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?

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.

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.)

Draw each of the following:

a. β-D-talopyranose

b. α-D-idopyranose  

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

A hexose is obtained when the residue of a shrub Sterculia setigeria undergoes acid-catalyzed hydrolysis. Identify the hexose from the following experimental information: it undergoes mutarotation; it does not react with Br₂; and D-galactonic acid and D-talonic acid are formed when it reacts with Tollens’ reagent.

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.)