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EXERCISE – III

Reaction quotient and equilibrium constant 1. The initial concentrations or pressure of reactants

and products are given for each of the following systems. Calculate the reaction quotient and determine the directions in which each system will shift to reach equilibrium.

(a) 2NH₃ (g) N₂(g) + 3H₂(g) K = 17

[NH₃] = 0.20 M ; [N₂] = 1.00 M ; [H₂]=1.00 M (b) 2NH₃ (g) N₂(g)+3H₂(g) K_p=6.8 × 104 _atm2

Initial pressure : NH₃ = 3.0 atm ; N₂ = 2.0 atm ; H₂ = 1.0 atm

(c) 2SO₃(g) 2SO₂(g)+O₂(g) K = 0.230 atm [SO₃]=0.00 M;[SO₂]= 1.00 M ;[O₂] = 1.00 M (d) 2SO₃(g) 2SO₂ (g) + O₂(g) K_p = 16.5 atm

Initial pressure : SO₃ = 1.0 atm; SO₂ = 1.0 atm ; O₂ = 1.0 atm

(e) 2NO(g)+Cl₂(g) 2NOCl(g) K = 4.6 × 104

[NO]=1.00 M ; [Cl₂] = 1.00 M ;[NOCl] = 0 M Sol.

2. Among the solubility rules is the statement that all chlorides are soluble except Hg₂ Cl₂, AgCl, PbCl₂ and CuCl.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation. AgCl (s) Ag+ _{(aq) + Cl}– _(aq)

Is k greater than 1, less than 1, or about equal to 1 ? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation Pb2+ _{(aq) + 2Cl}– _{(aq) PbCl}

2(S)

Is K greater than 1, less than 1, or about equal to ? Explain your answer.

Sol.

3. Among the solubility rules is the statement that carbonates, phosphates, borates, arsenates, and arsenites, except those of the ammonium ion and the alkali metals are insoluble.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation CaCO₃ (s) Ca2+ _{(aq) + CO}

3 2– _(aq)

Is K greater than 1, less than 1, or about equal to 1? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by equation. 3Ba2+_{(aq) + 2PO}

4

3– _{(aq) Ba}

3(PO4)2 (s)

Is K greater than 1, less than 1, or about equal to 1 ? Explain your answer.

4. Benzene is one of the compounds used as octane enha nc er s i n unl ea de d ga sol i ne . It i s manufactured by the catalytic conversion of acetylene to benzene. 3C₂H₂  C₆H₆

Would this reaction be most useful commercially if K were about 0.01, about 1, or about 10 ? Explain your answer.

Sol.

5. Show the complete chemical equation and the net ionic equation for the reaction represented by the equation

Kl (aq) + I₂ (aq) KI₃(aq)

give the same expression for the reaction quotient. KI₃ is composed of the ions K+ _{and I}

3 –_.

Sol.

Using the equilibrium constant

6. Which of the following reactions goes almost all the way to completion, and which proceeds hardly at all ?

(a) N₂(g) + O₂(g) 2NO (g); K_c = 2.7 × 10–18

(b) 2NO(g) + O₂(g) 2NO₂ (g) ; K_c = 6.0 × 1013

Sol.

7. For which of the following reactions will the equilibrium mixture contain an appreciable concentration of both reactants and products ? (a) Cl₂(g) 2Cl (g) ;K_c = 6.4 × 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 Sol.

8. The value of K_c for the reaction

3O₂(g) 2O₃ (g) is 1.7 × 10–56 _{at 25°C. Do}

you expect pure air at 25°C to contain much O₃ (ozone) when O₂ and O₃ are in equilibrium ? If the equilibrium concentration of O₂ in air at 25°C i s 8 × 10–3 _{M, what i s the equi l i bri um}

concentration of O₃ ? Sol.

9. At 1400 K, K_c = 2.5 × 10–3 _{for the reaction}

CH₄ (g) + 2H₂S CS₂(g) + 4 H₂(g). A 10.0 L reaction vessel at 1400 K contains 2.0 mol of CH₄. 3.0 mol of CS₂, 3.0 mol of H₂ and 4.0 mol of H₂S. Is the reaction mixture at equilibrium ? If not, in which direction does the reaction proceed to reach equilibrium ?

10. The first step in the industrial synthesis of hydrogen is the reaction of steam and methane to give water gas, a mixture of carbon monoxide and hydrogen.

H₂O(g) + CH₄(g) CO(g) + 3H₂(g) K_c = 4.7 at 1400 K

A mixture of reactants and product at 1400 K contains 0.035 M H₂O, 0.050 M CH₄, 0.15 M CO, and 0.20 M H₂. In which direction does the reaction proceed to reach equilibrium ?

Sol.

11. An equilibrium mixture of N₂, H₂, and NH₃ at 700 K contains 0.036 M N₂ and 0.15 M H₂. At this temperature, K_c for the reaction

N₂(g) + 3H₂(g) 2NH₃ (g) is 0.29. What is the concentration of NH₃ ?

Sol.

12. The air pollutant NO is produced in automobile engines from the high temperature reaction N₂(g) + O₂(g) 2 NO (g) ; K_c = 1.7 × 10–3 _at

2300 K. If the initial concentrations of N₂ and O₂ at 2300 K are both 1.40 M, what are the concentrations of NO, N₂ and O₂ when the reaction mixture reaches equilibrium ?

Sol.

13. At a certain temperature, the reaction

PCl₅(g) PCl₃(g) + Cl₂(g) has an equilibrium constant K_c = 5.8 × 10–2_{. Calculate the equilibrium}

concentrations of PCl₅, PCl₃ and Cl₂ if only PCl₅ is present initially, at a concentration of 0.160 M. Sol.

14. At 700 K, K_p = 0.140 for the reaction

ClF₃(g) ClF(g) + F₂(g). Calculate the equilibrium partial pressure of ClF₃, ClF, and F₂ if only ClF₃ is present initially, at a partial pressure of 1.47 atm.

H omog en eous e qu il ib ri a de gr ee of dissociation, vapour density and equilibrium constant.

Sol.

15. The degree of dissociation of N₂O₄ into NO₂ at 1.5 atmospher and 40°C is 0.25. Calculate its K_p at 40°C. Also report degree of dissociation at 10 atmospheric pressure at same temperature. Sol.

16. At 46° C K_p for the reaction

N₂O₄ (g) 2NO₂(g) is 0.667 atm. Compute the percent dissociation of N₂O₄ at 46°C at a total pressure of 380 Torr.

Sol.

17. When 36.8 g N₂O₄(g) is introduced into a 1.0- litre flask at 27°C. The following equilibrium reaction occurs :

N₂O₄(g) 2NO₂(g) ; K_p = 0.1642 atm. (a) Calculate K_c of the equilibrium reaction. (b) What are the number of moles of N₂O₄ and NO₂ at equilirbium ?

(c) What is the total gas pressure in the flask at equilibrium ?

(d) What is the percent dissociation of N₂O₄ ? Sol.

18. At some temperature and under a pressure of 4 atm, PCl₅ is 10% dissociated. Calculate the pressure at which PCl₅ will be 20% dissociated, temperature remaining same.

Sol.

19. In a mixture of N₂ and H₂ in the ratio of 1 : 3 at 64 atmopheri c pressure and 300°C, the percentage of ammonia under equlibrium is 33.33 by volume. Calculate the equilibrium constant of the reaction using the equation.

N₂(g) + 3H₂(g) 2NH₃(g) Sol.

20. The system N₂O₄ 2 NO₂ maintained in a closed vessel at 60° C & a pressure of 5 atm has an average (i.e. observed) molecular weight of 69, calculate K_p. At what pressure at the same temperature would the observed molecular weight be (230/3) ?

Sol.

21. The vapour density of N₂O₄ and NO₂ mixture at a certain temperature is 30. Cal cul ate the pe rc ent ag e d i ss oc i at i on of N₂O₄ a t thi s temperature. N₂O₄(g) 2NO₂(g)

22. In the esterfication

C₂H₅OH(1)+CH₃COOH(1) CH₃COOC₂H₅(l)+H₂O (l) an equimolar mixture of alcohol and acid taken initially yields under equilibrium, the water with mole fraction = 0.333. Calculate the equilibrium constant.

Sol.

Hetrogeneous equilibrium

23. Solid Ammonium carbamate dissociates as : NH₂COO NH₄ (s) 2NH₃(g) + CO₂(g). In a closed vessel solid ammonium carbamate is in equilibrium with its dissociation products. At equilibrium, ammonia is added such that the partial pressure of NH₃ at new equilibrium now equals the original total pressure. Calculate the ratio of total pressure at new equilibrium to that of original total pressure.

Sol.

24. A sample of CaCO₃(s) is introduced into a sealed container of volume 0.821 litre & heated to 1000K until equilibrium is reached. The equilibrium constant for the reaction

CaCO₃ (s) CaO(s) + CO₂(g) is 4 × 10–2 _atm

at this temperature. Calculate the mass of CaO present at equilibrium.

Sol.

25. Anhydrous calcium chloride is often used as a dessicant. In the presence of excess of CaCl₂, the amount of the water taken up is governed by K_p = 6.4 × 1085 _{for the following reaction at}

room temperature,

CaCl₂(s) + 6H₂O(g) CaCl₂.6H₂O(s). What is the equilibrium vapour pressure of water in a closed vessel that contains CaCl₂(s) ?

Sol.

26. 20.0 grams of CaCO₃(s) were placed in a closed vessel, heated & maintained at 727° C under equilibrium CaCO₃(s) CaO(s) + CO₂(g) and it is found that 75% of CaCO₃ was decomposed. What is the value of K_p ? The volume of the container was 15 litres.

Sol.

Changes in concentration at equilibrium Le Chatelier's principle

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

N₂(g) + 2H₂(g) N₂H₄(g) H = 95 kJ Sol.

28. How will an increase in temperature affect each of the following equilibria ? An increase in pressure ? (a) 2NH₃ (g) N₂(g) + 3H₂(g)H = 92 kJ (b) N₂(g) + O₂(g) 2NO (g)H = 181 kJ (c) 2O₃ (g) 3O₂(g) H = – 285 kJ (d) CaO(s)+CO₂(g) CaCO₃(s) H=–176 kJ Sol.

29. (a) Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and additional hydrogen at high temperature and pressure in the presence of a suitable catalyst. Write the expression for the equilibrium constant for the reversible reaction.

2H₂(g)+CO(g) CH₃OH(g) H = – 90.2 kJ (b) Assume that equilibrium has been established and predict how the concentration of H₂, CO and CH₃OH will differ at a new equilibrium if (i) more H₂ is added. (2) CO is removed. (3) CH₃OH is added. (4) the pressure on the system is increased. (5) the temperature of the system is increased.. (6) more catalyst is added.

Sol.

30. (a) Water gas, a mixture of H₂ and CO, is an important industrial fuel produced by the reaction of steam with red-hot coke, essentially pure carbon, Write the expression for the equilibrium constant for the reversible reaction.

C(s)+H₂O(g) CO (g)+H₂(g) H=131.30 kJ (b) Assume that equilibrium has been established and predict how the concentration of each reactant and product will differ at a new equilibrium if (1) more C is added. (2) H₂O is removed. (3) CO is added. (4) the pressure on the system is increased. (5) the temperature of the system is increased.

Sol.

31 Ammonia is a weak base that reacts with water according to the equation

NH₃(aq) + H₂O (l) NH₄+ _{+ OH}– _(aq)

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

(a) Addition of NaOH. (b) Addition of HCl (c) Addition of NH₄Cl.

Sol.

32. Suggest two ways in which the equilibrium concentration of Ag+ _{can be reduced in a solution}

of Na+_{, Cl}–_{, Ag}+ _{and NO} 3

– _{, in contact with solid}

AgCl.

Na+_{(aq) + Cl}– _{(aq) + Ag}+_{(aq) + NO} 3

– _(aq)

AgCl(s) + Na+_{(aq) + NO} 3

Sol.

33. Additional solid silver sulfate, a slightly soluble solid, is added to a solution of silver ion and sulfate ion in equilibrium with solid silver sulfate. Which of the following will occur ? (a) The Ag+

and SO₄2– _{concentration will not change. (b) The}

added silver sulfate will dissolve. (c) Additional silver sulfate will form and precipitate from solutino as Ag+ _{ions and SO}

4

2– _{ions combine. (d)}

The Ag+ _{ion concentration will increase and the}

SO₄2– _{ion concentration will decrease.}

Sol.

Kinetics and equilibrium constant

34. Consider a general, single-step reaction of the type A + B C. Show that the equilibrium constant is equal to the ratio of the rate constant for the forward and reverse reaction, K_c = k_kf

r . Sol. Sol. 36. Cons i d er t he g as -p ha se hyd ra ti on of hexafluoroacetone, (CF₃)₂ CO : (CF₃)₂ CO (g) + H₂O (g) k_f k_r (CF3)2C(OH)2(g)

At 76° C, the forward and reverse rate constants are k_f = 0.13 M–1 _s–1 _{and k}

r = 6.02 × 10 –4 _s–1_.

What is the value of the equilibrium constant K_c ? Sol.

37. Consider the reaction of chloromethane with OH–

in aqueous solution CH₃Cl(aq) + OH–_(aq)

k_f

k_r CH3OH(aq) + Cl – _(aq)

At 25°C, the rate constant for the forward reaction is 6× 10–6 _M–1 _s–1_{, and the equilibrium}

constant K_c is 1 × 1016_{. Calculate the rate}

constant for the reverse reaction at 25°C. Sol.

38. The progress of the reaction

A nB with time, is presented in figure. Determine 0.5 0.3 0.1 1 3 5 7 Time/Hour

(i) the value of n.

(ii) the equilibrium constant K.

(iii) the initial rate of conversion of A. Sol.

Temperature dependence of equilibrium constant

39. Listed in the table are forward and reverse rate constnats for the reactions

2NO(g) N₂(g) + O₂(g) Temperature (K) k_f(M–1_S–1_{) k} r(M –1_s–1₎ 1400 0.29 1.1 × 10–6 1500 1.3 1.4 × 10–5

Is the reaction endothermic or exothermic? Explain in tems of kinetics.

Sol.

40. Forward and reverse rate constant for the reaction CO₂(g) + N₂(g) CO(g) + N₂O exhibit the following temperature dependence.

Temperature (K) k_f(M–1_S–1_{) k} r(M

–1_s–1₎

1200 9.1 × 10–11 _{1.5 × 10}5

1500 2.7 × 10–9 _{2.6 × 10}5

Is the reaction endothermic or exothermic? Explain in terms of kinetics.

Sol.

41. The equilibrium constant K_p for the reaction PCl₅(g) PCl₃(g) + Cl₂(g) is 3.81 × 102 _at

600 K and 2.69 × 103 _{at 700 K. Calculate } rH.

Sol.

Temperature dependence of equilibrium constant

42. Rate of disappearance of the reactant A at two different temperature is given by

A B– [ ]d A ( –2 –1)[ ] dt  2 10 S A –4×10 –3 _S–1 _{[B] ; 300 K} – [ ]d A ( –2 –1)[ ] dt  4 10 S A – 16 × 10 –4 _{[B] ; 400 K}

Cal cul a te heat of re acti on i n the gi ven temperature range. When equilibrium is set up. Sol.

43. The K_p for reaction A + B C + D is 1.34 at 60° C and 6.64 at 100°C. Determine the standard free energy change of this reaction at each temperature and H° for the reaction over this range of temperature ?

Sol.

Equilibrium expressions and equilibrium constants

44. If K_c = 7.5 × 10–9 _{at 1000 k for the reaction}

N₂(g) + O₂(g) 2NO(g), what is K_c at 1000 K for the reaction 2NO(g) N₂(g) + O₂(g) ? Sol.

45. An equilibrium mixture of PCl₅, PCl₃ and Cl₂ at a certain temperature contains 8.3 × 10–3 _{M PCl}

5,

1.5 × 10–2 _{M PCl}

3, and 3.2 × 10 –2 _{M Cl}

2. Calculate

the equilibrium constant K_c for the reaction PCl₅(g) PCl₃(g) + Cl₂(g).

Sol.

46. A sample of HI (9.30 × 10–3 _{mol) was placed in}

an empty 2.00 L container at 1000 K. After equilibrium was reached, the concentration of I₂ was 6.29 × 10–4 _{M. Calculate the value of K}

c at

1000 K fo the reaction H₂(g)+I₂(g) 2HI (g). Sol.

47. The vapour pressure of water at 25°C is 0.0313 atm. Calculate the values of K_p and K_c at 25°C for the equilibrium H₂O(1) H₂O(g).

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