molecules. For example, 33.9 kcal/mol can be converted to joules per molecule by dividing the total energy in joules by Avogadro's number.
Step 3: Rearrange the equation E = hν to solve for frequency (ν). The formula becomes ν = E/h, where E is the energy in joules per molecule and h is Planck's constant.
Step 4: Substitute the calculated energy value (in joules per molecule) and Planck's constant into the equation ν = E/h to determine the frequency of light required to excite the electron.
Step 5: Ensure the frequency is expressed in appropriate units, such as hertz (Hz), which is equivalent to s⁻¹. If needed, convert the frequency to other units like THz (terahertz) for better interpretation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
HOMO-LUMO Gap
The HOMO-LUMO gap refers to the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in a molecule. This gap is crucial in determining the electronic properties of a compound, including its reactivity and color. A smaller gap typically indicates that a molecule can absorb lower energy light, while a larger gap requires higher energy light for electronic transitions.
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02:35
HOMO vs. LUMO
Energy and Frequency Relationship
The energy of a photon is directly related to its frequency through the equation E = hν, where E is energy, h is Planck's constant, and ν (nu) is the frequency. This relationship implies that higher energy photons correspond to higher frequencies. Understanding this relationship is essential for calculating the frequency of light needed to excite an electron across the HOMO-LUMO gap.
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06:07Introduction to free energy diagrams.
Conversion of Energy Units
In organic chemistry, energy is often expressed in different units, such as kcal/mol or kJ/mol. To calculate the frequency of light required for an electronic transition, it is necessary to convert these energy units into joules (J). This conversion is essential for applying the energy-frequency relationship accurately, as the standard unit for energy in the equation E = hν is joules.
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Related Practice
Textbook Question
Draw two important resonance structures involving the C―O π bond for the molecule shown. To which carbons would you expect a nucleophile to add?
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Textbook Question
Draw two important resonance structures involving the lone pair on oxygen for the molecule shown. Which carbons are most likely to act as nucleophiles?
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Textbook Question
Draw the molecular orbital picture for (a) ethene. Label the HOMO and LUMO of each.
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Textbook Question
We have studied a number of pericyclic reactions previously. Draw the mechanism of the steps shown. The section number where this material was first studied is given for your review.
(b)
726
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Textbook Question
The SN2 reaction is the concerted, backside displacement of a good leaving group by a nucleophile. Why do nucleophiles attack from the back in SN2 reactions?
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