Chapter 13

1.

The reaction can proceed in both the forward and reverse directions.

3.

When a system has reached equilibrium, no further changes in the reactant and product concentrations occur; the forward and reverse reactions continue to proceed, but at equal rates.

5.

Not necessarily. A system at equilibrium is characterized by constant reactant and product concentrations, but the values of the reactant and product concentrations themselves need not be equal.

7.

Equilibrium cannot be established between the liquid and the gas phase if the top is removed from the bottle because the system is not closed; one of the components of the equilibrium, the Br₂ vapor, would escape from the bottle until all liquid disappeared. Thus, more liquid would evaporate than can condense back from the gas phase to the liquid phase.

9.

(a) K_c = [Ag⁺][Cl⁻] < 1. AgCl is insoluble; thus, the concentrations of ions are much less than 1 M; (b) > 1 because PbCl₂ is insoluble and formation of the solid will reduce the concentration of ions to a low level (<1 M).

11.

Since a value of K_c ≈ 10 means that C₆H₆ predominates over C₂H₂. In such a case, the reaction would be commercially feasible if the rate to equilibrium is suitable.

13.

K_c > 1

15.

(a) (b) (c) (d) Q_c = [SO₂]; (e) (f) (g) (h) Q_c = [H₂O]⁵

17.

(a) Q_c 25 proceeds left; (b) Q_P 0.22 proceeds right; (c) Q_c undefined proceeds left; (d) Q_P 1.00 proceeds right; (e) Q_P 0 proceeds right; (f) Q_c 4 proceeds left

19.

The system will shift toward the reactants to reach equilibrium.

21.

(a) homogenous; (b) homogenous; (c) homogenous; (d) heterogeneous; (e) heterogeneous; (f) homogenous; (g) heterogeneous; (h) heterogeneous

23.

This situation occurs in (a) and (b).

25.

(a) K_P = 1.6 10⁻⁴; (b) K_P = 50.2; (c) K_c = 5.34 10⁻³⁹; (d) K_c = 4.60 10⁻³

27.

29.

31.

The amount of CaCO₃ must be so small that is less than K_P when the CaCO₃ has completely decomposed. In other words, the starting amount of CaCO₃ cannot completely generate the full required for equilibrium.

33.

The change in enthalpy may be used. If the reaction is exothermic, the heat produced can be thought of as a product. If the reaction is endothermic the heat added can be thought of as a reactant. Additional heat would shift an exothermic reaction back to the reactants but would shift an endothermic reaction to the products. Cooling an exothermic reaction causes the reaction to shift toward the product side; cooling an endothermic reaction would cause it to shift to the reactants’ side.

34.

No, it is not at equilibrium. Because the system is not confined, products continuously escape from the region of the flame; reactants are also added continuously from the burner and surrounding atmosphere.

36.

Add N₂; add H₂; decrease the container volume; heat the mixture.

38.

(a) T increase = shift right, V decrease = shift left; (b) T increase = shift right, V = no effect; (c) T increase = shift left, V decrease = shift left; (d) T increase = shift left, V decrease = shift right.

40.

(a) (b) [H₂] increases, [CO] decreases, [CH₃OH] increases; (c), [H₂] increases, [CO] decreases, [CH₃OH] decreases; (d), [H₂] increases, [CO] increases, [CH₃OH] increases; (e), [H₂] increases, [CO] increases, [CH₃OH] decreases; (f), no changes.

42.

(a) (b) [H₂O] no change, [CO] no change, [H₂] no change; (c) [H₂O] decreases, [CO] decreases, [H₂] decreases; (d) [H₂O] increases, [CO] increases, [H₂] decreases; (e) [H₂O] decreases, [CO] increases, [H₂] increases. In (b), (c), (d), and (e), the mass of carbon will change, but its concentration (activity) will not change.

44.

Only (b)

46.

Add NaCl or some other salt that produces Cl⁻ to the solution. Cooling the solution forces the equilibrium to the right, precipitating more AgCl(s).

48.

Though the solution is saturated, the dynamic nature of the solubility equilibrium means the opposing processes of solid dissolution and precipitation continue to occur (just at equal rates, meaning the dissolved ion concentrations and the amount of undissolved solid remain constant). The radioactive Ag⁺ ions detected in the solution phase come from dissolution of the added solid, and their presence is countered by precipitation of nonradioactive Ag⁺.

50.

[A] = 0.1 M, [B] = 0.1 M, [C] = 1 M; and [A] = 0.01, [B] = 0.250, [C] = 0.791.

52.

K_c = 6.00 10⁻²

54.

K_c = 0.50

56.

K_P = 1.9 10³

58.

K_P = 3.06

60.

(a) −2x, +2x; (b) , , −2x; (c) −2x, 3x; (d) x, –x, −3x; (e) +x; (f)

62.

Activities of pure crystalline solids equal 1 and are constant; however, the mass of Ni does change.

64.

[NH₃] = 9.1 10⁻² M

66.

P_BrCl = 4.9 10⁻² atm

68.

[CO] = 2.04 10⁻⁴ M

70.

72.

Calculate Q based on the calculated concentrations and see if it is equal to K_c. Because Q does equal 4.32, the system must be at equilibrium.

74.

(a) [NO₂] = 1.17 10⁻³ M; [N₂O₄] = 0.128 M; (b) The assumption that x is negligibly small compared to 0.129 is confirmed by comparing the initial concentration of the N₂O₄ to its concentration at equilibrium (they differ by just 1 in the least significant digit’s place).

76.

(a) [H₂S] = 0.810 atm, [H₂] = 0.014 atm, [S₂] = 0.0072 atm; (b) The assumption that 2x is negligibly small compared to 0.824 is confirmed by comparing the initial concentration of the H₂S to its concentration at equilibrium (0.824 atm versus 0.810 atm, a difference of less than 2%).

78.

[PCl₅] = 1.80 M; [Cl₂] = 0.195 M; [PCl₃] = 0.195 M.

79.

507 g

81.

330 g

84.

(a) 0.33 mol. (b) [CO₂] = 0.50 M. Added H₂ forms some water as a result of a shift to the left after H₂ is added.

86.

(a) (b) [NH₃] must increase for Q_c to reach K_c. (c) The increase in system volume would lower the partial pressures of all reactants (including NO₂). (d)

88.