Question

The specific rotations of $\alpha$-maltose, $\beta$-maltose and equilibrium mixture of $\alpha$ and $\beta$-maltose are $+{168}^{\circ },+{112}^{\circ }$ and $+{136}^{\circ }$, respectively. The mole fractions of $\alpha$ and $\beta$-maltoses in the equilibrium mixture respectively are:

• A. $0.57,0.43$
• B. $0.43,0.57$
• C. $0.67,0.23$
• D. $0.23,0.67$

Answer 1

The correct option is B $0.43,0.57$

Let the mole fractions of $\alpha$ and $\beta$ - maltoses be $x$ and $(1-x)$ respectively.

Therefore;

$+136=\left(x\right)\ast \left({168}^o\right)+(1-x)\left({112}^o\right)$

$136=168x+112-112x$

$24=56x$

$x=0.43$

$1-x=0.57$

Therefore, the mole fractions of $\alpha$ and $\beta$ - maltoses in the equilibrium mixture are $0.43$ and $0.57$ respectively.