Question

a. Label the four stereogenic centres in sorbitol as R or S.

b. How are sorbitol and A related?

c. How are sorbitol and B related?

Short answer

a.

b. Diastereomers.

c. Enantiomers.

Step-by-step solution

Stereogenic centres

The stereogenic centers or chiral centers are directly related to the groups or substituents in the molecule. If the four different substituents are bonded with a common carbon atom, then the carbon atom is a stereogenic center.

Enantiomers  

The inverted stereochemistry is obtained in the enantiomers. The mirror images are non-superimposable in this case.

Diastereomers

The pairs which are not mirror images of each other are diastereomers. The stereochemistry of the diastereomers differs at only one carbon center.

Explanation

a. The sorbitol has three isomers. The three isomers are obtained by

changing the stereochemistry of the groups at the chiral center.

The R and S nomenclature are assigned according to the priority of the groups.

The order of the given groups is as:

$\text{OH>R>H}$

Therefore, the clockwise movement in the molecule gives R, and the anticlockwise movement gives S.

b. The sorbitol has R, R, R, S, and the A molecule has R, R, S, S. Therefore, it is a diastereomer.

c. The sorbitol has R, R, R, S, and the B molecule has S, S, S, R. Therefore, it is an enantiomer.