Question #44311

An aqueous solution at 298 K contains $0.10\text{ M } B(OH)_3$ and $0.10\text{ M } Si(OH)_4$. To $1.0\text{ L}$ of this solution, $0.25\text{ moles}$ of sucrose is added along with a catalytic amount of invertase, leading to complete hydrolysis into D-glucose and D-fructose. D-fructose (acting as a cis-diol, denoted as $L$) forms a stable spirane complex with the borate anion but does not complex with the silicate species. Assume D-glucose does not complex significantly.

Given: \ce{B(OH)3(aq) + H2O(l) <=> [B(OH)4]^{-}(aq) + H+(aq)}, $K_{a1} = 1.0 \times 10^{-9}$ \ce{[B(OH)4]^{-}(aq) + 2L(aq) <=> [BL2]^{-}(aq) + 4H2O(l)}, $K_f = 1.0 \times 10^4$ \ce{Si(OH)4(aq) <=> [SiO(OH)3]^{-}(aq) + H+(aq)}, $K_{a1} = 1.0 \times 10^{-10}$

Assume the volume remains $1.0\text{ L}$ and the temperature is constant. Calculate the final pH of the solution at equilibrium. (Given: $\log 2 = 0.30$, $\log 5 = 0.70$, $\log 7.07 = 0.85$)