Answer to Question #97953 in Chemistry for Shants

Question

-TOPIC_ inversion of sugar Cane
I plotted a graph of ln(Optical rotation -
Infinite optical rotation) vs time..obtained the pseudo rate constant
How do I use optical rotation to determine the rotation at time zero

Answer 1

Inversion of cane sugar is a pseudo first order reaction.

$Rate constant (k)×t= 2.303log((a_t-a_{\infty})/(a_0-a_{\infty}))$

$Rate constant (k)×t= 2.303log(a_t-a_{\infty})-2.303log(a_0-a_{\infty})$

$t= 2.303log(a_t-a_{\infty})/k-2.303log(a_0-a_{\infty})/k$

a_t= optical rotation at time $t=t$

a₀= optical rotation at time $t=0$

$a_{\infty}=optical$ rotation after infinite time

It is of the form $x=my+c$

$x=t$

$m=2.303/k$

$y=log(a_t-a_{\infty})$

$c=-(2.303log(a_0-a_{\infty}))/k$

Now in the graph, when $x=0$ ,we obtain x intercept which is equal to c.

We know k,$a_{\infty}$ and c from the graph so using all these in equation (1) we obtain optical rotation at time 0.