Adenosine triphosphate, ATP, is used as a free-energy source by biological cells. (See the essay on page 750.) ATP hydrolyzes in the presence of enzymes to give ADP:
ATP(aq) + H2O(l) → ADP(aq) + H2PO4 (aq);
∆Go 30.5 kJ/mol at 25oC
Consider a hypothetical biochemical reaction of molecule A to give molecule B:
A(aq) → B(aq); ∆Go = +15.0 kJ/mol at 25oC
a. Calculate the ratio [B]/[A] at 25oC at equilibrium.
b. Now consider this reaction “coupled” to the reaction for the hydrolysis of ATP:
A(aq) +ATP(aq) + H2O(l) →
B(aq) +ADP(aq) + H2PO4 (aq)
If a cell maintains a high ratio of ATP to ADP and H2PO4  by continuously making ATP, the conversion of A to B can be made highly spontaneous. A characteristic value of this ratio is
[ATP]/[ADP][H2PO4] = 500.
Calculate the ratio [B][A] in this case and compare it with the uncoupled reaction. Compared with the uncoupled reaction, how much larger is this ratio when coupled to the hydrolysis of ATP?