Identify the following as diastereomers, enantiomers, and/or anomers.
(a) β-D-fructose and β-D-fructose
(b) D-galactose and L-galactose
(c) L-allose and D-glucose (both aldohexoses)

Verified step by step guidance

1. Step 1: Understand the definitions of the terms. Diastereomers are stereoisomers that are not mirror images of each other. Enantiomers are stereoisomers that are non-superimposable mirror images. Anomers are a specific type of diastereomer that differ in configuration at the anomeric carbon (the carbon derived from the carbonyl group in a sugar).
2. Step 2: Analyze part (a). Compare ß-d-fructose and ß-d-fructose. Since they are the same molecule, they are neither diastereomers, enantiomers, nor anomers. They are identical.
3. Step 3: Analyze part (b). Compare d-galactose and l-galactose. These are mirror images of each other and are non-superimposable. Therefore, they are enantiomers.
4. Step 4: Analyze part (c). Compare l-allose and d-glucose. Both are aldohexoses, but they differ in the arrangement of groups at multiple chiral centers. Since they are not mirror images, they are diastereomers.
5. Step 5: Summarize the findings. (a) Identical molecules, not diastereomers, enantiomers, or anomers. (b) Enantiomers. (c) Diastereomers.

Key Concepts

Diastereomers

Diastereomers are stereoisomers that are not mirror images of each other. They occur when two or more stereocenters are present in a molecule, leading to different spatial arrangements of atoms. Unlike enantiomers, which have identical physical properties except for their interaction with polarized light, diastereomers can have significantly different chemical and physical properties.

Enantiomers

Enantiomers are a type of stereoisomer that are non-superimposable mirror images of each other. Each enantiomer has at least one chiral center, and they often exhibit different optical activities, meaning they rotate plane-polarized light in opposite directions. Enantiomers can have vastly different biological activities, making their distinction crucial in fields like pharmacology.

Anomers

Anomers are a specific type of stereoisomer that differ at the anomeric carbon, which is the carbon atom that becomes a new chiral center when a sugar cyclizes. In the case of carbohydrates, anomers are typically designated as alpha (α) or beta (β) based on the orientation of the hydroxyl group at the anomeric carbon. This distinction is important in understanding the reactivity and properties of sugars in biological systems.