The hydrolysis of glucose 6-phosphate in aqueous solution at is represented by…

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

The hydrolysis of glucose 6-phosphate in aqueous solution at 298 K298\,\text{K} is represented by Glucose 6-phosphate+H2O⇌Glucose+PiΔG∘=+13.8 kJ mol−1\text{Glucose 6-phosphate} + H_2O \rightleftharpoons \text{Glucose} + P_i \quad \Delta G^\circ = +13.8\,\text{kJ}\,\text{mol}^{-1} Hydrolysis of ATP under the same conditions is ATP+H2O⇌ADP+Pi+H+ΔG∘=−30.5 kJ mol−1\text{ATP} + H_2O \rightleftharpoons \text{ADP} + P_i + H^+ \quad \Delta G^\circ = -30.5\,\text{kJ}\,\text{mol}^{-1} A metabolic engineer wants to use ATP hydrolysis to drive the unfavorable hydrolysis of glucose 6-phosphate so that the overall process is strongly spontaneous. (1) Part 1: (a) Write the chemical equation obtained when one mole of ATP hydrolysis is coupled to one mole of glucose 6-phosphate hydrolysis. Cancel any intermediates and show the net stoichiometry. (2) Part 2: (b) Calculate the overall ΔG∘\Delta G^\circ when one mole of ATP is coupled as in part (a). Show your work with units. (3) Part 3: (c) Determine the minimum integer number of moles of ATP that must be hydrolyzed per mole of glucose 6-phosphate so that the overall ΔG∘\Delta G^\circ is at most −10 kJ mol−1-10\,\text{kJ}\,\text{mol}^{-1}. Explain your reasoning. (4) Part 4: (d) Discuss qualitatively how increasing the cellular temperature from 298 K298\,\text{K} to 310 K310\,\text{K} could influence the spontaneity of the coupled reaction, assuming ΔH∘\Delta H^\circ and ΔS∘\Delta S^\circ for each individual reaction remain approximately temperature-independent over this range.

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