Chapter 6 Solutions — Equilibrium

Exercises

1. 1.
   A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

   • (a) What is the initial effect of the change on vapour pressure?
   • (b) How do rates of evaporation and condensation change initially?
   • (c) What happens when equilibrium is restored finally and what will be the final vapour pressure?
2. 2.
   What is Kc for the following equilibrium when the equilibrium concentration of each substance is: [SO₂] = 0.60 M, [O₂] = 0.82 M and [SO₃] = 1.90 M? 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)
3. 3.
   At a certain temperature and total pressure of 10⁵ Pa, iodine vapour contains 40% by volume of I atoms. I₂(g) ⇌ 2I(g). Calculate Kp for the equilibrium.
4. 4.
   Write the expression for the equilibrium constant, Kc for each of the following reactions:

   • (i) 2NOCl(g) ⇌ 2NO(g) + Cl₂(g)
   • (ii) 2Cu(NO₃)₂(s) ⇌ 2CuO(s) + 4NO₂(g) + O₂(g)
   • (iii) CH₃COOC₂H₅(aq) + H₂O(l) ⇌ CH₃COOH(aq) + C₂H₅OH(aq)
   • (iv) Fe³⁺(aq) + 3OH⁻(aq) ⇌ Fe(OH)₃(s)
   • (v) I₂(s) + 5F₂ ⇌ 2IF₅
5. 5.
   Find out the value of Kc for each of the following equilibria from the value of Kp:

   • (i) 2NOCl(g) ⇌ 2NO(g) + Cl₂(g); Kp = 1.8 × 10⁻² at 500 K
   • (ii) CaCO₃(s) ⇌ CaO(s) + CO₂(g); Kp = 167 at 1073 K
6. 6.
   For the following equilibrium, Kc = 6.3 × 10¹⁴ at 1000 K: NO(g) + O₃(g) ⇌ NO₂(g) + O₂(g). Both forward and reverse reactions are elementary bimolecular reactions. What is Kc for the reverse reaction?
7. 7.
   Explain why pure liquids and solids can be ignored while writing the equilibrium constant expression.
8. 8.
   Reaction between N₂ and O₂ takes place as follows: 2N₂(g) + O₂(g) ⇌ 2N₂O(g). If a mixture of 0.482 mol N₂ and 0.933 mol of O₂ is placed in a 10 L reaction vessel and allowed to form N₂O at a temperature for which Kc = 2.0 × 10⁻³⁷, determine the composition of the equilibrium mixture.
9. 9.
   Nitric oxide reacts with Br₂ and gives nitrosyl bromide: 2NO(g) + Br₂(g) ⇌ 2NOBr(g). When 0.087 mol of NO and 0.0437 mol of Br₂ are mixed in a closed container at constant temperature, 0.0518 mol of NOBr is obtained at equilibrium. Calculate equilibrium amount of NO and Br₂.
10. 10.
    At 450 K, Kp = 2.0 × 10¹⁰ bar for the reaction: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g). What is Kc at this temperature?
11. 11.
    A sample of HI(g) is placed in a flask at a pressure of 0.2 atm. At equilibrium the partial pressure of HI(g) is 0.04 atm. What is Kp for the given equilibrium? 2HI(g) ⇌ H₂(g) + I₂(g)
12. 12.
    A mixture of 1.57 mol of N₂, 1.92 mol of H₂ and 8.13 mol of NH₃ is introduced into a 20 L reaction vessel at 500 K. The equilibrium constant Kc for N₂(g) + 3H₂(g) ⇌ 2NH₃(g) is 1.7 × 10². Is the reaction mixture at equilibrium? If not, what is the direction of the net reaction?
13. 13.
    The equilibrium constant expression for a gas reaction is: Kc = [NH₃]⁴ [O₂]⁵ / ([NO]⁴ [H₂O]⁶). Write the balanced chemical equation corresponding to this expression.
14. 14.
    One mole of H₂O and one mole of CO are taken in a 10 L vessel and heated to 725 K. At equilibrium 40% of water (by mass) reacts with CO: H₂O(g) + CO(g) ⇌ H₂(g) + CO₂(g). Calculate the equilibrium constant for the reaction.
15. 15.
    At 700 K, equilibrium constant Kc for H₂(g) + I₂(g) ⇌ 2HI(g) is 54.8. If 0.5 mol L⁻¹ of HI(g) is present at equilibrium at 700 K, what are the concentrations of H₂(g) and I₂(g), assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700 K?
16. 16.
    What is the equilibrium concentration of each of the substances in the equilibrium when the initial concentration of ICl was 0.78 M? 2ICl(g) ⇌ I₂(g) + Cl₂(g); Kc = 0.14
17. 17.
    Kp = 0.04 atm at 899 K for the equilibrium C₂H₆(g) ⇌ C₂H₄(g) + H₂(g). What is the equilibrium concentration of C₂H₆ when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium?
18. 18.
    Ethyl acetate is formed by the reaction: CH₃COOH(l) + C₂H₅OH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l).

    • (i) Write the concentration ratio (reaction quotient) Qc.
    • (ii) At 293 K, starting with 1.00 mol acetic acid and 0.18 mol ethanol, 0.171 mol ethyl acetate is found at equilibrium. Calculate Kc.
    • (iii) Starting with 0.5 mol ethanol and 1.0 mol acetic acid at 293 K, 0.214 mol ethyl acetate is found after some…
19. 19.
    A sample of pure PCl₅ was introduced into an evacuated vessel at 473 K. After equilibrium was attained, concentration of PCl₅ was found to be 0.5 × 10⁻¹ mol L⁻¹. If value of Kc is 8.3 × 10⁻³, what are the concentrations of PCl₃ and Cl₂ at equilibrium? PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)
20. 20.
    FeO(s) + CO(g) ⇌ Fe(s) + CO₂(g); Kp = 0.265 atm at 1050 K. What are the equilibrium partial pressures of CO and CO₂ at 1050 K if the initial partial pressures are pCO = 1.4 atm and pCO₂ = 0.80 atm?
21. 21.
    Equilibrium constant Kc for N₂(g) + 3H₂(g) ⇌ 2NH₃(g) at 500 K is 0.061. At a particular time, the composition is: 3.0 mol L⁻¹ N₂, 2.0 mol L⁻¹ H₂ and 0.5 mol L⁻¹ NH₃. Is the reaction at equilibrium? If not, in which direction does it tend to proceed?
22. 22.
    Bromine monochloride, BrCl decomposes into bromine and chlorine: 2BrCl(g) ⇌ Br₂(g) + Cl₂(g). Kc = 32 at 500 K. If initially pure BrCl is present at a concentration of 3.3 × 10⁻³ mol L⁻¹, what is its molar concentration at equilibrium?
23. 23.
    At 1127 K and 1 atm pressure, a gaseous mixture of CO and CO₂ in equilibrium with solid carbon has 90.55% CO by mass. C(s) + CO₂(g) ⇌ 2CO(g). Calculate Kc for this reaction at the above temperature.
24. 24.
    Calculate

    • (a) ΔG° and
    • (b) the equilibrium constant for the formation of NO₂ from NO and O₂ at 298 K: NO(g) + ½O₂(g) ⇌ NO₂(g). Given: ΔfG°(NO₂) = 52.0 kJ/mol, ΔfG°(NO) = 87.0 kJ/mol, ΔfG°(O₂) = 0 kJ/mol.
25. 25.
    Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?

    • (a) PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)
    • (b) CaO(s) + CO₂(g) ⇌ CaCO₃(s)
    • (c) 3Fe(s) + 4H₂O(g) ⇌ Fe₃O₄(s) + 4H₂(g)
26. 26.
    Which of the following reactions will get affected by increasing the pressure? Also, mention whether change will cause the reaction to go into forward or backward direction.

    • (i) COCl₂(g) ⇌ CO(g) + Cl₂(g)
    • (ii) CH₄(g) + 2S₂(g) ⇌ CS₂(g) + 2H₂S(g)
    • (iii) CO₂(g) + C(s) ⇌ 2CO(g)
    • (iv) 2H₂(g) + CO(g) ⇌ CH₃OH(g)
    • (v) CaCO₃(s) ⇌ CaO(s) + CO₂(g)
    • (vi) 4NH₃(g) + 5O₂(g) ⇌ 4NO(g) + 6H₂O(g)
27. 27.
    The equilibrium constant for H₂(g) + Br₂(g) ⇌ 2HBr(g) is 1.6 × 10⁵ at 1024 K. Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024 K.
28. 28.
    Dihydrogen gas is obtained from natural gas by partial oxidation with steam in the endothermic reaction: CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g).

    • (a) Write an expression for Kp for the above reaction.
    • (b) How will the values of Kp and composition of equilibrium mixture be affected by
    • (i) increasing the pressure
    • (ii) increasing the temperature
    • (iii) using a catalyst?
29. 29.
    Describe the effect of:

    • (a) addition of H₂
    • (b) addition of CH₃OH
    • (c) removal of CO
    • (d) removal of CH₃OH on the equilibrium: 2H₂(g) + CO(g) ⇌ CH₃OH(g)
30. 30.
    At 473 K, Kc for decomposition of PCl₅ is 8.3 × 10⁻³. PCl₅(g) ⇌ PCl₃(g) + Cl₂(g); ΔrH° = 124.0 kJ mol⁻¹.

    • (a) Write expression for Kc.
    • (b) What is the value of Kc for the reverse reaction at the same temperature?
    • (c) What would be the effect on Kc if
    • (i) more PCl₅ is added
    • (ii) pressure is increased
    • (iii) the temperature is increased?
31. 31.
    In the water gas shift reaction CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g), a reaction vessel at 400°C is charged with an equimolar mixture of CO and steam such that pCO = pH₂O = 4.0 bar. What will be the partial pressure of H₂ at equilibrium? Kp = 10.1 at 400°C.
32. 32.
    Predict which of the following reactions will have appreciable concentration of reactants and products:

    • (a) Cl₂(g) ⇌ 2Cl(g); Kc = 5 × 10⁻³⁹
    • (b) Cl₂(g) + 2NO(g) ⇌ 2NOCl(g); Kc = 3.7 × 10⁸
    • (c) Cl₂(g) + 2NO₂(g) ⇌ 2NO₂Cl(g); Kc = 1.8
33. 33.
    The value of Kc for the reaction 3O₂(g) ⇌ 2O₃(g) is 2.0 × 10⁻⁵⁰ at 25°C. If the equilibrium concentration of O₂ in air at 25°C is 1.6 × 10⁻² M, what is the concentration of O₃?
34. 34.
    The reaction CO(g) + 3H₂(g) ⇌ CH₄(g) + H₂O(g) is at equilibrium at 1300 K in a 1 L flask containing 0.30 mol CO, 0.10 mol H₂, 0.02 mol H₂O and an unknown amount of CH₄. Determine the concentration of CH₄. Kc = 3.90.
35. 35.
    What is meant by the conjugate acid-base pair? Find the conjugate acid/base for the following species: HNO₂, CN⁻, HClO₄, F⁻, OH⁻, CO₃²⁻, and S²⁻.
36. 36.
    Which of the followings are Lewis acids? H₂O, BF₃, H⁺, and NH₄⁺.
37. 37.
    What will be the conjugate bases for the Bronsted acids: HF, H₂SO₄ and HCO₃⁻?
38. 38.
    Write the conjugate acids for the following Bronsted bases: NH₂⁻, NH₃ and HCOO⁻.
39. 39.
    The species H₂O, HCO₃⁻, HSO₄⁻ and NH₃ can act both as Bronsted acids and bases. For each case give the corresponding conjugate acid and base.
40. 40.
    Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base:

    • (a) OH⁻
    • (b) F⁻
    • (c) H⁺
    • (d) BCl₃.
41. 41.
    The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10⁻³ M. What is its pH?
42. 42.
    The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.
43. 43.
    The ionization constants of HF, HCOOH and HCN at 298 K are 6.8 × 10⁻⁴, 1.8 × 10⁻⁴ and 4.8 × 10⁻⁹ respectively. Calculate the ionization constants of the corresponding conjugate bases.
44. 44.
    The ionization constant of phenol is 1.0 × 10⁻¹⁰. What is the concentration of phenolate ion in 0.05 M solution of phenol? What will be its degree of ionization if the solution is also 0.01 M in sodium phenolate?
45. 45.
    The first ionization constant of H₂S is 9.1 × 10⁻⁸. Calculate the concentration of HS⁻ ion in its 0.1 M solution. How will this concentration be affected if the solution is 0.1 M in HCl also? If the second dissociation constant of H₂S is 1.2 × 10⁻¹³, calculate the concentration of S²⁻ under both conditions.
46. 46.
    The ionization constant of acetic acid is 1.74 × 10⁻⁵. Calculate the degree of dissociation of acetic acid in its 0.05 M solution. Calculate the concentration of acetate ion in the solution and its pH.
47. 47.
    It has been found that the pH of a 0.01 M solution of an organic acid is 4.15. Calculate the concentration of the anion, the ionization constant of the acid and its pKa.
48. 48.
    Assuming complete dissociation, calculate the pH of the following solutions:

    • (a) 0.003 M HCl
    • (b) 0.005 M NaOH
    • (c) 0.002 M HBr
    • (d) 0.002 M KOH
49. 49.
    Calculate the pH of the following solutions:

    • (a) 2 g of TlOH dissolved in water to give 2 litre of solution
    • (b) 0.3 g of Ca(OH)₂ dissolved in water to give 500 mL of solution
    • (c) 0.3 g of NaOH dissolved in water to give 200 mL of solution
    • (d) 1 mL of 13.6 M HCl diluted with water to give 1 litre of solution.
50. 50.
    The degree of ionization of a 0.1 M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pKa of bromoacetic acid.
51. 51.
    The pH of 0.005 M codeine (C₁₈H₂₁NO₃) solution is 9.95. Calculate its ionization constant and pKb.
52. 52.
    What is the pH of 0.001 M aniline solution? The ionization constant of aniline can be taken from Table 6.7. Calculate the degree of ionization of aniline in the solution. Also calculate the ionization constant of the conjugate acid of aniline.
53. 53.
    Calculate the degree of ionization of 0.05 M acetic acid if its pKa value is 4.74. How is the degree of dissociation affected when its solution also contains

    • (a) 0.01 M
    • (b) 0.1 M HCl?
54. 54.
    The ionization constant of dimethylamine is 5.4 × 10⁻⁴. Calculate its degree of ionization in its 0.02 M solution. What percentage of dimethylamine is ionized if the solution is also 0.1 M in NaOH?
55. 55.
    Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

    • (a) Human muscle-fluid, 6.83
    • (b) Human stomach fluid, 1.2
    • (c) Human blood, 7.38
    • (d) Human saliva, 6.4.
56. 56.
    The pH of milk, black coffee, tomato juice, lemon juice and egg white are 6.8, 5.0, 4.2, 2.2 and 7.8 respectively. Calculate corresponding hydrogen ion concentration in each.
57. 57.
    If 0.561 g of KOH is dissolved in water to give 200 mL of solution at 298 K. Calculate the concentrations of potassium, hydrogen and hydroxyl ions. What is its pH?
58. 58.
    The solubility of Sr(OH)₂ at 298 K is 19.23 g/L of solution. Calculate the concentrations of strontium and hydroxyl ions and the pH of the solution.
59. 59.
    The ionization constant of propanoic acid is 1.32 × 10⁻⁵. Calculate the degree of ionization of the acid in its 0.05 M solution and also its pH. What will be its degree of ionization if the solution is 0.01 M in HCl also?
60. 60.
    The pH of 0.1 M solution of cyanic acid (HCNO) is 2.34. Calculate the ionization constant of the acid and its degree of ionization in the solution.
61. 61.
    The ionization constant of nitrous acid is 4.5 × 10⁻⁴. Calculate the pH of 0.04 M sodium nitrite solution and also its degree of hydrolysis.
62. 62.
    A 0.02 M solution of pyridinium hydrochloride has pH = 3.44. Calculate the ionization constant of pyridine.
63. 63.
    Predict if the solutions of the following salts are neutral, acidic or basic: NaCl, KBr, NaCN, NH₄NO₃, NaNO₂ and KF.
64. 64.
    The ionization constant of chloroacetic acid is 1.35 × 10⁻³. What will be the pH of 0.1 M acid and its 0.1 M sodium salt solution?
65. 65.
    Ionic product of water at 310 K is 2.7 × 10⁻¹⁴. What is the pH of neutral water at this temperature?
66. 66.
    Calculate the pH of the resultant mixtures:

    • (a) 10 mL of 0.2 M Ca(OH)₂ + 25 mL of 0.1 M HCl
    • (b) 10 mL of 0.01 M H₂SO₄ + 10 mL of 0.01 M Ca(OH)₂
    • (c) 10 mL of 0.1 M H₂SO₄ + 10 mL of 0.1 M KOH
67. 67.
    Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298 K from their solubility product constants given in Table 6.9. Determine also the molarities of individual ions.
68. 68.
    The solubility product constants of Ag₂CrO₄ and AgBr are 1.1 × 10⁻¹² and 5.0 × 10⁻¹³ respectively. Calculate the ratio of the molarities of their saturated solutions.
69. 69.
    Equal volumes of 0.002 M solutions of sodium iodate and cupric chlorate are mixed together. Will it lead to precipitation of copper iodate? (For cupric iodate Cu(IO₃)₂: Ksp = 7.4 × 10⁻⁸)
70. 70.
    The ionization constant of benzoic acid is 6.46 × 10⁻⁵ and Ksp for silver benzoate is 2.5 × 10⁻¹³. How many times is silver benzoate more soluble in a buffer of pH 3.19 compared to its solubility in pure water?
71. 71.
    What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, Ksp = 6.3 × 10⁻¹⁸).
72. 72.
    What is the minimum volume of water required to dissolve 1 g of calcium sulphate at 298 K? (For calcium sulphate, Ksp is 9.1 × 10⁻⁶).
73. 73.
    The concentration of sulphide ion in 0.1 M HCl solution saturated with hydrogen sulphide is 1.0 × 10⁻¹⁹ M. If 10 mL of this is added to 5 mL of 0.04 M solution of the following: FeSO₄, MnCl₂, ZnCl₂ and CdCl₂. In which of these solutions will precipitation take place?