Question

The CORRECT order of stability for the following carbocations is 

• A. I < III < IV < II
• B. III < II < IV < I
• C. II < IV < III < I
• D. IV < I < III < II

Hint:

The stability of carbocations increases with the number of substituents and the presence of resonance structures. Tertiary carbocations are the most stable.

Answer 1

The Correct Option is C

Step 1: Analysis of Carbocation Stability

The stability of a carbocation ($\text{R}^+$) is primarily determined by the extent to which the positive charge on the carbon atom can be delocalized or neutralized. The main factors governing stability are:

Resonance/Delocalization: Carbocations stabilized by resonance (conjugation with $\pi$ systems or lone pairs) are highly stable.

Hyperconjugation: Alkyl groups attached to the cationic carbon can donate electron density to the empty $p$ orbital via hyperconjugation (donation from adjacent $\text{C}-\text{H}$ or $\text{C}-\text{C}$ $\sigma$ bonds).

Inductive Effect: Electron-donating groups (like alkyl groups) stabilize the positive charge through the $\sigma$ framework.

Geometry and Hybridization: The empty orbital must be a pure $p$ orbital, which requires a planar, $sp^2$ hybridized carbocation. Non-planar carbocations or those on $sp$ or $sp^2$ hybridized carbons (like bridgehead or vinylic) are destabilized.

Step 2: Stability Ranking

1. Carbocation I (Phenyl-substituted secondary carbocation)

The positive charge is adjacent to a benzene ring.

Stability Factor: Highly stabilized by resonance (delocalization of the positive charge over the $\pi$ system of the entire phenyl group). * Result: This is the most stable carbocation in this set.

$$\text{Stability: I (Most Stable)}$$

2. Carbocation III ($t$-Butyl carbocation)

A tertiary carbocation ($\text{3}^\circ$).

Stability Factor: Stabilized by the electron-donating inductive effect and hyperconjugation from the nine adjacent $\text{C}-\text{H}$ bonds of the three methyl groups.

Result: Highly stable, second only to the resonance-stabilized system I.

$$\text{Stability: III}$$

3. Carbocation IV (Vinylic Carbocation)

The positive charge is on a carbon that is part of a double bond ($sp^2$-hybridized carbon), similar to an aryl carbocation.

Stability Factor: The cationic carbon is $sp^2$ hybridized, which is more electronegative than the $sp^2$ or $sp^3$ carbons typically carrying a charge. Placing a positive charge on a more electronegative atom is highly destabilizing.

Result: Less stable than alkyl carbocations (I and III).

$$\text{Stability: IV}$$

4. Carbocation II (Bridgehead Carbocation)

The positive charge is at the bridgehead position of a bicyclo[2.2.1]heptane system.

Stability Factor: To be stable, a carbocation must be planar, requiring the cationic carbon to be $sp^2$ hybridized with the empty $p$ orbital perpendicular to the plane. The rigid, small ring structure of bicyclo[2.2.1]heptane prevents the bridgehead carbon from becoming planar (violates Bredt's Rule). The empty orbital is forced to be non-coplanar, leading to very poor $\text{C}-\text{H}$ orbital overlap (minimal hyperconjugation) and high angle strain.

Result: This is the least stable carbocation in this set, even less stable than the vinylic carbocation.

$$\text{Stability: II (Least Stable)}$$

Step 3: Final Stability Order

Combining the results, the stability increases in the following order:

$$\text{II} < \text{IV} < \text{III} < \text{I}$$