How many stereoisomers of 2,3-dihydroxypentane are possible?

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Answer

Number of Stereoisomers of 2,3-Dihydroxypentane

2,3-Dihydroxypentane is a pentane molecule with two hydroxyl (-OH) groups attached to the second and third carbon atoms. Stereoisomers are isomers that have the same molecular formula and connectivity but differ in the arrangement of their atoms in space. There are two types of stereoisomers:

Enantiomers: non-superimposable mirror images of each other

Diastereomers: stereoisomers that are not enantiomers

Enantiomers

For a molecule to have enantiomers, it must have at least one chiral center. A chiral center is a carbon atom that is bonded to four different groups. In 2,3-dihydroxypentane, carbon atoms 2 and 3 are chiral centers since they are bonded to four different groups (two hydroxyl groups and two hydrogen atoms). Therefore, 2,3-dihydroxypentane can have enantiomers.

The number of enantiomers a molecule can have is 2ⁿ, where n is the number of chiral centers. In this case, there are two chiral centers, so the number of enantiomers is:

2² = 4

Therefore, 2,3-dihydroxypentane can have four enantiomers.

Diastereomers

Diastereomers are stereoisomers that are not enantiomers. In 2,3-dihydroxypentane, there are two chiral centers, so there are four possible stereoisomers:

RR: both hydroxyl groups are on the same side of the molecule

SS: both hydroxyl groups are on the opposite side of the molecule

RS: one hydroxyl group is on the same side of the molecule as the first chiral center, and the other hydroxyl group is on the opposite side

SR: one hydroxyl group is on the opposite side of the molecule as the first chiral center, and the other hydroxyl group is on the same side

Since there are four possible stereoisomers, 2,3-dihydroxypentane can have four diastereomers.

Total Number of Stereoisomers

The total number of stereoisomers is the sum of the enantiomers and diastereomers:

Total number of stereoisomers = number of enantiomers + number of diastereomers

Total number of stereoisomers = 4 + 4 = 8

Therefore, 2,3-dihydroxypentane can have eight stereoisomers.

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