See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1: Identify all stereocenters and sources of stereoisomerism in the molecule. The molecule is a cyclohexanone derivative. Let us label the ring carbons. The carbonyl is at C1. Going around the ring: - C2 bears a Cl substituent → potential stereocenter - C3 bears a CH2OH substituent → potential stereocenter - C4 bears the side chain -CH2-CH=CH-CH=CH-CH2CH3 (conjugated diene) → potential stereocenter - C5 bears a Cl substituent → potential stereocenter - C6 is a CH2 group (no substituent other than ring) → not a stereocenter Step 2: Count ring stereocenters. C2 (Cl, adjacent to C=O): has four different groups → stereocenter C3 (CH2OH): has four different groups → stereocenter C4 (diene chain): has four different groups → stereocenter C5 (Cl): has four different groups → stereocenter Total ring stereocenters = 4 Step 3: Count geometric (E/Z) isomerism in the side chain. The side chain from C4 is: -CH2-CH=CH-CH=CH-CH2CH3 This contains two C=C double bonds (a conjugated diene): - First double bond (C=C): can be E or Z → 2 possibilities - Second double bond (C=C): can be E or Z → 2 possibilities Total geometric combinations = 2 × 2 = 4 Step 4: Calculate total stereoisomers. From 4 ring stereocenters: 2^4 = 16 configurations From 2 double bonds in the side chain: 2^2 = 4 configurations Total = 16 × 4 = 64 Step 5: Check for any meso forms or symmetry that would reduce the count. Given the different substituents (Cl at C2, CH2OH at C3, diene chain at C4, Cl at C5) around the ring and the asymmetric side chain, no meso form is possible that would reduce the count. Therefore, the correct answer is 64.