Electrode Potentials and Their Measurement

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1 Electrochemistry

2 Electrode Potentials and Their Measurement Cu(s) + 2Ag + (aq) Cu(s) + Zn 2+ (aq) Cu 2+ (aq) + 2 Ag(s) No reaction

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4 Zn(s) + Cu 2+ (aq) Cu(s) + Zn 2+ (aq) In this reaction: Zn (s) g Zn 2+ (aq) Oxidation Cu 2+ (aq) g Cu (s) Reduction

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7 If Zn (s) and Cu 2+ (aq) is in the same solution, then the electron is a transferred directly between the Zn and Cu. No useful work is obtained. However if the reactants are separated and the electrons shuttle through an external path...

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9 An Electrochemical Cell/2 (Daniell) Anode (-) Negative electrode generates electrons Oxidation occurs Cathode (+) Positive electrode accepts electrons Reduction occurs Zn(s) Zn 2+ (aq) Cu 2+ (aq) Cu(s) ΔE cell = V

10 An Electrochemical Cell/1 Anode (-) Negative electrode generates electrons Oxidation occurs Cathode (+) Positive electrode accepts electrons Reduction occurs Cu(s) Cu 2+ (aq) Ag + (aq) Ag(s) ΔE cell = V

11 Electron Transfer at the Electrodes Anode Cathode

12 Terminology Electromotive force, ΔE cell. The cell voltage or cell potential. Cell diagram. Shows the components of the cell in a symbolic way. Anode (where oxidation occurs) on the left. Cathode (where reduction occurs) on the right. Boundary between phases shown by. Boundary between half cells (usually a salt bridge) shown by. Couple, M Mn + A pair of species related by a change in number of e -.

13 Terminology Galvanic cells. Produce electricity as a result of spontaneous reactions. Electrolytic cells. Non-spontaneous chemical change driven by electricity.

14 Standard Electrode Potentials Cell voltages, the potential differences between electrodes, are among the most precise scientific measurements. The potential of an individual electrode is difficult to establish. Arbitrary zero is chosen. The Standard Hydrogen Electrode (SHE)

15 Standard Hydrogen Electrode 2 H + (a = 1) + 2 e - D H 2 (g, 1 bar) E = 0 V Pt H 2 (g, 1 bar) H + (a = 1)

16 Standard Electrode Potential, E E defined by international agreement. The tendency for a reduction process to occur at an electrode. All ionic species present at a = 1 (approximately 1 M). All gases are at 1 bar (approximately 1 atm). Where no metallic substance is indicated, the potential is established on an inert metallic electrode (ex. Pt).

17 Reduction Couples Cu 2+ (1M) + 2 e - D Cu(s) E Cu 2+ /Cu =? Pt H 2 (g, 1 bar) H + (a = 1) Cu 2+ (1 M) Cu(s) ΔE cell = V anode cathode Standard cell potential: the potential difference of a cell formed from two standard electrodes. ΔE cell = E cathode - E anode

18 Standard Cell Potential Pt H 2 (g, 1 bar) H + (a = 1) Cu 2+ (1 M) Cu(s) ΔE cell = V ΔE cell = E cathode - E anode ΔE cell = E Cu 2+ /Cu - E H + /H V = E Cu 2+ /Cu - 0 V E Cu 2+ /Cu = V H 2 (g, 1 atm) + Cu 2+ (1 M) D 2H + (1 M) + Cu(s) ΔE cell = V

19 Measuring Standard Reduction Potential anode cathode cathode anode

20 Standard Reduction Potentials Most spontaneous <Reduction occurs> Oxidizing Agent Most nonspontaneous Spontaneous in the reverse direction. <Oxidation occurs> Reducing Agent

21 ΔE cell, ΔG, and K eq Cells do electrical work. Moving electric charge. w elec, rev = ΔG = -QΔE Faraday constant, F = 96,488 C mol -1 = q N A = C mol -1 = charge of one mole of electrons. ΔG = -nfδe ΔG = -nfδe

22 Spontaneous Change ΔG < 0 for spontaneous change. Therefore ΔE cell > 0 because ΔG cell = -nfδe cell ΔE cell > 0 Reaction proceeds spontaneously as written. ΔE cell = 0 Reaction is at equilibrium. ΔE cell < 0 Reaction proceeds in the reverse direction spontaneously.

23 The Behavior or Metals Toward Acids M(s) D M 2+ (aq) + 2 e - E = -E M 2+ /M 2 H + (aq) + 2 e - D H 2 (g) E H + /H 2 = 0 V 2 H + (aq) + M(s) D H 2 (g) + M 2+ (aq) ΔE cell = E H + /H 2 - E M 2+ /M = -E M 2+ /M When E M 2+ /M < 0, E cell > 0. Therefore ΔG < 0. Metals with negative reduction potentials react with acids

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26 ΔE cell, ΔG, and K eq Cells do electrical work. Moving electric charge. w elec, rev = ΔG = -QΔE Faraday constant, F = 96,488 C mol -1 = q N A = C mol -1 = charge of one mole of electrons. ΔG = -nfδe ΔG = -nfδe

27 Relationship Between ΔE cell and K eq ΔG = -RT ln K eq = -nfδe cell 0 ΔE cell = RT nf ln K eq

28 Summary of Thermodynamic, Equilibrium and Electrochemical Relationships.

29 ΔE cell as a Function of Concentration ΔG = ΔG +RT ln Q -nfδe cell = -nfδe cell +RT ln Q 0 ΔE cell = ΔE cell RT nf lnq R = J K 1 mol 1 F = C mol 1 T = 298K Convert to log 10 and calculate constants The Nernst Equation: 0 ΔE cell = ΔE cell n logq

30 Example Applying the Nernst Equation for Determining ΔE cell. What is the value of ΔE cell for the voltaic cell pictured below and diagrammed as follows? Pt Fe 2+ (0.10 M),Fe 3+ (0.20 M) Ag + (1.0 M) Ag(s)

31 Pt Fe 2+ (0.10 M),Fe 3+ (0.20 M) Ag + (1.0 M) Ag(s) Fe 2+ (aq) + Ag + (aq) D Fe 3+ (aq) + Ag (s) 0 ΔE cell = ΔE cell n logq 0 ΔE cell = ΔE cell n log Fe 2+ Fe 3+ Ag+ ΔE cell = V V = V

32 ΔE cell as a Function of Concentration: an Alternative Route Cathode: Ox 1 è Red 1 Anode: Red 2 è Ox 2

33 Alternative Route C A

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36 Combining Half-Cell Reactions/1 Reaction 1: Cu 2+ (aq) + 2e - D Cu(s) Reaction 2: Cu + (aq) + e - D Cu(s) Reaction 3: Cu 2+ (aq) + e - D Cu + (aq) Since Reaction 3 = Reaction 1 - Reaction 2 NO!!

37 Reaction 1: Cu 2+ (aq) + 2e - D Cu(s) Reaction 2: Cu + (aq) + e - D Cu(s) Reaction 3: Cu 2+ (aq) + e - D Cu + (aq)

38 Combining Half Reactions/2 Fe 3+ (aq) + 3e - D Fe(s) E Fe 3+ /Fe =? Fe 2+ (aq) + 2e - D Fe(s) E Fe 2+ /Fe = V Fe 3+ (aq) + e - D Fe 2+ (aq) E Fe 3+ /Fe 2+ = V 1 2 Fe 3+ (aq) + 3e - D Fe(s) E Fe 3+ /Fe = V 3 Equation 3 = Equation 1 + Equation 2

39 Dismutation/1 Spontaneous

40 Dismutation/2 Non-spontaneous

41 Concentration Cells Two half cells with identical electrodes but different ion concentrations. Pt H 2 (1 atm) H + (x M) H + (1.0 M) H 2 (1 atm) Pt(s) 2 H + (1 M) + 2 e - D H 2 (g, 1 atm) H 2 (g, 1 atm) D 2 H + (x M) + 2 e - 2 H + (1 M) D 2 H + (x M)

42 Concentration Cells 2 H + (1 M) D 2 H + (x M) 0 ΔE cell = ΔE cell n logq 0 ΔE cell = ΔE cell log x2 1 2 ΔE cell = log x = ph

43 Measurement of K sp Ag Ag + (sat d AgI) Ag + (0.10 M) Ag(s) Ag + (0.100 M) + e - D Ag(s) Ag(s) D Ag + (sat d) + e - Ag + (0.100 M) D Ag + (sat d M)

44 Example Using a Voltaic Cell to Determine K sp of a Slightly Soluble Solute. With the date given for the reaction on the previous slide, calculate K sp for AgI. AgI(s) D Ag + (aq) + I - (aq) Let [Ag + ] in a saturated Ag + solution be x: 0 ΔE cell = ΔE cell = log Ag C 1 log Ag+ A = log Ag+ Ag C = log Ag A = log Ag + A Ag + A = ( ) ( ) 2 = K S 0 = log Ag + A = A

45 Batteries: Producing Electricity Through Chemical Reactions Primary Cells (or batteries). Cell reaction is not reversible. Secondary Cells. Cell reaction can be reversed by passing electricity through the cell (charging). Flow Batteries and Fuel Cells. Materials pass through the battery which converts chemical energy into electric energy.

46 The Leclanché (Dry) Cell

47 Dry Cell Oxidation: Zn(s) D Zn 2+ (aq) + 2 e - Reduction: 2 MnO 2 (s) + H 2 O(l) + 2 e - D Mn 2 O 3 (s) + 2 OH - Acid-base reaction: NH OH - D NH 3 (g) + H 2 O(l) Precipitation reaction: NH 3 + Zn 2+ (aq) + Cl - [Zn(NH 3 ) 2 ]Cl 2 (s)

48 Alkaline Dry Cell Reduction: 2 MnO 2 (s) + H 2 O(l) + 2 e - D Mn 2 O 3 (s) + 2 OH - Oxidation reaction can be thought of in two steps: Zn(s) D Zn 2+ (aq) + 2 e - Zn 2+ (aq) + 2 OH - D Zn (OH) 2 (s) Zn (s) + 2 OH - D Zn (OH) 2 (s) + 2 e -

49 Lead-Acid (Storage) Battery The most common secondary battery

50 Lead-Acid Battery Reduction: PbO 2 (s) + 3 H + (aq) + HSO 4- (aq) + 2 e - D PbSO 4 (s) + 2 H 2 O(l) Oxidation: Pb (s) + HSO 4- (aq) D PbSO 4 (s) + H + (aq) + 2 e - PbO 2 (s) + Pb(s) + 2 H + (aq) + HSO 4- (aq) D 2 PbSO 4 (s) + 2 H 2 O(l) ΔE cell = E - E PbO 2/PbSO4 PbSO4/Pb = 1.74 V ( 0.28 V) = 2.02 V

51 The Silver-Zinc Cell: A Button Battery Zn(s),ZnO(s) KOH(sat d) Ag 2 O(s),Ag(s) Zn(s) + Ag 2 O(s) D ZnO(s) + 2 Ag(s) E cell = 1.8 V

52 The Nickel-Cadmium Cell Cd(s) + 2 NiO(OH)(s) + 2 H 2 O(L) D 2 Ni(OH) 2 (s) + Cd(OH) 2 (s)

53 Fuel Cells O 2 (g) + 2 H 2 O(l) + 4 e - D 4 OH - (aq) 2{H 2 (g) + 2 OH - (aq) D 2 H 2 O(l) + 2 e - } 2H 2 (g) + O 2 (g) D 2 H 2 O(l) ΔE cell = ΔE O 2/OH - - ΔE H2O/H2 = V ( V) = V

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