Solved: Spontaneous Processes (Section)Consider the

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 H and S 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 19.1 and 19.2]

As shown here, one type of computer keyboard cleaner contains liquefied 1,1-difluoroethane 1C2H4F22, 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? (c) Predict whether 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 enthalpy or entropy? [Sections 19.1 and 19.2]

(a) What are the signs of S and H for the process depicted here? (b) 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 19.2 and 19.5]

Predict the signs of H and S for this reaction. Explain your choice. [Section 19.3]

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 2? (b) Why is the entropy change for 2 larger than that for 1? (c) If this substance is a perfect crystal at T = 0 K, what is the value of S at this temperature? [Section 19.3]

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, C5H12. (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]

The accompanying diagram shows how H (red line) and TS (blue line) change with temperature for a hypothetical reaction. (a) What is the significance of the point at 300 K, where H and TS are equal? (b) In what temperature range is this reaction spontaneous? [Section 19.6]

The accompanying diagram shows how G 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 H positive or negative? (d) Is S positive or negative? [Sections 19.5 and 19.6]

Consider a reaction A21g2 + B21g2 2 AB1g2, with atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If Kc = 1, which box represents the system at equilibrium? (b) If Kc = 1, which box represents the system at Q 6 Kc? (c) Rank the boxes in order of increasing magnitude of G for the reaction. [Sections 19.5 and 19.7]

The accompanying diagram shows how the free energy, G, changes during a hypothetical reaction A1g2 + B1g2 C1g2. On the left are pure reactants A and B, each at 1 atm, and on the right is the pure product, C, also at 1 atm. Indicate whether each of the following statements is true or false. (a) The minimum of the graph corresponds to the equilibrium mixture of reactants and products for this reaction. (b) At equilibrium, all of A and B have reacted to give pure C. (c) The entropy change for this reaction is positive. (d) The x on the graph corresponds to G for the reaction. (e) G for the reaction corresponds to the difference between the top left of the curve and the bottom of the curve. [Section 19.7]

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 O2 molecules from CO2 and H2O at room temperature and 1 atm of pressure?

Which of the following processes are spontaneous: (a) the melting of ice cubes at -10 C and 1 atm pressure; (b) separating a mixture of N2 and O2 into two separate samples, one that is pure N2 and one that is pure O2; (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor at room temperature; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?

(a) Can endothermic chemical reactions be spontaneous? (b) Can a process that is spontaneous at one temperature be nonspontaneous at a different temperature?

The crystalline hydrate Cd1NO322 # 4 H2O1s2 loses water when placed in a large, closed, dry vessel at room temperature: Cd1NO322 # 4 H2O1s2 Cd1NO3221s2 + 4 H2O1g2 This process is spontaneous and H is positive at room temperature. (a) What is the sign of S at room temperature? (b) If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does S change for this reaction at room temperature?

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 nonspontaneous process? (d) At what temperature are the two phases in equilibrium?

The normal freezing point of n-octane 1C8H182 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 nonspontaneous process? (d) Is there any temperature at which liquid n-octane and solid n-octane are in equilibrium? Explain

Indicate whether each statement is true or false. (a) If a system undergoes a reversible process, the entropy of the universe increases. (b) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (c) If a system undergoes a reversible process, the entropy change of the system must be zero. (d) Most spontaneous processes in nature are reversible

Indicate whether each statement is true or false. (a) All spontaneous processes are irreversible. (b) The entropy of the universe increases for spontaneous processes. (c) The change in entropy of the surroundings is equal in magnitude and opposite in sign for the change in entropy of the system, for an irreversible process. (d) The maximum amount of work can be gotten out of a system that undergoes an irreversible process, as compared to a reversible process.

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?

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?

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?

Consider what happens when a sample of the explosive TNT (Section 8.8: 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.

Indicate whether each statement is true or false. (a) S for an isothermal process depends on both the temperature and the amount of heat reversibly transferred. (b) S is a state function. (c) The second law of thermodynamics says that the entropy of the system increases for all spontaneous processes.

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.

The normal boiling point of Br21l2 is 58.8 C, and its molar enthalpy of vaporization is Hvap = 29.6 kJ>mol. (a) When Br21l2 boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of S when 1.00 mol of Br21l2 is vaporized at 58.8 C

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.

Indicate whether each statement is true or false. (a) The second law of thermodynamics says that entropy is conserved. (b) If the entropy of the system increases during a reversible process, the entropy change of the surroundings must decrease by the same amount. (c) In a certain spontaneous process the system undergoes an entropy change of 4.2 J>K; therefore, the entropy change of the surroundings must be -4.2 J>K

(a) Does the entropy of the surroundings increase for spontaneous processes? (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of Ssurr? (c) During a certain reversible process, the surroundings undergo an entropy change, Ssurr = -78 J>K. What is the entropy change of the system for this process?

(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) What sign for 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.

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 thesystem during this process. (c) What is the driving force for the expansionof the gas: enthalpy or entropy?

(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?

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?

(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.

(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?

(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?

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?

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?

Indicate whether each statement is true or false. (a) The third law of thermodynamics says that the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) Translational motion of molecules refers to their change in spatial location as a function of time. (c) Rotational and vibrational motions contribute to the entropy in atomic gases like He and Xe. (d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in H, we can know absolute values of S. (b) If you heat a gas such as CO2, you will increase its degrees of translational, rotational and vibrational motions. (c) CO21g2 and Ar(g) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

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) CO21g2 or CO21s2.

For each of the following pairs, indicate which substance possesses the larger standard entropy: (a) 1 mol of P41g2 at 300 C, 0.01 atm, or 1 mol of As41g2 at 300 C, 0.01 atm; (b) 1 mol of H2O1g2 at 100 C, 1 atm, or 1 mol of H2O1l2 at 100 C, 1 atm; (c) 0.5 mol of N21g2 at 298 K, 20-L volume, or 0.5 mol CH41g2 at 298 K, 20-L volume; (d) 100 g Na2SO41s2 at 30 C or 100 g Na2SO41aq2 at 30 C.

Predict the sign of the entropy change of the system for each of the following reactions: (a) N21g2 + 3 H21g2 2 NH31g2 (b) CaCO31s2 CaO1s2 + CO21g2 (c) 3 C2H21g2 C6H61g2 (d) Al2O31s2 + 3 H21g2 2 Al1s2 + 3 H2O1g

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 Ca1NO3221aq2 and 1NH423PO41aq2.

(a) Using Figure 19.12 as a model, sketch how the entropy of water changes as it is heated from -50 C to 110 C 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.

Propanol 1C3H7OH2 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

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) C2H21g2 or C2H61g2, (b) CO21g2 or CO(g)?

Cyclopropane and propylene are isomers that both have the formula C3H6. Based on the molecular structures shown, which of these isomers would you expect to have the higher standard molar entropy at 25 C?

Use Appendix C to compare the standard entropies at 25 C for the following pairs of substances: (a) Sc(s) and Sc(g), (b) NH31g2 and NH31aq2, (c) 1 mol P41g2 and 2 mol P21g2, (d) C(graphite) and C(diamond).

Using Appendix C, compare the standard entropies at 25 C for the following pairs of substances: (a) CuO(s) and Cu2O1s2, (b) 1 mol N2O41g2 and 2 mol NO21g2, (c) SiO21s2 and CO21g2, (d) CO(g) and CO21g2.

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 S values of graphite and diamond in light of their structures (Figure 12.29, p. 503). (b) What would you expect for the S value of buckminsterfullerene (Figure 12.47, p. 516) relative to the values for graphite and diamond? Explain.

Using S values from Appendix C, calculate S values for the following reactions. In each case account for the sign of S. (a) C2H41g2 + H21g2 C2H61g2 (b) N2O41g2 2 NO21g2 (c) Be1OH221s2 BeO1s2 + H2O1g2 (d) 2 CH3OH1g2 + 3 O21g2 2 CO21g2 + 4 H2O1g2

Calculate S values for the following reactions by using tabulated S values from Appendix C. In each case explain the sign of S. (a) HNO31g2 + NH31g2 NH4NO31s2 (b) 2 Fe2O31s2 4 Fe1s2 + 3 O21g2 (c) CaCO31s, calcite2 + 2HCl1g2 CaCl21s2 + CO21g2 + H2O1l2 (d) 3 C2H61g2 C6H61l2 + 6 H21g2

(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 G for a process is large, is the rate at which it occurs fast?

(a) Is the standard free-energy change, G, always larger than G? (b) For any process that occurs at constant temperature and pressure, what is the significance of G = 0? (c) For a certain process, G is large and negative. Does this mean that the process necessarily has a low activation barrier?

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?

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?

Using data in Appendix C, calculate H, S, and G at 298 K for each of the following reactions. (a) H21g2 + F21g2 2 HF1g2 (b) C1s, graphite2 + 2 Cl21g2 CCl41g2 (c) 2 PCl31g2 + O21g2 2 POCl31g2 (d) 2 CH3OH1g2 + H21g2 C2H61g2 + 2 H2O1g2

Use data in Appendix C to calculate H, S, and G at 25 C for each of the following reactions. (a) 4 Cr1s2 + 3 O21g2 2 Cr2O31s2 (b) BaCO31s2 BaO1s2 + CO21g2 (c) 2 P1s2 + 10 HF1g2 2 PF51g2 + 5 H21g2 (d) K1s2 + O21g2 KO21s2

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 SO21g2 + O21g2 2 SO31g2 (b) NO21g2 + N2O1g2 3 NO1g2 (c) 6 Cl21g2 + 2 Fe2O31s2 4 FeCl31s2 + 3 O21g2 (d) SO21g2 + 2 H21g2 S1s2 + 2 H2O1g2

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 Ag1s2 + Cl21g2 2 AgCl1s2 (b) P4O101s2 + 16 H21g2 4 PH31g2 + 10 H2O1g2 (c) CH41g2 + 4 F21g2 CF41g2 + 4 HF1g2 (d) 2 H2O21l2 2 H2O1l2 + O21g

Octane 1C8H182 is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline. (a) Write a balanced equation for the combustion of C8H181l2 to form CO21g2 and H2O1l2.(b) Without using thermochemical data, predict whether G for this reaction is more negative or less negative than H.

Sulfur dioxide reacts with strontium oxide as follows: SO21g2 + SrO1g2 SrSO31s2 (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

Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low T but not spontaneous at high T; (iv) spontaneous at high T but not spontaneous at low T. (a) N21g2 + 3 F21g2 2 NF31g2 H = -249 kJ; S = -278 J>K (b) N21g2 + 3 Cl21g2 2 NCl31g2 H = 460 kJ; S = -275 J>K (c) N2F41g2 2 NF21g2 H = 85 kJ; S = 198 J>K

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 PbS1s2 + 3 O21g2 2 PbO1s2 + 2 SO21g2 H = -844 kJ; S = -165 J>K (b) 2 POCl31g2 2 PCl31g2 + O21g2 H = 572 kJ; S = 179 J>K

A particular constant-pressure reaction is barely spontaneous at 390 K. The enthalpy change for the reaction is +23.7 kJ. EstimateS for the reaction.

A certain constant-pressure reaction is barely nonspontaneous at 45 C. The entropy change for the reaction is 72 J>K. Estimate H

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 nonspontaneous?

Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds according to: CH3COOH1l2 CH3OH1g2 + CO1g2 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.

Consider the following reaction between oxides of nitrogen: NO21g2 + N2O1g2 3 NO1g2 (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?

Methanol 1CH3OH2 can be made by the controlled oxidation of methane: CH41g2 + 1 2O21g2 CH3OH1g2 (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?

(a) Use data in Appendix C to estimate the boiling point of benzene, C6H61l2. (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?

(a) Using data in Appendix C, estimate the temperature at which the free-energy change for the transformation from I21s2 to I21g2 is zero. What assumptions must you make in arriving at this estimate? (b) Use a reference source, such as Web Elements (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?

Acetylene gas, C2H21g2, is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to CO21g2 and H2O1l2. (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?

The fuel in high-efficiency natural gas vehicles consists primarily of methane 1CH42. (a) How much heat is produced in burning 1 mol of CH41g2 under standard conditions if reactants and products are brought to 298 K and H2O1l2 is formed? (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

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 CO1g2 + O21g2 2 CO21g2 (b) 2 H2O21l2 2 H2O1l2 + O21g2 (c) 2 KClO31s2 2 KCl1s2 + 3 O21g2

Indicate whether G increases, decreases, or does not change when the partial pressure of H2 is increased in each of the following reactions: (a) N21g2 + 3 H21g2 2 NH31g2 (b) 2 HBr1g2 H21g2 + Br21g2 (c) 2 H21g2 + C2H21g2 C2H61g

Consider the reaction 2 NO21g2 N2O41g2. (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

Consider the reaction 3 CH41g2 C3H81g2 + 2 H21g2. (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 C3H81g2, and 0.0180 atm of H2

Use data from Appendix C to calculate the equilibrium constant, K, and G at 298 K for each of the following reactions: (a) H21g2 + I21g2 2 HI1g2 (b) C2H5OH1g2 C2H41g2 + H2O1g2 (c) 3 C2H21g2 C6H61g2

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) NaHCO31s2 NaOH1s2 + CO21g2 (b) 2 HBr1g2 + Cl21g2 2 HCl1g2 + Br21g2 (c) 2 SO21g2 + O21g2 2 SO31g2

Consider the decomposition of barium carbonate: BaCO31s2 BaO1s2 + CO21g2 Using data from Appendix C, calculate the equilibrium pressure of CO2 at (a) 298 K and (b) 1100 K.

Consider the reaction PbCO31s2 PbO1s2 + CO21g2 Using data in Appendix C, calculate the equilibrium pressure of CO2 in the system at (a) 400 C and (b) 180 C

The value of Ka for nitrous acid 1HNO22 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 3H+4 = 5.0 * 10-2 M, 3NO2 -4 = 6.0 * 10-4 M, and 3HNO24 = 0.20 M?

The Kb for methylamine 1CH3NH22 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 3H+4 = 6.7 * 10- 9 M, 3CH3NH3 +4 = 2.4 * 10-3 M, and 3CH3NH24 = 0.098 M?

(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.

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 N21g2 + 3 H21g2 2 NH31g2. (b) The reaction of Na(s) with Cl21g2 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.

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 CO21g2 and H2O1g2

The reaction 2 Mg1s2 + O21g2 2 MgO1s2 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. (f) Calculate the absolute entropy of the two-dice system.

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

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as CH2F2. 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 C. Some time after the air conditioner is turned on, the house is cooled to 24 C. Is this process spontaneous or nonspontaneous?

Troutons 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 Troutons rule holds. (b) Look up the normal boiling point of Br2 in a chemistry handbook or at the WebElements Web site (www.webelements. com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation?

For the majority of the compounds listed in Appendix C, the value of Gf is more positive (or less negative) than the value of Hf . (a) Explain this observation, using NH31g2, CCl41l2, and KNO31s2 as examples. (b) An exception to this observation is CO(g). Explain the trend in the Hf and Gf values for this molecule.

Consider the following three reactions: (i) Ti1s2 + 2 Cl21g2 TiCl41g2 (ii) C2H61g2 + 7 Cl21g2 2 CCl41g2 + 6 HCl1g2 (iii) BaO1s2 + CO21g2 BaCO31s2 (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

Using the data in Appendix C and given the pressures listed, calculate Kp and G for each of the following reactions: (a) N21g2 + 3 H21g2 2 NH31g2 PN2 = 2.6 atm, PH2 = 5.9 atm, PNH3 = 1.2 atm (b) 2 N2H41g2 + 2 NO21g2 3 N21g2 + 4 H2O1g2 PN2H4 = PNO2 = 5.0 * 10-2 atm, PN2 = 0.5 atm, PH2O = 0.3 atm (c) N2H41g2 N21g2 + 2 H21g2 PN2H4 = 0.5 atm, PN2 = 1.5 atm, PH2 = 2.5 atm

(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 7 1. (c) In each case indicate whether K should increase or decrease with increasing temperature. (i) 2 Mg1s2 + O21g2 2 MgO1s2 (ii) 2 KI1s2 2 K1g2 + I21g2 (iii) Na21g2 2 Na1g2 (iv) 2 V2O51s2 4 V1s2 + 5 O21g2

Acetic acid can be manufactured by combining methanol with carbon monoxide, an example of a carbonylation reaction: CH3OH1l2 + CO1g2 CH3COOH1l2 (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.)

The oxidation of glucose 1C6H12O62 in body tissue produces CO2 and H2O. In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol 1C2H5OH2 and CO2. (a) Using data given in Appendix C, compare the equilibrium constants for the following reactions: C6H12O61s2 + 6 O21g2 6 CO21g2 + 6 H2O1l2 C6H12O61s2 2 C2H5OH1l2 + 2 CO21g2 (b) Compare the maximum work that can be obtained from these processes under standard conditions.

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane 1C2H62, is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: 2 CH41g2 C2H61g2 + H21g2 In practice, this reaction is carried out in the presence of oxygen: 2 CH41g2 + 1 2 O21g2 C2H61g2 + H2O1g2 (a) Using the data in Appendix C, calculate K for these reactions at 25 C and 500 C. (b) Is the difference in G for the two reactions due primarily to the enthalpy term 1H2 or the entropy term 1-TS2? (c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the Chemistry and Life box in Section 19.7. (d) The reaction of CH4 and O2 to form C2H6 and H2O must be carried out carefully to avoid a competing reaction. What is the most likely competing reaction?

Cells use the hydrolysis of adenosine triphosphate (ATP) as a source of energy (Figure 19.16). The conversion of ATP to ADP has a standard free-energy change of -30.5 kJ>mol. If all the free energy from the metabolism of glucose, C6H12O61s2 + 6 O21g2 6 CO21g2 + 6 H2O1l2 goes into the conversion of ADP to ATP, how many moles of ATP can be produced for each mole of glucose?

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+?

One way to derive Equation 19.3 depends on the observation that at constant T the number of ways, W, of arranging m ideal-gas particles in a volume V is proportional to the volume raised to the m power: W Vm Use this relationship and Boltzmanns 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 n moles of an ideal gas.

About 86% of the worlds 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 1Thigh - Tlow2>Thigh, where Thigh is the temperature of the heat going into the engine and Tlow 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 700 K and an exit temperature of 288 K? (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 100% 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 (p. 175) 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.

Most liquids follow Troutons rule (see Exercise 19.95), 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: (a) Calculate Svap for each of the liquids. Do all the liquids obey Troutons rule? (b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Troutons rule? By using data in Appendix B, check the accuracy of your conclusion. (d) Chlorobenzene 1C6H5Cl2 boils at 131.8 C. Use Troutons rule to estimate Hvap for this substance.

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 14.15.

At what temperatures is the following reaction, the reduction of magnetite by graphite to elemental iron, spontaneous? Fe3O41s2 + 2 C 1s, graphite2 2 CO21g2 + 3 Fe 1s2

The following processes were all discussed in Chapter 18, Chemistry of the Environment. Estimate whether the entropy of the system increases or decreases during each process: (a) photodissociation of O21g2, (b) formation of ozone from oxygen molecules and oxygen atoms, (c) diffusion of CFCs into the stratosphere, (d) desalination of water by reverse osmosis

An ice cube with a mass of 20 g at -20 C (typical freezer temperature) is dropped into a cup that holds 500 mL of hot water, initially at 83 C. What is the final temperature in the cup? The density of liquid water is 1.00 g>mL; the specific heat capacity of ice is 2.03 J>g@C; the specific heat capacity of liquid water is 4.184 J>g@C; the enthalpy of fusion of water is 6.01 kJ>mol.

Carbon disulfide 1CS22 is a toxic, highly flammable substance. The following thermodynamic data are available for CS21l2 and CS21g2 at 298 K: (a) Draw the Lewis structure of the molecule. What do you predict for the bond order of the CS 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 CO21g2 and SO21g2. 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 CS21l2. 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 CS21l2. Do you predict that the substance will be a liquid or a gas at 298 K and 1 atm?

The following data compare the standard enthalpies and free energies of formation of some crystalline ionic substances and aqueous solutions of the substances: Write the formation reaction for AgNO31s2. Based on this reaction, do you expect the entropy of the system to increase or decrease upon the formation of AgNO31s2? (b) Use Hf and Gf of AgNO31s2 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.

Consider the following equilibrium: N2O41g2 2 NO21g2 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 Chteliers principle. [Section 15.7]

The reaction SO21g2 + 2 H2S1g2 3 S1s2 + 2 H2O1g2 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)?

Problem 1DE Problem You are measuring the equilibrium constant for a drug candidate binding to its DMA target over a series of different temperatures. You chose your drug candidate based on computer-aided molecular modeling, which indicates that the drug molecule likely would make many hydrogen bonds and favorable dipole-dipole interactions with the DMA site. You perform a set of experiments in buffer solution for the drug-DNA complex and generate a table of Ks at different 7s. (a) Derive an equation that relates equilibrium constant to standard enthalpy and entropy changes. (Hint: equilibrium constant, enthalpy and entropy are all related to free energy), (b) Show how you can graph your K and 7data to calculate the standard entropy and enthalpy changes for the drug candidate + DMA binding interaction, (c) You are surprised to learn that the enthalpy change for the binding reaction is close to zero, and the entropy change is large and positive. Suggest an explanation and design an experiment to test it. (Hint: think about water and ions), (d) You try another drug candidate with the DMA target and find that this drug candidate has a large negative enthalpy change upon DMA binding, and the entropy change is small and positive. Suggest an explanation, at the molecular level, and design an experiment to test your hypothesis

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 (equi- librium) state. (b) Predict the signs of \(\Delta H\) and \(\Delta S\) 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 19.1 and 19.2] Equation transcription: Text transcription: \Delta H \Delta S

As shown here, one type of computer keyboard cleaner contains liquefied 1,1 -difluoroethane \(\left(C_{2} H_{4} F_{2}\right)\), 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 \(q_{\text {eye }}\) for the process to be positive or negative? (c) Predict whether 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 enthalpy or entropy? [Sections and Equation transcription: Text transcription: \left(C_{2} H_{4} F_{2}\right) q_{\text {eye }}

(a) What are the signs of \(\Delta S\) and \(\Delta H\) for the process depicted here? (b) 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 19.2 and 19.5] Equation transcription: Text transcription: \Delta H \Delta S

Predict the signs of \(\Delta H\) and \(\Delta S\) for this reaction. Explain your choice. [Section 19.3] Equation transcription: Text transcription: \Delta H \Delta S

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 2? (b) Why is the entropy change for 2 larger than that for (c) If this substance is a perfect crystal at \(T=0 K\), what is the value of at this temperature? [Section 19.3] Equation transcription: Text transcription: T=0 K

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, \(C_{5} H_{12}\) (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] Equation transcription: Text transcription: C_{5} H_{12}

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

The accompanying diagram shows how \(\Delta G\) 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 \(\Delta H\) positive or negative? (d) Is \(\triangle S\) positive or negative? [Sections and Equation transcription: Text transcription: \Delta G \Delta H \triangle S

Consider a reaction \(A_{2}(g)+B_{2}(g) \leftrightarrow 2 A B(g)\), with atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If \(K_{c}=1\), which box represents the system at equilibrium? (b) If \(K_{c}=1\), which box represents the system at \(Q<K_{{ }_{c}}\)? (c) Rank the boxes in order of increasing magnitude of \(\Delta G\) for the reaction. [Sections and Equation transcription: Text transcription: A_{2}(g)+B_{2}(g) \leftrightarrow 2 A B(g) K_{c}=1 Q<K_{{ }_{c}} \Delta G

The accompanying diagram shows how the free energy, , changes during a hypothetical reaction \(A(g)+B(g) \rightarrow C(g)\). On the left are pure reactants and , each at , and on the right is the pure product, , also at . Indicate whether each of the following statements is true or false. (a) The minimum of the graph corresponds to the equilibrium mixture of reactants and products for this reaction. (b) At equilibrium, all of and have reacted to give pure C. (c) The entropy change for this reaction is positive. (d) The " "on the graph corresponds to for the reaction. (e) \(\Delta G\) for the reaction corresponds to the difference between the top left of the curve and the bottom of the curve. [Section 19.7] Equation transcription: Text transcription: A(g)+B(g) \rightarrow C(g) \Delta G

Problem 11E Problem 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 02 molecules from C02 and H20 at room temperature and 1 atm of pressure?

Problem 12E Problem Spontaneous Processes (Section) Which of the following processes are spontaneous: (a) the melting of ice cubes at -10 °C and 1 atm pressure; (b) separating a mixture of N2 and 02 into two separate samples, one that is pure N2 and one that is pure 02; (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor at room temperature; (e) the dissolution of HCI(g) in water to form concentrated hydrochloric acid?

Problem 13E Problem Spontaneous Processes (Section) (a) Can endothermic chemical reactions be spontaneous? (b) Can a process that is spontaneous at one temperature be non-spontaneous at a different temperature?

Problem 14E Problem Spontaneous Processes (Section) The crystalline hydrate Cd(N03)2*4 H20(s) loses water when placed in a large, closed, dry vessel at room temperature: Cd(N03)2 4 H20(s) -» Cd(N03)2(s) + 4 H20(g) This process is spontaneous and &rf is positive at room temperature, (a) What is the sign of AS1 at room temperature? (b) If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does AS1 change for this reaction at room temperature?

Problem 15E Problem 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) n what temperature range is it a non-spontaneous process? (d) At what temperature are the two phases in equilibrium?

Problem 16E Problem Spontaneous Processes (Section) The normal freezing point of fl-octane (C8H18) is -57 °C. (a) Is the freezing of fl-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 fl-octane and solid fl-octane are in equilibrium? Explain.

Problem 17E Problem Spontaneous Processes (Section) indicate whether each statement is true or false, (a) If a system undergoes a reversible process, the entropy of the universe increases, (b) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings, (c) If a system undergoes a reversible process, the entropy change of the system must be zero, (d) Most spontaneous processes in nature are reversible.

Problem 18E Problem Spontaneous Processes (Section) Indicate whether each statement is true or false, (a) All spontaneous processes are irreversible, (b) The entropy of the universe increases for spontaneous processes, (c) The change in entropy of the surroundings is equal in magnitude and opposite in sign for the change in entropy of the system, for an irreversible process, (d) The maximum amount of work can be gotten out of a system that undergoes an irreversible process, as compared to a reversible process.

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, \(\Delta E\), depend on the particular pathway taken to carry out this change of state? Equation transcription: Text transcription: \Delta E

Problem 20E Problem Spontaneous Processes (Section) A system goes from state 1 to state 2 and back to state 1. (a) Is A£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?

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 \(\Delta E\) zero for the process? Equation transcription: Text transcription: \Delta E

Consider what happens when a sample of the explosive TNT (Section 8.8: "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 for this process? (c) Is it possible to tell whether is positive, negative, or zero for the process? Explain. (d) Can you determine the sign of \(\Delta E\) for the process? Explain. Equation transcription: Text transcription: \Delta E

Indicate whether each statement is true or false. (a) for an isothermal process depends on both the temperature and the amount of heat reversibly transferred. (b)\(\Delta S\) is a state function. (c) The second law of thermodynamics says that the entropy of the system increases for all spontaneous processes. Equation transcription: Text transcription: \Delta S

Problem 24E Problem 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.

The normal boiling point of \(\operatorname{Br}_{2}(I)\) is \(58.8^{0} \mathrm{C}\), and its molar enthalpy of vaporization is \(\Delta H_{v a p}=29.6 \mathrm{~kJ} / \mathrm{mol}\). (a) When \(\operatorname{Br}_{2}(I)\) boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when mol of \(\operatorname{Br}_{2}(I)\) is vaporized at \(58.8^{0} \mathrm{C}\) Equation transcription: Text transcription \operatorname{Br}_{2}(I): 58.8^{0} \mathrm{C} \Delta H_{v a p}=29.6 \mathrm{~kJ} / \mathrm{mol} \Delta S

The element gallium (Ga) freezes at \(29.8^{0} \mathrm{C}\) and its molar enthalpy of fusion is \(\Delta H_{f v s}=5.59 \mathrm{~kJ} / \mathrm{mol}\). (a) When molten gallium solidifies to at its normal melting point, is \(\triangle S\) positive or negative? (b) Calculate the value of when of solidifies at \(29.8^{0} \mathrm{C}\) Equation transcription: Text transcription: 29.8^{0}{C} \Delta H_{f v s}=5.59{~kJ} /{mol} \triangle S

Problem 27E Problem Entropy and the Second Law of Thermodynamics (Section) indicate whether each statement is true or false, (a) The second law of thermodynamics says that entropy is conserved, (b) If the entropy of the system increases during a reversible process, the entropy change of the surroundings must decrease by the same amount, (c) In a certain spontaneous process the system undergoes an entropy change of 4.2 J/K; therefore, the entropy change of the surroundings must be -4.2 J/K.

(a) Does the entropy of the surroundings increase for spontaneous processes? (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of \(\Delta S_{\text {surr }}\) (c) During a certain reversible process, the surroundings undergo an entropy change, \(\Delta S_{\text {surr }}=-78 j / K\). What is the entropy change of the system for this process? Equation transcription: Text transcription: \Delta S_{\text {surr }} \Delta S_{\text {surr }}=-78 j / K

(a) What sign for \(\Delta S\) do you expect when the volume of mol of an ideal gas at \(27^{0} \mathrm{C}\) is increased isothermally from an initial volume of (b) If the final volume is , calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain. Equation transcription: Text transcription: \Delta S 27^{0}{C}

(a) What sign for \(\triangle S\) do you expect when the pressure on of an ideal gas at is increased isothermally from an initial pressure of ? (b) If the final pressure on the gas is , calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain. Equation transcription: Text transcription: \triangle S

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0\), 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? Equation transcription: Text transcription: \Delta E=0, q=0

(a) What is the difference between a state and a microstate of a system? (b) As a system goes from state to state , 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 \(\Delta S_{\text {surr }}\)? Equation transcription: Text transcription: \Delta S_{\text {surr }}

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

Problem 34E Problem 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.

(a) What do you expect for the sign of \(\triangle S\) 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 does the entropy of the system increase? Equation transcription: Text transcription: \triangle S

(a) In a chemical reaction two gases combine to form a solid. What do you expect for the sign of \(\triangle \mathrm{S}\)? (b) How does the entropy of the system change in the processes described in Exercise 19.12? Equation transcription: Text transcription: \triangle {S}

Problem 37E Problem 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 Problem 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 Problem The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) Indicate whether each statement is true or false, (a) The third law of thermodynamics says that the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal, (b) "Translational motion" of molecules refers to their change in spatial location as a function of time, (c) "Rotational" and "vibrational" motions contribute to the entropy in atomic gases like He and Xe. (d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

Problem 40E Problem The Molecular Interpretation of Entropy and the Third Law of Thermodynamics (Section) Indicate whether each statement is true or false, (a) Unlike enthalpy, where we can only ever know changes in H, we can know absolute values of S. (b) If you heat a gas such as C02, you will increase its degrees of translational, rotational and vibrational motions, (c) C02(g) and Ar(g) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

Problem 41E Problem 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(£cr 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) C02(g) or C02(s).

Problem 42E Problem 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 H20(g) at 100 "C, 1 atm, or 1 mol of H20(!) 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 Na2S04(s) at 30 "C or 100 g Na2S04(^ at 30 °C.

Problem 43E Problem 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(5) + 3 H2(g)—>2 NH3(g) (b) CaC03( s)—»CaO( s) + 002(5). c) 3 C2H2(g)—»C6H6(g) (d) AI203(s) + 3 H2(5)—»2 Al(s) + 3 H20(g)

Predict the sign of \(\Delta S_{s y s}\) for each of the following processes: (a) Molten gold solidifies. (b) Gaseous \(C I_{2}\) dissociates in the stratosphere to form gaseous Cl atoms. (c) Gaseous CO reacts with gaseous \(H_{2}\) to form liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}\). (d) Calcium phosphate precipitates upon mixing \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) and \(\left(N H_{4}\right)_{3} P O_{4}(a q)\). Equation transcription: Text transcription: \Delta S_{s y s} C I_{2} H_{2} {CH}_{3}{OH} {Ca}({NO}_{3})_{2}(a q) (N H_{4})_{3} P O_{4}(a q)

(a) Using Figure 19.12 as a model, sketch how the entropy of water changes as it is heated from \(-50^{\circ} \mathrm{C}\) to \(110^{\circ} \mathrm{C}\) 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. Equation transcription: Text transcription: -50^{\circ}{C} 110^{\circ}{C}

Problem 46E Problem Entropy Changes in Chemical Reactions (Section) Propanol (C3H70H) 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 47E Problem Entropy Changes in Chemical Reactions (Section) In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) C2H2(g) or C2H6(g), (b) C02(g) or CO(g)?

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

Problem 49E Problem 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(s^0, (c) 1 mol P4(g) and 2 mol P2(g), (d) C(graphite) and C(diamond).

Problem 50E Problem 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 Cu20(s), (b) 1 mol N204(&) and 2 mol N02(g), (c) Si02(s) and C02(g), (d) CO(g) and C02(^).

Problem 51E Problem 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, Si1 s2 = 18.81 J/ mol-K, Ge1 s2 = 31.09 J/mol-K, and Sn1 s2 = 51.818 JAnol-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 \(S^{0}\) values of graphite and diamond in light of their structures (Figure 12.29, p. 503). (b) What would you expect for the \(S^{0}\) value of buckminsterfullerene (Figure 12.47, p. 516) relative to the values for graphite and diamond? Explain. Equation transcription: Text transcription: S^{0}

Using \(S^{0}\) values from Appendix C, calculate \(\Delta S^{0}\) values for the following reactions. In each case account for the sign of \(\Delta S^{0}\). a) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)) (b) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\) (c) \(\operatorname{Be}(O H)^{2}(s) \rightarrow \operatorname{BeO}(s)+H_{2}(g)\) (d) \(2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) Equation transcription: Text transcription: S^{0} \Delta S^{0} {C}_{2}{H}_{4}(g)+{H}_{2}(g) \rightarrow{C}_{2}{H}_{6}(g) {N}_{2}{O}_{4}(g) rightarrow 2{NO}_{2}(g) {Be}(O H)^{2}(s) \rightarrow{BeO}(s)+H_{2}(g) 2 {CH}_{3}{OH}(g)+3{O}_{2}(g) rightarrow 2{CO}_{2}(g)+4{H}_{2}{O}(g)

Calculate \(\Delta S^{0}\) values for the following reactions by using tabulated \(S^{0}\) values from Appendix C. In each case explain the sign of \(\Delta S^{0}). (a) \(\mathrm{HNO}_{3}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{~s})\) (b) \(2 F e_{2} O_{3}(s) \rightarrow 4 F e(s)+3 O_{2}(g)\) (c) \(\mathrm{CaCO}_{3}(s, \text { calcite })+2 \mathrm{HCl}(g) \rightarrow \mathrm{CaCl}_{2}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(I)\) (d) \(3 C_{2} H_{6}(g) \rightarrow C_{6} H_{6}(I)+6 H_{2}(g)\) Equation transcription: Text transcription: \Delta S^{0} S^{0} {HNO}_{3}(g)+{NH}_{3}(g) rightarrow{NH}_{4}{NO}_{3}({~s}) 2 F e_{2} O_{3}(s) rightarrow 4 F e(s)+3 O_{2}(g) {CaCO}_{3}(s, \text { calcite })+2{HCl}(g) rightarrow{CaCl}_{2}(s)+{CO}_{2}(g)+{H}_{2}{O}(I) 3 C_{2} H_{6}(g) rightarrow C_{6} H_{6}(I)+6 H_{2}(g)

(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 \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast? Equation transcription: Text transcription: \Delta G

(a) Is the standard free-energy change, \(\triangle G^{0}\), always larger than \(\triangle G\)? (b) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0\)? (c) For a certain process, \(\triangle G\) is large and negative. Does this mean that the process necessarily has a low activation barrier? Equation transcription: Text transcription: \triangle G^{0} \triangle G \Delta G=0

For a certain chemical reaction, \(\Delta H^{0}=-35.5 \mathrm{kj}\) and \(\Delta S^{0}=-85.5 j / k\). (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 \(\Delta G^{0}\) for the reaction at 298 K. (d) Is the reaction spontaneous at 298 K under standard conditions? Equation transcription: Text transcription: \Delta H^{0}=-35.5{kj} \Delta S^{0}=-85.5 j / k \Delta G^{0}

A certain reaction has \(\Delta H^{0}=+23.7 K J\) and \(\Delta S^{0}=+52.4 J / K\). (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 \(\Delta G^{0}\) for the reaction at 298 K. (d) Is the reaction spontaneous at 298 K under standard conditions? Equation transcription Text transcription: \Delta H^{0}=+23.7 K J \Delta S^{0}=+52.4 J / K \Delta G^{0}

Use data in Appendix C to calculate \(\Delta H^{0}, \Delta S^{0}\), and \(\Delta G^{0}\) at 25 °C for each of the following reactions. (a) \(4 \operatorname{Cr}(s)+3 O_{2}(g) \rightarrow 2 \operatorname{Cr}_{2} O_{3}(s)\) (b) \(\mathrm{BaCO}_{3}(s) \rightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)\) (c) \(2 P(s)+10 H F(g) \rightarrow 2 P F_{5}(g)+5 H_{2}(g)\) (d) \(K(s)+O_{2}(g) \rightarrow K O_{2}(s)\) Equation transcription: Text transcription: \Delta H^{0}, \Delta S^{0} \Delta G^{0} 4 {Cr}(s)+3 O_{2}(g) rightarrow 2{Cr}_{2} O_{3}(s) {BaCO}_{3}(s) rightarrow{BaO}(s)+{CO}_{2}(g) 2 P(s)+10 H F(g) rightarrow 2 P F_{5}(g)+5 H_{2}(g) K(s)+O_{2}(g) rightarrow K O_{2}(s)

Using data from Appendix C, calculate \(\Delta G^{0}\) for the following reactions. Indicate whether each reaction is spontaneous at 298 K under standard conditions. 1. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) 2. \(\mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \rightarrow 3 \mathrm{NO}(g)\) 3. \(6 \mathrm{CI}_{2}(s)+2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \rightarrow 4 \mathrm{FeCI}_{3}(s)+3 \mathrm{O}_{2}(g)\) 4. \(\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2}(g) \rightarrow \mathrm{S}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(g)\) Equation transcription: Text transcription: \Delta G^{0} 2{SO}_{2}(g)+{O}_{2}(g) rightarrow 2{SO}_{3}(g) {NO}_{2}(g)+{N}_{2}{O}(g) rightarrow 3{NO}(g) 6{CI}_{2}(s)+2{Fe}_{2}{O}_{3}(s) rightarrow 4{FeCI}_{3}(s)+3{O}_{2}(g) {SO}_{2}(g)+2{H}_{2}(g) rightarrow{S}({s})+2{H}_{2}{O}(g)

Problem 62E Problem 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) + CI2(g)->2 AgCI(s) (b) P4010(s) + 16 H2(g)->4 PH3(g) + 10 H20(g) (c) CH4(g) + 4 F2(g)—>CF4(g) + 4 HF(g) (d) 2 H2O2(/)—»2 H2O(/) + 02(g)

Octane \(\left(C_{8} H_{18}\right)\) is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline. (a) Write a balanced equation for the combustion of \(C_{8} H_{18}(I)\) to form \(\mathrm{CO}_{2}(g)\) and \(H_{2} O(I)\).(b) Without using thermochemical data, predict whether \(\Delta G^{0}\) for this reaction is more negative or less negative than \(\Delta H^{0}\). Equation transcription: Text transcription: (C_{8} H_{18}) C_{8} H_{18}(I) {CO}_{2}(g) H_{2} O(I) \Delta G^{0} \Delta H^{0}

Sulfur dioxide reacts with strontium oxide as follows: \(\mathrm{SO}_{2}(g)+\operatorname{SrO}(g) \rightarrow \operatorname{SrSO}_{3}(s)\) (a) Without using thermochemical data, predict whether \(\Delta G^{0}\) for this reaction is more negative or less negative than \(\Delta H^{0}\). (b) If you had only standard enthalpy data for this reaction, estimate of the value of \(\Delta G^{0}\) at 298 K, using data from Appendix C on other substances. Equation transcription: Text transcription: {SO}_{2}(g)+{SrO}(g) rightarrow {SrSO}_{3}(s) \Delta G^{0} \Delta H^{0}

Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low T but not spontaneous at high T; (iv) spontaneous at high T but not spontaneous at low T. 1. \(N_{2}(g)+3 F_{2}(g) \rightarrow 2 N F_{2}(g) \Delta H^{0}=-249 K J ; \Delta S^{0}=-278 J / K\) 2. \(\mathrm{N}_{2}(g)+3 \mathrm{CI}_{2}(g) \rightarrow 2 \mathrm{NCI}_{3}(g) \Delta H^{0}=460 \mathrm{Kl} ; \Delta S^{0}=-275 \mathrm{~J} / \mathrm{K}\) 3. \(N_{2} F_{4}(g) \rightarrow 2 N F_{2}(g) \Delta H^{0}=85 K j ; \Delta S^{0}=198 J / K\) Equation transcription: Text transcription: N_{2}(g)+3 F_{2}(g) rightarrow 2 N F_{2}(g) \Delta H^{0}=-249 K J ; \Delta S^{0}=-278 J / K {N}_{2}(g)+3{CI}_{2}(g) rightarrow 2{NCI}_{3}(g) Delta H^{0}=460{Kl} ; \Delta S^{0}=-275{~J} /{K} N_{2} F_{4}(g) rightarrow 2 N F_{2}(g) \Delta H^{0}=85 K j ; \Delta S^{0}=198 J / K

From the values given for \(\Delta F^{0}\) and \(\Delta S^{0}\), calculate \(\Delta G^{0}\) 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? 1. \(2 P b S(S)+3 O_{2}(g) \rightarrow 2 P b O(S)+2 S O_{2}(g) \Delta H^{0}=-844 K J ; \Delta S^{0}=-165 J / K\) 2. \(2 P O C I_{3}(g) \rightarrow 2 P C I_{3}(g)+O_{2}(g) \Delta H^{0}=572 K J ; \Delta S^{0}=179 J / K\) Equation transcription: Text transcription: \Delta F^{0} \Delta S^{0} \Delta G^{0} 2 P b S(S)+3 O_{2}(g) rightarrow 2 P b O(S)+2 S O_{2}(g) Delta H^{0}=-844 K J ; Delta S^{0}=-165 J / K 2 P O C I_{3}(g) rightarrow 2 P C I_{3}(g)+O_{2}(g) \Delta H^{0}=572 K J ; \Delta S^{0}=179 J / K

Problem 67E Problem 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 AS for the reaction.

A certain constant-pressure reaction is barely nonspontaneous at \(45^{0} C\). The entropy change for the reaction is 72 J/K. Estimate \(\triangle H\). Equation transcription: Text transcription: 45^{0} C \triangle H

For a particular reaction, \(\Delta H=32 K J\) and \(\Delta S=98 J / K\). Assume that \(\Delta H\) and \(\Delta S\) do not vary with temperature. (a) At what temperature will the reaction have \(\Delta G=0\)? (b) If T is increased from that in part (a), will the reaction be spontaneous or nonspontaneous? Equation transcription: Text transcription: \Delta H=32 K J \Delta S=98 J / K \Delta H \Delta S \Delta G=0

Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds according to: \(\mathrm{CH}_{3} \mathrm{COOH}\left(\mathrm{O} \rightarrow \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{CO}(g)\right.\) By using data from Appendix C, calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that \(\Delta H^{0}\) and \(\Delta S^{0}\) do not vary with temperature. Equation transcription: Text transcription: {CH}_{3}{COOH}({O} rightarrow{CH}_{3}{OH}(g)+{CO}(g). \Delta H^{0} \Delta S^{0}

Consider the following reaction between oxides of nitrogen: \(N O_{2}(g)+N_{2}(g) \rightarrow 3 N O(g)\) (a) Use data in Appendix C to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate ?G at 800 K, assuming that \(\Delta H^{0}\) and \(\Delta S^{0}\) do not change with temperature. Under standard conditions is the reaction spontaneous at 800 K? (c) Calculate \(\Delta G\) at 1000 K. Is the reaction spontaneous under standard conditions at this temperature? Equation transcription: Text transcription: N O_{2}(g)+N_{2}(g) \rightarrow 3 N O(g) \Delta G \Delta H^{0} \Delta S^{0}

Methanol 1CH3OH2 can be made by the controlled oxidation of methane: \(\mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CH}_{3} \) (a) Use data in Appendix C to calculate \(\Delta H^{0}\) and \(\Delta S^{0}\) for this reaction. (b) Will \(\Delta G\) for the reaction increase, decrease, or stay unchanged with increasing temperature? (c) Calculate \(\Delta G^{0}\) 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? Equation transcription: Text transcription: {CH}_{4}(g)+\frac{1}{2}{O}_{2}(g) \rightarrow{CH}_{3}{OH}(g) \Delta G \Delta H^{0} \Delta S^{0} \Delta G^{0}

Problem 73E Problem Gibbs Free Energy (Sections) (a) Use data in Appendix C to estimate the boiling point of benzene, C6H6(0- (b) Use a refe source, such as the CRC Handbook of Chemistry and Physics, to find the experimental bo point of benzene. How do you explain any deviation between your answer in part (a) and t experimental value?

Problem 74E Problem 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 12. (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 Problem Gibbs Free Energy (Sections) Acetylene gas, C2H2(g), is used in welding, (a) Write a balanced equation for the combustion of acetylene gas to 002(g) and H20(f). (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?

Problem 76E Problem 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 H2O0(/) is formed? (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

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

Problem 79E Problem Free Energy and Equilibrium (Section) Consider the reaction 2 N02(^)-»N204(^). (a) Using data from Appendix C, calculate A G° at 298 K. (b) Calculate A G at 298 K if the partial pressures of N02 and N204 are 0.40 atm and 1.60 atm, respectively.

Problem 80E Problem Free Energy and Equilibrium (Section) Consider the reaction 3 CH4(g)-»C3H3(g) + 2 H2(g). (a) Using data from Appendix C, calculate A G° at 293 K. (b) Calculate A G at 293 K if the reaction mixture consists of 40.0 atm of CH4, 0.0100 atm of C3H3(g), and 0.0130 atm of H2.

Use data from Appendix C to calculate the equilibrium constant, K, and \(\Delta G^{0}\) at 298 K for each of the following reactions: 1. \(I_{2}(g)+I_{2}(g) \leftrightarrow 2 H I(g)\) 2. \(C_{2} H_{5} O H(g) \leftrightarrow C_{2} H_{4}(g)+H_{2} O(g)\) 3. \(3 C_{2} H_{2}(g) \leftrightarrow C_{6} H_{6}(g)\) Equation transcription: Text transcription: \Delta G^{0} I_{2}(g)+I_{2}(g) \leftrightarrow 2 H I(g) C_{2} H_{5} O H(g) \leftrightarrow C_{2} H_{4}(g)+H_{2} O(g) 3 C_{2} H_{2}(g) \leftrightarrow C_{6} H_{6}(g)

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: 1. \(\mathrm{NaHCO}_{3}(s) \leftrightarrow \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g)\) 2. \(2 H B r(g)+C I_{2}(g) \leftrightarrow 2 H C I(g)+B r_{2}(g)\) 3. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \leftrightarrow 2 \mathrm{SO}_{3}(g)\) Equation transcription: Text transcription: {NaHCO}_{3}(s) leftrightarrow{NaOH}(s)+{CO}_{2}(g) 2 H B r(g)+C I_{2}(g) leftrightarrow 2 H C I(g)+B r_{2}(g) 2{SO}_{2}(g)+{O}_{2}(g) leftrightarrow 2{SO}_{3}(g)

Consider the decomposition of barium carbonate: \(\mathrm{BaCO}_{3}(s) \leftrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)\) Using data from Appendix C, calculate the equilibrium pressure of \(\mathrm{CO}_{2}\) at (a) 298 K and (b) 1100 K. Equation transcription: Text transcription: {BaCO}_{3}(s) leftrightarrow{BaO}(s)+{CO}_{2}(g) {CO}_{2}

Consider the reaction \(\mathrm{PbCO}_{3}(s) \leftrightarrow \mathrm{PBO}(s)+\mathrm{CO}_{2}(g)\) Using data in Appendix C, calculate the equilibrium pressure of \(\mathrm{CO}_{2}\) in the system at (a) 400 °C and (b) 180 °C. Equation transcription: Text transcription: {PbCO}_{3}(s) leftrightarrow{PBO}(s)+{CO}_{2}(g) {CO}_{2}

Problem 85E Problem Free Energy and Equilibrium (Section) The value of Ks for nitrous acid (HN02) at 25 °C is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to K&. (b) By using the value of /fa, calculate A G° for the dissociation of nitrous acid in aqueous solution, (c) What is the value of A G at equilibrium? (d) What is the value of A G when [H+] = 5.0 x 10-2 M, [N02 -] = 6.0 x 10-4 M, and [HN02] = 0.20 M?

Problem 86E Free Energy and Equilibrium (Section) The Kb for methylamine (CH3WH2) at 25 °C is given in Appendix D. (a) Wfite the chemical equation for the equilibrium that corresponds to Kb. (b) By using the value of Kb, calculate A G° for the equilibrium in part (a), (c) What is the value of A G at equilibrium? (d) What is the value of A G when [H+] = 6.7 x 10-9 M, [CH3NH3 +] = 2.4 x 10-3 M, and [CH3NH2] = 0.093 M?

(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 \(\Delta E\) in terms of q and w and an expression for \(\triangle S\) in terms of q and T. Equation transcription: Text transcription: \Delta E \triangle S

Problem 88AE Problem 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 for the process N2(g) + 3 H2(5)->2 NH3(g). (b) The reaction of Na(s) with CI2(^) to form NaCI(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.

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) 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 \(\mathrm{CO}_{2}(g)\) and \(H_{2} O(g)\). Equation transcription: Text transcription: \Delta S \Delta H {CO}_{2}(g) H_{2} O(g)

Problem 90AE Problem The reaction 2 Mg(s) + 02(g)->2 MgO(s) is highly spontaneous. A classmate calculates tl entropy change for this reaction and obtains a large negative value for AS’. 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. (f) Calculate the absolute entropy of the two-dice system.

Ammonium nitrate dissolves spontaneously and endother-mally in water at room temperature. What can you deduce about the sign of \(\triangle S\) for this solution process? Equation transcription: Text transcription: triangle S

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as \(\mathrm{CH}_{2} F_{2}\). 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 °C. Some time after the air conditioner is turned on, the house is cooled to 24 °C. Is this process spontaneous or nonspontaneous? Equation transcription: Text transcription: \mathrm{CH}_{2} F_{2}

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, \(B r_{2}\), by determining \(\Delta H_{\text {vap }}^{0}\) for \(B r_{2}\) using data from Appendix C. Assume that \(\Delta H_{\text {vap }}^{0}\) remains constant with temperature and that Trouton’s rule holds. (b) Look up the normal boiling point of \(B r_{2}\) in a chemistry handbook or at the WebElements Web site (www.webelements. com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation? Equation transcription: Text transcription: B r_{2} \Delta H_{\text {vap }}^{0}

For the majority of the compounds listed in Appendix C, the value of \(\Delta G_{f}^{0}\) is more positive (or less negative) than the value of \(\Delta H_{f}^{0}\) . (a) Explain this observation, using \(\mathrm{NH}_{3}(g), \mathrm{CCl}_{4}(I)\), and \(\mathrm{KNO}_{3}(\mathrm{~s})\) as examples. (b) An exception to this observation is \(\cos (g)\). Explain the trend in the \(\Delta H_{f}^{0}\) and \(\Delta G_{f}^{0}\) values for this molecule. Equation transcription: Text transcription: \Delta G_{f}^{0} \Delta H_{f}^{0} {NH}_{3}(g),{CCl}_{4}(I) {KNO}_{3}({~s}) \cos (g)

Consider the following three reactions: 1. \(T i(s)+2 C I_{2}(g) \rightarrow T i C I_{4}(g)\) 2. \(\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+7 \mathrm{CI}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{CCI}_{4}(\mathrm{~g})+6 \mathrm{HCI}(\mathrm{g})\) 3. \(\mathrm{BaO}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{BaCO}_{3}(s)\) (a) For each of the reactions, use data in Appendix C to calculate \(\Delta H^{0}, \Delta G^{0}, K\), and \(\Delta S^{0}\) 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. Equation transcription: Text transcription: T i(s)+2 C I_{2}(g) rightarrow T i C I_{4}(g) {C}_{2}{H}_{6}({~g})+7{CI}_{2}({~g}) rightarrow 2{CCI}_{4}({~g})+6{HCI}({g}) {BaO}(s)+{CO}_{2}(g) rightarrow{BaCO}_{3}(s) \Delta H^{0}, \Delta G^{0}, K \Delta S^{0}

Using the data in Appendix C and given the pressures listed, calculate Kp and ?G for each of the following reactions:

(a) For each of the following reactions, predict the sign of \(\Delta H^{0}\) and \(\Delta S^{0}\) 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. 1. \(2 M g(s)+O_{2}(g) \leftrightarrow 2 M g O(s)\) 2. \(2 K I(s) \leftrightarrow 2 K(g)+I_{2}(g)\) 3. \(N a_{2}(g) \leftrightarrow 2 N a(g)\) 4. \(2 \mathrm{~V}_{2} \mathrm{O}_{5}(s) \leftrightarrow 4 \mathrm{~V}(s)+5 \mathrm{O}_{2}(g)\) Equation transcription: Text transcription: \Delta H^{0} \Delta S^{0} 2 M g(s)+O_{2}(g) leftrightarrow 2 M g O(s) 2 K I(s) leftrightarrow 2 K(g)+I_{2}(g) N a_{2}(g) leftrightarrow 2 N a(g) 2{~V}_{2}{O}_{5}(s) leftrightarrow 4{~V}(s)+5{O}_{2}(g)

Problem 100AE Problem Acetic acid can be manufactured by combining methanol with carbon monoxide, an example of a carbonylation reaction: CH3OH(/) + CO(g)—>CH3COOH(/) (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 AW and A S’ are temperature independent, and you may ignore any phase changes that might occur.)

The oxidation of glucose \(\left(C_{6} H_{12} O_{6}\right)\) in body tissue produces \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and \(\mathrm{CO}_{2}\). (a) Using data given in Appendix C, compare the equilibrium constants for the following reactions: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \leftrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{I})\) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \leftrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{I})+2 \mathrm{CO}_{2}(\mathrm{~g})\) (b) Compare the maximum work that can be obtained from these processes under standard conditions. Equation transcription: Text transcription: (C_{6} H_{12} O_{6}) {CO}_{2} {H}_{2}{O} ({C}_{2}{H}_{5}{OH}\right) {C}_{6}{H}_{12}{O}_{6}(s)+6{O}_{2}(g) leftrightarrow 6{CO}_{2}(g)+6{H}_{2}{O}({I}) {C}_{6}{H}_{12}{O}_{6}(s) leftrightarrow 2{C}_{2}{H}_{5}{OH}({I})+2{CO}_{2}({~g})

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane \(\left(C_{2} H_{6}\right)\), is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: \(2 C H_{4}(g) \rightarrow C_{2} H_{6}(g)+H_{2}(g)\) In practice, this reaction is carried out in the presence of oxygen: \(2 C H_{4}(g)+\frac{1}{2} O_{2}(g) \rightarrow C_{2} H_{6}(g)+H_{2} O(g)\) (a) Using the data in Appendix C, calculate K for these reactions at 25 °C and 500 °C. (b) Is the difference in \(\Delta G^{0}\) for the two reactions due primarily to the enthalpy term \((\Delta H)\) or the entropy term \((-T \Delta S)\)? (c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the “Chemistry and Life” box in Section 19.7. (d) The reaction of \(\mathrm{CH}_{4}\) and \(O_{2}\) to form \(C_{2} H_{6}\) and \(\mathrm{H}_{2} \mathrm{O}\) must be carried out carefully to avoid a competing reaction. What is the most likely competing reaction? Equation transcription: Text transcription: \left(C_{2} H_{6}\right) 2 C H_{4}(g) \rightarrow C_{2} H_{6}(g)+H_{2}(g) 2 C H_{4}(g)+\frac{1}{2} O_{2}(g) \rightarrow C_{2} H_{6}(g)+H_{2} O(g) \Delta G^{0} (\Delta H) (-T \Delta S) \mathrm{CH}_{4} O_{2} C_{2} H_{6} \mathrm{H}_{2} \mathrm{O}

Cells use the hydrolysis of adenosine triphosphate (ATP) as a source of energy (Figure 19.16). The conversion of ATP to ADP has a standard free-energy change of -30.5 kJ/mol. If all the free energy from the metabolism of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{I})\) goes into the conversion of ADP to ATP, how many moles of ATP can be produced for each mole of glucose? Equation transcription: Text transcription: {C}_{6}{H}_{12}{O}_{6}(s)+6{O}_{2}(g) rightarrow 6{CO}_{2}(g)+6{H}_{2}{O}({I})

Problem 104AE Problem 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 A 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+?

One way to derive Equation 19.3 depends on the observation that at constant T the number of ways, W, of arranging m ideal-gas particles in a volume V is proportional to the volume raised to the m power: \(W x V^{t h}\) 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 n moles of an ideal gas. Equation transcription: Text transcription: W x V^{t h}

About 86% 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 \(\left(T_{h i g h}-T_{l o w}\right) / T_{h i g h}\), where \(T_{\text {high }}\) is the temperature of the heat going into the engine and \(T_{\text {low }}\) 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 700 K and an exit temperature of 288 K? (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 100% 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 (p. 175) 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. Equation transcription: Text transcription: \left(T_{h i g h}-T_{l o w}\right) / T_{h i g h} T_{\text {high }} T_{\text {low }}

Most liquids follow Trouton’s rule (see Exercise 19.95), which states that the molar entropy of vaporization is approximately \(88 \pm 5 J / m o l-K\). The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: (a) Calculate \(\Delta S_{v a p}\) for each of the liquids. Do all the liquids obey Trouton’s rule? (b) With reference to intermolecular forces (Section 11.2), 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 \(\left(C_{6} H_{5} C I\right)\) boils at 131.8 °C. Use Trouton’s rule to estimate \(\Delta H_{v a p}\) for this substance. Equation transcription: Text transcription: 88 \pm 5 J / m o l-K \Delta S_{v a p} \left(C_{6} H_{5} C I\right) \Delta H_{v a p}

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 14.15.

Problem 109IE At what temperatures is the following reaction, the reduction of magnetite by graphite to elemental iron, spontaneous? Fe3O4(s) + 2 C (s, graphite) 2 CO2(g) + 3 Fe (s)

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 02(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.

Problem 111IE An ice cube with a mass of 20 g at -20 °C (typical freezer temperature) is dropped into a cup that holds 500mL of hot water, initially at 83 °C. What is the final temperature in the cup? The density of liquid water is 1.00 g/mL; the specific heat capacity of ice is 2.03 J/g-C; the specific heat capacity of liquid water is 4.184 J/g-C; the enthalpy of fusion of water is 6.01 kJ/mol.

Carbon disulfide \(\left(C S_{2}\right)\) is a toxic, highly flammable substance. The following thermodynamic data are available for \(C S_{2}(I)\) and \(C S_{2}(g)\) at 298 K: (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 \(C S_{2}\) molecule. (c) Liquid \(C S_{2}\) burns in \(O_{2}\) with a blue flame, forming \(\mathrm{CO}_{2}(g)\) and \(\mathrm{SO}_{2}(g)\). Write a balanced equation for this reaction. (d) Using the data in the preceding table and in Appendix C, calculate \(\Delta H^{0}\) and \(\Delta G^{0}\) 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 \(\Delta S^{0}\) at 298 K for the vaporization of \(C S_{2}(I)\). Is the sign of \(\Delta S^{0}\) as you would expect for a vaporization? (f) Using data in the table and your answer to part (e), estimate the boiling point of \(C S_{2}(I)\). Do you predict that the substance will be a liquid or a gas at 298 K and 1 atm? Equation transcription: Text transcription: \left(C S_{2}\right) C S_{2}(I) C S_{2}(g) C S_{2} \mathrm{CO}_{2}(g) \mathrm{SO}_{2}(g) \Delta H^{0} \Delta G^{0} \Delta S^{0} O_{2}

The following data compare the standard enthalpies and free energies of formation of some crystalline ionic substances and aqueous solutions of the substances: Write the formation reaction for \(\mathrm{AgNO}_{3}(s)\). Based on this reaction, do you expect the entropy of the system to increase or decrease upon the formation of \(\mathrm{AgNO}_{3}(s)\)? (b) Use \(\Delta H_{f}^{0}\) and \(\Delta G_{f}^{0}\) of \(\mathrm{AgNO}_{3}(s)\) to determine the entropy change upon formation of the substance. Is your answer consistent with your reasoning in part (a)? (c) Is dissolving \(\mathrm{AgNO}_{3}(s)\) in water an exothermic or endothermic process? What about dissolving \(\mathrm{MgSO}_{4}\) in water? (d) For both \(\mathrm{AgNO}_{3}(s)\) and \(\mathrm{MgSO}_{4}\), 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. Equation transcription: Text transcription: {AgNO}_{3}(s) \Delta H_{f}^{0} \Delta G_{f}^{0} {MgSO}_{4}

Problem 114IE Consider the following equilibrium: N2O4(g)?2 NO2(g) Thermodynamic data on these gases are given in Appendix C. You may assume that and AS° 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 N02 as N204? (c) At what temperature will an equilibrium mixture of 10 atm total pressure contain twice as much N02 as N204? (d) Rationalize the results from parts (b) and (c) by using Le Chatelier's principle.[Section]

Problem 115IE The reaction SO2(g) + 2H2S(g)?3 S(s) + 2 H2)(g) is the basis of a suggested method for removal of S02 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 S02? (c) If PS02 = PH2S and the vapor pressure of water is 25 torr, calculate the equilibrium S02 pressure in the system at 298 K. (d) Would you expect the process to be more or less effective at higher temperatures?

Problem 116IE 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)? Design an Experiment