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5.E: Fundamental Equilibrium Concepts (Exercises)

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    5.2 Chemical Equilibria

    Exercise \(\PageIndex{1}\)

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

    Answer

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

    Exercise \(\PageIndex{2}\)

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

    Answer

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

    Exercise \(\PageIndex{3\)

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

    Answer

    The concept of equilibrium does not imply equal concentrations, though it is possible.

    5.3 Equilibrium Constants

    Exercise \(\PageIndex{4}\)

    Explain why an equilibrium between Br2(l) and Br2(g) would not be established if the container were not a closed vessel shown below:

    CNX_Chem_13_01_bromine.jpg

    Answer

    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.

    Exercise \(\PageIndex{5}\)

    (a) Write the expression for the equilibrium constant for the reaction represented by the equation \(\ce{AgCl}(s) \rightleftharpoons \ce{Ag+}(aq)+\ce{Cl-}(aq)\). Is Kc > 1, < 1, or ≈ 1? Explain your answer.

    (b) Write the expression for the equilibrium constant for the reaction represented by the equation \(\ce{Pb^2+}(aq)+\ce{2Cl-}(aq) \rightleftharpoons \ce{PbCl2}(s)\). Is Kc > 1, < 1, or ≈ 1? Explain your answer.

    Answer

    (a) Kc = [Ag+][Cl−] < 1. AgCl is insoluble; thus, the concentrations of ions are much less than 1 M

    (b) \(K_c=\ce{\dfrac{1}{[Pb^2+][Cl- ]^2}}\) > 1 because PbCl2 is insoluble and formation of the solid will reduce the concentration of ions to a low level (<1 M).

    Exercise \(\PageIndex{6}\)

    Benzene is one of the compounds used as octane enhancers in unleaded gasoline. It is manufactured by the catalytic conversion of acetylene to benzene: \(\ce{3C2H2}(g)⟶\ce{C6H6}(g)\). Which value of Kc would make this reaction most useful commercially? Kc ≈ 0.01, Kc ≈ 1, or Kc ≈ 10. Explain your answer.

    Answer

    Since \(K_c=\ce{\dfrac{[C6H6]}{[C2H2]^3}}\), 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.

    Exercise \(\PageIndex7}\)

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

    Answer

    Kc > 1

    Exercise \(\PageIndex{8}\)

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

    1. \(\ce{CH4}(g)+\ce{Cl2}(g) \rightleftharpoons \ce{CH3Cl}(g)+\ce{HCl}(g)\)
    2. \(\ce{N2}(g)+\ce{O2}(g) \rightleftharpoons \ce{2NO}(g)\)
    3. \(\ce{2SO2}(g)+\ce{O2}(g) \rightleftharpoons \ce{2SO3}(g)\)
    4. \(\ce{BaSO3}(s) \rightleftharpoons \ce{BaO}(s)+\ce{SO2}(g)\)
    5. \(\ce{P4}(g)+\ce{5O2}(g) \rightleftharpoons \ce{P4O10}(s)\)
    6. \(\ce{Br2}(g) \rightleftharpoons \ce{2Br}(g)\)
    7. \(\ce{CH4}(g)+\ce{2O2}(g) \rightleftharpoons \ce{CO2}(g)+\ce{2H2O}(l)\)
    8. \(\ce{CuSO4⋅5H2O}(s) \rightleftharpoons \ce{CuSO4}(s)+\ce{5H2O}(g)\)
    Answer

    (a) \(Q_c=\ce{\dfrac{[CH3Cl][HCl]}{[CH4][Cl2]}}\); (b) \(Q_c=\ce{\dfrac{[NO]^2}{[N2][O2]}}\); (c) \(Q_c=\ce{\dfrac{[SO3]^2}{[SO2]^2[O2]}}\); (d) \(Q_c\) = [SO2]; (e) \(Q_c=\ce{\dfrac{1}{[P4][O2]^5}}\); (f) \(Q_c=\ce{\dfrac{[Br]^2}{[Br2]}}\); (g) \(Q_c=\ce{\dfrac{[CO2]}{[CH4][O2]^2}}\); (h) \(Q_c\) = [H2O]5

    Exercise \(\PageIndex{9}\)

    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.

    1. \(\ce{2NH3}(g) \rightleftharpoons \ce{N2}(g)+\ce{3H2}(g) \hspace{20px} K_c=17\); [NH3] = 0.20 M, [N2] = 1.00 M, [H2] = 1.00 M
    2. \(\ce{2NH3}(g) \rightleftharpoons \ce{N2}(g)+\ce{3H2}(g) \hspace{20px} K_P=6.8×10^4\); initial pressures: NH3 = 3.0 atm, N2 = 2.0 atm, H2 = 1.0 atm
    3. \(\ce{2SO3}(g) \rightleftharpoons \ce{2SO2}(g)+\ce{O2}(g) \hspace{20px} K_c=0.230\); [SO3] = 0.00 M, [SO2] = 1.00 M, [O2] = 1.00 M
    4. \(\ce{2SO3}(g) \rightleftharpoons \ce{2SO2}(g)+\ce{O2}(g) \hspace{20px} K_P=16.5\); initial pressures: SO3 = 1.00 atm, SO2 = 1.00 atm, O2 = 1.00 atm
    5. \(\ce{2NO}(g)+\ce{Cl2}(g) \rightleftharpoons \ce{2NOCl}(g) \hspace{20px} K_c=4.6×10^4\); [NO] = 1.00 M, [Cl2] = 1.00 M, [NOCl] = 0 M
    6. \(\ce{N2}(g)+\ce{O2}(g) \rightleftharpoons \ce{2NO}(g) \hspace{20px} K_P=0.050\); initial pressures: NO = 10.0 atm, N2 = O2 = 5 atm
    Answer

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

    Exercise \(\PageIndex{10}\)

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

    Answer

    \[Q_c=\ce{\dfrac{[NH4+][OH- ]}{[HN3]}}\]

    5.4 Equilibrium Calculations

    Exercise \(\PageIndex{11}\)

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

    \[\ce{N2}(g)+\ce{3H2}(g)⇌\ce{2NH3}(g)\]

    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 × 10−1 M NH3.

    Answer

    Kc = 6.00 × 10−2

    Exercise \(\PageIndex{12}\)

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

    \[\ce{CH4}(g)+\ce{H2O}(g)⇌\ce{3H2}(g)+\ce{CO}(g)\]

    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?

    Answer

    Kc = 6.28

    Exercise \(\PageIndex{13}\)

    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.

    Answer

    Kc = 0.50

    Exercise \(\PageIndex{14}\)

    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.

    \[\ce{N2}(g)+\ce{3H2}(g)⇌\ce{2NH3}(g) \hspace{20px} K_c=\textrm{0.50 at 400 °C}\]

    Calculate the equilibrium molar concentration of NH3.

    Answer

    [NH3] = 9.1 × 10−2 M

    Exercise \(\PageIndex{15}\)

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

    \(\ce{CoO}(s)+\ce{CO}(g)⇌\ce{Co}(s)+\ce{CO2}(g) \hspace{20px} K_c=4.90×10^2\textrm{ at 550 °C}\)

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

    Answer

    [CO] = 2.0 × 10−4 M

    Exercise \(\PageIndex{16}\)

    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:

    \(\ce{2SO2}(g)+\ce{O2}(g)⇌\ce{2SO3}(g) \hspace{20px} K_c=4.32\)

    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?

    Answer

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

    Exercise \(\PageIndex{17}\)

    What are the concentrations of H2O, Cl2O, and HOCl in an equilibrium mixture produced by the reaction below when 2.00 mol of H2O (g) is added to 2.00 mol of Cl2O (g) in a 2.00 L flask?

    \[\ce{H2O}(g)+\ce{Cl2O}(g)⇌\ce{2HOCl}(g) \hspace{20px} K_c=0.180\]

    Answer

    [H2O] = 0.825 M; [Cl2O] = 0.825 M; [HOCl] = 0.350 M.

    Exercise \(\PageIndex{18}\)

    Calculate the equilibrium concentrations of N2O4 and NO2 in a 1.00 L vessel that was prepared staring from 0.129 mol of N2O4.

    \[\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g) \quad K_c=1.07 \times 10^{-5}\]

    Answer

    [NO2] = 1.17 x 10-3 M

    [N2O4] = 0.128 M

    Exercise \(\PageIndex{19}\)

    Calculate the equilibrium concentrations of I2, Br2 and IBr in a 1.00 L vessel that was prepared staring from 0.129 mol of N2O4.

    \[\mathrm{I}_2 (g) + \mathrm{Br}_2(g) \rightleftharpoons 2 \mathrm{IBr}(g) \quad K_c=280.0 \]

    Answer

    [I2] = 0.053 M

    [Br2] = 0.053 M

    [IBr] = 0.893 M

    5.5 Shifting Equilibria - Le Chatelier’s Principle

    Exercise \(\PageIndex{20}\)

    The following equation represents a reversible decomposition:

    \(\ce{CaCO3}(s)\rightleftharpoons\ce{CaO}(s)+\ce{CO2}(g)\)

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

    Answer

    The amount of CaCO3 must be so small that \(P_{\ce{CO2}}\) is less than KP when the CaCO3 has completely decomposed. In other words, the starting amount of CaCO3 cannot completely generate the full \(P_{\ce{CO2}}\) required for equilibrium.

    Exercise \(\PageIndex{21}\)

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

    Answer

    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.

    Exercise \(\PageIndex{22}\)

    The following reaction occurs when a burner on a gas stove is lit:

    \(\ce{CH4}(g)+\ce{2O2}(g)\rightleftharpoons\ce{CO2}(g)+\ce{C2H2O}(g)\)

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

    Answer

    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.

    Exercise \(\PageIndex{23}\)

    Suggest four ways in which the concentration of hydrazine, N2H4, could be increased in an equilibrium described by the following equation:

    \[\mathrm{N}_2(g)+2 \mathrm{H}_2(g) \rightleftharpoons \mathrm{N}_2 \mathrm{H}_4(g) \quad \Delta H=95 \mathrm{~kJ}\]

    Answer

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

    Exercise \(\PageIndex{24}\)

    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?

    1. \(\ce{2NH3}(g)\rightleftharpoons\ce{N2}(g)+\ce{3H2}(g) \hspace{20px} ΔH=\mathrm{92\:kJ}\)
    2. \(\ce{N2}(g)+\ce{O2}(g)\rightleftharpoons\ce{2NO}(g) \hspace{20px} ΔH=\mathrm{181\:kJ}\)
    3. \(\ce{2O3}(g)\rightleftharpoons\ce{3O2}(g) \hspace{20px} ΔH=\mathrm{−285\:kJ}\)
    4. \(\ce{CaO}(s)+\ce{CO2}(g)\rightleftharpoons\ce{CaCO3}(s) \hspace{20px} ΔH=\mathrm{-176\:kJ}\)
    Answer

    (a) ΔT increase = shift right, ΔP increase = shift left; (b) ΔT increase = shift right, ΔP increase = no effect; (c) ΔT increase = shift left, ΔP increase = shift left; (d) ΔT increase = shift left, ΔP increase = shift right.

    Exercise \(\PageIndex{25}\)

    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:

    \[\ce{H2O}(g)+\ce{C}(s)\rightleftharpoons\ce{H2}(g)+\ce{CO}(g).\]

    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.

    1. Write the expression for the equilibrium constant (\(K_c\)) for the reversible reaction \[\ce{2H2}(g)+\ce{CO}(g)\rightleftharpoons\ce{CH3OH}(g) \hspace{20px} ΔH=\mathrm{-90.2\:kJ}\]
    2. What will happen to the concentrations of \(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if more H2 is added?
    3. What will happen to the concentrations of H\(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if CO is removed?
    4. What will happen to the concentrations of \(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if CH3OH is added?
    5. What will happen to the concentrations of H\(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if the temperature of the system is increased?
    6. What will happen to the concentrations of \(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if more catalyst is added?
    Answer

    \(K_c=\ce{\dfrac{[CH3OH]}{[H2]^2[CO]}}\); [H2] increases, [CO] decreases, [CH3OH] increases; [H2] increases, [CO] decreases, [CH3OH] decreases; [H2] increases, [CO] increases, [CH3OH] increases; [H2] increases, [CO] increases, [CH3OH] decreases; no changes.

    Exercise \(\PageIndex{26}\)

    Ammonia is a weak base that reacts with water according to this equation:

    \[\mathrm{NH}_3(a q)+\mathrm{H}_2 \mathrm{O}(l) \rightleftharpoons \mathrm{NH}_4{ }^{+}(a q)+\mathrm{OH}^{-}(a q)\]

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

    1. Addition of NaOH
    2. Addition of HCl
    3. Addition of NH4Cl
    Answer

    Only (b)

    Exercise \(\PageIndex{27}\)

    Suggest two ways in which the equilibrium concentration of Ag+ can be reduced in a solution of Na+, Cl−, Ag+, and \(\ce{NO3-}\), in contact with solid AgCl.

    \[\mathrm{Na}{}^+(a q)+\mathrm{Cl}{}^- +\mathrm{Ag}{}^+(aq) \rightleftharpoons \mathrm{AgCl}(a q)+\mathrm{Na}^{+}(a q) + \mathrm{NO}_3{}^{-}(a q)\]

    \(ΔH=\mathrm{−65.9\:kJ}\)

    Answer

    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).

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