1. The maximum non-expansion work available from a reversible spontaneous process ( < 0) at constant T and p is equal to, that is 1441

2. The maximum non-expansion work available from a reversible spontaneous process ( < 0) at constant T and p is equal to, that is 1442

3. The maximum non-expansion work available from a reversible spontaneous process ( < 0) at constant T and p is equal to, that is This is a second important application of. 1443

4. The maximum non-expansion work available from a reversible spontaneous process ( < 0) at constant T and p is equal to, that is This is a second important application of. The key constraints are indicated in blue type. 1444

5. To prove that, start with a summary of previous results: 1445

6. To prove that, start with a summary of previous results: G = H – T S (1) 1446

7. To prove that, start with a summary of previous results: G = H – T S (1) H = E + pV (2) 1447

8. To prove that, start with a summary of previous results: G = H – T S (1) H = E + pV (2) (3) 1448

9. To prove that, start with a summary of previous results: G = H – T S (1) H = E + pV (2) (3) (4) 1449

10. To prove that, start with a summary of previous results: G = H – T S (1) H = E + pV (2) (3) (4) (5) 1450

11. Plug Eq. (2) into Eq. (1) so that G = E + pV – TS (6) 1451

12. Plug Eq. (2) into Eq. (1) so that G = E + pV – TS (6) Now take a change in each variable 1452

13. Plug Eq. (2) into Eq. (1) so that G = E + pV – TS (6) Now take a change in each variable (7) 1453

14. Plug Eq. (2) into Eq. (1) so that G = E + pV – TS (6) Now take a change in each variable (7) Plug Eq. (4) into Eq. (3) and insert the result into Eq. (7): 1454

15. Plug Eq. (2) into Eq. (1) so that G = E + pV – TS (6) Now take a change in each variable (7) Plug Eq. (4) into Eq. (3) and insert the result into Eq. (7): (8) 1455

16. Now fix the conditions: 1456

17. Now fix the conditions: (a) constant temperature, so that, 1457

18. Now fix the conditions: (a) constant temperature, so that, (b) constant pressure, so that, 1458

19. Now fix the conditions: (a) constant temperature, so that, (b) constant pressure, so that, (c) and reversible process, 1459

20. Now fix the conditions: (a) constant temperature, so that, (b) constant pressure, so that, (c) and reversible process, then Eq. (8) simplifies to (9) 1460

21. Now fix the conditions: (a) constant temperature, so that, (b) constant pressure, so that, (c) and reversible process, then Eq. (8) simplifies to (9) which simplifies using Eq. (5) to yield 1461

22. Now fix the conditions: (a) constant temperature, so that, (b) constant pressure, so that, (c) and reversible process, then Eq. (8) simplifies to (9) which simplifies using Eq. (5) to yield (10) 1462

23. Now fix the conditions: (a) constant temperature, so that, (b) constant pressure, so that, (c) and reversible process, then Eq. (8) simplifies to (9) which simplifies using Eq. (5) to yield (10) For a reversible change, hence 1463

24. Now fix the conditions: (a) constant temperature, so that, (b) constant pressure, so that, (c) and reversible process, then Eq. (8) simplifies to (9) which simplifies using Eq. (5) to yield (10) For a reversible change, hence 1464

25. A true reversible process takes an infinite amount of time to complete. Therefore we can never obtain in any process the amount of useful work predicted by the value of. 1465

26. The Gibbs Energy and Equilibrium 1466

27. The Gibbs Energy and Equilibrium When a system goes from an initial to a final state, a indicates a spontaneous change left to right, a indicates a non-spontaneous process, the reaction is spontaneous right to left. 1467

28. The Gibbs Energy and Equilibrium When a system goes from an initial to a final state, a indicates a spontaneous change left to right, a indicates a non-spontaneous process, the reaction is spontaneous right to left. It is possible that, and hence 1468

29. The Gibbs Energy and Equilibrium When a system goes from an initial to a final state, a indicates a spontaneous change left to right, a indicates a non-spontaneous process, the reaction is spontaneous right to left. It is possible that, and hence When, the system is at equilibrium, there is no net change. 1469

30. Example: Consider a mixture of ice and water at 0 o C and 1 bar. 1470

31. Example: Consider a mixture of ice and water at 0 o C and 1 bar. Neither freezing nor melting is spontaneous, provided no heat is added or removed from the system. 1471

32. Example: Consider a mixture of ice and water at 0 o C and 1 bar. Neither freezing nor melting is spontaneous, provided no heat is added or removed from the system. There is a dynamic equilibrium: 1472

33. Example: Consider a mixture of ice and water at 0 o C and 1 bar. Neither freezing nor melting is spontaneous, provided no heat is added or removed from the system. There is a dynamic equilibrium: ice water 1473

34. Example: Consider a mixture of ice and water at 0 o C and 1 bar. Neither freezing nor melting is spontaneous, provided no heat is added or removed from the system. There is a dynamic equilibrium: ice water The ice lattice is broken down to form liquid water and water freezes to form ice at every instant. At equilibrium, and therefore the amount of useful work that can be extracted from the system is zero. 1474

35. Predicting the Outcome of Chemical Reactions 1475

36. Predicting the Outcome of Chemical Reactions 1476 Consider the “simple” reaction A B

37. Predicting the Outcome of Chemical Reactions 1477 Consider the “simple” reaction A B How do we tell which is the spontaneous direction:

38. Predicting the Outcome of Chemical Reactions 1478 Consider the “simple” reaction A B How do we tell which is the spontaneous direction: A B or B A ?

39. Predicting the Outcome of Chemical Reactions 1479 Consider the “simple” reaction A B How do we tell which is the spontaneous direction: A B or B A ? Examination of for each reaction gives the answer.

40. Predicting the Outcome of Chemical Reactions 1480 Consider the “simple” reaction A B How do we tell which is the spontaneous direction: A B or B A ? Examination of for each reaction gives the answer. Suppose A B is spontaneous

41. Predicting the Outcome of Chemical Reactions 1481 Consider the “simple” reaction A B How do we tell which is the spontaneous direction: A B or B A ? Examination of for each reaction gives the answer. Suppose A B is spontaneous – will the reaction B A take place to any extent?

42. All chemical reactions proceed so as to reach the minimum of the total Gibbs energy of the system. 1482

43. All chemical reactions proceed so as to reach the minimum of the total Gibbs energy of the system. Always between the total Gibbs energy of the products and the total Gibbs energy of the reactants, there will be some point where the total Gibbs energy of a mixture of reactants and products has a minimum Gibbs energy. 1483

44. All chemical reactions proceed so as to reach the minimum of the total Gibbs energy of the system. Always between the total Gibbs energy of the products and the total Gibbs energy of the reactants, there will be some point where the total Gibbs energy of a mixture of reactants and products has a minimum Gibbs energy. The minimum indicates the composition at equilibrium, i.e. A B. 1484

45. take place to some extent. It is necessary to keep in mind that all reactions for which is positive in the forward direction, take place to some extent. However the extent of the reaction may be extremely small (particularly for many typical inorganic reactions). 1485

46. 1486

47. 1487

48. Standard Gibbs Energy and the Equilibrium Constant 1488

49. Standard Gibbs Energy and the Equilibrium Constant The Gibbs energy for a species X which is not in its standard state is given by 1489

50. Standard Gibbs Energy and the Equilibrium Constant The Gibbs energy for a species X which is not in its standard state is given by 1490

51. Standard Gibbs Energy and the Equilibrium Constant The Gibbs energy for a species X which is not in its standard state is given by where a X is the activity of species X. 1491

52. Standard Gibbs Energy and the Equilibrium Constant The Gibbs energy for a species X which is not in its standard state is given by where a X is the activity of species X. Recall that. 1492

53. Standard Gibbs Energy and the Equilibrium Constant The Gibbs energy for a species X which is not in its standard state is given by where a X is the activity of species X. Recall that. In a number of situations the activity coefficient satisfies, so that, 1493

54. Standard Gibbs Energy and the Equilibrium Constant The Gibbs energy for a species X which is not in its standard state is given by where a X is the activity of species X. Recall that. In a number of situations the activity coefficient satisfies, so that, so that the above result simplifies to 1494

55. Standard Gibbs Energy and the Equilibrium Constant 1495

56. Standard Gibbs Energy and the Equilibrium Constant If a reaction is run under conditions such that all of the reactants and products are not in their standard states – then for a reaction 1496

57. Standard Gibbs Energy and the Equilibrium Constant If a reaction is run under conditions such that all of the reactants and products are not in their standard states – then for a reaction a A + b B c C + d D 1497

58. Standard Gibbs Energy and the Equilibrium Constant If a reaction is run under conditions such that all of the reactants and products are not in their standard states – then for a reaction a A + b B c C + d D is given by = c G C + d G D – a G A – b G B 1498

59. Standard Gibbs Energy and the Equilibrium Constant If a reaction is run under conditions such that all of the reactants and products are not in their standard states – then for a reaction a A + b B c C + d D is given by = c G C + d G D – a G A – b G B = + – – 1499

60. 1500