Answer
Percentages of the two anomers present at equilibrium are 28% of the alpha anomer and 72% of the beta anomer.
Work Step by Step
The specific rotation of alpha-D-galactopyranose is +150.7° and the specific rotation of beta-D-galactopyranose is +52.8°.
a = fraction of alpha anomer
b = fraction of beta anomer
a $\times$ (+150.7°) + b $\times$ (+52.8°) = +80.2°
a + b = 1 --> a = 1 - b
(1 - b) $\times$ (+150.7°) + b $\times$ (+52.8°) = +80.2°
+150.7° - b $\times$ (+150.7°) + b $\times$ (+52.8°) = +80.2°
b $\times$ (+52.8° - (+150.7°)) = +80.2° - (+150.7°)
- 97.9° $\times$ b = -70,5° /(- 97.9°)
b = 0.72
a = 1 - b
a = 0.28
