See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Concept: A stereogenic (chiral) carbon is a carbon atom bearing four different substituents. Cocaine has the molecular structure of methyl (1R,2R,3S,5S)-3-(benzoyloxy)-8-methyl-8-azabicyclo[3.2.1]octane-2-carboxylate. It is a tropane alkaloid with a bicyclic ring system. Step 1: Identify the ring system. Cocaine is based on the tropane skeleton — a bicyclo[2.2.1] system with a nitrogen bridge (N-CH3). Step 2: Identify the stereocenters in cocaine: - C-1 (bridgehead carbon bonded to N): This carbon is at the junction of the two rings, bonded to four different groups — it is a stereocenter. - C-2 (carbon bearing the carbomethoxy group, -COOCH3): bonded to C-1, C-3, H, and COOCH3 — four different groups — stereocenter. - C-3 (carbon bearing the benzoyloxy group, -OC(=O)Ph): bonded to C-2, C-4, H, and OBz — four different groups — stereocenter. - C-5 (the other bridgehead carbon bonded to N): bonded to four different groups in the bicyclic framework — stereocenter. Step 3: Count the stereocenters. The known structure of cocaine (natural: 1R,2R,3S,5S) has exactly 4 stereogenic carbon atoms: C-1, C-2, C-3, and C-5. Step 4: Eliminate wrong options: - (a) 1: Undercounts; multiple chiral centers exist. - (b) 2: Undercounts; misses the bridgehead carbons. - (c) 3: Undercounts by one; misses one of the bridgehead stereocenters. - (d) 4: Correct — all four carbons C-1, C-2, C-3, C-5 are stereogenic. Therefore, the correct answer is D.