Sherril Soman Grand Valley State University

1. Lecture Presentation Chapter 14Chemical Equilibrium Sherril Soman Grand Valley State University

2. Hemoglobin • Hemoglobin is a protein (Hb), found in red blood cells, that reacts with O2. • It enhances the amount of O2 that can be carried through the bloodstream. Hb + O2Û HbO2 • The Û is used to describe a process that is in dynamic equilibrium.

3. Hemoglobin Equilibrium SystemHb + O2Û HbO2 • The concentrations of Hb, O2, and HbO2 are all interdependent. • The relative amounts of Hb, O2, and HbO2 at equilibrium are related to a constant called the equilibrium constant, K. • A large value of K indicates a high concentration of products at equilibrium. • Changing the concentration of any one of these necessitates changes the other concentrations to restore equilibrium.

4. O2 Transport • In the lungs: • High concentration of O2 • The equilibrium shifts to the right • Hb and O2 combine to make more HbO2 Insert cartoon at top on page 650: shifting of reaction to the right

5. O2 Transport • In the muscles: • Low concentration of O2, • The equilibrium shifts to the right • HbO2 breaks down (dissociates) increasing the amount of free O2. Insert cartoon at middle on page 650 : shifting of reaction to the left

6. Fetal Hemoglobin, HbF HbF + O2Û HbFO2 • Fetal hemoglobin’s equilibrium constant is larger than adult hemoglobin’s constant. • Fetal hemoglobin is more efficient at binding O2. • O2 is transferred to the fetal hemoglobin from the mother’s hemoglobin in the placenta. HbO2 O2 HbO2 Hb O2 Hb + Û O2 HbFO2 O2 HbFO2 HbF HbF + O2 Û

7. Oxygen Exchange between Mother and Fetus

8. Arrow Conventions • Chemists commonly use two kinds of arrows in reactions to indicate the degree of completion of the reactions. • A single arrow indicates all the reactant molecules are converted to product molecules at the end. • A double arrow indicates the reaction stops when only some of the reactant molecules have been converted into products. •  in these notes

9. Reaction Dynamics • When a reaction starts, the reactants are consumed and products are made. • The reactant concentrations decrease and the product concentrations increase. • As reactant concentration decreases, the forward reaction rate decreases. • Eventually, the products can react to re-form some of the reactants, assuming the products are not allowed to escape. • As product concentration increases, the reverse reaction rate increases. • Processes that proceed in both the forward and reverse direction are said to be reversible. reactants Û products

10. Dynamic Equilibrium • As the forward reaction slows and the reverse reaction accelerates, eventually they reach the same rate. • Dynamic equilibriumis the condition wherein the rates of the forward and reverse reactions are equal. • Once the reaction reaches equilibrium, the concentrations of all the chemicals remain constant because the chemicals are being consumed and made at the same rate.

11. H2(g) + I2(g) Û 2 HI(g) At time 0, there are only reactants in the mixture, so only the forward reaction can take place. [H2] = 8, [I2] = 8, [HI] = 0

12. H2(g) + I2(g) Û 2 HI(g) At time 16, there are both reactants and products in the mixture, so both the forward reaction and reverse reaction can take place. [H2] = 6, [I2] = 6, [HI] = 4

13. H2(g) + I2(g) Û 2 HI(g) At time 32, there are now more products than reactants in the mixture, the forward reaction has slowed down as the reactants run out, and the reverse reaction accelerated. [H2] = 4, [I2] = 4, [HI] = 8

14. H2(g) + I2(g) Û 2 HI(g) At time 48, the amounts of products and reactants in the mixture haven’t changed; the forward and reverse reactions are proceeding at the same rate. It has reached equilibrium.

15. H2(g) + I2(g) Û 2 HI(g) As the concentration of product increases and the concentrations of reactants decrease, the rate of the forward reaction slows down, and the rate of the reverse reaction speeds up.

16. H2(g) + I2(g) Û 2 HI(g) At dynamic equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction. The concentrations of reactants and products no longer change.

17. Equilibrium  Equal • The rates of the forward and reverse reactions are equal at equilibrium. • But that does not mean the concentrations of reactants and products are equal. • Some reactions reach equilibrium only after almost all the reactant molecules are consumed; we say the position of equilibrium favors the products. • Other reactions reach equilibrium when only a small percentage of the reactant molecules are consumed; we say the position of equilibrium favors the reactants.

18. An Analogy: Population Changes When Country A citizens feel overcrowded, some will emigrate to Country B .

19. An Analogy: Population Changes However, after a time, emigration will occur in both directions at the same rate, leading to populations in Country A and Country B that are constant, but not necessarily equal.

20. Equilibrium Constant • Even though the concentrations of reactants and products are not equal at equilibrium, there is a relationship between them. • The relationship between the chemical equation and the concentrations of reactants and products is called the law of mass action.

21. Equilibrium Constant • For the general equation aA + bB ÛcC + dD, the law of mass action gives the relationship below. • The lowercase letters represent the coefficients of the balanced chemical equation. • Always products over reactants • Kis called the equilibrium constant. • Unitless

22. Writing Equilibrium Constant Expressions • So, for the reaction • 2 N2O5(g)Û 4 NO2(g) + O2(g) • the equilibrium constant expression is as follows:

23. What Does the Value of Keq Imply? • When the value of Keq >> 1, when the reaction reaches equilibrium there will be many more product molecules present than reactant molecules. • The position of equilibrium favors products.

24. What Does the Value of Keq Imply? • When the value of Keq << 1, when the reaction reaches equilibrium there will be many more reactant molecules present than product molecules. • The position of equilibrium favors reactants.

25. A Large Equilibrium Constant

26. A Small Equilibrium Constant

27. Relationships between K and Chemical Equations • When the reaction is written backward, the equilibrium constant is inverted. For the reaction aA + bB ÛcC + dD the equilibrium constant expression is as follows: For the reaction cC + dD ÛaA + bB the equilibrium constant expression is as follows:

28. Relationships between K and Chemical Equations • When the coefficients of an equation are multiplied by a factor, the equilibrium constant is raised to that factor. For the reaction aA + bB ÛcC the equilibrium constant expression is as follows: For the reaction 2aA + 2bB Û 2cC the equilibrium constant expression is as follows:

29. Relationships between K and Chemical Equations • When you add equations to get a new equation, the equilibrium constant of the new equation is the product of the equilibrium constants of the old equations. For the reactions (1) aA ÛbB and (2) bBÛcC the equilibrium constant expressions are as follows: For the reaction aA ÛcC the equilibrium constant expression is as follows:

30. Equilibrium Constants for Reactions Involving Gases • The concentration of a gas in a mixture is proportional to its partial pressure. • Therefore, the equilibrium constant can be expressed as the ratio of the partial pressures of the gases. • For aA(g) + bB(g) ÛcC(g) + dD(g) the equilibrium constant expressions are as follows: or

31. Kc and Kp • In calculating Kp, the partial pressures are always in atm. • The values of Kp and Kc are not necessarily the same because of the difference in units. • Kp = Kc when Dn = 0 • The relationship between them is as follows: Dn is the difference between the number of moles of reactants and moles of products.

32. Deriving the Relationship between Kp and Kc

33. Deriving the Relationship between Kp and Kc for aA(g) + bB(g)  cC(g) + dD(g) substituting

34. Heterogeneous Equilibria • The concentrations of pure solids and pure liquids do not change during the course of a reaction. • Because their concentration doesn’t change, solids and liquids are not included in the equilibrium constant expression. • For the reaction the equilibrium constant expression is as follows:

35. Heterogeneous Equilibria The amount of C is different, but the amounts of CO and CO2 remain the same. Therefore, the amount of C has no effect on the position of equilibrium.

36. Calculating Equilibrium Constants from Measured Equilibrium Concentrations • The most direct way of finding the equilibrium constant is to measure the amounts of reactants and products in a mixture at equilibrium. • The equilibrium mixture may have different amounts of reactants and products, but the value of the equilibrium constant will always be the same, as long as the temperature is kept constant. • The value of the equilibrium constant is independent of the initial amounts of reactants and products.

37. Initial and Equilibrium Concentrations forH2(g) + I2(g) Û 2HI(g) at 445 °C

38. Calculating Equilibrium Concentrations • Stoichiometry can be used to determine the equilibrium concentrations of all reactants and products if you know initial concentrations and one equilibrium concentration. • Use the change in the concentration of the material that you know to determine the change in the other chemicals in the reaction.

39. The Reaction Quotient • If a reaction mixture containing both reactants and products is not at equilibrium, how can we determine in which direction it will proceed? • The answer is to compare the current concentration ratios to the equilibrium constant. • The concentration ratio of the products (raised to the power of their coefficients) to the reactants (raised to the power of their coefficients) is called the reaction quotient, Q.

40. The Reaction Quotient For the gas phase reaction aA + bB ÛcC + dD the reaction quotient is as follows:

41. The Reaction Quotient: Predicting the Direction of Change • If Q > K, the reaction will proceed fastest in the reverse direction. • The products will decrease and reactants will increase.

42. The Reaction Quotient: Predicting the Direction of Change • If Q < K, the reaction will proceed fastest in the forward direction. • The products will increase and reactants will decrease.

43. The Reaction Quotient: Predicting the Direction of Change • If Q = K, the reaction is at equilibrium • The products and reactants will not change. • If a reaction mixture contains just reactants, then Q = 0, and the reaction will proceed in the forward direction. • If a reaction mixture contains just products, then Q = ∞, and the reaction will proceed in the reverse direction.

44. Finding Equilibrium Concentrations When Given the Equilibrium Constant and Initial Concentrations or Pressures Step 1: Decide in which direction the reaction will proceed. • Compare Q to K. Step 2: Define the changes of all materials in terms of x. • Use the coefficient from the chemical equation as the coefficient of x. • The x change is + for materials on the side the reaction is proceeding toward. • The x change is  for materials on the side the reaction is proceeding away from. Step 3: Solve for x. • For second order equations, take square roots of both sides or use the quadratic formula. • Simplify and approximate answer for very large or small equilibrium constants, if possible.

45. Approximations to Simplify the Math • When the equilibrium constant is very small, the position of equilibrium favors the reactants. • For relatively large initial concentrations of reactants, the reactant concentration will not change significantly when it reaches equilibrium. • assuming the reaction is proceeding forward • The [X]equilibrium = ([X]initial ax) [X]initial • We are approximating the equilibrium concentration of reactant to be the same as the initial concentration.

46. Checking the Approximation and Refining as Necessary • We can check our approximation by comparing the approximate value of x to the initial concentration. • If the approximate value of x is less than 5% of the initial concentration, the approximation is valid.

47. Disturbing and Restoring Equilibrium • Once a reaction is at equilibrium, the concentrations of all the reactants and products remain the same. • However, if the conditions are changed, the concentrations of all the chemicals will change until equilibrium is restored. • The new concentrations will be different, but the equilibrium constant will be the same, unless you change the temperature.

48. Le Châtelier’s Principle • Le Châtelier's principle guides us in predicting the effect various changes in conditions have on the position of equilibrium. • It says that if a system at equilibrium is disturbed, the position of equilibrium will shift to minimize the disturbance. • Disturbances all involve making the system open.

49. An Analogy: Population Changes When the populations of Country A and Country B are in equilibrium, the emigration rates between the two countries are equal so the populations stay constant.

50. An Analogy: Population Changes When an influx of population enters Country B from somewhere outside Country A, it disturbs the equilibrium established between Country A and Country B.