Unit 3 Equilibrium

3.3 Exercises

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Section 3.3 Exercises

  1. Explain why an equilibrium between Br2(l) and Br2(g) would not be established if the container were not a closed vessel.
  2. Among the solubility rules 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 [latex]\text{AgCl}(s)\;{\rightleftharpoons}\;\text{Ag}^{+}(aq)\;+\;\text{Cl}^{-}(aq)[/latex]. Is Kc > 1, < 1, or ≈ 1? Explain your answer.
    (b) Write the expression for the equilibrium constant for the reaction represented by the equation [latex]\text{Pb}^{2+}(aq)\;+\;2\text{Cl}^{-}(aq)\;{\rightleftharpoons}\;\text{PbCl}_2(s)[/latex]. Is Kc > 1, < 1, or ≈ 1? Explain your answer.

  3. Benzene is one of the compounds used as octane enhancers in unleaded gasoline. It is manufactured by the catalytic conversion of acetylene to benzene: [latex]3\text{C}_2\text{H}_2(g)\;{\longrightarrow}\;\text{C}_6\text{H}_6(g)[/latex]. Which value of Kc would make this reaction most useful commercially? Kc ≈ 0.01, Kc ≈ 1, or Kc ≈ 10. Explain your answer.
  4. Write the mathematical expression for the reaction quotient, Qc, for each of the following reactions:

    (a) [latex]\text{CH}_4(g)\;+\;\text{Cl}_2(g)\;{\rightleftharpoons}\;\text{CH}_3\text{Cl}(g)\;+\;\text{HCl}(g)[/latex]
    (b) [latex]\text{N}_2(g)\;+\;\text{O}_2(g)\;{\rightleftharpoons}\;2\text{NO}(g)[/latex]
    (c) [latex]2\text{SO}_2(g)\;+\;\text{O}_2(g)\;{\rightleftharpoons}\;2\text{SO}_3(g)[/latex]
    (d) [latex]\text{BaSO}_3(s)\;{\rightleftharpoons}\;\text{BaO}(s)\;+\;\text{SO}_2(g)[/latex]
    (e) [latex]\text{P}_4(g)\;+\;5\text{O}_2(g)\;{\rightleftharpoons}\;\text{P}_4\text{O}_{10}(s)[/latex]
    (f) [latex]\text{Br}_2(g)\;{\rightleftharpoons}\;2\text{Br}(g)[/latex]
    (g) [latex]\text{CH}_4(g)\;+\;2\text{O}_2(g)\;{\rightleftharpoons}\;\text{CO}_2(g)\;+\;2\text{H}_2\text{O}(l)[/latex]
    (h) [latex]\text{CuSO}_4{\cdot}5\text{H}_2\text{O}(s)\;{\rightleftharpoons}\;\text{CuSO}_4(s)\;+\;5\text{H}_2\text{O}(g)[/latex]

  5. 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.

    (a) [latex]2\text{NH}_3(g)\;{\rightleftharpoons}\;\text{N}_2(g)\;+\;3\text{H}_2(g)\;\;\;\;\;\;\;K_\text{c} = 17[/latex]; [NH3] = 0.20 M, [N2] = 1.00 M, [H2] = 1.00 M
    (b) [latex]2\text{NH}_3(g)\;{\rightleftharpoons}\;\text{N}_2(g)\;+\;3\text{H}_2(g)\;\;\;\;\;\;\;K_\text{p} = 6.8\;\times\;10^4[/latex]; initial pressures: NH3 = 3.0 atm, N2 = 2.0 atm, H2 = 1.0 atm
    (c) [latex]2\text{SO}_3(g)\;{\rightleftharpoons}\;2\text{SO}_2(g)\;+\;\text{O}_2(g)\;\;\;\;\;\;\;K_\text{c} = 0.230[/latex]; [SO3] = 0.00 M, [SO2] = 1.00 M, [O2] = 1.00 M
    (d) [latex]2\text{SO}_3(g)\;{\rightleftharpoons}\;2\text{SO}_2(g)\;+\;\text{O}_2(g)\;\;\;\;\;\;\;K_\text{p} = 16.5[/latex]; initial pressures: SO3 = 1.00 atm, SO2 = 1.00 atm, O2 = 1.00 atm
    (e) [latex]2\text{NO}(g)\;+\;\text{Cl}_2(g)\;{\rightleftharpoons}\;2\text{NOCl}(g)\;\;\;\;\;\;\;K_\text{c} = 4.6\;\times\;10^4[/latex]; [NO] = 1.00 M, [Cl2] = 1.00 M, [NOCl] = 0 M
    (f) [latex]\text{N}_2(g)\;+\;\text{O}_2(g)\;{\rightleftharpoons}\;2\text{NO}(g)\;\;\;\;\;\;\;K_\text{p} = 0.050[/latex]; initial pressures: NO = 10.0 atm, N2 = O2 = 5 atm

  6. The following reaction has Kp = 4.50 × 10−5 at 720 K.
    [latex]\text{N}_2(g)\;+\;3\text{H}_2(g)\;{\rightleftharpoons}\;2\text{NH}_3(g)[/latex]

    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

  7. Which of the systems described in Exercise 4 give homogeneous equilibria? Which give heterogeneous equilibria?
  8. What is the value of the equilibrium constant expression for the change [latex]\text{H}_2\text{O}(l)\;{\rightleftharpoons}\;\text{H}_2\text{O}(g)[/latex] at 30 °C?  Hint: See Table 1 of Section 1.5 — convert torr to atm at 30 °C.
  9. Water gas is a 1:1 mixture of carbon monoxide and hydrogen gas and is called water gas because it is formed from steam and hot carbon in the following reaction: [latex]\text{H}_2\text{O}(g)\;+\;\text{C}(s)\;{\rightleftharpoons}\;\text{H}_2(g)\;+\;\text{CO}(g)[/latex]
    (a) Write the expression for the equilibrium constant (Kc) for the reversible reaction.
    (b) Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and hydrogen at high temperature and pressure in the presence of a suitable catalyst.  Write the expression for the equilibrium constant (Kc) for the reversible reaction [latex]2\text{H}_2(g)\;+\;\text{CO}(g)\;{\rightleftharpoons}\;\text{CH}_3\text{OH}(g)\;\;\;\;\;\;\;{\Delta}H = -90.2\;\text{kJ}[/latex]

Solutions

  1. 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.
  2. (a) Kc = [Ag+][Cl−] < 1. AgCl is insoluble; thus, the concentrations of ions are much less than 1 M
    (b) [latex]K_\text{c} = \frac{1}{[\text{Pb}^{2+}][\text{Cl}^{-}]^2}\;>\;1[/latex] because PbCl2 is insoluble and formation of the solid will reduce the concentration of ions to a low level (< 1 M).
  3. Since [latex]K_\text{c} = \frac{[\text{C}_6\text{H}_6]}{[\text{C}_2\text{H}_2]^3}[/latex], a value of Kc ≈ 10 means that C6H6 predominates over C2H2. In such a case, the reaction would be commercially feasible if the rate to equilibrium is suitable.
  4. (a) [latex]Q_\text{c} = \frac{[\text{CH}_3\text{Cl}][\text{HCl}]}{[\text{CH}_4][\text{Cl}_2]}[/latex]
    (b) [latex]Q_\text{c} = \frac{[\text{NO}]^2}{[\text{N}_2][\text{O}_2]}[/latex]
    (c) [latex]Q_\text{c} = \frac{[\text{SO}_3]^2}{[\text{SO}_2]^2[\text{O}_2]}[/latex]
    (d) [latex]Q_\text{c} = [\text{SO}_2][/latex]
    (e) [latex]Q_\text{c} = \frac{1}{[\text{P}_4][\text{O}_2]^5}[/latex]
    (f) [latex]Q_\text{c} = \frac{[\text{Br}]^2}{[\text{Br}_2]}[/latex]
    (g) [latex]Q_\text{c} = \frac{[\text{CO}_2]}{[\text{CH}_4][\text{O}_2]^2}[/latex]
    (h) [latex]Q_\text{c} = [\text{H}_2\text{O}]^5[/latex]
  5. (a) Qc 25 proceeds left
    (b) Qp 0.22 proceeds right
    (c) Qc undefined proceeds left
    (d) Qp 1.00 proceeds right
    (e) Qp 0 proceeds right
    (f) Qc 4 proceeds left
  6. The system will shift toward the reactants to reach equilibrium.
  7. (a) homogenous
    (b) homogenous
    (c) homogenous
    (d) heterogeneous
    (e) heterogeneous
    (f) homogenous
    (g) heterogeneous
    (h) heterogeneous
  8. [latex]K_\text{p} = P_{\text{H}_2\text{O}} = 0.042[/latex]
  9. (a) [latex]K_\text{c} = \frac{[\text{CO}][\text{H}_2]}{[\text{H}_2\text{O}]}[/latex]
    (b) [latex]K_\text{c} = \frac{[\text{CH}_3\text{OH}]}{[\text{H}_2]^2[\text{CO}]}[/latex]

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