Mutarotation Practice Problems

Glucose undergoes mutarotation in an aqueous solution. The specific rotation of pure α-D-glucose is +112.2° and pure β-D-glucose is +18.7°. When the pure α or β anomer is dissolved in water, it mutarotates and the specific rotation changes to +52.6°. Using the specific rotation values, calculate the percent of each anomer present in the solution at equilibrium.

Determine the equilibrium percentages of α-D-fructose and β-D-fructose using their specific rotations. The specific rotation of α-D-fructose is +92°, that of β-D-fructose is +18°, and the equilibrium mixture has a specific rotation of +38.5°.

A scientist wants to determine the percentage of α-D-mannose and β-D-mannose in an equilibrium solution. The specific rotation of α-D-mannose is +20.3°, while that of β-D-mannose is −17.0°. At equilibrium, the specific rotation is +14.2. What are the percentages at equilibrium?

When lactose hydrolyzes, a mixture of galactose and glucose with a ratio of 1:1 has a specific rotation of +112°. What is the specific rotation of an equilibrium mixture of galactose? [Note: The specific rotation of glucose at equilibrium is +52.7°.]

Propose a mechanism for the conversion of α-D-galactopyranose to β-D-galactopyranose in an acidic environment.

Propose a mechanism for the transformation of α-D-mannopyranose to β-D-mannopyranose under basic conditions.