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Chemistry 2012

JOHN E. MCMURRY, ROBERT C. FAY, JORDAN FANTINI

Chapter 16

Thermodynamics: Entropy, Free Energy, and Equilibrium

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SS

Problem 1

Which of the following processes are spontaneous? Which are nonspontaneous?
(a) Diffusion of perfume molecules from one side of a room to the other
(b) Heat flow from a cold object to a hot object
(c) Decomposition of rust $\left(\mathrm{Fe}_{2} \mathrm{O}_{3} \cdot \mathrm{H}_{2} \mathrm{O}\right)$ to iron metal, oxygen, and water
(d) Decomposition of solid $\mathrm{CaCO}_{3}$ to solid CaO and gaseous $\mathrm{CO}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 atm pressure $\left(K_{\mathrm{p}}=1.4 \times 10^{-23}\right)$

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Problem 2

Predict the sign of $\Delta S$ in the system for each of the following processes:
(a) $\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)$ (formation of rain droplets)
(b) $\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{I}(g)$
(c) $\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$
(d) $\mathrm{Ag}^{+}(a q)+\mathrm{Br}^{-}(a q) \longrightarrow \mathrm{AgBr}(s)$

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Problem 3

Consider the gas-phase reaction of $\mathrm{AB}_{3}$ and $\mathrm{A}_{2}$ molecules:
(a) Write a balanced equation for the reaction.
(b) What is the sign of the entropy change for the reaction?

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Problem 4

Which state has the higher entropy? Explain in terms of probability.
(a) A perfectly ordered crystal of solid nitrous oxide (N $(\mathrm{N} \equiv \mathrm{N}-\mathrm{O})$ or a disordered crystal in which the molecules are oriented randomly
(b) Quartz glass (Section 10.10) or a quartz crystal
(c) 1 $\mathrm{mol}$ of $\mathrm{N}_{2}$ gas at $\mathrm{STP}$ or 1 $\mathrm{mol}$ of $\mathrm{N}_{2}$ gas at 273 $\mathrm{K}$ in a volume of 11.2 $\mathrm{L}$
(d) 1 $\mathrm{mol}$ of $\mathrm{N}_{2}$ gas at $\mathrm{STP}$ or 1 $\mathrm{mol}$ of 1 $\mathrm{mol}$ of $\mathrm{N}_{2}$ gas at 273 $\mathrm{K}$ and 0.25 $\mathrm{atm}$

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Problem 5

Calculate the standard entropy of reaction at $25^{\circ} \mathrm{C}$ for the decomposition of calcium carbonate:
$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(g)$$

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Problem 6

By determining the sign of $\Delta S_{\text { total }}$, show whether the decomposition of calcium carbonate is spontaneous under standard-state conditions at $25^{\circ} \mathrm{C}$.
$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(g)$$

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Problem 7

Consider the decomposition of gaseous $\mathrm{N}_{2} \mathrm{O}_{4}$:
$$\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H^{\circ}=+55.3 \mathrm{kJ} ; \Delta S^{\circ}=+175.7 \mathrm{J} / \mathrm{K}$$
(a) Is this reaction spontaneous under standard-state conditions at $25^{\circ} \mathrm{C} ?$
(b) Estimate the temperature at which the reaction becomes spontaneous.

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Problem 8

The following data apply to the vaporization of mercury: $\Delta H_{\mathrm{vap}}=59.11 \mathrm{kJ} / \mathrm{mol} ; \Delta S_{\mathrm{vap}}=93.9 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$
(a) Does mercury boil at 325 °C and 1 atm pressure?
(b) What is the normal boiling point of mercury?

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Problem 9

What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for the following spontaneous reaction of A atoms (red) and B atoms (blue)?

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Problem 10

Consider the thermal decomposition of calcium carbonate:
$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(g)$$
(a) Use the data in Appendix B to calculate the standard free-energy change for this reaction at $25^{\circ} \mathrm{C}$.
(b) Will a mixture of solid $\mathrm{CaCO}_{3}$, solid $\mathrm{CaO}$, and gaseous $\mathrm{CO}_{2}$ at 1 atm pressure react spontaneously at $25^{\circ} \mathrm{C}$ to produce more $\mathrm{CaO}$ and $\mathrm{CO}_{2}$?
(c) Assuming that and are independent of temperature, estimate the temperature at which the reaction becomes spontaneous.

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Problem 11

Consider the following endothermic decomposition of $\mathrm{AB}_{2}$ molecules:
(a) What is the $\operatorname{sign}(+,-, \text { or } 0)$ of $\Delta S^{\circ}$ for the reaction?
(b) Is the reaction more likely to be spontaneous at high temperatures or at low temperatures? Explain.

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Problem 12

(a) Using values of $\Delta G^{\circ}_{f}$ in Appendix B, calculate the standard free-energy change for
the reaction of calcium carbide $\left(\mathrm{CaC}_{2}\right)$ with water. Might this reaction be used for synthesis of acetylene $\left(\mathrm{HC} \equiv \mathrm{CH}, \text { or } \mathrm{C}_{2} \mathrm{H}_{2}\right) ?$
$$\mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{Ca}(\mathrm{OH})_{2}(s)$$
(b) Is it possible to synthesize acetylene from solid graphite and gaseous $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 atm pressure?

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Problem 13

Calculate $\Delta G$ for the formation of ethylene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$ from carbon and hydrogen at $25^{\circ} \mathrm{C}$ when the partial pressures are 100 atm $\mathrm{H}_{2}$ and 0.10 $\mathrm{atm} \mathrm{C}_{2} \mathrm{H}_{4}$.
$$2 \mathrm{C}(s)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g) \quad \Delta G^{\circ}=68.1 \mathrm{kJ}$$
Is the reaction spontaneous in the forward or the reverse direction?

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Problem 14

Consider the following gas-phase reaction of $\mathrm{A}_{2}$ (red) and $\mathrm{B}_{2}$ (blue) molecules:
$$\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB} \quad \Delta G^{\circ}=15 \mathrm{kJ}$$
(a) Which of the following reaction mixtures has the largest $\Delta G$ of reaction? Which has the smallest?
(b) If the partial pressure of each reactant and product in reaction mixture 1 is equal to 1 atm, what is the value of $\Delta G$ for the reaction in mixture 1$?$

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Problem 15

Given the data in Appendix $\mathrm{B}$ , calculate $K_{\mathrm{p}}$ at $25^{\circ} \mathrm{C}$ for the reaction $\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$.

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Problem 16

Use the data in Appendix B to calculate the vapor pressure of water at $25^{\circ} \mathrm{C}$

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Problem 17

At $25^{\circ} \mathrm{C}, K_{\mathrm{w}}$ for the dissociation of water is $1.0 \times 10^{-14} .$ Calculate $\Delta G^{\circ}$ for the reaction $2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q)$.

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Problem 18

Consider the growth of a human adult from a single cell. Does this process violate the second law of thermodynamics? Explain.

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Problem 19

If you watched a movie run backward, would you expect to see violations of the second law? Explain.

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Problem 20

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.
(a) Sketch the final (equilibrium) state of the system.
(b) What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for this process? Explain.
(c) How does this process illustrate the second law of thermodynamics?
(d) Is the reverse process spontaneous or nonspontaneous? Explain.

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Problem 21

What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for the spontaneous sublimation of a crystalline solid? Explain.

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Problem 22

What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for the spontaneous condensation of a vapor to a liquid? Explain.

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Problem 23

An ideal gas is compressed at constant temperature. What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for the process? Explain.

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Problem 24

Consider the following spontaneous reaction of $\mathrm{A}_{2}$ molecules (red) and $\mathrm{B}_{2}$ molecules (blue):
(a) Write a balanced equation for the reaction.
(b) What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for the reaction? Explain.

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Problem 25

Consider the dissociation reaction $\mathrm{A}_{2}(g) \Longrightarrow 2 \mathrm{A}(g) .$ The following pictures represent two possible initial states and the equilibrium state of the system:
(a) Is the reaction quotient $Q_{\mathrm{P}}$ for initial state 1 greater than, less than, or equal to the equilibrium constant $K_{\mathrm{p}} ?$ Is $Q_{\mathrm{p}}$ for initial state 2 greater than, less than, or equal to $K_{\mathrm{p}} ?$
(b) What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ when the system goes from initial state 1 to the equilibrium state? Explain. Is this a spontaneous process?
(c) What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ when the system goes from initial state 2 to the equilibrium state? Explain. Is this a spontaneous process?
(d) Relate each of the pictures to the graph in Figure 16.10

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Problem 26

Consider again the dissociation reaction $\mathrm{A}_{2}(g) \rightleftharpoons 2 \mathrm{A}(g)$ (Problem 16.25$)$
(a) What are the signs $(+,-, \text { or } 0)$ of the standard enthalpy change, $\Delta H^{\circ},$ and the standard entropy change, $\Delta S^{\circ},$ for the forward reaction?
(b) Distinguish between the meaning of $\Delta S^{\circ}$ for the dissociation reaction and $\Delta S$ for the process in which the system goes from initial state 1 to the equilibrium state (pictured in Problem 16.25$)$
(c) Can you say anything about the sign of $\Delta G^{\circ}$ for the dissociation reaction? How does $\Delta G^{\circ}$ depend on temperature? Will $\Delta G^{\circ}$ increase, decrease, or remain the same if the temperature increases?
(d) Will the equilibrium constant $K_{\mathrm{p}}$ increase, decrease, or remain the same if the temperature increases? How will the picture for the equilibrium state (Problem 16.25$)$ change if the temperature increases?
(e) What is the value of $\Delta G$ for the dissociation reaction when the system is at equilibrium?

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Problem 27

Consider the following graph of the total free energy of reactants and products versus reaction progress for a general reaction, Reactants $\longrightarrow$ Products:
(a) Account for the shape of the curve, and identify the point at which $\Delta G=0 .$ What is the significance of that point?
(b) Why is the minimum in the plot on the left side of the graph?

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Problem 28

The following pictures represent equilibrium mixtures for the interconversion of A molecules (red) and X, Y, or Z molecules (blue):
What is the sign of $\Delta G^{\circ}$ for each of the three reactions?

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Problem 29

The following pictures represent the composition of the equilibrium mixture at $25^{\circ} \mathrm{C}$ and $45^{\circ} \mathrm{C}$ for the reaction $\mathrm{A} \rightleftharpoons \mathrm{B}$ , where A molecules are represented by red spheres and $\mathrm{B}$ molecules by blue spheres:
What are the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the forward reaction $\mathrm{A} \longrightarrow \mathrm{B}$ ? Explain. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.)

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Problem 30

Which of the following processes are spontaneous, and which are nonspontaneous?
(a) Freezing of water at $2^{\circ} \mathrm{C}$
(b) Corrosion of iron metal
(c) Expansion of a gas to fill the available volume
(d) Separation of an unsaturated aqueous solution of potassium chloride into solid $\mathrm{KCl}$ and liquid water

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Problem 31

Tell whether the following processes are spontaneous or nonspontaneous:
(a) Dissolving sugar in hot coffee
(b) Decomposition of NaCl to solid sodium and gaseous chlorine at $25^{\circ} \mathrm{C}$ and 1 atm pressure
(c) Uniform mixing of bromine vapor and nitrogen gas
(d) Boiling of gasoline at $25^{\circ} \mathrm{C}$ and 1 atm pressure

SS
Summer S.
Numerade Educator

Problem 32

Assuming that gaseous reactants and products are present at 1 atm partial pressure, which of the following reactions are spontaneous in the forward direction?
(a) $\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(l) ; K_{\mathrm{p}}=7 \times 10^{-27}$
(b) $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) ; K_{\mathrm{p}}=2 \times 10^{198}$
(c) $\mathrm{MgCO}_{3}(s) \longrightarrow \mathrm{MgO}(\mathrm{s})+\mathrm{CO}_{2}(g) ; K_{\mathrm{p}}=9 \times 10^{-10}$
(d) $2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) ; K_{\mathrm{p}}=1 \times 10^{90}$

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Problem 33

Assuming that dissolved reactants and products are present at 1 M concentrations, which of the following reactions are nonspontaneous in the forward direction?
$\begin{aligned} \text { (a) } \mathrm{HCN}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{3} \mathrm{O}^{+}(a q)+& \mathrm{CN}^{-}(a q) \\ & K=4.9 \times 10^{-10} \end{aligned}$
(b) $\mathrm{HCN}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) ; K=1.0 \times 10^{14}$
(c) $\mathrm{Ba}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}_{3}(s) ; K=3.8 \times 10^{8}$
(d) $\mathrm{AgCl}(s) \longrightarrow \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) ; K=1.8 \times 10^{-10}$

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Problem 34

Define entropy, and give an example of a process in which the entropy of a system increases.

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Problem 35

Comment on the following statement: Exothermic reactions are spontaneous, but endothermic reactions are nonspontaneous.

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Problem 36

Predict the sign of the entropy change in the system for each of the following processes:
(a) A solid sublimes $\quad$ (b) A liquid freezes
(c) $\mathrm{Ag}$ precipitates from a solution containing $\mathrm{Ag}^{+}$ and $\mathrm{I}^{-}$ ions
(d) Gaseous $\mathrm{CO}_{2}$ bubbles out of a carbonated beverage

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Problem 37

Predict the sign of $\Delta S$ in the system for each of the following reactions:
(a) $\mathrm{PCl}_{5}(s) \longrightarrow \mathrm{PCl}_{3}(l)+\mathrm{Cl}_{2}(g)$
(b) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
(c) $2 \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \longrightarrow \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)$
(d) $\mathrm{Mg}(\mathrm{s})+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{MgCl}_{2}(s)$

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Problem 38

Predict the sign of $\Delta S$ for each process in Problem 16.30

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Problem 39

Predict the sign of $\Delta S$ for each process in Problem 16.31

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Problem 40

Consider a disordered crystal of monodeuteriomethane in which each tetrahedral $\mathrm{CH}_{3} \mathrm{D}$ molecule is oriented randomly in one of four possible ways. Use Boltzmann's formula to calculate the entropy of the disordered state of the crystal if the crystal contains:
(a) 12 molecules $\quad$ (b) 120 molecules
(c) 1 mol of molecules
What is the entropy of the crystal if the C-D bond of each of the $\mathrm{CH}_{3} \mathrm{D}$ molecules points in the same direction?

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Problem 41

Consider the distribution of ideal gas molecules among three bulbs (A, B, and C) of equal volume. For each of the following states, determine the number of ways that the state can be achieved, and use Boltzmann’s formula to calculate the entropy of the state:
(a) 2 molecules in bulb A
(b) 2 molecules randomly distributed among bulbs A, B, and C
(c) 3 molecules in bulb A
(d) 3 molecules randomly distributed among bulbs A, B, and C
(e) 1 mol of molecules in bulb A
(f) 1 mol of molecules randomly distributed among bulbs A, B, and C
What is $\Delta S$ on going from state (e) to state (f)? Compare your result with $\Delta S$ calculated from the equation $\Delta S=n R \ln \left(V_{\text { final }} / V_{\text { initial }}\right)$

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Problem 42

What is the entropy of 100 molecules in a system of 1000 boxes?

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Problem 43

What is the entropy of 100 molecules in a system of 10,000 boxes?

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Problem 44

By what factor does the entropy increase for a collection of 1000 molecules moved from $1 \times 10^{6}$ boxes to $1 \times 10^{7}$ boxes? For a move from $1 \times 10^{16}$ to $1 \times 10^{17}$ boxes? (Express your answers to three significant figures.)

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Problem 45

If the entropy of a collection of molecules in $50,000$ boxes is $3.73 \times 10^{-20} \mathrm{J} / \mathrm{K}$ , how many molecules are there?

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Problem 46

Which state in each of the following pairs has the higher entropy per mole of substance?
(a) $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ in a volume of 10 $\mathrm{L}$ or $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ in a volume of 50 $\mathrm{L}$
(b) $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$ or $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 10 $\mathrm{atm}$
(c) $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$ or $\mathrm{H}_{2}$ at $100^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$
(d) $\mathrm{CO}_{2}$ at $\mathrm{STP}$ or $\mathrm{CO}_{2}$ at $100^{\circ} \mathrm{C}$ and 0.1 $\mathrm{atm}$

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Problem 47

Which state in each of the following pairs has the higher entropy per mole of substance?
(a) Ice at $-40^{\circ} \mathrm{C}$ or ice at $0^{\circ} \mathrm{C}$
(b) $\mathrm{N}_{2}$ at $\mathrm{STP}$ or $\mathrm{N}_{2}$ at $0^{\circ} \mathrm{C}$ and 10 $\mathrm{atm}$
(c) $\mathrm{N}_{2}$ at $\mathrm{STP}$ or $\mathrm{N}_{2}$ at $0^{\circ} \mathrm{C}$ in a volume of 50 $\mathrm{L}$
(d) Water vapor at $150^{\circ} \mathrm{C}$ and 1 atm or water vapor at $100^{\circ} \mathrm{C}$ and 2 $\mathrm{atm}$

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Problem 48

What is the entropy change when the volume of 1.6 $\mathrm{g}$ of $\mathrm{O}_{2}$ increases from 2.5 $\mathrm{L}$ to 3.5 $\mathrm{L}$ at a constant temperature of $75^{\circ} \mathrm{C} ?$ Assume that $\mathrm{O}_{2}$ behaves as an ideal gas.

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Problem 49

What is the value of $\Delta S$ when 2.4 $\mathrm{g}$ of $\mathrm{CH}_{4}$ is compressed from 30.0 $\mathrm{L}$ to 20.0 $\mathrm{L}$ at a constant temperature of $100^{\circ} \mathrm{C} ?$ Assume that $\mathrm{CH}_{4}$ behaves as an ideal gas.

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Problem 50

Which substance in each of the following pairs would you expect to have the higher standard molar entropy? Explain.
(a) $\mathrm{C}_{2} \mathrm{H}_{2}(g)$ or $\mathrm{C}_{2} \mathrm{H}_{6}(g) \quad$ (b) $\mathrm{CO}_{2}(g)$ or $\mathrm{CO}(g)$
(c) $\mathrm{I}_{2}(s)$ or $\mathrm{I}_{2}(g) \quad$ (d) $\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})$ or $\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})$

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Problem 51

Which substance in each of the following pairs would you expect to have the higher standard molar entropy? Explain.
(a) $\mathrm{NO}(g)$ or $\mathrm{NO}_{2}(g) \quad$ (b) $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(l)$ or $\mathrm{HCO}_{2} \mathrm{H}(l)$
(c) $\mathrm{Br}_{2}(l)$ or $\mathrm{Br}_{2}(s) \quad$ (d) $\mathrm{S}(s)$ or $\mathrm{SO}_{3}(g)$

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Problem 52

Use the standard molar entropies in Appendix B to calculate the standard entropy of reaction for the oxidation of carbon monoxide to carbon dioxide:
$$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$$

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Problem 53

Use the standard molar entropies in Appendix B to calculate the standard entropy of reaction for the oxidation of graphite to carbon dioxide:
$$\mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$$

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Problem 54

Use the standard molar entropies in Appendix $\mathrm{B}$ to calculate $\Delta S^{\circ}$ at $25^{\circ} \mathrm{C}$ for each of the following reactions. Account for the sign of the entropy change in each case.
(a) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$
(b) $2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NaCl}(s)$
(c) 2 $\mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g)$
(d) $4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)$

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Problem 55

Use the $S^{\circ}$ values in Appendix $B$ to calculate $\Delta S^{\circ}$ at $25^{\circ} \mathrm{C}$ for each of the following reactions. Suggest a reason for the sign of $\Delta S^{\circ}$ in each case.
(a) $2 \mathrm{S}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)$
(b) $\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q)$
(c) $\mathrm{AgCl}(s) \longrightarrow \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q)$
(d) $\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$

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Problem 56

State the second law of thermodynamics.

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Problem 57

An isolated system is one that exchanges neither matter nor energy with the surroundings. What is the entropy criterion for spontaneous change in an isolated system? Give an example of a spontaneous process in an isolated system.

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Problem 58

Give an equation that relates the entropy change in the surroundings to the enthalpy change in the system. What is the sign of $\Delta S_{\text { surr }}$ for the following?
(a) An exothermic reaction
(b) An endothermic reaction

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Problem 59

When heat is added to the surroundings, the entropy of the surroundings increases. How does $\Delta S_{\text { surr }}$ depend on the temperature of the surroundings? Explain.

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Problem 60

Reduction of mercury(II) oxide with zinc gives metallic mercury:
$$\mathrm{HgO}(s)+\mathrm{Zn}(s) \longrightarrow \mathrm{ZnO}(s)+\mathrm{Hg}(l)$$
(a) If $\Delta H^{\circ}=-259.7 \mathrm{kJ} / \mathrm{mol}$ and $\Delta S^{\circ}=+7.8 \mathrm{J} / \mathrm{K},$ what is $\Delta \mathrm{S}_{\text { total }}$ for this reaction? Is the reaction spontaneous under standard-state conditions at $25^{\circ} \mathrm{C}$ ?
(b) Estimate at what temperature, if any, the reaction will become nonspontaneous.

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Problem 61

Elemental sulfur is formed by the reaction of zinc sulfide with oxygen:
$$2 \mathrm{ZnS}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)+2 \mathrm{S}(s)$$
(a) If $\Delta H^{\circ}=-289.0 \mathrm{kJ} / \mathrm{mol}$ and $\Delta S^{\circ}=-169.4 \mathrm{J} / \mathrm{K},$ what is $\Delta S_{\text { total }}$ for this reaction? Is the reaction spontaneous under standard-state conditions at $25^{\circ} \mathrm{C}$ ?
(b) At what temperature, if any, will the reaction become nonspontaneous?

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Problem 62

In lightning storms, oxygen is converted to ozone:
$3 $\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}_{3}(g)$$
By determining the sign of $\Delta S_{\text { total }},$ show whether the reaction is spontaneous at $25^{\circ} \mathrm{C} .$

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Problem 63

Sulfur dioxide emitted from coal-fired power plants is oxidized to sulfur trioxide in the atmosphere:
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)$$
By determining the sign of $\Delta S_{\text { total }}$ show whether the reaction is spontaneous at $25^{\circ} \mathrm{C}$ .

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Problem 64

Elemental mercury can be produced from its oxide:
$$2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)$$
(a) Use data in Appendix $\mathrm{B}$ to calculate $\Delta S_{\mathrm{sys}}, \Delta S_{\mathrm{surr}}$ and $\Delta S_{\mathrm{total}}$ for this reaction. Is the reaction spontaneous under standard-state conditions at $25^{\circ} \mathrm{C} ?$
(b) Estimate the temperature at which the reaction will become spontaneous.

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Problem 65

Phosphorus pentachloride forms from phosphorus trichloride and chlorine:
$$\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g)$$
(a) Use data in Appendix $\mathrm{B}$ to calculate $\Delta S_{\mathrm{sys}}, \Delta S_{\mathrm{surr}},$ and $\Delta S_{\mathrm{total}}$ for this reaction. Is the reaction spontaneous under standard-state conditions at $25^{\circ} \mathrm{C}$ ?
(b) Estimate the temperature at which the reaction will become nonspontaneous.

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Problem 66

For the vaporization of benzene, $\Delta H_{\mathrm{vap}}=30.7 \mathrm{kJ} / \mathrm{mol}$ and $\Delta S_{\mathrm{vap}}=87.0 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol}) .$ Calculate $\Delta S_{\mathrm{surr}}$ and $\Delta S_{\mathrm{total}}$ at:
(a) $70^{\circ} \mathrm{C} \quad$ (b) $80^{\circ} \mathrm{C} \quad$ (c) $90^{\circ} \mathrm{C}$
Does benzene boil at $70^{\circ} \mathrm{C}$ and 1 atm pressure? Calculate the normal boiling point of benzene.

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Problem 67

For the melting of sodium chloride, $\Delta H_{\text { fusion }}=28.16 \mathrm{kJ} / \mathrm{mol}$ and $\Delta S_{\text { fusion }}=26.22 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol}) .$ Calculate $\Delta S_{\text { surr }}$ and $\Delta S_{\text { total }}$ at:
(a) 1050 $\mathrm{K}$ (b) 1074 $\mathrm{K} \quad$ (c) 1100 $\mathrm{K}$
Does NaCl melt at 1100 $\mathrm{K}$ ? Calculate the melting point of NaCl.

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Problem 68

Describe how the signs of $\Delta H$ and $\Delta S$ determine whether a reaction is spontaneous or nonspontaneous at constant temperature and pressure.

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Problem 69

What determines the direction of a spontaneous reaction when $\Delta H$ and $\Delta S$ are both positive or both negative? Explain.

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Problem 70

The melting point of benzene is $5.5^{\circ} \mathrm{C} .$ Predict the signs of $\Delta H, \Delta S,$ and $\Delta G$ for melting of benzene at:
(a) $0^{\circ} \mathrm{C} \quad$ (b) $15^{\circ} \mathrm{C}$

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Problem 71

Consider a twofold expansion of 1 mol of an ideal gas at $25^{\circ} \mathrm{C}$ in the isolated system shown in Figure 16.1 on page 641 .
(a) What are the values of $\Delta H, \Delta S,$ and $\Delta G$ for the process?
(b) How does this process illustrate the second law of thermodynamics?

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Problem 72

Given the data in Problem $16.66,$ calculate $\Delta G$ for the vaporization of benzene at:
(a) $70^{\circ} \mathrm{C} \quad$ (b) $80^{\circ} \mathrm{C} \quad$ (c) $90^{\circ} \mathrm{C}$
Predict whether benzene will boil at each of these temperatures and 1 atm pressure.

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Problem 73

Given the data in Problem 16.67 , calculate $\Delta G$ for the melting of sodium chloride at:
(a) 1050 $\mathrm{K} \quad$ (b) 1074 $\mathrm{K} \quad$ (c) 1100 $\mathrm{K}$
Predict whether NaCl will melt at each of these temperatures and 1 atm pressure.

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Problem 74

Calculate the melting point of benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\right)$ given the following data: $\Delta H_{\text { fusion }}=18.02 \mathrm{kJ} / \mathrm{mol}$ and $\Delta S_{\text { fusion }}=45.56 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$

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Problem 75

Calculate the enthalpy of fusion of naphthalene $\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)$ given that its melting point is $128^{\circ} \mathrm{C}$ and its entropy of fusion is 47.7 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ .

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Problem 76

Define (a) the standard free-energy change, $\Delta G^{\circ},$ for a reaction and (b) the standard free energy of formation, $\Delta G^{\circ}_{f},$ of a substance.

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Problem 77

What is meant by the standard state of a substance?

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Problem 78

Use the data in Appendix $\mathrm{B}$ to calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for each of the following reactions. From the values of $\Delta H^{\circ}$ and $\Delta S^{\circ},$ calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ and predict whether each reaction is spontaneous under standard-state conditions.
(a) $\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$
(b) $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$
(c) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(l)+\mathrm{H}_{2} \mathrm{O}(l)$

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Problem 79

Use the data in Appendix $\mathrm{B}$ to calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for each of the following reactions. From the values of $\Delta H^{\circ}$ and $\Delta S^{\circ},$ calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ and predict whether each reaction is spontaneous under standard-state conditions.
(a) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)$
(b) $\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(l)$
(c) $\mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{HCO}_{2} \mathrm{H}(l)+\mathrm{H}_{2} \mathrm{O}(l)$

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Problem 80

Use the standard free energies of formation in Appendix $\mathrm{B}$ to calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each reaction in Problem 16.78 .

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Problem 81

Use the standard free energies of formation in Appendix $\mathrm{B}$ to calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each reaction in Problem $16.79 .$

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Problem 82

Use the data in Appendix $\mathrm{B}$ to tell which of the following compounds are thermodynamically stable with respect to their constituent elements at $25^{\circ} \mathrm{C} :$
(a) $\mathrm{BaCO}_{3}(s) \quad$ (b) $\mathrm{HBr}(g)$
(c) $\mathrm{N}_{2} \mathrm{O}(g) \quad$ (d) $\mathrm{C}_{2} \mathrm{H}_{4}(g)$

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Problem 83

Use the data in Appendix $\mathrm{B}$ to decide whether synthesis of the following compounds from their constituent elements is thermodynamically feasible at $25^{\circ} \mathrm{C}$ :
(a) $C_{6} \mathrm{H}_{6}(l) \qquad$ (b) $\mathrm{NO}(g)$
(c) $\mathrm{PH}_{3}(g) \quad$ (d) $\mathrm{FeO}(s)$

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Problem 84

Use the values of $\Delta G^{\circ}_{f}$ in Appendix $B$ to calculate the standard free-energy change for the synthesis of dichloroethane from ethylene and chlorine.
$$\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CH}_{2} \mathrm{ClCH}_{2} \mathrm{Cl}(l)$$
Is it possible to synthesize dichloroethane from gaseous $\mathrm{C}_{2} \mathrm{H}_{4}$ and $\mathrm{Cl}_{2},$ each at $25^{\circ} \mathrm{C}$ and 1 atm pressure?

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Problem 85

Use the values of $\Delta G^{\circ}_{f}$ in Appendix $B$ to calculate the standard free-energy change for the conversion of ammonia tohydrazine:
$$2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{N}_{2} \mathrm{H}_{4}(l)$$
Is it worth trying to find a catalyst for this reaction under standard-state conditions at $25^{\circ} \mathrm{C} ?$

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Problem 86

Use the data in Appendix $\mathrm{B}$ to calculate $\Delta G$ for the decomposition of nitrosyl chloride at $25^{\circ} \mathrm{C}$ when the partial pressures are 2.00 $\mathrm{atm}$ of $\mathrm{NOCl}, 1.00 \times 10^{-3}$ atm of $\mathrm{NO}$ , and $1.00 \times 10^{-3} \mathrm{atm}$ of $\mathrm{Cl}_{2}$
$$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)$$
Is the reaction spontaneous in the forward or the reverse direction under these conditions?

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Problem 87

What is $\Delta G$ for the formation of solid uranium hexafluoride from uranium and fluorine at $25^{\circ} \mathrm{C}$ when the partial pressure of $\mathrm{F}_{2}$ is 0.045 atm? The standard free energy of formation of $\mathrm{UF}_{6}(s)$ is $-2068 \mathrm{kJ} / \mathrm{mol} .$
$$\mathrm{U}(s)+3 \mathrm{F}_{2}(g) \longrightarrow \mathrm{UF}_{6}(\mathrm{s})$$
Is the reaction spontaneous in the forward or the reverse direction under these conditions?

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Problem 88

Ethanol is manufactured in industry by the hydration of ethylene:
$$\mathrm{CH}_{2}=\mathrm{CH}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)$$
Using the data in Appendix $\mathrm{B}$ , calculate $\Delta G^{\circ}$ and show that this reaction is spontaneous at $25^{\circ} \mathrm{C}$ . Why does this reaction become nonspontaneous at higher temperatures? Estimate the temperature at which the reaction becomes nonspontaneous.

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Problem 89

Sulfur dioxide in the effluent gases from coal-burning electric power plants is one of the principal causes of acid rain. One method for reducing $\mathrm{SO}_{2}$ emissions involves partial conversion of $\mathrm{SO}_{2}$ to $\mathrm{H}_{2} \mathrm{S},$ followed by catalytic conversion of the $\mathrm{H}_{2} \mathrm{S}$ and the remaining $\mathrm{SO}_{2}$ to elemental sulfur:
$$2 \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{SO}_{2}(g) \longrightarrow 3 \mathrm{S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)$$
Using the data in Appendix $\mathrm{B}$ , calculate $\Delta G^{\circ}$ and show that this reaction is spontaneous at $25^{\circ} \mathrm{C}$ . Why does this reaction become nonspontaneous at high temperatures? Estimate the temperature at which the reaction becomes nonspontaneous.

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Problem 90

Consider the conversion of acetylene to benzene:
$3 $\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(l)$$
Is a catalyst for this reaction possible? Is it possible to synthesize benzene from graphite and gaseous $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 atm pressure?

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Problem 91

Consider the conversion of 1,2-dichloroethane to vinyl chloride, the starting material for manufacturing
poly(vinyl chloride) (PVC) plastics:
$$\mathrm{CH}_{2} \mathrm{ClCH}_{2} \mathrm{Cl}(l) \longrightarrow \mathrm{CH}_{2}=\mathrm{CHCl}(g)+\mathrm{HCl}(g)$$
Is this reaction spontaneous under standard-state conditions? Would it help to carry out the reaction in the presence of base to remove HCl? Explain. Is it possible to synthesize vinyl chloride from graphite, gaseous $\mathrm{H}_{2}$ , and gaseous $\mathrm{Cl}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 atm pressure?

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Problem 92

What is the relationship between the free-energy change under nonstandard-state conditions, $\Delta G,$ the free-energy change under standard-state conditions, $\Delta G^{\circ},$ and the reaction quotient, $Q ?$

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Problem 93

Compare the values of $\Delta G$ and $\Delta G^{\circ}$ when:
(a) $Q<1 \quad$ (b) $Q=1 \quad$ (c) $Q>1$
Does the thermodynamic tendency for the reaction to occur increase or decrease as increases?

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Problem 94

Sulfuric acid is produced in larger amounts by weight than any other chemical. It is used in manufacturing fertilizers, oil refining, and hundreds of other processes. An inter- mediate step in the industrial process for the synthesis of $\mathrm{H}_{2} \mathrm{SO}_{4}$ is the catalytic oxidation of sulfur dioxide:
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(\mathrm{g}) \quad \Delta G^{\circ}=-141.8 \mathrm{kJ}$$
Calculate $\Delta G$ at $25^{\circ} \mathrm{C},$ given the following sets of partial pressures:
(a) $100 \mathrm{atm} \mathrm{SO}_{2}, 100 \mathrm{atm} \mathrm{O}_{2}, 1.0 \mathrm{atm} \mathrm{SO}_{3}$
(b) $2.0 \mathrm{atm} \mathrm{SO}_{2}, 1.0 \mathrm{atm} \mathrm{O}_{2}, 10 \mathrm{atm} \mathrm{SO}_{3}$
(c) Each reactant and product at a partial pressure of 1.0 $\mathrm{atm}$

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Problem 95

Urea $\left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right),$ an important nitrogen fertilizer, is produced industrially by the reaction
$$ 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l) $$
Given that $\Delta G^{\circ}=-13.6 \mathrm{kJ}$ , calculate $\Delta G$ at $25^{\circ} \mathrm{C}$ for the following sets of conditions:
(a) $10 \mathrm{atm} \mathrm{NH}_{3}, 10 \mathrm{atm} \mathrm{CO}_{2}, 1.0 \mathrm{M} \mathrm{NH}_{2} \mathrm{CONH}_{2}$
(b) $0.10 \mathrm{atm} \mathrm{NH}_{3}, 0.10 \mathrm{atm} \mathrm{CO}_{2}, 1.0 \mathrm{M} \mathrm{NH}_{2} \mathrm{CONH}_{2}$
Is the reaction spontaneous for the conditions in part (a) and/or part (b)?

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Problem 96

What is the relationship between the standard free-energy change, $\Delta G^{\circ},$ for a reaction and the equilibrium constant, $K ?$ What is the sign of $\Delta G^{\circ}$ when:
(a) $K>1 \qquad$ (b) $K=1 \quad$ (c) $K<1$

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Problem 97

Do you expect a large or small value of the equilibrium constant for a reaction with the following values of $\Delta G^{\circ} ?$
(a) $\Delta G^{\circ}$ is positive.
(b) $\Delta G^{\circ}$ is negative.

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Problem 98

Calculate the equilibrium constant $K_{\mathrm{p}}$ at $25^{\circ} \mathrm{C}$ for the reaction in Problem $16.94 .$

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Problem 99

Calculate the equilibrium constant at $25^{\circ} \mathrm{C}$ for the reaction in Problem 16.95 .

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Problem 100

Given values of $\Delta G_{f}^{\circ}$ at $25^{\circ} \mathrm{C}$ for liquid ethanol $(-174.9 \mathrm{kJ} / \mathrm{mol})$ and gaseous ethanol $(-167.9 \mathrm{kJ} / \mathrm{mol})$ , calculate the vapor pressure of ethanol at $25^{\circ} \mathrm{C} .$

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Problem 101

At $25^{\circ} \mathrm{C}, K_{\mathrm{a}}$ for acid dissociation of aspirin $\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)$ is $3.0 \times 10^{-4}$ . Calculate $\Delta G^{\circ}$ for the reaction $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}(a q)+$ $\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{C}_{9} \mathrm{H}_{7} \mathrm{O}_{4}^{-}(a q)$

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Problem 102

If $\Delta G^{\circ}_{f}$ for gaseous bromine is 3.14 $\mathrm{kJ} / \mathrm{mol}$ at $25^{\circ} \mathrm{C},$ what is the vapor pressure of bromine at $25^{\circ} \mathrm{C} ?$

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Problem 103

Calculate the equilibrium partial pressure of iodine vapor above solid iodine at $25^{\circ} \mathrm{C}$ if $\Delta G_{\mathrm{f}}^{\circ}$ for gaseous iodine is 19.4 $\mathrm{kJ} / \mathrm{mol}$ at $25^{\circ} \mathrm{C} .$

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Problem 104

Ethylene oxide, $\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O},$ is used to make antifreeze (ethylene glycol, $\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} )$ . It is produced industrially by
$$2 \mathrm{CH}_{2}=\mathrm{CH}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CH}_{2}-\mathrm{CH}_{2}(g)$$
Use the data in Appendix $\mathrm{B}$ to calculate $\Delta G^{\circ}$ and $K_{\mathrm{p}}$ for this reaction at $25^{\circ} \mathrm{C} .$

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Problem 105

The first step in the commercial production of titaniummetal is the reaction of rutile $\left(\mathrm{T} \mathrm{O}_{2}\right)$ with chlorine and graphite:
$$\mathrm{T} \mathrm{O}_{2}(s)+2 \mathrm{Cl}_{2}(g)+2 \mathrm{C}(s) \longrightarrow \mathrm{TiCl}_{4}(l)+2 \mathrm{CO}(g)$$
Use the data in Appendix $\mathrm{B}$ to calculate $\Delta G^{\circ}$ and the equilibrium constant for this reaction at $25^{\circ} \mathrm{C}$ .

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Problem 106

What is the entropy change when 1.32 of propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ at 0.100 atm pressure is compressed by a factor of five at a constant temperature of $20^{\circ} \mathrm{C} ?$ Assume that propane behaves as an ideal gas.

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Problem 107

Indicate whether the following processes are spontaneous or nonspontaneous:
(a) Heat transfer from a block of ice to a room maintained at $25^{\circ} \mathrm{C}$
(b) Evaporation of water from an open beaker
(c) Conversion of iron(III) oxide to iron metal and oxygen
(d) Uphill motion of an automobile

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Problem 108

Do you agree with the following statements? If not, explain.
(a) Spontaneous reactions are always fast.
(b) In any spontaneous process, the entropy of the system always increases.
(c) An endothermic reaction is always nonspontaneous.
(d) A reaction that is nonspontaneous in the forward direction is always spontaneous in the reverse direction.

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Problem 109

When rolling a pair of dice, there are two ways to get a point total of 3$(1+2 ; 2+1)$ but only one way to get a point total of 2$(1+1) .$ How many ways are there of getting point totals of $4-12 ?$ What is the most probable point total?

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Problem 110

Make a rough, qualitative plot of the standard molar entropy versus temperature for methane from 0 $\mathrm{K}$ to 298 $\mathrm{K} .$ Incorporate the following data into your plot: $\mathrm{mp}=-182^{\circ} \mathrm{C} ;$ $\mathrm{bp}=-164^{\circ} \mathrm{C} ; S^{\circ}=186.2 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ at $25^{\circ} \mathrm{C}$

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Problem 111

The standard free-energy change at $25^{\circ} \mathrm{C}$ for the dissociation of water is $79.9 \mathrm{kJ} :$
$$\quad 2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{OH}^{-}(a q) \quad \Delta G^{\circ}=79.9 \mathrm{kJ}$$
For each of the following sets of concentrations, calculate $\Delta G$ at $25^{\circ} \mathrm{C}$ and indicate whether the reaction is spontaneous in the forward or reverse direction:
(a) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=\left[\mathrm{OH}^{-}\right]=1.0 \mathrm{M}$
(b) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}$
(c) $\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M},[\mathrm{OH}]=1.0 \times 10^{-10} \mathrm{M}$
Are your results consistent with Le Chatelier’s principle? Use the thermodynamic data to calculate the equilibrium constant for the reaction.

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Problem 112

Calculate the normal boiling point of ethanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$ , given that its enthalpy of vaporization is 38.6 $\mathrm{kJ} / \mathrm{mol}$ and its entropy of vaporization is 110 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$

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Problem 113

Chloroform $\left(\mathrm{CHCl}_{3}\right)$ has a normal boiling point of $61^{\circ} \mathrm{C}$ and an enthalpy of vaporization of 29.24 $\mathrm{kJ} / \mathrm{mol} .$ What are its values of $\Delta G_{\mathrm{vap}}$ and $\Delta S_{\mathrm{vap}}$ at $61^{\circ} \mathrm{C} ?$

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Problem 114

The entropy change for a certain nonspontaneous reaction at $50^{\circ} \mathrm{C}$ is 104 $\mathrm{J} / \mathrm{K}$ .
(a) Is the reaction endothermic or exothermic?
(b) What is the minimum value of $\Delta H(\text { in } \mathrm{kJ})$ for the reaction?

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Problem 115

Ammonium nitrate is dangerous because it decomposes (sometimes explosively) when heated:
$$\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$
(a) Using the data in Appendix $\mathrm{B}$ , show that this reaction is spontaneous at $25^{\circ} \mathrm{C}$ .
(b) How does $\Delta G^{\circ}$ for the reaction change when the temperature is raised?
(c) Calculate the equilibrium constant $K_{\mathrm{p}}$ at $25^{\circ} \mathrm{C}$ .
(d) Calculate $\Delta \mathrm{G}$ for the reaction when the partial pressure of each gas is 30 $\mathrm{atm} .$

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Problem 116

Use the data in Appendix $\mathrm{B}$ to calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each of the following reactions:
(a) $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)$
(b) $\mathrm{MgCO}_{3}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{CO}_{2}(g)$
(c) $\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Fe}(s)$
(d) $2 \mathrm{NaHCO}_{3}(s) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3 (s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
Are these reactions spontaneous or nonspontaneous at $25^{\circ} \mathrm{C}$ and 1 atm pressure? How does $\Delta G^{\circ}$ change when the temperature is raised?

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Problem 117

Trouton’s rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids:
$\Delta H_{\mathrm{vap}} / T_{\mathrm{bp}} \approx 88 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$
(a) Check the reliability of Trouton's rule for the liquids listed in the following table.
(b) Explain why liquids tend to have the same value of $\Delta H_{\text { vap }} / T_{\mathrm{bp}}$ .
(c) Which of the liquids in the table deviate(s) from Trouton's rule? Explain.

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Problem 118

Ammonium hydrogen sulfide, a stink bomb ingredient, decomposes to ammonia and hydrogen sulfide.
$$\mathrm{NH}_{4} \mathrm{HS}(s) \longrightarrow \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g)$$
Calculate the standard free energy of formation of $\mathrm{NH}_{4} \mathrm{HS}(s)$ at $25^{\circ} \mathrm{C}$ if the total pressure resulting from $\mathrm{NH}_{4} \mathrm{HS}$ placed in an evacuated container is 0.658 $\mathrm{atm}$ at $25^{\circ} \mathrm{C}$

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Problem 119

Nickel tetracarbonyl, a volatile liquid used to purify nickel, forms when carbon monoxide contacts nickel. For $\operatorname{Ni}(\mathrm{CO})_{4}(l), \quad \Delta H_{\mathrm{f}}^{\circ}=-633.0 \mathrm{kJ} / \mathrm{mol}$ and $S^{\circ}=313.4$ $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$
$$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(l)$$
(a) Calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for the reaction under standard-state conditions at $25^{\circ} \mathrm{C}$ .
(b) Estimate the temperature at which the reaction becomes nonspontaneous.
(c) Calculate $\Delta G_{\mathrm{f}}^{\circ}$ for $\mathrm{Ni}(\mathrm{CO})_{4}(l)$ .

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Problem 120

Just as we can define a standard enthalpy of formation $\left(\Delta H_{f}^{\circ}\right)$ and a standard free energy of formation $\left(\Delta G_{\mathrm{f}}^{\circ}\right),$ we can define an analogous standard entropy of formation $\left(\Delta S^{\circ}\right)$ as being the entropy change for the formation of a substance in its standard state from its constituent elements in their standard states. Use the standard molar entropies given in Appendix $\mathrm{B}$ to calculate $\Delta S^{\circ} \mathrm{f}$ for the following substances:
(a) Benzene, $\mathrm{C}_{6} \mathrm{H}_{6}(l) \quad$ (b) $\mathrm{CaSO}_{4}(s)$
(c) Ethanol, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)$
Check your answers by calculating $\Delta S_{\mathrm{f}}^{\circ}$ from the values given in Appendix $\mathrm{B}$ for $\Delta H_{\mathrm{f}}^{\circ}$ and $\Delta G_{\mathrm{f}}^{\circ} .$

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Problem 121

Use the data in Appendix $\mathrm{B}$ to calculate the equilibrium pressure of $\mathrm{CO}_{2}$ in a closed 1 $\mathrm{L}$ vessel that contains each of the following samples:
(a) 15 $\mathrm{g}$ of $\mathrm{MgCO}_{3}$ and 1.0 $\mathrm{g}$ of MgO at $25^{\circ} \mathrm{C}$
(b) 15 $\mathrm{g}$ of $\mathrm{MgCO}_{3}$ and 1.0 $\mathrm{g}$ of MgO at $280^{\circ} \mathrm{C}$
(c) 30 $\mathrm{g}$ of $\mathrm{MgCO}_{3}$ and 1.0 $\mathrm{g}$ of MgO at $280^{\circ} \mathrm{C}$
Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.

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Problem 122

The equilibrium constant $K_{\mathrm{b}}$ for dissociation of aqueous ammonia is $1.710 \times 10^{-5}$ at $20^{\circ} \mathrm{C}$ and $1.892 \times 10^{-5}$ at $50^{\circ} \mathrm{C} .$ What are the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the reaction?
$$\mathrm{NH}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{NH}_{4}^{+}(a q)+\mathrm{OH}^{-}(a q)$$

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Problem 123

Consider the Haber synthesis of gaseous $\mathrm{NH}_{3}\left(\Delta H_{\mathrm{f}}^{\circ}=\right.$ $-46.1 \mathrm{kJ} / \mathrm{mol} ; \Delta G_{\mathrm{f}}^{\circ}=-16.5 \mathrm{kJ} / \mathrm{mol} ) :$
$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$
(a) Use only these data to calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the reaction at $25^{\circ} \mathrm{C}$ .
(b) Account for the sign of $\Delta S^{\circ}$ .
(c) Is the reaction spontaneous under standard-state conditions at $25^{\circ} \mathrm{C}$ ? Explain.
(d) What are the equilibrium constants $K_{\mathrm{p}}$ and $K_{\mathrm{c}}$ for the reaction at 350 $\mathrm{K} ?$ Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.

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Problem 124

Consider the dissolution of AgBr in water at $25^{\circ} \mathrm{C}$ :
$$\mathrm{AgBr}(s) \rightleftharpoons \mathrm{Ag}^{+}(a q)+\mathrm{Br}^{-}(a q)$$
(a) Use the standard heats of formation and standard molar entropies in Appendix $\mathrm{B}$ to calculate $\Delta G^{\circ}$ for the reaction at $25^{\circ} \mathrm{C}$ .
(b) Calculate $K_{\text { sp }}$ for $\mathrm{AgBr}$ at $25^{\circ} \mathrm{C}$.
(c) Calculate $\Delta G$ for the dissolution of AgBr at $25^{\circ} \mathrm{C}$ when $\left[\mathrm{Ag}^{+}\right]=[\mathrm{Br}]=1.00 \times 10^{-5} \mathrm{M} .$ Is your result consistent with the relative values of $Q$ and $K_{\mathrm{sp}} ?$

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Problem 125

The temperature dependence of the equilibrium constant is given by the equation
$$\ln K=\frac{-\Delta H^{\circ}}{R}\left(\frac{1}{T}\right)+\frac{\Delta S^{\circ}}{R}$$
where $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are assumed to be independent of temperature.
(a) Derive this equation from equations given in this chapter.
(b) Explain how this equation can be used to determine experimental values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ from values of $K$ at several different temperatures.
(c) Use this equation to predict the sign of $\Delta H^{\circ}$ for a reaction whose equilibrium constant increases with increasing temperature. Is the reaction endothermic or exothermic? Is your prediction in accord with Le Chatelier's principle?

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Problem 126

The normal boiling point of bromine is $58.8^{\circ} \mathrm{C},$ and the standard entropies of the liquid and vapor are $S^{\circ}\left[\mathrm{Br}_{2}(l)\right]=152.2 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol}) ; S^{\circ}\left[\mathrm{Br}_{2}(g)\right]=245.4 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ . At what temperature does bromine have a vapor pressure of 227 $\mathrm{mm}$ Hg?

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Problem 127

The molar solubility of lead iodide is $1.45 \times 10^{-3} \mathrm{M}$ at $20^{\circ} \mathrm{C}$ and $6.85 \times 10^{-3} \mathrm{M}$ at $80^{\circ} \mathrm{C}$ . What are the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for dissolution of $\mathrm{PbI}_{2} ?$
$$\mathrm{PbI}_{2}(s) \longrightarrow \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)$$
Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.

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Problem 128

Use the data in Appendix $\mathrm{B}$ to calculate the equilibrium constant $K$ for the following reaction at $80^{\circ} \mathrm{C} :$
$$2 \mathrm{Br}^{-}(a q)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{Br}_{2}(l)+2 \mathrm{Cl}^{-}(a q)$$
Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.

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Problem 129

Use the data from Appendix $\mathrm{B}$ to determine the normal boiling point of carbon disulfide $\left(\mathrm{CS}_{2}\right)$

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Problem 130

A humidity sensor consists of a cardboard square that is colored blue in dry weather and red in humid weather. The color change is due to the reaction:
$$ \begin{array}{c}\quad {\mathrm{CoCl}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{2}(s)} \\ {\text { Blue }} \quad\quad\quad\quad\quad\quad\quad\quad\quad {\text { Red }}\end{array} $$
For this reaction at $25^{\circ} \mathrm{C}, \Delta H^{\circ}=-352 \mathrm{kJ} / \mathrm{mol}$ and $\Delta S^{\circ}=-899 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol}) .$ Assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature, what is the vapor pressure of water (in mm Hg) at equilibrium for the above reaction at $35^{\circ} \mathrm{C}$ on a hot summer day?

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Problem 131

The following reaction, sometimes used in the laboratory to generate small quantities of oxygen gas, has $\Delta G^{\circ}=$ $-224.4 \mathrm{kJ} / \mathrm{mol}$ at $25^{\circ} \mathrm{C} :$
$$2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$$
Use the following additional data at $25^{\circ} \mathrm{C}$ to calculate the standard molar entropy $S^{\circ}$ of $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C} : \Delta H^{\circ} \mathrm{AClO}_{3} )=$ $-397.7 \mathrm{kJ} / \mathrm{mol}, \Delta H^{\circ} \mathrm{f}(\mathrm{KCl})=-436.5 \mathrm{kJ} / \mathrm{mol}, S^{\circ}\left(\mathrm{KClO}_{3}\right)=$ $143.1 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol}),$ and $S^{\circ}(\mathrm{KCl})=82.6 \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$.

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Problem 132

Consider the equilibrium $\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$.
(a) Use the thermodynamic data in Appendix $\mathrm{B}$ to determine the temperature at which an equilibrium mixture with a total pressure of 1.00 $\mathrm{atm}$ will contain twice as much $\mathrm{NO}_{2}$ as $\mathrm{N}_{2} \mathrm{O}_{4}$ . Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.
(b) At what temperature will an equilibrium mixture with a total pressure of 1.00 atm contain equal amounts of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4} ?$

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Problem 133

Sorbitol $\left(\mathrm{C}_{6} \mathrm{H}_{14} \mathrm{O}_{6}\right),$ a substance used as a sweetener in foods, is prepared by the reaction of glucose with hydrogen in the presence of a catalyst:
$$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{14} \mathrm{O}_{6}(a q)$$
Which of the following quantities are affected by the catalyst?
(a) Rate of the forward reaction
(b) Rate of the reverse reaction
(c) Spontaneity of the reaction
(d) $\Delta H^{\circ}$
(e) $\Delta S^{\circ}$
(f) $\Delta G^{\circ}$
(g) The equilibrium constant
(h) Time required to reach equilibrium

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Problem 134

A mixture of 14.0 $\mathrm{g}$ of $\mathrm{N}_{2}$ and 3.024 $\mathrm{g}$ of $\mathrm{H}_{2}$ in a 5.00 $\mathrm{L}$ container is heated to $400^{\circ} \mathrm{C}$ . Use the data in Appendix $\mathrm{B}$ to calculate the molar concentrations of $\mathrm{N}_{2}, \mathrm{H}_{2},$ and $\mathrm{NH}_{3}$ at equilibrium. Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature, and remember that the standard state of a gas is defined in terms of pressure.
$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$

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Problem 135

One step in the commercial synthesis of sulfuric acid is the catalytic oxidation of sulfur dioxide:
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$
(a) A mixture of 192 $\mathrm{g}$ of $\mathrm{SO}_{2}, 48.0 \mathrm{g}$ of $\mathrm{O}_{2}$ and a $\mathrm{V}_{2} \mathrm{O}_{5}$ catalyst is heated to 800 $\mathrm{K}$ in a 15.0 $\mathrm{L}$ vessel. Use the data in Appendix $\mathrm{B}$ to calculate the partial pressures of $\mathrm{SO}_{3}$ $\mathrm{SO}_{2},$ and $\mathrm{O}_{2}$ at equilibrium. Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.
(b) Does the percent yield of $\mathrm{SO}_{3}$ increase or decrease on raising the temperature from 800 $\mathrm{K}$ to 1000 $\mathrm{K}$ ? Explain.
(c) Does the total pressure increase or decrease on raising the temperature from 800 $\mathrm{K}$ to 1000 $\mathrm{K}$ ? Calculate the total pressure (in atm) at 1000 $\mathrm{K}$

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Problem 136

The lead storage battery uses the reaction
$\mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{HSO}_{4}^{-(a q)} \longrightarrow_{$2 \mathrm{PbSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)}$
(a) Use the data in Appendix $\mathrm{B}$ to calculate $\Delta G^{\circ}$ for this reaction.
(b) Calculate $\Delta G$ for this reaction on a cold winter's day $\left(10^{\circ} \mathrm{F}\right)$ in a battery that has run down to the point where the sulfuric acid concentration is only 0.100 $\mathrm{M} .$

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Problem 137

What is the molar solubility of $\mathrm{CaCO}_{3}$ at $50^{\circ} \mathrm{C}$ in a solution prepared by dissolving 1.000 $\mathrm{L}$ of $\mathrm{CO}_{2}$ gas $\left(\text { at } 20^{\circ} \mathrm{C} \text { and }\right.$ 731 $\mathrm{mm} Hg )$ and 3.335 $\mathrm{g}$ of solid $\mathrm{Ca} (\mathrm{OH})_{2}$ in enough water to make 500.0 $\mathrm{mL}$ of solution at $50^{\circ} \mathrm{C} ?$ Is the solubility of $\mathrm{CaCO}_{3}$ at $50^{\circ} \mathrm{C}$ larger or smaller than at $25^{\circ} \mathrm{C}$ ? Explain. You may assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.

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Problem 138

A 1.00 $\mathrm{L}$ volume of gaseous ammonia at $25.0^{\circ} \mathrm{C}$ and 744 $\mathrm{mm}$ Hg was dissolved in enough water to make 500.0 $\mathrm{mL}$ of aqueous ammonia at $2.0^{\circ} \mathrm{C}$ . What is $K_{\mathrm{b}}$ for $\mathrm{NH}_{3}$ at $2.0^{\circ} \mathrm{C},$ and what is the pH of the solution? Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.

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Problem 139

Consider the unbalanced equation:
$$\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}^{-}(a q)+\mathrm{IO}_{3}^{-}(a q)$$
(a) Balance the equation for this reaction in basic solution.
(b) Use the data in Appendix $\mathrm{B}$ and $\Delta G^{\circ}$ for $\mathrm{IO}_{3}^{-}(a q)=$
$-128.0 \mathrm{kJ} / \mathrm{mol}$ to calculate $\Delta G^{\circ}$ for the reaction at $25^{\circ} \mathrm{C}$
(c) Is the reaction spontaneous or nonspontaneous under standard-state conditions?
(d) What pH is required for the reaction to be at equilibrium at $25^{\circ}$ C when $[\mathrm{I}^{-}]=0.10 \mathrm{M}$ and $\left[\mathrm{IO}_{3}\right]=0.50 \mathrm{M} ?$

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Problem 140

A mixture of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4},$ each at an initial partial pressure of 1.00 $\mathrm{atm}$ and a temperature of $100^{\circ} \mathrm{C},$ is allowed to react. Use the data in Appendix $\mathrm{B}$ to calculate the partial pressure of each gas at equilibrium. Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are independent of temperature.
$$\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$

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