The specific rotations of pure -D-glucopyranose and -D-glucopyranose are and , respectively. The spe — Biomolecules Chemistry Question
Question
The specific rotations of pure $\alpha$ -D-glucopyranose and $\beta$ -D-glucopyranose are $+110^\circ$ and $+19^\circ$, respectively. The specific rotation of their constant equilibrium mixture in water is $+52.7^\circ$. Calculate the approximate percentage of the $\beta$ -anomer present in the equilibrium mixture. (Round off to the nearest integer)
Answer: 63
💡 Solution & Explanation
Let the fraction of the $\alpha$ -anomer be $x$. The fraction of the $\beta$ -anomer is $(1-x)$. Using the additive property of specific rotation: $110x + 19(1-x) = 52.7$. Solving for $x$: $91x = 33.7 \implies x \approx 0.370$ ($37\%$). Therefore, the $\beta$ -anomer percentage is $100\% - 37\% = 63\%$.
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