Question

Which of the following carbocation is most stable? (a) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C} . \mathrm{C} \mathrm{H}_{2}\) (b) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}\) (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{C} \mathrm{H}_{2}\) (d) \(\mathrm{CH}_{3} \mathrm{C} \mathrm{H} \mathrm{CH}_{2} \mathrm{CH}_{3}\)

Short answer

The most stable carbocation is (b) \((\mathrm{CH}_{3})_{3} \mathrm{C}\).

Step-by-step solution

Understand Carbocation Stability Factors

Carbocation stability is influenced by factors such as hyperconjugation, induction, and resonance. According to these factors, tertiary carbocations are generally more stable than secondary, which are more stable than primary carbocations due to the number of alkyl groups donating electron density to the positively charged carbon center.

Classify Each Given Carbocation

Identify the type of each carbocation:- (a) \( (\mathrm{CH}_{3})_{3} \mathrm{C} . \mathrm{C} \mathrm{H}_{2} \) is a primary carbocation because the positively charged carbon is attached to one other carbon.- (b) \( (\mathrm{CH}_{3})_{3} \mathrm{C} \) is a tertiary carbocation attached to three other carbon groups.- (c) \( \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{C} \mathrm{H}_{2} \) is a primary carbocation as the positively charged carbon is only attached to one other carbon group.- (d) \( \mathrm{CH}_{3} \mathrm{C} \mathrm{H} \mathrm{CH}_{2} \mathrm{CH}_{3} \) is a secondary carbocation as its positively charged carbon is attached to two other carbon groups.

Determine the Most Stable Carbocation

Based on the classification, the tertiary carbocation (b) \( (\mathrm{CH}_{3})_{3} \mathrm{C} \) is the most stable because it benefits from the maximum hyperconjugative and inductive effects due to the presence of three alkyl groups donating electron density.

Key concepts

Tertiary Carbocation

A tertiary carbocation is a type of positively charged carbon center where the carbon is attached to three other carbon atoms or alkyl groups. This structure is key to understanding carbocation stability. It is generally more stable than secondary or primary carbocations.
This stability arises because the three alkyl groups can donate electron density through hyperconjugation and the inductive effect.

• The electron-donating nature of these alkyl groups helps to disperse and stabilize the positive charge on the carbocation.
• Tertiary carbocations have more of these alkyl groups, making them particularly stable compared to others.

Thus, in the realm of organic chemistry, if you need to determine the most stable carbocation, looking for a tertiary carbocation is often a good bet.

Hyperconjugation

Hyperconjugation refers to the interaction between the electrons in a sigma (\(\sigma\)) bond, such as a C-H bond, and an adjacent empty p-orbital on the carbocation. This phenomenon allows for stabilization of carbocations.
Imagine the way electrons can "swing" or "delocalize" across bonds, spreading out the positive charge.

• In a carbocation, hyperconjugation occurs more effectively when there are more adjacent alkyl groups.
• These groups provide C-H bonds that can overlap with the vacant p-orbital of the positively charged carbon.

The more opportunities for these interactions, the more stable the carbocation becomes. Therefore, tertiary carbocations can exhibit more hyperconjugation than primary or secondary carbocations.

Inductive Effect

The inductive effect is the transmission of charge through a chain of atoms in a molecule by electrostatic induction. In carbocations, this is particularly important for stability.
Alkyl groups attached to the positively charged carbon atom can donate electron density through the inductive effect, helping to stabilize the positive charge.

• Each alkyl group draws electron density towards the carbocation, aiding in its stabilization.
• This effect diminishes with distance, so it is more pronounced when alkyl groups are directly attached to the carbocation.

This is why tertiary carbocations, with three alkyl groups, are more stable: they can benefit the most from the inductive effect. Understanding these principles helps explain why tertiary carbocations are often the most stable carbocations in organic chemistry.