Problem 201 - A Complete Resource Book in Chemistry for JEE Main

Question

The increasing order of stability of the following free radicals is \(\quad\) [2006] (a) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}<\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}<\left(\mathrm{C}_{6} \mathrm{H}_{3}\right)_{2} \mathrm{C} \mathrm{H}<\left(\mathrm{C}_{6} \mathrm{H}_{3}\right)_{3} \dot{\mathrm{C}}\) (b) \(\left(\mathrm{C}_{6} \mathrm{H}_{5}\right), \dot{\mathrm{C}}<\left(\mathrm{C}_{5} \mathrm{H}_{5}\right)_{2} \overrightarrow{\mathrm{C}} \mathrm{H}<\left(\mathrm{CH}_{3}\right)_{3} \dot{\mathrm{C}}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}\) (c) \(\left(\mathrm{C}_{6} \mathrm{H}_{3}\right)_{2} \dot{\mathrm{C}} \mathrm{H}<\left(\mathrm{C}_{6} \mathrm{H}_{3}\right), \overrightarrow{\mathrm{C}}<\left(\mathrm{CH}_{3}\right)_{3} \overrightarrow{\mathrm{C}}<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}\) (d) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}<\left(\mathrm{CH}_{3}\right)_{3} \overrightarrow{\mathrm{C}}<\left(\mathrm{C}_{6} \mathrm{H}_{3}\right)_{3} \mathrm{C}<\left(\mathrm{C}_{6} \mathrm{H}_{4}\right)_{2} \mathrm{CH}\)

Step-by-Step Solution

Answer

The increasing order of stability is correctly reflected in option (a).

Step 1: Understanding the Free Radical Stability

Free radical stability is often determined by the degree of substitution and resonance effects. More substituted free radicals are generally more stable due to hyperconjugation and inductive effects. Additionally, free radicals that are stabilized by resonance, such as those involving benzene rings, tend to be more stable.

Step 2: Analyzing the Options

Each option presents a sequence of free radicals. We must determine the stability order based on known factors such as hyperconjugation, resonance, and substitution. Typically, tertiary free radicals (\((CH_3)_3\dot{C}\)) are more stable than secondary (\((CH_3)_2CH\)) and primary radicals. Free radicals adjacent to aromatic rings, especially more than one, are significantly stabilized by resonance.

Step 3: Evaluating Option (a)

This option presents the order:\((CH_3)_2CH < (CH_3)_3C < (C_6H_3)_2CH < (C_6H_3)_3\dot{C}\).Starting with \((CH_3)_2CH\), a secondary radical, then a tertiary radical, followed by radicals with one and two benzene rings, respectively. This aligns with the expected increased stability due to added resonance.

Step 4: Evaluating Other Options

Compare this with options (b), (c), and (d): - Option (b) incorrectly places radicals without benzene rings as more stable than radicals with resonance stabilization. - Option (c) jumbles the expected order, placing tertiary radicals after other lesser-substituted radicals. - Option (d) does not correctly account for increased resonance stability in aromatic systems.

Step 5: Conclusion

Based on the evaluation, option (a) correctly reflects the increasing stability of the radicals, considering both hyperconjugation and resonance effects.

Key Concepts

Hyperconjugation

Hyperconjugation is a fundamental concept in organic chemistry that plays a critical role in determining the stability of free radicals. It refers to the delocalization of electrons in sigma bonds (like C-H or C-C bonds) that are adjacent to a positively charged carbon atom or a radical center. This effect allows some electron density from these bonds to help stabilize the radical center.

The more adjacent sigma bonds that can participate in hyperconjugation, the greater the stabilization of the radical. For example, tertiary radicals, where the carbon center is bonded to three other carbon groups, exhibit more hyperconjugation than secondary or primary radicals. This is because the tertiary radical has more C-H bonds available to donate electron density.

• Increased hyperconjugation leads to increased radical stability.
• Tertiary radicals have more hyperconjugative interactions than secondary or primary radicals.

In summary, the phenomenon of hyperconjugation contributes significantly to the stability of organic radicals and is most effective when more alkyl groups surround the radical center.

Resonance Effects

Resonance effects are another key factor in determining the stability of free radicals. This involves the distribution of electrons across a molecule, which allows the radical to be delocalized over multiple atoms. When free radicals are adjacent to aromatic compounds like benzene rings, they benefit from extra stability due to resonance.

A radical on a benzene ring can have its unpaired electron delocalized across the ring, providing significant stabilization. This effect is much stronger than hyperconjugation and makes aromatic radicals much more stable than non-aromatic ones.

• Resonance allows the radical's electron to be spread over multiple atoms.
• Radicals next to benzene or other aromatic rings are highly stable due to resonance effects.

In practice, when comparing radicals, the presence of resonance stabilization often leads to a higher rank in stability compared to radicals stabilized by hyperconjugation alone.

Degree of Substitution

The degree of substitution refers to the number of alkyl groups attached to the radical center. Typically, the more substituted a free radical is, the more stable it becomes. This is primarily due to the increased hyperconjugative interactions and inductive effects from multiple alkyl groups.

Tertiary radicals, which have three alkyl groups attached, are usually more stable than secondary radicals, which only have two. Primary radicals have just one alkyl group and are the least stable due to fewer stabilizing interactions.

• More substituted radicals have higher stability.
• Tertiary radicals are more stable than secondary, which in turn are more stable than primary radicals.

The concept of degree of substitution underscores why certain radicals form preferentially in organic reactions, as stability often dictates the path of chemical transformations.

Aromatic Stability

Aromatic stability is one of the prime contributors to the stability of free radicals when they involve aromatic rings. Aromatic compounds, such as benzene, have a unique system of delocalized electrons that contribute to their exceptional stability.

When a free radical is adjacent to or part of an aromatic system, the unpaired electron can become delocalized over the system, granting the radical a substantial increase in stability. This is much more effective than hyperconjugation or other stabilizing effects from non-aromatic compounds.

• Aromatic rings provide significant stabilization to adjacent radicals.
• The stability is due to the delocalization of the unpaired electron across the aromatic system.

In assessing the stability of different radicals, radicals associated with aromatic systems are often found to be the most stable, reflecting the powerful influence of aromatic stability.