Chemical Equilibrium Practice Problems #2 2-20-2015 1. A CPHS student does an equilibrium experiment with the general chemical equation and derives the 2 graphs below: A = B: a. When at equilibrium is the value of K greater to, less than or equal to one? Explain. b. At what point on the left and right graphs is Q = K? Explain. c. The student makes the claim that at equilibrium the concentration of A and b are as follows. [A] = [A] o x [B] = x Are they correct? Explain. d. Write a rate law for this first order reaction. e. If more A were added, discuss how both graphs would change. f. In e would the value of K change? Explain. 2. Consider the following equilibrium: 2O 3(g) 3O 2(g) K = 65 Initially 0.10 mole of O 3 and 0.10 mole of O 2 are placed in a 1.0 L container. a. Find the value of Q for this reaction. b. Would the reaction shift to the left or the right? Explain. c. Find the equilibrium concentrations of O 3 and O 2. d. Calculate K p and K for this reaction. 3. A mixture of 0.500 mol H 2 and 0.500 mol I 2 was placed in a 1.00L flask. The equilibrium constant Kc for the reaction H 2(g) + I 2(g) 2HI (g) is 54.3. What is the concentration of HI at equilibrium? 4. Consider the following reaction C 2 H 4(g) + H 2(g) C 2 H 6(g) Kc = 0.99 What is the concentration for each substance at equilibrium if the initial concentration of ethene, C 2 H 4(g), is 0.335 M and that of hydrogen is 0.526 M? 5. Consider the following reaction N2O4(g) 2NO2(g) A reaction flask is charged with 3.00 atm of dinitrogen tetroxide gas and 2.00 atm of nitrogen dioxide gas. At 25 o C, the gases are allowed to reach equilibrium. The pressure of the nitrogen dioxide was found to have decreased by 0.952 atm. Calculate the value of Kp for this system. 1
6. Consider the following reaction. The initial concentrations are [HSO 4 ] = 0.50 M, [H 3 O + ] = 0.020 M, [SO 4 2 ] = 0.060 M. HSO 4 (aq) + H 2 O (l) H 3 O + (aq) + SO 4 2 (aq) K = 0.012 (a) Which way would the reaction shift to reach equilibrium? Explain (b) What are the equilibrium concentrations of the products and reactants. 7. Consider the following reaction: CO 2(g) + H 2(g) CO (g) + H 2 O (g) There are 0.1908 moles of CO 2, 0.0908 moles of H 2, 0.0092 moles of CO, and 0.0092 moles of H 2 O vapour were present in a 2.00 L reaction vessel at equilibrium. a) Calculate the value of the equilibrium constant, K. b) Calculate K P for this reaction. c) If additional hydrogen gas were added to the system, describe what would happen to the partial pressure of the 3 other gases. d) One the graph below, make a graph showing the changes of partial pressure over time for each of the 4 gases. Pressure time 2
Equilibrium constants are independent of mechanism! (Unlike rate laws!) 3
Writing Equilibrium Constant Expressions 1. Write the equilibrium constant expression for each of the following reactions. a. 2 H 2 O 2 (g) 2 H 2 O (g) + O 2 (g) b. 6 H 2 O 2 (g) 6 H 2 O (g) + 3 O 2 (g) c. The reverse of the reaction in part a d. 2 PbS (s) + 3 O 2 (g) 2 PbO (s) + 2 SO 2 (g) e. MgCl 2 (s) Mg 2+ (aq) + 2 Cl - (aq) f. The reverse of the reaction in part e 2. Consider the following mechanism N 2 (g) + O 2 (g) 2 NO (g) K eq =K 1 2 NO (g) + O 2 (g) 2 NO 2 (g) K eq =K 2 Overall: N 2 (g) + O 2 (g) 2 NO 2 (g) K eq = K 1 K 2 (SHOW THAT THIS IS TRUE.) 4
Reaction quotient (Q) At any point during a reaction, if we know the concentrations of reactants and products, we can calculate the reaction quotient (Q). Q = [ C] c [ A] [ D] a [ B] concentrations) d b (notice that the concentrations are NOT necessarily equilibrium Make sure you understand the difference between Q and K eq : Q tells you how far a reaction is from equilibrium. K eq tells you where the reaction is trying to go. By comparing the values of Q and K eq, you can determine whether or not the reaction is at equilibrium. If the reaction is not at equilibrium, you can decide whether the (net) reaction is going in the forward or reverse direction. If Q = K eq, then rate f = rate r, the reaction is at equilibrium and no NET reaction occurs If Q < K eq then rate f > rate r, reaction will proceed from left to right ( ; more products) If Q > K eq, then rate f < rate r, reaction will proceed from right to left ( ; more reactants) Note: rate f is the rate of the forward reaction and rate r is the rate of the reverse reaction. 1. At 1000 K, the value of K p for the reaction 2SO 3 (g) = 2SO 2 (g) + O 2 (g) is 0.338. Calculate the value for Q, and predict the direction in which the reaction will proceed toward equilibrium if the initial pressures of reactants are P SO3 = 2 x 10-3 atm; P SO2 = 5 x 10-3 atm; P O2 = 3 x 10-2 atm. 5
2. Chemists always want to find ways to increase the yield of a reaction. It would appear that equilibrium is the chemist s worst enemy! (At least when a reaction has a small equilibrium constant. Read important point 5.) Two common ways for a chemist to increase the yield of a reaction are described below. Explain why they increase the yield. a. Method 1: Add more of one of the reactants. b. Method 2: Remove one of the products as it is being made. 3. At 573 K, the equilibrium constant for: N 2 (g) + 3 H 2 (g) 2 NH 3 (g) is 4.34 x 10-3. At 700 K, K c = 1.04 x 10-4. a. Is this an endothermic or exothermic reaction (in the forward direction)? (See important points 1 and 8.) Explain your answer. b. The formation of ammonia from nitrogen gas and hydrogen gas is an important industrial process (called the Haber process ). As you can see from the information above, the equilibrium constant for this reaction decreases as the temperature increases. Why, then, is the reaction performed at very high temperature? How do you think the yield of ammonia is maximized? 6