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JEE Advanced 2025 Paper 2 · Chemistry · General Organic Chemistry and Isomerism · hard

The compound hepta-2,5-dien-4-ol, CH3CH=CH-CH(OH)-CH=CHCH3, can exist in several stereoisomeric forms because of its two double bonds and its…

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The compound hepta-2,5-dien-4-ol, CH3CH=CH−CH(OH)−CH=CHCH3\mathrm{CH_3CH{=}CH{-}CH(OH){-}CH{=}CHCH_3}, can exist in several stereoisomeric forms because of its two double bonds and its carbinol carbon. If NN is the total number of stereoisomers and MM is the number of those that are optically active, the value of N+MN+M is ____.
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Answer: 6

Each double bond can be EE or ZZ, giving combinations (E,E)(E,E), (Z,Z)(Z,Z) and (E,Z)(E,Z) (the last equals (Z,E)(Z,E) by symmetry of the constitution). In (E,E)(E,E) and (Z,Z)(Z,Z) the two groups on C4\mathrm{C4} are identical, so C4\mathrm{C4} is not a stereocentre and each is a single achiral compound with a mirror plane through C4\mathrm{C4}: 22 stereoisomers, both optically inactive. In (E,Z)(E,Z) the two alkenyl groups on C4\mathrm{C4} are different (EE-propenyl versus ZZ-propenyl), so C4\mathrm{C4} carries four different groups (H\mathrm{H}, OH\mathrm{OH}, and two diastereomeric alkenyl groups) and is a stereocentre; this gives a pair of enantiomers, 22 stereoisomers, both optically active. Thus N=2+2=4N=2+2=4, M=2M=2, and N+M=6N+M=6.
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