Chapter 19

The Gibbs energy available from the complete combustion of 1 mol of glucose to carbon dioxide and water is $$\begin{array}{r} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq})+6 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 6 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \\ \Delta G^{\circ}=-2870 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$ (a) Under biological standard conditions, compute the maximum number of moles of ATP that could form from ADP and phosphate if all the energy of combustion of 1 mol of glucose could be utilized. (b) The actual number of moles of ATP formed by a cell under aerobic conditions (that is, in the presence of oxygen) is about \(38 .\) Calculate the efficiency of energy conversion of the cell. (c) Consider these typical physiological conditions. $$\begin{array}{l} P_{\mathrm{CO}_{2}}=0.050 \mathrm{bar} ; P_{\mathrm{O}_{2}}=0.132 \mathrm{bar} \\\ {[\mathrm{glucose}]=1.0 \mathrm{mg} / \mathrm{mL} ; \mathrm{pH}=7.0} \\ {[\mathrm{ATP}]=[\mathrm{ADP}]=\left[P_{\mathrm{i}}\right]=0.00010 \mathrm{M}} \end{array}$$ Calculate \(\Delta G\) for the conversion of 1 mol ADP to ATP and \(\Delta G\) for the oxidation of 1 mol glucose under these conditions. (d) Calculate the efficiency of energy conversion for the cell under the conditions given in part (c). Compare this efficiency with that of a diesel engine that attains \(78 \%\) of the theoretical efficiency operating with \(T_{\mathrm{h}}=1923 \mathrm{K}\) and \(T_{1}=873 \mathrm{K} .\) Suggest a reason for your result. [ Hint: See Feature Problem 95.]

In your own words, define the following symbols: (a) \(\Delta S_{\text {univ }} ;\) (b) \(\Delta G_{f}^{0} ;\) (c) \(K\).

Briefly describe each of the following ideas, methods, or phenomena: (a) absolute molar entropy; (b) coupled reactions; (c) Trouton's rule; (d) evaluation of an equilibrium constant from tabulated thermodynamic data.

Explain the important distinctions between each of the following pairs: (a) spontaneous and nonspontaneous processes; (b) the second and third laws of thermodynamics; (c) \(\Delta G\) and \(\Delta G^{\circ}\).

For a process to occur spontaneously, (a) the entropy of the system must increase; (b) the entropy of the surroundings must increase; (c) both the entropy of the system and the entropy of the surroundings must increase; (d) the net change in entropy of the system and surroundings considered together must be a positive quantity; (e) the entropy of the universe must remain constant.

The Gibbs energy change of a reaction can be used to assess (a) how much heat is absorbed from the surroundings; (b) how much work the system does on the surroundings; (c) the net direction in which the reaction occurs to reach equilibrium; (d) the proportion of the heat evolved in an exothermic reaction that can be converted to various forms of work.

The reaction, \(2 \mathrm{Cl}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \Delta H=\) \(-161 \mathrm{kJ},\) is expected to be (a) spontaneous at all temperatures; (b) spontaneous at low temperatures, but nonspontaneous at high temperatures; (c) nonspontaneous at all temperatures; (d) spontaneous at high temperatures only.

If \(\Delta G^{\circ}=0\) for a reaction, it must also be true that (a) \(K=0 ;\) (b) \(K=1 ;\) (c) \(\Delta H^{\circ}=0 ;\) (d) \(\Delta S^{\circ}=0\) (e) the equilibrium activities of the reactants and products do not depend on the initial conditions.

Two correct statements about the reversible reaction \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) are \((\mathrm{a}) K=K_{\mathrm{p}}\) (b) the equilibrium amount of NO increases with an increased total gas pressure; (c) the equilibrium amount of NO increases if an equilibrium mixture is transferred from a \(10.0 \mathrm{L}\) container to a \(20.0 \mathrm{L}\) container; (d) \(K=K_{c} ;\) (e) the composition of an equilibrium mixture of the gases is independent of the temperature.

Explain briefly why (a) the change in entropy in a system is not always a suitable criterion for spontaneous change; (b) \(\Delta G^{\circ}\) is so important in dealing with the question of spontaneous change, even though the conditions employed in a reaction are very often nonstandard.

A handbook lists the following standard a handbook lists the following standard enthalpies of formation at \(298 \mathrm{K}\) for cyclopentane, \(\mathrm{C}_{5} \mathrm{H}_{10}: \quad \Delta H_{\mathrm{f}}^{\mathrm{g}}\left[\mathrm{C}_{5} \mathrm{H}_{10}(1)\right]=-105.9 \mathrm{kJ} / \mathrm{mol} \quad\) and \(\Delta H_{\mathrm{f}}^{\mathrm{o}}\left[\mathrm{C}_{5} \mathrm{H}_{10}(\mathrm{g})\right]=-77.2 \mathrm{kJ} / \mathrm{mol}\) (a) Estimate the normal boiling point of cyclopentane. (b) Estimate \(\Delta G^{\circ}\) for the vaporization of cyclopentane at \(298 \mathrm{K}\). (c) Comment on the significance of the sign of \(\Delta G^{\circ}\) at \(298 \mathrm{K}\)

At room temperature and normal atmospheric pressure, is the entropy of the universe positive, negative, or zero for the transition of carbon dioxide solid to liquid?