(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 non-superimposable mirror images of a chiral molecule. \(\alpha\)-glucose and \(\beta\)-glucose only differ in the orientation of the hydroxyl group (-OH) at the anomeric carbon atom (C-1) in the cyclic form of glucose. In \(\alpha\)-glucose, the -OH group is positioned below the plane of the ring, while in \(\beta\)-glucose, the -OH group is positioned above the plane of the ring. However, \(\alpha\)-glucose and \(\beta\)-glucose are not mirror images of each other, they are actually anomers (stereoisomers), which are diastereomers (not mirror images) that differ only in the configuration at the anomeric center. Thus, \(\alpha\)-glucose and \(\beta\)-glucose are not enantiomers.

To form a disaccharide with an \(\alpha\) linkage, two glucose molecules undergo a condensation reaction at their anomeric carbons, with the oxygen atom from the -OH group at C-1 of one glucose molecule connecting to the oxygen atom from the -OH group at C-4 of the other glucose molecule, creating an \(\alpha\)-1,4-glycosidic bond. Follow these steps for the reaction: 1. Identify the anomeric carbon in both glucose molecules involved in the reaction. 2. Ensure that one glucose molecule has the -OH group at C-1 below the plane of the ring (to represent the \(\alpha\) configuration). 3. Form a bond between the oxygen atoms of the -OH groups at C-1 of the first glucose molecule and C-4 of the second glucose molecule. 4. Release a water molecule (H from C-1 of the first glucose molecule and OH from C-4 of the second glucose) as a byproduct of the condensation reaction. 5. The newly formed disaccharide has an \(\alpha\)-1,4-glycosidic bond connecting the glucose monomers.

Similarly, to form a disaccharide with a \(\beta\) linkage, two glucose molecules undergo a condensation reaction at their anomeric carbons, but with the -OH group in the \(\beta\) configuration at C-1 of one glucose molecule instead. Follow these steps for the reaction: 1. Identify the anomeric carbon in both glucose molecules involved in the reaction. 2. Ensure that one glucose molecule has the -OH group at C-1 above the plane of the ring (to represent the \(\beta\) configuration). 3. Form a bond between the oxygen atoms of the -OH groups at C-1 of the first glucose molecule and C-4 of the second glucose molecule. 4. Release a water molecule (H from C-1 of the first glucose molecule and OH from C-4 of the second glucose) as a byproduct of the condensation reaction. 5. The resulting disaccharide has a \(\beta\)-1,4-glycosidic bond connecting the glucose monomers.