Sucrose can be formed from glucose and fructose in a dehydration reaction whose standard free-energy change is +23.0 kJ mol⁻¹. A plant cell synthesizes exactly 5.00 g of sucrose (molar mass = 342 g mol⁻¹) under standard-state conditions by coupling the dehydration to the hydrolysis of ATP to ADP and inorganic phosphate (ΔG° = −30.5 kJ mol⁻¹).
(a) Calculate the number of moles of sucrose produced.
(b) Determine the minimum number of moles of ATP that must be hydrolyzed to drive the production of 5.00 g of sucrose, assuming 100 % efficiency and that the reactions occur under standard-state conditions.
(c) Express your answer to part (b) as the corresponding number of ATP molecules. Use Avogadro’s constant, NA=6.022×1023mol−1. Give your answer in scientific notation to three significant figures.