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

Question

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 :

Professor PC Thomas Classes · Answer

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