Question

The stability of the following carbocations decreases in the order. (1) [C]1CCCCC1 (2) [C+]1CC1 (3) [C+]1C=CC=C1 (4) [C+]1C=CC=CC=C1 (a) \(3>2>4>1\) (b) \(4>2>3>1\) (c) \(4>3>2>1\) (d) \(4>2>1>3\)

Short answer

The correct order is (4), (3), (2), (1) which matches option (c).

Step-by-step solution

Identify Carbocations

Carbocations are positively charged carbon atoms within a molecule. In this problem, we need to consider the stability of different carbocations in the given cyclic structures. Each structure presents a different scenario based on conjugation and hybridization.

Evaluate Stability Factors

The stability of a carbocation is influenced by factors such as resonance, hyperconjugation, and the inductive effect. Generally, more resonance (delocalization of charge) increases stability. Carbocations attached to more electron-donating groups or pi systems will typically be more stable due to better charge dispersion.

Apply Resonance Effects

For structures (3) and (4), there is conjugation due to the alternate pi bonds, which allows charge delocalization. Structure (4) has an extended conjugated system compared to (3), which increases its stability. Structures (1) and (2) lack such resonance stabilizing features.

Compare Systems

Structure (4) is the most stable due to extensive resonance across the entire ring. Structure (3) is second, benefitting from some resonance but less than (4). Then comes structure (2), and finally (1), which is a non-aromatic cyclohexyl carbocation, having the least stabilization.

Select Correct Order

From our analysis: (4) has the highest stability > (3) > (2) > (1). Thus, the correct decreasing order of stability, based on these principles, matches an option given in the question.

Key concepts

Resonance Effects

Resonance plays a crucial role in stabilizing carbocations. Unlike a static structure, resonance allows the positive charge in a carbocation to be delocalized over a wider area. This delocalization occurs through overlapping p orbitals that can form multiple structures with electrons being shared across bonds.
For example, in the case of structure (3), which has alternating single and double bonds, resonance allows the positive charge to move through pi bonds. Structure (4) has even more extensive resonance. This is due to its longer set of alternating pi bonds, which allow even greater charge dispersion. The more pi bonds involved, the greater the stabilization through resonance.

• Positive charge moves across pi system.
• Increases stability by spreading out charge.

This explains why structure (4) is more stable than structure (3). Structures (1) and (2) lack such resonance options, making them less stable.

Hyperconjugation

Hyperconjugation is another factor that can enhance the stability of carbocations. It involves delocalization of sigma (σ) electrons from a C-H bond to the empty p-orbital of a carbocation. This form of delocalization, while less powerful than resonance, still contributes to the stability of carbocations.
In simpler terms, the more alkyl groups a carbocation has, the more hyperconjugation can occur, spreading out the positive charge. However, in our original exercise scenario, the differences in stability are not primarily due to hyperconjugation because of the nature of the structures.
While hyperconjugation helps, it's not the deciding factor here due to limited alkyl group interactions in cyclic structures.

• Involves electron donation from adjacent C-H bonds.
• Leads to marginal increase in stabilization.

It's important to understand that hyperconjugation complements resonance and should not be the sole factor in isolation.

Inductive Effect

The inductive effect pertains to the electron donation or withdrawal through sigma bonds due to electronegativity differences. Although it's another aspect of stabilization, its impact is lesser compared to resonance and hyperconjugation.
With carbocations, any nearby electron-donating groups stabilize the positive charge through the inductive effect. This mechanism is less relevant in isolated cyclic structures like those in the exercise because they lack significant electron-donating or withdrawing groups near the carbocation.

• Involves electron shift through sigma bonds.
• Provides minor stability improvement.

In comparison to resonance, its influence on carbocation stability is limited.

Conjugation

Conjugation describes a scenario where electrons are shared along alternating single and double bonds, creating a system with overlapping p orbitals. In our carbocations, conjugation is key because it allows for the sharing and movement of electrons, stabilizing the positive charge.
Structure (3) and (4) benefit from conjugation due to their pi bonds. However, structure (4)'s extended conjugation provides superior stabilization, with the charge being spread over an entire system of alternating single and double bonds.

• Leads to distribution of positive charge.
• Structures with greater conjugation show increased stability.

This extensive sharing of electrons enhances the stability, particularly evident in systems like polyenes, making conjugation a primary stabilizing feature in the context of the exercise.

Charge Delocalization

Charge delocalization is essentially the result of effective resonance and conjugation. It's the process where the positive charge in a carbocation is spread across several atoms, reducing the concentration of charge on any single atom. This greatly increases the stability of the molecule.
In our exercise, the carbocation's stability hinges on how well the positive charge can move through resonance and conjugation. The larger extent of delocalization seen in structure (4) versus structure (3) is what places it higher in the stability ranking.

• Involves movement of charge over a wider area.
• Achieved through overlap of p orbitals in conjugated systems.

By reducing the electron deficiency at any single point, charge delocalization dramatically enhances the stability of carbocations, making it an essential concept to grasp.