28. Carbohydrates

Calculate the percentages of a-d-glucose and b-d-glucose present at equilibrium from the specific rotations of a-d-glucose, b-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 a-d-glucose times the fraction of glucose present in the a-form plus the specific rotation of b-d-glucose times the fraction of glucose present in the b-form.)

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

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

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

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(•••) (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?