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Zumdahl’s Chapter 17. Electrochemistry: Making Charges Work. Galvanic Cells Cell Potential Std. Reduction Potential, E ° Electrical Work Potential and Free Energy, G. E ’s concentration dependence Nernst Equation K from E ° Batteries Corrosion Electrolysis. Chapter Contents.

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zumdahl s chapter 17

Zumdahl’s Chapter 17


Making Charges Work

chapter contents
Galvanic Cells

Cell Potential

Std. Reduction Potential, E°

Electrical Work

Potential and Free Energy, G

E ’s concentration dependence

Nernst Equation

K from E°




Chapter Contents
  • Conversion of chemical to electrical energy (discharge).
    • And its reverse (electrolysis).
    • Both subject to entropic caution:
      • Convert reversibly to keep systems at equilibrium and convert all available chemical work (G) to and from the equivalent electrical work (QV).
    • Electrons from REDOX reactions.
redox half reactions
RedOx Half Reactions
  • The e– are visible in ½ reactions.

3 H2O2 3 O2 + 6 H+ + 6 e–

2 Au3+ + 6 e– 2 Au

2 Au3+ + 3 H2O2 3 O2 + 6 H+ + 2 Au

  • But while ½ cells were a math convenience in stoichiometry, they are real in electrochemistry
galvanic cells
One ½ cell rxn. occurs in each compartment.

Zn Zn2+ + 2e– in the anode.

Cu2+ + 2e– Cu in cathode.

But not without a connection.



Galvanic Cells







Zn + Cu2+ Zn2+ + Cu

ion salt bridge
But even with a connection of the electrodes, no current flows.

We need to allow neutrality in the solutions with a salt bridge to shift counterions.



Ion (“salt”) Bridge







Zn + Cu2+ Zn2+ + Cu

standard reduction potentials e
Standard Reduction Potentials, E°
    • The voltage generated by the Zn/Cu galvanic cell is +1.1V under standard conditions.
  • Standard conditions are:
    • T = 25°C and P = 1 bar for gases.
    • Solids and liquids are pure.
    • Solutions are 1 M in all species.
  • E°cell is sum of ½ cell E° values.
cell reduction potentials
½ cell Reduction Potentials
  • All ½ cells are catalogued as reduction reactions & assigned reduction potentials, E°.
    • The lower reduction potential ½ rxn is reversed to become the oxidation. E°oxidation = –E°reduction
      • That makes spontaneous E°cell > 0.
    • But E°red can’t be found w/o E°ox!
origin for reduction potentials
Origin for Reduction Potentials
    • We had the same problem for S°ions and solved it by making H+ special.
  • 2H+(aq) + 2e– H2(1 bar) E°  0 V
    • 1 bar H2 flows over a Pt electrode, and the full E°cell is assigned to the other electrode. E°SHE = 0 V.
    • E.g., standard calomel electrode:
        • Hg2Cl2(s) + 2e– 2 Hg(l) + Cl–E°SCE = +0.27V
        • a more physically convenient reference.
active metal series
Ag+ + e–  Ag .80V

Cu2+ + 2e–  Cu .34

2H+ + 2e–  H2 .00

Fe2+ + 2e–  Fe –.44

Zn2+ + 2e–  Zn –.76

Mg2+ + 2e–  Mg –2.37


Remember: reverse the lower potential to make it an oxidation instead of a reduction.

A cursory glance at the standard reduction E°s at left tells us why Cu is immune to 1 M HCl while metals with lower E° merrily bubble off H2.

Active Metal Series
corroding copper
Cu isn’t immortal

H+ doesn’t do it.

We fried that penny not with HCl but with HNO3.

So HNO3 isn’t merely acid but oxidizing acid!

Cu2+ + 2e–  Cu

has E° = +0.34V

NO3– + 4H+ + 3e– NO + H2O

has E° = + 0.96V

So reversing the Cu and adding HNO3 gives a cell E° = + 0.62 V

Corroding Copper
galvanic line notation
Galvanic Line Notation
  • Shorthand for a complete redox cell is of the form:
  • Anode | anodic soln. || cathodic soln. | Cathode
      • but written all on the same line.
      • So making a cell of Cu corrosion,
  • Cu | Cu2+ || NO3–, NO(g), H+ |Pt
      • where all ions should be suffixed (aq) and both metals should have (s).
free energy and work
Free Energy and Work
      • Were all (aq) concentrations in the Cu corrosion cell at 1 M, the cell potential would be + 0.62V (spontaneous).
  • Spontaneous reactions have negativeG° = max (non-PV) work.
    • Electrical work = chargepotential
    • ne moles of e– carry neF Coulombs.
    •  G° = –neF E° J ( J = C V )
      • F = 96,485 C mol–1, the Faraday const.
temperature dependence of e
Temperature Dependence of E°
  • Since E° = – G° /n F,
    • and E = –G /n F for that matter,
  • dE/ dT = ( –1 / n F ) dG / dT
    • But dG = VdP – SdT, so dG/dT = – S
  • Or dE / dT = + S / n F  S° / n F
        • where we’ve presumed that neither S nor H will change much with moderate T.
        • Since S° = + 124 J/mol K for a car battery, it’s harder to start in winter. For 0°C, the 6 cell battery puts out 0.1V less than at 25°C
nernst eqn potentials and concentrations
Nernst Eqn: Potentials and Concentrations
    • Both G° and E° refer to unit (standard) concentrations.
    • But at equilibrium, G = 0 and the cell potential E = 0 as well (see no °).
  • G = G° + RT ln(Q)

 – neFE = – neFE° + RT ln(Q)

E = E° – 2.303 (RT/neF) log(Q)

  • E = E° – (59.1 mV/ne) log(Q) @ 25°C
k from e
K from E°
  • Just as G = G° + RT ln(K) = 0 implies G° = – RT ln(K),
  • – neF E° = – RT ln(K) implies
  • K = e+neF E° / RT
      • where, as before, ne = moles of electrons involved in the overall reaction as written!
      • Very large K can be calculated.
confession time
Confession Time
    • On slide 9, I touted the Hg2Cl2/Hg couple as a convenient standard and drew its E° from the table.
  • But S.C.E. stands for “saturated” calomel electrode and E = 0.241 not E° = 0.268 V (with saturated Cl–) .
    • Since Q = [Cl–], by inverting Nernst, we find [Cl–]sat’d = 2.86 M. Cool.
potential from a single reaction
Potential from a SINGLE ½ Reaction?!?
  • Don’t we need an oxidation as well as a reduction?
      • Yes, but they can be the same reaction (but for a reversal)!
    • Concentrationsmust differ between the anode and cathode.
      • I.e., Q must less be than 1 so log(Q) is negative; then although E°=0 still E >0.
      • The cell brings Q to 1 at equilibrium by equalizing concentrations in ½ cells.
ion selective electrodes
Ion-selective Electrodes
  • [Ag+] can be obtained by E from simple Ag wire referred to SCE.
  • [H+] is much more important!
    • pH electrodes, enclosed in glass, swap H+ for Na+ at silicate surface.
    • Potential difference thus induced is calibrated for [H+]external.
    • See your Harris § 15.4 for details.
assaulted with batteries
Assaulted with Batteries
  • “Battery” refers to a series of Galvanic cells whose E add.
      • (Parallel hookup adds current, I, not E.)
  • Rechargeable NiCad reactions:

Cd + 2 OH– Cd(OH)2 + 2e–

NiO2 + 2H2O + 2e– Ni(OH)2 + 2 OH–

Notice the cancellation of OH– in final reaction.  Q=1 always so E fixed! It doesn’t run down; it just stops.

better batteries
Better Batteries
  • NiCad, though rechargeable, will accept progressively smaller charges; “battery memory.”
  • NiMH replaces anode rxn with
    • MH + OH– M + H2O + e–
    • with a much longer recharge life.
    • M might be Mg2Ni with  = 4.1 and effective H densitytwice H2(liquid)
best battery
Best Battery
      • OK, I’m prejudiced. E°

2 H2 + 4 OH– 4 H2O + 4 e– +0.83V

O2 + 2 H2O + 4 e–  4 OH– +0.40V

  • Is nothing more than hydrogen combustion; no Greenhouse gas.
  • Best example of “fuel cell”
    • so called because H2 and O2 are not built into the battery but supplied externally.
    • Notice that [OH–] is again unchanging.
  • A battery is electrochemistry happening where you want it.
  • Corrosion is where you don’t.
    • All M/MOx couples at E° < 0.4V are corroded even in caustic solutions:
    • O2 + 2 H2O + 4 e– 4 OH–E° = 0.40
    • O2 + 4 H+ + 4 e– 2 H2O E° = 1.23
      • So acid does even better. Q effect!
metal corrosion
Metal Corrosion
  • Metal oxides are lower density (higher volume) than their metals.
    • So oxide formation opens blossoms of corrosion and spreads.
    • Salt spray is worst; it’s electrolytic!
    • Some oxides (e.g., Cr2O3) form impervious oxide coats, slowing further O2 attack.
sacrificial anodes
Sacrificial Anodes

Mg  Mg2+ + 2e–

O2 + 2H2O + 4e–  4 OH–

  • Structural metals like Fe are perfectly protected by more active (lower E°) metals like Mg.
    • If conductive contact is made, O2 gets reduced (to H2O) on Fe by e– released from Mg instead.
    • Replacing the active metal plate is cheaper than a rusted ship!
electromotive force as a chemical reactant
Electromotive Force as a “Chemical Reactant”
    • If instead of doing work with a Galvanic cell potential, you supply a reverse potential, you run the reaction in the non-spontaneous direction! Uphill. Endoergically.
  • This is electrolysis, a synthesis.
    • You supply E not e–; the e– are taken from a cathode reaction, but anode and cathode have swapped.
electrolysis cell
Electrolysis can only proceed with a potential more negative than –E°.

Then the cell runs in reverse.

External work supplies needed G.




Electrolysis Cell







Zn + Cu2+ Zn2+ + Cu

electrolytic stoichiometry
Electrolytic Stoichiometry
  • Charge ( current  time = I  t ) determines amount of product.
      • (Coulombs = Amperes  Seconds)
    • Electrons are the limiting reactant in electrolysis.
    • Moles electrons = ne = Q/F = It/F
    • The usual stoichiometric ratios convert between ne and moles of product.
concentration electrolysis
Concentration Electrolysis?
  • Does it make any sense to run a concentration cell backwards?
      • All you seem to do is to create a concentration difference rather than exploiting one that tends to uniformity.
    • This is the way we purify metals!
      • Force impure metals to be anodes.
      • They shed ions that are “plated” as pure metal on the cathodes!
making active metals
Making Active Metals
      • You can’t “plate” Na, say, out of an aqueous solution!
      • It will simply redox react with H2O to make NaOH(aq).
  • We electrolyze active metals from their melts (which conduct).
    • 2 NaCl(liq)  2 Na(liq) + Cl2(g)
    • Al2O3(liq) + 3C  2 Al(liq) + 3 CO2(g)
      • 5% of all U.S. electricity goes here!
recharging your car
Recharging your Car
      • As the engine runs, a dynamo (i.e., reverse motor) generates a voltage to reverse battery drain from ignition.
  • 2PbSO4 + 2H2O  Pb + PbO2 + 2H2SO4
      • And it takes about 20 km of driving to recharge after an average ignition.
        • With many shorter trips, the battery will die, necessitating an external recharge whose voltage will reduce H+ ion to H2 too.
        • Sparks from disconnect may detonate H2!