Question

The stability of the following carbocations decreases in the order. (1) [C]1CCCCC1 (2) [C+]1C=C1 (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 answer is (c) \(4>3>2>1\).

Step-by-step solution

Analyze Carbocation Stability Factors

Carbocation stability is influenced by resonance, hyperconjugation, and inductive effects. Resonance, which involves the delocalization of electrons, is a significant factor for carbocation stability. Also, more substituted carbocations are generally more stable than less substituted ones.

Evaluate Structure (1)

Structure (1), cyclohexyl cation, is a non-resonance-supported carbocation with no double bonds to stabilize the positive charge, making it the least stable.

Evaluate Structure (2)

Structure (2), cyclopropenyl cation, is significant because the positive charge is part of a conjugated system but with limited resonance. Despite this, cyclopropenyl cation is more stable than non-resonance-supported carbocations.

Evaluate Structure (3)

Structure (3), cyclopentadienyl cation, has resonance involving multiple conjugated double bonds which exceptionally stabilizes the positive charge.

Evaluate Structure (4)

Structure (4), cycloheptatrienyl cation (tropylium ion), is highly stable due to extensive resonance across the seven-membered ring, distributing the positive charge effectively.

Determine Stability Order

Based on the evaluation, the order of stability from most to least stable is: cycloheptatrienyl (4)>cyclopentadienyl (3)>cyclopropenyl (2)>cyclohexyl (1).

Select the Correct Answer

The stability decreases in the order (c): \(4>3>2>1\).

Key concepts

Resonance

Resonance is a powerful factor that can significantly increase the stability of carbocations. When a carbocation is capable of resonance, the positive charge can be delocalized over multiple atoms. This sharing of the charge across more than one atom reduces the energy of the system. It effectively disperses the charge, making the molecule energetically more favorable.
For resonance to occur, there must be available conjugated double bonds or other electrons that can freely move across atoms.

• In Structure (3), the cyclopentadienyl cation, the resonance is extensive due to multiple conjugated double bonds. This extensive delocalization makes this cation very stable.
• Structure (4), the cycloheptatrienyl cation (or tropylium ion), is even more stable because the resonance is spread across a seven-membered ring. This allows the charge to be very effectively distributed, making it the most stable carbocation of all the given structures.

Resonance is key in understanding why some carbocations are more stable than others.

Hyperconjugation

Hyperconjugation is another concept that helps stabilize carbocations. It involves the interaction of the electrons in a sigma bond (specifically, C−H or C−C bonds) with the empty p-orbital of the carbocation. This interaction allows for slight electron donation into the empty orbital, slightly reducing the electron deficiency.
Unlike resonance, hyperconjugation doesn't involve actual charge movement over different atoms but rather a sort of 'smoothing' of the charge on the cationic carbon.

• The number of adjacent hydrogen atoms and alkyl groups that can participate in hyperconjugation is important. More such groups typically lead to better stabilization.
• While hyperconjugation has lesser impact compared to resonance major players, it still plays a critical role when combined with resonance or in the absence of resonance.

Understanding hyperconjugation gives a deeper appreciation of carbocation stability, especially when comparing molecules without significant resonance.

Substituted Carbocations

The stability of a carbocation can also be influenced by the type and number of substituents attached to the positively charged carbon. Substituted carbocations are generally more stable than their less substituted counterparts for several reasons.

• The presence of alkyl groups provides electron-donating properties via both hyperconjugation and inductive effect. These groups push electron density towards the positively charged carbon, reducing its deficit.
• Tertiary carbocations (where the positive carbon is connected to three other carbon atoms) are typically more stable than secondary (connected to two), which are more stable than primary (connected to one).

In the analysis of structures, though the cyclohexyl cation (Structure 1) has no resonance capabilities and therefore remains the least stable, any additional substitution in carbocations would enhance stability without resonance being a requirement. Considering substituents, Structure (1) remains the least stable due to its minimalistic structure lacking both resonance and hyperconjugation influences.