Atkins & de Paula: Elements of Physical Chemistry: 5e

1. Atkins & de Paula: Elements of Physical Chemistry: 5e Chapter 7: Chemical Equilibrium: The Principles

2. End of chapter 7 assignments Discussion questions: • 2 Exercises: • 1, 2, 3, 4, 5, 6, 7, 10, 11, 15, 18 Use Excel if data needs to be graphed

3. Homework Assignment • How many of you have already read all of chapter 7 in the textbook? • In the future, read the entire chapter in the textbook before we begin discussing it in class

4. Homework Assignment • Connect to the publisher’s website and access all “Living Graphs” • http://bcs.whfreeman.com/elements4e/ • Change the parameters and observe the effects on the graph • Sarah: these “Living Graphs” are not really living; this is just a hokey name!

5. Homework Assignments • Read Chapter 7. • Work through all of the “Illustration” boxes and the “Example” boxes and the “Self-test” boxes in Chapter 7. • Work the assigned end-of-chapter exercises by the due date

6. Principles of chemical equilibrium Central Concepts: • Thermodynamics can predict whether a rxn has a tendency to form products, but it says nothing about the rate • At constant T and P, a rxn mixture tends to adjust its composition until its Gibbs energy is at a minimum

7. Gibbs Energy vs Progress of Rxn • Fig 7.1 (158) • (a) does not go • (b) equilibrium with amount of reactants ~amount of products • (c) goes to completion

8. Example Rxns • G6P(aq)  F6P(aq) • N2(g) + 3 H2(g)  2 NH3(g) • Reactions are of this form: aA + bBcC + dD • If n is small enough, then,G = (F6P x n) – (G6P x n) --now divide by n • rG = G/n = F6P– G6P

9. The Rxn Gibbs Energy • rG = G/n = F6P– G6P • rG is the difference of the chemical potentials of the products and reactants at the composition of the rxn mixture • We recognize that rG is the slope of the graph of the (changing) G vs composition of the system (Fig 7.1, p154)

10. Effect of composition on rG • Fig 7.2 (154) • The relationship of G to composition of the reactions • rG changes as n(the composition) changes

11. Reaction Gibbs energy • Consider this reaction: aA + bB  cC + dD • rG = (cC + dD) –(aA + bB) μJtμJ+ RT lnaJ (derived in sec 6.6) • Chemical potential (μ) changes as [J] changes • The criterion for chemical equilibrium at constant T,P is:rG = 0 (7.2) 

12. Meaning of the value of rG • Fig 7.3 (155) • When is rG<0? • When is rG=0? • When is rG>0? • What is the signifi-cance of each?

13. Variation of rG with composition For solutes in an ideal solution: • aJ = [J]/c, the molar concentration of J relative to the standard value c = 1 mol/dm3 For perfect gases: • aJ = pJ/p, the partial pressure of J relative to the standard pressure p = 1 bar For pure solids and liquids, aJ = 1 p155f

14.         Variation of rG with composition • rG = (cC + dD) –(aA + bB) (7.1c) • rG = (cC + dD) –(aA + bB) (7.4a) • rG = {cGm(C)+dGm(D)} – {(aGm(A)+bGm(B)} (7.4b) • 7.4a and 7.4b are the same Is there an error in 7.1c in the textbook?

15. c d aC aD c d aC aD a b aA aB a b aA aB Q = Variation of rG with composition rG = rG + RT ln ( ) Since Then rG = rG + RT ln Q

16. c c d d aC aD aC aD a a b b aA aB aA aB Q = Reactions at equilibrium • Again, consider this reaction: aA + bBcC + dD • Q, arbitrary position; K, equilibrium • 0 = rG + RTlnK and • rG = –RTlnK ( ) K = equilibrium

17. Equilibrium constant • With these equations…. • 0 = rG + RTlnK • rG = –RTlnK (7.8) • We can use values of rG from a data table to predict the equilibrium constant • We can measure K of a reaction and calculate rG

18. Relationship between rG and K • Fig 7.4 (157) • Remember, • rG = –RT ln K • So, ln K = –(rG/RT) • If rG<0, then K>1; & products predominate at equilibrium • And the rxn is thermo-dynamically feasible At K > 1, rG < 0 At K = 1, rG = 0 At K < 1, rG > 0

19. Relationship between rG and K • On the other hand… • If rG>0, then K<1 and the reactants predominate at equilibrium… • And the reaction is not thermo-dynamically feasible HOWEVER…. • Products will predominate over reactants significantly if K1 (>103) • But even with a K<1 you may have products formed in some rxns

20. rH T = rS Relationship between rG and K • For an endothermic rxn to have rG<0, its rS>0; furthermore, • Its temperature must be high enough for its TrS to be greater than rH • The switch from rG>0 to rG<0 corresponds to the switch from K<1 to K>1 • This switch takes place at a temperature at which rH - TrS = 0, OR….

21. Table 7.1 Thermodynamic criteria of spontaneity DG = DH – TDS

22. Table 7.1 Thermodynamic criteria of spontaneity DG = DH – TDS 4. If DH is positive and DS is negative, DG will always be positive—regardless of the temperature. These two statements are an attempt to say the same thing.

23. DG = DH– TDS If DH is negative and DS is positive, then DG will always be negative regardless of temperature. If DH is negative and DS is negative, then DG will be negative only when TDS is smaller in magnitude than DH. This condition is met when T is small. If both DH and DS are positive, then DG will be negative only when the TDS term is larger than DH. This occurs only when T is large. If DH is positive and DS is negative, DG will always be positive—regardless of the temperature.

24. DG = DH–TDS Factors Affecting the Sign of DG

25. Gibbs Free Energy (G) G = H–TS All quantities in the above equation refer to the system For a constant-temperature process: The change in Gibbs free energy (DG) DG = DHsys– TDSsys If DG is negative (DG<0), there is a release of usable energy, and the reaction is spontaneous! If DG is positive (DG>0), the reaction is not spontaneous! 18.4

26. Gibbs Free Energy (G) For a constant-temperature process: DG = DHsys– TDSsys DG < 0 The reaction is spontaneous in the forward direction. DG > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction. DG = 0 The reaction is at equilibrium. 18.4

27. The standard free-energy of reaction (DG0 )is the free-energy change for a reaction when it occurs under standard-state conditions. aA + bB cC + dD – [ + ] [ + ] = – mDG0 (reactants) S S = f DG0 DG0 rxn rxn dDG0 (D) nDG0 (products) cDG0 (C) bDG0 (B) aDG0 (A) f f f f f Gibbs Free Energy (G) rxn 7.10 p158

28. Who will explain this graph to the class?

29. rH T = rS Relationship between rG and K • For an endothermic rxn to have rG<0, its rS>0; furthermore, • Its temperature must be high enough for its TrS to be greater than rH • The switch from rG>0 to rG<0 corresponds to the switch from K<1 to K>1 • This switch takes place at a temperature at which rH - TrS = 0, OR….

30. rH T = rS Reactions at equilibrium • Fig 7.5 (162) • An endothermic rxn with K>1 must have T high enough so that the result of subtract-ing TrS from rH is negative • Or rH–TrS < 0 • Set rH–TrS=0 and solve for T DrG = DrH – TDrS equilibrium

31. DrG = DrH – TDrS equilibrium Reactions at equilibrium

32. Table 7.2 Standard Gibbs energies of formation at 298.15 K* (gases)

33. Table 7.2 Standard Gibbs energies of formation at 298.15 K* (liquids & solids)

34. Standard Gibbs Energy of Formation • Fig 7.6 (159) • Analogous to altitude above or below sea level • Units of kJ/mol

35. The equilibrium composition • The magnitude of K is a qualitative indicator • If K 1 (>103) then rG < –17 kJ/mol @ 25ºC, the rxn has a strong tendency to form products • If K 1 (<10–3) then rG > +17 kJ/mol @ 25ºC, the rxn will remain mostly unchanged reactants • If K  1 (10–3-103), then rG is between –17 to +17 kJ/mol @ 25ºC, and the rxn will have significant concentrations of both reactants and products p.160

36. Calculating an equilibrium concentration • Example 7.1 (p165) • Example 7.2 (p166)

37. Standard reaction Gibbs energy • rG = Gm(products) – Gm(reactants) • rG = rH–TrS      

38. pC pD c d aA + bB cC + dD Kp = pA pB a b Kc = In most cases Kc Kp [C]c[D]d [A]a[B]b aA (g) + bB (g)cC (g) + dD (g) 7.6 Kc and Kp Kp = Kc(RT)Dn Kp = Kc(RT)Dn When does Kp = Kc ?

39. Dvgas [ ] cRT K = Kc  p Dvgas [ ] T K = Kc  12.07K Derivation 7.1: Kc and Kp Atkins uses Substituting values for c, p, and R, we get What is this K? What is Dvgas? Work through Derivation 7.1, p.162

40. Coupled reactions • Box 7.1 (164) • Weights as analogy to rxns • A rxn with a large rG can force another rxn with a smaller rG to run in its nonspontan-eous direction • Enzymes couple biochemical rxns

41. Coupled reactions • Biological standard state (pH = 7) • Typical symbols for standard state: ¤ ´ ° Read the last paragraph in Box 7.1 on p164 regarding ATP and the “high energy” bond ¤ +

42. Equilibrium response to conditions • What effect will a change in temperature, in pressure, or the presence of a catalyst have on the equilibrium position? • Presence of a catalyst? None. Why? • rG is unchanged, so K is not changed • How about a change in temperature? • Or a change in pressure? Let’s see…

43. The effect of temperature • Fig 7.7 (163) • rG of a rxn that results in fewer moles of gas increases with increasing T • rG of a rxn with no net change… • rG of a rxn that produces more moles of gas decreases with increasing T

44. Equilibrium response to conditions • Le Chatelier’s principle suggestsWhen a system at equilibrium is compressed, the composition of a gas-phase equilibrium adjusts so as to reduce the number of molecules in the gas phase p.172

45. The effect of pressure • Fig 7.9 (174) • A change in pressure does not change the value of K, but it does have other consequences (composition) • As p0, xHI1 • What is [I2]? H2(g) + I2(s)  2 HI(g)

46. Key Ideas

47. Key Ideas

48. The End …of this chapter…”

49. Spare parts to copy and paste • μJtμJ+RT ln aJ • Chemical potential (μ) changes as [J] changes 

50. Box 7.1 pp.172f • O2 binding in hemoglobin and myoglobin… • …In resting tissue and in lung tissue