Problem 41 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

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

Step 1: Understanding Carbonium Ion Stability

Carbonium ions, also known as carbocations, are positively charged ions with a carbon atom bearing the positive charge. The stability of a carbonium ion is greatly influenced by the nature of groups attached to the carbon atom with a positive charge. In general, the more substituted the carbon atom is, the more stable the carbonium ion because of the electron-releasing inductive effect (+I effect) and hyperconjugation. Tertiary carbonium ions, where the positively charged carbon is connected to three other carbon groups, are more stable than secondary or primary carbonium ions.

Step 2: Examine Each Ion

(a) \((\mathrm{CH}_{3})_{2} \mathrm{CH}^{+}\) is a secondary carbonium ion.(b) \(\mathrm{CH}_{3} \mathrm{CH}_{2}^{+}\) is a primary carbonium ion.(c) \(\mathrm{CH}_{3})_{3} \mathrm{C}-\mathrm{CH}_{2}^{+}\) has a primary carbon with an extra secondary structure.(d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\) is a tertiary carbonium ion. We need to determine which of these structures has the highest degree of substitution at the carbon atom bearing the positive charge.

Step 3: Determine the Most Stable Structure

(d) \((\mathrm{CH}_{3})_{3} \mathrm{C}^{+}\) is a tertiary carbonium ion, meaning the positively charged carbon is bonded to three methyl groups (the most substituted). This structure benefits from the +I effect due to the presence of three methyl groups which donate electron density towards the positively charged carbon, and also from hyperconjugation, which further stabilizes the positive charge. Compared with the other options, (d) is the most stable.

Key Concepts

Inductive Effect

The inductive effect is a fundamental concept when discussing carbocation stability. It describes the electron-donating or withdrawing influence of substituents bonded to a carbon atom. When considering carbocations, the inductive effect is often about how alkyl groups (like methyl or ethyl) can donate electron density towards the positively charged carbon atom. This helps to disperse the positive charge and stabilize the carbocation.

In the case of a carbocation, groups attached to the charged carbon can either have a +I (electron-donating) or a -I (electron-withdrawing) effect. Alkyl groups tend to have a +I effect, meaning they release electrons towards the carbocation, making it more stable. For example, in a tertiary carbonium ion like \((\mathrm{CH}_{3})_{3}\mathrm{C}^{+}\), each methyl group donates electron density, which enhances stability.

Therefore, the more alkyl groups attached to the carbocation, the greater the +I effect and hence more stable the ion. This is why tertiary carbocations are more stable than secondary or primary ones.

Hyperconjugation

Hyperconjugation is another key player in the stability of carbocations. It refers to the delocalization of electrons in \(\sigma\) bonds (typically C-H bonds) with an adjacent empty p-orbital, such as those found in carbocations. This phenomenon allows for the spreading out of the positive charge over the neighboring atoms, reducing electron deficiency and lending stability to the ion.

For instance, a tertiary carbocation like \(\left(\mathrm{CH}_{3}\right)_{3}\mathrm{C}^{+}\) can participate in hyperconjugation with the C-H bonds of its three methyl groups. Each methyl group can contribute several hyperconjugative interactions, allowing the positive charge to be partially "shared" or delocalized over multiple atoms.

Thus, hyperconjugation serves as a vital factor for enhancing carbocation stability. It explains why more substituted carbocations, with more possibilities for hyperconjugation, are generally more stable than less substituted ones.

Tertiary Carbonium Ion

A tertiary carbonium ion, also known as a tertiary carbocation, is a specific type of carbocation where the positively charged carbon atom is directly connected to three carbon-containing substituents. This structure is crucial because of how it affects carbocation stability.

Tertiary carbonium ions are known for being the most stable variety compared to primary and secondary carbocations. This increased stability can be attributed to two main factors:

• **Inductive Effect:** As previously mentioned, the presence of multiple alkyl groups offers significant electron donation to the carbocation, making the positive charge more stable.
• **Hyperconjugation:** A tertiary carbocation has the maximum opportunity for hyperconjugation due to the abundance of adjacent \(\sigma\) bonds, allowing extensive delocalization of charge.

Both these effects work synergistically to lower the energy of the carbocation and enhance its stability. As a result, in a given set of carbocations, the tertiary carbonium ion is usually the preferred structure in terms of stability.