Question #44996

An aqueous solution contains an equimolar mixture (1 mole each) of four disaccharides: Sucrose, Lactose, Maltose, and Cellobiose. Four identical aliquots of this solution (each containing 1 mole of all four disaccharides) are subjected to different hydrolytic conditions at $298\text{ K}$ and optimal pH:

Aliquot I: Treated with Invertase (strictly specific to sucrose). Aliquot II: Treated with $\beta$-galactosidase (strictly specific to $\beta$-D-galactoside linkages). Aliquot III: Treated with Maltase (strictly specific to $\alpha$-(1$\rightarrow$4)-D-glucosidic linkages). Aliquot IV: Heated with dilute aqueous \ce{H2SO4} until complete chemical hydrolysis occurs.

Assume all enzymatic and chemical hydrolyses proceed to 100% completion. Let $G_i$ be the total moles of free D-glucose molecules present in the final mixture of Aliquot $i$. Let $R_i$ be the total moles of reducing sugar molecules present in the final mixture of Aliquot $i$.

Calculate the value of $\sum_{i=1}^{4} G_i + \sum_{i=1}^{4} R_i$.