Thermal Rearrangement of 5-Butylnona-2,6-diene: Formation of 5-Ethyl-4-methyldeca-2,6-diene

An In-depth Exploration of the Cope Rearrangement Mechanism

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In the realm of organic chemistry, understanding the behavior of molecules under various conditions is essential for predicting reaction outcomes and synthesizing new compounds. One fascinating area of study is the thermal rearrangement of conjugated dienes, specifically through mechanisms known as sigmatropic shifts. When 5-butylnona-2,6-diene is heated, it undergoes a transformation that poses an intriguing question:

Which of the following molecules is formed when 5-butylnona-2,6-diene is heated?

4-ethyl-3-methyldeca-1,5-diene
5-ethylundeca-2,6-diene
5-ethyl-4-methyldeca-2,6-diene
5-ethyl-4-methyldeca-2,6-diene

To determine the correct product, we delve into the principles of thermal rearrangements, focusing on the Cope rearrangement, and examine how it applies to the given compound.

Key Takeaways

5-Butylnona-2,6-diene undergoes a Cope rearrangement upon heating, resulting in a structural isomer.
The Cope rearrangement is a [3,3]-sigmatropic shift involving a cyclic transition state that preserves the diene system.
The product formed is 5-ethyl-4-methyldeca-2,6-diene due to the redistribution of substituents during the rearrangement.

Understanding the Cope Rearrangement

Definition and Mechanism

The Cope rearrangement is a well-known thermal [3,3]-sigmatropic rearrangement occurring in 1,5-dienes. In this reaction, a sigma bond adjacent to two pi systems shifts position, resulting in the formation of a new sigma bond and the relocation of the double bonds. The rearrangement proceeds via a concerted mechanism through a six-membered cyclic transition state, preserving the total number of sigma and pi bonds.

The general form of the Cope rearrangement can be represented as:


      [1,5]-diene → [1,5]-diene (isomer)

During this rearrangement, the molecule undergoes a cyclic reorganization where electrons in the sigma bond and adjacent pi bonds migrate simultaneously. The result is a structural isomer with the same molecular formula but a different connectivity of atoms.

Characteristics of the Cope Rearrangement

Several key features characterize the Cope rearrangement:

Pericyclic Reaction: It proceeds through a concerted mechanism without intermediates, involving a cyclic flow of electrons.
Sigmatropic Shift: Classified as a [3,3]-sigmatropic rearrangement, indicating that both migrating groups span three atoms during the shift.
Thermal Activation: The reaction is facilitated by heat, as it requires sufficient energy to overcome the activation barrier.
Conservation of Orbital Symmetry: The reaction follows the Woodward-Hoffmann rules, allowing for a thermally allowed suprafacial shift.
Reversibility: The Cope rearrangement is reversible; the product can revert to the starting material under certain conditions.

The thermodynamics of the reaction are influenced by the stabilities of the starting material and the product. Factors such as substitution patterns and strain in the transition state play significant roles in determining the reaction's favorability.

Application to 5-Butylnona-2,6-diene

Structure of 5-Butylnona-2,6-diene

The compound 5-butylnona-2,6-diene is a 1,5-diene with a butyl substituent at the fifth carbon. Its structural formula can be depicted as:


CH₂=CH–CH₂–CH₂–CH(C₄H₉)–CH₂–CH=CH₂

Breaking down the structure:

Double Bonds: Located between carbons 2-3 and 6-7, forming the conjugated diene system necessary for the Cope rearrangement.
Butyl Substituent: Attached to carbon 5, the central carbon in the chain.
Carbon Chain: A nine-carbon backbone (nona-), forming the basis of the compound.

Visualizing the molecule is crucial for understanding how the rearrangement alters the structure. The alignment of the pi systems and the position of the substituent directly influence the outcome of the reaction.

Mechanism of the Rearrangement

Upon heating, 5-butylnona-2,6-diene undergoes a Cope rearrangement through the following steps:

Formation of the Transition State: The molecule adopts a chair-like six-membered transition state, where the sigma bond between carbons 3 and 4 breaks, and a new sigma bond forms between carbons 1 and 6.


Step 1: 
       C1      C6
        \      /
         C2--C5
        /      \
      C3        C4

Electron Migration: The electrons from the sigma bond between C3 and C4 shift to form a new sigma bond between C1 and C6. Simultaneously, the pi electrons adjust to maintain the conjugated system.
Formation of the Product: The new sigma bond formation results in a rearranged carbon skeleton. The butyl group attached to C5 is effectively redistributed, leading to an ethyl group at C5 and a methyl group at C4 in the product.


Product Structure:
CH₂=CH–CH₂–CH(CH₃)–CH(C₂H₅)–CH₂–CH=CH₂

The net effect is a shift in the position of the double bonds and substituents without changing the overall number of atoms or the unsaturation level. The rearrangement leads to a more stable molecule due to the increased substitution on the double bonds.

Energetics and Favorability

The Cope rearrangement proceeds when the product is thermodynamically more stable than the starting material. Factors contributing to the stability include:

Hyperconjugation: Greater alkyl substitution on double bonds stabilizes the alkene through hyperconjugation.
Reduced Steric Strain: Redistribution of substituents can alleviate steric hindrance in the molecule.
Entropy Considerations: The reaction involves a single molecule rearranging, with minimal entropy change.

In the case of 5-butylnona-2,6-diene, the formation of 5-ethyl-4-methyldeca-2,6-diene results in a more substituted and thus more stable alkene system.

Determining the Product

Formation of 5-Ethyl-4-methyldeca-2,6-diene

The rearranged molecule, 5-ethyl-4-methyldeca-2,6-diene, has the following structural formula:


CH₂=CH–CH₂–CH(CH₃)–CH(C₂H₅)–CH₂–CH=CH₂

Key changes from the starting material include:

Substituent Redistribution: The original butyl group (C₄H₉) is effectively divided into an ethyl group (C₂H₅) at C5 and a methyl group (CH₃) at C4.
Double Bond Positions: The positions of the double bonds remain between carbons 2-3 and 6-7, maintaining the diene system.
Carbon Chain Length: The backbone extends to ten carbons (deca-) due to the rearrangement.

The changes result from the concerted movement of electrons and atoms during the Cope rearrangement, leading to a new isomer that is more stable under the reaction conditions.

Analyzing the Options

Considering the nature of the Cope rearrangement and the structural changes involved, we can evaluate the given options:

4-ethyl-3-methyldeca-1,5-diene: This molecule implies a shift of the double bonds to positions 1-2 and 5-6, which is not consistent with the Cope rearrangement mechanism starting from 5-butylnona-2,6-diene.
5-ethylundeca-2,6-diene: This option suggests an increase in the carbon chain length to eleven carbons (undeca-), which is not possible without adding extra atoms not present in the starting material.
5-ethyl-4-methyldeca-2,6-diene: This molecule matches the expected product from the Cope rearrangement, with the correct redistribution of substituents and preservation of the diene system.

Given these analyses, the correct product formed when 5-butylnona-2,6-diene is heated is 5-ethyl-4-methyldeca-2,6-diene. The duplicates in the options appear to be an error, and the accurate answer aligns with the Cope rearrangement mechanism.

Why Other Options Are Incorrect

To further clarify why the other options are not the correct products:

Option 1: 4-ethyl-3-methyldeca-1,5-diene shows a shift in both the substituents and the positions of the double bonds inconsistent with a [3,3]-sigmatropic shift from the given starting material.
Option 2: 5-ethylundeca-2,6-diene implies an addition of two carbons, which cannot occur through a rearrangement that only involves the reorganization of existing atoms.

The Cope rearrangement does not result in changes to the total number of carbons or the positions of the double bonds beyond the scope of the sigmatropic shift.

Conclusion

Understanding the Cope rearrangement allows us to predict the outcome of heating 5-butylnona-2,6-diene. Through a [3,3]-sigmatropic shift, the molecule undergoes a concerted rearrangement resulting in the formation of 5-ethyl-4-methyldeca-2,6-diene. This product is favored due to the increased stability from greater alkyl substitution on the double bonds and the redistribution of substituents without altering the overall carbon count or unsaturation.

The analysis of the reaction mechanism demonstrates the importance of mechanistic knowledge in organic synthesis and the predictive power it provides in identifying reaction products.