Question

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

Short answer

Explain your answer. Answer: No, α-D-glucose and β-D-glucose are not enantiomers. They are diastereomers, as they have different configurations at the anomeric carbon but share the same configurations at other chiral carbons in the molecule. Enantiomers are non-superimposable mirror images, which does not apply to α-D-glucose and β-D-glucose.

Step-by-step solution

Define Enantiomers and Stereoisomers

In order to determine if α-D-glucose and β-D-glucose are enantiomers, we first need to define enantiomers and stereoisomers. Stereoisomers are molecules that have the same molecular formula and the same arrangement of atoms in their structure but differ in their spatial arrangement of those atoms. Enantiomers, on the other hand, are a specific type of stereoisomers that are non-superimposable mirror images of each other.

Understand the Structure of Glucose and its Anomers

Glucose is an aldohexose sugar, meaning it is a six-carbon sugar with an aldehyde functional group. When glucose is in its linear form, it follows the Fischer projection for D-glucose. However, in solution, glucose predominantly exists in its cyclic, pyranose form, which is formed through an intramolecular hemiacetal reaction between the aldehyde group and the hydroxyl group on the fifth carbon. This cyclic form can exist in two different anomers: α-D-glucose and β-D-glucose. The difference between these two anomers lies in the orientation of the hydroxyl group at the anomeric carbon (carbon 1), which is either in an axial position (α) or an equatorial position (β).

Comparing the Structures of α-D-glucose and β-D-glucose

Now that we understand the structures of α-D-glucose and β-D-glucose, we can compare them to determine if they are enantiomers. As mentioned earlier, the main difference between the two molecules are the axial (α) and equatorial (β) orientations of the hydroxyl group on the anomeric carbon (carbon 1). The rest of the molecule has the same structure and stereochemistry.

Determine if α-D-glucose and β-D-glucose are Enantiomers

Given the differences between α-D-glucose and β-D-glucose, they do not meet the definition of enantiomers because they are not non-superimposable mirror images of each other. Instead, they are diastereomers, a different type of stereoisomer, because they have different configurations at the anomeric carbon while having the same configurations at the other chiral carbons in the molecule. Therefore, α-D-glucose and β-D-glucose are not enantiomers. In conclusion, α-D-glucose and β-D-glucose are not enantiomers, as they do not fit the definition of being non-superimposable mirror images of each other. Instead, they are diastereomers, having different configurations at the anomeric carbon while sharing the same configurations at other chiral carbons.