Ch. 15 - Conjugated Systems, Orbital Symmetry, and Ultraviolet Spectroscopy

Wade9th EditionOrganic ChemistryISBN: 9780135213728Not the one you use?Change textbook

Wade 9th Edition

Ch. 15 - Conjugated Systems, Orbital Symmetry, and Ultraviolet Spectroscopy

Problem 3

Chapter 15, Problem 3

The central carbon atom of an allene is a member of two double bonds, and it has an interesting orbital arrangement that holds the two ends of the molecule at right angles to each other.
a. Draw an orbital diagram of allene, showing why the two ends are perpendicular.
b. Draw the two enantiomers of penta-2,3-diene. A model may be helpful.

Verified step by step guidance

Step 1: Understand the structure of allene. Allene (propadiene) has a central carbon atom bonded to two other carbon atoms via double bonds. The central carbon is sp-hybridized, meaning it has two perpendicular p orbitals available for π bonding.

Step 2: Draw the orbital diagram for allene. Represent the central carbon atom with two sp orbitals forming sigma bonds with the adjacent carbons. The two perpendicular p orbitals on the central carbon overlap with the p orbitals of the terminal carbons to form π bonds. This arrangement forces the two ends of the molecule to be perpendicular to each other.

Step 3: Analyze the structure of penta-2,3-diene. This molecule contains two double bonds between carbons 2 and 3. The molecule can exist as enantiomers due to the chiral nature of the arrangement of substituents around the double bonds.

Step 4: Draw the enantiomers of penta-2,3-diene. Use wedge and dash notation to represent the spatial arrangement of substituents. One enantiomer will have the substituents arranged in a clockwise manner, while the other will have them arranged counterclockwise.

Step 5: Verify the chirality of the enantiomers. Ensure that the two structures are non-superimposable mirror images of each other, confirming their enantiomeric relationship.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hybridization

Hybridization is the concept that describes the mixing of atomic orbitals to form new hybrid orbitals, which can explain the geometry of molecular structures. In the case of allene, the central carbon atom undergoes sp² hybridization, allowing it to form two π bonds with adjacent carbon atoms, resulting in a unique arrangement where the terminal groups are perpendicular to each other.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. For allene, the presence of two double bonds leads to a linear arrangement around the central carbon, while the terminal carbons adopt a perpendicular orientation due to the sp² hybridization, creating a distinctive 'cross' shape that is crucial for understanding its reactivity and stereochemistry.

Stereoisomerism

Stereoisomerism is a form of isomerism where molecules have the same molecular formula and connectivity but differ in the spatial arrangement of atoms. In the case of penta-2,3-diene, the presence of double bonds allows for the formation of enantiomers, which are non-superimposable mirror images, highlighting the importance of stereochemistry in organic compounds and their reactions.

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Related Practice

Textbook Question

Rank each group of compounds in order of increasing heat of hydrogenation.

(b)

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Textbook Question

When 3-bromo-1-methylcyclohexene undergoes solvolysis in hot ethanol, two products are formed. Propose a mechanism that accounts for both of these products.

Textbook Question

Draw another resonance form for each of the substituted allylic cations shown in the preceding figure, showing how the positive charge is shared by another carbon atom. In each case, state whether your second resonance form is a more important or less important resonance contributor than the first structure. (Which structure places the positive charge on the more-substituted carbon atom?)

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Textbook Question

Treatment of an alkyl halide with AgNO₃ in alcohol often promotes ionization.

Ag⁺ + R–Cl → AgCl + R⁺

When 4-chloro-2-methylhex-2-ene reacts with AgNO₃ in ethanol, two isomeric ethers are formed. Suggest structures, and propose a mechanism for their formation

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Textbook Question

In a strongly acidic solution, cyclohexa-1,4-diene tautomerizes to cyclohexa-1,3-diene. Propose a mechanism for this rearrangement, and explain why it is energetically favorable.

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Textbook Question

Rank each group of compounds in order of increasing heat of hydrogenation.

(a) hexa-1,2-diene; hexa-1,3,5-triene; hexa-1,3-diene; hexa-1,4-diene; hexa-1,5-diene; hexa-2,4-diene

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