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

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?

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

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