The optical rotation of the $\alpha$-form of a pyranose is $+ {150.7}^{\circ}$, that of the $\beta$-

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The optical rotation of the $\alpha$-form of a pyranose is $+ {150.7}^{\circ}$, that of the $\beta$-form is $+ {52.8}^{\circ}$. In solution an equilibrium mixture of these anomers has an optical rotation of $+ {80.2}^{\circ}$. The percentage of the $\alpha$-form in equilibrium mixture is :

Accepted Answer

$150.7(X) + 52.8(1 - X) = + 80.2$$$\begin{matrix} 150.7X + 52.8 - 52.8X & \ = + 80.2 \ 97.9X & \ = 27.4 \ X & \ = 0.279 = 0.28 \end{matrix}$$

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