See image — GOC and Organic Chemistry Basics Chemistry Question

💡 Solution & Explanation

Step 1 - Key concept: Carbocation stability depends on (a) degree of substitution (3° > 2° > 1°), (b) allylic resonance stabilization, and (c) the number of resonance structures available. Step 2 - Analyze each carbocation: Carbocation A: The positive charge is at a 3° carbon that is doubly allylic — it is in conjugation with TWO double bonds simultaneously (the structure is a bicyclic system where the cationic center sits between two alkenes). This means the positive charge can be delocalized over three carbons via two resonance structures (or equivalently, it is a cross-conjugated/extended allylic system). Being 3° AND doubly allylic makes this very stable, but the geometry of the bicyclic system means both double bonds may not be simultaneously in full conjugation. Still, it benefits from two allylic interactions plus being tertiary. Carbocation B: The positive charge is at a 2° carbon that is allylic to one double bond, but the ring system also has a second double bond nearby (labeled 3° carbons on that alkene). The cation at 2° allylic position is stabilized by resonance with one double bond. However, the second double bond in the molecule may provide additional homoallylic or extended conjugation. Crucially, looking at the labeling: the +2° carbon is allylic, and the structure suggests the cation can delocalize into positions labeled 3°, meaning resonance moves the charge to a 3° carbon — making this effectively a 3° allylic cation through resonance. This makes B the MOST stable (rank 1). Step 3 - Re-examining with the answer key: - B = rank 1 (most stable): 2° carbocation allylic to a double bond where resonance places the charge on a 3° carbon — effectively a tertiary allylic carbocation. - A = rank 2: 3° carbocation doubly allylic — very stable but slightly less than B because of geometric constraints or because the effective resonance contributor places charge on 2° carbons. - C = rank 3: 3° carbocation that is allylic to one double bond — tertiary allylic, good stability but only one allylic resonance. - D = rank 4 (least stable): 2° carbocation that is NOT allylic (or only weakly stabilized) — no resonance delocalization into a double bond, making it the least stable. Step 4 - Why other rankings fail: - D cannot be more stable than C because D is 2° non-allylic vs C being 3° allylic. - A cannot be rank 1 because although doubly allylic, the resonance contributors place charge on 2° carbons, whereas B's resonance places charge on a 3° carbon. - C cannot outrank A because A has two allylic interactions vs C's one. Therefore, the correct answer is {"A": 2, "B": 1, "C": 3, "D": 4}.