28. Carbohydrates

Like glucose, galactose mutarotates when it dissolves in water. The specific rotation of α-D-galactopyranose is +150.7°, and that of the β anomer is +52.8°. When either of the pure anomers dissolves in water, the specific rotation gradually changes to +80.2°. Determine the percentages of the two anomers present at equilibrium.

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.)

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?

Suggest a mechanism by which α-d-glucopyranose is converted to β-d-glucopyranose in acid. [See Figure 27.18.]

Suggest a mechanism by which α-d-glucopyranose is converted to β-d-glucopyranose in base. [See Figure 27.18.]

(a) Suggest an arrow-pushing mechanism for the mutarotation of α-d-glucose to β-d-glucose in the presence of acid. Acid isn’t necessary, but it does increase the rate of the process.

(b) What is the role of acid in your mechanism?