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
CHEM 1310 A/B Fall 2006
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?ξω ∆−= Qelec
Joules Coulombs JoulesCoulomb = Volt
CHEM 1310 A/B Fall 2006
Example: Computer Power
• A workstation computer might draw ~10Amps. At 120 V, how many watts?
CHEM 1310 A/B Fall 2006
Working with the Current
• Recall:
• Note: ωelec sometimes also measured in kilowatt hours.
Total charge = current x timet⋅= IQ
ξω ∆−= QelecSo:
ξ∆−= I t
J/s 1 watt1 =
( ) J106.3s 3600s
J10hr kW 1 63
×=⎟⎟⎠
⎞⎜⎜⎝
⎛=⋅
CHEM 1310 A/B Fall 2006
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.
• Positive ∆ξ means negative ∆G (this Q is defined positive), so ∆ξ > 0 is spontaneous. [sign convention opposite of ∆G!]
max,G elecω=∆ξ∆−=∆∴ QG
(const T,P)
(const T,P)
CHEM 1310 A/B Fall 2006
Galvanic 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>0 Galvanic cell ωelec<0 cell does work
∆ξ<0 Electrolytic cell ωelec>0 work done on cell
CHEM 1310 A/B Fall 2006
Charge, 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 2006
Standard 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.
ooG ξ∆−=∆ Fn
CHEM 1310 A/B Fall 2006
Example:• 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 States
CHEM 1310 A/B Fall 2006
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)|Ni2+(aq)||Cu2+(aq)|Cu(s)
Ni2+(aq) + 2e- Ni(s) ξ°(Ni2+|Ni)Cu2+(aq) + 2e- Cu(s) ξ°(Cu2+|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.
CHEM 1310 A/B Fall 2006
Standard Cell Potentials (cont.)
Ni(s)|Ni2+(aq)||Cu2+(aq)|Cu(s)Ni2+(aq) + 2e- Ni(s) ξ°(Ni2+|Ni)
Cu2+(aq) + 2e- Cu(s) ξ°(Cu2+|Cu)
∆ξ° = ξ°(cathode) - ξ°(anode)
for a galvanic cell.
(reduction)(oxidation, reverse sign
of reduction ξ°)
CHEM 1310 A/B Fall 2006
Measuring Standard PotentialsHow are ξ° measured?• Set reduction of H+(aq) to
0V• Measure chemical
potentials of half-reactions coupled with H+
reduction below
2H+(aq) + 2e- H2(g)ξ°=0V (by definition)
Stronger reducing
reducingagents
Stro
nger
oxi
dizi
ngox
idiz
ing
agen
ts
Cations don’t want the e- back, they want to give up the e-
(compared to H)
Table 13-1: Standard Reduction Potentials
Reduction half-reaction ξ°(V)
CHEM 1310 A/B Fall 2006
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 reducing
reducingagents
Stro
nger
oxi
dizi
ngox
idiz
ing
agen
ts
Table 13-1: Standard Reduction Potentials
CHEM 1310 A/B Fall 2006
Effect of pH on Oxidizing and Reducing Agents
• Oxygen is a good oxidizing agentO2(g) + 4H+ + 4e- 2H2O(l) ξ°=1.229VO2(g) + 2H2O(l) + 4e- 4OH-(aq) ξ°=0.401VBetter oxidizing agent in acid than base!
NO3- + 3H++ 2e- HNO2 + H2O ξ°= 0.94
HSO4-+3H++2e- SO2+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 2006
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)
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Nernst Equation∆G=∆G°+RT ln(Q)
∆G=-nF∆ξ∆G°=-nF∆ξ°
-nF∆ξ=-nF∆ξ°+RT ln(Q)
( )( ) (Q)log∆ξ∆ξ also
ln(Q)∆ξ∆ξ
10n0.0592VnRT
−°=
−°= F
So if:
Nernst Equation
CHEM 1310 A/B Fall 2006
Example• 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- Zn(s) ξ°(Zn2+|Zn)=-0.763Cr3+(aq) + 3e- Cr(s) ξ°(Cr3+|Cr)=-0.74
( )( ) (Q)log∆ξ∆ξ also
ln(Q)∆ξ∆ξ
10n0.0592VnRT
−°=
−°= F
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Example
CHEM 1310 A/B Fall 2006
Example
∆ξ = -0.052 V• Negative ∆ξ for these concentrations, but
positive for standard state conditions.• What does this mean?
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Nernst Equation and pH meters( ) (Q)log∆ξ∆ξ 10n
0.0592V−°=
• 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 2006
Equilibrium Constants and Electrochemistry
∆G°=-nF∆ξ°∆G°=-RT ln(K)RT ln(K)=nF∆ξ°
• K can be obtained from ∆ξ° and vice versa.• Standard Potentials are related to equilibrium constants• Note:
( ) ( ) °∆⎟⎠⎞
⎜⎝⎛=°∆⎟
⎠⎞
⎜⎝⎛= ξξ
V 0.0592nlogor
RTnln 10 KK F
(for T = 298.15K)
∆ξ°>0, K>1 (reaction goes forward)∆ξ°<0, K<1 (reaction goes backward)
CHEM 1310 A/B Fall 2006
Batteries and Fuel Cellsanode:
Zn(s) Zn2+(aq) + 2e-
cathode:2MnO2(s) +2NH4
+(aq) + 2e-
Mn2O3(s) + 2NH3(aq) + H2O(l)also at cathode:2NH4
+(aq) + 2e- 2NH3(g) + H2(g)• Gas build up at the cathode
presents a problem!!
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Why batteries (usually) don’t explode…
• Gas build up at the cathode is prevented the following reactions:Zn2+(aq) + 2NH3(g) [Zn(NH3)2]2+(aq)2MnO2(s) + H2(g) Mn2O3(s) + H2O(l)
Net reaction:Zn(s) + 2MnO2(s) + 2NH4
+(aq) [Zn(NH3)2]2+(aq) + Mn2O3(s) + H2O(l)
CHEM 1310 A/B Fall 2006
Mercury Battery(watch batteries,
etc.)
Anode: Zn(s) + 2OH-(aq) Zn(OH)2(s) + 2e-
Cathode: HgO(s) + H2O(l) + 2e- Hg(l) + 2OH-(aq)Net: Zn(s) + HgO(s) + H2O(l) Zn(OH)2(s) + Hg(l) Other batteries: Nickel-Cadmium (rechargeable),
Lead-acid (car batteries)CHEM 1310 A/B Fall 2006
Fuel Cells• Batteries are used
up (and maybe recharged and used again).
• Fuel cells are used continuously (constantly replenished with new fuel).
CHEM 1310 A/B Fall 2006
