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JEE Advanced 2022 Paper 2 · Chemistry · General Organic Chemistry and Isomerism · hard

Cyclohexane-1,2,3,4,5,6-hexol (inositol), C6H12O6, has six OH groups, one on each ring carbon of a planar-represented cyclohexane ring. Counting each…

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Cyclohexane-1,2,3,4,5,6-hexol (inositol), C6H12O6\mathrm{C_6H_{12}O_6}, has six OH\mathrm{OH} groups, one on each ring carbon of a planar-represented cyclohexane ring. Counting each enantiomer separately and each meso form once, the total number of stereoisomers of this compound is _____.
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Answer: 9

Each of the six ring carbons carries OH and H, so each can be labelled 'up' or 'down' (relative OH orientation): 26=642^6=64 labellings. Many are the same molecule: rotating the ring, turning it over (which swaps up/down everywhere) and reflecting it map labellings onto each other. Collapsing them gives 8 diastereomers (the familiar inositols: myo, scyllo, cis, epi, allo, neo, muco and chiro). Seven of the eight (myo, scyllo, cis, epi, allo, neo, muco) have an internal mirror plane, so each is a single achiral meso compound. The eighth, chiro-inositol, has no mirror plane or inversion centre and exists as a pair of enantiomers. Total =7+2=9=7+2=9. The answer is 99.
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