Question

The increasing order of stability of the following free radicals is (a) \(\left(\mathrm{CH}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}<\left(\mathrm{CH}_{3}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{2} \dot{\mathrm{C}} \mathrm{H}<\left(\mathrm{C}_{6} \mathrm{H}_{3}\right)_{3} \dot{\mathrm{C}}\) (b) \(\left(\mathrm{C}_{6} \mathrm{H}_{3}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{2} \dot{\mathrm{C}} \mathrm{H}<\left(\mathrm{CH}_{3}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{CH}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}\) (c) \(\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{2} \dot{\mathrm{C}} \mathrm{H}<\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{CH}_{3}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{CH}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}\) (d) \(\left(\mathrm{CH}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}<\left(\mathrm{CH}_{3}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{C}_{6} \mathrm{H}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}\)

Short answer

(c) The order is correct based on resonance and hyperconjugation effects.

Step-by-step solution

Understanding Stability of Radicals

The stability of free radicals is affected by several factors, including resonance stabilization and hyperconjugation. Typically, radicals that can delocalize their unpaired electron over a larger structure or into aromatic systems are more stable.

Identify Resonance in Aromatic Radicals

Free radicals involving phenyl groups, such as \(\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{2} \dot{\mathrm{C}} \mathrm{H}\) and \(\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3} \dot{\mathrm{C}}\), have their stability increased due to the resonance offered by the phenyl rings. These radicals are generally more stable than those with only alkyl groups because of this resonance stabilization.

Effect of Hyperconjugation with Alkyl Groups

Alkyl groups, such as methyl (\(\mathrm{CH}_3\)), stabilize radicals by hyperconjugation. The more alkyl groups adjacent to the radical center, the more stable the radical. Therefore, \(\left(\mathrm{CH}_{3}\right)_{3} \dot{\mathrm{C}}\) is more stable than \(\left(\mathrm{CH}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}\).

Ranking Stability Based on Observations

Upon reviewing the options:- Radicals containing phenyl groups are expected to be more stable due to resonance. Thus \(\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3} \dot{\mathrm{C}}\) should be the most stable.- Among the alkyl-containing radicals, \(\left(\mathrm{CH}_{3}\right)_{3} \dot{\mathrm{C}}\) is more stable than \(\left(\mathrm{CH}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}\) due to greater hyperconjugative interactions.From the given options, option (c) correctly arranges the free radicals in increasing order of stability, which reflects these principles.

Key concepts

Radical Stability

Free radicals are atoms, molecules, or ions with unpaired electrons. These electrons make them highly reactive and often unstable. However, certain factors can influence radical stability, making some radicals more stable than others.
Free radical stability is often governed by both structural factors and electronic effects. Two primary structural factors that stabilize radicals are resonance and hyperconjugation. Elevated stability is achieved when the radical's lone electron can be delocalized across a larger molecular framework.
Typically, radicals that permit electron delocalization, whether through resonance in conjugated systems or hyperconjugation through alkyl groups, exhibit greater stability. This delocalization distributes the radical's energy and makes the entire molecule more stable.

Resonance Stabilization

Resonance stabilization is a key factor in determining the stability of free radicals. It refers to the distribution or delocalization of the unpaired electron throughout the molecule.
Molecules with aromatic phenyl rings, like benzene, are prime examples where electrons can resonate between different locations. This ability to spread out the electron density makes such radicals more stable than those that do not have resonance capability.
Resonance comes into play with radicals such as

• Those containing phenyl groups,
• Polyphenyl radicals,
• Benzyl radicals.

The greater number of resonance structures available for the radical, the more stable the radical becomes. This is because each resonance form contributes to delocalizing the radical's unpaired electron.

Hyperconjugation

Hyperconjugation is another critical stabilization mechanism for free radicals, particularly in alkyl groups.
This effect occurs when electrons in sigma bonds (typically C-H or C-C bonds) adjacent to the radical center overlap with the free radical's p orbital.
The interaction aids in dispersing the electron density away from the radical center and slightly reduces the radical's reactivity.
For example, larger alkyl radicals like

• Tertiary radicals are generally
• More stable than secondary radicals,
• And secondary radicals are more stable than primary radicals.

This is due to the greater number of hyperconjugative structures, which increase with the number of surrounding alkyl groups.

Phenyl Groups

Phenyl groups, derived from benzene, play a significant role in radical stabilization through their resonance capabilities.
These groups are composed of an aromatic ring with alternating double and single bonds, allowing for extensive electron delocalization.
Radicals that feature phenyl groups can effectively stabilize an unpaired electron due to resonance diffusion across the aromatic ring, effectively utilizing the ring's conjugated double bonds.

• Phenyl radicals like the triphenylmethyl radical,
• And diphenylmethyl radical exhibit stability due to
• The expanded electron distribution within their aromatic systems.

This expanded distribution is the key reason aromatic substitutes often lend greater radical stability than non-aromatic groups.

Alkyl Groups

Alkyl groups are carbon and hydrogen-based chains that influence a radical's stability via hyperconjugation.
Their role becomes more significant with increasing numbers of carbon atoms surrounding the radical center.
Tertiary alkyl radicals, in particular, benefit from enhanced stability because they have numerous C-H bonds capable of participating in hyperconjugation.

• As you move from methyl radicals to tertiary carbon radicals,
• The stability increases due to a higher number of supporting
• C-H bonds involved in hyperconjugation.

Hence, the order of radical stability generally follows the sequence: tertiary > secondary > primary > methyl. Alkyl groups, by providing additional hyperconjugative structures, disburse radical energy effectively.