Which of the following carbocations is most stable?

Solution

Chemistry ma’am · 3 steps

Follow the + charge along the chain and see whether it ever lands on the carbon carrying OCH₃.

1. Where the charge goes. In a conjugated cation the + charge spreads only to alternate carbons. Number from the CH₂⁺ end as C1. The charge then sits on C1, C3, C5 and so on, never on C2 or C4.
2. When OCH3 helps. OCH₃ stabilises the cation by +M only when it sits on a carbon that carries the charge in some resonance structure. Its lone pair then forms C=O⁺, where every atom has an octet. On any other carbon it can only pull electrons by -I, which destabilises.

   Option	Cation	OCH₃ on	Effect
   (a)	CH₂=C(OCH₃)-CH₂⁺	C2, never charged	allyl, -I only
   (b)	CH₂=C(OCH₃)-CH=CH-CH₂⁺	C4, never charged	long conjugation, but -I only
   (c)	CH₃O-CH=CH-CH₂⁺	C3, charged	+M, but charge on only C1 and C3
   (d)	CH₃O-CH=CH-CH=CH-CH₂⁺	C5, charged	+M and charge spread over C1, C3, C5

3. So. Only (d) has both things at once: the longest conjugation and an OCH₃ placed where it can donate its lone pair. So (d) is the most stable carbocation.

The idea to keep. A +M group stabilises a cation only if it sits at an odd position counted from the C⁺ (C1, C3, C5). Among those, the cation with longer conjugation and more resonance structures wins.

Answer from the NTA final answer key. Solution by PrepWiser.