See image — GOC and Organic Chemistry Basics Chemistry Question

💡 Solution & Explanation

Step 1 - Concept: Carbocation stability is governed by (i) degree of substitution (tertiary > secondary > primary), (ii) resonance/conjugation (allylic, dienylic delocalization), and (iii) hyperconjugation. The more resonance structures that delocalize the positive charge and the more substituted the cationic carbon, the more stable the carbocation. Step 2 - Analyze each option: Option (a): The positive charge is on a carbon that is part of a conjugated diene system (the cation is flanked by two double bonds, one on each side), making it a cross-conjugated or dienyl carbocation. However, looking at the structure, the charge is at an internal position with a methyl substituent, giving allylic stabilization but the substitution pattern limits extended conjugation. Option (b): The positive charge is on a carbon that is allylic to a double bond AND is part of an extended conjugated system. The cationic center is secondary/tertiary, and importantly it sits within a system where the charge can be delocalized over multiple carbons through two conjugated double bonds (a 2-carbon extended delocalization: C(+)-C=C-C=C). Additionally, the cationic carbon has an isobutyl substituent providing hyperconjugation. This gives maximum resonance delocalization plus substitution, making it the most stable. Option (c): The positive charge is on a carbon adjacent to a double bond (allylic) and bears substituents, but the geometry places it at a vinylic-like or less effectively conjugated position compared to option (b). Option (d): The positive charge appears to be on a terminal or less substituted carbon at the end of the chain, away from the main conjugated system, providing less stabilization. Step 3 - Why (b) is best: In option (b), the carbocation is stabilized by extended allylic conjugation across a diene unit (the charge is delocalized over 3 carbons via two double bonds: C=C-C=C-C(+) allows resonance to spread the positive charge), AND the carbon bearing the charge has alkyl substituents contributing hyperconjugation. This combination of extended conjugation plus substitution makes (b) the most stable carbocation among the four options. Step 4 - Why others fail: (a) has good conjugation but less extended delocalization than (b). (c) and (d) have the charge in positions with less effective delocalization or lower substitution. Therefore, the correct answer is B.