Chapter 3

An enzymatic hydrolysis of fructose- \(1-P\) \\[\text { Fructose- } 1-\mathrm{P}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \text { fructose }+\mathrm{P}_{1}\\] was allowed to proceed to equilibrium at \(25^{\circ} \mathrm{C}\). The original concentration of fructose-1-P was \(0.2 \mathrm{M}\), but when the system had reached equilibrium the concentration of fructose-1-P was only \(6.52 \times 10^{-5} \mathrm{M}\). Calculate the equilibrium constant for this reaction and the free energy of hydrolysis of fructose- \(1-P\).

The equilibrium constant for some process \(A=B\) is 0.5 at \(20^{\circ} \mathrm{C}\) and 10 at \(30^{\circ} \mathrm{C}\). Assuming that \(\Delta H^{*}\) is independent of temperature, calculate \(\Delta H^{\circ}\) for this reaction. Determine \(\Delta G^{\circ}\) and \(\Delta S^{\circ}\) at \(20^{\circ}\) and at \(30^{\circ} \mathrm{C}\). Why is it important in this problem to assume that \(\Delta H^{\circ}\) is independent of temperature?

The standard-state free energy of hydrolysis for acetyl phosphate is \\[ \begin{aligned} \Delta G^{\circ}=-42.3 \mathrm{kJ} / \mathrm{mol} \\ \text { Actyl-P }+\mathrm{H}_{2} \mathrm{O} \longrightarrow \text { acctate }+\mathrm{P}_{\mathrm{i}} \end{aligned} \\] Calculate the free energy change for acetyl phosphate hydrolysis in a solution of \(2 \mathrm{m} M\) acctate, \(2 \mathrm{m} M\) phosphate, and \(3 \mathrm{n} M\) acetyl phosphate.

Define a state function. Name three themodynamic quantities that are state functions and three that are not.

ATP hydrolysis at pH 7.0 is accompanicd by release of a hydrogen ion to the medium \\[\mathrm{ATP}^{6-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{ADP}^{3-}+\mathrm{HPO}_{4}^{2-}+\mathrm{H}^{+}\\] If the \(\Delta G^{\circ}\) for this reaction is \(-30.5 \mathrm{kJ} / \mathrm{mol}\), what is \(\Delta G^{*}\) (that is, the free energy change for the same reaction with all components, including \(\mathrm{H}^{+},\) at a standard state of \(1 \mathrm{M}\) )?

For the process \(A \equiv B, K_{c g}(A B)\) is 0.02 at \(37^{\circ} \mathrm{C}\). For the process \(\mathrm{B} \rightleftharpoons \mathrm{C}, K_{\mathrm{eq}}(\mathrm{BC})=1000\) at \(37^{\circ} \mathrm{C}\) a. Determine \(K_{\mathrm{rg}}(\mathrm{AC}),\) the equilibrium constant for the overall process \(A \rightleftharpoons C,\) from \(K_{c q}(A B)\) and \(K_{c g}(B C)\) b. Determine standardstate free energy changes for all three processes, and \(\mathrm{us}=\Delta G^{\circ}(\mathrm{AC})\) to determine \(K_{\mathrm{rg}}(\mathrm{AC}) .\) Make sure that this value agrees with that determined in part a of this problem.

Draw all possible resonance structures for creatine phosphate and discuss their possible effects on resonance stabilization of the molecule.

Calculate the free energy of hydrolysis of ATP in a rat liver cell in which the ATP, ADP, and \(P\), concentrations are \(3.4,1.3,\) and \(4.8 \mathrm{m} M\) respectively.

Consider carbamoyl phosphate, a precursor in the biosynthesis of pyrimidines: Based on the discussion of high-energy phosphates in this chapter, would you expect carbamoyl phosphate to possess a high free energy of hydrolysis? Provide a chemical rationale for your answer.

You are studying the various components of the venom of a poisonous lizard. One of the venom components is a protein that appears to be temperature sensitive. When heated, it denatures and is no longer toxic. The process can be described by the following simple equation: \\[ \mathbf{T}(\text { toxic }) \rightleftharpoons \mathrm{N} \text { (nontoxic) } \\] There is only enough protein from this venom to carry out two equilibrium measurements. At \(298 \mathrm{K}\), you find that \(98 \%\) of the protein is in its toxic form. However, when you raise the temperature to \(320 \mathrm{K},\) you find that only \(10 \%\) of the protein is in its toxic form. a. Calculate the equilibrium constants for the T to N conversion at these two temperatures. b. Use the data to determine the \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ}\) for this process.

The hydrolysis of 1,3 -bisphosphoglycerate is favorable, due in part to the increased resonance stabilization of the products of the reaction. Draw resonance structures for the reactant and the products of this reaction to establish that this statement is true..

The acyl-Co.A synthetase reaction activates fatty acids for oxidation in cells: \\[ \mathrm{R}-\mathrm{COO}^{-}+\mathrm{CaASH}+\mathrm{ATP} \longrightarrow \mathrm{R}-\mathrm{COSCOA}+\mathrm{AMP}+\text { pyrophosphate } \\] The reaction is driven forward in part by hydrolysis of ATP to AMP and pyrophosphate. However, pyrophosphate undergoes further cleavage to yield two phosphate anions. Discuss the energetics of this reaction both in the presence and absence of pyrophosphate cleavage.