Redox Potentials and Equilibria

1. Redox Potentials and Equilibria GLY 4241 - Lecture 12 Fall, 2014

2. Equilibrium Treatments • Free energy (ΔG = ΔH – TΔS) • Using equilibrium constants • Use of oxidation-reduction reactions • Reactions written in half-cells

3. Example Half-Cell Reactions • Oxidation: • Reduction: • Full cell:

4. Oxidation-Reduction Video

5. Redox Reactions Video

6. Complicated Reaction

7. Balancing Half Reactions

8. Arbitrary Standard • Measuring the absolute value of the potential for an ion to gain or lose an electron is impossible • Therefore, an arbitrary standard is chosen:

9. Standard Conditions • This has an arbitrary standard potential (at standard conditions [H2] = 1 atmosphere and 25C) E= 0.00 volts • E denotes standard potential

10. Half-Cells in Terms of Standard • Once a standard is chosen, all other half-cell reactions can be defined in terms of the standard • Example:

11. Is a Reaction Favorable? • A table of electrode potentials (these are readily available) can be used to judge which reactions are thermodynamically favorable • A reduced ion will react with any oxidized species less negative than itself

12. Favorable Reaction • Thus, uranium U3+ will reduce tin Sn2+

13. Unfavorable Reaction • Uranium cannot reduce magnesium

14. Combining Half-Cells • A reaction's potential difference can be found by combining two half cell reactions: • Doubling a reaction does not change the potential • Potential is an intensive variable

15. Potential and Free Energy • where • n = # of electrons transferred, • f = Faraday constant = 23,061 calories/volt, • E is the potential in volts • Faraday constant may also be expressed as 96,420 coulombs if the energies are to be given as volt-coulombs, which equal joules

16. Standard Free Energy • For the uranium-tin equation, this gives: • If the reaction is at standard conditions the standard potential, E, is used to calculate the standard free energy, ΔG

17. Calculation of Equilibrium Constant • Relationship of standard potential and the equilibrium constant

18. Nernst Equation • The preceding equation is a special case of the Nernst Equation

19. Relationship of Potential and Equilibrium Constant • The relationship of E to Keq can easily be derived:

20. Redox Potential • Usual method of determining E is to insert two electrodes into the solution of interest • One electrode is platinum, and the other is hydrogen • A hydrogen electrode can be made by allowing hydrogen at one atmosphere to bubble over a platinum electrode • Potential determined in this way is known as the redox potential, Eh

21. Eh and pH • pH: Measures the ability of a solution to accept or donate hydrogen ion • Eh: Measures the ability of a solution to accept electrons from a reducing agent, or supply electrons to an oxidizing agent

22. Which Iron Ion is Present? • Consider an acidic solution containing iron, with a measured Eh of 0.48 volts is the iron ferrous or ferric?

23. Ferrous Ion Dominates • This calculation assumes that no complexes are formed which may not always be true, especially if organic anions are present

24. Kinetic Barriers • Kinetic barriers may keep a reaction from proceeding quickly to completion • If the reaction is slow, the measured Eh value will be less than the equilibrium values and will usually be too low • Reactions involving oxygen often have this problem

25. Eh vs. pH Diagram • pH is plotted on the abscissa with 0 on the left and 14 on the right • Eh is plotted on the ordinate, with negative values at the bottom increasing toward positive values at the top • This type of representation is primarily useful for low temperature environments in which water is stable and pH is a useful parameter

26. Limits in Terrestrial Environments • If an agent, stronger than oxygen, existed in nature, it would react with water to liberate oxygen

27. Oxygen Concentration • Using a concentration or 0.2 atm for oxygen: • Empirically, 1.22 was found to be too high, and a value of 1.04 was suggested

28. Reduction Limit • Reducing agents in nature cannot be stronger than hydrogen since they would reduce water and liberate hydrogen

29. Hydrogen Nernst Equation • Since [H2] cannot exceed one atmosphere near the surface, this equation reduces to:

30. pH Limits • Often, the pH in natural systems ranges between 4 and 9 but we have seen exceptions to that rule • Using limits of 4 to 9 for the pH allows us to draw a parallelogram in Eh-pH space • The boundaries of this parallelogram are the natural limits of most aqueous systems.

31. Eh – pH Diagram • Area outlined by the parallelogram shows natural limits applicable to most systems

32. Activity • Activity is a thermodynamic concept that considers the actual reactivity instead of the concentration • Activity may be thought of as an effective concentration

33. pe • By analogy with pH, pe = - log ae-

34. Applying pe

35. Expressing As pe

36. Calculating Keq • Keq may be calculated from standard thermodynamic data

37. Insert Values

38. Solve of Keq

39. Generalized Reaction with n Electrons

40. Eh and pe • Thus, expressing the activity of electrons in solution in units of volts (Eh) or in units of electron activity (as either ae- or pe) is possible • The two quantities may be related:

41. Natural Limits • At 25 ̊ C, • pe = 16.9 Eh • Eh = 0.059 pe