Lecture 8 Ch 15 PDF

Lecture 8 2 Oct 2024 15.4 Using Equilibrium Expressions to Solve Problems Topics Predicting the Direction of a Reaction Calculating Equilibrium Concentrations 2  15.4 Usin...

Lecture 8 2 Oct 2024 15.4 Using Equilibrium Expressions to Solve Problems Topics Predicting the Direction of a Reaction Calculating Equilibrium Concentrations 2  15.4 Using Equilibrium Expressions to Solve Problems Predicting the Direction of a Reaction To determine the direction of a reaction, compare Q with K: QK The ratio of initial concentrations of products to reactants is too large. To reach equilibrium, products must be converted to reactants. The system proceeds in the reverse direction (from right to left). The comparison of Q with K can refer either to Qc and Kc or QP and KP. 4 SAMPLE PROBLEM 15.7 At 375°C, the equilibrium constant for the reaction is 1.2. At the start of a reaction, the concentrations of N2, H2, and NH3 are 0.071 M, 9.2 × 10–3 M, and 1.83 × 10–4 M, respectively. Determine whether this system is at equilibrium, and if not, determine in which direction it must proceed to establish equilibrium. 5 SAMPLE PROBLEM 15.7 Setup Solution The calculated value of Qc is less than Kc. Therefore, the reaction is not at equilibrium and must proceed to the right to establish equilibrium. 6  15.4 Using Equilibrium Expressions to Solve Problems Calculating Equilibrium Concentrations K c = 24.0 7  15.4 Using Equilibrium Expressions to Solve Problems Calculating Equilibrium Concentrations 8  15.4 Using Equilibrium Expressions to Solve Problems Calculating Equilibrium Concentrations Check: 9 SAMPLE PROBLEM 15.8 Kc for the reaction of hydrogen and iodine to produce hydrogen iodide, is 54.3 at 430°C. What will the concentrations be at equilibrium if we start with 0.240 M concentrations of both H2 and I2? 10 SAMPLE PROBLEM 15.8 Setup 11 SAMPLE PROBLEM 15.8 Solution 12 SAMPLE PROBLEM 15.8 Solution 13 SAMPLE PROBLEM 15.9 For the same reaction and temperature as in Sample Problem 15.8, calculate the equilibrium concentrations of all three species if the starting concentrations are as follows: [H2] = 0.00623 M, [I2] = 0.00414 M, and [HI] = 0.0424 M. Setup K c = 54.3 Qc > Kc, so the system will have to proceed to the left. 14 SAMPLE PROBLEM 15.9 Solution 15 SAMPLE PROBLEM 15.9 Solution 16 SAMPLE PROBLEM 15.9 Solution 17  15.4 Using Equilibrium Expressions to Solve Problems Calculating Equilibrium Concentrations When the magnitude of K (either Kc or KP) is very small, the solution to an equilibrium problem can be simplified—making it unnecessary to use the quadratic equation. 18 SAMPLE PROBLEM 15.10 At elevated temperatures, iodine molecules break apart to give iodine atoms according to the equation Kc for this reaction at 205°C is 3.39 × 10–13. Determine the concentration of atomic iodine when a 1.00-L vessel originally charged with 0.00155 mol of molecular iodine at this temperature is allowed to reach equilibrium. Setup The initial concentration of I2(g) is 0.00155 M and the original concentration of I(g) is zero. Kc = 3.39 × 10–12. 19 SAMPLE PROBLEM 15.10 Solution 20 SAMPLE PROBLEM 15.10 Solution According to our table, the equilibrium concentration of atomic iodine is 2x; therefore, [I(g)] = 2 × 3.62 × 10–8 = 7.24 × 10–8 M. 21  15.4 Using Equilibrium Expressions to Solve Problems Calculating Equilibrium Concentrations Summary 1. Construct an equilibrium table, and fill in the initial concentrations (including any that are zero). 2. Use initial concentrations to calculate the reaction quotient, Q, and compare Q to K to determine the direction in which the reaction will proceed. 3. Define x as the amount of a particular species consumed, and use the stoichiometry of the reaction to define (in terms of x) the amount of other species consumed or produced 22  15.4 Using Equilibrium Expressions to Solve Problems Calculating Equilibrium Concentrations 4. For each species in the equilibrium, add the change in concentration to the initial concentration to get the equilibrium concentration. 5. Use the equilibrium concentrations and the equilibrium expression to solve for x. 6. Using the calculated value of x, determine the concentrations of all species at equilibrium. 23  15.4 Using Equilibrium Expressions to Solve Problems Calculating Equilibrium Concentrations 7. Check your work by plugging the calculated equilibrium concentrations into the equilibrium expression. The result should be very close to the Kc stated in the problem. The same procedure applies to KP. 24 SAMPLE PROBLEM 15.11 A mixture of 5.75 atm of H2 and 5.75 atm of I2 is contained in a 1.0-L vessel at 430°C. The equilibrium constant (KP) for the reaction at this temperature is 54.3. Determine the equilibrium partial pressures of H2, I2, and HI. 25 SAMPLE PROBLEM 15.11 Setup Solution 26 SAMPLE PROBLEM 15.11 Solution 27 15.5 Factors That Affect Chemical Equilibrium Topics Addition or Removal of a Substance Changes in Volume and Pressure Changes in Temperature Catalysis 28  15.5 Factors That Affect Chemical Equilibrium Le Châtelier’s Principle Le Châtelier’s principle states that when a stress is applied to a system at equilibrium, the system will respond by shifting in the direction that minimizes the effect of the stress. In this context, “stress” refers to a disturbance of the system at equilibrium by any of the following means: The addition of a reactant or product The removal of a reactant or product A change in volume of the system, resulting in a change in concentration or partial pressure of the reactants and products A change in temperature 29  15.5 Factors That Affect Chemical Equilibrium Le Châtelier’s Principle “Shifting” refers to the occurrence of either the forward or reverse reaction such that the effect of the stress is partially offset as the system reestablishes equilibrium. 30  15.5 Factors That Affect Chemical Equilibrium Addition or Removal of a Substance Increase [N2] from 2.05 M to 3.51 M: 31  15.5 Factors That Affect Chemical Equilibrium Addition or Removal of a Substance Q is less than K, so the reaction will proceed to the right to achieve equilibrium. An equilibrium that is stressed in such a way that Q becomes less than K will shift to the right to reestablish equilibrium. Likewise, an equilibrium that is stressed in such a way that Q becomes greater than K will shift to the left to reestablish equilibrium. 32 SAMPLE PROBLEM 15.12 Hydrogen sulfide (H2S) is a contaminant commonly found in natural gas. It is removed by reaction with oxygen to produce elemental sulfur. For each of the following scenarios, determine whether the equilibrium will shift to the right, shift to the left, or neither: (a) addition of O2(g), (b) removal of H2S(g), (c) removal of H2O(g), and (d) addition of S(s). 33 SAMPLE PROBLEM 15.12 Strategy Use Le Châtelier’s principle to predict the direction of shift for each case. Remember that the position of the equilibrium is only changed by the addition or removal of a species that appears in the reaction quotient expression. Setup 34 SAMPLE PROBLEM 15.12 Solution (a) addition of O2(g), (b) removal of H2S(g), (c) removal of H2O(g), and (d) addition of S(s). 35  15.5 Factors That Affect Chemical Equilibrium Changes in Volume and Pressure 36  15.5 Factors That Affect Chemical Equilibrium Changes in Volume and Pressure  Kc 37  15.5 Factors That Affect Chemical Equilibrium Changes in Volume and Pressure In general, a decrease in volume of a reaction vessel will cause a shift in the equilibrium in the direction that minimizes the total number of moles of gas. Conversely, an increase in volume will cause a shift in the direction that maximizes the total number of moles of gas. 38 SAMPLE PROBLEM 15.13 For each reaction, predict in what direction the equilibrium will shift when the volume of the reaction vessel is decreased. Strategy Determine which direction minimized the number of moles of gas in the reaction. Count only moles of gas. 39 SAMPLE PROBLEM 15.13 Setup We have (a) 1 mole of gas on the reactant side and 2 moles of gas on the product side, (b) 3 moles of gas on the reactant side and 2 moles of gas on the product side, and (c) 2 moles of gas on each side. 40 SAMPLE PROBLEM 15.13 Setup We have (a) 1 mole of gas on the reactant side and 2 moles of gas on the product side, (b) 3 moles of gas on the reactant side and 2 moles of gas on the product side, and (c) 2 moles of gas on each side. Solution (a) Shift to the left (b) Shift to the right (c) No shift 41  15.5 Factors That Affect Chemical Equilibrium Changes in Temperature A change in concentration or volume may alter the position of an equilibrium (i.e., the relative amounts of reactants and products), but it does not change the value of the equilibrium constant. Only a change in temperature can alter the value of the equilibrium constant. 42  15.5 Factors That Affect Chemical Equilibrium Changes in Temperature If we treat heat as though it was a reactant, we can use Le Châtelier’s principle to predict what will happen if we add or remove heat. Increasing the temperature (adding heat) will shift the reaction in the forward direction because heat appears on the reactant side. Lowering the temperature (removing heat) will shift the reaction in the reverse direction. 43 SAMPLE PROBLEM 15.14 The Haber process, which is used industrially to generate ammonia—largely for the production of fertilizers—is represented by the equation Using data from Appendix 2, determine the ΔH°rxn for the process and indicate what direction the equilibrium will shift if the temperature is increased. What direction will it shift if the temperature is decreased? 44 SAMPLE PROBLEM 15.14 Setup From Appendix 2, Solution The reaction is exothermic; therefore, the equilibrium will shift to the left if temperature is increased and to the right if temperature is decreased. 45  15.5 Factors That Affect Chemical Equilibrium Catalysis A catalyst speeds up a reaction by lowering the reaction’s activation energy. However, a catalyst lowers the activation energy of the forward and reverse reactions to the same extent. The presence of a catalyst, therefore, does not alter the equilibrium constant, nor does it shift the position of an equilibrium system. 46