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(A) meso compound is an achiral molecule that has stereogenic centers but possesses an internal plane of symmetry or center of inversion,making it opt

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$I, II, IV$

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(A) meso compound is an achiral molecule that has stereogenic centers but possesses an internal plane of symmetry or center of inversion,making it optically inactive.Let us analyze the given structures:$(I)$ $1,2$-dibromocyclopentane: This has $5$ carbons and $2$ stereogenic centers. The cis-isomer has a plane of symmetry,making it a meso compound.$(II)$ $2,4$-dihydroxypentanedioic acid: This has $5$ carbons and $2$ stereogenic centers. The meso form exists where the two stereocenters have opposite configurations ($R,S$ or $S,R$),creating a plane of symmetry.$(III)$ $2,3$-dibromopentane: This has $5$ carbons and $2$ stereogenic centers,but it does not have a plane of symmetry in any conformation,so it cannot be meso.$(IV)$ $2,4$-pentanediol: This has $5$ carbons and $2$ stereogenic centers. The meso form exists where the two stereocenters have opposite configurations,creating a plane of symmetry.$(V)$ $1,5$-dibromopentane: This has $5$ carbons but no stereogenic centers.Thus,structures $(I)$,$(II)$,and $(IV)$ are meso compounds with $5$ carbons and $2$ stereogenic centers.

$A$ compound was synthesized by a student,but its structure was not identified. However,his instructor told him that it was a meso compound with $5$ carbons and $2$ stereogenic centers. Which of the following structures should the student consider as possibilities for his compound?

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