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# The rate of reaction between sucrose and water catalyzed by hydrogen ion is followed by measuring the angle of rotation of polarized light passing through the solution. The angle of rotation of polarized light passing through the solution is measured with a polarimeter.

The reaction is: $C_{12}H_{22}O_{11}+H_2O+H^+\rightarrow C_6H_{12}O_6+C_6H_{12}O_6+H^+$.

As the sucrose is used up and the glucose-fructose mixture is formed, the angle of rotation to the right (as the observer looks into the polarimeter tube) becomes less and less, and finally the light is rotated to the left. The rotation is determined at the beginning ($\alpha_ο$) and at the end of the reaction ($\alpha_{\infty}$).

What is the rate constant?

$\begin{array}{1 1}(A)\;K=ln\big(\large\frac{r_o-r_{\infty}}{r_o-r_t}\big)/t \\(B)\;K=ln\big(\large\frac{r_o}{r_o-r_t}\big)/t \\ (C)\;K=ln\big(\large\frac{r_{\infty}}{r_{\infty}-r_t}\big)/t \\ (D) None \end{array}$

Here $r_{\infty}$ & $r_t$ are the rotation of glucose & fructose not the sample .
Hence (c) is the correct answer.