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JEE Advanced 2020 Paper 2 · Chemistry · General Organic Chemistry and Isomerism · hard

The compound CH3CH=CH-CH(OH)-CH=CH-CH3 (hepta-2,5-dien-4-ol) is considered with all its possible configurational stereoisomers, counting enantiomers…

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The compound CH3CH=CH−CH(OH)−CH=CH−CH3\mathrm{CH_3CH{=}CH{-}CH(OH){-}CH{=}CH{-}CH_3} (hepta-2,5-dien-4-ol) is considered with all its possible configurational stereoisomers, counting enantiomers and diastereomers separately. The total number of distinct stereoisomers is ______.
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Answer: 4

There are two C=C\mathrm{C{=}C} bonds, each of which can be EE or ZZ, and one carbinol carbon, C4\mathrm{C_4}, carrying H\mathrm{H}, OH\mathrm{OH} and two propenyl arms. Take the combinations of double-bond geometry. In the (E,E)(E,E) and (Z,Z)(Z,Z) isomers the two arms at C4\mathrm{C_4} are identical, so C4\mathrm{C_4} is not stereogenic and each molecule is achiral with a mirror plane. This gives 1 isomer each, so 2 in total. In the (E,Z)(E,Z) combination one arm is an (E)(E)-propenyl and the other a (Z)(Z)-propenyl group. These arms are diastereomorphic (not mirror images), so C4\mathrm{C_4} carries four different groups and is a genuine stereocentre; by the CIP rule Z>EZ>E it can be RR or SS. The (E,Z)(E,Z) molecule has no mirror plane, so it exists as a pair of enantiomers, (4R)(4R) and (4S)(4S). The (Z,E)(Z,E) combination is the same molecule as (E,Z)(E,Z) read from the other end, so it adds nothing new. Total =1+1+2=4=1+1+2=4.
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