(a) Are \(\alpha\) -glucose and \(\beta\) -glucose enantiomers? (b) Show the condensation of two glucose molecules to form a disaccharide with an \(\alpha\) linkage. (c) Repeat part (b) but with a \(\beta\) linkage.

Enantiomers are stereoisomers that are non-superimposable mirror images of each other, which means they have the same chemical formula and bond structure, but differ in the arrangement of atoms in space. The easiest way to determine if they are enantiomers is to look at their structures. α-glucose and β-glucose are both forms of glucose with the same molecular formula, C6H12O6. They differ only in the position of the hydroxyl group (-OH) at the anomeric carbon (C1): In α-glucose, the hydroxyl group is below the plane of the ring (cis), while in β-glucose, it is above the plane of the ring (trans). However, they are not mirror images of each other. Thus, the answer to part (a) is NO, α-glucose and β-glucose are not enantiomers. They are actually epimers, which are a type of diastereomer.

To form a disaccharide with an α-linkage, two glucose molecules will undergo a condensation reaction. In this reaction, the hydroxyl group ( -OH) of one glucose molecule will react with another glucose molecule's hydroxyl group at the anomeric carbon (C1). Here's a step-by-step illustration of the reaction: 1. Identify the α-glucose anomeric carbon (C1), where the hydroxyl group is below the plane of the ring (cis). 2. Combine the hydroxyl groups of the two α-glucose molecules by breaking the O-H bond and removing a water molecule (H2O). 3. Form a glycosidic bond between the two α-glucose molecules, creating an α-linkage (α-1,4 glycosidic bond). 4. The resulting disaccharide formed in this linkage is maltose.

Similar to part (b), we'll perform a condensation reaction between two glucose molecules, but this time with a β-linkage. Here's the step-by-step breakdown of the reaction: 1. Identify the β-glucose anomeric carbon (C1), where the hydroxyl group is above the plane of the ring (trans). 2. Combine the hydroxyl groups of the two β-glucose molecules by breaking the O-H bond and removing a water molecule (H2O). 3. Form a glycosidic bond between the two β-glucose molecules, creating a β-linkage (β-1,4 glycosidic bond). 4. The resulting disaccharide formed in this linkage is cellobiose.