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I am studying spin-spin coupling theory in NMR. Below is an exercise from Mcmurry's organic chemistry.

cyclohexanol

The textbook says that * stands for chiral center. But is it true? When I searched for it some said that there is no chiral center in cyclohexanol. Then, Aren't this hydrogens enantiotopic?

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The substitution of one of the two hydrogens leads to the cis or the trans isomer of the disubstituted cyclohexane. Thus, they are certainly diastereotopic.

Perhaps, what confused you, as well me in a previous answer focused on 1,3-cyclohexandiol, is that substitution with an OH group leads to two diastereoisomers one of which consists of a couple of enantiomers (the other is the meso form).

A prochiral H on a stereogenic center does not imply its enantiotopic character. The obtained diastereoisomers can be optically active in fact, but not enantiomers.

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Cyclohexanol does not have a chiral carbon but hydrogen atoms are diasteotopic because the substitution for one of the two hydrogen atoms (in alternate fashion) would give diastereomers, as the $\ce{C-1}$ carbon of cyclohexanol will now become either chiral (for C-2 and C-3 H-substitution) or will have specific cis or trans geometry(for C-4 H-substitution).

The enantiotopic hydrogen word is used only when one of the hydrogen replacement generates an enantiomer with only one chiral carbon (at the site of hydrogen replacement).

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