Question #44802

The acid-catalyzed hydrolysis of sucrose to D-glucose and D-fructose at 298 K is monitored by polarimetry. The apparent pseudo-first-order rate constant is calculated as $k_{app} = \frac{1}{t} \ln \left( \frac{r_0 - r_\infty}{r_t - r_\infty} \right)$. In a very dilute acid, the mutarotation rate of the products is comparable to the hydrolysis rate, causing $k_{app}$ to deviate from the true hydrolysis rate constant $k_{true}$ during the early stages of the reaction. Given the specific rotations $[\alpha]_D^{25}$: Sucrose = $+66.5^\circ$, $\alpha$-D-Glucopyranose = $+112.2^\circ$, $\beta$-D-Glucopyranose = $+18.7^\circ$, equilibrium D-Glucose = $+52.7^\circ$. Assuming the hydrolysis proceeds via the most stable oxocarbenium ion intermediate, identify the specific rotation of the D-glucose anomer initially released, and the relationship between $k_{app}$ and $k_{true}$ at early times ($t > 0$).