Chapter 13 Chemical Thermodynamics

1. In chapter 7 we considered the thermal characteristics of a chemical reaction. In this chapter, we expand our understanding of thermodynamics to include a criterion for calculating how far a reaction will proceed to reach equilibrium. Chapter 13Chemical Thermodynamics

2. Spontaneous Chemical and Physical Processes • What determines the direction of a process? • Tendency to give off heat. • Many processes do not give off heat. • Consider the disorder of the system. • Entropy

3. Entropy and Disorder • Entropy, S, is a measure of the disorder in a system. • Ice has less entropy than steam. • Hot gas has more entropy than cool gas. • S=klnW • k is Boltzmann’s constant. • W is a measure of disorder.

4. Entropy and the Second Law of Thermodynamics • First Law: heat changes • Second Law: spontaneous direction ΔSuniv≥ 0

5. Entropy and the Second Law of Thermodynamics • ΔSuniv = ΔSsys + ΔSsurr • ΔSsys > 0: system becomes more disordered • ΔSsys < 0: system becomes less ordered • Entropy is a state function like enthalpy. ΔS= Sfinal – Sinitial

6. Entropy and the Second Law of Thermodynamics • Some generalizations: • Ssolid < Sliquid < Sgas. • More particles have a greater S than fewer particles. • ΔH < 0 reactions are often spontaneous. • ΔS > 0 reactions are often spontaneous.

7. Standard-State Entropies of Reactions • ΔS°, standard state entropy of reaction • Solutions at 1 M • Gases at 1 bar • Temperature is typically 25 °C (not required) • ΔS°ac for compounds given in Appendix B.13

8. The Third Law of Thermodynamics • The entropy of a perfect crystal is zero when the temperature of the crystal is equal to absolute zero (0 K).

9. The Third Law of Thermodynamics Table 13.1

10. The Third Law of Thermodynamics Figure 13.2

11. Calculating Entropy Changes for a Chemical Reaction • Method is same as for calculating ΔH° • ΔS°ac < 0 because many particles (atoms) are becoming 1 particle (molecule)

12. Gibbs Free Energy • Recall that spontaneous reactions are favored when ΔH < 0 and ΔS > 0. • What happens when ΔH < 0 and ΔS < 0? e. g. N2(g) + 3H2(g) ⇄ 2 NH3(g) Is the forward or reverse reaction favored?

13. Gibbs Free Energy • The question is answered by introducing a new thermodynamic variable, the Gibbs free energy, G. • G = H – TS • ΔG = ΔH – TΔS

14. Gibbs Free Energy • Now we have a better criterion for spontaneity. • ΔG < 0: spontaneous process • Exergonic process • ΔG > 0: nonspontaneous process • Endergonic process

15. Gibbs Free Energy • Knowing ΔH° and ΔS° for a reaction at a given T, we can calculate ΔG°, the standard-state free energy of reaction, ΔG° =ΔH° – TΔS°.

16. Gibbs Free Energy • ΔG° will be negative when ΔH° < 0 and ΔS° > 0. • ΔG° will be positive when ΔH° > 0 and ΔS° < 0. • For other combinations of ΔH° and ΔS°, ΔG° must be calculated to determine its sign.

17. The Effect of Temperature on the Free Energy of a Reaction • If ΔH° and ΔS° do not themselves vary too much with temperature, then • at low temperature, ΔG° will be dominated by ΔH°. • at high temperature, ΔG° will be dominated by -TΔS°.

18. The Effect of Temperature on the Free Energy of a Reaction • An exothermic reaction can become nonspontaneous if ΔS° < 0 and the temperature becomes large. • Such is the case with N2(g) + 3H2(g) ⇄ 2 NH3(g).

19. Beware of Oversimplifications • If you attempt to predict ΔG° at a temperature very far from where ΔH° and ΔS° were determined, your calculation will be in error. ΔH° and ΔS° vary slowly over a wide temperature range.

20. Standard-State Free Energies of Reaction • ΔG° for a reaction determined from ΔG°ac, such as those tabulated in Appendix B.13 • Calculation done in same fashion as ΔH° and ΔS°

21. Equilibria Expressed in Partial Pressures • When an equilibrium constant is written as Kc, reactants and products are expressed in molarities. • For an all-gas phase equilibrium, an alternative is to express reactants and products as partial pressures. • The equilibrium constant is then written Kp.

22. Equilibria Expressed in Partial Pressures • Consider again N2(g) + 3H2(g) ⇄ 2 NH3(g)

23. Equilibria Expressed in Partial Pressures • In terms of partial pressures, N2(g) + 3H2(g) ⇄ 2 NH3(g)

24. Equilibria Expressed in Partial Pressures • Kc and Kp are related. • PV = nRT • P = [gas]RT • Kp=Kc× (RT)Δn • Δn = (number of moles of product gas) – (number of moles of reactant gas)

25. Equilibria Expressed in Partial Pressures • For this reaction, Δn = -2. N2(g) + 3H2(g) ⇄ 2 NH3(g)

26. Interpreting Standard-State Free Energy of Reaction Data • For this reaction, ΔG° = -33.0 kJ. N2(g) + 3H2(g) ⇄ 2 NH3(g) • What does this value of ΔG° tell us about the reaction?

27. Interpreting Standard-State Free Energy of Reaction Data • For this reaction, ΔG° = -33.0 kJ. N2(g) + 3H2(g) ⇄ 2 NH3(g) • What does this value of ΔG° tell us about the reaction? • With ΔG° < 0, this equilibrium favors the product. If ΔG° had been > 0, the reactants would have been favored.

28. The Relationship Between Free Energy and Equilibrium Constants • Saying the reactants or products are favored is equivalent to saying K is small or large. • Small K, reactants favored • Large K, products favored

29. The Relationship Between Free Energy and Equilibrium Constants Table 13.2

30. The Relationship Between Free Energy and Equilibrium Constants • What is the relationship between ΔG° and K?

31. The Relationship Between Free Energy and Equilibrium Constants • What is the relationship between ΔG° and K? ΔG° = -RT lnK

32. The Relationship Between Free Energy and Equilibrium Constants • ΔG° = -RT lnK • Using tabulated ΔG°ac values, ΔG°reaction is calculated • With ΔG°reaction (= ΔG°), K can be calculated K = e-ΔG°/RT

33. The Temperature Dependence of Equilibrium Constants • ΔG° = -RT lnK • ΔG°=ΔH° – TΔS° • K must depend on temperature. • We have already seen qualitatively how K changes with temperature when we discussed Le Châtelier’s principle in Chapter 10.

34. The Temperature Dependence of Equilibrium Constants • Consider this equilibrium • 2NO2(g) ⇄ N2O4(g) • NO2 is brown, N2O4 is colorless. • When this equilibrium is cooled, the system becomes colorless. • When this equilibrium is heated, the system turns dark brown.

35. The Temperature Dependence of Equilibrium Constants Table 13.3 2NO2(g) ⇄ N2O4(g)

36. The Temperature Dependence of Equilibrium Constants • ΔG° can increase with temperature (ΔH°>0 and ΔS°<0) with Kalso increasing with temperature. • Normally ΔG° decreases when K increases. • This is illustrated with this equilibrium 2CH4(g) ⇄ C2H6(g) + H2(g).

37. The Temperature Dependence of Equilibrium Constants Table 13.4

38. Gibbs Free Energies of Formation and Absolute Entropies • Instead of using ΔG°ac to calculate ΔG°, you can use ΔG°f, the Gibbs free energy of formation. • Gibbs free energy of formation values are tabulated in Appendix B.16.

39. Gibbs Free Energies of Formation and Absolute Entropies aA + bB ⇄ cC + dD

40. Gibbs Free Energies of Formation and Absolute Entropies • Entropies of reaction can be calculated from tabulated values of absolute entropies. These are found in Appendix B.16. aA + bB ⇄ cC + dD