Question

Consider the following carbocations and arranged them in the increasing order of their stability: (1) (2) \(\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}_{3}\) (3) \(\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}_{2}\) (4) \(\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}-\mathrm{C}_{6} \mathrm{H}_{5}\) (5) \(\mathrm{CH}_{3}-\mathrm{CO}-\mathrm{C}^{+} \mathrm{H}_{2}\) (a) \(5<2<3<4<1\) (b) \(5<3<2<4<1\) (c) \(5<1<2<4<3\) (d) \(3<2<4<1<5\)

Short answer

The correct order is (a) 5 < 2 < 3 < 4 < 1.

Step-by-step solution

Identify Stability Factors

The stability of carbocations is primarily influenced by three factors: hyperconjugation, resonance, and inductive effects. Tertiary carbocations are generally more stable due to hyperconjugation. Allylic or benzylic carbocations are stabilized by resonance.

Analyze Each Carbocation

1. 2. The 3. The 4. The 5. The carbocation on the carbonyl carbon ( 6. The tertiary carbocation in structure (1) is the most stable due to the maximum number of hyperconjugative structures. Next is structure (4) because it is benzylic and has resonance stabilization from two benzene rings. Structure (3) is also benzylic but with only one benzene ring, providing less stabilization than (4). Structure (2) is secondary and lacks resonance stabilization, making it less stable. Finally, structure (5) is a primary carbocation next to an electron-withdrawing carbonyl, making it the least stable option.

Arrange in Order of Increasing Stability

Based on analysis, the order from least to most stable is: 5, 2, 3, 4, 1. This corresponds to option (a) in the provided choices.

Key concepts

Hyperconjugation

Hyperconjugation is a crucial concept in understanding the stability of carbocations. It involves the interaction between the filled orbitals of a C-H or C-C bond with the empty p-orbital of the positively charged carbon in carbocations. This interaction helps to delocalize the positive charge, which reduces its intensity and increases the stability of the carbocation.

Hyperconjugation is most efficient in tertiary carbocations because they have more C-H bonds available to participate in this stabilizing effect. The more alkyl groups attached to the positively charged carbon, the greater the number of hyperconjugative structures you can form.

In tertiary carbocations, numerous hyperconjugative structures lead to a more evenly distributed positive charge. This effectively lowers the energy of the molecule, making it more stable. In comparison, primary carbocations are the least stable due to having fewer alkyl groups to donate electrons and therefore have less hyperconjugative stabilization.

Think of hyperconjugation as the carbocation’s way of "sharing the load" of the positive charge with its neighbors. It's this ability that typically makes tertiary carbocations more stable than secondary or primary ones.

Resonance

Resonance stability is another key player in assessing carbocation stability. Resonance occurs when electrons can be delocalized over two or more atoms. This delocalization spreads out the positive charge over a larger volume, which significantly stabilizes the structure.

Benzylic and allylic carbocations are classic examples where resonance plays a major role. A benzylic carbocation, for instance, has a positive charge adjacent to a benzene ring. The electrons from the benzene ring can move in and help stabilize the positive charge through resonance. This results in multiple resonance forms that give the carbocation added stability.

Consider the stability imparted by resonance in carbocations:

• Benzylic carbocations, with a benzene ring donating electron density, enjoy substantial resonance stabilization.
• Allylic carbocations, located next to a double bond, can also disperse charge efficiently via resonance.

In structures with two benzene rings, like compound (4) from our example, the resonance effect is even more pronounced, increasing stability further compared to single-ring benzylic carbocations.

Inductive Effects

The inductive effect is the transmission of charge through a chain of atoms in a molecule, caused by differences in electronegativity between atoms. It influences carbocation stability by affecting the electron density around the positively charged carbon.

In the context of carbocations, electronegative atoms or groups pull electron density away from the positive charge. This results in a phenomenon known as the electron-withdrawing inductive effect, which typically destabilizes carbocations. Conversely, electron-donating groups can push electron density towards the carbocation, improving its stability.

For example, a notable case of destabilization by inductive effect is in the primary carbocation adjacent to a carbonyl group, like structure (5) from our exercise. The carbonyl group is highly electronegative, pulling electrons away from the carbocation and increasing the magnitude of the positive charge.

• This essentially makes the carbocation more 'hungry' for electrons, hence less stable.
• In contrast, alkyl groups display an inductive effect that slightly donates electron density toward the carbocation, enhancing its stability.

Understanding these inductive effects adds another layer to predicting and explaining carbocation stability patterns.