In biological cells, the energy released by the oxidation of foods is stored in adenosine triphosphate (ATP or ATP4). The essence of ATPs action is its ability to lose its terminal phosphate group by hydrolysis and to form adenosine diphosphate (ADP or ADP3):

ATP4(aq) + H2O(l)ADP3(aq) + HPO42 (aq) + H3O+(aq)

At pH = 7.0 and 37C (310 K, blood temperature) the enthalpy and Gibbs energy of hydrolysis are rH = 20 kJ mol1 and rG = 31 kJ mol1, respectively. Under these conditions, the hydrolysis of 1 mol ATP4(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, and the activation of neuronal circuits in our brains.

(a) Calculate and account for the sign of the entropy of hydrolysis of ATP at pH = 7.0 and 310 K. (b) Suppose that the radius of a typical biological cell (sphere) is 10 m and that inside it 106 ATP molecules are hydrolysed each second. What is the power density of the cell in watts per cubic metre (1 W = 1 J s1)? 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?

(c) The formation of glutamine from glutamate and ammonium ions requires 14.2 kJ mol1 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 hydrolysed to form 1 mol glutamine?