Chapter 17, Problem 63E

The hydrolys s of ATP, shown in Problem 57, is often used to drive nonspontaneous process-such as muscle contraction and protein synthesis-in living organisms. The nonspontaneous process must be coupled to the ATP hydrolysis reaction. For example, suppose the nonspontaneous process is A + B S AB ( $\Delta G°$ positive). The coupling of a nonspontaneous reaction such as this one to the hydrolysis of ATP is often accomplished by this mechanism.
a. $\text{A}+\text{ATP}+{\text{H}}_{\text{2}}\text{O}\to \text{A}-\text{Pi}+\text{ADP}$

b. $\text{A}-\text{Pi}+\text{B}\to \text{AB}+\text{Pi}$

c. $\text{A}+\text{B}+\text{ATP}+{\text{H}}_{\text{2}}\text{O}\to \text{AB}+\text{ADP}+\text{Pi}$

a. Calculate K for the reaction between glutamate and ammonia. (The standard free energy change for the reaction is + 14.2 kJ/mol: Assume the temperature is 298 K)
b. Write set of reaction such as these showing how the glutamate and ammonia reaction and couple with the hydrolysis of ATP. What is $\Delta G_{\text{rxn}}^{°}$ and K for the coupled reaction?