Question

The reaction, $Sucrose\to Fructose+Glucose$, takes place at a certain temperature while the volume of the solution is maintained at 1 L. At t = 0, the initial rotation of the mixture is ${34}^{\circ }$. After 30 minutes the total rotation is ${19}^{\circ }$and after a very long time, the total rotation is $-{11}^{\circ }$. Find the time when solution was optically inactive.

• A. 135 minutes
• B. 103.7 minutes
• C. 38.7 minutes
• D. 45 minutes

Answer 1

The correct option is B

103.7 minutes

Rate constant for this condition:
$k=\frac{1}{t}\frac{[{\theta }_{\infty }-{\theta }_0]}{[{\theta }_{\infty }-{\theta }_t]}$
Given that:
${\theta }_{\infty }=-{11}^0$
${\theta }_o=-{34}^0$
${\theta }_{t=30mint}=-{19}^0$

$k=\frac{1}{30}\frac{[-11-(-34\left)\right]}{[-11-(-19\left)\right]}\left(1\right)$
Solution optically inactive when ${\theta }_t=0$
$k=\frac{1}{t}\frac{[-11-(-34\left)\right]}{[-11-(0\left)\right]}\left(1\right)$
On substituting value of k from (1), we get
$t=103.7minutes$