Question

An optically active compound A(specific solution $100$) undergoes mutarotation in aqueous solution to form another optically active compound B(specific rotation $200$) till the specific rotation of the solution finally attains the constant value of $180$. Find Kc for the mutarotation.

Answer 1

$A\rightleftharpoons B$ $A_{{\theta }_1}=100$

$1-\alpha$ $\alpha$ $b_{{\theta }_1}=200$

total rotation $\Rightarrow$ (1-2)100 + (2)(200) = 180

100 + 100$\alpha$=180

$\alpha$=180

$\Rightarrow \frac{\alpha }{1-\alpha }\Rightarrow \frac{0.8}{1.08}=\frac{0.8}{0.2}=4$