Chapter 19, Problem 97E

Review the subsection in this chapter entitled Making a Nonspontaneous Process Spontaneous in Section 18.8The hydrolysis of ATP, shown in Problem 91is often used to drive nonspontaneous processes—such as muscle contraction and protein synthesis—in living organisms. The nonspontaneous process to be driven must be coupled to the ATP hydrolysis reaction. For example, suppose the nonspontaneous process is $\text{A+B}\to \text{AB(}\Delta G°\text{ positive})$ . The coupling of a nonspontaneous reaction such as this one to the hydrolysis of ATP is often accomplished by the mechanism:

   $\begin{array}{l}{\text{A+ATP+H}}_2\text{O}\to {\text{A–P}}_{\text{i}}\text{+ADP}\\ {\text{ A–P}}_{\text{i}}\text{+B}\to {\text{AB+P}}_{\text{i}}\\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\ {\text{A+B+ATP+H}}_2\text{O}\to {\text{AB+ADP+P}}_{\text{i}}\end{array}$

As long as $\Delta G_{\text{rxn}}$ for the nonspontaneous reaction is less than 30.5 kJ, the reaction can be made spontaneous by coupling in this way to the hydrolysis of ATP. Suppose that ATP is to drive the reaction between glutamate and ammonia to form glutamine:

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

91. Living organisms use energy from the metabolism of food to create an energy-rich molecule called adenosine triphosphate (ATP). The ATP then acts as an energy source for a variety cl reactions that the living organism must carry out to survive. ATP provides energy through its hydrolysis, which can be symbolized as follows:

   $\text{ATP}\left(aq\right)+{\text{ H}}_{\text{2}}\text{O}\left(l\right) \to \text{ADP}\left(aq\right)+{\text{ P}}_{\text{1}}\left(aq\right)\Delta G_{\text{rxn}}^{°}=-30.5\text{ kJ}$

where ADP represents adenosine diphosphate and P_i represents an inorganic phosphate group (such as ${\text{HPO}}_4^{2-}$ ).

Calculate the equilibrium constant, K, for the given reaction at 298 K.

The free energy obtained from the oxidation (reaction with oxygen) of glucose (C₆H₁₂O₆) to farm carbon dioxide and water can be used to re-form ATP by driving the given reaction in reverse. Calculate the standard free energy change for the oxidation of glucose and estimate the maximum number of moles of ATP that can be formed by the oxidation of one mole of glucose.