CHAPTER 13: Electrochemistry and Cell VoltageElectrical WorkExample: Computer PowerWorking with the CurrentGibbs Free Energy, Voltage, and Electrical WorkGalvanic and Electrolytic CellsCharge, Electrons, FaradayStandard States and Cell VoltageExample:Standard Cell PotentialsStandard Cell Potentials (cont.)Measuring Standard PotentialsUsing Table 13-1Effect of pH on Oxidizing and Reducing AgentsConcentrations and the Nerst EquationNernst EquationExampleExampleExampleNernst Equation and pH metersEquilibrium Constants and ElectrochemistryBatteries and Fuel CellsWhy batteries (usually) don’t explode…Mercury BatteryFuel CellsCHAPTER 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 cellsCHEM 1310 A/B Fall 2006Electrical 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?ξω∆−= QelecJoulesCoulombs JoulesCoulomb= VoltCHEM 1310 A/B Fall 2006Example: Computer Power• A workstation computer might draw ~10Amps. At 120 V, how many watts?CHEM 1310 A/B Fall 2006Working with the Current• Recall:•Note: ωelecsometimes also measured in kilowatt hours.Total charge = current x timet⋅=IQξω∆−= QelecSo:ξ∆−= I tJ/s 1 watt1=()J106.3s 3600sJ10hr kW 163×=⎟⎟⎠⎞⎜⎜⎝⎛=⋅CHEM 1310 A/B Fall 2006Gibbs Free Energy, Voltage, and Electrical Work• The maximum amount of electrical work that can be achieved is if allthe change in Gibbs energy of the system (assuming constant T,P) is turned into electrical work and no heat is generated.• Positive∆ξ means negative ∆G (this Q is defined positive), so ∆ξ > 0 is spontaneous. [sign convention opposite of ∆G!]max,Gelecω=∆ξ∆−=∆∴QG (const T,P)(const T,P)CHEM 1310 A/B Fall 2006Galvanic and Electrolytic Cells• Galvanic cells like the Cu(s)|Cu2+(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.ξω∆−= Qelec∆ξ>0Galvanic cellωelec<0cell doeswork∆ξ<0Electrolytic cellωelec>0work done oncellCHEM 1310 A/B Fall 2006Charge, Electrons, Faraday• Recall that 1 mol of e-has a charge of 1F(Faraday). • If we measure Q in moles of e-,• 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 Fn=Qξξ∆−=∆−=∆ FnQG(const T,P)CHEM 1310 A/B Fall 2006Standard States and Cell Voltage• If we work with standard states, then ∆G becomes ∆G°. This will also change ∆ξinto ∆ξ°.• ∆ξ° is the potential difference (voltage) of a galvanic cell in which all reactants and products are in standard states.ooGξ∆−=∆ FnCHEM 1310 A/B Fall 2006Example:• What is ∆G° if one mol of Ni is dissolved in the cell:Ni(s)|Ni2+(aq)||Cu2+(aq)|Cu(s) when [Ni2+]=[Cu2+]=1.00 M and 25°C and ∆ξ°is measured to be 0.57V?Standard StatesCHEM 1310 A/B Fall 2006Standard 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)|Ni2+(aq)||Cu2+(aq)|Cu(s)Ni2+(aq) + 2e-Æ Ni(s) ξ°(Ni2+|Ni)Cu2+(aq) + 2e-Æ Cu(s) ξ°(Cu2+|Cu)•Customaryto write the half-reactions as reductions• The nickel is actually oxidized (at the anode). So reverse the sign of the standard potential.CHEM 1310 A/B Fall 2006Standard Cell Potentials (cont.)Ni(s)|Ni2+(aq)||Cu2+(aq)|Cu(s)Ni2+(aq) + 2e-Æ Ni(s) ξ°(Ni2+|Ni)Cu2+(aq) + 2e-Æ Cu(s) ξ°(Cu2+|Cu)∆ξ°= ξ°(cathode) - ξ°(anode)for a galvanic cell.(reduction)(oxidation, reverse signof reduction ξ°)CHEM 1310 A/B Fall 2006Measuring Standard PotentialsHow are ξ° measured?• Set reduction of H+(aq) to 0V• Measure chemical potentials of half-reactions coupled with H+ reduction below2H+(aq) + 2e-Æ H2(g)ξ°=0V (by definition)Stronger reducingreducing agentsStronger oxidizingoxidizing agentsCations don’t want the e-back, they want to give up the e-(compared to H)Table 13-1: Standard Reduction PotentialsReduction half-reactionξ°(V)CHEM 1310 A/B Fall 2006Using 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 reducingreducing agentsStronger oxidizingoxidizing agentsTable 13-1: Standard Reduction PotentialsCHEM 1310 A/B Fall 2006Effect of pH on Oxidizing and Reducing Agents• Oxygen is a good oxidizing agentO2(g) + 4H+ + 4e-Æ 2H2O(l) ξ°=1.229VO2(g) + 2H2O(l) + 4e-Æ 4OH-(aq) ξ°=0.401VBetter oxidizing agent in acid than base!NO3-+ 3H++ 2e-Æ HNO2 + H2O ξ°= 0.94HSO4-+3H++2e-ÆSO2+2H2O ξ°= 0.17• Nitric acid is a better oxidizing agent than sulfuric acid(hmm, how could we test this hypothesis?)CHEM 1310 A/B Fall 2006Concentrations and the Nerst Equation• We saw that if all reaction conditions are in their standard state,∆G°=-nF∆ξ°• What if things are notin 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)CHEM 1310 A/B Fall 2006Nernst Equation∆G=∆G°+RT ln(Q)∆G=-nF∆ξ∆G°=-nF∆ξ°-nF∆ξ=-nF∆ξ°+RT ln(Q)()()(Q)log∆ξ∆ξ alsoln(Q)∆ξ∆ξ10n0.0592VnRT−°=−°=FSo if:Nernst EquationCHEM 1310 A/B Fall 2006Example• Suppose we have a cell Zn|Zn2+||Cr3+|Cr with [Zn2+]=0.78M and [Cr3+]=0.00011M. What is ∆ξ at 25°C?What is ∆ξ°? n? Q?Zn2+(aq) + 2e-Æ Zn(s) ξ°(Zn2+|Zn)=-0.763Cr3+(aq) + 3e-Æ Cr(s) ξ°(Cr3+|Cr)=-0.74()()(Q)log∆ξ∆ξ alsoln(Q)∆ξ∆ξ10n0.0592VnRT−°=−°=FCHEM 1310 A/B Fall 2006ExampleCHEM 1310 A/B Fall 2006Example∆ξ= -0.052 V• Negative∆ξ for these concentrations, but positive for standard state conditions.• What does this mean?CHEM 1310 A/B Fall 2006Nernst Equation and pH meters()(Q)log∆ξ∆ξ10n0.0592V−°=• 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.CHEM 1310 A/B Fall 2006Equilibrium Constants and