1. CHAPTER 12 ELECTRODE POTENTIALS AND THEIR APPLICATIONS TO XIDATION/REDUCTION TITRATIONS Introduction to Analytical Chemistry

2. Copyright © 2011 Cengage Learning 3-2 Example 12-1 Calculate the thermodynamic potential of the following cell and the free energy change associated with the cell reaction. (12-2) (12-3)

3. Copyright © 2011 Cengage Learning 3-3 Example 12-1

4. Copyright © 2011 Cengage Learning 3-4 Example 12-4 Calculate the cell potential for Note that this cell does not require two compartments (nor a salt bridge) because molecular H2 has little tendency to react directly with the low concentration of Ag in the electrolyte solution.

5. Copyright © 2011 Cengage Learning 3-5 Example 12-4

6. Copyright © 2011 Cengage Learning 3-6 Example 12-4 The negative sign indicates that the cell reaction as considered, is nonspontaneous.

7. Copyright © 2011 Cengage Learning 3-7 12B Calculating Redox Equilibrium Constants At chemical equilibrium, we may write (12-5) (12-4) (12-6)

8. Copyright © 2011 Cengage Learning 3-8 12B Calculating Redox Equilibrium Constants Rearrangement of Equation 12-7 gives (12-7) (12-8)

9. Copyright © 2011 Cengage Learning 3-9 12B Calculating Redox Equilibrium Constants At 25°C (12-9)

10. Copyright © 2011 Cengage Learning 3-10 Example 12-5 Calculate the equilibrium constant for the reaction shown in Equation 12-4. Substituting numerical values into Equation 12-8 yields

11. Copyright © 2011 Cengage Learning 3-11 12C-1 Electrode Potentials during Redox Titrations Let us now consider the redox titration of iron(II) with a standard solution of cerium(IV). This reaction is rapid and reversible so that the system is at equilibrium at all times throughout the titration.

12. Copyright © 2011 Cengage Learning 3-12 12C-1 Electrode Potentials during Redox Titrations If a redox indicator has been added to this solution, the ratio of the concentrations of its oxidized and reduced forms must adjust so that the electrode potential for the indicator, E In, is also equal to the system potential. Because, data for a titration curve can be obtained by applying the Nernst equation for either the cerium(IV) half-reaction or the iron(III) half-reaction.

13. Copyright © 2011 Cengage Learning 3-13 12C-1 Electrode Potentials during Redox Titrations Equivalence-Point Potentials At the equivalence point in the titration of iron(II) with cerium(IV), the potential of the system E eq is controlled by both half reactions:

14. Copyright © 2011 Cengage Learning 3-14 12C-1 Electrode Potentials during Redox Titrations The definition of equivalence point requires that (12-10)

15. Copyright © 2011 Cengage Learning 3-15 12C-1 Electrode Potentials during Redox Titrations (12-11)

16. Copyright © 2011 Cengage Learning 3-16 Example 12-8 Obtain an expression for the equivalence-point potential in the titration of 0.0500 M U⁴⁺ with 0.1000 M Ce⁴⁺. Assume that both solutions are 1.0 M in H₂SO₄.

17. Copyright © 2011 Cengage Learning 3-17 Example 12-8 To combine the log terms, we must multiply the first equation by 2 to give

18. Copyright © 2011 Cengage Learning 3-18 Example 12-8 At equivalence

19. Copyright © 2011 Cengage Learning 3-19 Example 12-8 The equivalence-point potential for this titration is pH- dependent. 12-19

20. Copyright © 2011 Cengage Learning 3-20 12C-2 The Titration Curve Let us first consider the titration of 50.00 mL of 0.0500 M Fe²⁺ with 0.1000 M Ce⁴⁺ in a medium that is 1.0 M in H₂SO₄ at all times.

21. Copyright © 2011 Cengage Learning 3-21 12C-2 The Titration Curve Initial Potential  we lack sufficient information to calculate an initial potential. Potential after the Addition of 5.00 mL of Cerium(IV)

22. Copyright © 2011 Cengage Learning 3-22 12C-2 The Titration Curve Redox reactions used in titrimetry are sufficiently complete Ce⁴⁺ is minuscule with respect to the other species present in the solution.

23. Copyright © 2011 Cengage Learning 3-23 12C-2 The Titration Curve Equivalence-Point Potential  Substitution of the two formal potentials into Equation 12-11 yields

24. Copyright © 2011 Cengage Learning 3-24 12C-2 The Titration Curve Potential after the Addition of 25.10 mL of Cerium(IV) − the iron(II) concentration is negligible

25. Copyright © 2011 Cengage Learning 3-25 Figure 12-3 Figure 12-3 Titration curves for 0.1000 M Ce4 titration. A: Titration of 50.00 mL of 0.05000 M Fe2. B: Titration of 50.00 mL of 0.02500 M U4.

26. Copyright © 2011 Cengage Learning 3-26 12C-3 Effect of Variables on Redox Titration Curves Reactant Concentration  titration curves for oxidation/reduction reactions are usually independent of analyte and reagent concentrations. Completeness of the Reaction  The change in the equivalence-point region of an oxidation/reduction titration becomes larger as the reaction becomes more complete.

27. Copyright © 2011 Cengage Learning 3-27 Figure 12-6 Figure 12-6 Effect of titrant electrode potential on reaction completeness. The standard electrode potential for the analyte is 0.200 V; starting with curve A, standard electrode potentials for the titrant are 1.20, 1.00, 0.80, 0.60, and 0.40, respectively. Both analyte and titrant undergo a oneelectron change.

28. Copyright © 2011 Cengage Learning 3-28 12D-1 General Redox Indicators General oxidation/reduction indicators are substances that change color upon being oxidized or reduced. (12-12)

29. Copyright © 2011 Cengage Learning 3-29 12D-1 General Redox Indicators A color change is seen when changes to

30. Copyright © 2011 Cengage Learning 3-30 12D-1 General Redox Indicators The potential change required to produce the full color change of a typical general indicator a typical general indicator exhibits a detectable color change when a titrant causes the system potential to shift from to or about (0.118/n) V.

31. Copyright © 2011 Cengage Learning 3-31 12D-1 General Redox Indicators Starch/Iodine Solutions  A starch solution containing a little triiodide or iodide ion can also function as a true redox indicator.

32. Copyright © 2011 Cengage Learning 3-32 12D-2 Specific Indicators The best-known specific indicator is starch, which forms a dark blue complex with triiodide ion as discusssed above. This complex signals the end point in titrations in which iodine is either produced or consumed.

33. Copyright © 2011 Cengage Learning 3-33 12E Potentiometric End Points End points for many oxidiation/reduction titrations are readily observed by making the solution of the analyte part of the cell:

34. Copyright © 2011 Cengage Learning 3-34 12F Auxiliary Oxidizing And Reducing Reagents The analyte in an oxidation /reduction titration must be in a single oxidation state at the outset. When an iron-containing sample is dissolved usually contains a mixture of iron(II) and iron(III) ions.

35. Copyright © 2011 Cengage Learning 3-35 12F Auxiliary Oxidizing And Reducing Reagents We must first treat the sample solution with an auxiliary reducing agent to convert all the iron to iron(II). To be useful as a preoxidant or a prereductant, a reagent must react quantitatively with the analyte. In addition, any reagent excess must be readily removable because the excess reagent usually interferes by reacting with the standard solution.

36. Copyright © 2011 Cengage Learning 3-36 12F-1 Auxiliary Reducing Reagents A number of metals are good reducing agents and have been used for the prereduction of analytes. Included among these are zinc, aluminum, cadmium, lead, nickel, copper, and silver.

37. Copyright © 2011 Cengage Learning 3-37 12F-2 Auxiliary Oxidizing Reagents Sodium Bismuthate  Sodium bismuthate is a powerful oxidizing agent; it is capable, for example, of converting manganese(II) quantitatively to permanganate ion.  The half-reaction for the reduction of sodium bismuthate can be written as 12-37

38. Copyright © 2011 Cengage Learning 3-38 12F-2 Auxiliary Oxidizing Reagents Ammonium Peroxydisulfate Sodium Peroxide and Hydrogen Peroxide

39. Copyright © 2011 Cengage Learning 3-39 12G-1 Iron(II) Solutions Numerous oxidizing agents are conveniently determined by treatment of the analyte solution with a measured excess of standard iron(II) followed by immediate titration of the excess with a standard solution of potassium dichromate or cerium(IV)

40. Copyright © 2011 Cengage Learning 3-40 12G-2 Sodium Thiosulfate The scheme used to determine oxidizing agents involves adding an unmeasured excess of potassium iodide to a slightly acidic solution of the analyte. Reduction of the analyte produces a stoichiometrically equivalent amount of iodine. The liberated iodine is then titrated with a standard solution of sodium thiosulfate, Na₂S₂O₃.

41. Copyright © 2011 Cengage Learning 3-41 12G-2 Sodium Thiosulfate (12-13)

42. Copyright © 2011 Cengage Learning 3-42 12H-1 The Strong Oxidants: Potassium Permanganate and Cerium(IV) The formal potential shown for the reduction of cerium(IV) is for solutions that are 1 M in sulfuric acid. In 1 M perchloric acid and 1 M nitric acid, the potentials are 1.70 and 1.61 V, respectively. Solutions of cerium(IV) in the latter two acids are not very stable. The half-reaction shown for permanganate ion occurs only in solutions that are 0.1 M or greater in strong acid.

43. Copyright © 2011 Cengage Learning 3-43 12H-5 Determining Water with the Karl Fischer Reagent Determination of water in various types of solids and organic liquids. (12-15) (12-14)

44. Copyright © 2011 Cengage Learning 3-44 Detecting the End Point End points are obtained by electroanalytical measurements. 12H-5 Determining Water with the Karl Fischer Reagent

45. Copyright © 2011 Cengage Learning 3-45 THE END