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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 l.jpg

Zumdahl’s Chapter 17

Electrochemistry:

Making Charges Work


Chapter contents l.jpg

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


Electrochemistry l.jpg
Electrochemistry

  • 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 l.jpg
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 l.jpg

One ½ cell rxn. occurs in each compartment.

Zn Zn2+ + 2e– in the anode.

Cu2+ + 2e– Cu in cathode.

But not without a connection.

Cu

Zn

Galvanic Cells

Cathode=Reduction

Anode=Oxidation

SO42–

SO42–

Zn2+

Cu2+

Zn + Cu2+ Zn2+ + Cu


Ion salt bridge l.jpg

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.

2e–

2e–

Ion (“salt”) Bridge

Cu

Zn

SO42–

SO42–

Zn2+

Cu2+

Zn + Cu2+ Zn2+ + Cu


Standard reduction potentials e l.jpg
Standard Reduction Potentials, flows.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 l.jpg
    ½ cell Reduction Potentials flows.

    • 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 l.jpg
    Origin for Reduction Potentials flows.

    • 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 l.jpg

    Ag flows.+ + e–  Ag .80V

    Cu2+ + 2e–  Cu .34

    2H+ + 2e–  H2 .00

    Fe2+ + 2e–  Fe –.44

    Zn2+ + 2e–  Zn –.76

    Mg2+ + 2e–  Mg –2.37

    Etc.

    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 l.jpg

    Cu isn’t immortal flows.

    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 l.jpg
    Galvanic Line Notation flows.

    • 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 l.jpg
    Free Energy and Work flows.

    • 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 l.jpg
    Temperature Dependence of flows.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 l.jpg
    Nernst Eqn: Potentials and Concentrations flows.

    • 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 l.jpg
    K from flows.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 l.jpg
    Confession Time flows.

    • 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 l.jpg
    Potential from a flows.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 l.jpg
    Ion-selective Electrodes flows.

    • [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 l.jpg
    Assaulted with Batteries flows.

    • “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 l.jpg
    Better Batteries flows.

    • 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 l.jpg
    Best Battery flows.

    • 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.


  • Corrosion l.jpg
    Corrosion flows.

    • 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 l.jpg
    Metal Corrosion flows.

    • 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 l.jpg
    Sacrificial Anodes flows.

    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 l.jpg
    Electromotive Force as a “Chemical Reactant” flows.

    • 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 l.jpg

    Electrolysis can only proceed with a potential more negative than –E°.

    Then the cell runs in reverse.

    External work supplies needed G.

    2e–

    2e–

    +

    Electrolysis Cell

    Cu

    Zn

    SO42–

    SO42–

    Zn2+

    Cu2+

    Zn + Cu2+ Zn2+ + Cu


    Electrolytic stoichiometry l.jpg
    Electrolytic Stoichiometry than –

    • 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 l.jpg
    Concentration Electrolysis? than –

    • 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 l.jpg
    Making Active Metals than –

    • 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 l.jpg
    Recharging your Car than –

    • 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!


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