1. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 CHEMICAL POTENTIAL A QUANTITY IN SEARCH OF RECOGNITION Measuring the Chemical Potential with an Electrochemical Cell Joel Rosenberg, The Engineering School, Boston, USA Friedrich Herrmann, Karlsruhe University, Germany

2. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 high pressure low pressure high  low  energy wasted production of entropy energy used no production of entropy

3. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 energy wasted production of entropy energy used no production of entropy Selective conductor protons Selective conductor electrons

4. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006

7. Concentration cellFuel cell

8. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 William Grove The “Gas Voltaic Battery” 1839

9. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 “…never thought of the gas battery as a practical means of generating voltaic power.” William Grove 1839

10. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 “…never thought of the gas battery as a practical means of generating voltaic power.” “…science to me generally ceases to be interesting as it becomes useful.” William Grove 1839

11. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 William Grove “The gas battery, though not of such practical importance, is still of great scientific interest.” James Clerk Maxwell 1839

12. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 William Grove Michael Faraday 1839 1834

13. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 1839 1834 2H 2 O 2H 2 + 1O 2 → ←

14. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 1839 1834 2H 2 O 2H 2 + 1O 2 → ←

15. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 1839 1834 2H 2 O 2H 2 + 1O 2 → ← One “chemical transformation”

16. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 2H 2 O 2H 2 + 1O 2 → ← extent of reaction, ξ Extensive quantity describing the progress of a chemical reaction equal to the number of chemical transformations, as indicated by the reaction equation on a molecular scale, divided by the Avogadro constant (it is essentially the amount of chemical transformations). One “chemical transformation”

17. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 2H 2 O 2H 2 + 1O 2 → ← extent of reaction, ξ Extensive quantity describing the progress of a chemical reaction equal to the number of chemical transformations, as indicated by the reaction equation on a molecular scale, divided by the Avogadro constant (it is essentially the amount of chemical transformations). One “chemical transformation” ξ smallest = = 1.66 x 10 −24 mol 1NA1NA

18. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 2H 2 O 2H 2 + 1O 2 → ← extent of reaction, ξ Extensive quantity describing the progress of a chemical reaction equal to the number of chemical transformations, as indicated by the reaction equation on a molecular scale, divided by the Avogadro constant (it is essentially the amount of chemical transformations). n H 2 = 2ξ n H 2 O = 2ξ n O 2 = 1ξ One “chemical transformation” 1NA1NA ξ smallest = = 1.66 x 10 −24 mol

19. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 2H 2 O 2H 2 + 1O 2 → ←

20. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 2H 2 O 2H 2 + 1O 2 → ← 2H 2 O → 4e - + 4H + + 1O 2 4H + + 4e - → 2H 2 n e- = 4ξ One “chemical transformation”

21. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 Faraday constant Fundamental physical constant representing molar elementary charge.

22. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 Faraday constant Fundamental physical constant representing molar elementary charge. F = e ⋅ N A

23. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 Faraday constant Fundamental physical constant representing molar elementary charge. F = e ⋅ N A = 1NA1NA e

24. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 Faraday constant Fundamental physical constant representing molar elementary charge. F = e ⋅ N A = = 1NA1NA e1.60 x 10 −19 C 1.66 x 10 -24 mol

25. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 Faraday constant Fundamental physical constant representing molar elementary charge. F = e ⋅ N A = = 1NA1NA e1.60 x 10 −19 C 1.66 x 10 -24 mol F ≈ 96,500 C mol

26. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 Faraday constant Fundamental physical constant representing molar elementary charge. F = e ⋅ N A = = 1NA1NA e1.60 x 10 −19 C 1.66 x 10 -24 mol F ≈ 96,500 C mol Q = F ⋅ n e- = F ⋅ 4ξ

27. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E elec = (  A -  B ) · Q Q = F ⋅ n e- = F ⋅ 4ξ

28. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E elec = (  A -  B ) · F ⋅ 4ξ

29. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E elec = (  A -  B ) · F ⋅ 4ξ E chem = (  A -  B ) · ξ

30. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ Fuel cell

31. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ Fuel cell Electrolytic cell

32. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ Fuel cell Electrolytic cell

33. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4

34. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 C mol

35. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 JCJC C mol

36. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 JCJC C mol

37. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 (  A -  B ) = 474,780 J mol (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 JCJC C mol

38. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 2H 2 (g) + 1O 2 (g) 2H 2 O (l) → ← (  A -  B ) = 474,780 J mol (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 JCJC C mol

39. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 2H 2 (g) + 1O 2 (g) 2H 2 O (l) → ← (  A -  B ) = 474,780 2 ⋅ μ H 2 + 1 ⋅ μ O 2 − 2 μ H 2 O J mol (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 JCJC C mol

40. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 2H 2 (g) + 1O 2 (g) 2H 2 O (l) → ← (  A -  B ) = 474,780 2 ⋅ 0 + 1 ⋅ 0 − 2 μ H 2 O = 474,780 J mol (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 JCJC C mol J mol

41. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 E chem = (  A -  B ) · ξ = E elec = (  A -  B ) · F ⋅ 4ξ (  A -  B ) = (  A -  B ) · F ⋅ 4 2H 2 (g) + 1O 2 (g) 2H 2 O (l) → ← (  A -  B ) = 474,780 2 ⋅ 0 + 1 ⋅ 0 − 2 μ H 2 O = 474,780 J mol (  A -  B ) = (1.23 V) · 96,500 ⋅ 4 JCJC C mol J mol μ H 2 O = − 237,390 J mol

42. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 J. Willard Gibbs ∆μ = z ⋅ F ⋅ ∆V

43. Chemical Potential – A Quantity in Search of Recognition Torino 10 August 2006 J. Willard Gibbs “I cannot say that [chemical potential] has been adopted by physicists…[but] I do not see how we can do very well without the idea in certain kinds of investigations.” ∆μ = z ⋅ F ⋅ ∆V