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Chapter 19: Problem 15

Which of the following changes in a thermodynamic property would you expect to find for the reaction \(\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Br}(\mathrm{g})\) at all temperatures: \((\mathrm{a}) \Delta H<0\) (b) \(\Delta S>0 ;\) (c) \(\Delta G<0 ;\) (d) \(\Delta S<0 ?\) Explain.

Short Answer

Expert verified
The appropriate changes for the reaction \(Br_{2} (g) \longrightarrow 2 Br (g)\) at all temperatures would be that: (a) \(\Delta H > 0\) because the breaking of bromine molecules to form atoms is an endothermic process. (b) \(\Delta S > 0\) because disorder increases as a molecule is broken down to individual atoms. (c) This reaction necessarily has \(\Delta G > 0\) because the \(\Delta H\) and \(\Delta S\) are both positive, so this reaction is only spontaneous at high temperature, not at all temperatures. (d) \(\Delta S < 0\) doesn't apply to this reaction as the disorder increases.

Step by step solution

01

Understand Enthalpy change (\(\Delta H\))

Enthalpy (\(\Delta H\)) change is the heat transfer in a process at constancy pressure. The reaction amounts to the breaking of Br-Br bond to give free Br atoms. For this process, energy is required to break the bond, so it will absorb heat from the surroundings, hence the enthalpy (\(\Delta H\)) change is positive or the reaction is endothermic.
02

Understand Entropy change (\(\Delta S\))

Entropy (\(\Delta S\)) is a measure of disorder in the system. In the reaction, a single molecule breaks down into two individual atoms, hence the disorder or randomness increases. As a result, the entropy, (\(\Delta S\)) change will be positive for such cases.
03

Understand Gibbs free energy (\(\Delta G\))

The Gibbs free energy change (\(\Delta G\)) for a reaction at constant temperature and pressure is given by \(\Delta G = \Delta H - T\Delta S\). For \(\Delta G\), to be negative, which happens when a reaction is spontaneous at all temperatures, both \(\Delta H\) and \(\Delta S\) should be negative or both should be positive. If \(\Delta H\) is positive and \(\Delta S\) is positive, then the reaction is spontaneous at high temperature - not at all temperatures. So, this reaction has \(\Delta G > 0\).
04

Negative Entropy change (\(\Delta S\))

A negative entropy change (\(\Delta S\)) would suggest a decrease in randomness or disorder, which is not the case for this reaction where one molecule breaks down into two individual atoms. So this doesn't apply to the reaction.

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Most popular questions from this chapter

Sodium carbonate, an important chemical used in the production of glass, is made from sodium hydrogen carbonate by the reaction \(2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) Data for the temperature variation of \(K_{\mathrm{p}}\) for this reaction are \(K_{\mathrm{p}}=1.66 \times 10^{-5}\) at \(30^{\circ} \mathrm{C} ; 3.90 \times 10^{-4} \mathrm{at}\) \(50^{\circ} \mathrm{C} ; 6.27 \times 10^{-3}\) at \(70^{\circ} \mathrm{C} ;\) and \(2.31 \times 10^{-1}\) at \(100^{\circ} \mathrm{C}\) (a) Plot a graph similar to Figure \(19-12,\) and determine \(\Delta H^{\circ}\) for the reaction. (b) Calculate the temperature at which the total gas pressure above a mixture of \(\mathrm{NaHCO}_{3}(\mathrm{s})\) and \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})\) is \(2.00 \mathrm{atm}\).

Which substance in each of the following pairs would have the greater entropy? Explain. (a) at \(75^{\circ} \mathrm{C}\) and 1 atm: \(1 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}(1)\) or \(1 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (b) at \(5^{\circ} \mathrm{C}\) and 1 atm: \(50.0 \mathrm{g} \mathrm{Fe}(\mathrm{s})\) or \(0.80 \mathrm{mol} \mathrm{Fe}(\mathrm{s})\) (c) 1 mol \(\mathrm{Br}_{2}\left(1,1 \text { atm }, 8^{\circ} \mathrm{C}\right)\) or \(1 \mathrm{mol} \mathrm{Br}_{2}(\mathrm{s}, 1 \mathrm{atm},\) \(\left.-8^{\circ} \mathrm{C}\right)\) (d) \(0.312 \mathrm{mol} \mathrm{SO}_{2}\left(\mathrm{g}, 0.110 \mathrm{atm}, 32.5^{\circ} \mathrm{C}\right)\) or \(0.284 \mathrm{mol}\) \(\mathrm{O}_{2}\left(\mathrm{g}, 15.0 \mathrm{atm}, 22.3^{\circ} \mathrm{C}\right)\)

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.]

Following are some standard Gibbs energies of formation, \(\Delta G_{f}^{2},\) per mole of metal oxide at \(1000 \mathrm{K}: \mathrm{NiO},\) \(-115 \mathrm{kJ} ; \mathrm{MnO},-280 \mathrm{kJ} ; \mathrm{TiO}_{2},-630 \mathrm{kJ} .\) The standard Gibbs energy of formation of \(\mathrm{CO}\) at \(1000 \mathrm{K}\) is \(-250 \mathrm{kJ}\) per mol CO. Use the method of coupled reactions (page 851 ) to determine which of these metal oxides can be reduced to the metal by a spontaneous reaction with carbon at \(1000 \mathrm{K}\) and with all reactants and products in their standard states.

For the dissociation of \(\mathrm{CaCO}_{3}(\mathrm{s})\) at \(25^{\circ} \mathrm{C}, \mathrm{CaCO}_{3}(\mathrm{s})\) \(\rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \Delta G^{\circ}=+131 \mathrm{kJ} \mathrm{mol}^{-1} .\) A sample of pure \(\mathrm{CaCO}_{3}(\mathrm{s})\) is placed in a flask and connected to an ultrahigh vacuum system capable of reducing the pressure to \(10^{-9} \mathrm{mmHg}\) (a) Would \(\mathrm{CO}_{2}(\mathrm{g})\) produced by the decomposition of \(\mathrm{CaCO}_{3}(\mathrm{s})\) at \(25^{\circ} \mathrm{C}\) be detectable in the vacuum system at \(25^{\circ} \mathrm{C} ?\) (b) What additional information do you need to determine \(P_{\mathrm{CO}_{2}}\) as a function of temperature? (c) With necessary data from Appendix D, determine the minimum temperature to which \(\mathrm{CaCO}_{3}(\mathrm{s})\) would have to be heated for \(\mathrm{CO}_{2}(\mathrm{g})\) to become detectable in the vacuum system.
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