CHEM 160 Equilibrium Chemistry Example Problems (Chapter 15) This list of equilibrium problems contains problems that will be worked as examples in class and additional problems for students to try on their own. 1. (a) Phosphorous pentachloride dissociates on heating: PCl5(g) ⇔ PCl3(g) + Cl2(g) If Kc = 3.26 x 10-2 at 191°C, what is Kp at this temperature? Ans.: Kp = 1.24 (b) The value of Kc for the following reaction at 900°C is 0.28. CS2(g) + 4H2(g) ⇔ CH4(g) + 2H2S(g) What is Kp at this temperature? Ans.: Kp = 3.0 x 10-5 2. (a) Consider the following reaction at 1000°C: CO(g) + 3H2(g) ⇔ CH4(g) + H2O(g) At equilibrium, the following concentrations are measured: [CO] = 0.0613 M, [H2] = 0.1839 M, [CH4] = 0.0387, [H2O] = 0.0387 M. Calculate the value of Kc for this reaction. Calculate the value of Kp. Ans.: Kc = 3.93, Kp = 3.60 x 10-4 (b) A 5.00 L vessel contained 0.0185 mol of phosphorus trichloride, 0.0158 mol of phosphorus pentachloride, and 0.0870 mol chlorine at 503 K in an equilibrium mixture. Calculate the value of Kc at this temperature. The reaction is PCl3(g) + Cl2(g) ⇔ PCl5(g) Ans.: Kc = 49.1 3. (a) Carbon dioxide decomposes at elevated temperatures to carbon monoxide and oxygen: 2CO2(g) ⇔ 2CO(g) + O2(g) At 3000 K, 2.00 mol of CO2 is placed into a 1.00 L container and allowed to come to equilibrium. At equilibrium, 0.90 mol CO2 remains. What is the value for Kc at this temperature? Ans.: Kc = 0.82 1(b) Consider the following reaction at 1000°C: CO(g) + 3H2(g) ⇔ CH4(g) + H2O(g) The original concentrations of CO and H2 were 0.2000 M and 0.3000 M, respectively. At equilibrium, the concentration of CH4 was measured to be 0.0478 M. Calculate the values of Kc and Kp. Ans.: Kc = 3.91, Kp = 3.60 x 10-4 (c) Consider the following reaction at 1000°C: 2HI(g) ⇔ H2(g) + I2(g) When 4.00 mol of HI was placed into the 5.0 L reaction vessel at 458°C, the equilibrium mixture was found to contain 0.422 mol I2. Calculate the value of Kc for the decomposition of HI. Ans.: Kc = 1.79 x 10-2 (d) Hydrogen sulfide, a colorless gas with a foul odor, dissociates on heating: 2H2S(g) ⇔ 2H2(g) + S2(g) When 0.100 mol H2S was put into a 10.0 L vessel and heated to 1132°C, it gave an equilibrium mixture containing 0.0285 mol H2. Calculate the value of Kc at this temperature. Ans.: Kc = 1.35 x 10-6 M 4. The following reaction has an equilibrium constant Kc of 3.07 x 10-4 at 24°C: 2NOBr(g) ⇔ 2NO(g) + Br2(g) For each of the following compositions, decide whether the reaction is at equilibrium. If not, decide which direction the reaction should go. (a) [NOBr] = 0.0610 M,[NO] = 0.0151 M, [Br2] = 0.0108 M (b) [NOBr] = 0.115 M,[NO] = 0.0169 M, [Br2] = 0.0142 M (c) [NOBr] = 0.181 M,[NO] = 0.0123 M, [Br2] = 0.0201 M (d) [NOBr] = 0.0450 M,[NO] = 0.0105 M, [Br2] = 0.0100 M (e) [NOBr] = 0.0750 M,[NO] = 0.0085 M, [Br2] = 0.0096 M Ans.: a.) goes left; b.) equilibrium; c.) goes right; d.) goes left; e.) goes right 25. (a) Nitrogen and oxygen form nitric oxide: N2(g) + O2(g) ⇔ 2NO(g) If an equilibrium mixture at 25°C contains 0.040 mol/L N2 and 0.010 mol/L O2, what is the concentration of NO in this mixture? Kc = 1 x 10-30 at this temperature. Ans.: 2 x 10-17 M (b) An equilibrium mixture at 1200 K contains 0.30 mol CO, 0.10 mol H2, and 0.020 mol H2O, plus an unknown amount of CH4 in each liter. What is the concentration of CH4 in this mixture if Kc = 3.92? The reaction is: CO(g) + 3H2(g) ⇔ CH4(g) + H2O(g) Ans.: 0.059 M 6. (a) The reaction CO(g) + H2O(g) ⇔ CO2(g) + H2(g) Is used to increase the ratio of hydrogen in synthesis gas (mixtures of CO and H2. Suppose you start with 1.00 mol each of carbon monoxide and water in a 50.0 L vessel. What is the concentration of each substance in the equilibrium mixture at 1000°C given that Kc = 0.58 at this temperature? Ans.: [CO] = [H2O] = 0.0114 M, [CO2] = [H2] = 0.0086 M (b) Hydrogen iodide decomposes to hydrogen gas and iodine gas: 2HI(g) ⇔ H2(g) + I2(g) At 800 K, Kc for this reaction is 0.016. If 0.50 mol HI is placed into a 5.0 L flask, what will be the composition of the mixture at equilibrium? Ans.: [HI] = 0.080 M, [H2] = [I2] = 0.010 M 7. (a) N2O4 decomposes to NO2 according to the reaction: N2O4(g) ⇔ 2NO2(g) At 100°C, Kc = 0.36. If a 1.00 L flask initially contains 0.100 mol N2O4, what will be the concentrations of N2O4 and NO2 at equilibrium? Ans.: [N2O4] =0.040 M, [NO2] = 0.12 M 3(b) Hydrogen and iodine react according to the equation: H2(g) + I2(g) ⇔ 2HI(g) Suppose 1.00 mol H2 and 2.00 mol I2 are placed into a 1.00 L vessel. How many moles of each substance are in the equilibrium mixture at 458°C if Kc = 49.7 at this temperature? Ans.: 1.86 mol HI, 0.07 mol H2, 1.07 mol I2 (c) Iodine and bromine react to give iodine monobromide: I2(g) + Br2(g) ⇔ 2IBr(g) What is the equilibrium composition of a mixture at 150°C that initially contained 0.0015 mol each of iodine and bromine in a 5.0 L vessel if Kc = 1.2 x 102 at this temperature? Ans.: [IBr] = 5.1 x 10-4 M, [Br2] = [I2] = 4.7 x 10-5 M 8. Predict the effect of the following concentration changes on the reaction below. CH4(g) + 2S2(g) ⇔ CS2(g) + 2H2S(g) (a) Some CH4(g) is removed. (b) Some S2(g) is added. (c) Some CS2(g) is added. (d) Some H2S(g) is removed. (e) Some argon gas is added. Ans.: a.) goes left; b.) goes right; c.) goes left; d.) goes right ; e.) no effect 9. Predict the effect of increasing pressure (decreasing volume) on each of the following reactions. (a) CH4(g) + 2S2(g) ⇔ CS2(g) + 2H2S(g) (b) H2(g) + Br2(g) ⇔ 2HBr(g) (c) CO2(g) + C(s) ⇔ 2CO(g) (d) PCl5(g) ⇔ PCl3(g) + Cl2(g) (e) N2O4(g) ⇔ 2NO2(g) Ans.: a.) no effect; b.) no effect; c.) goes left; d.) goes right ; e.) goes left 45 10. Predict the effect of increasing temperature on each of the following reactions. What effect does this change have on Kc? (a) CO(g) + 3H2(g) ⇔ CH4(g) + H2O(g) ∆H < 0 (b) CO2(g) + C(s) ⇔ 2CO(g) ∆H > 0 (c) 4NH3(g) + 5O2(g) ⇔ 4NO(g) + 6H2O(g) ∆H < 0 (d) 2H2O(g) ⇔ 2H2(g) + O2(g) ∆H > 0 Ans.: a.) goes left, Kc decreases; b.) goes right, Kc increases; c.) goes left, Kc decreases; d.) goes right, Kc increases 11. What would you expect to be the general temperature and pressure conditions for an optimum yield of