General Chemistry II ELECTROCHEMISTRY 17.1 Electrochemical Cells 17.2 Cell Potentials and the Gibbs Free Energy 17.3 Molecular Interpretation of Electrochemical Processes 17.4 Concentration Effects and the Nernst Equation 17.5 Molecular Electrochemistry 17 CHAPTER General Chemistry II
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General Chemistry II
ELECTROCHEMISTRY
17.1 Electrochemical Cells
17.2 Cell Potentials and the Gibbs Free Energy
17.3 Molecular Interpretation of Electrochemical
Processes
17.4 Concentration Effects and the Nernst Equation
17.5 Molecular Electrochemistry
17CHAPTER
General Chemistry II
General Chemistry II
ELECTROCHEMISTRY
17.6 Batteries and Fuel Cells
17.7 Corrosion and Corrosion Prevention
17.8 Electrometallurgy
17.9 Electrolysis of Water and Aqueous Solutions
17CHAPTER
General Chemistry II
General Chemistry II
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General Chemistry II
Electrochemical reactions interconvert chemical and electrical
energy through the oxidation (anode) and reduction (cathode)
half reactions occurring on the surfaces of electrodes.
17.1 ELECTROCHEMICAL CELLS764
Galvanic cell (or Voltaic cell):
~ Spontaneous chemical reaction (∆G < 0) → producing
electricity
Electrolytic cell
~ External input of electricity
→ driving nonspontaneous chemical reactions (∆G > 0)
General Chemistry II
Galvanic Cells
Fig. 17.1 & 2 Cu (anode) – Ag (cathode) in a Galvanic cell.
M: molar massn’: number of moles of electrons transferred per mole
of substance in the corresponding redox reaction
General Chemistry II
1. The mass (W) of a substance that is produced or consumedin an electrochemical reaction is proportional to the quantity of electric charge passed. W ∝ Q ∝ n
2. Equivalent masses (Weq) of different substances are producedor consumed in electrochemical reactions by a given amount of electric charge passed. W ∝ Weq ∝ (n’)–1
1+ 2 W = nWeq
Faraday's Law (1833)
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General Chemistry II
General Chemistry II
Cu-(AgCl/Ag) Electrolytic cell. 0.500 A current for 101 min.Mass of Cu dissolved and the mass of Ag deposited?
( )( )12
3
1
0.500 C s 6.06 10 s96,485 C mol
3.14 10 mol inF
et − −−
−
×= = = ×
Half-reactions:
(cathode) AgCl(s) + 1e–→ Ag(s) + Cl–(aq) (n’ = 1)
Weq(Ag) = (107.8)/1 =107.8 g mol–1
(anode) Cu(s) → Cu2+(aq) + 2e– (n’ = 2)
Weq(Cu) = (63.55)/2 = 31.78 g mol–1
W(Ag) = nWeq(Ag) = (3.14ⅹ10–2 mol)(107.8 g mol–1) = 3.38 g
W(Cu) = nWeq(Cu) = (3.14ⅹ10–2 mol)(31.78 g mol–1) = 0.998 g
769
EXAMPLE 17.2
General Chemistry II
Electrical work, welec
~ Change in the potential energy, ∆EP (in joules), associated
with the transfer of Q coulombs of negative charge through
a potential difference ∆E (in volts) given by
welec = ∆EP = – Q ∆E ≡ – QEcell 1 C×1 V = 1 J
= – Q (Ecathode – Eanode) = – itEcell
Ecell > 0 for a galvanic cell
~ work done by the cell producing electrical work
Ecell < 0 for an electrolytic cell
~ work done on the cell by an external power supply
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17.2 CELL POTENTIALS AND THE GIBBS FREE ENERGY
General Chemistry II
General Chemistry II
Maximum electrical work utilizing a spontaneous reaction
(E = q + w, w = welec – Pext ∆V )For a reversible process, Pext = P and qrev = T∆S.
welec,rev = ∆G
If n moles of electrons pass through the external circuit
of a reversible galvanic cell,
elec,rev cell cell (reversible) w G QE nFE= ∆ = − = −
elec,rev elec,max (at constant and ) w w G T P= = ∆
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General Chemistry II
General Chemistry II
General Chemistry II
Standard hydrogen electrode (SHE)
~ Primary reference electrode
2 H3O+(aq) + 2 e–
→ H2(g) + 2 H2O(l), Eo(SHE) = 0.00 V
Standard cell potentials of half reactions
are measured with reference to the SHE.
Standard cell potential of a Galvanic cell
33 H O
H O 1 M (or a 1) ++ = =
2 2H H 1 atm (or a 1)p = =
Standard Reduction Potentials
Fig. 17.4 Schematic of astandard hydrogen electrode
o o ocell cathode anode E E E= −
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General Chemistry II
Ex. 2 Calculate the standard cell potential for the Cu|Cu2+||Ag+|Ag cell.
Ag+(aq) + e– → Ag(s), Eo = 0.799 V
Cu2+(aq) + 2 e– → Cu(s), Eo = 0.340 V
o o ocell cathode anode 0.799 (0.34 V) 0.459 VV E E E= − = − =
o o 1cell ( 2 mol)(96,500 C mol )(0.459 V) 0.886 kJG nFE −∆ = − = − = −
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Cathode: 2 Ag+(aq) + 2 e– → 2 Ag(s)
Anode: Cu(s) → Cu2+(aq) + 2 e–
Overall: 2 Ag+(aq) + Cu(s) → 2 Ag(s) + Cu2+(aq)
Cell potential:
*The standard cell potential is an intensive property.
Gibbs free energy change (or work done on the system)
A work of -0.886 kJ was done on the system.A work of +0.886 kJ was done by the system.
**Corrected from the typo in the textbook (p774)
**
General Chemistry II
Adding and subtracting half-cell reactions
Ex. 3 Find Eo for a half-reaction from Eo’s of other two half-reactions.
Cu2+(aq) + e– → Cu+(aq), E3o = Eo (Cu2+|Cu+) = ?
775
General Chemistry II
Adding and subtracting half-cell reactions
Ex. 3 Find Eo for a half-reaction from Eo’s of other two half-reactions.
Cu2+(aq) + 2 e– → Cu(s), E1o = Eo (Cu2+|Cu) = 0.340 V
Cu+(aq) + e– → Cu(s), E2o = Eo (Cu+|Cu) = 0.522 V
Cu2+(aq) + e– → Cu+(aq), E3o = Eo (Cu2+|Cu+) = ?
775
∆G (not Eo ) is an extensive property.
∆Ghco = –nhc FEo
∆G3o = ∆G1
o – ∆G2o = –n1FE1
o + n2FE2o = –n3FE3
o
E3o = (n1 E1
o – n2 E2o) / n3 = (2 × 0.340 – 1 × 0.522) / 1 = 0.158 V
General Chemistry II
General Chemistry II
General Chemistry II
Oxidizing and Reducing Agents
Oxidizing agent: easily reduced, large positive Eo (F2, H2O2, MnO4–)
Reducing agent: easily oxidized, large negative Eo,
(alkali & alkaline earth metals)
of 3(O ) 0G∆ >
776
Oxidizing powers of O2 and O3
~ Effective oxidizing agents in acidic solution at pH 0:
O2 + 4 H3O+ + 4 e– → 6 H2O Eo = 1.229 V
O3 + 2 H3O+ + 2 e– → O2 +3 H2O Eo = 2.07 V
O3 is a stronger oxidizing agent than O2 because .
→ ∆G for the reduction of H3O+(aq) by O3 is more negative than
∆G for its reduction by O2.
-
-
General Chemistry II
Reduction Potential Diagram Latimer diagram:
A species can disproportionate if and only ifEo (left; reverse) < Eo (right; forward).
Then, thermodynamically feasible disproportionation of Cu+ is
2 Cu+ → Cu2+ + Cu
Eo = 0.522 V (right) – 0.158 V (left) = + 0.364 V > 0
Eo > 0 → ∆Go < 0 , spontaneous process !
777
General Chemistry II
Adding and subtracting half-cell reactions
Ex. 3 Find Eo for a half-reaction from Eo’s of other two half-reactions.
Cu2+(aq) + 2 e– → Cu(s), E1o = Eo (Cu2+|Cu) = 0.340 V
Cu+(aq) + e– → Cu(s), E2o = Eo (Cu+|Cu) = 0.522 V
Cu2+(aq) + e– → Cu+(aq), E3o = Eo (Cu2+|Cu+) = ?
775
∆G (not Eo ) is an extensive property.
∆Ghco = –nhc FEo
∆G3o = ∆G1
o – ∆G2o = –n1FE1
o + n2FE2o = –n3FE3
o
E3o = (n1 E1
o – n2 E2o) / n3 = (2 × 0.340 – 1 × 0.522) / 1 = 0.158 V
General Chemistry II
General Chemistry II
General Chemistry II
Saturated calomel electrode
Hg2Cl2 (calomel) + 2 e–
→ 2 Hg + 2 Cl–(saturated)
Eo = 0.242 V
~ Phased out due to environmental
problem of Hg contamination
Ag/AgCl electrode or
Ag|AgCl|KCl(saturated, aq) electrode
AgCl + e– → Ag + Cl–
Eo = 0.197 V Fig. Schematic of a saturatedAg/AgCl electrode
Alternative Reference Electrodes 778
General Chemistry II
Graphical representation of the standard reference potentials
Fig. 17.5 Orbital energy level Fig. 17.6 Orbital energy level for the (left) and potential (right). SHE (left) and the “absolute” (vacuum)εα = – IEα (Koopmans) potential (right).
Potential energy scales plotted such that εα = – eEα.
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General Chemistry II
“Absolute” potential scale for the SHE, EH
Established by estimating the energy required to remove electron
from Pt|H2|H+ under standard conditions and transfer it to a vacuum
at rest. → IE = 4.5 eV of a hydrogen atom at standard conditions
εH = –IEH = –4.5 eV → EH = εH /(–e) = 4.5 V
Fig. 17.7 Relationships among SHE, SCE, and absolute (vacuum) potential scales.
Ex. (E vs. SHE) = (E vs. SCE) + 0.242 V
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General Chemistry II
Using ∆G = –nFEcell and ,
∆G = ∆Go + RT ln Q (p. 647) →
o ocellG nFE∆ = −
ocell cell lnnFE nFE RT Q− = − +
Nernst Equation
ocell cell ln RTE E Q
nF= − o o
cell cell 100.0592 log (at 25 C) E E Q
n= −
ohc hc 10 hc
hc
0.0592 log VE E Qn
= −
or
Nernst equation for half-cell reactions (written as reductions)
Ex. Zn2+ + 2 e– → Zn nhc = 2, Qhc = 1/[Zn2+]
n : number of moles of electrons transferred in the overall reaction as written.
17.4 CONCENTRATION EFFECTS AND THE NERNST EQUATION
Many cycles of charge-discharge, Large current as large as 100 A,Heavy (low energy density) → limits the range of the electric vehicles
Fig. 17.24 A lead-acid storage battery consists of several cells connected in series. The electrodes are both constructed from lead grids filled with spongy Pb (cathode) and PbO2 (anode) and the electrolyte is sulfuric acid.
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General Chemistry II
Lithium-ion batteryHigh energy density (light Li)Much safer than lithium battery (no elemental Li, only Li+ ions)Electrodes: LiCoO2 (cathode), LiyC6 (graphite anode)
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General Chemistry II
Single Li+ ions shuttle back and forth: LiC6 → Li+ + e– + C6 (anode)
Further oxidization of Fe2+(aq) migrated to cathode to form rust2 Fe2+(aq) + 1/2 O2(g) + (6 + x) H2O(l) → Fe2O3∙xH2O(s) +4 H3O+(aq)
rustOverall corrosion reaction:
2 3 22 2 2 Fe( ) 3/2 O ( ) H O Fe O H O() )(s g l x sx+ + → ⋅
Fig. 17.30 Schematic of iron corrosion. Hydrogen ions move through the hydrated rust pile.
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General Chemistry II
– Pitting on the anode (oxygen-poor areas under the paint)– Rust on the cathode (oxygen-rich exposed area)– Dissolved salts increase the conductivity.– High acidity due to air pollution or CO2 speeds up the
reduction at the cathode.
Spontaneous aluminum oxidation (Al2O3)Stainless steel (alloy of iron and chromium)Rust preventing (superficial oxidation) paints containing K2Cr2O7 and Pb3O4
Passivation: Protective thin metal oxide layer
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General Chemistry II
General Chemistry II
Fe2+(aq) + 2 e– → Fe(s) Eo = –0.41 VMg2+(aq) + 2 e– → Mg(s) Eo = –2.39 V
~ Mg2+ is much harder to reduce than Fe2+
Sacrificial Anode: A piece of Mg in contact with Fe