Key Terms, Key Equations, Summaries, and Exercises (Chapter 13)

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Private: Chapter Thirteen

Key Terms, Key Equations, Summaries, and Exercises (Chapter 13)

Key Terms

equilibrium: state of a reversible reaction in which the forward and reverse processes occur at equal rates

equilibrium constant (K): value of the reaction quotient for a system at equilibrium; may be expressed using concentrations (K_c) or partial pressures (K_p)

heterogeneous equilibria: equilibria in which reactants and products occupy two or more different phases

homogeneous equilibria: equilibria in which all reactants and products occupy the same phase

law of mass action: when a reversible reaction has attained equilibrium at a given temperature, the reaction quotient remains constant

Le Châtelier’s principle: an equilibrium subjected to stress will shift in a way to counter the stress and re-establish equilibrium

reaction quotient (Q): mathematical function describing the relative amounts of reactants and products in a reaction mixture; may be expressed in terms of concentrations (Q_c) or pressures (Q_p)

reversible reaction: chemical reaction that can proceed in both the forward and reverse directions under given conditions

Key Equations

Q_{c} = \frac{[C]^{x} {[D]}^{y}}{[A]^{m} {[B]}^{n}} for the reaction m A + n B ⇌ x C + y D

Q_{P} = \frac{{(P_{C})}^{x} {(P_{D})}^{y}}{{(P_{A})}^{m} {(P_{B})}^{n}} for the reaction m A + n B ⇌ x C + y D

P = MRT

K_c = Q_c at equilibrium

K_p = Q_p at equilibrium

K_P = K_c (RT)^Δn

ΔG = ΔG° + RT ln Q

ΔG° = −RT ln K

Summaries

13.1 Chemical Equilibria

A reversible reaction is at equilibrium when the forward and reverse processes occur at equal rates. Chemical equilibria are dynamic processes characterized by constant amounts of reactant and product species.

13.2 Equilibrium Constants

The composition of a reaction mixture may be represented by a mathematical function known as the reaction quotient, Q. For a reaction at equilibrium, the composition is constant, and Q is called the equilibrium constant, K.

A homogeneous equilibrium is an equilibrium in which all components are in the same phase. A heterogeneous equilibrium is an equilibrium in which components are in two or more phases.

13.3 Shifting Equilibria: Le Châtelier’s Principle

Systems at equilibrium can be disturbed by changes to temperature, concentration, and, in some cases, volume and pressure. The system’s response to these disturbances is described by Le Châtelier’s principle: An equilibrium system subjected to a disturbance will shift in a way that counters the disturbance and re-establishes equilibrium. A catalyst will increase the rate of both the forward and reverse reactions of a reversible process, increasing the rate at which equilibrium is reached but not altering the equilibrium mixture’s composition (K does not change).

13.4 Equilibrium Calculations

Calculating values for equilibrium constants and/or equilibrium concentrations is of practical benefit to many applications. A mathematical strategy that uses initial concentrations, changes in concentrations, and equilibrium concentrations (and goes by the acronym ICE) is useful for several types of equilibrium calculations. We also learned that a negative value for ΔG indicates a spontaneous process; a positive ΔG indicates a nonspontaneous process; and a ΔG of zero indicates that the system is at equilibrium. We also saw how free energy, spontaneity, and equilibrium relate.

Exercises

13.1 Chemical Equilibria

1.

What does it mean to describe a reaction as “reversible”?

2.

When writing an equation, how is a reversible reaction distinguished from a nonreversible reaction?

3.

If a reaction is reversible, when can it be said to have reached equilibrium?

4.

Is a system at equilibrium if the rate constants of the forward and reverse reactions are equal?

5.

If the concentrations of products and reactants are equal, is the system at equilibrium?

13.2 Equilibrium Constants

6.

Explain why there may be an infinite number of values for the reaction quotient of a reaction at a given temperature but there can be only one value for the equilibrium constant at that temperature.

7.

Explain why an equilibrium between Br₂(l) and Br₂(g) would not be established if the container were not a closed vessel shown in Figure 13.4.

8.

If you observe the following reaction at equilibrium, is it possible to tell whether the reaction started with pure NO₂ or with pure N₂O₄?
$2 {NO}_{2} (g) ⇌ N_{2} O_{4} (g)$

9.

Among the solubility rules previously discussed is the statement: All chlorides are soluble except Hg₂Cl₂, AgCl, PbCl₂, and CuCl.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation $AgCl (s) ⇌ {Ag}^{+} (a q) + {Cl}^{−} (a q) .$ Is K_c > 1, < 1, or ≈ 1? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation ${Pb}^{2+} (a q) + 2 {Cl}^{−} (a q) ⇌ {PbCl}_{2} (s) .$ Is K_c > 1, < 1, or ≈ 1? Explain your answer.

10.

Among the solubility rules previously discussed is the statement: Carbonates, phosphates, borates, and arsenates—except those of the ammonium ion and the alkali metals—are insoluble.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation ${CaCO}_{3} (s) ⇌ {Ca}^{2+} (a q) + {CO}_{3}^{2−} (aq) .$ Is K_c > 1, < 1, or ≈ 1? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation $3 {Ba}^{2+} (a q) + 2 {PO}_{4}^{3−} (a q) ⇌ {Ba}_{3} {({PO}_{4})}_{2} (s) .$ Is K_c > 1, < 1, or ≈ 1? Explain your answer.

11.

Benzene is one of the compounds used as octane enhancers in unleaded gasoline. It is manufactured by the catalytic conversion of acetylene to benzene: $3 C_{2} H_{2} (g) ⇌ C_{6} H_{6} (g) .$ Which value of K_c would make this reaction most useful commercially? K_c ≈ 0.01, K_c ≈ 1, or K_c ≈ 10. Explain your answer.

12.

Show that the complete chemical equation, the total ionic equation, and the net ionic equation for the reaction represented by the equation $KI (a q) + I_{2} (a q) ⇌ {KI}_{3} (a q)$ give the same expression for the reaction quotient. KI₃ is composed of the ions K⁺ and $I_{3}^{−} .$

13.

For a titration to be effective, the reaction must be rapid and the yield of the reaction must essentially be 100%. Is K_c > 1, < 1, or ≈ 1 for a titration reaction?

14.

For a precipitation reaction to be useful in a gravimetric analysis, the product of the reaction must be insoluble. Is K_c > 1, < 1, or ≈ 1 for a useful precipitation reaction?

15.

Write the mathematical expression for the reaction quotient, Q_c, for each of the following reactions:

(a) ${CH}_{4} (g) + {Cl}_{2} (g) ⇌ {CH}_{3} Cl (g) + HCl (g)$

(b) $N_{2} (g) + O_{2} (g) ⇌ 2 NO (g)$

(c) $2 {SO}_{2} (g) + O_{2} (g) ⇌ 2 {SO}_{3} (g)$

(d) ${BaSO}_{3} (s) ⇌ BaO (s) + {SO}_{2} (g)$

(e) $P_{4} (g) + 5 O_{2} (g) ⇌ P_{4} O_{10} (s)$

(f) ${Br}_{2} (g) ⇌ 2 Br (g)$

(g) ${CH}_{4} (g) + 2 O_{2} (g) ⇌ {CO}_{2} (g) + 2 H_{2} O (l)$

(h) ${CuSO}_{4} · 5 H_{2} O (s) ⇌ {CuSO}_{4} (s) + 5 H_{2} O (g)$

16.

Write the mathematical expression for the reaction quotient, Q_c, for each of the following reactions:

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

(b) $4 {NH}_{3} (g) + 5 O_{2} (g) ⇌ 4 NO (g) + 6 H_{2} O (g)$

(c) $N_{2} O_{4} (g) ⇌ 2 {NO}_{2} (g)$

(d) ${CO}_{2} (g) + H_{2} (g) ⇌ CO (g) + H_{2} O (g)$

(e) ${NH}_{4} Cl (s) ⇌ {NH}_{3} (g) + HCl (g)$

(f) $2 Pb {({NO}_{3})}_{2} (s) ⇌ 2 PbO (s) + 4 {NO}_{2} (g) + O_{2} (g)$

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

(h) $S_{8} (g) ⇌ 8 S (g)$

17.

The initial concentrations or pressures of reactants and products are given for each of the following systems. Calculate the reaction quotient and determine the direction in which each system will proceed to reach equilibrium.

$\begin{matrix} (a) 2 {NH}_{3} (g) ⇌ N_{2} (g) + 3 H_{2} (g) & K_{c} = 17; [{NH}_{3}] = 0.20 M, [N_{2}] = 1.00 M, [H_{2}] = 1.00 M \\ (b) 2 {NH}_{3} (g) ⇌ N_{2} (g) + 3 H_{2} (g) & K_{P} = 6.8 \times 10^{4}; {NH}_{3} = 3.0 atm, N_{2} = 2.0 atm, H_{2} = 1.0 atm \\ (c) 2 {SO}_{3} (g) ⇌ 2 {SO}_{2} (g) + O_{2} (g) & K_{c} = 0.230; [{SO}_{3}] = 0.00 M, [{SO}_{2}] = 1.00 M, [O_{2}] = 1.00 M \\ (d) 2 {SO}_{3} (g) ⇌ 2 {SO}_{2} (g) + O_{2} (g) & K_{P} = 16.5; {SO}_{3} = 1.00 atm, {SO}_{2} = 1.00 atm, O_{2} = 1.00 atm \\ (e) 2 NO (g) + {Cl}_{2} (g) ⇌ 2 NOCl (g) & K_{c} = 4.6 \times 10^{4}; [NO] = 1.00 M, [{Cl}_{2}] = 1.00 M, [NOCl] = 0 M \\ (f) N_{2} (g) + O_{2} (g) ⇌ 2 NO (g) & K_{P} = 0.050; NO = 10.0 atm, N_{2} = O_{2} = 5 atm \end{matrix}$

18.

The initial concentrations or pressures of reactants and products are given for each of the following systems. Calculate the reaction quotient and determine the direction in which each system will proceed to reach equilibrium.

$\begin{matrix} (a) 2 {NH}_{3} (g) ⇌ N_{2} (g) + 3 H_{2} (g) & K_{c} = 17; [{NH}_{3}] = 0.50 M, [N_{2}] = 0.15 M, [H_{2}] = 0.12 M \\ (b) 2 {NH}_{3} (g) ⇌ N_{2} (g) + 3 H_{2} (g) & K_{P} = 6.8 \times 10^{4}; {NH}_{3} = 2.00 atm, N_{2} = 10.00 atm, H_{2} = 10.00 atm \\ (c) 2 {SO}_{3} (g) ⇌ 2 {SO}_{2} (g) + O_{2} (g) & K_{c} = 0.230; [{SO}_{3}] = 2.00 M, [{SO}_{2}] = 2.00 M, [O_{2}] = 2.00 M \\ (d) 2 {SO}_{3} (g) ⇌ 2 {SO}_{2} (g) + O_{2} (g) & K_{P} = 6.5 atm; {SO}_{2} = 1.00 atm, O_{2} = 1.130 atm, {SO}_{3} = 0 atm \\ (e) 2 NO (g) + {Cl}_{2} (g) ⇌ 2 NOCl (g) & K_{P} = 2.5 \times 10^{3}; NO = 1.00 atm, {Cl}_{2} = 1.00 atm, NOCl = 0 atm \\ (f) N_{2} (g) + O_{2} (g) ⇌ 2 NO (g) & K_{c} = 0.050; [N_{2}] = 0.100 M, [O_{2}] = 0.200 M, [NO] = 1.00 M \end{matrix}$

19.

The following reaction has K_P = 4.50 $\times$ 10⁻⁵ at 720 K.
$N_{2} (g) + 3 H_{2} (g) ⇌ 2 {NH}_{3} (g)$

If a reaction vessel is filled with each gas to the partial pressures listed, in which direction will it shift to reach equilibrium? P(NH₃) = 93 atm, P(N₂) = 48 atm, and P(H₂) = 52 atm

20.

Determine if the following system is at equilibrium. If not, in which direction will the system need to shift to reach equilibrium?
${SO}_{2} {Cl}_{2} (g) ⇌ {SO}_{2} (g) + {Cl}_{2} (g)$

[SO₂Cl₂] = 0.12 M, [Cl₂] = 0.16 M and [SO₂] = 0.050 M. K_c for the reaction is 0.078.

21.

Which of the systems described in Exercise 13.15 are homogeneous equilibria? Which are heterogeneous equilibria?

22.

Which of the systems described in Exercise 13.16 are homogeneous equilibria? Which are heterogeneous equilibria?

23.

For which of the reactions in Exercise 13.15 does K_c (calculated using concentrations) equal K_P (calculated using pressures)?

24.

For which of the reactions in Exercise 13.16 does K_c (calculated using concentrations) equal K_P (calculated using pressures)?

25.

Convert the values of K_c to values of K_P or the values of K_P to values of K_c.

$\begin{matrix} (a) N_{2} (g) + 3 H_{2} (g) ⇌ 2 {NH}_{3} (g) & K_{c} = 0.50 at 400 °C \\ (b) H_{2} (g) + I_{2} (g) ⇌ 2 HI (g) & K_{c} = 50.2 at 448 °C \\ (c) {Na}_{2} {SO}_{4} · 10 H_{2} O (s) ⇌ {Na}_{2} {SO}_{4} (s) + 10 H_{2} O (g) & K_{P} = 4.08 \times 10^{−25} at 25 °C \\ (d) H_{2} O (l) ⇌ H_{2} O (g) & K_{P} = 0.122 at 50 °C \end{matrix}$

26.

Convert the values of K_c to values of K_P or the values of K_P to values of K_c.

$\begin{matrix} (a) {Cl}_{2} (g) + {Br}_{2} (g) ⇌ 2 BrCl (g) & K_{c} = 4.7 \times 10^{−2} at 25 °C \\ (b) 2 {SO}_{2} (g) + O_{2} (g) ⇌ 2 {SO}_{3} (g) & K_{P} = 48.2 at 500 °C \\ (c) {CaCl}_{2} · 6 H_{2} O (s) ⇌ {CaCl}_{2} (s) + 6 H_{2} O (g) & K_{P} = 5.09 \times 10^{−44} at 25 °C \\ (d) H_{2} O (l) ⇌ H_{2} O (g) & K_{P} = 0.196 at 60 °C \end{matrix}$

27.

What is the value of the equilibrium constant expression for the change $H_{2} O (l) ⇌ H_{2} O (g)$ at 30 °C? (See Appendix E.)

28.

Write the expression of the reaction quotient for the ionization of HOCN in water.

29.

Write the reaction quotient expression for the ionization of NH₃ in water.

30.

What is the approximate value of the equilibrium constant K_P for the change $C_{2} H_{5} {OC}_{2} H_{5} (l) ⇌ C_{2} H_{5} {OC}_{2} H_{5} (g)$ at 25 °C. (The equilibrium vapor pressure for this substance is 570 torr at 25 °C.)

13.3 Shifting Equilibria: Le Châtelier’s Principle

31.

The following equation represents a reversible decomposition:
${CaCO}_{3} (s) ⇌ CaO (s) + {CO}_{2} (g)$

Under what conditions will decomposition in a closed container proceed to completion so that no CaCO₃ remains?

32.

Explain how to recognize the conditions under which changes in volume will affect gas-phase systems at equilibrium.

33.

What property of a reaction can we use to predict the effect of a change in temperature on the value of an equilibrium constant?

34.

The following reaction occurs when a burner on a gas stove is lit:
${CH}_{4} (g) + 2 O_{2} (g) ⇌ {CO}_{2} (g) + 2 H_{2} O (g)$

Is an equilibrium among CH₄, O₂, CO₂, and H₂O established under these conditions? Explain your answer.

35.

A necessary step in the manufacture of sulfuric acid is the formation of sulfur trioxide, SO₃, from sulfur dioxide, SO₂, and oxygen, O₂, shown here. At high temperatures, the rate of formation of SO₃ is higher, but the equilibrium amount (concentration or partial pressure) of SO₃ is lower than it would be at lower temperatures.
$2 {SO}_{2} (g) + O_{2} (g) ⟶ 2 {SO}_{3} (g)$

(a) Does the equilibrium constant for the reaction increase, decrease, or remain about the same as the temperature increases?

(b) Is the reaction endothermic or exothermic?

36.

Suggest four ways in which the concentration of hydrazine, N₂H₄, could be increased in an equilibrium described by the following equation:
$N_{2} (g) + 2 H_{2} (g) ⇌ N_{2} H_{4} (g) Δ H = 95 kJ$

37.

Suggest four ways in which the concentration of PH₃ could be increased in an equilibrium described by the following equation:
$P_{4} (g) + 6 H_{2} (g) ⇌ 4 {PH}_{3} (g) Δ H = 110.5 kJ$

38.

How will an increase in temperature affect each of the following equilibria? How will a decrease in the volume of the reaction vessel affect each?

(a) $2 {NH}_{3} (g) ⇌ N_{2} (g) + 3 H_{2} (g) Δ H = 92 kJ$

(b) $N_{2} (g) + O_{2} (g) ⇌ 2 NO (g) Δ H = 181 kJ$

(c) $2 O_{3} (g) ⇌ 3 O_{2} (g) Δ H = −285 kJ$

(d) $CaO (s) + {CO}_{2} (g) ⇌ {CaCO}_{3} (s) Δ H = −176 kJ$

39.

How will an increase in temperature affect each of the following equilibria? How will a decrease in the volume of the reaction vessel affect each?

(a) $2 H_{2} O (g) ⇌ 2 H_{2} (g) + O_{2} (g) Δ H = 484 kJ$

(b) $N_{2} (g) + 3 H_{2} (g) ⇌ 2 {NH}_{3} (g) Δ H = −92.2 kJ$

(c) $2 Br (g) ⇌ {Br}_{2} (g) Δ H = −224 kJ$

(d) $H_{2} (g) + I_{2} (s) ⇌ 2 HI (g) Δ H = 53 kJ$

40.

Methanol can be prepared from carbon monoxide and hydrogen at high temperature and pressure in the presence of a suitable catalyst.

(a) Write the expression for the equilibrium constant (K_c) for the reversible reaction
$2 H_{2} (g) + CO (g) ⇌ {CH}_{3} OH (g) Δ H = −90.2 kJ$

(b) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if more H₂ is added?

(c) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if CO is removed?

(d) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if CH₃OH is added?

(e) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if the temperature of the system is increased?

41.

Nitrogen and oxygen react at high temperatures.

(a) Write the expression for the equilibrium constant (K_c) for the reversible reaction
$N_{2} (g) + O_{2} (g) ⇌ 2 NO (g) Δ H = 181 kJ$

(b) What will happen to the concentrations of N₂, O₂, and NO at equilibrium if more O₂ is added?

(c) What will happen to the concentrations of N₂, O₂, and NO at equilibrium if N₂ is removed?

(d) What will happen to the concentrations of N₂, O₂, and NO at equilibrium if NO is added?

(e) What will happen to the concentrations of N₂, O₂, and NO at equilibrium if the volume of the reaction vessel is decreased?

(f) What will happen to the concentrations of N₂, O₂, and NO at equilibrium if the temperature of the system is increased?

42.

Water gas, a mixture of H₂ and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon.

(a) Write the expression for the equilibrium constant for the reversible reaction
$C (s) + H_{2} O (g) ⇌ CO (g) + H_{2} (g) Δ H = 131.30 kJ$

(b) What will happen to the concentration of each reactant and product at equilibrium if more C is added?

(c) What will happen to the concentration of each reactant and product at equilibrium if H₂O is removed?

(d) What will happen to the concentration of each reactant and product at equilibrium if CO is added?

(e) What will happen to the concentration of each reactant and product at equilibrium if the temperature of the system is increased?

43.

Pure iron metal can be produced by the reduction of iron(III) oxide with hydrogen gas.

(a) Write the expression for the equilibrium constant (K_c) for the reversible reaction
${Fe}_{2} O_{3} (s) + 3 H_{2} (g) ⇌ 2 Fe (s) + 3 H_{2} O (g) Δ H = 98.7 kJ$

(b) What will happen to the concentration of each reactant and product at equilibrium if more Fe is added?

(c) What will happen to the concentration of each reactant and product at equilibrium if H₂O is removed?

(d) What will happen to the concentration of each reactant and product at equilibrium if H₂ is added?

(e) What will happen to the concentration of each reactant and product at equilibrium if the volume of the reaction vessel is decreased?

(f) What will happen to the concentration of each reactant and product at equilibrium if the temperature of the system is increased?

44.

Ammonia is a weak base that reacts with water according to this equation:
${NH}_{3} (a q) + H_{2} O (l) ⇌ {NH}_{4}^{+} (a q) + {OH}^{−} (a q)$

Will any of the following increase the percent of ammonia that is converted to the ammonium ion in water?

(a) Addition of NaOH

(b) Addition of HCl

(c) Addition of NH₄Cl

45.

Acetic acid is a weak acid that reacts with water according to this equation:
${CH}_{3} {CO}_{2} H (a q) + H_{2} O (a q) ⇌ H_{3} O^{+} (a q) + {CH}_{3} {CO}_{2}^{−} (a q)$

Will any of the following increase the percent of acetic acid that reacts and produces ${CH}_{3} {CO}_{2}^{−}$ ion?

(a) Addition of HCl

(b) Addition of NaOH

(c) Addition of NaCH₃CO₂

46.

Suggest two ways in which the equilibrium concentration of Ag⁺ can be reduced in a solution of Na⁺, Cl⁻, Ag⁺, and ${NO}_{3}^{−},$ in contact with solid AgCl.
${Na}^{+} (a q) + {Cl}^{−} (a q) + {Ag}^{+} (a q) + {NO}_{3}^{−} (a q) ⇌ AgCl (s) + {Na}^{+} (a q) + {NO}_{3}^{−} (a q)$
$Δ H = −65.9 kJ$

47.

How can the pressure of water vapor be increased in the following equilibrium?
$H_{2} O (l) ⇌ H_{2} O (g) Δ H = 41 kJ$

48.

A solution is saturated with silver sulfate and contains excess solid silver sulfate:
${Ag}_{2} {SO}_{4} (s) ⇌ 2 {Ag}^{+} (a q) + {SO}_{4}^{2−} (a q)$

A small amount of solid silver sulfate containing a radioactive isotope of silver is added to this solution. Within a few minutes, a portion of the solution phase is sampled and tests positive for radioactive Ag⁺ ions. Explain this observation.

49.

When equal molar amounts of HCl and HOCl are dissolved separately in equal amounts of water, the solution of HCl freezes at a lower temperature. Which compound has the larger equilibrium constant for acid ionization?

(a) HCl

(b) H ⁺ + Cl ^–

(c) HOCl

(d) H ⁺ + OCl ^–

13.4 Equilibrium Calculations

50.

A reaction is represented by this equation: $A (a q) + 2 B (a q) ⇌ 2 C (a q) K_{c} = 1 \times 10^{3}$

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations ≤1 M, identify two sets of concentrations that describe a mixture of A, B, and C at equilibrium.

51.

A reaction is represented by this equation: $2 W (a q) ⇌ X (a q) + 2 Y (a q) K_{c} = 5 \times 10^{−4}$

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations of ≤1 M, identify two sets of concentrations that describe a mixture of W, X, and Y at equilibrium.

52.

What is the value of the equilibrium constant at 500 °C for the formation of NH₃ according to the following equation?

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

An equilibrium mixture of NH₃(g), H₂(g), and N₂(g) at 500 °C was found to contain 1.35 M H₂, 1.15 M N₂, and 4.12 $\times$ 10⁻¹ M NH₃.

53.

Hydrogen is prepared commercially by the reaction of methane and water vapor at elevated temperatures.

${CH}_{4} (g) + H_{2} O (g) ⇌ 3 H_{2} (g) + CO (g)$

What is the equilibrium constant for the reaction if a mixture at equilibrium contains gases with the following concentrations: CH₄, 0.126 M; H₂O, 0.242 M; CO, 0.126 M; H₂ 1.15 M, at a temperature of 760 °C?

54.

A 0.72-mol sample of PCl₅ is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl₃(g) and 0.40 mol of Cl₂(g). Calculate the value of the equilibrium constant for the decomposition of PCl₅ to PCl₃ and Cl₂ at this temperature.

55.

At 1 atm and 25 °C, NO₂ with an initial concentration of 1.00 M is 0.0033% decomposed into NO and O₂. Calculate the value of the equilibrium constant for the reaction.

$2 {NO}_{2} (g) ⇌ 2 NO (g) + O_{2} (g)$

56.

Calculate the value of the equilibrium constant K_P for the reaction $2 NO (g) + {Cl}_{2} (g) ⇌ 2 NOCl (g)$ from these equilibrium pressures: NO, 0.050 atm; Cl₂, 0.30 atm; NOCl, 1.2 atm.

57.

When heated, iodine vapor dissociates according to this equation:

$I_{2} (g) ⇌ 2 I (g)$

At 1274 K, a sample exhibits a partial pressure of I₂ of 0.1122 atm and a partial pressure due to I atoms of 0.1378 atm. Determine the value of the equilibrium constant, K_P, for the decomposition at 1274 K.

58.

A sample of ammonium chloride was heated in a closed container.

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

At equilibrium, the pressure of NH₃(g) was found to be 1.75 atm. What is the value of the equilibrium constant K_P for the decomposition at this temperature?

59.

At a temperature of 60 °C, the vapor pressure of water is 0.196 atm. What is the value of the equilibrium constant K_P for the vaporization equilibrium at 60 °C?

$H_{2} O (l) ⇌ H_{2} O (g)$

60.

Complete the changes in concentrations (or pressure, if requested) for each of the following reactions.

(a)

$\begin{array}{l} 2 {SO}_{3} (g) & ⇌ & 2 {SO}_{2} (g) + & O_{2} (g) \\ ___ & ___ & + x \\ ___ & ___ & 0.125 M \end{array}$

(b)

$\begin{array}{l} 4 {NH}_{3} (g) & + 3 O_{2} (g) & ⇌ & 2 N_{2} (g) + & 6 H_{2} O (g) \\ ___ & 3 x & ___ & ___ \\ ___ & 0.24 M & ___ & ___ \end{array}$

(c) Change in pressure:

$\begin{array}{l} 2 {CH}_{4} (g) & ⇌ & C_{2} H_{2} (g) + & 3 H_{2} (g) \\ ___ & x & ___ \\ ___ & 25 torr & ___ \end{array}$

(d) Change in pressure:

$\begin{array}{l} {CH}_{4} (g) + & H_{2} O (g) & ⇌ & CO (g) + & 3 H_{2} (g) \\ ___ & x & ___ & ___ \\ ___ & 5 atm & ___ & ___ \end{array}$

(e)

$\begin{array}{l} {NH}_{4} Cl (s) & ⇌ & {NH}_{3} (g) + & HCl (g) \\ x & ___ \\ 1.03 \times 10^{−4} M & ___ \end{array}$

(f) change in pressure:

$\begin{matrix} Ni (s) + & 4 CO (g) & ⇌ & Ni {(CO)}_{4} (g) \\ 4 x & ___ \\ 0.40 atm & ___ \end{matrix}$

61.

Complete the changes in concentrations (or pressure, if requested) for each of the following reactions.

(a)

$\begin{matrix} 2 H_{2} (g) + & O_{2} (g) & ⇌ & 2 H_{2} O (g) \\ ___ & ___ & + 2 x \\ ___ & ___ & 1.50 M \end{matrix}$

(b)

$\begin{matrix} {CS}_{2} (g) + & 4 H_{2} (g) & ⇌ & {CH}_{4} (g) + & 2 H_{2} S (g) \\ x & ___ & ___ & ___ \\ 0.020 M & ___ & ___ & ___ \end{matrix}$

(c) Change in pressure:

$\begin{matrix} H_{2} (g) + & {Cl}_{2} (g) & ⇌ & 2 HCl (g) \\ x & ___ & ___ \\ 1.50 atm & ___ & ___ \end{matrix}$

(d) Change in pressure:

$\begin{matrix} 2 {NH}_{3} (g) & + 2 O_{2} (g) & ⇌ & N_{2} O (g) + & 3 H_{2} O (g) \\ ___ & ___ & ___ & x \\ ___ & ___ & ___ & 60.6 torr \end{matrix}$

(e)

$\begin{matrix} {NH}_{4} HS (s) & ⇌ & {NH}_{3} (g) + & H_{2} S (g) \\ x & ___ \\ 9.8 \times 10^{−6} M & ___ \end{matrix}$

(f) Change in pressure:

$\begin{matrix} Fe (s) + & 5 CO (g) & ⇌ & Fe {(CO)}_{5} (g) \\ ___ & x \\ ___ & 0.012 atm \end{matrix}$

62.

Why are there no changes specified for Ni in Exercise 13.60, part (f)? What property of Ni does change?

63.

Why are there no changes specified for NH₄HS in Exercise 13.61, part (e)? What property of NH₄HS does change?

64.

Analysis of the gases in a sealed reaction vessel containing NH₃, N₂, and H₂ at equilibrium at 400 °C established the concentration of N₂ to be 1.2 M and the concentration of H₂ to be 0.24 M.

$N_{2} (g) + 3 H_{2} (g) ⇌ 2 {NH}_{3} (g) K_{c} = 0.50 at 400 ° C$

Calculate the equilibrium molar concentration of NH₃.

65.

Calculate the number of moles of HI that are at equilibrium with 1.25 mol of H₂ and 1.25 mol of I₂ in a 5.00−L flask at 448 °C.

$H_{2} + I_{2} ⇌ 2 HI K_{c} = 50.2 at 448 ° C$

66.

What is the pressure of BrCl in an equilibrium mixture of Cl₂, Br₂, and BrCl if the pressure of Cl₂ in the mixture is 0.115 atm and the pressure of Br₂ in the mixture is 0.450 atm?

${Cl}_{2} (g) + {Br}_{2} (g) ⇌ 2 BrCl (g) K_{P} = 4.7 \times 10^{−2}$

67.

What is the pressure of CO₂ in a mixture at equilibrium that contains 0.50 atm H₂, 2.0 atm of H₂O, and 1.0 atm of CO at 990 °C?

$H_{2} (g) + {CO}_{2} (g) ⇌ H_{2} O (g) + CO (g) K_{P} = 1.6 at 990 °C$

68.

Cobalt metal can be prepared by reducing cobalt(II) oxide with carbon monoxide.

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

What concentration of CO remains in an equilibrium mixture with [CO₂] = 0.100 M?

69.

Carbon reacts with water vapor at elevated temperatures.

$C (s) + H_{2} O (g) ⇌ CO (g) + H_{2} (g) K_{c} = 0.2 at 1000 °C$

Assuming a reaction mixture initially contains only reactants, what is the concentration of CO in an equilibrium mixture with [H₂O] = 0.500 M at 1000 °C?

70.

Sodium sulfate 10−hydrate, Na₂SO₄·10H₂O, dehydrates according to the equation

${Na}_{2} {SO}_{4} · 10 H_{2} O (s) ⇌ {Na}_{2} {SO}_{4} (s) + 10 H_{2} O (g) K_{P} = 4.08 \times 10^{−25} at 25 °C$

What is the pressure of water vapor at equilibrium with a mixture of Na₂SO₄·10H₂O and NaSO₄?

71.

Calcium chloride 6−hydrate, CaCl₂·6H₂O, dehydrates according to the equation

${CaCl}_{2} · 6 H_{2} O (s) ⇌ {CaCl}_{2} (s) + 6 H_{2} O (g) K_{P} = 5.09 \times 10^{−44} at 25 °C$

What is the pressure of water vapor at equilibrium with a mixture of CaCl₂·6H₂O and CaCl₂ at 25 °C?

72.

A student solved the following problem and found the equilibrium concentrations to be [SO₂] = 0.590 M, [O₂] = 0.0450 M, and [SO₃] = 0.260 M. How could this student check the work without reworking the problem? The problem was: For the following reaction at 600 °C:

$2 {SO}_{2} (g) + O_{2} (g) ⇌ 2 {SO}_{3} (g) K_{c} = 4.32$

What are the equilibrium concentrations of all species in a mixture that was prepared with [SO₃] = 0.500 M, [SO₂] = 0 M, and [O₂] = 0.350 M?

73.

A student solved the following problem and found [N₂O₄] = 0.16 M at equilibrium. How could this student recognize that the answer was wrong without reworking the problem? The problem was: What is the equilibrium concentration of N₂O₄ in a mixture formed from a sample of NO₂ with a concentration of 0.10 M?

$2 {NO}_{2} (g) ⇌ N_{2} O_{4} (g) K_{c} = 160$

74.

Assume that the change in concentration of N₂O₄ is small enough to be neglected in the following problem.

(a) Calculate the equilibrium concentration of both species in 1.00 L of a solution prepared from 0.129 mol of N₂O₄ with chloroform as the solvent.

$N_{2} O_{4} (g) ⇌ 2 {NO}_{2} (g) K_{c} = 1.07 \times 10^{−5}$ in chloroform

(b) Confirm that the change is small enough to be neglected.

75.

Assume that the change in concentration of COCl₂ is small enough to be neglected in the following problem.

(a) Calculate the equilibrium concentration of all species in an equilibrium mixture that results from the decomposition of COCl₂ with an initial concentration of 0.3166 M.

${COCl}_{2} (g) ⇌ CO (g) + {Cl}_{2} (g) K_{c} = 2.2 \times 10^{−10}$

(b) Confirm that the change is small enough to be neglected.

76.

Assume that the change in pressure of H₂S is small enough to be neglected in the following problem.

(a) Calculate the equilibrium pressures of all species in an equilibrium mixture that results from the decomposition of H₂S with an initial pressure of 0.824 atm.

$2 H_{2} S (g) ⇌ 2 H_{2} (g) + S_{2} (g) K_{P} = 2.2 \times 10^{−6}$

(b) Confirm that the change is small enough to be neglected.

77.

What are all concentrations after a mixture that contains [H₂O] = 1.00 M and [Cl₂O] = 1.00 M comes to equilibrium at 25 °C?

$H_{2} O (g) + {Cl}_{2} O (g) ⇌ 2 HOCl (g) K_{c} = 0.0900$

78.

Calculate the number of grams of HI that are at equilibrium with 1.25 mol of H₂ and 63.5 g of iodine at 448 °C.

$H_{2} + I_{2} ⇌ 2 HI K_{c} = 50.2 at 448 °C$

79.

Butane exists as two isomers, n−butane and isobutane.

K_P = 2.5 at 25 °C

What is the pressure of isobutane in a container of the two isomers at equilibrium with a total pressure of 1.22 atm?

80.

What is the minimum mass of CaCO₃ required to establish equilibrium at a certain temperature in a 6.50-L container if the equilibrium constant (K_c) is 0.50 for the decomposition reaction of CaCO₃ at that temperature?

${CaCO}_{3} (s) ⇌ CaO (s) + {CO}_{2} (g)$

81.

The equilibrium constant (K_c) for this reaction is 1.60 at 990 °C:

$H_{2} (g) + {CO}_{2} (g) ⇌ H_{2} O (g) + CO (g)$

Calculate the number of moles of each component in the final equilibrium mixture obtained from adding 1.00 mol of H₂, 2.00 mol of CO₂, 0.750 mol of H₂O, and 1.00 mol of CO to a 5.00-L container at 990 °C.

82.

In a 3.0-L vessel, the following equilibrium partial pressures are measured: N₂, 190 torr; H₂, 317 torr; NH₃, 1.00 $\times$ 10³ torr.

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

(a) How will the partial pressures of H₂, N₂, and NH₃ change if H₂ is removed from the system? Will they increase, decrease, or remain the same?

(b) Hydrogen is removed from the vessel until the partial pressure of nitrogen, at equilibrium, is 250 torr. Calculate the partial pressures of the other substances under the new conditions.

83.

The equilibrium constant (K_c) for this reaction is 5.0 at a given temperature.

$CO (g) + H_{2} O (g) ⇌ {CO}_{2} (g) + H_{2} (g)$

(a) On analysis, an equilibrium mixture of the substances present at the given temperature was found to contain 0.20 mol of CO, 0.30 mol of water vapor, and 0.90 mol of H₂ in a liter. How many moles of CO₂ were there in the equilibrium mixture?

(b) Maintaining the same temperature, additional H₂ was added to the system, and some water vapor was removed by drying. A new equilibrium mixture was thereby established containing 0.40 mol of CO, 0.30 mol of water vapor, and 1.2 mol of H₂ in a liter. How many moles of CO₂ were in the new equilibrium mixture? Compare this with the quantity in part (a), and discuss whether the second value is reasonable. Explain how it is possible for the water vapor concentration to be the same in the two equilibrium solutions even though some vapor was removed before the second equilibrium was established.

84.

Antimony pentachloride decomposes according to this equation:

${SbCl}_{5} (g) ⇌ {SbCl}_{3} (g) + {Cl}_{2} (g)$

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. How many grams of each will be found if the mixture is transferred into a 2.00-L flask at the same temperature?

85.

Consider the equilibrium

$4 {NO}_{2} (g) + 6 H_{2} O (g) ⇌ 4 {NH}_{3} (g) + 7 O_{2} (g)$

(a) What is the expression for the equilibrium constant (K_c) of the reaction?

(b) How must the concentration of NH₃ change to reach equilibrium if the reaction quotient is less than the equilibrium constant?

(c) If the reaction were at equilibrium, how would an increase in the volume of the reaction vessel affect the pressure of NO₂?

(d) If the change in the pressure of NO₂ is 28 torr as a mixture of the four gases reaches equilibrium, how much will the pressure of O₂ change?

86.

The binding of oxygen by hemoglobin (Hb), giving oxyhemoglobin (HbO₂), is partially regulated by the concentration of H₃O⁺ and dissolved CO₂ in the blood. Although the equilibrium is complicated, it can be summarized as

${HbO}_{2} (a q) + H_{3} O^{+} (a q) + {CO}_{2} (g) ⇌ {CO}_{2} − Hb − H^{+} + O_{2} (g) + H_{2} O (l)$

(a) Write the equilibrium constant expression for this reaction.

(b) Explain why the production of lactic acid and CO₂ in a muscle during exertion stimulates release of O₂ from the oxyhemoglobin in the blood passing through the muscle.

87.

Liquid N₂O₃ is dark blue at low temperatures, but the color fades and becomes greenish at higher temperatures as the compound decomposes to NO and NO₂. At 25 °C, a value of K_P = 1.91 has been established for this decomposition. If 0.236 moles of N₂O₃ are placed in a 1.52-L vessel at 25 °C, calculate the equilibrium partial pressures of N₂O₃(g), NO₂(g), and NO(g).

88.

A 1.00-L vessel at 400 °C contains the following equilibrium concentrations: N₂, 1.00 M; H₂, 0.50 M; and NH₃, 0.25 M. How many moles of hydrogen must be removed from the vessel to increase the concentration of nitrogen to 1.1 M? The equilibrium reaction is

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

89.

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

(a) $I_{2} (s) + {Cl}_{2} (g) ⟶ 2ICl (g) Δ G ° = −10.88 kJ$

(b) $H_{2} (g) + I_{2} (s) ⟶ 2HI (g) Δ G ° = 3.4 kJ$

(c) ${CS}_{2} (g) + {3Cl}_{2} (g) ⟶ {CCl}_{4} (g) + S_{2} {Cl}_{2} (g) Δ G ° = −39 kJ$

(d) ${2SO}_{2} (g) + O_{2} (g) ⟶ {2SO}_{3} (g) Δ G ° = −141.82 kJ$

(e) ${CS}_{2} (g) ⟶ {CS}_{2} (l) Δ G ° = −1.88 kJ$

90.

Calculate the equilibrium constant at the temperature given.

(a) $O_{2} (g) + {2F}_{2} (g) ⟶ {2F}_{2} O (g) (T = 100 °C)$

(b) $I_{2} (s) + {Br}_{2} (l) ⟶ 2IBr (g) (T = 0.0 °C)$

(c) $2LiOH (s) + {CO}_{2} (g) ⟶ {Li}_{2} {CO}_{3} (s) + H_{2} O (g) (T = 575 °C)$

(d) $N_{2} O_{3} (g) ⟶ NO (g) + {NO}_{2} (g) (T = −10.0 °C)$

(e) ${SnCl}_{4} (l) ⟶ {SnCl}_{4} (g) (T = 200 °C)$

91.

Calculate the equilibrium constant at the temperature given.

(a) $I_{2} (s) + {Cl}_{2} (g) ⟶ 2ICl (g) (T = 100 °C)$

(b) $H_{2} (g) + I_{2} (s) ⟶ 2HI (g) (T = 0.0 °C)$

(c) ${CS}_{2} (g) + {3Cl}_{2} (g) ⟶ {CCl}_{4} (g) + S_{2} {Cl}_{2} (g) (T = 125 °C)$

(d) ${2SO}_{2} (g) + O_{2} (g) ⟶ {2SO}_{3} (g) (T = 675 °C)$

(e) ${CS}_{2} (g) ⟶ {CS}_{2} (l) (T = 90 °C)$

92.

Consider the following reaction at 298 K:
$N_{2} O_{4} (g) ⇌ {2NO}_{2} (g) K_{P} = 0.142$

What is the standard free energy change at this temperature? Describe what happens to the initial system, where the reactants and products are in standard states, as it approaches equilibrium.

93.

Determine the normal boiling point (in kelvin) of dichloroethane, CH₂Cl₂. Find the actual boiling point using the Internet or some other source, and calculate the percent error in the temperature. Explain the differences, if any, between the two values.

94.

Under what conditions is $N_{2} O_{3} (g) ⟶ NO (g) + {NO}_{2} (g)$ spontaneous?

95.

At room temperature, the equilibrium constant (K_w) for the self-ionization of water is 1.00 $\times$ 10⁻¹⁴. Using this information, calculate the standard free energy change for the aqueous reaction of hydrogen ion with hydroxide ion to produce water. (Hint: The reaction is the reverse of the self-ionization reaction.)

96.

Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction ${2H}_{2} S (g) + {SO}_{2} (g) ⇌ \frac{3}{8} S_{8} (s, rhombic) + {2H}_{2} O (l) .$ What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?

97.

Consider the decomposition of CaCO₃(s) into CaO(s) and CO₂(g). What is the equilibrium partial pressure of CO₂ at room temperature?

98.

In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH₃(g)) often escape from bottles of their solutions and react to form the ammonium chloride (NH₄Cl(s)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH₃ in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)

99.

Benzene can be prepared from acetylene. ${3C}_{2} H_{2} (g) ⇌ C_{6} H_{6} (g) .$ Determine the equilibrium constant at 25 °C and at 850 °C. Is the reaction spontaneous at either of these temperatures? Why is all acetylene not found as benzene?

100.

Carbon dioxide decomposes into CO and O₂ at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO₂ was 1.15 atm?

101.

Carbon tetrachloride, an important industrial solvent, is prepared by the chlorination of methane at 850 K.
${CH}_{4} (g) + {4Cl}_{2} (g) ⟶ {CCl}_{4} (g) + 4HCl (g)$

What is the equilibrium constant for the reaction at 850 K? Would the reaction vessel need to be heated or cooled to keep the temperature of the reaction constant?

102.

Acetic acid, CH₃CO₂H, can form a dimer, (CH₃CO₂H)₂, in the gas phase.
${2CH}_{3} {CO}_{2} H (g) ⟶ {({CH}_{3} {CO}_{2} H)}_{2} (g)$

The dimer is held together by two hydrogen bonds with a total strength of 66.5 kJ per mole of dimer.

At 25 °C, the equilibrium constant for the dimerization is 1.3 $\times$ 10³ (pressure in atm). What is ΔS° for the reaction?

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Key Terms

Key Equations

Summaries

13.1 Chemical Equilibria

13.2 Equilibrium Constants

13.3 Shifting Equilibria: Le Châtelier’s Principle

13.4 Equilibrium Calculations

Exercises

13.1 Chemical Equilibria

13.2 Equilibrium Constants

13.3 Shifting Equilibria: Le Châtelier’s Principle

13.4 Equilibrium Calculations

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