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JEE Advanced 2021 Paper 2 · Chemistry · General Organic Chemistry and Isomerism · hard

The total number of stereoisomers (counting enantiomers and geometric isomers separately) of the compound CH3CH(Cl)CH=CHCH(Cl)CH3 is ______.

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The total number of stereoisomers (counting enantiomers and geometric isomers separately) of the compound CH3CH(Cl)CH=CHCH(Cl)CH3\mathrm{CH_3CH(Cl)CH{=}CHCH(Cl)CH_3} is ______.
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Answer: 6

The molecule has two stereogenic carbons (C∗\mathrm{C^*} bearing Cl\mathrm{Cl}, CH3\mathrm{CH_3}, H\mathrm{H} and the vinyl carbon) and one stereogenic double bond. Because the two ends are identical, the molecule is symmetric and some combinations coincide. For each geometry of the double bond (E or Z), the centre pairs (R,R)(R,R) and (S,S)(S,S) are enantiomers (two isomers), while (R,S)(R,S) and (S,R)(S,R) are the same meso compound (one isomer). That gives 33 per geometry, and 2×3=62\times3=6 in total. A naive 23=82^3=8 overcounts because of the symmetry of the molecule.
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