Which of the following is a least stable carbocation?
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Stability order of common carbocations: Benzyl>Allyl $\approx$ 3$^\circ$>2$^\circ$>1$^\circ$>Methyl. Vinylic and Aryl carbocations (where the charge is on a double-bonded carbon) are extremely unstable and are less stable than even the methyl carbocation.
The stability of carbocations depends on factors such as hyperconjugation, resonance, and inductive effects.
(A) CH$_3$ - C$^+$H$_2$ (Ethyl cation):
This is a primary carbocation. Stability is provided by the +I effect of the methyl group and hyperconjugation with three alpha-hydrogens.
(B) CH$_2$ = C$^+$H (Vinyl cation):
The positive charge is on an sp-hybridized carbon of a double bond. Carbon with higher s-character is more electronegative, destabilizing the positive charge. The empty p-orbital is perpendicular to the $\pi$-bond, preventing resonance. This makes the vinyl carbocation extremely unstable.
(C) CH$_2$ = CH - C$^+$H$_2$ (Allyl cation):
The positive charge is adjacent to a double bond. Resonance delocalizes the positive charge:
\[
\text{CH}_2=\text{CH}-\text{C}^+\text{H}_2 \leftrightarrow ^+\text{CH}_2-\text{CH}=\text{CH}_2
\]
Resonance stabilization makes the allyl cation relatively stable.
(D) C$_6$H$_5$ - C$^+$H$_2$ (Benzyl cation):
The positive charge is adjacent to a benzene ring, allowing resonance delocalization over the aromatic system. This makes the benzyl cation very stable.
Comparing the stabilities:
Benzyl (D) and allyl (C) cations are stabilized by resonance, ethyl cation (A) by hyperconjugation and inductive effect, while vinyl cation (B) is highly destabilized.
