In biological cells, the energy released by the oxidation of foods is stored in adenosine triphosphate (ATP or ATP 4! ). The essence of ATP’s action is its ability to lose its terminal phosphate group by hydrolysis to form adenosine diphosphate (ADP or ADP3! ): ATP 4! (aq) + H2O (R) 6 ADP3! (aq) + HPO4 2! (aq) + H3O + (aq) At pH = 7.0 and 37EC (310K, blood temperature) the enthalpy and Gibbs energy of hydrolysis are ÄH = !20 kJ/mol and ÄG = !31 kJ/mol, respectively. Under these conditions, the hydrolysis of one mole of ATP 4! (aq) results in the extraction of up to 31 kJ of energy that can be used to do non-expansion work, such as the synthesis of proteins from amino acids, muscular contraction, or the activation of neuronal circuits in our brains. a. Calculate the entropy of hydrolysis of ATP at pH = 7 and 310 K. Explain the sign of S. b. Suppose that the radius of a typical biological cell is 10 ìm and that inside it 106 ATP molecules are hydrolyzed each second. What is the power density of the cell in watts per cubic meter (1 W = 1 J/s)? A computer battery delivers about 15 W and has a volume of 100 cm3 . Which has the greater power density, the cell or the battery? Express your answer as a percent or a ratio (as in “X has three times the power density of Y” or in “Y has a power density that is 51% higher than X”; use the former statement when there is a big difference, i.e. don’t say “Y has a power density that is 0.00000012% that of X” or “Y has a power density that is 123456789% higher than X”). c. The synthesis of the amino acid glutamine from glutamate and ammonium ions requires 14.2 kJ/mol of energy input. It is driven by the hydrolysis of ATP to ADP mediated by the enzyme glutamine synthetase. How many moles of ATP must be hydrolyzed to form one mole of glutamine?