Question

The ease of formation of carbonium ions is \(3^{\circ}>2^{\circ}>1^{\circ}>\mathrm{Ch}_{3}+\). Explain why.

Short answer

The ease of formation of carbonium ions follows the order \(3^{\circ}>2^{\circ}>1^{\circ}>\mathrm{CH}_3^+\) because tertiary (3°) carbonium ions are more stable than secondary (2°), primary (1°), and methyl (\(\mathrm{CH}_3^+\)) ions. This stability arises from a combination of electronic factors, including electron delocalization, inductive effect, and hyperconjugation. Tertiary (3°) carbonium ions have the most electron delocalization, strongest inductive effect, and greatest hyperconjugation due to their three attached alkyl groups, making them easier to form compared to the other carbonium ions with fewer or no alkyl groups.

Step-by-step solution

Understanding Carbonium Ions

Carbonium ions (also called carbocations) are electron-deficient species with only three bonds and a positive charge on the carbon atom. They have an empty p-orbital and are sp2 hybridized. These ions can be classified based on the number of carbon atoms directly attached to the positively charged carbon: primary (1°) has one carbon attached, secondary (2°) has two carbons attached, tertiary (3°) has three carbons attached, and methyl (\(\mathrm{CH}_3^+\)) has no carbons attached.

Examining Electron Delocalization

Electron delocalization is the spreading of electron density over a larger area, contributing to the stability of a species. In the case of carbonium ions, the positive charge can be distributed to nearby atoms, making the electron-deficient carbon less positively charged and more stable. Tertiary (3°) carbonium ions have more neighboring carbon atoms compared to secondary (2°), primary (1°), and methyl (\(\mathrm{CH}_3^+\)) ions, allowing for greater electron delocalization and increased stability.

Understanding the Inductive Effect

The inductive effect is the transmission of electron density through sigma (σ) bonds due to the electronegativity differences between atoms. In the case of carbonium ions, neighboring alkyl groups can draw electron density towards themselves, thus helping to stabilize the positively charged carbon. Since tertiary (3°) carbonium ions have more alkyl groups attached to the positively charged carbon, they experience a stronger inductive effect, which results in greater stability compared to secondary (2°), primary (1°), and methyl (\(\mathrm{CH}_3^+\)) ions.

Considering Hyperconjugation

Hyperconjugation is the interaction between electrons in a σ-bond and an adjacent empty p-orbital, stabilizing the positive charge on the carbonium ion. More alkyl groups attached to the positively charged carbon imply more σ-bonds available for hyperconjugation. Thus, tertiary (3°) carbonium ions exhibit the most hyperconjugation due to their three alkyl groups, followed by secondary (2°) and primary (1°) ions, while methyl (\(\mathrm{CH}_3^+\)) ions have no hyperconjugation.

Conclusion

The stability of carbonium ions is determined by a combination of electronic factors such as electron delocalization, inductive effect, and hyperconjugation. Tertiary (3°) carbonium ions benefit the most from these factors due to their three attached alkyl groups, making them more stable and easier to form than secondary (2°), primary (1°), and methyl (\(\mathrm{CH}_3^+\)) ions, which have fewer or no alkyl groups for electron delocalization, inductive effect, and hyperconjugation. Therefore, the ease of formation of carbonium ions follows the order \(3^{\circ}>2^{\circ}>1^{\circ}>\mathrm{CH}_3^+\).

Key concepts

Electron Delocalization

Electron delocalization plays a crucial role in the stability of carbonium ions, also known as carbocations. Imagine a carbon atom with a positive charge. This isn't a stable situation, right? Electron delocalization helps to mitigate that instability. It allows the positive charge to spread over a larger area, often reaching neighbouring atoms. This spread reduces the intensity of the positive charge on the carbon atom, making the carbonium ion more stable.

With tertiary (3°) carbonium ions, there are three carbon atoms surrounding the positively charged carbon, as compared to only two in secondary (2°), one in primary (1°), and none in methyl (CH₃⁺) ions. These additional neighboring carbons assist in spreading out the charge over a larger area. This delocalization is maximized in tertiary ions, giving them the greatest stability. Thus, this explains why tertiary carbonium ions are more stable compared to their counterparts.

Inductive Effect

The inductive effect describes the sharing of electron density through sigma bonds. This phenomenon is driven by differences in electronegativity between atoms connected by these bonds. In the context of carbonium ions, let's think about the role that nearby alkyl groups (like CH₃) play. They push electron density towards the positively charged carbon.

Since tertiary (3°) carbonium ions have three alkyl groups attached directly to the positively charged carbon, they experience a strong inductive effect. This effect helps to stabilize the positive charge. Secondary (2°) ions have only two alkyl groups contributing to the inductive effect, lessening the stabilization. In primary (1°) and methyl (CH₃⁺) ions, the inductive effect is even weaker or nonexistent. Thus, the inductive effect contributes to the order of stability, where tertiary is the most stable due to the strongest positive charge reduction.

Hyperconjugation

Hyperconjugation is another factor that dramatically enhances the stability of carbonium ions. It involves the interaction between electrons in sigma bonds (σ-bonds) and an adjacent vacant p-orbital, present in the positively charged carbon atom. This interaction allows some electron density to be shared with the empty p-orbital.

The number of adjacent alkyl groups influences how much hyperconjugation occurs. More alkyl groups mean more sigma bonds adjacent to the empty p-orbital. Tertiary (3°) ions, with three alkyl groups, have the maximum number of nearby sigma bonds interacting with the empty p-orbital, leading to the highest level of hyperconjugation. Secondary (2°) and primary (1°) carbonium ions have fewer such interactions, and methyl ions (CH₃⁺) lack them entirely.

This means that hyperconjugation supports the highest stability in tertiary ions, making them have the most secure positive charge, aligning with the observed trend of 3° > 2° > 1° > CH₃⁺ in terms of stability.