Question #44951

D-Glucose exists in a catalytic solvent system at $300\text{ K}$ as an equilibrium mixture of $\alpha$- and $\beta$-anomers. The standard free energy change for the mutarotation equilibrium ($\alpha \rightleftharpoons \beta$) is $\Delta G^\circ = -1.725\text{ kJ mol}^{-1}$.

Excess acetic anhydride is added to completely acetylate the glucose. Under these specific conditions, the rate of mutarotation is significantly faster than the rate of esterification, placing the reaction under Curtin-Hammett control.

The absolute free energy of the transition state ($G^\ddagger$) for the rate-determining step of the $\alpha$-anomer acetylation is $4.475\text{ kJ mol}^{-1}$ lower than that of the $\beta$-anomer acetylation.

Calculate the mole percentage of $\alpha$-D-glucopyranose pentaacetate in the final product mixture.

(Given: $RT = 2.5\text{ kJ mol}^{-1}$ at $300\text{ K}$, $\ln 2 = 0.69$, $\ln 6 = 1.79$)