Question

The most stable carbonium ion is (a) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}^{+}\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2}^{+}\) (c) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{CH}_{2}^{+}\) (d) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{2}\)

Short answer

The most stable carbonium ion is (d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\).

Step-by-step solution

Understand Carbonium Ions

Carbonium ions, also known as carbocations, are positively charged carbon species. Their stability is influenced by the number of alkyl groups attached to the positively charged carbon. Alkyl groups are electron-donating and help stabilize the positive charge.

Identify the Types of Carbocations

Evaluate the given options:(a) \((\mathrm{CH}_{3})_{2} \mathrm{CH}^{+}\): Secondary carbocation with two methyl groups attached.(b) \(\mathrm{CH}_{3} \mathrm{CH}_{2}^{+}\): Primary carbocation with only one alkyl group.(c) \((\mathrm{CH}_{3})_{3} \mathrm{C}-\mathrm{CH}_{2}^{+}\): Primary carbocation with one alkyl and one extra carbon group, but less alkyl substitution on the charged carbon.(d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\): Tertiary carbocation with three methyl groups attached.

Apply the Rule of Carbocation Stability

The stability order of carbocations is typically tertiary > secondary > primary, due to the hyperconjugation and inductive effects that stabilize the positive charge via electron donation.

Determine the Most Stable Carbocation

From Step 3, option (d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\) is a tertiary carbocation with three methyl groups, making it the most stable due to maximum alkyl substitution.

Key concepts

Hyperconjugation

Hyperconjugation is a key factor that stabilizes carbocations. It is a phenomenon where sigma bonds (C-H or C-C) adjacent to an empty p-orbital of the carbocation align and partially overlap, allowing for a delocalization of electrons. This enhances the stability of carbocations as the positive charge is spread over several atoms rather than being localized on the carbocation.

In practical terms, consider a carbocation like the tertiary carbocation (\((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\)). Here, hyperconjugation arises from the three methyl groups attached to the positively charged carbon. Each methyl group can contribute electrons through hyperconjugation, reducing the positive charge density on the central carbon and thus stabilizing it further.

• This stabilization mechanism is more effective in tertiary carbocations as they have more neighboring carbon-hydrogen bonds available to participate in hyperconjugation.
• Secondary and primary carbocations exhibit less hyperconjugative stabilization, hence they are less stable.

Inductive Effect

The inductive effect is another important concept in understanding carbocation stability. It refers to the electron-withdrawing or electron-donating effect exerted by substituents through sigma bonds. Alkyl groups are typically electron-donating, exerting a positive inductive effect that pushes electron density toward the positively charged carbon center, thus stabilizing the carbocation.

In carbocations, this electron donation mitigates the electron deficiency at the positively charged carbon, enhancing stability. Tertiary carbocations, such as (\((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\)), benefit the most as they have multiple alkyl groups applying the inductive effect. This is why tertiary carbocations are more stable than secondary and primary ones.

• More alkyl substitutions mean more electron-donating inductive effects, leading to increased stability.
• The inductive effect diminishes with distance from the charged center, which explains why the closer the alkyl group, the greater the stabilization.

Alkyl Substitution

Alkyl substitution plays a crucial role in determining the stability of carbocations. The concept is simple: more alkyl groups attached to the positively charged carbon improve carbocation stability. This is because alkyl groups donate electron density through both inductive effects and hyperconjugation.

The more alkyl groups present, the more effective these stabilizing factors become.

• For example, tertiary carbocations have three alkyl groups, which makes them more stable than secondary carbocations with two alkyl groups, which in turn are more stable than primary carbocations with only one alkyl group.
• In the context of the exercise, option (d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\) stands out due to its three methyl groups, offering maximum stabilization.

Tertiary Carbocation

A tertiary carbocation has three alkyl groups attached to the positively charged carbon. This highly substituted nature lends high stability to tertiary carbocations. The stability primarily arises from the combined effects of hyperconjugation and inductive effects contributed by each alkyl group.

In the exercise, the tertiary carbocation (\((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\)) is the most stable due to multiple stabilizing interactions.

• It receives maximal electron-donating support through hyperconjugation.
• Furthermore, it benefits from strong inductive effects from its three methyl groups, spreading out the positive charge.

Tertiary carbocations are key intermediates in many organic reactions due to their enhanced stability, making them more likely to form and thus participate in reaction pathways.