Equilibrium Class 11 Notes

• K >> 1: the reaction goes nearly to completion (products dominate).
• K << 1: the reaction hardly proceeds (reactants dominate).
• K ~ 1: both reactants and products are present in comparable amounts.
• For a reaction written in reverse, K' = 1/K; doubling the equation squares K.

• Adding a reactant or removing a product shifts the equilibrium forward.
• Increasing pressure favours the side with fewer moles of gas; decreasing pressure favours more gas moles.
• For an exothermic reaction, heating shifts equilibrium backward; cooling shifts it forward (and the reverse for endothermic).
• Adding an inert gas at constant volume does not change the equilibrium.

• Acidic buffer example: CH₃COOH + CH₃COONa.
• Basic buffer example: NH₄OH + NH₄Cl.
• Blood is a natural buffer (HCO₃⁻/H₂CO₃ system) keeping pH near 7.4.

• For AgCl, Ksp = [Ag⁺][Cl⁻] = s² where s is the molar solubility.
• For PbCl₂, Ksp = [Pb²⁺][Cl⁻]² = 4s³.
• Adding a common ion suppresses solubility (common-ion effect), useful in qualitative analysis and precipitation.

Example: The pH of a solution is 3. What is its [H⁺] and is the solution acidic or basic?

Solution: [H⁺] = 10⁻³ mol L⁻¹. With pH < 7 the solution is acidic, and [OH⁻] = Kw/[H⁺] = 1×10⁻¹¹ mol L⁻¹.

Example: For the reaction N₂ + 3H₂ ⇌ 2NH₃, state the direction of shift if pressure is increased.

Solution: The forward step converts 4 moles of gas (1 N₂ + 3 H₂) into 2 moles of NH₃. Increasing pressure favours the side with fewer gas moles, so the equilibrium shifts forward, producing more ammonia.

Exercises (NCERT Q6.1–Q6.73)

• 6.1) 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?
• 6.2) What is K_c 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)
• 6.3) At a certain temperature and total pressure of 10⁵ Pa, iodine vapour contains 40% by volume of I atoms. I₂(g) ⇌ 2I(g) Calculate K_p for the equilibrium.
• 6.4) Write the expression for the equilibrium constant, K_c, 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
• 6.5) Find out the value of K_c for each of the following equilibria from the value of K_p: (i) 2NOCl(g) ⇌ 2NO(g) + Cl₂(g); K_p = 1.8 × 10⁻² at 500 K (ii) CaCO₃(s) ⇌ CaO(s) + CO₂(g); K_p = 167 at 1073 K
• 6.6) For the following equilibrium, K_c = 6.3 × 10¹⁴ at 1000 K: NO(g) + O₃(g) ⇌ NO₂(g) + O₂(g) Both the forward and reverse reactions in the equilibrium are elementary bimolecular reactions. What is K_c for the reverse reaction?
• 6.7) Explain why pure liquids and solids can be ignored while writing the equilibrium constant expression.
• 6.8) 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 K_c = 2.0 × 10⁻³⁷, determine the composition of the equilibrium mixture.
• 6.9) Nitric oxide reacts with Br₂ and gives nitrosyl bromide as per the reaction given below: 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 the equilibrium amounts of NO and Br₂.
• 6.10) At 450 K, K_p = 2.0 × 10¹⁰ bar⁻¹ for the given reaction at equilibrium: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g) What is K_c at this temperature?
• 6.11) 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 K_p for the given equilibrium? 2HI(g) ⇌ H₂(g) + I₂(g)
• 6.12) 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. At this temperature, the equilibrium constant, K_c, for the reaction 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?
• 6.13) The equilibrium constant expression for a gas reaction is, K_c = [NH₃]⁴[O₂]⁵ / ([NO]⁴[H₂O]⁶) Write the balanced chemical equation corresponding to this expression.
• 6.14) 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 according to the equation, H₂O(g) + CO(g) ⇌ H₂(g) + CO₂(g) Calculate the equilibrium constant for the reaction.
• 6.15) At 700 K, the equilibrium constant for the reaction 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?
• 6.16) 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); K_c = 0.14
• 6.17) K_p = 0.04 atm at 899 K for the equilibrium shown below. 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? C₂H₆(g) ⇌ C₂H₄(g) + H₂(g)
• 6.18) Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as: CH₃COOH(l) + C₂H₅OH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l) (i) Write the concentration ratio (reaction quotient), Q_c, for this reaction (note: water is not in excess and is not a solvent in this reaction). (ii) At 293 K, if one starts with 1.00 mol of acetic acid and 0.18 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant. (iii) Starting with 0.5 mol of ethanol and 1.0 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after some time. Has equilibrium been reached?
• 6.19) A sample of pure PCl₅ was introduced into an evacuated vessel at 473 K. After equilibrium was attained, the concentration of PCl₅ was found to be 0.5 × 10⁻¹ mol L⁻¹. If the value of K_c is 8.3 × 10⁻³, what are the concentrations of PCl₃ and Cl₂ at equilibrium? PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)
• 6.20) One of the reactions that takes place in producing steel from iron ore is the reduction of iron(II) oxide by carbon monoxide to give iron metal and CO₂: FeO(s) + CO(g) ⇌ Fe(s) + CO₂(g); K_p = 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 p_CO = 1.4 atm and p_CO₂ = 0.80 atm?
• 6.21) Equilibrium constant, K_c, for the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g) at 500 K is 0.061. At a particular time, the analysis shows that the composition of the reaction mixture 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 the reaction tend to proceed to reach equilibrium?
• 6.22) Bromine monochloride, BrCl, decomposes into bromine and chlorine and reaches the equilibrium: 2BrCl(g) ⇌ Br₂(g) + Cl₂(g) for which K_c = 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 in the mixture at equilibrium?
• 6.23) 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 K_c for this reaction at the above temperature.
• 6.24) Calculate (a) ΔG° and (b) the equilibrium constant for the formation of NO₂ from NO and O₂ at 298 K: NO(g) + 1/2 O₂(g) ⇌ NO₂(g) where ΔfG°(NO₂) = 52.0 kJ/mol, ΔfG°(NO) = 87.0 kJ/mol and ΔfG°(O₂) = 0 kJ/mol.
• 6.25) Does the number of moles of reaction products increase, decrease or remain the 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)
• 6.26) Which of the following reactions will get affected by increasing the pressure? Also, mention whether the change will cause the reaction to go into the 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)
• 6.27) The equilibrium constant for the following reaction is 1.6 × 10⁵ at 1024 K: H₂(g) + Br₂(g) ⇌ 2HBr(g) Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024 K.
• 6.28) Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per the following endothermic reaction: CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g) (a) Write an expression for K_p for the above reaction. (b) How will the values of K_p and the composition of the equilibrium mixture be affected by (i) increasing the pressure (ii) increasing the temperature (iii) using a catalyst?
• 6.29) Describe the effect of: (a) addition of H₂ (b) addition of CH₃OH (c) removal of CO (d) removal of CH₃OH on the equilibrium of the reaction: 2H₂(g) + CO(g) ⇌ CH₃OH(g)
• 6.30) At 473 K, the equilibrium constant K_c for the decomposition of phosphorus pentachloride, PCl₅, is 8.3 × 10⁻³. If the decomposition is depicted as: PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), ΔrH° = 124.0 kJ mol⁻¹ (a) write an expression for K_c for the reaction. (b) what is the value of K_c for the reverse reaction at the same temperature? (c) what would be the effect on K_c if (i) more PCl₅ is added (ii) pressure is increased (iii) the temperature is increased?
• 6.31) Dihydrogen gas used in Haber's process is produced by reacting methane from natural gas with high-temperature steam. The first stage of the two-stage reaction involves the formation of CO and H₂. In the second stage, CO formed in the first stage is reacted with more steam in the water–gas shift reaction: CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g) If a reaction vessel at 400 °C is charged with an equimolar mixture of CO and steam such that p_CO = p_H₂O = 4.0 bar, what will be the partial pressure of H₂ at equilibrium? K_p = 10.1 at 400 °C.
• 6.32) Predict which of the following reactions will have appreciable concentrations of reactants and products: (a) Cl₂(g) ⇌ 2Cl(g) K_c = 5 × 10⁻³⁹ (b) Cl₂(g) + 2NO(g) ⇌ 2NOCl(g) K_c = 3.7 × 10⁸ (c) Cl₂(g) + 2NO₂(g) ⇌ 2NO₂Cl(g) K_c = 1.8
• 6.33) The value of K_c 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, what is the concentration of O₃?
• 6.34) The reaction, CO(g) + 3H₂(g) ⇌ CH₄(g) + H₂O(g), is at equilibrium at 1300 K in a 1 L flask. It also contains 0.30 mol of CO, 0.10 mol of H₂ and 0.02 mol of H₂O and an unknown amount of CH₄ in the flask. Determine the concentration of CH₄ in the mixture. The equilibrium constant, K_c, for the reaction at the given temperature is 3.90.
• 6.35) 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⁻.
• 6.36) Which of the following are Lewis acids? H₂O, BF₃, H⁺ and NH₄⁺.
• 6.37) What will be the conjugate bases for the Brønsted acids: HF, H₂SO₄ and HCO₃⁻?
• 6.38) Write the conjugate acids for the following Brønsted bases: NH₂⁻, NH₃ and HCOO⁻.
• 6.39) The species H₂O, HCO₃⁻, HSO₄⁻ and NH₃ can act both as Brønsted acids and bases. For each case give the corresponding conjugate acid and base.
• 6.40) 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
• 6.41) The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10⁻³ M. What is its pH?
• 6.42) The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.
• 6.43) 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.
• 6.44) The ionization constant of phenol is 1.0 × 10⁻¹⁰. What is the concentration of phenolate ion in a 0.05 M solution of phenol? What will be its degree of ionization if the solution is also 0.01 M in sodium phenolate?
• 6.45) 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.
• 6.46) 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.
• 6.47) 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 pK_a.
• 6.48) 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
• 6.49) Calculate the pH of the following solutions: (a) 2 g of TlOH dissolved in water to give 2 litres 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 is diluted with water to give 1 litre of solution.
• 6.50) The degree of ionization of a 0.1 M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pK_a of bromoacetic acid.
• 6.51) The pH of a 0.005 M codeine (C₁₈H₂₁NO₃) solution is 9.95. Calculate its ionization constant and pK_b.
• 6.52) What is the pH of a 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.
• 6.53) Calculate the degree of ionization of 0.05 M acetic acid if its pK_a value is 4.74. How is the degree of dissociation affected when its solution also contains (a) 0.01 M (b) 0.1 M in HCl?
• 6.54) 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?
• 6.55) 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
• 6.56) 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 the corresponding hydrogen ion concentration in each.
• 6.57) 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?
• 6.58) 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.
• 6.59) 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?
• 6.60) The pH of a 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.
• 6.61) The ionization constant of nitrous acid is 4.5 × 10⁻⁴. Calculate the pH of a 0.04 M sodium nitrite solution and also its degree of hydrolysis.
• 6.62) A 0.02 M solution of pyridinium hydrochloride has pH = 3.44. Calculate the ionization constant of pyridine.
• 6.63) Predict if the solutions of the following salts are neutral, acidic or basic: NaCl, KBr, NaCN, NH₄NO₃, NaNO₂ and KF.
• 6.64) The ionization constant of chloroacetic acid is 1.35 × 10⁻³. What will be the pH of a 0.1 M acid and its 0.1 M sodium salt solution?
• 6.65) Ionic product of water at 310 K is 2.7 × 10⁻¹⁴. What is the pH of neutral water at this temperature?
• 6.66) 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
• 6.67) 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.
• 6.68) 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.
• 6.69) 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, K_sp = 7.4 × 10⁻⁸.)
• 6.70) The ionization constant of benzoic acid is 6.46 × 10⁻⁵ and K_sp 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?
• 6.71) 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, K_sp = 6.3 × 10⁻¹⁸.)
• 6.72) What is the minimum volume of water required to dissolve 1 g of calcium sulphate at 298 K? (For calcium sulphate, K_sp is 9.1 × 10⁻⁶.)
• 6.73) The concentration of sulphide ion in a 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?

Answers at a glance

1. 1
   Q6.1 → (a) Vapour pressure decreases initially (same vapour in a larger volume). (b) Rate of evaporation stays the same; rate of condensation decreases. (c) At the new equilibrium the two rates are equal and the final vapour pressure equals the original vapour pressure.
2. 2
   Q6.2 → K_c = 12.23 M⁻¹ (≈ 12.24 M⁻¹).
3. 3
   Q6.3 → K_p = 2.67 × 10⁴ Pa.
4. 4
   Q6.4 → (i) K_c = [NO]²[Cl₂]/[NOCl]² (ii) K_c = [NO₂]⁴[O₂] (iii) K_c = [CH₃COOH][C₂H₅OH]/[CH₃COOC₂H₅] (iv) K_c = 1/([Fe³⁺][OH⁻]³) (v) K_c = [IF₅]²/[F₂]⁵.
5. 5
   Q6.5 → (i) K_c = 4.33 × 10⁻⁴ (ii) K_c = 1.87.
6. 6
   Q6.6 → K_c for the reverse reaction = 1.59 × 10⁻¹⁵.
7. 7
   Q6.7 → For a pure liquid or solid, [substance] = density / molecular mass, which is constant at a given temperature and is absorbed into the equilibrium constant; hence pure liquids and solids are omitted from the expression.
8. 8
   Q6.8 → [N₂] = 0.0482 M, [O₂] = 0.0933 M, [N₂O] = 6.6 × 10⁻²¹ M (the concentrations of N₂ and O₂ are practically unchanged).
9. 9
   Q6.9 → At equilibrium, NO = 0.0352 mol and Br₂ = 0.0178 mol.
10. 10
    Q6.10 → K_c = 7.48 × 10¹¹ M⁻¹.
11. 11
    Q6.11 → K_p = 4.0.
12. 12
    Q6.12 → The mixture is not at equilibrium; Q_c = 2.4 × 10³ > K_c = 1.7 × 10², so the net reaction proceeds in the reverse direction.
13. 13
    Q6.13 → 4NO(g) + 6H₂O(g) ⇌ 4NH₃(g) + 5O₂(g).
14. 14
    Q6.14 → K_c = 0.444 (approximately).
15. 15
    Q6.15 → [H₂] = [I₂] = 0.068 mol L⁻¹.
16. 16
    Q6.16 → [Cl₂] = [I₂] = 0.167 M and [ICl] = 0.446 M.
17. 17
    Q6.17 → Equilibrium concentration of C₂H₆ = 3.62 atm.
18. 18
    Q6.18 → (i) Q_c = [CH₃COOC₂H₅][H₂O]/([CH₃COOH][C₂H₅OH]) (ii) K_c = 3.92 (iii) Q_c = 0.204 < K_c, so equilibrium has not been reached.
19. 19
    Q6.19 → [PCl₃] = [Cl₂] = 0.02 mol L⁻¹.
20. 20
    Q6.20 → p_CO₂ = 0.461 atm and p_CO = 1.739 atm.
21. 21
    Q6.21 → The reaction is not at equilibrium (Q_c = 0.0104 ≠ K_c = 0.061); it proceeds in the forward direction.
22. 22
    Q6.22 → [BrCl] at equilibrium = 3.0 × 10⁻⁴ mol L⁻¹.
23. 23
    Q6.23 → K_c = 0.154 (approximately).
24. 24
    Q6.24 → (a) ΔG° = −35.0 kJ mol⁻¹ (b) K_c = 1.36 × 10⁶.
25. 25
    Q6.25 → (a) Increase (b) Decrease (c) Remain the same.
26. 26
    Q6.26 → Reactions (i), (iii), (iv), (v) and (vi) are affected by pressure. (iv) shifts forward; (i), (iii), (v) and (vi) shift backward.
27. 27
    Q6.27 → p_H₂ = p_Br₂ = 2.49 × 10⁻² bar and p_HBr = 9.95 bar (≈ 10 bar).
28. 28
    Q6.28 → (a) K_p = p_CO·p_H₂³/(p_CH₄·p_H₂O) (b)(i) shifts backward (ii) shifts forward and K_p increases (iii) no effect on K_p or composition, only faster attainment of equilibrium.
29. 29
    Q6.29 → (a) Forward (b) Backward (c) Backward (d) Forward.
30. 30
    Q6.30 → (a) K_c = [PCl₃][Cl₂]/[PCl₅] (b) K_c' = 120.48 (c)(i) unchanged (ii) unchanged (iii) K_c increases.
31. 31
    Q6.31 → Equilibrium partial pressure of H₂ = 3.04 bar.
32. 32
    Q6.32 → Only reaction (c), K_c = 1.8, will have appreciable concentrations of reactants and products.
33. 33
    Q6.33 → [O₃] = 2.86 × 10⁻²⁸ mol L⁻¹.
34. 34
    Q6.34 → [CH₄] at equilibrium = 5.85 × 10⁻² M.
35. 35
    Q6.35 → HNO₂ → NO₂⁻ (base); CN⁻ → HCN (acid); HClO₄ → ClO₄⁻ (base); F⁻ → HF (acid); OH⁻ → H₂O (acid) or O²⁻ (base); CO₃²⁻ → HCO₃⁻ (acid); S²⁻ → HS⁻ (acid).
36. 36
    Q6.36 → BF₃ and H⁺ are the Lewis acids among the given species.
37. 37
    Q6.37 → HF → F⁻; H₂SO₄ → HSO₄⁻; HCO₃⁻ → CO₃²⁻.
38. 38
    Q6.38 → NH₂⁻ → NH₃; NH₃ → NH₄⁺; HCOO⁻ → HCOOH.
39. 39
    Q6.39 → H₂O: H₃O⁺/OH⁻; HCO₃⁻: H₂CO₃/CO₃²⁻; HSO₄⁻: H₂SO₄/SO₄²⁻; NH₃: NH₄⁺/NH₂⁻.
40. 40
    Q6.40 → Lewis bases: OH⁻ and F⁻ (donate electron pairs); Lewis acids: H⁺ and BCl₃ (accept electron pairs).
41. 41
    Q6.41 → pH of the soft drink = 2.42.
42. 42
    Q6.42 → [H⁺] in the vinegar sample = 1.74 × 10⁻⁴ mol L⁻¹.
43. 43
    Q6.43 → K_b(F⁻) = 1.5 × 10⁻¹¹, K_b(HCOO⁻) = 5.6 × 10⁻¹¹ and K_b(CN⁻) = 2.08 × 10⁻⁶.
44. 44
    Q6.44 → In 0.05 M phenol, [C₆H₅O⁻] = 2.2 × 10⁻⁶ M. In the presence of 0.01 M sodium phenolate the degree of ionisation falls to 1 × 10⁻⁸.
45. 45
    Q6.45 → [HS⁻] = 9.54 × 10⁻⁵ M without HCl, falling to 9.1 × 10⁻⁸ M in 0.1 M HCl. [S²⁻] = 1.2 × 10⁻¹³ M without HCl and 1.092 × 10⁻¹⁹ M in 0.1 M HCl.
46. 46
    Q6.46 → α = 1.86 × 10⁻², [CH₃COO⁻] = 9.3 × 10⁻⁴ M and pH = 3.03.
47. 47
    Q6.47 → [A⁻] = 7.08 × 10⁻⁵ M, K_a = 5.01 × 10⁻⁷ and pK_a = 6.30.
48. 48
    Q6.48 → (a) 2.52 (b) 11.70 (c) 2.69 (d) 11.31.
49. 49
    Q6.49 → (a) 11.65 (b) 12.21 (c) 12.57 (d) 1.87.
50. 50
    Q6.50 → pH = 1.88 and pK_a ≈ 2.76.
51. 51
    Q6.51 → K_b = 1.58 × 10⁻⁶ and pK_b = 5.80.
52. 52
    Q6.52 → pH = 7.81, α = 6.53 × 10⁻⁴ and K_a of the conjugate acid = 2.34 × 10⁻⁵.
53. 53
    Q6.53 → α = 1.91 × 10⁻² in pure water; it falls to 1.82 × 10⁻³ in 0.01 M HCl and to 1.82 × 10⁻⁴ in 0.1 M HCl.
54. 54
    Q6.54 → α = 0.1643 in water; in 0.1 M NaOH only 0.54% of dimethylamine is ionised.
55. 55
    Q6.55 → (a) 1.48 × 10⁻⁷ M (b) 0.063 M (c) 4.17 × 10⁻⁸ M (d) 3.98 × 10⁻⁷ M.
56. 56
    Q6.56 → Milk 1.5 × 10⁻⁷ M, black coffee 10⁻⁵ M, tomato juice 6.31 × 10⁻⁵ M, lemon juice 6.31 × 10⁻³ M, egg white 1.58 × 10⁻⁸ M.
57. 57
    Q6.57 → [K⁺] = [OH⁻] = 0.05 M, [H⁺] = 2 × 10⁻¹³ M and pH = 12.70.
58. 58
    Q6.58 → [Sr²⁺] = 0.1581 M, [OH⁻] = 0.3126 M and pH = 13.50.
59. 59
    Q6.59 → α = 1.63 × 10⁻² and pH = 3.09 in water; in 0.01 M HCl the degree of ionisation falls to 1.32 × 10⁻³.
60. 60
    Q6.60 → K_a = 2.02 × 10⁻⁴ and α = 0.045.
61. 61
    Q6.61 → pH = 7.97 and degree of hydrolysis = 2.35 × 10⁻⁵.
62. 62
    Q6.62 → Ionisation constant of pyridine, K_b = 1.52 × 10⁻⁹ (≈ 1.5 × 10⁻⁹).
63. 63
    Q6.63 → NaCl and KBr neutral; NaCN, NaNO₂ and KF basic; NH₄NO₃ acidic.
64. 64
    Q6.64 → pH of 0.1 M chloroacetic acid = 1.94 and pH of its 0.1 M sodium salt = 7.94.
65. 65
    Q6.65 → The pH of neutral water at 310 K is 6.78 (pH is no longer 7 because K_w is larger than 10⁻¹⁴).
66. 66
    Q6.66 → (a) pH = 12.63 (b) pH = 7 (c) pH = 1.30.
67. 67
    Q6.67 → Ag₂CrO₄: s = 0.65 × 10⁻⁴ M, [Ag⁺] = 1.30 × 10⁻⁴ M, [CrO₄²⁻] = 0.65 × 10⁻⁴ M. BaCrO₄: s = 1.09 × 10⁻⁵ M, both ions 1.09 × 10⁻⁵ M. Fe(OH)₃: s = 1.39 × 10⁻¹⁰ M, [Fe³⁺] = 1.39 × 10⁻¹⁰ M, [OH⁻] = 4.16 × 10⁻¹⁰ M. PbCl₂: s = 1.58 × 10⁻² M, [Pb²⁺] = 1.58 × 10⁻² M, [Cl⁻] = 3.17 × 10⁻² M. Hg₂I₂: s = 2.24 × 10⁻¹⁰ M, [Hg₂²⁺] = 2.24 × 10⁻¹⁰ M, [I⁻] = 4.48 × 10⁻¹⁰ M.
68. 68
    Q6.68 → The ratio of the molarities of the saturated solutions = 91.9.
69. 69
    Q6.69 → Ionic product = 1 × 10⁻⁹ < K_sp = 7.4 × 10⁻⁸, so precipitation will not occur.
70. 70
    Q6.70 → Silver benzoate is about 3.3 times more soluble in the pH 3.19 buffer than in pure water.
71. 71
    Q6.71 → If each solution has a concentration equal to or less than 5.02 × 10⁻⁹ M, no precipitation of iron sulphide will occur.
72. 72
    Q6.72 → The minimum volume of water required is 2.44 L.
73. 73
    Q6.73 → Precipitation will take place in the ZnCl₂ and CdCl₂ solutions (the ionic product 8.89 × 10⁻²² exceeds the K_sp of ZnS and CdS), and not in FeSO₄ or MnCl₂.

MCQ Questions

1 Mark Questions

1. 1
   State the law of chemical equilibrium. (Ans: at equilibrium the product of concentrations of products divided by that of reactants (each raised to its coefficient) is a constant at a given temperature)
2. 2
   What is the Kc–Kp relation based on changes in gaseous moles? (Ans: Kp = Kc(RT)^Δn)
3. 3
   What is the common ion effect? (Ans: suppression of ionisation of a weak electrolyte by adding a strong electrolyte which provides a common ion, e.g. CH₃COOH + CH₃COONa)
4. 4
   Write the ionic product of water at 25 °C. (Ans: Kw = 10⁻¹⁴)

2 Mark Questions

1. 1
   State and explain Le Chatelier's principle with one example of each, effect of concentration and temperature.
2. 2
   Differentiate between a strong acid and a weak acid. (Ans: fully ionised vs partially ionised; e.g. HCl vs CH₃COOH)
3. 3
   Calculate the pH of 0.05 M NaOH solution. (Ans: [OH⁻] = 0.05 M, pOH = 1.3, pH = 12.7)

3 Mark Questions

1. 1
   Explain the Arrhenius, Bronsted–Lowry and Lewis concepts of acids and bases with examples for each.
2. 2
   What is a buffer solution? Derive the Henderson–Hasselbalch equation for an acidic buffer. (Ans: pH = pKa + log[salt]/[acid]; buffer resists pH change)
3. 3
   The solubility product of AgCl is 1.8 × 10⁻¹⁰. Calculate its solubility in water in mol L⁻¹. (Ans: s = √Ksp ≈ 1.34 × 10⁻⁵ mol L⁻¹)

5 Mark Questions

1. 1
   Discuss Le Chatelier's principle in detail, and apply it to the Haber process (N₂ + 3H₂ ⇌ 2NH₃; ΔH = −92 kJ) showing how temperature, pressure and concentration are chosen to maximise yield. (Ans: high pressure, moderate temperature, removal of NH₃)
2. 2
   Explain the concept of ionic equilibrium: degree of ionisation, the ionisation of weak acids and bases, Kw, pH and pOH scales, and calculate the pH of 0.1 M acetic acid (Ka = 1.8 × 10⁻⁵). (Ans: [H⁺] ≈ 1.34 × 10⁻³ M, pH ≈ 2.87)