Problem 166 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following $$ \begin{array}{ll} \hline \text { Column-I } & \text { Column-II } \\ \hline \text { (a) Triphenyl methyl } & \text { (p) Benzyl } \\ \text { carbonium ion is mor } \\ \text { stable than } \\ \text { (b) } 3^{\circ} \text { alkyl carbonium ion is } & \text { (q) Tropylium ion } \\ \text { more stable than } \\ \text { (c) Allyl carbonium ion is } & \text { (r) } \mathrm{CH}^{+}=\mathrm{CH}_{2} \\ \text { less stable than } \\ \text { (d) }{\underline{\phantom{xx}}}^{+} \mathrm{CH}_{3} \text { is less stable than } & \text { (s) } 1^{\circ} \text { alkyl } \\ & \text { (t) } 2^{\circ} \text { alkyl } \end{array} $$

Step-by-Step Solution

Answer

(a)-(q), (b)-(t), (c)-(r), (d)-(s).

Step 1: Analyze the stability in Column I

Understand the order of stability for the given ions in Column I. Triphenyl methyl cation is very stable due to resonance involving three phenyl rings. A tertiary (\(3^\circ\)) alkyl cation is more stable than secondary (\(2^\circ\)) or primary (\(1^\circ\)) due to hyperconjugation and inductive effects. Allyl cation has resonance stabilization which places it intermediate in stability. A methyl cation (\(^{+} \mathrm{CH}_{3}\)) has no resonance or hyperconjugation, making it least stable.

Step 2: Match Column I with Column II

For each entry in Column I, find a corresponding stability description from Column II:- (a) Triphenyl methyl cation is more stable due to resonance with aromatic rings, matching it to (q) Tropylium ion which also has a resonance-stabilized ring.- (b) \(3^\circ\) alkyl cation is more stable due to greater hyperconjugation and inductive effects, matching with (t) \(2^\circ\) alkyl which is the immediate level below tertiary.- (c) Allyl cation's stability from resonance makes it less stable than a highly aromatic system; so it doesn't match directly with tropylium, focusing instead within lower stable ions can be matched with (r) \(\mathrm{CH}^{+} = \mathrm{CH}_{2}\) which portrays resonance relevance.- (d) \(^{+} \mathrm{CH}_{3}\) is the least stable due to no resonance or hyperconjugation, naturally matching it with (s) \(1^\circ\) alkyl as having more hyperconjugation or inductive factors.

Key Concepts

Resonance

Resonance is a fundamental concept in understanding carbocation stability, especially in organic chemistry. It involves the delocalization of electrons across a molecule, which stabilizes the structure by distributing charge more evenly. This phenomenon is particularly important in carbocations, where a positive charge is spread over multiple atoms or groups rather than being localized on a single atom.

For example, the triphenyl methyl cation is highly stable due to resonance. The positive charge can be delocalized through three phenyl rings, allowing resonance structures to form. Each of these resonance structures contributes to the overall stability of the cation, reducing energy due to the spread of charge over a greater volume.

This delocalization is also present in the tropylium ion, a cyclic arrangement, where the positive charge is shared within a seven-membered ring through resonance. The shared nature of the charge results in significant stabilization, making such ions more stable than those without resonance possibilities.

Hyperconjugation

Hyperconjugation is another key factor influencing the stability of carbocations. It involves the interaction of filled sigma (σ) orbitals with an adjacent empty p-orbital, allowing for charge delocalization. This effect is sometimes referred to as "no-bond resonance" and contributes significantly to the stability of certain cations, especially alkyl carbocations.

The effect of hyperconjugation is most pronounced in tertiary (\(3^{\circ}\)) alkyl carbocations. Here, several alkyl groups provide multiple C-H bonds adjacent to the positively charged carbon atom. Each of these C-H bonds can overlap with the empty p-orbital, stabilizing the positive charge through the release of energy.

This explains why a tertiary alkyl cation is more stable compared to secondary or primary (\(1^{\circ}\)) alkyl cations. As the number of alkyl substituents increases, so do the hyperconjugation interactions, and thus stability.

Inductive Effect

The inductive effect is an important concept for understanding carbocation stability. It involves the transmission of charge through a chain of atoms in a molecule, affecting the distribution of electrons. Substituents that can push electrons towards or pull electrons away from a carbocation influence its stability significantly.

In general, electron-releasing groups can stabilize a carbocation by donating electron density, which helps in offsetting the positive charge. This is referred to as a positive inductive effect. In contrast, electron-withdrawing groups can destabilize a carbocation through a negative inductive effect, increasing the electron deficiency at the carbocation center.

For instance, a tertiary (\(3^{\circ}\)) alkyl cation displays increased stability due to a positive inductive effect from the multiple connected alkyl chains. These chains push electron density towards the positively charged carbon atom, thereby enhancing stability as opposed to a primary (\(1^{\circ}\)) alkyl cation, which benefits much less from this type of stabilization.