Consider the following equilibrium:N2O4(g)?2

Two different gases occupy the two bulbs shown here. Consider the process that occurs when the stopcock is opened, assuming the gases behave ideally. (a) Draw the final (equilibrium) state. (b) Predict the signs of and for the process. (c) Is the process that occurs when the stopcock is opened a reversible one? (d) How does the process affect the entropy of the surroundings? [Sections and

Problem 1PE Identifying Spontaneous Processes Predict whether each process is spontaneous as described, spontaneous in the reverse direction, or at equilibrium: (a) Water at 40 °C gets hotter when a piece of metal heated to 150 °C is added. (b) Water at room temperature decomposes into H2(g) and O2(g). (c) Benzene vapor, C6H6(g), at a pressure of 1 atm condenses to liquid benzene at the normal boiling point of benzene, 80.1 °C. At 1 atm pressure, CO2(s) sublimes at -78 °C. Is this process spontaneous at -100 °C and 1 atm pressure?

As shown here, one type of computer keyboard cleaner contains liquefied 1,1 -difluoroethane (C2H4F2), which is a gas at atmospheric pressure. When the nozzle is squeezed, the 1,1 -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects. (a) Based on your experience, is the vaporization a spontaneous process at room temperature? (b) Defining the 1,1 -difluoroethane as the system, do you expect qsys for the process to be positive or negative? Explain. (c) Predict whether \(\Delta\)S is positive or negative for this process. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on heat flow or more on entropy change?

(a) What are the signs of and for the process depicted here? (b) How might temperature affect the sign of ? (c) If energy can flow in and out of the system to maintain a constant temperature during the process, what can you say about the entropy change of the surroundings as a result of this process? [Sections and 19.5]

Problem 3PE Predicting the Sign of ?S Predict whether ?S is positive or negative for each process, assuming each occurs at constant temperature: (a) H2O(l)?H2O(g) ________________ (b) Ag+(aq) + Cl-(aq)?AgCl(s) ________________ (c) 4 Fe(s) + 3?O2(g)?2 Fe2O3(s) ________________ (d) N2(g) + O2(g)?2 NO(g) Indicate whether each process produces an increase or decrease in the entropy of the system: (a) CO2(s)?CO2(g) ________________ (b) CaO(s) + CO2(g)?CaCO3(s) ________________ (c) HCl(g) + NH3(g)?NH4Cl(s) ________________ (d) 2 SO2(g) + O2(g)?2 SO3(g)

Predict the sign of accompanying this reaction. Explain your choice. [Section 19.3]

Problem 4PE Predicting Relative Entropies In each pair, choose the system that has greater entropy and explain your choice: (a) 1 mol of NaCl(s) or 1 mol of HCl(g) at 25 °C, (b) 2 mol of HCl(g) or 1 mol of HCl(g) at 25 °C, (c) 1 mol of HCl(g) or 1 mol of Ar(g) at 298 K. Choose the system with the greater entropy in each case: (a) 1 mol of H2(g) at STP or 1 mol of SO2(g) at STP, (b) 1 mol of N2O4(g) at STP or 2 mol of NO2(g) at STP

Problem 2PE Calculating ?S for a Phase Change Elemental mercury is a silver liquid at room temperature. Its normal freezing point is -38.9 °C, and its molar enthalpy of fusion is ?Hfusion = 2.29 kJ/mol. What is the entropy change of the system when 50.0 g of Hg(l) freezes at the normal freezing point? The normal boiling point of ethanol, C2H5OH, is 78.3 °C, and its molar enthalpy of vaporization is 38.56 kJ/mol. What is the change in entropy in the system when 68.3 g of C2H5OH(g) at 1 atm condenses to liquid at the normal boiling point?

The accompanying diagram shows how entropy varies with temperature for a substance that is a gas at the highest temperature shown. (a) What processes correspond to the entropy increases along the vertical lines labeled 1 and (b) Why is the entropy change for 2 larger than that for Section

Problem 5PE Calculating ?S° from Tabulated Entropies Calculate the change in the standard entropy of the system, ?S°, for the synthesis of ammonia from N2(g) and H2(g) at 298 K: N2(g) + 3 H2(g)?2 NH3(g) Using the standard molar entropies in Appendix C, calculate the standard entropy change, ?S°, for the following reaction at 298 K: Al2O3(s) + 3 H2(g)?2 Al(s) + 3 H2O(g)

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, . (a) Do you expect a significant difference in the enthalpy of combustion of the two isomers? Explain. (b) Which isomer do you expect to have the higher standard molar entropy? Explain. [Section 19.4]

Problem 6PE Calculating Free-Energy Change from ?Hº, T, and ?Sº Calculate the standard free-energy change for the formation of NO(g) from N2(g) and O2(g) at 298 K: N2(g) + O2(g)?2 NO(g) given that ?H° = 180.7 kJ and ?S° = 24.7 J/K. Is the reaction spontaneous under these conditions? Calculate ?G° for a reaction for which ?H° = 24.6 kJ and ?S° = 132 J/K at 298 K. Is the reaction spontaneous under these conditions?

The accompanying diagram shows how (red line) and T\DeltaS (blue line) change with temperature for a hypothetical reaction. (a) What is the significance of the point at , where and are equal? (b) In what temperature range is this reaction spontaneous? [Section 19.6]

Calculating Standard Free-Energy Change from Free Energies of Formation (a) Use data from Appendix C to calculate the standard free-energy change for the reaction P4(g) + 6Cl2(g) ? 4PCl3(g) at 298 K. (b) What is ?G° for the reverse of this reaction? Use data from Appendix C to calculate ?G°at 298 K for the combustion of methane: CH4(g) + 202(g) ? CO2(g) + 2H2O(g)

The accompanying diagram shows how for a hypothetical reaction changes as temperature changes. (a) At what temperature is the system at equilibrium? (b) In what temperature range is the reaction spontaneous? (c) Is positive or negative? (d) Is positive or negative? [Sections and

Problem 8PE Predicting and Calculating ?Gº In Section we used Hess’s law to calculate ?H° for the combustion of propane gas at 298 K: C3H8(g) + 5 O2(g)?3 CO2(g) + 4 H2O(l) ?H° = -2220 kJ (a) Without using data from Appendix C, predict whether ?G° for this reaction is more negative or less negative than ?H°. (b) Use data from Appendix C to calculate ?G° for the reaction at 298 K. Is your prediction from part (a) correct? For the combustion of propane at 298 K, C3H8(g) + 5 O2(g)?3 CO2(g) + 4 H2O(g), do you expect ?G° to be more negative or less negative than ?H°?

Consider a reaction , with atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If , which box represents the system at equilibrium? (b) What is the sign of for any process in which the contents of a reaction vessel move to equilibrium? (c) Rank the boxes in order of increasing magnitude of for the reaction. [Sections and 19.7]

Problem 9PE Determining the Effect of Temperature on Spontaneity The Haber process for the production of ammonia involves the equilibrium N2(g) + 3 H2(g)?2 NH3(g) Assume that ?H° and ?S° for this reaction do not change with temperature. (a) Predict the direction in which ?G for the reaction changes with increasing temperature. (b) Calculate ?G at 25 °C and at 500 °C. (a) Using standard enthalpies of formation and standard entropies in Appendix C, calculate ?H° and ?S° at 298 K for the reaction 2 SO2(g) + O2(g)?2 SO3(g). (b) Use your values from part (a) to estimate ?G at 400 K.

The accompanying diagram shows how the free energy, , changes during a hypothetical reaction . On the left are pure reactants, each at , and on the right is the pure product, also at 1 atm. (a) What is the significance of the minimum in the plot? (b) What does the quantity x, shown on the right side of the diagram, represent? [Section 19.7]

Use data in Appendix C to estimate the normal boiling point, in K, for elemental bromine, Br2(l). (The experimental value is given in Figure 11.5.)

Problem 11E Spontaneous Processes (Section) Which of the following processes are spontaneous and which are nonspontaneous: (a) the ripening of a banana, (b) dissolution of sugar in a cup of hot coffee, (c) the reaction of nitrogen atoms to form N2 molecules at 25 °C and 1 atm, (d) lightning, (e) formation of CH4 and O2molecules from CO2 and H2O at room temperature and 1 atm of pressure?

Problem 11PE Calculating the Free-Energy Change under Nonstandard Conditions Calculate ?G at 298 K for a mixture of 1.0 atm N2, 3.0 atm H2, and 0.50 atm NH3 being used in the Haber process: N2(g) + 3 H2(g)?2 NH3(g) Calculate ?G at 298 K for the Haber reaction if the reaction mixture consists of 0.50 atm N2, 0.75 atm H2, and 2.0 atm NH3.

Which of the following processes are spontaneous: (a) the melting of ice cubes at and 1 atm pressure; (b) separating a mixture of and into two separate samples, one that is pure and one that is pure (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor; (e) the dissolution of in water to form concentrated hydrochloric acid?

Problem 12PE Calculating an Equilibrium Constant from ?Gº The standard free-energy change for the Haber process at 25 °C was obtained in Sample Exercise 19.9 for the Haber reaction: N2(g) + 3 H2(g)?2 NH3(g) ?G° = -33.3 kJ/mol = -33,300 J/mol Use this value of ?G° to calculate the equilibrium constant for the process at 25 °C. Use data from Appendix C to calculate ?G° and K at 298 K for the reaction H2(g) + Br2(l) ? 2 HBr(g).

Problem 13E (a) Give two examples of endothermic processes that are spontaneous. (b) Give an example of a process that is spontaneous at one temperature but nonspontaneous at a different temperature.

The crystalline hydrate loses water when placed in a large, closed, dry vessel: This process is spontaneous and is positive. Is this process an exception to Bertholet's generalization that all spontaneous changes are exothermic? Explain.

Problem 15E Spontaneous Processes (Section) Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic? (b) In what temperature range is it a spontaneous process? (c) In what temperature range is it a non-spontaneous process? (d) At what temperature are the two phases in equilibrium?

Problem 16E Spontaneous Processes (Section) The normal freezing point of n-octane (C8H18) is -57 °C. (a) Is the freezing of n-octane an endothermic or exothermic process? (b) In what temperature range is the freezing of n-octane a spontaneous process? (c) In what temperature range is it a non-spontaneous process? (d)Is there any temperature at which liquid n-octane and solid n-octane are in equilibrium? Explain.

Problem 17E (a)What is special about a reversible process? (b) Suppose a reversible process is reversed, restoring the system to its original state. What can be said about the surroundings after the process is reversed? (c) Under what circumstances will the vaporization of water to steam be a reversible process? (d) Are any of the processes that occur in the world around us reversible in nature? Explain.

Problem 18E (a) What is meant by calling a process irreversible? (b) After a particular irreversible process, the system is restored to its original state. What can be said about the condition of the surroundings after the system is restored to its original state? (c) Under what conditions will the condensation of a liquid be an irreversible process?

Problem 19E Spontaneous Processes (Section) Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from 300 K to 200 K. (a) Does the temperature change depend on whether the process is reversible or irreversible? (b) Is this process isothermal? (c) Does the change in the internal energy, ?E, depend on the particular pathway taken to carry out this change of state?

Problem 20E Spontaneous Processes (Section) A system goes from state 1 to state 2 and back to state 1. (a) Is ?E the same in magnitude for both the forward and reverse processes? (b) Without further information, can you conclude that the amount of heat transferred to the system as it goes from state 1 to state 2 is the same or different as compared to that upon going from state 2 back to state 1? (c) Suppose the changes in state are reversible processes. Is the work done by the system upon going from state 1 to state 2 the same or different as compared to that upon going from state 2 back to state 1?

Problem 21E Spontaneous Processes (Section) Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is ?E zero for the process?

Problem 22E Spontaneous Processes (Section) Consider what happens when a sample of the explosive TNT (Section: “Chemistry Put to Work: Explosives and Alfred Nobel”) is detonated under atmospheric pressure. (a) Is the detonation a spontaneous process? (b) What is the sign of q for this process? (c) Is it possible to tell whether w is positive, negative, or zero for the process? Explain. (d) Can you determine the sign of ?E for the process? Explain.

(a) How can we calculate for an isothermal process? (b) Does for a process depend on the path taken from the initial state to the final state of the system? Explain.

Problem 24E Entropy and the Second Law of Thermodynamics (Section) Suppose we vaporize a mole of liquid water at 25 °C and another mole of water at 100 °C. (a)Assuming that the enthalpy of vaporization of water does not change much between 25 °C and 100 °C, which process involves the larger change in entropy? (b) Does the entropy change in either process depend on whether we carry out the process reversibly or not? Explain.

Problem 25E Entropy and the Second Law of Thermodynamics (Section) The normal boiling point of Br2(l) is 58.8 °C, and its molar enthalpy of vaporization is ?Hvap = 29.6 kJ/mol. (a) When Br2(l) boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of ?S when 1.00 mol of Br2(l) is vaporized at 58.8 °C.

Problem 26E Entropy and the Second Law of Thermodynamics (Section) The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ?Hfus = 5.59 kJ/mol. (a) When molten gallium solidifies to Ga(s) at its normal melting point, is ?S positive or negative? (b) Calculate the value of ?S when 60.0 g of Ga(l) solidifies at 29.8 °C.

(a) Express the second law of thermodynamics in words. (b) If the entropy of the system increases during a reversible process, what can you say about the entropy change of the surroundings? (c) In a certain spontaneous process the system undergoes an entropy change, What can you conclude about

Problem 29E Entropy and the Second Law of Thermodynamics (Section) (a) What sign for ?S do you expect when the volume of 0.200 mol of an ideal gas at 27 °C is increased isothermally from an initial volume of 10.0 L? (b) If the final volume is 18.5 L, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain.

(a) Express the second law of thermodynamics as a mathematical equation. (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of (c) During a certain reversible process, the surroundings undergo an entropy change, . What is the entropy change of the system for this process?

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at 350 K is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain.

Problem 31E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) For the isothermal expansion of a gas into a vacuum, ?E = 0, q = 0, and w = 0. (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. (c) What is the “driving force” for the expansion of the gas: enthalpy or entropy?

Problem 32E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) (a) What is the difference between a state and a microstate of a system? (b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state? (c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of ?Ssurr?

Problem 33E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (a) increase in temperature, (b) decrease in volume, (c)change of state from liquid to gas?

Problem 34E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) (a) Using the heat of vaporization in Appendix B, calculate the entropy change for the vaporization of water at 25 °C and at 100 °C. (b) From your knowledge of microstates and the structure of liquid water, explain the difference in these two values.

Problem 35E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) (a) What do you expect for the sign of ?S in a chemical reaction in which two moles of gaseous reactants are converted to three moles of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Problem 36E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) (a) In a chemical reaction two gases combine to form a solid. What do you expect for the sign of ?S? (b) How does the entropy of the system change in the processes described in Exercise 19.12?

Problem 37E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) Does the entropy of the system increase, decrease, or stay the same when (a) a solid melts, (b) a gas liquefies, (c) a solid sublimes?

Problem 38E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, (c) equal volumes of ethanol and water are mixed to form a solution?

Problem 39E (a) State the third law of thermodynamics. (b) Distinguish between translational motion, vibrational motion, and rotational motion of a molecule. (c) Illustrate these three kinds of motion with sketches for the HCl molecule.

Problem 40E (a) If you are told that the entropy of a certain system is zero, what do you know about the system and the temperature? (b) The energy of a gas is increased by heating it. Using CO2 as an example, illustrate the different ways in which additional energy can be distributed among the molecules of the gas. (c) CO2(g) and Ar(g) have nearly the same molar mass. At a given temperature, will they have the same number of microstates? Explain.

Problem 41E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) For each of the following pairs, choose the substance with the higher entropy per mole at a given temperature: (a) Ar(l)or Ar(g), (b) He(g) at 3 atm pressure or He(g) at 1.5 atm pressure, (c) 1 mol of Ne(g) in 15.0 L or 1 mol of Ne(g) in 1.50 L, (d) CO2(g) or CO2(s).

Problem 42E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) For each of the following pairs, indicate which substance possesses the larger standard entropy: (a) 1 mol of P4(g) at 300 °C, 0.01 atm, or 1 mol of As4(g) at 300 °C, 0.01 atm; (b) 1 mol of H2O(g) at 100 °C, 1 atm, or 1 mol of H2O(l) at100 °C, 1 atm; (c) 0.5 mol of N2(g) at 298 K, 20-L volume, or 0.5 mol CH4(g) at 298 K, 20-L volume; (d) 100 g Na2SO4(s) at 30 °C or 100 g Na2SO4(aq) at 30 °C.

Problem 44E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) Predict the sign of ?Ssys for each of the following processes: (a) Molten gold solidifies. (b)Gaseous Cl2 dissociates in the stratosphere to form gaseous Cl atoms. (c) Gaseous CO reacts with gaseous H2 to form liquid methanol, CH3OH. (d) Calcium phosphate precipitates upon mixing Ca(NO3)2(aq) and (NH4)3PO4(aq).

Problem 43E The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) Predict the sign of the entropy change of the system for each of the following reactions: (a) N2(g) + 3 H2(g)?2 NH3(g) ________________ (b) CaCO3(s)?CaO(s) + CO2(g). ________________ c) 3 C2H2(g)?C6H6(g) ________________ (d) Al2O3(s) + 3 H2(g)?2 Al(s) + 3 H2O(g)

(a) Using Figure 19.13 as a model, sketch how the entropy of water changes as it is heated from -50 0C to 110 0C at sea level. Show the temperatures at which there are vertical increases in entropy. (b) Which process has the larger entropy change: melting ice or boiling water? Explain.

Entropy Changes in Chemical Reactions (Section) Propanol (C3H7OH) melts at -126.5 °C and boils at 97.4 °C. Draw a qualitative sketch of how the entropy changes as propanol vapor at 150 °C and 1 atm is cooled to solid propanol at -150 °C and 1 atm.

Problem 48E Entropy Changes in Chemical Reactions (Section) Cyclopropane and propylene

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(C_2H_2(g)\) or \(C_2H_6(g)\), (b) \(CO_2(g)\) or \(CO(g)\)?

Problem 49E Entropy Changes in Chemical Reactions (Section) Use Appendix C to compare the standard entropies at 25 °C for the following pairs of substances: (a) Sc(s) and Sc(g), (b) NH3(g) and NH3(aq), (c) 1 mol P4(g) and 2 mol P2(g), (d)C(graphite) and C(diamond).

Problem 50E Entropy Changes in Chemical Reactions (Section) Using Appendix C, compare the standard entropies at 25 °C for the following pairs of substances: (a) CuO(s) and Cu2O(s), (b) 1 mol N2O4(g) and 2 mol NO2(g), (c) SiO2(s) and CO2(g), (d) CO(g) and CO2(g).

Problem 51E Entropy Changes in Chemical Reactions (Section) The standard entropies at 298 K for certain group 4A elements are: C(s, diamond) = 2.43 J/mol-K, Si1s2 = 18.81 J/ mol-K, Ge1s2 = 31.09 J/mol-K, and Sn1s2 = 51.818 J/mol-K. All but Sn have the same (diamond) structure. How do you account for the trend in the S° values?

Three of the forms of elemental carbon are graphite, diamond, and buckminsterfullerene. The entropies at 298 K for graphite and diamond are listed in Appendix C. (a) Account for the difference in the S0 values of graphite and diamond in light of their structures (Figure 12.30). (b) What would you expect for the S0 value of buckminsterfullerene (Figure 12.47) relative to the values for graphite and diamond? Explain.

Problem 53E Entropy Changes in Chemical Reactions (Section) Using S° values from Appendix C, calculate ?S° values for the following reactions. In each case account for the sign of ?S°. (a) C2H4(g) + H2(g)?C2H6(g) ________________ (b) N2O4(g)?2 NO2(g) ________________ (c) Be(OH)2(s)?BeO(s) + H2O(g) ________________ (d) 2 CH3OH(g) + 3 O2(g)?.2 CO2(g) + 4 H2O(g)

Problem 54E Entropy Changes in Chemical Reactions (Section) Calculate ?S° values for the following reactions by using tabulated S° values from Appendix C. In each case explain the sign of ?S°. (a) HNO3(g) + NH3(g)?NH4NO3(s) ________________ (b) 2 Fe2O3(s)?4 Fe(s) + 3 O2(g) ________________ (c) CaCO3(s) calcite2 + 2HCl(g) ? CaCl2(s) + CO2(g) + H2O(l) ________________ (d) 3 C2H6(g)?C6H6(l) + 6 H2(g)

Problem 55E Gibbs Free Energy (Sections) (a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant T and P, the value of ?G is positive. Is the process spontaneous? (c) If ?Gfor a process is large, is the rate at which it occurs fast?

(a) What is the meaning of the standard free-energy change, , as compared with (b) For any process that occurs at constant temperature and pressure, what is the significance of (c) For a certain process, is large and negative. Does this mean that the process necessarily occurs rapidly?

Problem 57E Gibbs Free Energy (Sections) For a certain chemical reaction, ?H° = -35.4 kJ and ?S° = -85.5 J/K. (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (c) Calculate ?G° for the reaction at 298 K. (d) Is the reaction spontaneous at 298 K under standard conditions?

Problem 58E Gibbs Free Energy (Sections) A certain reaction has ?H° = +23.7 kJ and ?S° = +52.4 J/K. (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (c) Calculate ?G° for the reaction at 298 K. (d) Is the reaction spontaneous at 298 K under standard conditions?

Problem 59E Gibbs Free Energy (Sections) Using data in Appendix C, calculate ?H°, ?S°, and ?G° at 298 K for each of the following reactions. (a) H2(g) + F2(g)?2 HF(g) (b) C(s, graphite) + 2 Cl2(g)?CCl4(g) (c) 2 PCl3(g) + O2(g)?2 POCl3(g) (d) 2 CH3OH(g) + H2(g) ?C2H6(g) + 2 H2O(g)

Problem 60E Gibbs Free Energy (Sections) Use data in Appendix C to calculate ?H°, ?S°, and ?G° at 25 °C for each of the following reactions. (a) 4 Cr(s) + 3 O2(g)?2 Cr2O3(s) ________________ (b) BaCO3(s)?BaO(s) + CO2(g) ________________ (c) 2 P(s) + 10 HF(g)?2 PF5(g) + 5 H2(g) ________________ (d) K(s) + O2(g)?KO2(s)

Problem 61E Gibbs Free Energy (Sections) Using data from Appendix C, calculate ?G° for the following reactions. Indicate whether each reaction is spontaneous at 298 K under standard conditions. (a) 2 SO2(g) + O2(g)?2 SO3(g) ________________ b) NO2(g) + N2O(g) ?3 NO(g) ________________ (c) 6 Cl2(g) + 2 Fe2O3(s) ?.4 FeCl3(s) + 3 O2(g) ________________ (d) SO2(g) + 2 H2(g) ?S(s) + 2 H2O(g)

Problem 62E Gibbs Free Energy (Sections) Using data from Appendix C, calculate the change in Gibbs free energy for each of the following reactions. In each case indicate whether the reaction is spontaneous at 298 K under standard conditions. (a) 2 Ag(s) + Cl2(g)?2 AgCl(s) ________________ (b) P4O10(s) + 16 H2(g)?4 PH3(g) + 10 H2O(g) ________________ (c) CH4(g) + 4 F2(g)?CF4(g) + 4 HF(g) ________________ (d) 2 H2O2(l)?2 H2O(l) + O2(g)

Problem 63E Gibbs Free Energy (Sections) Octane (C8H18) is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline. (a) Write a balanced equation for the combustion of C8H18(l) to form CO2(g) and H2O(l). (b) Without using thermochemical data, predict whether ?G° for this reaction is more negative or less negative than ?H°.

Problem 64E Gibbs Free Energy (Sections) Sulfur dioxide reacts with strontium oxide as follows: SO2(g) + SrO(g)?SrSO3(s) (a) Without using thermochemical data, predict whether ?G° for this reaction is more negative or less negative than ?H°. (b) If you had only standard enthalpy data for this reaction, estimate of the value of ?G° at 298 K, using data from Appendix C on other substances.

Problem 69E Gibbs Free Energy (Sections) For a particular reaction, ?H = -32 kJ and ?S = -98 J/K. Assume that ?H and ?S do not vary with temperature. (a) At what temperature will the reaction have ?G = 0? (b) If T is increased from that in part (a), will the reaction be spontaneous or non-spontaneous?

Problem 66E Gibbs Free Energy (Sections) From the values given for ?H° and ?S°, calculate ?G° for each of the following reactions at 298 K. If the reaction is not spontaneous under standard conditions at 298 K, at what temperature (if any) would the reaction become spontaneous? (a) 2 PbS(s) + 3 O2(g)?2 PbO(s) + 2 SO2(g) ?H° = -844 kJ; ?S° = -165 J/K ________________ (b) 2 POCl3(g) ?2 PCl3(g) + O2(g) ?H° = 572 kJ; ?S° = 179 J/K

Problem 67E Gibbs Free Energy (Sections) A particular constant-pressure reaction is barely spontaneous at 390 K. The enthalpy change for the reaction is +23.7 kJ. Estimate ?S for the reaction.

Problem 68E Gibbs Free Energy (Sections) A certain constant-pressure reaction is barely non-spontaneous at 45 °C. The entropy change for the reaction is 72 J/K. Estimate ?H.

Problem 69E Gibbs Free Energy (Sections) For a particular reaction, ?H = -32 kJ and ?S = -98 J/K. Assume that ?H and ?S do not vary with temperature. (a) At what temperature will the reaction have ?G = 0? (b) If T is increased from that in part (a), will the reaction be spontaneous or non-spontaneous?

Problem 70E Gibbs Free Energy (Sections) Reactions in which a substance decomposes by losing CO are called decarbonylationreactions. The decarbonylation of acetic acid proceeds according to: CH3COOH(l)?CH3OH(g) + CO(g) By using data from Appendix C, calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that ?H° and ?S° do not vary with temperature.

Problem 71E Gibbs Free Energy (Sections) Consider the following reaction between oxides of nitrogen: NO2(g) + N2O(g)?3 NO(g) (a) Use data in Appendix C to predict how ?G for the reaction varies with increasing temperature. (b) Calculate ?G at 800 K, assuming that ?H° and ?S° do not change with temperature. Under standard conditions is the reaction spontaneous at 800 K? (c) Calculate ?G at 1000 K. Is the reaction spontaneous under standard conditions at this temperature?

Problem 72E Gibbs Free Energy (Sections) Methanol (CH3OH) can be made by the controlled oxidation of methane: CH4(g) + ½ O2(g)?CH3OH(g) (a) Use data in Appendix C to calculate ?H° and ?S° for this reaction. (b) Will ?G for the reaction increase, decrease, or stay unchanged with increasing temperature? (c) Calculate ?G° at 298 K. Under standard conditions, is the reaction spontaneous at this temperature? (d) Is there a temperature at which the reaction would be at equilibrium under standard conditions and that is low enough so that the compounds involved are likely to be stable?

Problem 73E Gibbs Free Energy (Sections) (a) Use data in Appendix C to estimate the boiling point of benzene, C6H6(l). (b) Use a reference source, such as the CRC Handbook of Chemistry and Physics, to find the experimental boiling point of benzene. How do you explain any deviation between your answer in part (a) and the experimental value?

Problem 74E Gibbs Free Energy (Sections) (a) Using data in Appendix C, estimate the temperature at which the free-energy change for the transformation from I2(s) to I2(g) is zero. What assumptions must you make in arriving at this estimate? (b) Use a reference source, such as Web Elements (http://www.webelements.com), to find the experimental melting and boiling points of I2. (c)Which of the values in part (b) is closer to the value you obtained in part (a)? Can you explain why this is so?

Problem 75E Gibbs Free Energy (Sections) Acetylene gas, C2H2(g), is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to CO2(g) and H2O(l). (b) How much heat is produced in burning 1 mol of C2H2 under standard conditions if both reactants and products are brought to 298 K? (c) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?

Gibbs Free Energy (Sections) The fuel in high-efficiency natural gas vehicles consists primarily of methane (CH4). (a) How much heat is produced in burning 1 mol of CH4(g) under standard conditions if reactants and products are brought to 298 K and H2O(l) is formed? (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

Problem 78E Free Energy and Equilibrium (Section) Indicate whether ?G increases, decreases, or does not change when the partial pressure of H2is increased in each of the following reactions: (a) N2(g) + 3 H2(g)?2 NH3(g) ________________ (b) 2 HBr(g)?H2(g) + Br2(g) ________________ (c) 2 H2(g) + C2H2(g)?C2H6(g)

Problem 77E Free Energy and Equilibrium (Section) Indicate whether ?G increases, decreases, or stays the same for each of the following reactions as the partial pressure of O2 is increased: (a) 2 CO(g) + O2(g)?2 CO2(g) ________________ (b) 2 H2O2(l)?2 H2O(l) + O2(g) ________________ (c) 2 KClO3(s)?2 KCl(s) + 3 O2(g)

Problem 79E Free Energy and Equilibrium (Section) Consider the reaction 2 NO2(g)?N2O4(g). (a) Using data from Appendix C, calculate ?G° at 298 K. (b) Calculate ?G at 298 K if the partial pressures of NO2 and N2O4 are 0.40 atm and 1.60 atm, respectively.

Problem 80E Free Energy and Equilibrium (Section) Consider the reaction 3 CH4(g)?C3H8(g) + 2 H2(g). (a) Using data from Appendix C, calculate ?G° at 298 K. (b) Calculate ?G at 298 K if the reaction mixture consists of 40.0 atm of CH4, 0.0100 atm of C3H8(g), and 0.0180 atm of H2.

Problem 81E Free Energy and Equilibrium (Section) Use data from Appendix C to calculate the equilibrium constant, K, and ?G° at 298 K for each of the following reactions: (a) H2(g) + I2(g)?2 HI(g) ________________ (b) C2H5OH(g)?C2H4(g) + H2O(g) ________________ (c) 3 C2H2(g)?C6H6(g)

Problem 82E Free Energy and Equilibrium (Section) Using data from Appendix C, write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free-energy change for these reactions at 298 K: (a) NaHCO3(s)?NaOH(s) + CO2(g) ________________ (b) 2 HBr(g) + Cl2(g)?2 HCl(g) + Br2(g) ________________ (c) 2 SO2(g) + O2(g)?2 SO3(g)

Free Energy and Equilibrium (Section) Consider the decomposition of barium carbonate: BaCO3(s)?BaO(s) + CO2(g) Using data from Appendix C, calculate the equilibrium pressure of CO2 at (a) 298 K and (b)1100 K.

Problem 84E Free Energy and Equilibrium (Section) Consider the reaction PbCO3(s)?PbO(s) + CO2(g) Using data in Appendix C, calculate the equilibrium pressure of CO2 in the system at (a) 400 °C and (b) 180 °C.

Problem 85E Free Energy and Equilibrium (Section) The value of Ka for nitrous acid (HNO2) at 25 °C is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to Ka. (b) By using the value of Ka, calculate ?G° for the dissociation of nitrous acid in aqueous solution. (c) What is the value of ?G at equilibrium? (d) What is the value of ?G when [H+] = 5.0 × 10-2 M, [NO2 -] = 6.0 × 10-4 M, and [HNO2] = 0.20 M?

Problem 86E Free Energy and Equilibrium (Section) The Kb for methylamine (CH3NH2) at 25 °C is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to Kb. (b) By using the value of Kb, calculate ?G° for the equilibrium in part (a). (c) What is the value of ?G at equilibrium? (d) What is the value of ?G when [H+] = 6.7 × 10-9 M, [CH3NH3 +] = 2.4 × 10-3 M, and [CH3NH2] = 0.098 M?

Problem 87AE (a) Which of the thermodynamic quantities T, E, q, w, and S are state functions? (b) Which depend on the path taken from one state to another? (c) How many reversible paths are there between two states of a system? (d) For a reversible isothermal process, write an expression for ?E in terms of q and w and an expression for ?S in terms of q and T.

Problem 88AE Indicate whether each of the following statements is true or false. If it is false, correct it. (a) The feasibility of manufacturing NH3 from N2 and H2 depends entirely on the value of ?H for the process N2(g) + 3 H2(g)?2 NH3(g). (b) The reaction of Na(s) with Cl2(g) to form NaCl(s) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d)Spontaneous processes in general require that work be done to force them to proceed. (e)Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Problem 89AE For each of the following processes, indicate whether the signs of ?S and ?H are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of Co(s) is lowered from 60 °C to 25 °C. (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form CO2(g) and H2O(g).

Problem 90AE The reaction 2 Mg(s) + O2(g)?2 MgO(s) is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for ?S°. Did your classmate make a mistake in the calculation? Explain.

Suppose four gas molecules are placed in the left flask in Figure 19.6(a). Initially, the right flask is evacuated and the stopcock is closed. (a) After the stopcock is opened, how many different arrangements of the molecules are possible? (b) How many of the arrangements from part (a) have all the molecules in the left flask? (c) How does the answer to part (b) explain the spontaneous expansion of the gas?

Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (a) The two arrangements of top faces shown here can be viewed as two possible microstates of the system. Explain. (b) To which state does each microstate correspond? (c) How many possible states are there for the system? (d) Which state or states have the highest entropy? Explain. (e) Which state or states have the lowest entropy? Explain.

Ammonium nitrate dissolves spontaneously and endother-mally in water at room temperature. What can you deduce about the sign of for this solution process?

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as \(\mathrm{CH}_{2} \mathrm{F}_{2}\). An air-conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram). During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber.(a) What is the sign of q for the expansion? (b) What is the sign of q for the compression? (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why? (d) Imagine that a sample of liquid refrigerant undergoes expansion followed by compression, so that it is back to its original state. Would you expect that to be a reversible process? (e) Suppose that a house and its exterior are both initially at \(31^{\circ} \mathrm{C}\). Some time after the air conditioner is turned on, the house is cooled to \(24^{\circ} \mathrm{C}\). Is this process spontaneous or nonspontaneous?

Trouton's rule states that for many liquids at their normal boiling points, the standard molar entropy of vaporization is about . (a) Estimate the normal boiling point of bromine, , by determining for using data from Appendix . Assume that remains constant with temperature and that Trouton's rule holds. (b) Look up the normal boiling point of in a chemistry handbook or at the WebElements Web site (www.webelements.com).

Problem 97AE Consider the following three reactions: (i) Ti(s) + 2 Cl2(g)?TiCl4(g) ________________ (ii) C2H6(g) + 7 Cl2(g) ?2 CCl4(g) + 6 HCl(g) ________________ (iii) BaO(s) + CO2(g)?BaCO3(s) (a) For each of the reactions, use data in Appendix C to calculate ?H°, ?G°, K, and ?S° at 25 °C. (b) Which of these reactions are spontaneous under standard conditions at 25 °C? (c) For each of the reactions, predict the manner in which the change in free energy varies with an increase in temperature.

Problem 98AE Using the data in Appendix C and given the pressures listed, calculate Kp and ?G for each of the following reactions: (a) N2(g) + 3 H2(g)?2 NH3(g) PN2 = 2.6 atm, PH2 = 5.9 atm, PNH3 = 1.2 atm ________________ (b) 2 N2H4(g) + 2 NO2(g)?3 N2(g) + 4 H2O(g) PN2H4 = PNO2 = 5.0 × 10-2 atm, PN2 = 0.5 atm, PH2O = 0.3 atm ________________ (c) N2H4(g)?N2(g) + 2 H2(g) PN2H4 = 0.5 atm, PN2 = 1.5 atm, PH2 = 2.5 atm

Problem 99AE (a) For each of the following reactions, predict the sign of ?H° and ?S° without doing any calculations. (b) Based on your general chemical knowledge, predict which of these reactions will have K >1. (c) In each case indicate whether K should increase or decrease with increasing temperature. (i) 2 Mg(s) + O2(g)?2 MgO(s) ________________ (ii) 2 KI(s)?2 K(g) + I2(g) ________________ (iii) Na2(g)?2 Na(g) ________________ (iv) 2 V2O5(s)?4 V(s) + 5 O2(g)

Problem 96AE For the majority of the compounds listed in Appendix C, the value of ?G°f is more positive (or less negative) than the value of ?H°f. (a) Explain this observation, using NH3(g), CCl4(l), and KNO3(s) as examples. (b) An exception to this observation is CO(g). Explain the trend in the ?H°f and ?G°f values for this molecule.

Problem 100AE Acetic acid can be manufactured by combining methanol with carbon monoxide, an example of a carbonylation reaction: CH3OH(l) + CO(g)?CH3COOH(l) (a) Calculate the equilibrium constant for the reaction at 25 °C. (b) Industrially, this reaction is run at temperatures above 25 °C. Will an increase in temperature produce an increase or decrease in the mole fraction of acetic acid at equilibrium? Why are elevated temperatures used? (c) At what temperature will this reaction have an equilibrium constant equal to 1? (You may assume that ?H° and ?S° are temperature independent, and you may ignore any phase changes that might occur.)

Problem 101AE The oxidation of glucose [C6H12O6] in body tissue produces CO2 and H2O. In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol [C2H5OH] and CO2. (a) Using data given in Appendix C, compare the equilibrium constants for the following reactions: C6H12O6(s) + 6 O2(g)?6 CO2(g) + 6 H2O(l) C6H12O6(s)?2 C2H5OH(l) + 2 CO2(g) (b) Compare the maximum work that can be obtained from these processes under standard conditions.

Cells use the hydrolysis of adenosine triphosphate (ATP) as a source of energy (Figure 19.19). The conversion of ATP to ADP has a standard free-energy change of . If all the free energy from the metabolism of glucose, goes into the conversion of ADP to ATP, how many moles of ATP can be produced for each mole of glucose?

Problem 102AE The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane (C2H6), is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: 2 CH4(g)?C2H6(g) + H2(g) In practice, this reaction is carried out in the presence of oxygen: 2 CH4(g) + ½O2(g)?C2H6(g) + H2O(g) (a) Using the data in Appendix C, calculate K for these reactionsat 25 °C and 500 °C. (b) Is the difference in ?G° for thetwo reactions due primarily to the enthalpy term (?H) or theentropy term (-T?S)? (c) Explain how the preceding reactionsare an example of driving a nonspontaneous reaction, asdiscussed in the “Chemistry and Life” box in Section. (d)The reaction of CH4 and O2 to form C2H6 and H2O must becarried out carefully to avoid a competing reaction. What isthe most likely competing reaction?

Problem 104AE The potassium-ion concentration in blood plasma is about 5.0 × 10-3 M, whereas the concentration in muscle-cell fluid is much greater (0.15 M). The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to K+. (a) What is ?G for the transfer of 1 mol of K+ from blood plasma to the cellular fluid at body temperature 37 °C? (b) What is the minimum amount of work that must be used to transfer this K+?

The relationship between the temperature of a reaction, its standard enthalpy change, and the equilibrium constant at that temperature can be expressed as the following linear equation: $$\ln K=\frac{-\Delta H^{\circ}}{R T}+\text { constant }$$ (a) Explain how this equation can be used to determine \(\Delta H^{\circ} \mathrm{ex}-\) perimentally from the equilibrium constants at several different temperatures. (b) Derive the preceding equation using relationships given in this chapter. To what is the constant equal? Equation Transcription: ln? K= + constant ex- Text Transcription: ln? K= -delta H^circle/RT + constant delta H^circle ex-

One way to derive Equation depends on the observation that at constant the number of ways, , of arranging ideal-gas particles in a volume is proportional to the volume raised to the power: Use this relationship and Boltzmann's relationship between entropy and number of arrangements (Equation 19.5) to derive the equation for the entropy change for the isothermal expansion or compression of moles of an ideal gas.

About of the world's electrical energy is produced by using steam turbines, a form of heat engine. In his analysis of an ideal heat engine, Sadi Carnot concluded that the maximum possible efficiency is defined by the total work that could be done by the engine, divided by the quantity of heat available to do the work (for example, from hot steam produced by combustion of a fuel such as coal or methane). This efficiency is given by the ratio ( , where is the temperature of the heat going into the engine and is that of the heat leaving the engine. (a) What is the maximum possible efficiency of a heat engine operating between an input temperature of and an exit temperature of (b) Why is it important that electrical power plants be located near bodies of relatively cool water? (c) Under what conditions could a heat engine operate at or near efficiency? (d) It is often said that if the energy of combustion of a fuel such as methane were captured in an electrical fuel cell instead of by burning the fuel in a heat engine, a greater fraction of the energy could be put to useful work. Make a qualitative drawing like that in Figure 5.10 that illustrates the fact that in principle the fuel cell route will produce more useful work than the heat engine route from combustion of methane.

Problem 108IE Most liquids follow Trouton’s rule (see Exercise), which states that the molar entropy of vaporization is approximately 88 ± 5 J/mol-K. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: Substance Normal Boiling Point (ºC) ?Hvap(kJ/mol) Acetone, (CH3)2CO 56.1 29.1 Dimethyl ether, (CH3)2O -24.8 21.5 Ethanol, C2H5OH 78.4 38.6 Octane, C8H18 125.6 34.4 Pyridine, C5H5N 115.3 35.1 (a) Calculate ?Svap for each of the liquids. Do all the liquids obey Trouton’s rule? (b) With reference to intermolecular forces (Section), can you explain any exceptions to the rule? (c)Would you expect water to obey Trouton’s rule? By using data in Appendix B, check the accuracy of your conclusion. (d) Chlorobenzene (C6H5Cl) boils at 131.8 °C. Use Trouton’s rule to estimate ?Hvap for this substance. Exercise Trouton’s rule states that for many liquids at their normal boiling points, the standard molar entropy of vaporization is about 88 J/mol-K. (a) Estimate the normal boiling point of bromine, Br2, by determining ?H°vap for Br2 using data from Appendix C. Assume that ?H°vap remains constant with temperature and that Trouton’s rule holds. (b) Look up the normal boiling point of Br2 in a chemistry handbook or at the Web Elements Web site (http://www.webelements.com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation?

Problem 110IE The following processes were all discussed in Chapter, “Chemistry of the Environment.” Estimate whether the entropy of the system increases or decreases during each process: (a) photodissociation of O2(g), (b) formation of ozone from oxygen molecules and oxygen atoms, (c) diffusion of CFCs into the stratosphere, (d) desalination of water by reverse osmosis.

In chemical kinetics the entropy of activation is the entropy change for the process in which the reactants reach the activated complex. The entropy of activation for bimolecular processes is usually negative. Explain this observation with reference to Figure 14.17.

Problem 111IE Carbon disulfide (CS2) is a toxic, highly flammable substance. The following thermodynamic data are available for CS2(l) and CS2(g) at 298 K: ?Hfº(kJ/mol) ?Gfº(kJ/mol) CS2(l) 89.7 65.3 CS2(g) 117.4 67.2 (a) Draw the Lewis structure of the molecule. What do you predict for the bond order of the C—S bonds? (b) Use the VSEPR method to predict the structure of the CS2 molecule. (c) Liquid CS2 burns in O2 with a blue flame, forming CO2(g) and SO2(g). Write a balanced equation for this reaction. (d) Using the data in the preceding table and in Appendix C, calculate ?H° and ?G° for the reaction in part (c). Is the reaction exothermic? Is it spontaneous at 298 K? (e) Use the data in the table to calculate ?S° at 298 K for the vaporization of CS2(l). Is the sign of ?S° as you would expect for a vaporization? (f) Using data in the table and your answer to part (e), estimate the boiling point of CS2(l). Do you predict that the substance will be a liquid or a gas at 298 K and 1 atm?

Problem 112IE The following data compare the standard enthalpies and free energies of formation of some crystalline ionic substances and aqueous solutions of the substances: Substance ?Hfº(kJ/mol) ?Gfº(kJ/mol) AgNO3(s) -124.4 -33.4 AgNO3(aq) -101.7 -34.2 MgSO4(s) -1283.7 -1169.6 MgSO4(aq) -1374.8 -1198.4 Write the formation reaction for AgNO3(s). Based on this reaction, do you expect the entropy of the system to increase or decrease upon the formation of AgNO3(s)? (b) Use ?Hfº and ?Hfº of AgNO3(s) to determine the entropy change upon formation of the substance. Is your answer consistent with your reasoning in part (a)? (c) Is dissolving AgNO3 in water an exothermic or endothermic process? What about dissolving MgSO4 in water? (d) For both AgNO3 and MgSO4, use the data to calculate the entropy change when the solid is dissolved in water. (e)Discuss the results from part (d) with reference to material presented in this chapter and in the “A Closer Look” box on page 820.

Problem 113IE Consider the following equilibrium: N2O4(g)?2 NO2(g) Thermodynamic data on these gases are given in Appendix C. You may assume that ?H° and ?S° do not vary with temperature. (a) At what temperature will an equilibrium mixture contain equal amounts of the two gases? (b) At what temperature will an equilibrium mixture of 1 atm total pressure contain twice as much NO2 as N2O4? (c) At what temperature will an equilibrium mixture of 10 atm total pressure contain twice as much NO2 as N2O4? (d)Rationalize the results from parts (b) and (c) by using Le Châtelier’s principle.[Section]

Problem 114IE The reaction SO2(g) + 2 H2S(g)?3 S(s) + 2 H2O(g) is the basis of a suggested method for removal of SO2 from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (a) What is the equilibrium constant for the reaction at 298 K? (b) In principle, is this reaction a feasible method of removing SO2? (c) If PSO2 = PH2S and the vapor pressure of water is 25 torr, calculate the equilibrium SO2 pressure in the system at 298 K. (d) Would you expect the process to be more or less effective at higher temperatures?

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here: Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on). What do you observe? Are your observations consistent with your answer to part (b)?