Question

Arrange the following free radicals in increasing order of stability: (a) \(\mathrm{A}<\mathrm{B}<\mathrm{C}<\mathrm{D}<\mathrm{E}\) (b) \(E

Short answer

Option (a) \(\mathrm{A}<\mathrm{B}<\mathrm{C}<\mathrm{D}<\mathrm{E}\) represents increasing stability order.

Step-by-step solution

Understanding Free Radical Stability

Free radicals are species with an unpaired electron, and their stability is influenced by factors such as the degree of alkyl substitution around the radical center, resonance effects, and hyperconjugation. Generally, more substituted radicals are more stable.

Evaluate Given Orders

We are given multiple orderings of free radicals: (a) \(\mathrm{A}<\mathrm{B}<\mathrm{C}<\mathrm{D}<\mathrm{E}\), (b) \(E<C<D<B<A\), (c) \(C<A<B<E<D\), and (d) \(\mathrm{B}<\mathrm{A}<\mathrm{D}<\mathrm{E}<\mathrm{C}\). Our task is to determine which of these represents an increasing order of stability.

Increase in Stability with Substitution

Given the general rule that more substituted radicals are more stable, identify which order shows an increase in substitution throughout: typically tertiary (most stable) > secondary > primary > methyl (least stable).

Analyze Each Option

- **Option (a):** \(\mathrm{A}<\mathrm{B}<\mathrm{C}<\mathrm{D}<\mathrm{E}\). This implies a consistent increase in stability across the series.- **Option (b):** This option suggests \(E<C<D<B<A\), implying decreasing stability, which is contrary to general rules.- **Option (c):** This option \(C<A<B<E<D\) does not follow expected stability progression based on substitution pattern.- **Option (d):** This order \(\mathrm{B}<\mathrm{A}<\mathrm{D}<\mathrm{E}<\mathrm{C}\) might represent actual situations based on specific molecular contexts. To decide the true order, we rely on substitution and resonance considerations.

Choose the Correct Order

Considering typical stability patterns, Option (a) \(\mathrm{A}<\mathrm{B}<\mathrm{C}<\mathrm{D}<\mathrm{E}\) best represents increasing stability from least to most substituted radicals.

Key concepts

Factors Influencing Stability

Understanding the factors that influence the stability of free radicals is crucial for predicting their behavior. Free radicals are reactive species characterized by having an unpaired electron. The stability of these radicals can determine how they will react in chemical processes.

• Electronegative Atoms: Atoms with high electronegativity can destabilize radicals if they are located too close. This is because they attract electrons too strongly, making the radical more reactive.
• Polarizability: Elements that are able to spread their electron clouds over a larger volume can stabilize the radical by delocalizing the charge.
• Spin Density: The distribution of the unpaired electron across the molecule affects stability. More localized spin density often leads to less stable radicals.

Understanding these factors helps in predicting the order of stability among various free radicals.

Alkyl Substitution

Alkyl substitution plays a significant role in the stability of free radicals. The principle here is relatively straightforward: the more substituted a radical is, the more stable it tends to be.

• Tertiary Radicals: These have three alkyl groups attached, making them the most stable among the aliphatic radicals.
• Secondary Radicals: With two alkyl groups, they offer moderate stability compared to their tertiary counterparts.
• Primary Radicals: Featuring only one alkyl group, these are less stable due to fewer electron-donating groups.
• Methyl Radicals: These are the least stable, possessing no additional alkyl groups to share the electron density.

This order correlates with the degree of substitution and the radical's relative stability, making it an essential concept to grasp.

Resonance Effects

Resonance can significantly stabilize free radicals. This is because resonance allows the unpaired electron to be delocalized over several atoms, lowering the energy of the system.

• Conjugated Systems: Radicals within these systems benefit most as the resonance can spread across multiple pi bonds.
• Aromatic Stability: If a radical is present in an aromatic ring, it can gain significant stabilization from the resonance intrinsic to aromatic systems.

Such resonance effects are pivotal in determining radical stability, often more than just simple alkyl substitution.

Hyperconjugation

Hyperconjugation is a more subtle factor but plays a vital role in enhancing radical stability. It involves the interaction of the radical's unpaired electron with adjacent bond electrons, primarily in C-H bonds.

• Extended Delocalization: Hyperconjugation allows for an extended interaction network, spreading the radical character over more atoms.
• Participation of C-H Bonds: This interaction with C-H bonds aids in stabilizing the radical, albeit to a lesser degree than resonance.

Understanding hyperconjugation provides insight into the physical reasons behind the relative stabilities observed in different radicals. It emphasizes the capability of specific bonds to partake in stabilization beyond direct resonance or substitution effects.