Question

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

Short answer

(d) is the correct order of stability.

Step-by-step solution

Understanding Free Radical Stability

The stability of free radicals is influenced by the ability of substituents to disperse the unpaired electron's energy. The more delocalization and inductive effect present, the more stable the radical is. Aromatic rings like phenyl (\(\text{C}_6\text{H}_5\)) can stabilize radicals via resonance, while alkyl groups provide stability through hyperconjugation and the inductive effect.

Analyzing Free Radicals

Consider the radicals: \(\left(\text{C}_6\text{H}_5\right)_3 \dot{\text{C}}\), \(\left(\text{C}_6\text{H}_5\right)_2 \dot{\text{C}}\), \(\left(\text{CH}_3\right)_3 \dot{\text{C}}\), and \(\left(\text{CH}_3\right)_2 \dot{\text{C}}\text{H}\). The tri-phenyl (\(\left(\text{C}_6\text{H}_5\right)_3 \dot{\text{C}}\)) radical, with three phenyl groups, has extensive resonance stabilization, making it generally the most stable. The tertiary alkyl radical \(\left(\text{CH}_3\right)_3 \dot{\text{C}}\) has more inductive and hyperconjugation effects than \(\left(\text{CH}_3\right)_2 \dot{\text{C}}\text{H}\) and thus is more stable.

Arranging Radicals by Stability

Given the factors affecting stability, arrange the radicals from least to most stable. The least stable radicals will have fewer stabilizing effects (e.g., fewer phenyl groups for resonance, fewer alkyl groups for hyperconjugation).

Comparing Options Against Stability Order

Looking at each option:(a) and (d) both have \(\left(\text{CH}_3\right)_2 \dot{\text{C}}\text{H}\) < \(\left(\text{CH}_3\right)_3 \dot{\text{C}}\), and both options show \(\left(\text{C}_6\text{H}_5\right)_2 \dot{\text{C}}\text{H}\) and \(\left(\text{C}_6\text{H}_5\right)_3 \dot{\text{C}}\) reversed. Based on usual stability, \(\left(\text{C}_6\text{H}_5\right)_3 \dot{\text{C}}\) would be more stable than \(\left(\text{C}_6\text{H}_5\right)_2 \dot{\text{C}}\text{H}\). Therefore, (d) correctly places them.

Key concepts

Hyperconjugation

Hyperconjugation is a fascinating concept that enhances the stability of certain molecules, such as free radicals. It involves the interaction between the electrons in a sigma bond (usually \(-\text{C}-\text{H}\) bonds) and an adjacent empty or partially filled p-orbital or a pi orbital. This sharing or delocalization of electron density across bonds helps disperse energy in the molecule, leading to increased stability.

In terms of free radicals, hyperconjugation means that the more hydrogen or alkyl groups bonded to the carbon with the unpaired electron, the more stable the radical will be. This is because these groups can hyperconjugatively stabilize the radical center by dispersing the energy of the unpaired electron.

• A tertiary radical, which has three alkyl groups, benefits from more hyperconjugative interactions than a secondary or primary radical.
• Through hyperconjugation, \((\text{CH}_3)_3 \dot{\text{C}}\) is more stable than \((\text{CH}_3)_2 \dot{\text{C}}\text{H}\).

Resonance stabilization

Resonance stabilization is a key principle in chemistry that plays a crucial role in stabilizing free radicals, among other reactive species. It occurs when electrons can be delocalized over multiple atoms in a molecule, usually through p-orbitals or pi bonds, leading to several structures called resonance forms. These structures are not distinct entities but rather contribute to the molecule's overall stability by distributing the electron density more evenly.

Aromatic rings, such as phenyl groups, are adept at resonance stabilization. They allow the delocalization of the unpaired electron over the ring, making free radicals that have one or more phenyl groups quite stable. For example, \(\text{C}_6\text{H}_5\) acts as an electron-donating group.

• Radicals like \(\left(\text{C}_6\text{H}_5\right)_3 \dot{\text{C}}\) benefit significantly from resonance stabilization since each phenyl group offers a pathway for electron delocalization.
• This is why \(\left(\text{C}_6\text{H}_5\right)_3 \dot{\text{C}}\) tends to be more stable than its counterparts with fewer phenyl groups.

Inductive effect

The inductive effect is another concept often contributing to free radical stability. It refers to the electric polarization of bonds within a molecule due to the electronegativity of adjacent atoms. This effect can cause electrons to be pushed towards or pulled away from a certain group, affecting the charge distribution over the molecule.

When dealing with free radicals, the inductive effect can help stabilize the unpaired electron. \(+I\) effects, which involve electron donation, can increase stability by reducing the electron deficiency at the radical site. This means radicals attached to groups with positive inductive effects, such as alkyl chains, are generally more stable.

• A tertiary carbon radical usually experiences more \(+I\) effects compared to secondary or primary radicals due to the presence of more electron-donating alkyl groups.
• Thus, \(\left(\text{CH}_3\right)_3 \dot{\text{C}}\) is more stabilized through these effects than \(\left(\text{C}_6\text{H}_5\right)_2 \dot{\text{C}}\text{H}\).

Aromaticity

Aromaticity is a special kind of stability conferred to certain cyclic molecules due to their electron configuration, which follows Huckel's rule: having \(4n+2\) pi electrons, where n is a non-negative integer. This configuration allows for the continuous overlap of p-orbitals, leading to a significant stabilization called resonance energy.

In the context of free radicals, aromaticity can greatly affect stability. Phenyl groups are aromatic and contribute resonance stability to radicals they are a part of. The unpaired electron can be delocalized across the aromatic system, reducing the energy and increasing the stability of the radical.

• A radical with more phenyl groups like \(\left(\text{C}_6\text{H}_5\right)_3 \dot{\text{C}}\) is more stable due to extensive aromatic stabilization compared to one with fewer phenyl groups.
• This is why radicals with aromatic character often show enhanced stability.