The specific rotations of alpha-D-glucopyranose and beta-D-glucopyranose are +112.2 deg and +18.7 deg. At mutarotation equilibrium the specific rotation is +52.7 deg. Treating the equilibrium mixture as only these two anomers and the rotation as the mole-fraction weighted mean, the percentage of the alpha anomer is

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The specific rotations of alpha-D-glucopyranose and beta-D-glucopyranose are $+ 112. 2^{\circ}$ and $+ 18. 7^{\circ}$ . At mutarotation equilibrium the specific rotation is $+ 52. 7^{\circ}$ . Treating the equilibrium mixture as only these two anomers and the rotation as the mole-fraction weighted mean, the percentage of the alpha anomer is

A63.6%
B47.0%
C36.4%
D50.0%

Answer: C

Let x be the fraction of alpha: 112.2x + 18.7(1 - x) = 52.7, so x = (52.7 - 18.7)/(112.2 - 18.7) = 34/93.5 = 0.3636. The alpha percentage is 36.4%. The beta anomer is 63.6%.

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Answer: C

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