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The specific rotations of the α and β anomers of D-glucose are +112 degrees and +18.7...

The specific rotations of the α and β anomers of D-glucose are +112 degrees and +18.7 degrees, respectively. Specific rotation, [α]D, is defined as the observed rotation of light of wavelength 589 nm (the D line of a sodium lamp) passing through 10 cm of a 1 g/mL solution of a sample. When a crystalline sample of α-D-glucose 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 α and β anomers at equilibrium? Assume the concentration of the open-chain form is negligible.

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