Question

Are \(\alpha\)-D-glucose and \(\beta\)-D-glucose enantiomers? Explain.

Short answer

Answer: No, \(\alpha\)-D-glucose and \(\beta\)-D-glucose are not enantiomers; they are diastereomers - specifically, anomers. They differ only in the configuration of the hydroxyl group at the anomeric carbon (C1).

Step-by-step solution

Define Enantiomers

Enantiomers are a type of stereoisomers that are non-superimposable mirror images of each other. If two molecules cannot be superimposed (i.e., aligned exactly on top of each other when reflected in a mirror), and their structures are mirror images of each other, they are enantiomers.

Analyze the Structures of \(\alpha\)-D-glucose and \(\beta\)-D-glucose

\(\alpha\)-D-glucose and \(\beta\)-D-glucose are two anomers of glucose. They differ in the configuration of the hydroxyl group (OH) at the anomeric carbon (C1) - in \(\alpha\)-D-glucose, the hydroxyl group is in the axial position (below the plane), while in \(\beta\)-D-glucose, the hydroxyl group is in the equatorial position (above the plane). In both anomers, the rest of the structure is the same; they consist of a six-membered ring (five carbons and one oxygen) with the same configuration for all other carbons.

Compare the Structures of \(\alpha\)-D-glucose and \(\beta\)-D-glucose

Though both \(\alpha\)-D-glucose and \(\beta\)-D-glucose are stereoisomers of glucose, they are not enantiomers, as their structures are not non-superimposable mirror images of each other. Specifically, they are diastereomers, as they differ in the arrangement of only one stereocenter - the anomeric carbon (C1). In conclusion, \(\alpha\)-D-glucose and \(\beta\)-D-glucose are not enantiomers, but rather, they are diastereomers - specifically, anomers. Their structures differ only in the configuration of the hydroxyl group at the anomeric carbon (C1).