An unknown disaccharide gives a positive Tollens' test. A glycosidase hydrolyzes it to D-galactose and D-mannose. When the disaccharide is treated with methyl iodide and Ag2O and then hydrolyzed with dilute HCl, the products are 2,3,4,6-tetra-O-methylgalactose and 2,3,4-tri-O-methylmannose. Propose a structure for the disaccharide.

Trehalose, C₁₂H₂₂O₁₁, is a nonreducing sugar that is only 45% as sweet as sugar. When hydrolyzed by aqueous acid or the enzyme maltase, it forms only D-glucose. When it is treated with excess methyl iodide in the presence of Ag₂O and then hydrolyzed with water under acidic conditions, only 2,3,4,6-tetra-O-methyl-d-glucose is formed. Draw the structure of trehalose.

The specific rotation of α-D-galactose is 150.7 and that of β-D-galactose is 52.8. When an aqueous mixture that was initially 70% α-D-galactose and 30% β-D-galactose reaches equilibrium, the specific rotation is 80.2. What is the percentage of α-D-galactose and β-D galactose at equilibrium?

Predict whether D-altrose exists preferentially as a pyranose or a furanose. (Hint: In the most stable arrangement for a five-membered ring, all the adjacent substituents are trans.)

Propose a mechanism for the rearrangement that converts an ⍺-hydroxyimine to an ⍺-aminoketone in the presence of a trace amount of acid.

Draw the mechanism for the elimination step in the Wohl degredation.

Calculate the percentages of $\alpha$-D-glucose and $\beta$-D-glucose present at equilibrium from the specific rotations of $\alpha$-D-glucose, $\beta$-D-glucose, and the equilibrium mixture. Compare your values with those given in Section 20.10. (Hint: The specific rotation of the mixture equals the specific rotation of $\alpha$-D-glucose times the fraction of glucose present in the a-form plus the specific rotation of $\beta$-D-glucose times the fraction of glucose present in the $\beta$ -form.)