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.