From the specific rotations shown in Eq. 24.18, calculate the percentages of - and -D- glucopyranose present

From the specific rotations shown in Eq. 24.18, calculate the percentages of α- and β-D- glucopyranose present at equilibrium.Compare your answer to the data given in Table 24.1.

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TABLE 24.1 Compositions of Monosaccharides at Equilibrium in Aqueous Solution at 40 °C Percent at equilibrium furanose Sugar D-glucose D-galactose D-mannose D-allose D-altrose D-idose D-talose D-arabinose D-Xylose D-ribose D-fructose 36 27-36 68 18 27 39 40 63 37 20 0-3 pyranose B 64 64-73 32 70 40 36 29 34 63 56 57-75 trace 5 20 11 20 6 4-9 trace* trace 3 В 0 7 13 14 11 18 21-31 aldehyde or ketone 0.003 trace trace 0.02 0.25