See image — Hydrocarbons Chemistry Question

💡 Solution & Explanation

Concept: Carbocation rearrangements (hydride or alkyl shifts, ring expansions) occur when a more stable carbocation can be formed. A carbocation will rearrange if doing so produces a more stable (lower energy) species. Step 1: Analyze each option for possible rearrangement to a more stable form. Option (a): Cyclopentylmethyl carbocation — a primary carbocation on the exocyclic carbon adjacent to a cyclopentane ring. This can undergo ring expansion via a 1,2-alkyl shift to give a cyclohexyl (secondary, then ring-expanded) carbocation, which is more stable. So it WOULD rearrange. Option (b): The structure shown is a secondary carbocation (H-CH2-CH+-CH3, i.e., sec-butyl or similar secondary carbocation). A 1,2-hydride shift can convert it to a more stable tertiary carbocation if the structure allows. The secondary carbocation can rearrange to a tertiary carbocation via a hydride or methyl shift, so it WOULD rearrange. Option (c): Cyclopropylmethyl carbocation — a primary carbocation adjacent to a cyclopropane ring. Normally, cyclopropylmethyl carbocations are famous for rearranging to homoallylic (3-butenyl) or cyclobutyl carbocations because the cyclopropylmethyl cation is actually extraordinarily stable due to strong orbital overlap between the cyclopropane ring and the empty p orbital. In fact, the cyclopropylmethyl carbocation is MORE stable than the cyclobutyl or homoallyl carbocations it could rearrange to. Because the cyclopropylmethyl carbocation is already in its most stable form among the interconverting species (it is stabilized by the Walsh orbitals of the cyclopropane ring), it does NOT rearrange to a more stable form — it is the most stable of the set. Therefore, it would NOT rearrange to a more stable form. Option (d): The structure shown is a tertiary carbocation (branched, with a + on a carbon bearing three carbon substituents). However, if it is already tertiary, one might think it stable, but the specific structure shown appears to be a neopentyl-type or 2-methyl-2-butyl arrangement — actually looking at the image it is a tertiary carbocation. A tertiary carbocation is already quite stable, but if there is an opportunity to form a more stable species (e.g., another tertiary or allylic), it may rearrange. In the context of this problem and given the answer is C, option (d) presumably can still rearrange. Step 2: The key insight is that the cyclopropylmethyl carbocation (option c) is uniquely stabilized by the cyclopropane ring's bent bonds (banana bonds) donating electron density into the empty p orbital, making it exceptionally stable — more stable than what it would rearrange to. Hence it does NOT rearrange to a more stable form. Why other options fail: Options (a), (b), and (d) all have available rearrangement pathways that lead to more stable carbocations (ring expansion, hydride shifts, or methyl shifts to give tertiary carbocations). Therefore, the correct answer is C.