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) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{+}\)

Short answer

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

Step-by-step solution

Understanding Carbonium Ion Stability

The stability of carbonium ions (also known as carbocations) primarily depends on the capability of surrounding groups to donate electrons and stabilize the positive charge through hyperconjugation and inductive effects.

Analyze the Structure of Each Option

(a) \((\mathrm{CH}_{3})_{2} \mathrm{CH}^{+}\) is a secondary carbocation.(b) \(\mathrm{CH}_{3} \mathrm{CH}_{2}^{+}\) is a primary carbocation.(c) \((\mathrm{CH}_{3})_{3} \mathrm{C}-\mathrm{CH}_{2}^{+}\) is a primary carbocation with a tertiary substituent.(d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\) is a tertiary carbocation.

Consider Hyperconjugation

Hyperconjugation is the delocalization of electrons from C-H bonds adjacent to the carbocation center, which stabilizes the positive charge. Tertiary carbocations have more C-H bonds available for hyperconjugation than secondary or primary ones, leading to greater stability.

Assess Inductive Effects

Inductive effect refers to the electron-withdrawing or electron-donating properties of groups attached to the carbocation. Methyl groups \((\mathrm{CH}_3)\) are electron-donating via the inductive effect and increase stability, especially in tertiary carbocations.

Identify the Most Stable Carbocation

Given the above analyses, option (d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\) is the most stable. It is a tertiary carbocation stabilized by both the inductive effect and extensive hyperconjugation from three adjacent methyl groups.

Key concepts

Hyperconjugation

Hyperconjugation is a fascinating concept that plays a significant role in the stability of carbocations. It involves the interaction of the electrons in a sigma bond (typically C-H) with an adjacent empty or partially filled orbital, like the positively charged p-orbital in a carbocation. This electron delocalization helps to disperse the positive charge, which ultimately increases the stability of the carbocation.

In tertiary carbocations, such as d (\((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\)), multiple C-H bonds can participate in hyperconjugation, making these ions remarkably stable. More surrounding C-H bonds mean more available electrons to delocalize, leading to greater stabilization. In contrast, primary carbocations have fewer C-H bonds contributing to hyperconjugation, so they are less stable. This is why hyperconjugation is a crucial factor to consider when evaluating carbocation stability.

Inductive Effect

The inductive effect describes how the presence of specific atoms or groups can influence the distribution of electrons in adjacent chemical bonds. In the context of carbocations, it refers to the electron-withdrawing or electron-donating properties of substituents attached to the carbocation. This effect is a permanent phenomenon where electrons are either pulled towards or pushed away from the substituent.

Methyl groups are well-known electron donors due to the positive inductive effect, which enhances the stability of the carbocation. This effect is particularly beneficial for tertiary carbocations like (d \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\)). Here, the electron-releasing nature of the three methyl groups helps to partially offset the positive charge on the central carbon atom, making it more stable. On the other hand, primary carbocations have fewer or weaker electron-donating groups and are less stable as a result.

Tertiary Carbocation

A tertiary carbocation is a type of carbocation where the positively charged carbon is bonded to three alkyl groups. These carbocations are generally the most stable, thanks to both hyperconjugation and the inductive effect. Tertiary carbocations, such as (d \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\)), are stabilized because the three alkyl groups provide more C-H bonds for hyperconjugation.

Additionally, the electron-releasing inductive effect from three neighboring alkyl groups further contributes to the dispersion of positive charge, making them significantly more stable than secondary or primary carbocations. Ultimately, these phenomena work together to effectively lower the energy of tertiary carbocations, thus making them less reactive and more prevalent in chemical reactions when compared to their less stable counterparts.

Primary Carbocation

Primary carbocations are the least stable among carbocations because they have a positively charged carbon that is bonded to only one alkyl group. This limited connectivity severely restricts hyperconjugation opportunities. With fewer C-H bonds in the neighborhood, primary carbocations cannot benefit much from the stabilizing electron delocalization seen in more substituted carbocations.

Furthermore, the primary carbocations lack sufficient electron-donating groups to benefit from the inductive effect. In the case of (b \(\mathrm{CH}_{3} \mathrm{CH}_{2}^{+}\)), there is only one methyl group capable of donating electrons through the inductive effect, which is not enough to stabilize the positive charge effectively. As a result, primary carbocations like these show significantly lower stability and are less frequently encountered in reactions. These factors highlight why understanding the structural characteristics of carbocations can predict reactivity and stability in organic chemistry.