Total number of stereoisomers of product (B) | vedclass

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(B) The reaction of $1,2$-cyclohexanediol with $HIO_4$ gives $2,7$-octanedione $(A)$.Reduction of $(A)$ with excess $LiAlH_4$ followed by acidic worku

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$3$

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(B) The reaction of $1,2$-cyclohexanediol with $HIO_4$ gives $2,7$-octanedione $(A)$.Reduction of $(A)$ with excess $LiAlH_4$ followed by acidic workup yields $2,7$-octanediol $(B)$,which is $CH_3CH(OH)(CH_2)_4CH(OH)CH_3$.This molecule has $2$ identical chiral centers.The number of stereoisomers for a molecule with $n$ identical chiral centers is given by:If $n$ is even,total stereoisomers $= 2^{n-1} + 2^{(n/2)-1}$.Here $n=2$,so total stereoisomers $= 2^{2-1} + 2^{(2/2)-1} = 2^1 + 2^0 = 2 + 1 = 3$.The $3$ stereoisomers are $(I)$ and $(II)$ (a pair of enantiomers) and $(III)$ (a meso compound).

Total number of stereoisomers of product $(B)$ will be

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