Question #44530

A $34.2 \text{ g}$ sample of sucrose ($\ce{C12H22O11}$) is dissolved in $100.0 \text{ g}$ of water. A trace amount of an acid catalyst is added, and the solution is heated until the inversion of sucrose is complete. The resulting monosaccharides undergo mutarotation and reach their respective anomeric equilibria. For D-glucose, the equilibrium mixture contains $36\%$ $\alpha$-anomer and $64\%$ $\beta$-anomer. For D-fructose, the equilibrium mixture contains $70\%$ $\beta$-pyranose, $20\%$ $\beta$-furanose, and $10\%$ $\alpha$-furanose. Assuming the trace acid contributes negligibly to the molality, what is the boiling point elevation ($\Delta T_b$) of the final solution? ($K_b$ for water = $0.52 \text{ K kg mol}^{-1}$, Molar mass of sucrose = $342 \text{ g mol}^{-1}$, Molar mass of water = $18 \text{ g mol}^{-1}$)