Chapter 7 Equilibrium

Question 1. We know that the relationship between $K_c$ and $K_p$ is $K_p = K_c (RT)^{\Delta n}$. What would be the value of $\Delta n$ for the reaction

$NH_4Cl (s) \rightleftharpoons NH_3 (g) + HCl (g)$

(i) 1

(ii) 0.5

(iii) 1.5

(iv) 2

Question 2. For the reaction $H_2(g) + I_2(g) \rightleftharpoons 2HI (g)$, the standard free energy is $\Delta G^\ominus > 0$. The equilibrium constant (K) would be __________.

(i) K = 0

(ii) K > 1

(iii) K = 1

(iv) K < 1

Question 3. Which of the following is not a general characteristic of equilibria involving physical processes?

(i) Equilibrium is possible only in a closed system at a given temperature.

(ii) All measurable properties of the system remain constant.

(iii) All the physical processes stop at equilibrium.

(iv) The opposing processes occur at the same rate and there is dynamic but stable condition.

Question 4. $PCl_5$, $PCl_3$ and $Cl_2$ are at equilibrium at 500K in a closed container and their concentrations are $0.8 \times 10^{–3} \text{ mol L}^{–1}$, $1.2 \times 10^{–3} \text{ mol L}^{–1}$ and $1.2 \times 10^{–3} \text{ mol L}^{–1}$ respectively. The value of $K_c$ for the reaction $PCl_5 (g) \rightleftharpoons PCl_3 (g) + Cl_2 (g)$ will be

(i) $1.8 \times 10^3 \text{ mol L}^{–1}$

(ii) $1.8 \times 10^{–3}$

(iii) $1.8 \times 10^{–3} \text{ L mol}^{–1}$

(iv) $0.55 \times 10^4$

Question 5. Which of the following statements is incorrect?

(i) In equilibrium mixture of ice and water kept in perfectly insulated flask mass of ice and water does not change with time.

(ii) The intensity of red colour increases when oxalic acid is added to a solution containing iron (III) nitrate and potassium thiocyanate.

(iii) On addition of catalyst the equilibrium constant value is not affected.

(iv) Equilibrium constant for a reaction with negative $\Delta H$ value decreases as the temperature increases.

Question 6. When hydrochloric acid is added to cobalt nitrate solution at room temperature, the following reaction takes place and the reaction mixture becomes blue. On cooling the mixture it becomes pink. On the basis of this information mark the correct answer.

$[Co(H_2O)_6]^{3+} (aq) + 4Cl^– (aq) \rightleftharpoons [CoCl_4]^{2–} (aq) + 6H_2O (l)$

(pink) (blue)

(i) $\Delta H > 0$ for the reaction

(ii) $\Delta H < 0$ for the reaction

(iii) $\Delta H = 0$ for the reaction

(iv) The sign of $\Delta H$ cannot be predicted on the basis of this information.

Question 7. The pH of neutral water at 25°C is 7.0. As the temperature increases, ionisation of water increases, however, the concentration of $H^+$ ions and $OH^–$ ions are equal. What will be the pH of pure water at 60°C?

(i) Equal to 7.0

(ii) Greater than 7.0

(iii) Less than 7.0

(iv) Equal to zero

Question 8. The ionisation constant of an acid, $K_a$, is the measure of strength of an acid. The $K_a$ values of acetic acid, hypochlorous acid and formic acid are $1.74 \times 10^{–5}$, $3.0 \times 10^{–8}$ and $1.8 \times 10^{–4}$ respectively. Which of the following orders of pH of 0.1 mol $dm^{–3}$ solutions of these acids is correct?

(i) acetic acid > hypochlorous acid > formic acid

(ii) hypochlorous acid > acetic acid > formic acid

(iii) formic acid > hypochlorous acid > acetic acid

(iv) formic acid > acetic acid > hypochlorous acid

Question 9. $K_{a1}, K_{a2}$ and $K_{a3}$ are the respective ionisation constants for the following reactions.

$H_2S \rightleftharpoons H^+ + HS^–$

$HS^– \rightleftharpoons H^+ + S^{2–}$

$H_2S \rightleftharpoons 2H^+ + S^{2–}$

The correct relationship between $K_{a1}, K_{a2}$ and $K_{a3}$ is

(i) $K_{a3} = K_{a1} \times K_{a2}$

(ii) $K_{a3} = K_{a1} + K_{a2}$

(iii) $K_{a3} = K_{a1} – K_{a2}$

(iv) $K_{a3} = K_{a1} / K_{a2}$

Question 10. Acidity of $BF_3$ can be explained on the basis of which of the following concepts?

(i) Arrhenius concept

(ii) Bronsted Lowry concept

(iii) Lewis concept

(iv) Bronsted Lowry as well as Lewis concept.

Question 11. Which of the following will produce a buffer solution when mixed in equal volumes?

(i) $0.1 \text{ mol dm}^{–3} \ NH_4OH$ and $0.1 \text{ mol dm}^{–3} \ HCl$

(ii) $0.05 \text{ mol dm}^{–3} \ NH_4OH$ and $0.1 \text{ mol dm}^{–3} \ HCl$

(iii) $0.1 \text{ mol dm}^{–3} \ NH_4OH$ and $0.05 \text{ mol dm}^{–3} \ HCl$

(iv) $0.1 \text{ mol dm}^{–3} \ CH_3COONa$ and $0.1 \text{ mol dm}^{–3} \ NaOH$

Question 12. In which of the following solvents is silver chloride most soluble?

(i) $0.1 \text{ mol dm}^{–3} \ AgNO_3$ solution

(ii) $0.1 \text{ mol dm}^{–3} \ HCl$ solution

(iii) $H_2O$

(iv) Aqueous ammonia

Question 13. What will be the value of pH of $0.01 \text{ mol dm}^{–3} \ CH_3COOH \ (K_a = 1.74 \times 10^{–5})$?

(i) 3.4

(ii) 3.6

(iii) 3.9

(iv) 3.0

Question 14. $K_a$ for $CH_3COOH$ is $1.8 \times 10^{–5}$ and $K_b$ for $NH_4OH$ is $1.8 \times 10^{–5}$. The pH of ammonium acetate will be

(i) 7.005

(ii) 4.75

(iii) 7.0

(iv) Between 6 and 7

Question 15. Which of the following options will be correct for the stage of half completion of the reaction $A \rightleftharpoons B$.

(i) $\Delta G^\ominus = 0$

(ii) $\Delta G^\ominus > 0$

(iii) $\Delta G^\ominus < 0$

(iv) $\Delta G^\ominus = –RT \ln2$

Question 16. On increasing the pressure, in which direction will the gas phase reaction proceed to re-establish equilibrium, is predicted by applying the Le Chatelier’s principle. Consider the reaction.

$N_2 (g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g)$

Which of the following is correct, if the total pressure at which the equilibrium is established, is increased without changing the temperature?

(i) K will remain same

(ii) K will decrease

(iii) K will increase

(iv) K will increase initially and decrease when pressure is very high

Question 17. What will be the correct order of vapour pressure of water, acetone and ether at 30°C. Given that among these compounds, water has maximum boiling point and ether has minimum boiling point?

(i) Water < ether < acetone

(ii) Water < acetone < ether

(iii) Ether < acetone < water

(iv) Acetone < ether < water

Question 18. At 500 K, equilibrium constant, $K_c$, for the following reaction is 5.

$\frac{1}{2} H_2(g) + \frac{1}{2} I_2(g) \rightleftharpoons HI(g)$

What would be the equilibrium constant $K_c$ for the reaction

$2HI(g) \rightleftharpoons H_2(g) + I_2(g)$

(i) 0.04

(ii) 0.4

(iii) 25

(iv) 2.5

Question 19. In which of the following reactions, the equilibrium remains unaffected on addition of small amount of argon at constant volume?

(i) $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$

(ii) $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$

(iii) $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$

(iv) The equilibrium will remain unaffected in all the three cases.

Question 20. For the reaction $N_2O_4(g) \rightleftharpoons 2NO_2(g)$, the value of K is 50 at 400 K and 1700 at 500 K. Which of the following options is correct?

(i) The reaction is endothermic

(ii) The reaction is exothermic

(iii) If $NO_2(g)$ and $N_2O_4(g)$ are mixed at 400 K at partial pressures 20 bar and 2 bar respectively, more $N_2O_4(g)$ will be formed.

(iv) The entropy of the system increases.

Question 21. At a particular temperature and atmospheric pressure, the solid and liquid phases of a pure substance can exist in equilibrium. Which of the following term defines this temperature?

(i) Normal melting point

(ii) Equilibrium temperature

(iii) Boiling point

(iv) Freezing point

Question 22. The ionisation of hydrochloric in water is given below:

$HCl(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + Cl^–(aq)$

Label two conjugate acid-base pairs in this ionisation.

Question 23. The aqueous solution of sugar does not conduct electricity. However, when sodium chloride is added to water, it conducts electricity. How will you explain this statement on the basis of ionisation and how is it affected by concentration of sodium chloride?

Question 24. $BF_3$ does not have proton but still acts as an acid and reacts with $NH_3$. Why is it so? What type of bond is formed between the two?

Question 25. Ionisation constant of a weak base MOH, is given by the expression

$K_b = \frac{[M^+][OH^–]}{[MOH]}$

Values of ionisation constant of some weak bases at a particular temperature are given below:

Arrange the bases in decreasing order of the extent of their ionisation at equilibrium. Which of the above base is the strongest?

Question 26. Conjugate acid of a weak base is always stronger. What will be the decreasing order of basic strength of the following conjugate bases?

$OH^–, RO^–, CH_3COO^–, Cl^–$

Question 27. Arrange the following in increasing order of pH.

$KNO_3(aq), CH_3COONa(aq), NH_4Cl(aq), C_6H_5COONH_4(aq)$

Question 28. The value of $K_c$ for the reaction $2HI(g) \rightleftharpoons H_2(g) + I_2(g)$ is $1 \times 10^{–4}$.

At a given time, the composition of reaction mixture is

$[HI] = 2 \times 10^{–5} \text{ mol, } [H_2] = 1 \times 10^{–5} \text{ mol}$ and $[I_2] = 1 \times 10^{–5} \text{ mol}$

In which direction will the reaction proceed?

Question 29. On the basis of the equation $pH = – \log [H^+]$, the pH of $10^{–8} \text{ mol dm}^{–3}$ solution of HCl should be 8. However, it is observed to be less than 7.0. Explain the reason.

Question 30. pH of a solution of a strong acid is 5.0. What will be the pH of the solution obtained after diluting the given solution a 100 times?

Question 31. A sparingly soluble salt gets precipitated only when the product of concentration of its ions in the solution ($Q_{sp}$) becomes greater than its solubility product. If the solubility of $BaSO_4$ in water is $8 \times 10^{–4} \text{ mol dm}^{–3}$. Calculate its solubility in $0.01 \text{ mol dm}^{–3}$ of $H_2SO_4$.

Question 32. pH of $0.08 \text{ mol dm}^{–3}$ HOCl solution is 2.85. Calculate its ionisation constant.

Question 33. Calculate the pH of a solution formed by mixing equal volumes of two solutions A and B of a strong acid having pH = 6 and pH = 4 respectively.

Question 34. The solubility product of $Al(OH)_3$ is $2.7 \times 10^{–11}$. Calculate its solubility in $gL^{–1}$ and also find out pH of this solution. (Atomic mass of Al = 27 u).

Question 35. Calculate the volume of water required to dissolve 0.1 g lead (II) chloride to get a saturated solution. ($K_{sp}$ of $PbCl_2 = 3.2 \times 10^{–8}$, atomic mass of Pb = 207 u).

Question 36. A reaction between ammonia and boron trifluoride is given below:

$:NH_3 + BF_3 \rightarrow H_3N:BF_3$

Identify the acid and base in this reaction. Which theory explains it? What is the hybridisation of B and N in the reactants?

Question 37. Following data is given for the reaction: $CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$

$\Delta_f H^\ominus [CaO(s)] = – 635.1 \text{ kJ mol}^{–1}$

$\Delta_f H^\ominus [CO_2(g)] = – 393.5 \text{ kJ mol}^{–1}$

$\Delta_f H^\ominus [CaCO_3(s)] = – 1206.9 \text{ kJ mol}^{–1}$

Predict the effect of temperature on the equilibrium constant of the above reaction.

Question 38. Match the following equilibria with the corresponding condition

(i) Liquid $\rightleftharpoons$ Vapour

(ii) Solid $\rightleftharpoons$ Liquid

(iii) Solid $\rightleftharpoons$ Vapour

(iv) Solute(s) $\rightleftharpoons$ Solute (solution)

(a) Saturated solution

(b) Boiling point

(c) Sublimation point

(d) Melting point

(e) Unsaturated solution

Question 39. For the reaction : $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$

Equilibrium constant $K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$

Some reactions are written below in Column I and their equilibrium constants in terms of $K_c$ are written in Column II. Match the following reactions with the corresponding equilibrium constant

Column I (Reaction)

(i) $2N_2(g) + 6H_2(g) \rightleftharpoons 4NH_3(g)$

(ii) $2NH_3(g) \rightleftharpoons N_2(g) + 3H_2(g)$

(iii) $\frac{1}{2} N_2(g) + \frac{3}{2} H_2(g) \rightleftharpoons NH_3(g)$

Column II (Equilibrium constant)

(a) $2K_c$

(b) $\sqrt{K_c}$

(c) $\frac{1}{K_c}$

(d) $K_c^2$

Question 40. Match standard free energy of the reaction with the corresponding equilibrium constant

(i) $\Delta G^\ominus > 0$

(ii) $\Delta G^\ominus < 0$

(iii) $\Delta G^\ominus = 0$

(a) K > 1

(b) K = 1

(c) K = 0

(d) K < 1

Question 41. Match the following species with the corresponding conjugate acid

Species

(i) $NH_3$

(ii) $HCO_3^–$

(iii) $H_2O$

(iv) $HSO_4^–$

Conjugate acid

(a) $CO_3^{2–}$

(b) $NH_4^+$

(c) $H_3O^+$

(d) $H_2SO_4$

(e) $H_2CO_3$

Question 42. Match the following graphical variation with their description

A

(i)

(ii)

(iii)

B

(a) Variation in product concentration with time

(b) Reaction at equilibrium

(c) Variation in reactant concentration with time

Question 43. Match Column (I) with Column (II).

Column I

(i) Equilibrium

(ii) Spontaneous reaction

(iii) Non spontaneous reaction

Column II

(a) $\Delta G > 0, K < 1$

(b) $\Delta G = 0$

(c) $\Delta G^\ominus = 0$

(d) $\Delta G < 0, K > 1$

Question 44. Assertion (A) : Increasing order of acidity of hydrogen halides is $HF < HCl < HBr < HI$

Reason (R) : While comparing acids formed by the elements belonging to the same group of periodic table, H–A bond strength is a more important factor in determining acidity of an acid than the polar nature of the bond.

(i) Both A and R are true and R is the correct explanation of A.

(ii) Both A and R are true but R is not the correct explanation of A.

(iii) A is true but R is false.

(iv) Both A and R are false.

Question 45. Assertion (A) : A solution containing a mixture of acetic acid and sodium acetate maintains a constant value of pH on addition of small amounts of acid or alkali.

Reason (R) : A solution containing a mixture of acetic acid and sodium acetate acts as a buffer solution around pH 4.75.

(i) Both A and R are true and R is correct explanation of A.

(ii) Both A and R are true but R is not the correct explanation of A.

(iii) A is true but R is false.

(iv) Both A and R are false.

Question 46. Assertion (A): The ionisation of hydrogen sulphide in water is low in the presence of hydrochloric acid.

Reason (R) : Hydrogen sulphide is a weak acid.

(i) Both A and R are true and R is correct explanation of A.

(ii) Both A and R are true but R is not correct explanation of A.

(iii) A is true but R is false

(iv) Both A and R are false

Question 47. Assertion (A): For any chemical reaction at a particular temperature, the equilibrium constant is fixed and is a characteristic property.

Reason (R) : Equilibrium constant is independent of temperature.

(i) Both A and R are true and R is correct explanation of A.

(ii) Both A and R are true but R is not correct explanation of A.

(iii) A is true but R is false.

(iv) Both A and R are false.

Question 48. Assertion (A) : Aqueous solution of ammonium carbonate is basic.

Reason (R) : Acidic/basic nature of a salt solution of a salt of weak acid and weak base depends on $K_a$ and $K_b$ value of the acid and the base forming it.

(i) Both A and R are true and R is correct explanation of A.

(ii) Both A and R are true but R is not correct explanation of A.

(iii) A is true but R is false.

(iv) Both A and R are false.

Question 49. Assertion (A): An aqueous solution of ammonium acetate can act as a buffer.

Reason (R) : Acetic acid is a weak acid and $NH_4OH$ is a weak base.

(i) Both A and R are true and R is correct explanation of A.

(ii) Both A and R are true but R is not correct explanation of A.

(iii) A is false but R is true.

(iv) Both A and R are false.

Question 50. Assertion (A): In the dissociation of $PCl_5$ at constant pressure and temperature addition of helium at equilibrium increases the dissociation of $PCl_5$.

Reason (R) : Helium removes $Cl_2$ from the field of action.

(i) Both A and R are true and R is correct explanation of A.

(ii) Both A and R are true but R is not correct explanation of A.

(iii) A is true but R is false.

(iv) Both A and R are false.

Question 51. How can you predict the following stages of a reaction by comparing the value of $K_c$ and $Q_c$?

(i) Net reaction proceeds in the forward direction.

(ii) Net reaction proceeds in the backward direction.

(iii) No net reaction occurs.

Question 52. On the basis of Le Chatelier principle explain how temperature and pressure can be adjusted to increase the yield of ammonia in the following reaction.

$N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \quad \Delta H = – 92.38 \text{ kJ mol}^{–1}$

What will be the effect of addition of argon to the above reaction mixture at constant volume?

Question 53. A sparingly soluble salt having general formula $A_x^{p+} B_y^{q–}$ and molar solubility S is in equilibrium with its saturated solution. Derive a relationship between the solubility and solubility product for such salt.

Question 54. Write a relation between $\Delta G$ and Q and define the meaning of each term and answer the following :

(a) Why a reaction proceeds forward when Q < K and no net reaction occurs when Q = K.

(b) Explain the effect of increase in pressure in terms of reaction quotient Q. for the reaction : $CO(g) + 3H_2(g) \rightleftharpoons CH_4(g) + H_2O(g)$