Edward J. Neth; Paul Flowers; William R. Robinson, PhD; Klaus Theopold; Richard Langley

12.1 Spontaneity

1.

What is a spontaneous reaction?

2.

What is a nonspontaneous reaction?

3.

Indicate whether the following processes are spontaneous or nonspontaneous.

(a) Liquid water freezing at a temperature below its freezing point

(b) Liquid water freezing at a temperature above its freezing point

(c) The combustion of gasoline

(d) A ball thrown into the air

(e) A raindrop falling to the ground

(f) Iron rusting in a moist atmosphere

4.

A helium-filled balloon spontaneously deflates overnight as He atoms diffuse through the wall of the balloon. Describe the redistribution of matter and/or energy that accompanies this process.

5.

Many plastic materials are organic polymers that contain carbon and hydrogen. The oxidation of these plastics in air to form carbon dioxide and water is a spontaneous process; however, plastic materials tend to persist in the environment. Explain.

12.2 Entropy

6.

In Figure 12.8 all possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, ΔS, if the particles are initially evenly distributed between the two boxes, but upon redistribution all end up in Box (b).

7.

In Figure 12.8 all of the possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, ΔS, for the system when it is converted from distribution (b) to distribution (d).

8.

How does the process described in the previous item relate to the system shown in Figure 12.4?

9.

Consider a system similar to the one in Figure 12.8, except that it contains six particles instead of four. What is the probability of having all the particles in only one of the two boxes in the case? Compare this with the similar probability for the system of four particles that we have derived to be equal to $\frac{1}{8} .$ What does this comparison tell us about even larger systems?

10.

Consider the system shown in Figure 12.9. What is the change in entropy for the process where the energy is initially associated only with particle A, but in the final state the energy is distributed between two different particles?

11.

Consider the system shown in Figure 12.9. What is the change in entropy for the process where the energy is initially associated with particles A and B, and the energy is distributed between two particles in different boxes (one in A-B, the other in C-D)?

12.

Arrange the following sets of systems in order of increasing entropy. Assume one mole of each substance and the same temperature for each member of a set.

(a) H₂(g), HBrO₄(g), HBr(g)

(b) H₂O(l), H₂O(g), H₂O(s)

(c) He(g), Cl₂(g), P₄(g)

13.

At room temperature, the entropy of the halogens increases from I₂ to Br₂ to Cl₂. Explain.

14.

Consider two processes: sublimation of I₂(s) and melting of I₂(s) (Note: the latter process can occur at the same temperature but somewhat higher pressure).

$I_{2} (s) ⟶ I_{2} (g)$

$I_{2} (s) ⟶ I_{2} (l)$

Is ΔS positive or negative in these processes? In which of the processes will the magnitude of the entropy change be greater?

15.

Indicate which substance in the given pairs has the higher entropy value. Explain your choices.

(a) C₂H₅OH(l) or C₃H₇OH(l)

(b) C₂H₅OH(l) or C₂H₅OH(g)

(c) 2H(g) or H(g)

16.

Predict the sign of the entropy change for the following processes.

(a) An ice cube is warmed to near its melting point.

(b) Exhaled breath forms fog on a cold morning.

(c) Snow melts.

17.

Predict the sign of the entropy change for the following processes. Give a reason for your prediction.

(a) ${Pb}^{2+} (a q) + S^{2−} (a q) ⟶ PbS (s)$

(b) $2 Fe (s) + \frac{3}{2} O_{2} (g) ⟶ {Fe}_{2} O_{2} (s)$

(c) $2 C_{6} H_{14} (l) + 19 O_{2} (g) ⟶ 14 H_{2} O (g) + 12 {CO}_{2} (g)$

18.

Write the balanced chemical equation for the combustion of methane, CH₄(g), to give carbon dioxide and water vapor. Explain why it is difficult to predict whether ΔS is positive or negative for this chemical reaction.

19.

Write the balanced chemical equation for the combustion of benzene, C₆H₆(l), to give carbon dioxide and water vapor. Would you expect ΔS to be positive or negative in this process?

12.3 The Second and Third Laws of Thermodynamics

20.

What is the difference between ΔS, ΔS°, and $Δ S_{298}^{°}$ for a chemical change?

21.

Calculate $Δ S_{298}^{°}$ for the following changes.

(a) ${SnCl}_{4} (l) ⟶ {SnCl}_{4} (g)$

(b) ${CS}_{2} (g) ⟶ {CS}_{2} (l)$

(c) $Cu (s) ⟶ Cu (g)$

(d) $H_{2} O (l) ⟶ H_{2} O (g)$

(e) $2 H_{2} (g) + O_{2} (g) ⟶ 2 H_{2} O (l)$

(f) $2 HCl (g) + Pb (s) ⟶ {PbCl}_{2} (s) + H_{2} (g)$

(g) $Zn (s) + {CuSO}_{4} (s) ⟶ Cu (s) + {ZnSO}_{4} (s)$

22.

Determine the entropy change for the combustion of liquid ethanol, C₂H₅OH, under the standard conditions to give gaseous carbon dioxide and liquid water.

23.

Determine the entropy change for the combustion of gaseous propane, C₃H₈, under the standard conditions to give gaseous carbon dioxide and water.

24.

“Thermite” reactions have been used for welding metal parts such as railway rails and in metal refining. One such thermite reaction is ${Fe}_{2} O_{3} (s) + 2 Al (s) ⟶ {Al}_{2} O_{3} (s) + 2 Fe (s) .$ Is the reaction spontaneous at room temperature under standard conditions? During the reaction, the surroundings absorb 851.8 kJ/mol of heat.

25.

Using the relevant $S_{298}^{°}$ values listed in Appendix G, calculate $S_{Δ 298}^{°}$ for the following changes:

(a) $N_{2} (g) + 3 H_{2} (g) ⟶ 2 {NH}_{3} (g)$

(b) $N_{2} (g) + \frac{5}{2} O_{2} (g) ⟶ N_{2} O_{5} (g)$

26.

From the following information, determine $Δ S_{298}^{°}$ for the following:

$N (g) + O (g) ⟶ NO (g) Δ S_{298}^{°} = ?$

$N_{2} (g) + O_{2} (g) ⟶ 2 NO (g) Δ S_{298}^{°} = 24.8 J/K$

$N_{2} (g) ⟶ 2 N (g) Δ S_{298}^{°} = 115.0 J/K$

$O_{2} (g) ⟶ 2 O (g) Δ S_{298}^{°} = 117.0 J/K$

27.

By calculating ΔS_univ at each temperature, determine if the melting of 1 mole of NaCl(s) is spontaneous at 500 °C and at 700 °C.
$S_{NaCl (s)}^{°} = 72.11 \frac{J}{mol·K} S_{NaCl (l)}^{°} = 95.06 \frac{J}{mol·K} Δ H_{fusion}^{°} = 27.95 kJ/mol$

What assumptions are made about the thermodynamic information (entropy and enthalpy values) used to solve this problem?

28.

Use the standard entropy data in Appendix G to determine the change in entropy for each of the reactions listed in Exercise 12.30. All the processes occur at the standard conditions and 25 °C.

29.

Use the standard entropy data in Appendix G to determine the change in entropy for each of the reactions listed in Exercise 12.6. All the processes occur at the standard conditions and 25 °C.

12.4 Free Energy

30.

What is the difference between ΔG, ΔG°, and $Δ G_{298}^{°}$ for a chemical change?

31.

A reaction has $Δ H_{298}^{°}$ = 100 kJ/mol and $Δ S_{298}^{°} = 250 J/mol·K.$ Is the reaction spontaneous at room temperature? If not, under what temperature conditions will it become spontaneous?

32.

Explain what happens as a reaction starts with ΔG < 0 (negative) and reaches the point where ΔG = 0.

33.

Use the standard free energy of formation data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.

(a) ${MnO}_{2} (s) ⟶ Mn (s) + O_{2} (g)$

(b) $H_{2} (g) + {Br}_{2} (l) ⟶ 2HBr (g)$

(c) $Cu (s) + S (g) ⟶ CuS (s)$

(d) $2LiOH (s) + {CO}_{2} (g) ⟶ {Li}_{2} {CO}_{3} (s) + H_{2} O (g)$

(e) ${CH}_{4} (g) + O_{2} (g) ⟶ C (s, graphite) + {2H}_{2} O (g)$

(f) ${CS}_{2} (g) + {3Cl}_{2} (g) ⟶ {CCl}_{4} (g) + S_{2} {Cl}_{2} (g)$

34.

Use the standard free energy data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.

(a) $C (s, graphite) + O_{2} (g) ⟶ {CO}_{2} (g)$

(b) $O_{2} (g) + N_{2} (g) ⟶ 2NO (g)$

(c) $2Cu (s) + S (g) ⟶ {Cu}_{2} S (s)$

(d) $CaO (s) + H_{2} O (l) ⟶ Ca {(OH)}_{2} (s)$

(e) ${Fe}_{2} O_{3} (s) + 3CO (g) ⟶ 2Fe (s) + {3CO}_{2} (g)$

(f) ${CaSO}_{4} · {2H}_{2} O (s) ⟶ {CaSO}_{4} (s) + {2H}_{2} O (g)$

35.

Given:
$P_{4} (s) + {5O}_{2} (g) ⟶ P_{4} O_{10} (s) Δ G_{298}^{°} = −2697.0 kJ/mol$
${2H}_{2} (g) + O_{2} (g) ⟶ {2H}_{2} O (g) Δ G_{298}^{°} = −457.18 kJ/mol$
${6H}_{2} O (g) + P_{4} O_{10} (s) ⟶ {4H}_{3} {PO}_{4} (l) Δ G_{298}^{°} = −428.66 kJ/mol$

(a) Determine the standard free energy of formation, $Δ G_{f}^{°},$ for phosphoric acid.

(b) How does your calculated result compare to the value in Appendix G? Explain.

36.

Is the formation of ozone (O₃(g)) from oxygen (O₂(g)) spontaneous at room temperature under standard state conditions?

37.

Consider the decomposition of red mercury(II) oxide under standard state conditions.
$2HgO (s, red) ⟶ 2Hg (l) + O_{2} (g)$

(a) Is the decomposition spontaneous under standard state conditions?

(b) Above what temperature does the reaction become spontaneous?

38.

Among other things, an ideal fuel for the control thrusters of a space vehicle should decompose in a spontaneous exothermic reaction when exposed to the appropriate catalyst. Evaluate the following substances under standard state conditions as suitable candidates for fuels.

(a) Ammonia: ${2NH}_{3} (g) ⟶ N_{2} (g) + {3H}_{2} (g)$

(b) Diborane: $B_{2} H_{6} (g) ⟶ 2B (g) + {3H}_{2} (g)$

(c) Hydrazine: $N_{2} H_{4} (g) ⟶ N_{2} (g) + {2H}_{2} (g)$

(d) Hydrogen peroxide: $H_{2} O_{2} (l) ⟶ H_{2} O (g) + \frac{1}{2} O_{2} (g)$

39.

Calculate ΔG° for each of the following reactions from the equilibrium constant at the temperature given.

(a) $N_{2} (g) + O_{2} (g) ⟶ 2NO (g) T = 2000 °C K_{p} = 4.1 \times 10^{−4}$

(b) $H_{2} (g) + I_{2} (g) ⟶ 2HI (g) T = 400 °C K_{p} = 50.0$

(c) ${CO}_{2} (g) + H_{2} (g) ⟶ CO (g) + H_{2} O (g) T = 980 °C K_{p} = 1.67$

(d) ${CaCO}_{3} (s) ⟶ CaO (s) + {CO}_{2} (g) T = 900 °C K_{p} = 1.04$

(e) $HF (a q) + H_{2} O (l) ⟶ H_{3} O^{+} (a q) + F^{−} (a q) T = 25 °C K_{p} = 7.2 \times 10^{−4}$

(f) $AgBr (s) ⟶ {Ag}^{+} (a q) + {Br}^{−} (a q) T = 25 °C K_{p} = 3.3 \times 10^{−13}$

40.

Calculate ΔG° for each of the following reactions from the equilibrium constant at the temperature given.

(a) ${Cl}_{2} (g) + {Br}_{2} (g) ⟶ 2BrCl (g) T = 25 °C K_{p} = 4.7 \times 10^{−2}$

(b) ${2SO}_{2} (g) + O_{2} (g) ⇌ {2SO}_{3} (g) T = 500 °C K_{p} = 48.2$

(c) $H_{2} O (l) ⇌ H_{2} O (g) T = 60 °C K_{p} = 0.196 atm$

(d) $CoO (s) + CO (g) ⇌ Co (s) + {CO}_{2} (g) T = 550 °C K_{p} = 4.90 \times 10^{2}$

(e) ${CH}_{3} {NH}_{2} (a q) + H_{2} O (l) ⟶ {CH}_{3} {NH}_{3}^{+} (a q) + {OH}^{−} (a q) T = 25 °C K_{p} = 4.4 \times 10^{−4}$

(f) ${PbI}_{2} (s) ⟶ {Pb}^{2+} (a q) + {2I}^{−} (a q) T = 25 °C K_{p} = 8.7 \times 10^{−9}$

41.

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of ΔG° given.

(a) $O_{2} (g) + {2F}_{2} (g) ⟶ {2OF}_{2} (g) Δ G ° = −9.2 kJ$

(b) $I_{2} (s) + {Br}_{2} (l) ⟶ 2IBr (g) Δ G ° = 7.3 kJ$

(c) $2LiOH (s) + {CO}_{2} (g) ⟶ {Li}_{2} {CO}_{3} (s) + H_{2} O (g) Δ G ° = −79 kJ$

(d) $N_{2} O_{3} (g) ⟶ NO (g) + {NO}_{2} (g) Δ G ° = −1.6 kJ$

(e) ${SnCl}_{4} (l) ⟶ {SnCl}_{4} (l) Δ G ° = 8.0 kJ$

42.

Nitric acid, HNO₃, can be prepared by the following sequence of reactions:
${4NH}_{3} (g) + {5O}_{2} (g) ⟶ 4NO (g) + {6H}_{2} O (g)$
$2NO (g) + O_{2} (g) ⟶ {2NO}_{2} (g)$
${3NO}_{2} (g) + H_{2} O (l) ⟶ {2HNO}_{3} (l) + NO (g)$

How much heat is evolved when 1 mol of NH₃(g) is converted to HNO₃(l)? Assume standard states at 25 °C.

43.

Determine ΔGº for the following reactions.

(a) Antimony pentachloride decomposes at 448 °C. The reaction is:
${SbCl}_{5} (g) ⟶ {SbCl}_{3} (g) + {Cl}_{2} (g)$

An equilibrium mixture in a 5.00 L flask at 448 °C contains 3.85 g of SbCl₅, 9.14 g of SbCl₃, and 2.84 g of Cl₂.

(b) Chlorine molecules dissociate according to this reaction:
${Cl}_{2} (g) ⟶ 2 Cl (g)$

1.00% of Cl₂ molecules dissociate at 975 K and a pressure of 1.00 atm.

44.

Given that the $Δ G_{f}^{°}$ for Pb²⁺(aq) and Cl⁻(aq) is −24.3 kJ/mole and −131.2 kJ/mole respectively, determine the solubility product, K_sp, for PbCl₂(s).

45.

Determine the standard free energy change, $Δ G_{f}^{°},$ for the formation of S²⁻(aq) given that the $Δ G_{f}^{°}$ for Ag⁺(aq) and Ag₂S(s) are 77.1 k/mole and −39.5 kJ/mole respectively, and the solubility product for Ag₂S(s) is 8 $\times$ 10⁻⁵¹.

46.

Determine the standard enthalpy change, entropy change, and free energy change for the conversion of diamond to graphite. Discuss the spontaneity of the conversion with respect to the enthalpy and entropy changes. Explain why diamond spontaneously changing into graphite is not observed.

47.

The evaporation of one mole of water at 298 K has a standard free energy change of 8.58 kJ.
$H_{2} O (l) ⇌ H_{2} O (g) Δ G_{298}^{°} = 8.58 kJ$

(a) Is the evaporation of water under standard thermodynamic conditions spontaneous?

(b) Determine the equilibrium constant, K_P, for this physical process.

(c) By calculating ∆G, determine if the evaporation of water at 298 K is spontaneous when the partial pressure of water, $P_{H_{2} O},$ is 0.011 atm.

(d) If the evaporation of water were always nonspontaneous at room temperature, wet laundry would never dry when placed outside. In order for laundry to dry, what must be the value of $P_{H_{2} O}$ in the air?

48.

In glycolysis, the reaction of glucose (Glu) to form glucose-6-phosphate (G6P) requires ATP to be present as described by the following equation:
$Glu + ATP ⟶ G6P + ADP Δ G_{298}^{°} = −17 kJ$

In this process, ATP becomes ADP summarized by the following equation:
$ATP ⟶ ADP Δ G_{298}^{°} = −30 kJ$

Determine the standard free energy change for the following reaction, and explain why ATP is necessary to drive this process:
$Glu ⟶ G6P Δ G_{298}^{°} = ?$

49.

One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate (G6P) to form fructose-6-phosphate (F6P):
$G6P ⇌ F6P Δ G_{298}^{°} = 1.7 kJ$

(a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?

(b) Standard thermodynamic conditions imply the concentrations of G6P and F6P to be 1 M, however, in a typical cell, they are not even close to these values. Calculate ΔG when the concentrations of G6P and F6P are 120 μM and 28 μM respectively, and discuss the spontaneity of the forward reaction under these conditions. Assume the temperature is 37 °C.

50.

Without doing a numerical calculation, determine which of the following will reduce the free energy change for the reaction, that is, make it less positive or more negative, when the temperature is increased. Explain.

(a) $N_{2} (g) + {3H}_{2} (g) ⟶ {2NH}_{3} (g)$

(b) $HCl (g) + {NH}_{3} (g) ⟶ {NH}_{4} Cl (s)$

(c) ${({NH}_{4})}_{2} {Cr}_{2} O_{7} (s) ⟶ {Cr}_{2} O_{3} (s) + {4H}_{2} O (g) + N_{2} (g)$

(d) $2Fe (s) + {3O}_{2} (g) ⟶ {Fe}_{2} O_{3} (s)$

51.

When ammonium chloride is added to water and stirred, it dissolves spontaneously and the resulting solution feels cold. Without doing any calculations, deduce the signs of ΔG, ΔH, and ΔS for this process, and justify your choices.

52.

An important source of copper is from the copper ore, chalcocite, a form of copper(I) sulfide. When heated, the Cu₂S decomposes to form copper and sulfur described by the following equation:
${Cu}_{2} S (s) ⟶ Cu (s) + S (s)$

(a) Determine $Δ G_{298}^{°}$ for the decomposition of Cu₂S(s).

(b) The reaction of sulfur with oxygen yields sulfur dioxide as the only product. Write an equation that describes this reaction, and determine $Δ G_{298}^{°}$ for the process.

(c) The production of copper from chalcocite is performed by roasting the Cu₂S in air to produce the Cu. By combining the equations from Parts (a) and (b), write the equation that describes the roasting of the chalcocite, and explain why coupling these reactions together makes for a more efficient process for the production of the copper.

53.

What happens to $Δ G$ (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?

(a) $S (s) + O_{2} (g) ⟶ {SO}_{2} (g)$

(b) ${2SO}_{2} (g) + O_{2} (g) ⟶ {SO}_{3} (g)$

(c) $HgO (s) ⟶ Hg (l) + O_{2} (g)$

Exercises

12.1 Spontaneity

12.2 Entropy

12.3 The Second and Third Laws of Thermodynamics

12.4 Free Energy