5.E: Fundamental Equilibrium Concepts (Exercises)
5.2 Chemical Equilibria
What does it mean to describe a reaction as “reversible”?
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The reaction can proceed in both the forward and reverse directions.
If a reaction is reversible, when can it be said to have reached equilibrium?
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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.
If the concentrations of products and reactants are equal, is the system at equilibrium?
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The concept of equilibrium does not imply equal concentrations, though it is possible.
5.3 Equilibrium Constants
Explain why an equilibrium between Br 2 ( l ) and Br 2 ( g ) would not be established if the container were not a closed vessel shown below:
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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 Br 2 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.
(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 K c > 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 K c > 1, < 1, or ≈ 1? Explain your answer.
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(a) K c = [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 PbCl 2 is insoluble and formation of the solid will reduce the concentration of ions to a low level (<1 M ).
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 K c would make this reaction most useful commercially? K c ≈ 0.01, K c ≈ 1, or K c ≈ 10. Explain your answer.
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Since \(K_c=\ce{\dfrac{[C6H6]}{[C2H2]^3}}\), a value of K c ≈ 10 means that C 6 H 6 predominates over C 2 H 2 . In such a case, the reaction would be commercially feasible if the rate to equilibrium is suitable.
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?
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K c > 1
Write the mathematical expression for the reaction quotient, Q c , for each of the following reactions:
- \(\ce{CH4}(g)+\ce{Cl2}(g) \rightleftharpoons \ce{CH3Cl}(g)+\ce{HCl}(g)\)
- \(\ce{N2}(g)+\ce{O2}(g) \rightleftharpoons \ce{2NO}(g)\)
- \(\ce{2SO2}(g)+\ce{O2}(g) \rightleftharpoons \ce{2SO3}(g)\)
- \(\ce{BaSO3}(s) \rightleftharpoons \ce{BaO}(s)+\ce{SO2}(g)\)
- \(\ce{P4}(g)+\ce{5O2}(g) \rightleftharpoons \ce{P4O10}(s)\)
- \(\ce{Br2}(g) \rightleftharpoons \ce{2Br}(g)\)
- \(\ce{CH4}(g)+\ce{2O2}(g) \rightleftharpoons \ce{CO2}(g)+\ce{2H2O}(l)\)
- \(\ce{CuSO4⋅5H2O}(s) \rightleftharpoons \ce{CuSO4}(s)+\ce{5H2O}(g)\)
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(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) \(Q_c\) = [SO 2 ]; (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) \(Q_c\) = [H 2 O] 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.
- \(\ce{2NH3}(g) \rightleftharpoons \ce{N2}(g)+\ce{3H2}(g) \hspace{20px} K_c=17\); [NH 3 ] = 0.20 M , [N 2 ] = 1.00 M , [H 2 ] = 1.00 M
- \(\ce{2NH3}(g) \rightleftharpoons \ce{N2}(g)+\ce{3H2}(g) \hspace{20px} K_P=6.8×10^4\); initial pressures: NH 3 = 3.0 atm, N 2 = 2.0 atm, H 2 = 1.0 atm
- \(\ce{2SO3}(g) \rightleftharpoons \ce{2SO2}(g)+\ce{O2}(g) \hspace{20px} K_c=0.230\); [SO 3 ] = 0.00 M , [SO 2 ] = 1.00 M , [O 2 ] = 1.00 M
- \(\ce{2SO3}(g) \rightleftharpoons \ce{2SO2}(g)+\ce{O2}(g) \hspace{20px} K_P=16.5\); initial pressures: SO 3 = 1.00 atm, SO 2 = 1.00 atm, O 2 = 1.00 atm
- \(\ce{2NO}(g)+\ce{Cl2}(g) \rightleftharpoons \ce{2NOCl}(g) \hspace{20px} K_c=4.6×10^4\); [NO] = 1.00 M , [Cl 2 ] = 1.00 M , [NOCl] = 0 M
- \(\ce{N2}(g)+\ce{O2}(g) \rightleftharpoons \ce{2NO}(g) \hspace{20px} K_P=0.050\); initial pressures: NO = 10.0 atm, N 2 = O 2 = 5 atm
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(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
Write the reaction quotient expression for the ionization of NH 3 in water.
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\[Q_c=\ce{\dfrac{[NH4+][OH- ]}{[HN3]}}\]
5.4 Equilibrium Calculations
What is the value of the equilibrium constant at 500 °C for the formation of NH 3 according to the following equation?
\[\ce{N2}(g)+\ce{3H2}(g)⇌\ce{2NH3}(g)\]
An equilibrium mixture of NH 3 ( g ), H 2 ( g ), and N 2 ( g ) at 500 °C was found to contain 1.35 M H 2 , 1.15 M N 2 , and 4.12 × 10 −1 M NH 3 .
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K c = 6.00 × 10 −2
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: CH 4 , 0.126 M ; H 2 O, 0.242 M ; CO, 0.126 M ; H 2 1.15 M , at a temperature of 760 °C?
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K c = 6.28
A 0.72-mol sample of PCl 5 is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl 3 ( g ) and 0.40 mol of Cl 2 ( g ). Calculate the value of the equilibrium constant for the decomposition of PCl 5 to PCl 3 and Cl 2 at this temperature.
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K c = 0.50
Analysis of the gases in a sealed reaction vessel containing NH 3 , N 2 , and H 2 at equilibrium at 400 °C established the concentration of N 2 to be 1.2 M and the concentration of H 2 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 NH 3 .
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[NH 3 ] = 9.1 × 10 −2 M
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 [CO 2 ] = 0.100 M ?
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[CO] = 2.0 × 10 −4 M
A student solved the following problem and found the equilibrium concentrations to be [SO 2 ] = 0.590 M , [O 2 ] = 0.0450 M , and [SO 3 ] = 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 [SO 3 ] = 0.500 M , [SO 2 ] = 0 M , and [O 2 ] = 0.350 M ?
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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.
What are the concentrations of H 2 O, Cl 2 O, and HOCl in an equilibrium mixture produced by the reaction below when 2.00 mol of H 2 O (g) is added to 2.00 mol of Cl 2 O (g) in a 2.00 L flask?
\[\ce{H2O}(g)+\ce{Cl2O}(g)⇌\ce{2HOCl}(g) \hspace{20px} K_c=0.180\]
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[H 2 O] = 0.825 M ; [Cl 2 O] = 0.825 M ; [HOCl] = 0.350 M .
Calculate the equilibrium concentrations of N 2 O 4 and NO 2 in a 1.00 L vessel that was prepared staring from 0.129 mol of N 2 O 4 .
\[\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g) \quad K_c=1.07 \times 10^{-5}\]
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[NO 2 ] = 1.17 x 10 -3 M
[N 2 O 4 ] = 0.128 M
Calculate the equilibrium concentrations of I 2 , Br 2 and IBr in a 1.00 L vessel that was prepared staring from 0.129 mol of N 2 O 4 .
\[\mathrm{I}_2 (g) + \mathrm{Br}_2(g) \rightleftharpoons 2 \mathrm{IBr}(g) \quad K_c=280.0 \]
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[I 2 ] = 0.053 M
[Br 2 ] = 0.053 M
[IBr] = 0.893 M
5.5 Shifting Equilibria - Le Chatelier’s Principle
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 CaCO 3 remains?
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The amount of CaCO 3 must be so small that \(P_{\ce{CO2}}\) is less than K P when the CaCO 3 has completely decomposed. In other words, the starting amount of CaCO 3 cannot completely generate the full \(P_{\ce{CO2}}\) required for equilibrium.
What property of a reaction can we use to predict the effect of a change in temperature on the value of an equilibrium constant?
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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.
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 CH 4 , O 2 , CO 2 , and H 2 O established under these conditions? Explain your answer.
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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.
Suggest four ways in which the concentration of hydrazine, N 2 H 4 , could be increased in an equilibrium described by the following equation:
\[\mathrm{N}_2(g)+2 \mathrm{H}_2(g) \rightleftharpoons \mathrm{N}_2 \mathrm{H}_4(g) \quad \Delta H=95 \mathrm{~kJ}\]
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Add N 2 ; add H 2 ; decrease the container volume; heat the mixture.
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?
- \(\ce{2NH3}(g)\rightleftharpoons\ce{N2}(g)+\ce{3H2}(g) \hspace{20px} ΔH=\mathrm{92\:kJ}\)
- \(\ce{N2}(g)+\ce{O2}(g)\rightleftharpoons\ce{2NO}(g) \hspace{20px} ΔH=\mathrm{181\:kJ}\)
- \(\ce{2O3}(g)\rightleftharpoons\ce{3O2}(g) \hspace{20px} ΔH=\mathrm{−285\:kJ}\)
- \(\ce{CaO}(s)+\ce{CO2}(g)\rightleftharpoons\ce{CaCO3}(s) \hspace{20px} ΔH=\mathrm{-176\:kJ}\)
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(a) Δ T increase = shift right, Δ P increase = shift left; (b) Δ T increase = shift right, Δ P increase = no effect; (c) Δ T increase = shift left, Δ P increase = shift left; (d) Δ T increase = shift left, Δ P increase = shift right.
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.
- Write the expression for the equilibrium constant (\(K_c\)) for the reversible reaction \[\ce{2H2}(g)+\ce{CO}(g)\rightleftharpoons\ce{CH3OH}(g) \hspace{20px} ΔH=\mathrm{-90.2\:kJ}\]
- What will happen to the concentrations of \(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if more H 2 is added?
- What will happen to the concentrations of H\(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if CO is removed?
- What will happen to the concentrations of \(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if CH 3 OH is added?
- 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?
- What will happen to the concentrations of \(\ce{H2}\), \(\ce{CO}\), and \(\ce{CH3OH}\) at equilibrium if more catalyst is added?
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\(K_c=\ce{\dfrac{[CH3OH]}{[H2]^2[CO]}}\); [H 2 ] increases, [CO] decreases, [CH 3 OH] increases; [H 2 ] increases, [CO] decreases, [CH 3 OH] decreases; [H 2 ] increases, [CO] increases, [CH 3 OH] increases; [H 2 ] increases, [CO] increases, [CH 3 OH] decreases; no changes.
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?
- Addition of NaOH
- Addition of HCl
- Addition of NH 4 Cl
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Only (b)
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.
\[\mathrm{Na}{}^+(a q)+\mathrm{Cl}{}^- +\mathrm{Ag}{}^+(aq) \rightleftharpoons \mathrm{AgCl}(a q)+\mathrm{Na}^{+}(a q) + \mathrm{NO}_3{}^{-}(a q)\]
\(ΔH=\mathrm{−65.9\:kJ}\)
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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).