1. CHAPTER 11 ELEMENTS OF ELECTROCHEMISTRY Introduction to Analytical Chemistry

2. Copyright © 2011 Cengage Learning 3-2 11A Characterizing Oxidation/ Reduction Reactions An oxidation/reduction reaction. (11-1)

3. Copyright © 2011 Cengage Learning 3-3 11A Characterizing Oxidation/ Reduction Reactions For the oxidation of Fe 2 by MnO 4 - the half-reactions are

4. Copyright © 2011 Cengage Learning 3-4 11A-2 Oxidation/Reduction Reactions in Electrochemical Cells in an electrochemical cell in which the oxidizing agent and the reducing agent are physically separated from one another. Figure 11-2a shows such an arrangement. Note that a salt bridge isolates the reactants but maintains electrical contact between the two halves of the cell. cell potential, is a measure of the tendency of the cell reaction to proceed toward equilibrium.

5. Copyright © 2011 Cengage Learning 3-5 Figure 11-2

6. Copyright © 2011 Cengage Learning 3-6 Figure 11-2(cont.)

7. Copyright © 2011 Cengage Learning 3-7 Figure 11-2(cont.) Figure 11-2 (a) A galvanic cell at open circuit, (b) a galvanic cell doing work, and (c) an electrolytic cell.

8. Copyright © 2011 Cengage Learning 3-8 11B-1 Cathodes and Anodes The cathode in an electrochemical cell is the electrode at which a reduction reaction occurs. The anode is the electrode at which an oxidation takes place.

9. Copyright © 2011 Cengage Learning 3-9 11B-2 Two Types of Electrochemical Cells Galvanic, or voltaic, cells store electrical energy. Galvanic cells operate spontaneously, An electrolytic cell requires an external source of electrical energy for operation.

10. Copyright © 2011 Cengage Learning 3-10 11B-3 Representing Cells Schematically The cell in Figure 11-2a is described by An alternative way of writing the cell shown in Figure 11-2a is (11-5)

11. Copyright © 2011 Cengage Learning 3-11 11B-4 Describing Currents in Electrochemical Cells Figure 11-4 Movement of charge in a galvanic cell.

12. Copyright © 2011 Cengage Learning 3-12 11C Electrode Potentials The potential difference that develops between the electrodes of the cell in Figure 11-5a is a measure of the tendency for the reaction The cell potential E cell is related to the free energy of the reaction ∆G by where n is the number of electrons transferred in the reaction (11-6)

13. Copyright © 2011 Cengage Learning 3-13 11C Electrode Potentials The standard cell potential. where R is the gas constant, and T is the absolute temperature. (11-7)

14. Copyright © 2011 Cengage Learning 3-14 Figure 11-5

15. Copyright © 2011 Cengage Learning 3-15 Figure 11-5(cont.)

16. Copyright © 2011 Cengage Learning 3-16 Figure 11-5(cont.) Figure 11-5 Change in cell potential after passage of current until equilibrium is reached. In (a), the high-resistance voltmeter prevents any significant electron flow, and the full open circuit cell potential is measured. For the concentrations shown, this value is +0.412 V. In (b), the voltmeter is replaced with a low-resistance current meter and the cell discharges with time until eventually equilibrium is reached. In (c), after equilibrium is reached, the cell potential is again measured with a voltmeter and found to be 0.000 V. The concentrations in the cell are now those at equilibrium as shown.

17. Copyright © 2011 Cengage Learning 3-17 11C-1 Cell Potential Sign Convention What Are Half-Cell Potentials?  the half-reaction at the right-hand electrode (E right ), the other associated with the half-reaction at the left-hand electrode (E left ).  Although we cannot determine absolute potentials of electrodes such as these(see Feature 11-3), we can readily determine relative electrode potentials. (11-8)

18. Copyright © 2011 Cengage Learning 3-18 11C-2 The Standard Hydrogen Reference Electrode The standard hydrogen electrode (SHE), has been used a universal reference electrode. It is a typical gas electrode. The hydrogen electrode shown in Figure 11-7 can be represented schematically as (11-9)

19. Copyright © 2011 Cengage Learning 3-19 11C-2 The Standard Hydrogen Reference Electrode The reaction shown as Equation 11-9 involves two equilibria:

20. Copyright © 2011 Cengage Learning 3-20 Figure 11-7 Figure 11-7 The hydrogen gas electrode.

21. Copyright © 2011 Cengage Learning 3-21 11C-3 Defining Electrode Potential and Standard Electrode Potential The standard electrode potential, E⁰, of a half-reaction is defined as its electrode potential when the activities of the reactants and products are all unity.

22. Copyright © 2011 Cengage Learning 3-22 11C-4 Additional Implications of the IUPAC Sign Convention Electrode potential is reserved exclusively to describe half-reactions written as reductions. When the half-cell of interest exhibits a positive potential relative to the SHE, it will behave spontaneously as the cathode when the cell is discharging. When the half-cell of interest is negative relative to the SHE (Figure 11-9), it will behave spontaneously as the anode when the cell is discharging.

23. Copyright © 2011 Cengage Learning 3-23 11C-5 The Nernst Equation: How Does Concentration Affect Electrode Potentials? Consider the reversible half-reaction  E⁰= the standard electrode potential  R = the gas constant, 8.314 J K¯¹ mol¯¹  T = temperature, K  n = number of moles of electrons  F = the faraday  ln = natural logarithm 2.303 log (11-10) (11-11)

24. Copyright © 2011 Cengage Learning 3-24 11C-5 The Nernst Equation: How Does Concentration Affect Electrode Potentials? 25°C for the temperature, (11-12)

25. Copyright © 2011 Cengage Learning 3-25 Example 11-2 Typical half-cell reactions and their corresponding Nernst expressions follow. No term for elemental zinc is included in the logarithmic term because it is a pure solid. Thus, the electrode potential varies linearly with the logarithm of the reciprocal of the zinc ion concentration.

26. Copyright © 2011 Cengage Learning 3-26 Example 11-2 The potential for this couple can be measured with an inert metallic electrode immersed in a solution containing both iron species. The potential depends on the logarithm of the ratio between the molar concentrations of these ions.

27. Copyright © 2011 Cengage Learning 3-27 Example 11-2 In this example, p H ₂ is the partial pressure of hydrogen (in atmospheres) at the surface of the electrode. Ordinarily, its value will be the same as the atmospheric pressure.

28. Copyright © 2011 Cengage Learning 3-28 Example 11-2 Here, the potential depends not only on the concentrations of the manganese species but also on the pH of the solution.

29. Copyright © 2011 Cengage Learning 3-29 Example 11-2 This half-reaction describes the behavior of a silver electrode immersed in a chloride solution that is saturated with AgCl. To ensure this condition, an excess of the solid must always be present. Note that this electrode reaction is the sum of two reactions, namely,

30. Copyright © 2011 Cengage Learning 3-30 Example 11-2 Note also that the electrode potential is independent of the amount of AgCl present as long as there is some present to keep the solution saturated.

31. Copyright © 2011 Cengage Learning 3-31 11C-6 The Standard Electrode Potential, E ⁰ 1. The standard electrode potential is a relative quantity. 2. The standard electrode potential for a half-reaction refers exclusively to a reduction reaction. 3. The standard electrode potential measures the relative force tending to drive the half-reaction from a state in which the reactants and products are at unit activity

32. Copyright © 2011 Cengage Learning 3-32 11C-6 The Standard Electrode Potential, E ⁰ 4. The standard electrode potential is independent of the number of moles of reactant and product shown. 5. A positive electrode potential indicates that the half- reaction in question is spontaneous with respect to the standard hydrogen electrode half-reaction. 6. The standard electrode potential for a half-reaction is temperature dependent.

33. Copyright © 2011 Cengage Learning 3-33 11C-6 The Standard Electrode Potential, E ⁰ Systems Involving Precipitates or Complex Ions

34. Copyright © 2011 Cengage Learning 3-34 11C-6 The Standard Electrode Potential, E ⁰ The Nernst expression for the first half-reaction is

35. Copyright © 2011 Cengage Learning 3-35 11C-6 The Standard Electrode Potential, E ⁰ The standard potential for the second half-reaction is the potential where [Cl¯] = 1.00. (11-13)

36. Copyright © 2011 Cengage Learning 3-36 Example 11-3 Calculate the electrode potential of a silver electrode immersed in a 0.0500 M solution of NaCl using

37. Copyright © 2011 Cengage Learning 3-37 Example 11-3 The Ag⁺ concentration of this solution is given by Substituting into the Nernst expression gives

38. Copyright © 2011 Cengage Learning 3-38 Example 11-3 (b) Here we may write

39. Copyright © 2011 Cengage Learning 3-39 11C-7 Limitations to the Use of Standard Electrode Potentials Use of Concentrations Instead of Activities  The standard potential for the half-reaction is +0.771 V. When the potential of a platinum electrode, immersed in a solution that is 10¯⁴ M in iron(III) ion, iron(II) ion, and perchloric acid, is measured against a standard hydrogen electrode, a reading of close to +0.77 V is obtained as predicted by theory.

40. Copyright © 2011 Cengage Learning 3-40 11C-7 Limitations to the Use of Standard Electrode Potentials Use of Concentrations Instead of Activities  If, however, perchloric acid is added to this mixture until the acid concentration is 0.1 M, the potential is found to decrease to about +0.75 V.  This difference is because the activity coefficient of iron(III) is considerably smaller than that of iron(II) (0.4 versus 0.18).

41. Copyright © 2011 Cengage Learning 3-41 11C-7 Limitations to the Use of Standard Electrode Potentials Effect of Other Equilibria  The presence of 1 M hydrochloric acid in the iron(II)/iron(III) mixture we have just discussed leads to a measured potential of +0.70 V; in 1 M sulfuric acid, a potential of +0.68 V is observed; and in a 2 M phosphoric acid, the potential is +0.46 V.  In each of these cases, the iron(II)/iron(III) activity ratio is larger because the complexes of iron(III) with chloride, sulfate, and phosphate ions are more stable than those of iron(II); thus, the ratio of the species concentrations, [Fe 2+ ]/[Fe 3+ ], is greater than unity and the measured potential is less than the standard potential.

42. Copyright © 2011 Cengage Learning 3-42 11C-7 Limitations to the Use of Standard Electrode Potentials What Are Formal Potentials?  Formal potentials are empirically derived potentials that compensate for the types of activity and competing equilibria effects  For example, the formal potential for the half-reaction in 1.00 M HClO₄ could be

43. Copyright © 2011 Cengage Learning 3-43 THE END