Chapter 11: Problem 72
The most stable free radical among the following is (1) \(\mathrm{C}_{6} \mathrm{H}_{5} \cdot \mathrm{CH}_{2}\) (2) \(\mathrm{CH}_{3}-\cdot \mathrm{CH}-\mathrm{CH}_{3}\) (3) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHCH}_{3}\) (4) \(\mathrm{CH}_{3} \cdot \mathrm{CH}_{2}\) (a) \(3>1>4>2\) (b) \(1>3>2>4\) (c) \(3>1>2>4\) (d) \(3>2>1>4\)
Short Answer
Expert verified
Option (c): 3 > 1 > 2 > 4.
Step by step solution
01
Understanding Free Radical Stability
Free radicals are atoms or molecules that have unpaired electrons, which makes them highly reactive and unstable. The stability of free radicals is influenced primarily by factors such as resonance and hyperconjugation.
02
Analyzing Each Radical
- ** 31E 1.** 31D \( \mathrm{C}_{6} \mathrm{H}_{5} \cdot \mathrm{CH}_{2} \): This radical is benzyl, which benefits from resonance stabilization as the unpaired electron can delocalize into the aromatic ring.- ** 31E 2.** 31D \( \mathrm{CH}_{3}-\cdot \mathrm{CH}-\mathrm{CH}_{3} \): This is a secondary alkyl radical which gains stability from hyperconjugation and inductive effects.- ** 31E 3.** 31D \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHCH}_{3} \): This radical is an allyl radical, also benefitting from resonance as the heavy allylic resonance structure allows greater electron delocalization through the conjugated system.- ** 31E 4.** 31D \( \mathrm{CH}_{3} \cdot \mathrm{CH}_{2} \): This is a primary alkyl radical, which is the least stable due to lack of resonance or significant hyperconjugation.
03
Ranking Order Based on Stability
Resonance is a more stabilizing factor than hyperconjugation. The allylic radical (Option 3) is most stabilized due to resonance over the benzyl radical (Option 1). Secondary radical (Option 2) is stabilized by hyperconjugation but is less stable than options 1 and 3. Primary radical (Option 4) is the least stable. Thus, the stability order is determined as 3 > 1 > 2 > 4.
04
Selecting the Correct Option
The stability order 3 > 1 > 2 > 4 matches option (c).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Resonance Stabilization
Resonance stabilization plays a crucial role in the stability of free radicals. When a free radical can spread its unpaired electron over a larger structure through resonance, its energy decreases, leading to enhanced stability. An example of this can be observed in the benzyl and allylic radicals. In benzyl radicals, the unpaired electron can delocalize throughout the aromatic ring, thanks to resonance structures. This delocalization decreases the electron's energy, providing a more stable configuration for the molecule.
In the case of the allylic radical, resonance allows the unpaired electron to distribute over a conjugated system. The conjugated system of alternating single and double bonds offers a wider space for electron delocalization. As a result, a molecule with a structure that enables resonance will usually have greater stability. Therefore, when comparing the stability of free radicals, molecules benefitting from resonance stabilization are generally more stable than those relying on other stabilizing factors.
In the case of the allylic radical, resonance allows the unpaired electron to distribute over a conjugated system. The conjugated system of alternating single and double bonds offers a wider space for electron delocalization. As a result, a molecule with a structure that enables resonance will usually have greater stability. Therefore, when comparing the stability of free radicals, molecules benefitting from resonance stabilization are generally more stable than those relying on other stabilizing factors.
Hyperconjugation
Hyperconjugation is another pivotal factor in determining the stability of free radicals. It involves the interaction of the radical's unpaired electron with adjacent C-H bonds in a molecule. This overlap allows electron density to be shared with the radical center, thereby stabilizing it. Hyperconjugation is frequently observed in alkyl radicals, where sigma bonds interact with the radical's p-orbital.
Consider secondary radicals like \( \mathrm{CH}_3-\cdot \mathrm{CH}-\mathrm{CH}_3 \). Here, hydrogen atoms from adjacent C-H bonds contribute to hyperconjugative stabilization. More adjacent bonds enhance such stabilization, distributing the electron's energy and lowering the radical’s overall energy.
Nonetheless, while hyperconjugation provides a degree of stability, it is not as effective as resonance stabilization. Thus, radicals relying solely on hyperconjugation are typically less stable compared to those benefitting from resonance.
Consider secondary radicals like \( \mathrm{CH}_3-\cdot \mathrm{CH}-\mathrm{CH}_3 \). Here, hydrogen atoms from adjacent C-H bonds contribute to hyperconjugative stabilization. More adjacent bonds enhance such stabilization, distributing the electron's energy and lowering the radical’s overall energy.
Nonetheless, while hyperconjugation provides a degree of stability, it is not as effective as resonance stabilization. Thus, radicals relying solely on hyperconjugation are typically less stable compared to those benefitting from resonance.
Alkyl Radicals
Alkyl radicals are a specific class of radicals where the unpaired electron resides on an alkyl carbon. Their stability is influenced by the type of carbon they are attached to, namely primary, secondary, or tertiary. The stability order typically follows tertiary > secondary > primary.
This order is primarily because secondary and tertiary carbons can gain stability through both hyperconjugation and inductive effects. Secondary radicals like \( \mathrm{CH}_3-\cdot \mathrm{CH}-\mathrm{CH}_3 \) are more stable than primary radicals due to having more adjacent bonds contributing to hyperconjugation. Tertiary radicals have even more such interactions, often resulting in substantial stability.
Primary radicals, such as \( \mathrm{CH}_3 \cdot \mathrm{CH}_2 \), have limited stabilization options as they rely less on hyperconjugation and do not benefit significantly from inductive effects. This makes them the least stable among alkyl radicals.
This order is primarily because secondary and tertiary carbons can gain stability through both hyperconjugation and inductive effects. Secondary radicals like \( \mathrm{CH}_3-\cdot \mathrm{CH}-\mathrm{CH}_3 \) are more stable than primary radicals due to having more adjacent bonds contributing to hyperconjugation. Tertiary radicals have even more such interactions, often resulting in substantial stability.
Primary radicals, such as \( \mathrm{CH}_3 \cdot \mathrm{CH}_2 \), have limited stabilization options as they rely less on hyperconjugation and do not benefit significantly from inductive effects. This makes them the least stable among alkyl radicals.
Inductive Effects
Inductive effects refer to the transmission of charge through a chain of atoms in a molecule. This effect can either stabilize or destabilize a radical based on the nature of the groups involved. Electronegative atoms or groups pull electron density towards themselves, effectively spreading out the charge. In alkyl radicals, the inductive effect often acts in combination with hyperconjugation to stabilize the radical.
For secondary radicals, such as \( \mathrm{CH}_3-\cdot \mathrm{CH}-\mathrm{CH}_3 \), inductive effects can enhance stability, albeit to a lesser extent compared to resonance. Alkyl groups, which are slightly electron-donating, can push electron density towards the radical center, stabilizing it. The more alkyl groups surrounding the radical center, the greater the inductive stabilization.
Despite this, consider that while inductive effects contribute to stability, they are usually overpowered by other effects such as resonance, especially in systems where resonance is possible. Thus, in a comparative context, free radicals that are stabilized by resonance are generally more stable than those relying on inductive effects alone.
For secondary radicals, such as \( \mathrm{CH}_3-\cdot \mathrm{CH}-\mathrm{CH}_3 \), inductive effects can enhance stability, albeit to a lesser extent compared to resonance. Alkyl groups, which are slightly electron-donating, can push electron density towards the radical center, stabilizing it. The more alkyl groups surrounding the radical center, the greater the inductive stabilization.
Despite this, consider that while inductive effects contribute to stability, they are usually overpowered by other effects such as resonance, especially in systems where resonance is possible. Thus, in a comparative context, free radicals that are stabilized by resonance are generally more stable than those relying on inductive effects alone.
