Lecture 19 Equilibrium Constant Equilibrium oint of any reaction is characterized by a single number: K eq is the equilibrium constant for the reaction In general: ja + kb R + qs K eq [ R] [ S] [ A] [ B] q = = K j k c [ ] concentration exressed in M(mol/L) K = R j A q S B k P : artial ressures in atm Samle Problem The equilibrium constant K for the following reaction at 100 C is 0.416. 2NOBr(g) Br2(g)+ 2NO(g) Write the exression for the equilibrium constants for the reaction. What is the value of K for the following reaction at the same temerature? 2Br2(g)+ 4NO(g) 4NOBr(g) Summer 2005-72 - Chem 6 Study Guide
Lecture 19 Relationshi between K and K c K = K (RT) c n where n = n rod -n react K C (the number) DOES NOT deend on concentration It s a function of temerature only. --------------------------------------------------------------------------------------- Samle Problem At 25 C, a mixture of N2O4 and NO2 in equilibrium has a total ressure of 0.844 atm. If the artial ressure of N2O4 is 0.563 atm, calculate K and Kc for the reaction given below at 25 C: N2O4(g) 2NO2(g) Summer 2005-73 - Chem 6 Study Guide
Equilibrium Constant and its Meaning 1. Write the exressions for K eq for the following reactions. a) CH 4 (g) + 2 H 2 S(g) CS 2 (g) + 4 H 2 (g) b) 2 N 2 O 5 (g) 4 NO 2 (g) + O 2 (g) c) 3 O 2 (g) 2 O 3 (g) 2. The equilibrium constant for the reaction below is K c = 2.4 x 10 3 at 700 o C. 2 SO 3 (g) 2 SO 2 (g) + O 2 (g) a) Calculate K for this reaction at 700 o C. A) 2.4 x 10 3 B) 0.138 C) 0.192 D) 15.3 b) Calculate K c for the reaction 4 SO 2 (g) + 2 O 2 (g) 4 SO 3 (g) at 700 o C. A) 2.4 x 10 3 B) 4.8 x 10 3 C) 4.2 x 10 2 D) 1.7 x 10 5 c) At this temerature, does the equilibrium favor SO 3, or does it favor SO 2 and O 2? Summer 2005-74 - Chem 6 Study Guide
3. Which one of the following has the greatest tendency to roceed as written? (a) 4NH 3 (g) + 3O 2 (g) 2N 2 (g) + 6H 2 O(g) K = 1 10 228 (b) N 2 (g) + O 2 (g) 2NO(g) K = 5 10 31 (c) 2HF(g) F 2 (g) + H 2 (g) K = 1 10 13 (d) 2NOCl(g) 2NO(g) + Cl 2 (g) K = 4.7 10 4 Arrange the reactions in order of their increasing tendency to roceed toward comletion. 4A. For which of the reactions below is K c = K? (There can be more than one correct answer.) a) N 2 (g) + 3 H 2 (g) 2 NH 3 (g) b) H 2 (g) + Br 2 (g) 2 HBr(g) c) CH 4 (g) + 2 H 2 S(g) CS 2 (g) + 4 H 2 (g) d) 2 N 2 O 5 (g) 4 NO 2 (g) + O 2 (g) 4B For which reactions is K c > K P? (There can be more than one correct answer.) 5. The equilibrium constant at 100 C for the following reaction is 2.19 10 10. COCl 2 (g) CO(g) + Cl 2 (g) The equilibrium mixture should be a) mostly COCl 2 (g) b) mostly CO (g) c) mostly Cl 2 (g) d) an equal mixture of CO(g) and Cl 2 (g) with almost no COCl 2 (g) e) There is not enough information to determine anything about the equilibrium mixture. Summer 2005-75 - Chem 6 Study Guide
Heterogeneous Equilibria 1. Which of the following reactions involve heterogeneous equilibria? (There is more than one correct answer.) (a) CO(g) + 2H 2 (g) CH 3 OH(g) (b) PCl 3 (g) + Cl 2 (g) PCl 5 (g) (c) 2H 2 S(g) + 3O 2 (g) 2H 2 O(g) +2SO 2 (g) (d) NiO(s) + CO(g) Ni(s) +CO 2 (g) (e) BaSO 4 (s) Ba 2+ (aq) + SO 4 2 (aq) Write equilibrium exressions for K eq for each of the reactions. 2. The value of K c for this reaction is 1.10 at 25 C. What is the value of K for this reaction at the same temerature? 4CuO(s) + CH 4 (g) CO 2 (g) + 4Cu(s) + 2H 2 O(g) a) 658 b) 37.2 c) 26.9 d) 4.63 e) 1.53 10 3 Summer 2005-76 - Chem 6 Study Guide
Lecture 19 General Aroach to Equilibrium Constant Problems 1) Write the balanced reaction. 2) Write the general form for K eq. 3) Set u a data table: (may need algebraic unknowns) initial conditions changes in concentrations equilibrium concentrations 4) Substitute equilibrium concentrations into the exression for K eq and solve. ------------------------------------------------------------------------------------------ Samle Problem: For the following reaction, Kc = 6.4 10 7 at 2000 C: 2CO2(g) 2CO(g) + O2(g) If 2.3 mol of CO2 is laced in a 1.0L vessel at this temerature, what will the equilibrium concentration of CO be? 2CO2(g) 2CO(g) + O2(g) initial change equilibrium HINT: The equilibrium exression will be a cubic equation. Solve it by assuming that [O 2 ] = x << 2.3. After solving for x, use stoichiometry to determine [CO]. Summer 2005-77 - Chem 6 Study Guide
Equilibrium: Reaction Quotient 1. The equilibrium constant for the following reaction at 150 C is 8.5 10 3. 2IBr(g) Br 2 (g)+ I 2 (g) If there are 0.02 moles of I 2, 0.05 moles of Br 2 and 0.30 moles of IBr then a) the system is at equilibrium. b) the system is not at equilibrium and the roducts will react to roduce more IBr(g) in order to get to equilibrium. (The reaction will roceed to the left.) c) the system is not at equilibrium and the reactant (IBr) will react to roduce more Br 2 (g) and I 2 (g) in order to get to equilibrium. (The reaction will roceed to the right.) d) the system can never get to equilibrium. Show all calculations and exlain your reasoning. HINT Evaluate Q (the reaction quotient) for this set of concentrations. What does Q tell you about the extent and direction of a reaction? 2. Consider the following reaction at a constant temerature for which K eq = 2.7. CO(g) + H 2 O(g) CO 2 (g) + H 2 (g) If 0.153 mole of CO, 0.546 mole of H 2 O, 0.262 mole of CO 2 and 0.743 mole of H 2 are introduced into a 2 L vessel, which of the following statements will be true? a) The system is at equilibrium and no change will occur. b) The system is not at equilibrium and will roceed to the right to achieve equilibrium. c) The system is not at equilibrium and will roceed to the left to achieve equilibrium. d) The system is not at equilibrium and it cannot achieve equilibrium. e) The system is at equilibrium, but the addition of a catalyst will cause the reaction to roceed to the right. Summer 2005-78 - Chem 6 Study Guide
Equilibrium Problems 1. A mixture of 0.1000 mol of CO 2, 0.0500 mol of H 2, and 0.1000 mol of H 2 O is laced in a 1.0 L vessel. The following equilibrium is established: CO 2 (g) + H 2 (g) CO(g) + H 2 O(g) At equilibrium, [CO 2 ] = 0.0954 M. Calculate the equilibrium concentrations of H 2, CO, and H 2 O. [H 2 ] [CO] [H 2 O] a) 0.0954 0.0454 0.1046 b) 0.0454 4.60 10 3 0.1046 c) 0.1 0.05 0.1 d) 0.0954 4.60 10 3 4.60 10 3 2. At temeratures near 800 o C, steam assed 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 imortant industrial fuel called water gas. When equilibrium is achieved at 800 o C, [H 2 ] = 4.0 x 10 2 M, [CO] = 4.0 x 10 2, and [H 2 O] = 1.0 x 10 2 M. Calculate K c at this temerature a) 0.16 b) 1.6 10 3 c) 4.0 d) 6.25 e) There is not enough information to answer this question. Summer 2005-79 - Chem 6 Study Guide
3. A mixture of 1.374 g of H 2 and 70.31 g of Br 2 is heated in a 2.00 L vessel at 700 K. These substances react as follows: H 2 (g) + Br 2 (g) 2 HBr(g) At equilibrium the vessel is found to contain 0.566 g of H 2. a) Calculate the equilibrium concentrations of H 2, Br 2, and HBr. [H 2 ] [Br 2 ] [HBr] a) 0.341 0.220 0.201 b) 0.682 0.441 0.281 c) 0.140 0.0190 0.201 d) 0.281 0.0400 0.401 b) Calculate K c. a) 0.539 b) 14.3 c) 15.2 d) 0.0699 e) 0.0658 Summer 2005-80 - Chem 6 Study Guide
Lecture 20 What haens to a system at equilibrium when it is disturbed? Le Chatelier s Princile If a system at equilibrium is disturbed, the concentrations of reactants and roducts will shift to minimize the effect of the disturbance. WHAT IF TEMPERATURE CHANGES? K eq changes change deends on whether the reaction is exothermic ( H) or endothermic(+ H). Le Chatelier s Princile: Treat heat like a roduct (exothermic) or reactant (endothermic). When heat is added to a system, the reaction will shift in the direction that absorbs heat Reaction is exothermic (heat is a roduct) so adding heat will cause reaction to shift to left. Reaction is endothermic (heat is a reactant) so adding heat will cause reaction to shift to right. Samle Problem: Considering the following equilibrium situation: CaCO3(s) + heat CaO(s) + CO2(g) How will the amount of CaCO3(s) change for the disturbances given below? (Write increase or decrease after each answer.) (a) CaO(s) is added. (b) CO2(g) is added. (c) The volume of the container is increased. (d) The temerature is lowered. Summer 2005-81 - Chem 6 Study Guide
Le Chatelier s Princile 1. Considering the following equilibrium situation: 2N 2 O(g) + O 2 (g) 4NO(g) How will the amount of NO resent at equilibrium be affected when other disturbances occur? (Write increase, decrease, or no change.) (a) Adding N 2 O(g) to the system. (b) Removing O 2 (g). (c) Increasing the volume of the container. (d) Adding a catalyst. 2. For the following reaction, H = 2816 kj: 6 CO 2 (g) + 6 H 2 O(l) C 6 H 12 O 6 (s) + 6 O 2 (g) Which of the following statements about this equilibrium are true? A. Increasing P CO2 will cause it to shift to the left. B. Increasing temerature will cause it to shift to the left. C. Decreasing the total ressure at constant temerature will have no effect. D. Removing art of the C 6 H 12 O 6 will cause it to shift to the right. E. Adding a catalyst will cause it to shift to the left. Summer 2005-82 - Chem 6 Study Guide