Chapter 15. Chemical Equilibrium Sample Exercise 15.1 (p. 632) Write the equilibrium expression for K eq for these three reactions: a) 2 O 3(g) 3 O 2(g) b) 2 NO (g) + Cl 2(g) 2 NOCl (g) c) Ag + (aq) + 2 NH 3(g) Ag(NH 3 ) 2 + (aq) Practice Exercise 15.1 Write the equilibrium expression for K eq for these three reactions: a) H 2(g) + I 2(g) 2 HI (g) b) Cd 2+ (aq) + 4 Br - (aq) CdBr 4 2- (aq - 1 -
Sample Exercise 15.2 (p. 634) In the synthesis of ammonia from nitrogen and hydrogen, N 2(g) + 3 H 2(g) 2 NH 3(g) K c = 9.60 at 300 o C. Calculate K p for this reaction at this temperature. (4.34 x 10-3 ) Practice Exercise 15.2 For the equilibrium 2 SO 3(g) 2 SO 2(g) + O 2(g), K c is 4.08 x 10-3 at 1000 K. Calculate the value for K p. (0.335) Sample Exercise 15.3 The following diagrams represent three different systems at equilibrium, all in the same size containers. a) Without doing any calculations, rank the three systems in order of increasing equilibrium constant, K c. b) If the volume of the containers is 1.0 L and each sphere represents 0.10 mol, calculate K c for each system. Practice Exercise 15.3 The equilibrium constant for the reaction H 2(g) + I 2(g) 2 HI (g) varies with temperature as follows: K p = 792 at 298 K; K p = 54 at 700 K. Is the formation of HI favored more at the higher or lower temperature? - 2 -
Sample Exercise 15.4 (p. 637) The equilibrium constant for the reaction of N 2 with O 2 to form NO equals K c = 1 x 10-30 at 25 o C. N 2(g) + O 2(g) 2 NO (g) Using this information, write the equilibrium constant expression and calculate the equilibrium constant for the following reaction: 2 NO (g) N 2(g) + O 2(g) Practice Exercise 15.4 For the formation of NH 3 from N 2 and H 2, N 2(g) + H 2(g) 2 NH 3(g), K p = 4.34 x 10-3 at 300 o C. What is the value of K p for the reverse reaction? (2.30 x 10 2 ) Sample Exercise 15.5 (p. 638) Given the following information, HF (aq) H + (aq) + F - (aq) K c = 6.8 x 10-4 H 2 C 2 O 4(aq) 2 H + 2- (aq) + C 2 O 4 (aq) K c = 3.8 x 10-6 determine the value of K c for the following reaction: 2 HF (aq) + C 2 O 4 2- (aq) 2 F - (aq) + H 2 C 2 O 4(aq) (0.12) - 3 -
Practice Exercise 15.5 Given the following information at 700 K, H 2(g) + I 2(g) 2HI (g) K p = 54.0 N 2(g) + 3 H 2(g) 2 NH 3(g) K p = 1.04 x 10-4 determine the value of K p (at 700 K) (1.51 x 10 9 ) 2 NH 3(g) + 3 I 2(g) 6 HI (g) + N 2(g) Sample Exercise 15.6 (p. 640) Write the equilibrium-constant K c for each of the following reactions: a) CO 2(g) + H 2(g) CO (g) + H 2 O (l) K c = b) SnO 2(s) + 2 CO (g) Sn (s) + 2 CO 2(g) K c = Practice Exercise 15.6 Write the equilibrium-constant expressions for each of the following reactions: a) Cr (s) + 3 Ag + (aq) Cr 3+ (aq) + 3 Ag (s) K c = b) 3 Fe (s) + 4 H 2 O (g) Fe 3 O 4(s) + 4 H 2(g) K p = - 4 -
Sample Exercise 15.7 (p. 641) Each of the following mixtures was placed in a closed container and allowed to stand. Which of these mixtures is capable of attaining the equilibrium CaCO 3(s) CaO (s) + CO 2(g) a) pure CaCO 3 b) CaO and a pressure of CO 2 greater than the value of K p c) Some CaCO 3 and a pressure of CO 2 greater than the value of K p d) CaCO 3 and CaO Practice Exercise 15.7 When added to Fe 3 O 4(s) in a closed container, which one of the following substances H 2(g), H 2 O (g), O 2(g) - will allow equilibrium to be established in the reaction 3 Fe (s) + 4 H 2 O (g) Fe 3 O 4(s) + 4 H 2(g) Sample Exercise 15.8 (p. 642) A mixture of hydrogen and nitrogen in a reaction vessel is allowed to attain equilibrium at 472 o C. The equilibrium mixture of gases was analyzed and found to contain 7.38 atm H 2, 2.46 atm N 2, and 0.166 atm NH 3. From these data calculate the equilibrium constant, K p, for N 2(g) + 3 H 2(g) 2 NH 3(g) (2.79 x 10-5 ) - 5 -
Practice Exercise 15.8 An aqueous solution of acetic acid is found to have the following equilibrium concentrations at 25 o C: [HC 2 H 3 O 2 ] = 1.65 x 10-2 M; [H + ] = 5.44 x 10-4 M; and [C 2 H 3 O 2 - ] = 5.44 x 10-4 M. Calculate the equilibrium constant, K c, for the ionization of acetic acid at 25 o C. The reaction is (1.79 x 10-5 ) HC 2 H 3 O 2(aq) H + (aq) + C 2 H 3 O 2 - (aq) Sample Exercise 15.9 (p. 643) A closed system initially containing 1.000 x 10-3 M H 2 and 2.000 x 10-3 M I 2 at 448 o C is allowed to reach equilibrium. Analysis of the equilibrium mixture shows that the concentration of HI is 1.87 x 10-3 M. Calculate K c at 448 o C for the reaction taking place, which is H 2(aq) + I 2(g) 2 HI (g) (1.81 x 10-5 ) - 6 -
Practice Exercise 15.9 Sulfur trioxide decomposes at high temperature in a sealed container: 2 SO 3(g) 2 SO 2(g) + O 2(g) Initially the vessel is charged at 1000 K with SO 3(g) at a partial pressure of 0.500 atm. At equilibrium the SO 3 partial pressure is 0.200 atm. Calculate the value of K p at 1000 K. (0.338) Sample Exercise 15.10 (p. 645) At 448 o C the equilibrium constant, K c, for the reaction H 2(g) + I 2(g) 2 HI (g) is 51. Predict how the reaction will proceed to reach equilibrium at 448 o C if we start with 2.0 x 10-2 mol of HI, 1.0 x 10-2 mole of H 2, and 3.0 x 10-2 mol of I 2 in a 2.00-L container. (Q = 1.3, so reaction must proceed from left to right) - 7 -
Practice Exercise 15.10 At 1000 K the value of K p for the reaction 2 SO 3(g) 2 SO 2(g) + O 2(g) is 0.338. Calculate the value for Q p, and predict the direction in which the reaction will proceed toward equilibrium if the initial partial pressures of reactants are P SO3 = 0.16 atm; P SO2 = 0.41 atm; P O2 = 2.5 atm. (Q p = 16; Q p > K p, so reaction will proceed from right to left) Sample Exercise 15.11 (p. 646) For the Haber process, N 2(g) + 3 H 2(g) 2 NH 3(g), K p = 1.45 x 10-5 at 500 o C. In an equilibrium mixture of the three gases at 500 o C, the partial pressure of H 2 is 0.928 atm and that of N 2 is 0.432 atm. What is the partial pressure of NH 3 in this equilibrium mixture? (2.24 x 10-3 atm) - 8 -
Practice Exercise 15.11 At 500 K the reaction PCl 5(g) PCl 3(g) + Cl 2(g) has K p = 0.497. In an equilibrium mixture at 500 K, the partial pressure of PCl 5 is 0.860 atm and that of PCl 3 is 0.350 atm. What is the partial pressure of Cl 2 in the equilibrium mixture? (1.22 atm) Sample Exercise 15.12 (p. 646) A 1.000-L flask is filled with 1.000 mol of H 2 and 2.000 mol of I 2 at 448 o C. The value of the equilibrium constant, K c, for the reaction H 2(g) + I 2(g) 2 HI (g) at 448 o C is 50.5. What are the partial pressures of H 2, I 2, and HI in the flask at equilibrium? ([H 2 ] = 0.065 M, [I 2 ] = 1.065 M, [HI] = 1.87 M) - 9 -
Practice Exercise 15.12 For the equilibrium, PCl 5(g) PCl 3(g) + Cl 2(g), the equilibrium constant, K p, has the value 0.497 at 500 K. A gas cylinder at 500 K is charged with PCl 5(g) at an initial pressure of 1.66 atm. What are the equilibrium pressures of PCl 5, PCl 3, and Cl 2 at this temperature? (P PCl5 = 0.967 atm, P PCl3 = P Cl2 = 0.693 atm) - 10 -
Consider the following equilibrium: N 2 O 4(g) 2 NO 2(g) Sample Exercise 15.13 (p. 653) H o = 58.0 kj In what direction will the equilibrium shift when each of the following changes is made to a system at equilibrium: a) add N 2 O 4 b) remove NO 2 c) increase the total pressure by adding N 2(g) d) increase the volume e) decrease the temperature? Practice Exercise 15.13 For the reaction PCl 5(g) PCl 3(g) + Cl 2(g) in what direction will the equilibrium shift when H o = 87.9 kj a) Cl 2(g) is removed; b) The temperature is decreased; c) The volume of the reaction system is increased; d) PCl 3(g) is added? - 11 -
Sample Exercise 15.14 (p. 653) a) Using the standard heat of formation data in Appendix C, determine the standard enthalpy change for the reaction N 2(g) + 3 H 2(g) 2 NH 3(g) b) Determine how the equilibrium constant for this reaction should change with temperature. Practice Exercise 15.14 Using the thermodynamic data in Appendix C, determine the enthalpy change for the reaction 2 POCl 3(g) 2 PCl 3(g) + O 2(g) Use this result to determine how the equilibrium constant for the reaction should change with temperature. - 12 -
Sample Integrative Exercise 15 At temperatures near 800 o C, steam passed over hot coke (a form of carbon obtained from coal) reacts to form CO and H 2 : C (s) + H 2 O (g) CO (g) + H 2(g) The mixture of gases that results is an important industrial fuel called water gas. a) At 800 o C the equilibrium constant for this reaction is K p = 14.1. What are the equilibrium partial pressures of H 2 O, CO, and H 2 in the equilibrium mixture at this temperature if we start with solid carbon and 0.100 mol of H 2 O in a 1.00-L vessel? b) What is the minimum amount of carbon required to achieve equilibrium under these conditions? c) What is the total pressure in the vessel at equilibrium? d) At 25 o C the value of Keq for this reaction is 1.7 x 10-21. Is the reaction exothermic or endothermic? e) To produce the maximum amount of CO and H 2 at equilibrium, should the pressure of the system be increased or decreased? - 13 -