1. 2012 General Chemistry I 1 Chapter 8. THERMODYNAMICS: THE SECOND AND THIRD LAW 2012 General Chemistry I ENTROPY 8.1 Spontaneous Change 8.2 Entropy and Disorder 8.3 Changes in Entropy 8.4 Entropy Changes Accompanying Changes in Physical State 8.5 A Molecular Interpretation of Entropy 8.6 The Equivalence of Statistical and Thermodynamic Entropies 8.7 Standard Molar Entropies 8.8 Standard Reaction Entropies

2. 2012 General Chemistry I 2 ENTROPY (Sections 8.1-8.8) - The 1 st law of thermodynamics says if a reaction takes place, then the total energy of the universe remains unchanged. It cannot be used to predict the directionality of a process. - The natural progression of a system and its surroundings (or “the universe”) is from order to disorder, from organized to random. - A new thermodynamic state function is needed to predict directionality and extent of disorder.

3. 2012 General Chemistry I 3  Spontaneous change is a change that has a tendency to occur without needing to be driven by an external influence. - Spontaneous changes need not be fast: e.g. C(diamond)  C(graphite); H 2 (g) + 1/2O 2 (g)  H 2 O(l) 8.1 Spontaneous Change Heat flow Mixing of gases

4. 2012 General Chemistry I 4 8.2 Entropy and Disorder - Energy and matter tend to disperse in a disorderly fashion.  Entropy, S is defined as a measure of disorder.  The second law of thermodynamics: unit: J·K -1 - Entropy is a state function; the change in entropy of a system is independent of the path between its initial and final states. The entropy of an isolated system increases in any spontaneous change. At constant temperature

5. 2012 General Chemistry I 5

6. 6 8.3 Changes in Entropy - Thermal disorder: arising from the thermal motion of the molecules - Positional disorder: related to the locations of the molecules   S for a process with changing temperature: → (C V if V is constant, C P if P is constant)

7. 2012 General Chemistry I 7   S for a reversible, isothermal expansion of an ideal gas

8. 2012 General Chemistry I 8

9. 9

10. 10

11. 2012 General Chemistry I 11 EXAMPLE 8.5 In an experiment, 1.00 mol Ar(g) was compressed suddenly (and irreversibly) from 5.00 L to 1.00 L by driving in a piston. and in the process its temperature was increased from 20.0 o C to 25.2 o C. What is the change in entropy of the gas? To solve this problem, we consider two reversible stages between initial and final states. Then  S(irrev) =  S(rev 1) +  S(rev 2).

12. 2012 General Chemistry I 12 8.4 Entropy Changes Accompanying Changes in Physical State - Phase transition: solid → liquid, T f (fusion or melting point) liquid → solid, T b (boiling point) - At the transition temperature (such as T b ), The temperature remains constant as heat is supplied. The transfer of heat is reversible. The heat supplied is equal to the enthalpy change due to the constant pressure (at 1 atm).  Entropy of vaporization,  S vap q rev =  H vap > 0 in all cases

13. 2012 General Chemistry I 13 Some Standard entropies of vaporization at T b (Table 8.1) - Standard entropy of vaporization,  S vap o :  S vap at 1 bar

14. 2012 General Chemistry I 14  Trouton’s rule:  S vap o = ~85 J·K -1 mol -1 There is approximately the same increase in positional disorder for most liquids when evaporating. - Exceptions; water, methanol, ethanol, ··· due to extensive hydrogen bonding in liquid phases - Standard entropy of fusion,  S fus o > 0 in all cases

15. 2012 General Chemistry I 15  Temperature dependence of  S vap o -To determine the entropy of vaporization of water at 25 o C (not at T b ), we can use an entropy change cycle:

16. 2012 General Chemistry I 16 8.5 A Molecular Interpretation of Entropy  The third law of thermodynamics S → 0 as T → 0  Boltzmann formula - statistical entropy: S = k B ln W k B = 1.381 × 10 -23 J·K -1 = R/N A - W : the number of microstates the number of ways that the atoms or molecules in the sample can be arranged and yet still give rise to the same total energy - When we measure the bulk properties of a system, we are measuring an average taken over the many microstates (ensemble) that the system has occupied during the measurement.

17. 2012 General Chemistry I 17 EXAMPLE 8.7 Calculate the entropy of a tiny solid made up of four diatomic molecules of a compound such as carbon monoxide, CO, at T = 0 when (a) the four molecules have formed a perfectly ordered crystal in which all molecules are aligned with their C atoms on the left and (b) the four molecules lie in random orientations, but parallel. (a) 4 CO molecules perfectly ordered: (b) 4 CO in random, but parallel: (c) 1 mol CO in random, but parallel:

18. 2012 General Chemistry I 18 - Residual entropy at T = 0, arising from positional disorder 4.6 J·K -1 for the entropy of 1 mol CO < 5.76 J·K -1 Nearly random arrangement due to a small electric dipole moment - Solid HCl; S ~ 0 at T = 0 due to the bigger dipole moment leading strict head-to-tail arrangement

19. 2012 General Chemistry I 19 EXAMPLE 8.8 The entropy of 1.00 mol FClO 3 (s) at T = 0 is 10.1 J·K -1. Interpret it. 4 orientations possible nearly random arrangement

20. 2012 General Chemistry I 20 8.6 The Equivalence of Statistical and Thermodynamic Entropies Thermodynamic entropy  S = q rev /T behavior of bulk matter Statistical entropy S = k ln W behavior of molecules = - Consider a one-dimensional box, for the statistical entropy, At T = 0, only the lowest energy level occupied → W = 1 and S = 0 At T > 0, W > 1 and S > 0 When the box length is increased at constant T, the molecules are distributed across more levels. → W and S increase.

21. 2012 General Chemistry I 21 - W = constant × V - For N molecules, - The change when a sample expands isothermally from V 1 to V 2 is, = nR ln V2V2 V1V1 - By raising the temperature, The molecules have access to larger number of energy levels → W and S increase.

22. 2012 General Chemistry I 22 - The equations used to calculate changes in the statistical entropy and the thermal entropy lead to the same result. 1. Both are state functions. 3. Both increase in a spontaneous change. 2 × no. of molecules = entropy changes from k ln W to 2k ln W Number of microstates depends only on its current state. 2. Both are extensive (dependent on “extent”) properties. 4. Both increase with temperature. In any irreversible change, the overall disorder increases → no. of microstates increases. When T increases, more microstates become accessible.

23. 2012 General Chemistry I 23 8.7 Standard Molar Entropies For heating at constant P, C P and C P /T → 0 as T → 0 Molar entropy, S(T), can be determined from measurement of C p at different temperatures.

24. 2012 General Chemistry I 24  Standard molar entropy, S m o is the molar entropy of the pure substance at 1 bar.

25. 2012 General Chemistry I 25 - Diamond (2.4 J·K -1 ) vs. lead (64.8 J·K -1 ): rigid bonds vs. vibrational energy levels - H 2 (130.7 J·K -1 ) vs. N 2 (191.6 J·K -1 ): the greater the mass, the closer energy levels lightheavy - CaCO 3 (92.9 J·K -1 ) vs. CaO (39.8 J·K -1 ): large, complex vs. smaller, simpler - In general, S m o : gases >> liquids > solids Related to freedom of movement and disordered state  Standard molar entropy, S m o :

26. 2012 General Chemistry I 26 8.8 Standard Reaction Entropies  Standard reaction enthalpy,  S o, is the difference between the standard molar entropies of the products and those of the reactants, taking into account their stoichiometric coefficients.

27. 2012 General Chemistry I 27 EXAMPLE 8.9 Calculate  S o for N 2 (g) + 3H 2 (g) → 2NH 3 (g) at 25 o C.

28. 2012 General Chemistry I 28 Chapter 8. THERMODYNAMICS: THE SECOND AND THIRD LAW 2012 General Chemistry I GLOBAL CHANGES IN ENTROPY 8.9The Surroundings 8.10The Overall Change in Entropy 8.11Equilibrium GIBBS-FREE ENERGY 8.12Focusing on the System 8.13Gibbs Free Energy of Reaction 8.14The Gibbs Free Energy and Nonexpansion Work 8.15The Effect of Temperature 8.16Impact on Biology: Gibbs Free Energy Changes in Biological Systems

29. 2012 General Chemistry I 29 GLOBAL CHANGES IN ENTROPY (Sections 8.9-8.11) 8.9 The Surroundings - The second law refers to an isolated system (system + surroundings = universe). - Only if the total entropy change is positive will the process be spontaneous.

30. 2012 General Chemistry I 30 Sometimes  S surr can be difficult to compute, but in general it can be obtained from the enthalpy change for the process.

31. 2012 General Chemistry I 31

32. 2012 General Chemistry I 32 8.10 The Overall Change in Entropy - To use the entropy to judge the direction of spontaneous change, we must consider the change in the entropy of the system plus the entropy change in the surroundings:

33. 2012 General Chemistry I 33 EXAMPLE 8.11 Is the reaction spontaneous? 2 Mg(s) + O 2 (g) → 2 MgO(s)  S o = -217 J·K -1  H o = -1202 kJ The reaction is spontaneous

34. 2012 General Chemistry I 34 - Spontaneous endothermic (  H>0) reactions: There can still be an overall increase in entropy if the disorder of the system increases enough. Summary

35. 2012 General Chemistry I 35 - A process produces maximum work if it takes place reversibly.  Clausius inequality  S = > SS - For an isolated system (universe), q = 0 The entropy of an isolated system cannot decrease. - For two given states of the system,ΔS is a state function (path-independent) but ΔS tot is not. (See EXAMPLE 8.12)

36. 2012 General Chemistry I 36 EXAMPLE 8.12 Calculate  S,  S surr, and  S tot for (a) the isothermal, reversible expansion and (b) the isothermal, free expansion of 1.00 mol of ideal gas molecules from 8.00 L to 20.00 L at 292 K. Explain any differences between the two paths. (a) Isothermal reversible expansion at 292 K

37. 2012 General Chemistry I 37 (b) Isothermal free expansion 292 K

38. 2012 General Chemistry I 38 8.11 Equilibrium  Dynamic equilibrium is one where there is no net tendency to change but microscopic forward and reverse processes occur at matching rates. Thermal equilibrium: no net flow of energy as heat Mechanical equilibrium: no tendency to expand or contract Chemical equilibrium: no net change in composition at thermodynamic equilibrium

39. 2012 General Chemistry I 39 GIBBS FREE ENERGY (Sections 8.12-8.16) 8.12 Focusing on the System - at constant T and P  Gibbs free energy, G G = H - TS - Change in Gibbs free energy at constant T and P - The direction of spontaneous change is the direction of decreasing Gibbs free energy.

40. 2012 General Chemistry I 40

41. 2012 General Chemistry I 41  G sys < 0 Spontaneous, irreversible  G sys = 0 Reversible  G sys > 0 Nonspontaneous at constant T and P - the condition for equilibrium,  S tot = 0, and  G = 0 at constant T and P

42. 2012 General Chemistry I 42

43. 2012 General Chemistry I 43 EXAMPLE 8.13 Calculate the change in molar Gibbs free energy,  G m, for the process H 2 O(s) → H 2 O(l) at 1 atm and (a) 10 o C; (b) 0 o C. Decide for each temperature whether melting is spontaneous or not. Treat  H fus and  S fus as independent of temperature. (a) At 10 o C, = -0.22 kJ·mol -1 < 0; spontaneous melting

44. 2012 General Chemistry I 44 (b) At 0 o C, equilibrium (reversible)

45. 2012 General Chemistry I 45 - G decreases as its T is raised at constant P. G↓ = H – T↑S ; H and S vary little with T, S > 0 - Decreasing rate of G m : vapor >> liquid > solid S m (vapor) >> S m (liquid) > S m (solid) Variation of G with temperature: phase transitions In most cases (opposite), heating leads to melting, then boiling.

46. 2012 General Chemistry I 46 In some cases, at certain pressures, G for the liquid may never be lower than those of the other two phases. The liquid phase is unstable and the phase transition is solid vapor (sublimation).

47. 2012 General Chemistry I 47 8.13 Gibbs Free Energy of Reaction  Gibbs free energy of reaction  Standard Gibbs free energy of reaction (standard state: pure form at 1 bar) -  G o is fixed for a given reaction and temperature. -  G depends on the composition of the reaction mixture and so it varies – and might even change sign as the reaction proceeds.

48. 2012 General Chemistry I 48  Standard Gibbs free energy of formation,  G f o, is the standard Gibbs free energy of reaction per mole for the formation of a compound from its elements in their most stable form. - For most stable form of elements,  G f o = 0 E.g.  G f o (I 2, s) = 0;  G f o (I 2, g) > 0 Examples of most stable forms of elements (Table 8.6)

49. 2012 General Chemistry I 49 Some Standard Gibbs free Energies of Formation at 25 o C (kJ mol -1 ) (Table 8.7)

50. 2012 General Chemistry I 50 EXAMPLE 8.14 Calculate the standard Gibbs free energy of formation of HI(g) at 25 o C from its standard molar entropy and standard enthalpy of formation.

51. 2012 General Chemistry I 51 - Thermodynamically stable compound; - Thermodynamically unstable compound; Stable and unstable: thermodynamic tendency to decompose into its elements Labile, nonlabile, and inert: the rate at which a thermodynamic tendency to react is realized but nonlabile or even inert - Another solution for standard Gibbs free energies of reaction: Thermodynamic stability and reactivity

52. 2012 General Chemistry I 52 EXAMPLE 8.15 Calculate the standard Gibbs free energy of the reaction 4 NH 3 (g) + 5 O 2 (g) → 4 NO(g) + 6 H 2 O(g) and decide whether the reaction is spontaneous under standard conditions at 25 o C. The reaction is spontaneous

53. 2012 General Chemistry I 53 8.14 The Gibbs Free Energy and Nonexpansion Work - The Gibbs free energy is a measure of the energy free to do nonexpansion work.

54. 2012 General Chemistry I 54  E.g. Bioenergetics of glucose oxidation - The maximum nonexpansion work obtainable from 1 mol of glucose is +2879 kJ at 1 bar. - 180 g of glucose can be used to build 170 (= 2879/17) mole of peptide links. In practice, only about 10 moles of peptide links can be built. - If we know the change in Gibbs free energy of a process taking place at constant T and P, then we immediately know how much nonexpansion work it can do.

55. 2012 General Chemistry I 55 8.15 The Effect of Temperature - The values of  H o and  S o do not change much with temperature. - However,  G o does depend much on temperature.  G o =  H o - T  S o 1) For an exothermic reaction (  H o <0) with  S o <0,  G o <0 at low T but it may become >0 at high T.

56. 2012 General Chemistry I 56 3) For an endothermic reaction (  H o >0) with  S o <0,  G o >0 at all T and the reaction is never spontaneous. 2) For an endothermic reaction (  H o >0) with  S o >0,  G o >0 at low T but it may become <0 at high T.

57. 2012 General Chemistry I 57 4) For an exothermic reaction (  H o <0) with  S o >0,  G o <0 at all T and the reaction is always spontaneous. The Gibbs free energy increases with T for reactions with a negative  S o and decreases with T for reactions with a positive  S o.

58. 2012 General Chemistry I 58 EXAMPLE 8.16 Estimate T at which it is thermodynamically possible for carbon to reduce iron(III) oxide to iron under standard conditions by the endothermic reaction., above 565 o C

59. 2012 General Chemistry I 59 8.16 Impact on Biology: Gibbs Free Energy Changes in Biological Systems - A reaction that produces a lot of entropy can drive another nonspontaneous reaction forward. - A process may be driven uphill in Gibbs free energy by another reaction that rolls downhill.

60. 2012 General Chemistry I 60  Hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP): the reaction used for driving nonspontaneous biochemical reactions - The nonspontaneous reaction restoring of ATP from ADP is driven by the food we eat.

61. 2012 General Chemistry I 61 The End!

62. 2012 General Chemistry I 62 Thank you for listening to this lecture, and please continue to General Chemistry II to know a variety of Green World!