# CHAPTER 13: Electrochemistry and Cell Voltage

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1 CHAPTER 13: Electrochemistry and Cell Voltage In this chapter: More about redox reactions Cells, standard states, voltages, half-cell potentials Relationship between G and voltage and electrical work Equilibrium constants from electrochemistry Batteries and fuel cells

2 Electrical Work We can use batteries like the galvanic cell of the last chapter to perform electrical work (e.g., light up a light bulb) How to measure electrical work? ω = Q ξ elec Joules Coulombs Joules Coulomb = Volt

3 Example: Computer Power A workstation computer might draw ~10Amps. At 120 V, how many watts?

4 Working with the Current Recall: So: Total charge = current x time Q = I t = Q ω ξ elec = I t ξ Note: ω elec sometimes also measured in kilowatt hours. 1 watt = 1J/s 1kW hr 10 = s 3 J 6 ( 3600 s) = J

5 Gibbs Free Energy, Voltage, and Electrical Work The maximum amount of electrical work that can be achieved is if all the change in Gibbs energy of the system (assuming constant T,P) is turned into electrical work and no heat is generated. G G = ωelec,max = Q ξ (const T,P) (const T,P) Positive ξ means negative G (this Q is defined positive), so ξ > 0 is spontaneous. [sign convention opposite of G!]

6 Galvanic and Electrolytic Cells Galvanic cells like the Cu(s) Cu 2+ (aq) Ag + (aq) Ag(s) example from chapter 12 would have ξ>0. ξ>0 for all Galvanic cells (definition) If ξ<0, electrolytic cell must be driven by outside voltage. ω = Q ξ elec ξ>0 Galvanic cell ω elec <0 cell does work ξ<0 Electrolytic cell ω elec >0 work done on cell

7 Charge, Electrons, Faraday Recall that 1 mol of e - has a charge of 1F (Faraday). If we measure Q in moles of e -, Q = nf G = Q = nf ξ ξ (const T,P) Note: If the battery size doubles, G doubles but so does n therefore ξ doesn t depend on its size. AA and D batteries are both 1.5 V

8 Standard States and Cell Voltage If we work with standard states, then G becomes G. This will also change ξ into ξ. o o G = nf ξ ξ is the potential difference (voltage) of a galvanic cell in which all reactants and products are in standard states.

9 Example: What is G if one mol of Ni is dissolved in the cell: Ni(s) Ni 2+ (aq) Cu 2+ (aq) Cu(s) when [Ni 2+ ]=[Cu 2+ ]=1.00 M and 25 C and ξ is measured to be 0.57V? Standard States

10 Standard Cell Potentials In principle, ξ could be tabulated for all possible cells. But, don t need to can tabulate for each half-reaction! For example, Ni(s) Ni 2+ (aq) Cu 2+ (aq) Cu(s) Ni 2+ (aq) + 2e - Ni(s) ξ (Ni 2+ Ni) Cu 2+ (aq) + 2e - Cu(s) ξ (Cu 2+ Cu) Customary to write the half-reactions as reductions The nickel is actually oxidized (at the anode). So reverse the sign of the standard potential.

11 Standard Cell Potentials (cont.) Ni(s) Ni 2+ (aq) Cu 2+ (aq) Cu(s) Ni 2+ (aq) + 2e - Ni(s) ξ (Ni 2+ Ni) Cu 2+ (aq) + 2e - Cu(s) ξ (Cu 2+ Cu) ξ = ξ (cathode) - ξ (anode) (reduction) for a galvanic cell. (oxidation, reverse sign of reduction ξ )

12 Measuring Standard Potentials How are ξ measured? Set reduction of H + (aq) to 0V Measure chemical potentials of halfreactions coupled with H + reduction below 2H + (aq) + 2e - H 2 (g) ξ =0V (by definition) Stronger oxidizing agents Table 13-1: Standard Reduction Potentials Reduction half-reaction Stronger reducing agents ξ (V) Cations don t want the e - back, they want to give up the e - (compared to H)

13 Using Table 13-1 Table 13-1 allows one to determine which metal is dissolved (oxidized) and which is deposited (reduced) in a Galvanic cell. e.g. In a Nickel/Silver cell, which element plates out? What is ξ? Stronger oxidizing agents Table 13-1: Standard Reduction Potentials Stronger reducing agents

14 Effect of ph on Oxidizing and Reducing Agents Oxygen is a good oxidizing agent O 2 (g) + 4H + + 4e - 2H 2 O(l) ξ =1.229V O 2 (g) + 2H 2 O(l) + 4e - 4OH - (aq) ξ =0.401V Better oxidizing agent in acid than base! NO H + + 2e - HNO 2 + H 2 O ξ = 0.94 HSO 4- +3H + +2e - SO 2 +2H 2 O ξ = 0.17 Nitric acid is a better oxidizing agent than sulfuric acid (hmm, how could we test this hypothesis?)

15 Concentrations and the Nerst Equation We saw that if all reaction conditions are in their standard state, G =-nf ξ What if things are not in standard state? a) remove superscript! One could, but now you couldn t easily use tabulated data. b) Recall from chapter 11 that G= G +RT ln(q)

16 Nernst Equation G= G +RT ln(q) So if: G=-nF ξ G =-nf ξ Nernst Equation also -nf ξ=-nf ξ +RT ln(q) ξ ξ = ξ ( RT ) = ξ F n ln(q) ( V ) log (Q) n 10

17 Example Suppose we have a cell Zn Zn 2+ Cr 3+ Cr with [Zn 2+ ]=0.78M and [Cr 3+ ]= M. What is ξ at 25 C? also ξ ξ What is ξ? n? Q? Zn 2+ (aq) + 2e - Zn(s) Cr 3+ (aq) + 3e - Cr(s) ( RT ) = ξ F = ξ n ln(q) ( V ) log (Q) n 10 ξ (Zn 2+ Zn)= ξ (Cr 3+ Cr)=-0.74

18 Example

19 Example ξ= V Negative ξ for these concentrations, but positive for standard state conditions. What does this mean?

20 Nernst Equation and ph meters ( V ) log (Q) ξ = ξ 10 If we know ξ and ξ and n, we can solve for Q. If we also know all concentrations but one, then we can solve for that one concentration. For example, H + concentration - ph meter. n

21 Equilibrium Constants and Electrochemistry G =-nf ξ G =-RT ln(k) RT ln(k)=nf ξ nf n = ξ or log = ξ RT K V (for T = K) K can be obtained from ξ and vice versa. Standard Potentials are related to equilibrium constants Note: ln ( K ) ( ) ξ >0, K>1 (reaction goes forward) ξ <0, K<1 (reaction goes backward)

22 Batteries and Fuel Cells anode: cathode: Zn(s) Zn 2+ (aq) + 2e - 2MnO 2 (s) +2NH 4+ (aq) + 2e - Mn 2 O 3 (s) + 2NH 3 (aq) + H 2 O(l) also at cathode: 2NH 4+ (aq) + 2e - 2NH 3 (g) + H 2 (g) Gas build up at the cathode presents a problem!!

23 Why batteries (usually) don t explode Gas build up at the cathode is prevented the following reactions: Zn 2+ (aq) + 2NH 3 (g) [Zn(NH 3 ) 2 ] 2+ (aq) 2MnO 2 (s) + H 2 (g) Mn 2 O 3 (s) + H 2 O(l) Net reaction: Zn(s) + 2MnO 2 (s) + 2NH 4+ (aq) [Zn(NH 3 ) 2 ] 2+ (aq) + Mn 2 O 3 (s) + H 2 O(l)

24 Mercury Battery (watch batteries, etc.) Anode: Zn(s) + 2OH - (aq) Zn(OH) 2 (s) + 2e - Cathode: HgO(s) + H 2 O(l) + 2e - Hg(l) + 2OH - (aq) Net: Zn(s) + HgO(s) + H 2 O(l) Zn(OH) 2 (s) + Hg(l) Other batteries: Nickel-Cadmium (rechargeable), Lead-acid (car batteries)

25 Fuel Cells Batteries are used up (and maybe recharged and used again). Fuel cells are used continuously (constantly replenished with new fuel).

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