ch20

319

Thermodynamics: Entropy, Free Energy, and

the Direction of Chemical Reactions Chapter 20

Multiple Choice Questions

1. Which of the following is true for pure oxygen gas, O2(g) at 25 C? E

a. H f > 0

b. H f < 0

c. G f > 0

d. G f < 0

e. S > 0

2. A certain process has Suniv > 0 at 25 C. What does one know about the process? E

a. It is exothermic.

b. It is endothermic.

c. It is spontaneous at 25 C. d. It will move rapidly toward equilibrium.

e. None of the above.

3. Which of the following is necessary for a process to be spontaneous?

E

a. Hsys < 0

b. Ssys > 0

c. Ssurr< 0

d. Suniv > 0

e. Gsys = 0

4. Which of the following results in a decrease in the entropy of the system?

M

a. O2(g), 300 K O2(g), 400 K

b. H2O(s), 0 C H2O(l), 0 C

c. N2(g), 25 C N2(aq), 25 C

d. NH3(l), –34.5 C NH3(g), –34.5 C

e. 2H2O2(g) 2H2O(g) + O2(g)

5. Which of the following should have the greatest molar entropy at 298 K?

M

a. CH4(g)

b. H2O(l)

c. NaCl(s)

d. N2O4(g)

e. H2(g)

6. Which of the following is true for a system at equilibrium? M

a. S sys = S surr

b. S sys = – S surr

c. S sys = S surr = 0

d. S univ > 0

e. None of the above is a sufficient condition.

320

7. Which of the following is always true for an exothermic process?

M

a. q sys > 0, Ssurr < 0

b. q sys < 0, Ssurr > 0

c. q sys < 0, Ssurr < 0

d. q sys > 0, Ssurr > 0 e. w < 0

8. Which of the following is always true for an endothermic process?

M

a. q sys > 0, Ssurr < 0

b. q sys < 0, Ssurr > 0

c. q sys < 0, Ssurr < 0

d. q sys > 0, Ssurr > 0 e. w < 0

9. Which of the following values is based on the Third Law of Thermodynamics?

M

a. H f = 0 for Al(s) at 298 K

b. G f = 0 for H2(g) at 298 K

c. S = 51.446 J/(mol·K) for Na(s) at 298 K

d. q sys < 0 for H2O(l) H2O(s) at 0 C e. None of the above.

10. When a sky diver free-falls through the air, the process is

E

a. non-spontaneous because he is accelerating due to the force applied by gravity.

b. non-spontaneous because he is losing potential energy.

c. non-spontaneous because he had planned the jump for two weeks.

d. spontaneous.

e. in equilibrium.

11. Which, if any, of the following processes is spontaneous under the specified conditions?

M

a. H2O(l) H2O(s) at 25 C

b. CO2(s) CO2(g) at 0 C

c. 2H2O(g) 2H2(g) + O2(g)

d. C(graphite) C(diamond) at 25 C and 1 atm pressure e. None of the above is spontaneous.

12. Which relationship or statement best describes S for the following reaction? E

Pb(s) + Cl2(g) PbCl2(s)

a. S 0

b. S < 0

c. S > 0

d. S = H /T e. More information is needed to make a reasonable prediction.

321

13. Which relationship or statement best describes S for the following reaction? M

HgS(s) + O2(g) Hg(l) + SO2(g)

a. S 0

b. S < 0

c. S > 0


14. Which relationship or statement best describes S for the following reaction?

M

2H2S(g) + 3O2(g) 2H2O(g) + 2SO2(g)

a. S 0

b. S < 0

c. S > 0


15. Which relationship best describes S for the following reaction? M

CO(g) + H2O(g) CO2(g) + H2(g)

a. S = H

b. S = H /T

c. S > 0

d. S < 0

e. S 0


2NH3(g) + 2ClF3(g) 6HF(g) + N2(g) + Cl2(g)

a. S 0

b. S < 0

c. S > 0


17. Which relationship best describes S for the following reaction? H

8H2(g) + S8(s) 8H2S(g)

a. S = H

b. S = H /T

c. S 0

d. S < 0

e. S > 0

322


O3(g) + NO(g) O2(g) + NO2(g)

a. S 0

b. S < 0

c. S > 0



C2H5OH(l) + 3O2(g) 2CO2(g) + 3H2O(l)

a. S 0

b. S < 0

c. S > 0



K2SO4(s) 2K+(aq) + SO42–(aq)

a. S 0

b. S < 0

c. S > 0



BaCl2(aq) + Na2SO4(aq) BaSO4(s) + 2NaCl(aq)

a. S 0

b. S < 0

c. S > 0



CaO(s) + CO2(g) CaCO3(s)

a. S 0

b. S < 0

c. S > 0


323

23. Which of the following pairs has the member with the greater molar entropy listed first? All systems

E are at 25 C.

a. CO(g), CO2(g)

b. NaCl(s), NaCl(aq)

c. H2S(g), H2S(aq)

d. Li(s), Pb(s)

e. H2(g), H2O(g)

24. You are given pure samples of ethane, C2H6(g), and toluene, C7H8(l). What prediction would you make

H concerning their standard molar entropies at 298 K?

a. S ethane > S toluene

b. S ethane < S toluene

c. S ethane (S toluene) 3

d. S ethane S toluene e. Since toluene is much more complex than ethane, but ethane is in the gas phase while toluene is a liquid,

none of the above predictions can be confidently made without further information or calculations.

25. You are given pure samples of pentane, CH3CH2CH2CH2CH3(l), and 1,3-pentadiene,

M CH2=CHCH=CHCH3(l). What prediction would you make concerning the standard molar

entropies of pentane, S (pentane) and 1,3-pentadiene, S (1, 3-pentadiene), at 298 K?

a. S (pentane) > S (1, 3-pentadiene)

b. S (pentane) < S (1, 3-pentadiene)

c. S (pentane) S (1, 3-pentadiene)

d. S (pentane) S (1, 3-pentadiene) + 2 S (H2) e. More information is needed to make reasonable predictions.

26. You are given pure samples of ammonia, NH3(g), and nitrogen trifluoride, NF3(g). What prediction would

E you make concerning their standard molar entropies at 298 K?

a. S ammonia > S nitrogen trifluoride

b. S ammonia < S nitrogen trifluoride

c. S ammonia S nitrogen trifluoride

d. Other conditions need to be specified before a reliable prediction can be made.

e. Even if more conditions are specified, a reliable prediction cannot be made.

27. In which one of the following pairs will the first system have a higher entropy than the second?

E Assume P and T are the same for each pair, unless stated otherwise.

a. 1 mole He(g); 1 mole Kr(g)

b. 1 mole O2(g); 2 mole O(g)

c. 1 mole CH4(g); 1 mole C2H6(g)

d. 1 mole Xe(g) at 1 atmosphere; 1 mole Xe(g) at 0.5 atmosphere

e. 20 one-dollar bills distributed randomly among 20 people; 20 one-dollar bills distributed randomly

among 10 people

28. In which one of these pairs will the entropy of the first substance be greater than that of the second?

E Assume P and T are the same for each pair, unless stated otherwise.

a. 1 mole of F2(g); 1 mole of Cl2(g)

b. 1 mole of I2(s); 1 mole of I2(g)

c. 1 mole of CaCO3(s); 1 mole of CaO(s) plus 1 mole of CO2(g)

d. 1 mole of H2(g) at 25 C; 1 mole of H2(g) at 50 C e. 1 mole of O3(g); 1 mole of O2(g)

324

29. Calculate S for the reaction E

SiCl4(g) + 2Mg(s) 2MgCl2(s) + Si(s)

Substance: SiCl4(g) Mg(s) MgCl2(s) Si(s)

S (J/K mol): 330.73 32.68 89.62 18.83

a. –254.96 J/K

b. –198.02 J/K

c. 198.02 J/K

d. 254.96 J/K e. 471.86 J/K


4Cr(s) + 3O2(g) 2Cr2O3(s)

Substance: Cr(s) O2(g) Cr2O3(s)

S (J/K mol): 23.77 205.138 81.2

a. –548.1 J/K

b. –147.7 J/K

c. 147.7 J/K

d. 310.1 J/K

e. 548.1 J/K


2Cl2(g) + SO2(g) SOCl2(g) + Cl2O(g)

Substance: Cl2(g) SO2(g) SOCl2(g) Cl2O(g)

S (J/K mol) 223.0 248.1 309.77 266.1

a. –118.2 J/K

b. –104.8 J/K

c. 104.8 J/K

d. 118.2 J/K

e. 1270.0 J/K

32. Calculate S for the combustion of propane. E

C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(g)

Substance: C3H8(g) O2(g) CO2(g) H2O(g)

S (J/K mol): 269.9 205.138 213.74 188.825

a. –100.9 J/K b. –72.5 J/K

c. 72.5 J/K

d. 100.9 J/K

e. 877.5 J/K

325

33. Elemental boron can be formed by reaction of boron trichloride with hydrogen.

M

BCl3(g) + 1.5H2(g) B(s) + 3HCl(g)

Substance: BCl3(g) H2(g) B(s) HCl(g)

S °(J/K mol) ? 130.6 5.87 186.8

If S = 80.3 J/K, what is S for BCl3(g)?

a. –18.2 J/K mol

b. 18.2 J/K mol

c. 290.1 J/K mol

d. 355.4 J/K mol

e. 450.6 J/K mol

34. For a chemical reaction to be spontaneous only at high temperatures, which of the following conditions must

M be met?

a. S > 0, H > 0

b. S > 0, H < 0

c. S < 0, H < 0

d. S < 0, H > 0

e. G > 0

35. For a chemical reaction to be spontaneous only at low temperatures, which of the following conditions must M be met?

a. S > 0, H > 0

b. S > 0, H < 0

c. S < 0, H < 0

d. S < 0, H > 0

e. G > 0

36. For a chemical reaction to be spontaneous at all temperatures, which of the following conditions must

M be met?

a. S > 0, H > 0

b. S > 0, H < 0

c. S < 0, H < 0

d. S < 0, H > 0 e. It is not possible for a reaction to be spontaneous at all temperatures.

37. For a chemical reaction to be non-spontaneous at any temperature, which of the following conditions must be

M met?

a. S > 0, H > 0

b. S > 0, H < 0

c. S < 0, H < 0

d. S < 0, H > 0 e. All reactions are spontaneous at some temperature.

326

38. For a process with S < 0, which one of the following statements is correct? M

a. The process will definitely be spontaneous if H < 0.

b. The process will be definitely be spontaneous if H < T S. c. The process can never be spontaneous.

d. The process will definitely be spontaneous, regardless of H.

e. The process will definitely be spontaneous if Ssurr > 0.

39. Consider the following quantities used in thermodynamics: E, H, q, w, S, G. How many of them are

M state functions?

a. 0

b. 1

c. 2 d. 3

e. 4

40. In order for a process to be spontaneous,

E

a. H must be less than zero.

b. S must be greater than zero.

c. G must be greater than zero. d. it should be rapid.

e. Ssys + Ssurr must be greater than zero.

41. Calculate G° for the reaction E

SiCl4(g) + 2Mg(s) 2MgCl2(s) + Si(s)

Substance: SiCl4(g) Mg(s) MgCl2(s) Si(s)

G f (kJ/mol) –616.98 0 –591.79 0

a. 566.60 kJ

b. 50.38 kJ

c. 25.19 kJ d. –25.19 kJ

e. –566.60 kJ

42. Calculate G for the combustion of propane. E

C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(g)

Substance: C3H8(g) O2(g) CO2(g) H2O(g)

G f (kJ/mol): –24.5 0 –394.4 –228.6

a. –2073.1 kJ

b. –1387.3 kJ

c. –598.5 kJ

d. 598.5 kJ

e. 2073.1 kJ

327

43. Elemental boron can be formed by reaction of boron trichloride with hydrogen.

E

BCl3(g) + 1.5H2(g) B(s) + 3HCl(g)

Calculate G for the reaction.

Substance: BCI3(g) H2(g) B(s) HCl(g)

G f (kJ/mol): –388.7 0 0 –95.3

a. –293.4 kJ

b. 293.4 kJ c. –102.8 kJ

d. 102.8 kJ

e. none of the above

44. Calculate G for the reaction of ammonia with fluorine. E

2NH3(g) + 5F2(g) N2F4(g) + 6HF(g)

Substance: NH3(g) F2(g) N2F4(g) HF(g)

G f (kJ/mol): –16.4 0 79.9 –275.4

a. 179.1 kJ

b. –179.1 kJ

c. 1539.7 kJ

d. –1539.7 kJ

e. none of the above

45. Use the given data at 298 K to calculate G for the reaction H

2Cl2(g) + SO2(g) SOCl2(g) + Cl2O(g)

Substance: Cl2(g) SO2(g) SOCl2(g) Cl2O(g)

H f (kJ/mol): 0 –296.8 –212.5 80.3

S°(J/K mol): 223.0 248.1 309.77 266.1

a. 129.3 kJ

b. 133.6 kJ

c. 196.0 kJ

d. 199.8 kJ

e. 229.6 kJ

46. Hydrogen sulfide decomposes according to the following reaction

H

2H2S(g) 2H2(g) + S2(g)

For this reaction at 298K S = 78.1 J/K, H

= 169.4 kJ, and G = 146.1 kJ. What is the value of

G at 900 K?

a. –69881 kJ

b. 48.4 kJ

c. 99.1 kJ

d. 240 kJ

e. 441 kJ

328

47. Nitric oxide reacts with chlorine to form NOCl. The data refer to 298 K.

M

2NO(g) + Cl2(g) 2NOCl(g)

Substance: NO(g) Cl2(g) NOCl(g)

H f (kJ/mol): 90.29 0 51.71

G f (kJ/mol): 86.60 0 66.07

S°(J/K mol): 210.65 223.0 261.6

What is the value of G for this reaction at 550 K?

a. –143.76 kJ

b. –78.78 kJ

c. –22.24 kJ d. –10.56 kJ

e. 66600 kJ

48. Sulfuryl dichloride is formed when sulfur dioxide reacts with chlorine. The data refer to 298 K.

M

SO2(g) + Cl2(g) SO2Cl2(g)

Substance: SO2(g) Cl2(g) SO2Cl2(g)

H f (kJ/mol): –296.8 0 –364.0

G f (kJ/mol): –300.1 0 –320.0

S°(J/K mol): 248.2 223.0 311.9

What is the value of G for this reaction at 600 K?

a. –162.8 kJ

b. –40.1 kJ

c. –28.4 kJ

d. 28.4 kJ e. 162.8 kJ

49. The temperature at which the following process reaches equilibrium at 1.0 atm is the normal boiling point of

M hydrogen peroxide.

H2O2(l) H2O2(g)

Use the following thermodynamic information at 298 K to determine this temperature.

Substance: H2O2(l) H2O2(g)

H f (kJ/mol): –187.7 –136.3

G f (kJ/mol): –120.4 –105.6

S° (J/K mol): 109.6 232.7

a. 120 C

b. 144 C

c. 196 C

d. 418 C

e. 585 C

329

50. The temperature at which the following process reaches equilibrium at 1.0 atm is the normal melting point

M for phosphoric acid.

H3PO4(s) H3PO4(l)

Use the following thermodynamic data at 298 K to determine this temperature.

Substance: H3PO4(s) H3PO4(l)

H f (kJ/mol): –1284.4 –1271.7

G f (kJ/mol): –1124.3 –1123.6

S°(J/K mol): 110.5 150.8

a. 286 K

b. 305 K

c. 315 K

d. 347 K

e. 3170 K

51. Consider the figure alongside which

M shows G for a chemical process plotted against absolute temperature.

Which one of the following is an

incorrect conclusion, based on the

information in the diagram?

a. H > 0

b. S > 0 c. The reaction is spontaneous at high temperatures.

d. S increases with temperature while H remains constant.

e. There exists a certain temperature at which H = T S .


E shows G for a chemical process plotted against absolute temperature. From this plot,

it is reasonable to conclude that:

a. H > 0, S > 0

b. H > 0, S < 0

c. H < 0, S > 0

d. H < 0, S < 0 e. none of the above


E shows G for a chemical process plotted against absolute temperature. From this plot,

it is reasonable to conclude that:

a. H > 0, S > 0

b. H > 0, S < 0

c. H < 0, S > 0

d. H < 0, S < 0 e. none of the above

330

54. Iron(III) oxide can be reduced by carbon monoxide.

H

Fe2O3(s) + 3CO(g) 2Fe(s) + 3CO2(g)

Use the following thermodynamic data at 298 K to determine the equilibrium constant at this temperature.

Substance: Fe2O3(s) CO(g) Fe(s) CO2(g)

H f (kJ/mol): –824.2 –110.5 0 –393.5

G f (kJ/mol): –742.2 –137.2 0 –394.4

S°(J/K mol): 87.4 197.7 27.78 213.7

a. 7.0 10–6

b. 1.3 10–3

c. 2.2 104

d. 1.4 105

e. > 2.0 105

55. Calculate the equilibrium constant at 25°C for the reaction of methane with water to form carbon

H dioxide and hydrogen. The data refer to 25°C.

CH4(g) + 2H2O(g) CO2(g) + 4H2(g)

Substance: CH4(g) H2O(g) CO2(g) H2(g)

H f (kJ/mol): –74.87 –241.8 –393.5 0

G f (kJ/mol): –50.81 –228.6 –394.4 0

S° (J/K mol): 186.1 188.8 213.7 130.7

a. 8.2 1019 b. 0.96

c. 0.58

d. 1.2 10–20

e. 1.4 10–46

56. The reaction of methane with water to form carbon dioxide and hydrogen is non-spontaneous at 298 K.

M At what temperature will this system make the transition from non-spontaneous to spontaneous? The data

refer to 298 K.

CH4(g) + 2H2O(g) CO2(g) + 4H2(g)

Substance: CH4(g) H2O(g) CO2(g) H2(g)

H f (kJ/mol): –74.87 –241.8 –393.5 0

G f (kJ/mol): –50.81 –228.6 –394.4 0

S°(J/K mol): 186.1 188.8 213.7 130.7

a. 658 K

b. 683 K

c. 955 K

d. 1047 K

e. 1229 K

331

57. Use the thermodynamic data at 298 K below to determine the Ksp for barium carbonate, BaCO3 at

H this temperature.

Substance: Ba2+(aq) CO32–(aq) BaCO3(s)

H f (kJ/mol): –538.36 –676.26 –1219

G f (kJ/mol): –560.7 –528.1 –1139

S°(J/K mol): 13 –53.1 112

a. 5.86

b. 6.30 108

c. 1.59 10–9

d. 5.47 10–21

e. 2.18 10–27

58. What is the free energy change, G , for the equilibrium between hydrogen iodide, hydrogen, and iodine

M at 453 C? Kc = 0.020

2HI(g) H2(g) + I2(g)

a. 6.4 kJ

b. 8.8 kJ

c. 15 kJ

d. 19 kJ

e. 24 kJ

59. The formation constant for the reaction

M

Ag+(aq) + 2NH3(aq) Ag(NH3)2+(aq)

is Kf = 1.7 107 at 25 C. What is G at this temperature?

a. –1.5 kJ

b. –3.5 kJ

c. –18 kJ

d. –23 kJ

e. –41 kJ

Short Answer Questions

60. a. Explain what is meant by a spontaneous process.

E b. Is a spontaneous process necessarily a rapid one? Explain, and provide a real reaction as an

example to illustrate your answer.

61. For each of the following pairs, predict which (A or B) will have the greater entropy, and in one

E sentence indicate your reasoning.

A B

a. 1 mole of HI(g) 1 mole of HBr(g)

b. 1 mole of HI(g) at 20 C 1 mole of HI(g) at 30 C c. 3 moles of H2(g) + 1 mole of N2(g) 2 moles of NH3(g)

d. 1 mole of H2(g), pressure = 1 atm 1 mole of H2(g), pressure = 0.1 atm

e. 1 mole of CO2(g) 1 mole of CO2(aq)

f. 1 mole of HCOOH(l) 1 mole of HCOOH(aq)

62. In the expression, S = k ln W, W is called the number of microstates. Explain clearly the meaning of the word M “microstate”, and why a system under a given set of conditions normally has many microstates.

332

63 State the second and third laws of thermodynamics.

E

64. In tables of thermodynamic data provided in chemistry books, one finds H f , G f and S listed.

M Briefly, explain why the entropy data are supplied as S , while the enthalpy and free energy data are in the

form of H f and G f, respectively.

65. Given: C2H2(g) 2C(graphite) + H2(g) G = –209 kJ E

A sample of gaseous C2H2 (acetylene, or ethyne) was stored for one year, yet at the end of this period the

sample remained unchanged and no graphite or hydrogen gas had been formed. Briefly explain why there is

no inconsistency between the sign of G and the apparent stability of the sample.

66. The complete combustion of liquid benzene is represented by the equation:

M

C6H6(l) + 7½O2(g) 6CO2(g) + 3H2O(l)

Using the data below, calculate, for this reaction

a. H b. S c. G at 25 C.

Substance: C6H6(l) O2(g) CO2(g) H2O(l)

H f (kJ/mol): 49 0 –394 –286

S (J/mol K): 173 205 214 70

67. For the reaction of xenon and fluorine gases to form solid XeF4, H = –251 kJ and G = –121 kJ at

M 25 C. Calculate S for the reaction.

68. A chemical reaction has G = 10.0 kJ and S = 50.0 J/K

M a. Calculate H for this reaction at 25 C. b. Could this reaction ever be spontaneous? Explain your answer.

69. Photosynthesis can be represented by the equation

M

6CO2(g) + 6H2O(l) C6H12O6(s) + 6O2(g)

a. Calculate S for this process, given the following data:

Substance: CO2(g) H2O(l) C6H12O6(s) O2(g)

S (J/(mol K)): 214 70 212 205

b. Given that H for the reaction is 2802 kJ, calculate G at 25 C.

70. A chemical reaction has H = 42.8 kJ and S = 92.5 J/K, at 25 C. Calculate the temperature at

M which G = 0. State any approximation involved in your calculation.

71. Compare one mole of ice with one mole of liquid water, both at 1.0 atm and 0 C. The melting point

H of ice at 1.0 atm is 0 C. For the process

H2O(s) H2O(l)

under these conditions predict whether each of the following quantities will be greater than, less than, or

equal to, zero (i.e., > 0, < 0 or = 0). Explain each prediction in one sentence.

a. H b. S c. G

333

72. For what signs of H and S will a process E a. be spontaneous at high temperatures but not at low temperatures?

b. not be spontaneous at any temperatures?

73. A reaction has a positive value of H and a positive value of S .

M Draw a neat, labeled schematic plot to show how G (y-axis) will depend on absolute temperature (x-axis)

74. The water-gas shift reaction plays an important role in the production of clean fuel from coal.

H

CO(g) + H2O(g) CO2(g) + H2(g)

Use the following thermodynamic data to determine the equilibrium constant Kp at 700. K.

Substance: CO(g) H2O(g) CO2(g) H2(g)

H f (kJ/mol): –110.5 –241.8 –393.5 0

S°(J/mol K): 197.7 188.8 213.7 130.7

True/False Questions

75. Under a given set of conditions, all microstates of a system are equally probable.

M

76. The term microstate refers to the energy state of a single molecule in a system of many molecules.

M

77. The higher the pressure of a gas sample, the greater is its entropy.

M

78. In a spontaneous process, the entropy of the system always increases.

E

79. In some spontaneous processes, the entropy of the surroundings decreases.

M

80. For a reaction at equilibrium, Suniv = 0. M

81. The free energy of a perfect crystal at absolute zero, is zero.

M

82. For a given reaction, a change in the pressure may result in a change in the sign of G. M

83. For any reaction, if G > 0, then K < 1. E

84. As a chemical reaction proceeds toward equilibrium, the free energy of the system decreases. M

334

Thermodynamics: Entropy, Free Energy, and

the Direction of Chemical Reactions Chapter 20

Answer Key

1. e

2. c

3. d

4. c

5. d

6. b

7. b

8. a

9. c

10. d

11. b

12. b 13. c

14. b

15. e

16. c

17. e

18. a

19. b

20. c

21. b

22. b

23. c

24. e

25. a

26. b

27. e

28. e

29. b

30. a

31. a

32. d 33. c

34. a

35. c

36. b

37. d

38. b

39. e

40. e

41. e

42. a

43. d

44. d

45. d

46. c

47. d

48. d

49. b

50. c

51. d

52. a 53. b

54. d

55. d

56. c

57. c

58. e

59. e

60. a. A spontaneous process is one which will occur naturally, given enough time.

b. No, a spontaneous process may be immeasurably slow. An example is the conversion of diamond to graphite at room temperature and one atmosphere.

61. a. A has greater entropy. HI and HBr are chemically similar, but HI has the higher molar mass.

b. has greater entropy. At the higher temperature, the sample has greater energy and there are more ways

to distribute this energy among the molecules in the sample.

c. A has greater entropy, as it has more moles of gas phase molecules.

d. B has greater entropy. At the lower pressure, the volume is larger and there is more positional disorder

in the sample.

e. A has greater entropy. A substance has a greater entropy in the gas phase than in solution.

f. B has the greater entropy. When a solid or liquid dissolves, it has a greater volume available to it, and

is thus more disordered.

62. A microstate is a specific, quantized state of a system. Each microstate represents a different way of

distributing the available energy of a system among the various energy states (electronic, vibrational,

rotational and translational) of all the individual molecules. There are many different ways of distributing a

fixed total energy among the individual molecules, hence there are many different microstates of the system.

63. All spontaneous processes are accompanied by an increase in the total entropy of the universe.

The entropy of a perfect crystal at absolute zero, is zero.

64. The third law specifies the state of zero of entropy as being a perfect crystal at absolute zero. From this

starting point, absolute entropies can be determined for other temperatures too. There is no corresponding

absolute zero of enthalpy or free energy; their zero values are arbitrarily set as being the elements in their standard states at one atmosphere and a specified temperature. Standard enthalpies and free energies of

formation are relative to this arbitrary zero.

335

65. Relative to graphite and hydrogen, acetylene is unstable. Its decomposition to form these products is

spontaneous, as the negative sign of G suggests. However, the kinetics of the decomposition are immeasurably slow under normal conditions.

66. H = –3271 kJ S = –217 J/K G = –3206 kJ

67. S = –436 J/K

68. a. H = 24.9 kJ

b. Yes. Assuming that H and S do not change much with temperature, at a sufficiently high

temperature, H – T S will be less than zero, and the reaction will be spontaneous.

69. a. S = –262 J/K

b. G = 2880. kJ

70. T = 463 K. The calculation is based on the assumption that H and S do not change significantly with change in temperature.

71. a. H > 0. The solid-to-liquid phase change is always endothermic.

b. S > 0. A liquid is always more disordered than the corresponding solid.

c. G = 0. At this temperature and pressure, the solid and liquid phases are in equilibrium.

72. a. H > 0, S > 0

b. H > 0, S < 0

73.

74. Kp = 7.50

75. T

76. F

77. F

78. F

79. T

80. T

81. F

82. T

83. T

84. T

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