The specific rotations of the α- and β-anomers of D-glucose are +112 degrees and +18.7
degrees, respectively. When a crystalline sample of α-dglucopyranose is dissolved in water, the
specific rotation decreases from 112 degrees to an equilibrium value of 52.7 degrees. On the
basis of this result, what are the proportions of the α-and β-anomers at equilibrium? Assume that
the concentration of the open-chain form is negligible.