Question

The specific rotations of freshly prepared aqueous solutions of $I$ and $II$ are $+112$ and $+18.7$, respectively. On standing, the optical rotation of the aqueous solution of $I$ slowly decreases to give a final value of $+52.7$ due to equilibration with $II$. Under this state of equilibrium, what is the ratio of concentration of $II:I$?

• A. $0.57$
• B. $1.00$
• C. $1.75$
• D. $5.9$

Answer 1

The correct option is C $1.75$

Specific rotation of $\alpha$-glucose$\left(I\right)=+112$
$\beta$-glucose $\left(II\right)=+18.7$

At equilibrium,
$\left[I\right]=x,\left[II\right]=(1-x)$
$\therefore (112\times x)+(18.7\times (1-x\left)\right)=52.7$
$\Rightarrow 112x+18.7-18.7x=52.7$
$\Rightarrow 93.3x=34$
$\therefore x=\frac{34}{93.3}=0.36=\alpha$
$(1-x)=(1-0.36)=0.63=\beta$
$\Rightarrow \frac{\beta }{\alpha }=\frac{0.63}{0.36}=1.75$