A Molecular Approach, 4e - Notes for Chapter (15).doc

Chapter 15. Chemical Equilibrium Chapter 15. Chemical Equilibrium Chapter 15. Chemical Equilibrium Student Objectives 15.1 Fetal Hemoglobin and Equilibrium Know that hemoglobin is the bloodstream’s carrier for oxygen and that the binding of oxygen to hemoglobin is an equilibrium reaction. Know that the fetal–maternal oxygen equilibrium is maintained via the placenta where oxygen is exchanged. 15.2 The Concept of Dynamic Equilibrium Know and understand that in a dynamic equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. Understand the concept of dynamic equilibrium through the population analogy. 15.3 The Equilibrium Constant (K) Define and understand the law of mass action. Write and interpret equilibrium expressions using concentrations. Understand the significance of numerical values of the equilibrium constant, especially very large and very small values. Know and understand the mathematical relationships between chemical equations and equilibrium constants. 15.4 Expressing the Equilibrium Constant in Terms of Pressure Know and understand the relationship between equilibrium expressions written in terms of pressure or concentration. Write and interpret the equilibrium expressions given by Kp and Kc for a chemical reaction. Show the relationship between Kp and Kc for a gas-phase reaction. 15.5 Heterogeneous Equilibria: Reactions Involving Solids and Liquids Know and understand that the concentrations of solids and liquids in a reaction do not change over the course of a reaction and do not appear in the equilibrium expression. Write and interpret an equilibrium expression for a reaction involving a solid or liquid. 15.6 Calculating the Equilibrium Constant from Measured Equilibrium Concentrations Know and understand that the equilibrium constant will be identical for a given reaction at a given temperature; the equilibrium can be established at an infinite combination of concentrations. Write and compute the table of values for an equilibrium reaction at the initial, change in, and equilibrium concentrations. Know that this is often called the ICE table. 15.7 The Reaction Quotient: Predicting the Direction of Change Know that the reaction quotient Q is defined in the same way as the equilibrium constant K except that Q can be defined for a state other than equilibrium. Know and understand how Q can be compared with K and used to determine in which direction a reaction will proceed in order to establish equilibrium. Predict the direction of a reaction by comparing the values of Q and K. 15.8 Finding Equilibrium Concentrations Calculate equilibrium concentrations from the equilibrium constant K and all but one of the equilibrium concentrations or pressures of the reactants and products. Calculate equilibrium concentrations from the equilibrium constant K and initial concentrations or pressures of the reactants and products. Calculate equilibrium concentrations from initial concentrations or pressures in cases in which the equilibrium constant is small. 15.9 Le Châtelier’s Principle: How a System at Equilibrium Responds to Disturbances Define Le Châtelier’s Principle. Know and understand the effect of changing concentration on a system at equilibrium. Know and understand the effect of changing volume or pressure of a system at equilibrium that involves gases. Know and understand the effect of a temperature change on a system at equilibrium. Predict the effect of temperature change on a reaction for which the heat flow is known. Section Summaries Lecture Outline Terms, Concepts, Relationships, Skills Figures, Tables, and Solved Examples Teaching Tips Suggestions and Examples Misconceptions and Pitfalls Lecture Outline Terms, Concepts, Relationships, Skills Figures, Tables, and Solved Examples 15.1 Fetal Hemoglobin and Equilibrium Hemoglobin–oxygen equilibrium Oxygen transfer from maternal to fetal hemoglobin Intro figure: illustration of umbilical cord, red blood cells, and hemoglobin unnumbered figure: crystal structure of hemoglobin Figure 15.1 Oxygen Exchange between the Maternal and Fetal Circulation 15.2 The Concept of Dynamic Equilibrium Equilibrium reversible reactions dynamic population analogy Figure 15.2 Dynamic Equilibrium Figure 15.3 A Population Analogy for Chemical Equilibrium 15.3 The Equilibrium Constant (K) Representations chemical equation equilibrium constant, K equilibrium expression: law of mass action Values of K small K: reactants favored large K: products favored Rules for manipulating K values reverse equation: invert K multiply equation: raise K to power add equations together: multiply K values Example 15.1 Expressing Equilibrium Constants for Chemical Equations Figure 15.4 The Meaning of a Large Equilibrium Constant Figure 15.5 The Meaning of a Small Equilibrium Constant Chemistry and Medicine: Life and Equilibrium Example 15.2 Manipulating the Equilibrium Constant to Reflect Changes in the Chemical Equation 15.4 Expressing the Equilibrium Constant in Terms of Pressure Equilibrium constant types concentration: Kc pressure: Kp Kp = Kc(RT)n Units of K Example 15.3 Relating Kp and Kc Teaching Tips Suggestions and Examples Misconceptions and Pitfalls 15.1 Fetal Hemoglobin and Equilibrium More oxygen in the blood means a higher hemoglobin saturation level. The fetal-maternal oxygen-sharing model is a practical example of an equilibrium that occurs via the placenta. Ask the students to suggest other related equilibrium systems. The placenta exchanges oxygen but not blood between the mother and fetus. 15.2 The Concept of Dynamic Equilibrium The forward and reverse reactions in an equilibrium are different chemical reactions that can be characterized by a rate expression for each. At equilibrium, these reaction rates are equal. The rates of the forward and reverse reactions are equal at equilibrium, but the rate constants are almost never equal. 15.3 The Equilibrium Constant (K) The equilibrium expression is written by inspection of the chemical equation. Students can be asked to discuss qualitatively what is expected for each case: Large or small K? Large or small concentration? Conceptual Connection 15.1 The Magnitude of the Equilibrium Constant Conceptual Connection 15.2 Equilibrium Constants and Equilibrium Concentrations Conceptual Connection 15.3 The Equilibrium Constant and the Chemical Equation Practice using the rules for manipulating K values. Many students are initially confused by the rules for manipulating K values because of their experience with manipulating H values. Working through several examples will ease this confusion. A recurring confusion for this and the next few chapters is k (rate constant) versus K (equilibrium constant). 15.4 Expressing the Equilibrium Constant in Terms of Pressure Equilibrium expressions can be written in terms of pressure or concentration. The formal definition of K from thermodynamics references concentrations and pressures to 1 M and 1 bar, respectively, cancelling all the units and rendering K dimensionless. Emphasize to students that consistent communication requires concentrations in K expressions to be in M and pressures to be in atm (or bar, formally). Conceptual Connection 15.4 The Relationship between Kp and Kc The numerical value of K expressed as Kc is different from that expressed as Kp. Most chemistry disciplines use no units for K; some biochemists do use them. Lecture Outline Terms, Concepts, Relationships, Skills Figures, Tables, and Solved Examples 15.5 Heterogeneous Equilibria: Reactions Involving Solids and Liquids Liquids and solids no change in concentration during reaction not included in K expressions Figure 15.6 Heterogeneous Equilibrium Example 15.4 Writing Equilibrium Expressions for Reactions Involving a Solid or Liquid 15.6 Calculating the Equilibrium Constant from Measured Equilibrium Concentrations Law of mass action same value of K for given reaction at a given T particular equilibrium position dependent on initial condition ICE table initial change equilibrium Table 15.1 Initial and Equilibrium Concentrations for the Reaction H2(g) + I2(g) 2 HI(g) at 445 oC Examples 15.5 and 15.6 Finding Equilibrium Constants from Experimental Concentration Measurements 15.7 The Reaction Quotient: Predicting the Direction of Change Q expression same form as K expression concentrations (or pressures) often not at equilibrium Predicting direction of reaction Q > K: reverse Q < K: forward Q = K: equilibrium Figure 15.7 Q, K, and the Direction of a Reaction Example 15.7 Predicting the Direction of a Reaction by Comparing Q and K Teaching Tips Suggestions and Examples Misconceptions and Pitfalls 15.5 Heterogeneous Equilibria: Reactions Involving Solids and Liquids Liquids and solids do not appear in equilibrium expressions because their concentrations do not change. Conceptual Connection 15.5 Heterogeneous Equilibria, Kp, and Kc There is some misunderstanding between a solid or liquid concentration not changing versus having no value. The concentration of water has a value (55.5 M at 25 oC), but that concentration does not change when water participates in a chemical reaction. 15.6 Calculating the Equilibrium Constant from Measured Equilibrium Concentrations Equilibrium concentrations are calculated using the ICE table. Warn students about missing coefficients from balanced reactions, especially in the change or equilibrium concentrations. A reaction can have an infinite number of equilibrium positions (combinations of concentrations/pressures), but a given chemical reaction has only one value of K at a given temperature. 15.7 The Reaction Quotient: Predicting the Direction of Change The reaction quotient Q is the same as K but under non-equilibrium conditions. Conceptual Connection 15.6 Q and K Students sometimes think the Q expression is another type of calculation altogether, but it is just the value of the concentration expression under non-equilibrium conditions. Lecture Outline Terms, Concepts, Relationships, Skills Figures, Tables, and Solved Examples 15.8 Finding Equilibrium Concentrations Problem scenarios finding a missing equilibrium concentration given K and other concentrations finding equilibrium concentrations given K and initial concentrations finding equilibrium partial pressures given K and initial partial pressures finding equilibrium concentrations given initial concentrations and a small K Example 15.8 Finding Equilibrium Concentrations When You Know the Equilibrium Constant and All but One Equilibrium Concentrations of the Reactants and Products unnumbered table: ICE table Examples 15.9 and 15.10 Finding Equilibrium Concentrations from Initial Concentrations and the Equilibrium Constant Example 15.11 Finding Equilibrium Partial Pressures When You Are Given the Equilibrium Constant and Initial Partial Pressures Examples 15.12 and 15.13 Finding Equilibrium Concentrations from Initial Concentrations in Cases with a Small Equilibrium Constant 15.9 Le Châtelier’s Principle: How a System at Equilibrium Responds to Disturbances Le Châtelier’s Principle definition population analogy Equilibrium disturbances concentration change volume change in gaseous equilibrium temperature change exothermic reactions endothermic reactions Figure 15.8 A Population Analogy for Le Châtelier’s Principle Figure 15.9 Le Châtelier’s Principle: The Effect of a Concentration Change Figure 15.10 Le Châtelier’s Principle: Changing Concentration Example 15.14 The Effect of a Concentration Change on Equilibrium Figure 15.11 Le Châtelier’s Principle: The Effect of a Pressure Change Example 15.15 The Effect of a Volume Change on Equilibrium Figure 15.12 Le Châtelier’s Principle: The Effect of a Temperature Change Example 15.16 The Effect of a Temperature Change on Equilibrium Teaching Tips Suggestions and Examples Misconceptions and Pitfalls 15.8 Finding Equilibrium Concentrations Finding a missing equilibrium concentration simply involves the use of the other values and the equilibrium expression. Finding equilibrium concentrations from initial conditions often involves the quadratic equation. A review of algebra and the solutions of the quadratic equation are appropriate. Emphasize that while both roots are mathematically relevant, one of the roots will always be physically meaningless. A small value of K allows the use of an approximation that obviates the need for the quadratic equation. The trick is knowing when the approximation is valid. Conceptual Connection 15.7 The x is small Approximation These problems particularly represent the downfall of ‘spectator’ students. Proficiency in solving these types of problems comes with lots of practice and not through watching someone else work the problems. 15.9 Le Châtelier’s Principle: How a System at Equilibrium Responds to Disturbances A qualitative use of the Q expression to evaluate the effect of a concentration change eliminates the need to memorize particular effects. There are only two ways to change the value of K: write a different reaction, or change the temperature. Volume changes for gaseous equilibria are perhaps the toughest for students to understand. End of chapter problems 71 and 72 could be used as an excellent sample problem that illustrates all the relevant principles. Additional Problem for Finding Equilibrium Constants from Experimental Concentration Measurements (Examples 15.5, 15.6) Consider the reaction: CO(g) + 2 H2(g) CH3OH(g) A reaction mixture initially contains [CO] = 0.600 M and [H2] = 1.20 M. At equilibrium, the CO concentration is found to be 0.100 M. Find the equilibrium constant for the reaction. (1) Using the balanced equation as a guide, prepare an ICE table showing the known initial concentrations and equilibrium concentrations of the reagents and products. CO(g) + 2 H2(g) CH3OH(g) [CO] [H2] [CH3OH] Initial 0.600 1.20 0.000 Change Equil 0.100 (2) For the reactant or product whose concentration is known both initially and at equilibrium, calculate the change in concentration of all other reactants and products. CO(g) + 2 H2(g) CH3OH(g) [CO] [H2] [CH3OH] Initial 0.600 1.20 0.000 Change 0.500 Equil 0.100 (3) Use the change calculated in step 2 and the stoichiometric relationships from the balanced chemical equation to determine the changes in concentration of all other reactants and products. CO(g) + 2 H2(g) CH3OH(g) [CO] [H2] [CH3OH] Initial 0.600 1.20 0.000 Change 0.500 1.00 +0.500 Equil 0.100 (4) Sum each column for each reactant and product to determine the equilibrium concentrations. CO(g) + 2 H2(g) CH3OH(g) [CO] [H2] [CH3OH] Initial 0.600 1.20 0.000 Change 0.500 1.00 +0.500 Equil 0.100 0.20 0.500 (5) Use the balanced equation to write an expression for the equilibrium constant and substitute the equilibrium concentrations to compute K. Additional Problem for Finding Equilibrium Concentrations When You Are Given the Equilibrium Constant and All but One Equilibrium Concentrations of the Reactants and Products (Example 15.8) Consider the reaction: 2 COF2(g) CO2(g) + CF4(g) Kc = 2.00 In an equilibrium mixture, the concentration of COF2 is 0.35 M and the concentration of CO2 is 0.144 M. What is the equilibrium concentration of CF4? Sort You are given the equilibrium constant of a chemical reaction, together with the equilibrium concentrations of the reactant and one product. You are asked to find the equilibrium concentration of the other product. Given [COF2] = 0.35 M [CO2] = 0.144 M Kc = 2.00 Find [CF4] Strategize You can calculate the concentration of the product using the given quantities and the expression for Kc. Conceptual Plan [COF2], [CO2], Kc [CF4] Relationships Used Solve Solve the equilibrium expression for [CF4] and then substitute in the appropriate values to compute it. Solution Check The units of the answer are correct, and the magnitude makes sense just by estimating the answer. Additional Problem for Finding Equilibrium Concentrations from Initial Concentrations and the Equilibrium Constant (Examples 15.9, 15.10) Consider the reaction: N2O4(g) 2 NO2(g) Kc = 0.36 A reaction mixture initially contains [N2O4] = 0.100 M. Find the equilibrium concentrations of N2O4 and NO2. (1) Using the balanced equation as a guide, prepare a table showing the known initial concentrations of the reactants and products. N2O4(g) 2 NO2(g) Kc = 0.36 [N2O4] [NO2] Initial 0.100 0.000 Change Equil (2) Use the initial concentrations to calculate the reaction quotient Q for the initial concentrations. Compare Q to K and predict the direction in which the reaction will proceed. Q < K, so the reaction should proceed right. (3) Represent the change in the concentration of one of the reactants or products with the variable x. Define the changes in the concentrations of the other reactants or products in terms of x. N2O4(g) 2 NO2(g) Kc = 0.36 [N2O4] [NO2] Initial 0.100 0.000 Change x +2x Equil (4) Sum each column for each reactant and product to determine the equilibrium concentrations in terms of the initial concentrations and the variable x. N2O4(g) 2 NO2(g) Kc = 0.36 [N2O4] [NO2] Initial 0.100 0.000 Change x +2x Equil 0.100 x +2x (5) Substitute the expressions for the equilibrium concentrations (from step 4) into the expression for the equilibrium constant. Using the given value of the equilibrium constant, solve the expression for the variable x. (6) Substitute x into the expression for the equilibrium concentrations of the reactants and products (from step 4) and compute the concentrations. The negative x gives unrealistic concentrations. [N2O4] = 0.100 – x = 0.100 – 0.060 = 0.040 M [NO2] = +2x = 2(0.060) = 0.12 M (7) Check your answer by substituting the computed equilibrium values into the equilibrium expression. The computed value of K should match the given value of K. Additional Problem for Finding Equilibrium Concentrations from Initial Concentrations in Cases with a Small Equilibrium Constant (Examples 15.12, 15.13) Consider the reaction: 2 H2S(g) 2 H2(g) + S2(g) Kc = 1.67107 A reaction mixture initially contains [H2S] = 0.010 M. Find the equilibrium concentrations of H2 and S2. (1) Using the balanced equation as a guide, prepare a table showing the known initial concentrations of the reactants and products. 2 H2S(g) 2 H2(g) + S2(g) Kc = 1.67107 [H2S] [H2] [S2] Initial 0.010 0.000 0.000 Change Equil (2) Use the initial concentrations to calculate the reaction quotient Q for the initial concentrations. Compare Q to K and predict the direction in which the reaction will proceed. Q < K, so the reaction should proceed right. (3) Represent the change in the concentration of one of the reactants or products with the variable x. Define the changes in the concentrations of the other reactants or products in terms of x. 2 H2S(g) 2 H2(g) + S2(g) Kc = 1.67107 [H2S] [H2] [S2] Initial 0.010 0.000 0.000 Change 2x +2x +x Equil (4) Sum each column for each reactant and product to determine the equilibrium concentrations in terms of the initial concentrations and the variable x. 2 H2S(g) 2 H2(g) + S2(g) Kc = 1.67107 [H2S] [H2] [S2] Initial 0.010 0.000 0.000 Change 2x +2x +x Equil 0.0102x +2x +x (5) Substitute the expressions for the equilibrium concentrations (from step 4) into the expression for the equilibrium constant. Using the given value of the equilibrium constant, solve the expression for the variable x. Make the approximation for small equilibrium constants. (6) Substitute x into the expression for the equilibrium concentrations of the reactants and products (from step 4) and compute the concentrations. [H2S] = 0.0100 2(1.61 104) = 0.0100 M [H2] = +2x = 2(1.61 104) = 3.22 104 M [S2] = +x = 1.61 104 = 1.61 104 M 204 Copyright © 2017 by Education, Inc. 203 Copyright © 2017 by Education, Inc.