Zumdahl’s Chapter 17Zumdahl’s Chapter 17

Electrochemistry:Electrochemistry:

Making Charges WorkMaking Charges Work

Chapter ContentsChapter Contents

• Galvanic CellsGalvanic Cells– Cell PotentialCell Potential

• Std. Reduction Std. Reduction Potential, Potential, EE°°

• Electrical WorkElectrical Work– Potential and Potential and

Free Energy, GFree Energy, G

• E E ’s concentration ’s concentration dependencedependence– Nernst EquationNernst Equation– K from K from EE°°

• BatteriesBatteries• CorrosionCorrosion• ElectrolysisElectrolysis

ElectrochemistryElectrochemistry

• Conversion of Conversion of chemical to electricalchemical to electrical energy energy (discharge).(discharge).– And its reverse And its reverse (electrolysis).(electrolysis).– Both subject to entropic caution:Both subject to entropic caution:

• Convert Convert reversiblyreversibly to keep systems at to keep systems at equilibrium and convert all available equilibrium and convert all available chemical work (chemical work (G) to and from the G) to and from the equivalent electrical work (Qequivalent electrical work (QV).V).

– Electrons from Electrons from REDOXREDOX reactions. reactions.

RedOx Half ReactionsRedOx Half Reactions

• The eThe e–– are are visiblevisible in ½ reactions. in ½ reactions.3 H3 H22OO22 3 O 3 O22 + 6 H + 6 H++ + + 6 e6 e––

2 Au2 Au3+3+ + + 6 e6 e–– 2 Au 2 Au

2 Au2 Au3+3+ + 3 H + 3 H22OO22 3 O 3 O22 + 6 H + 6 H++ + 2 Au + 2 Au

• But while ½ cells were a math But while ½ cells were a math convenience in stoichiometry, they convenience in stoichiometry, they are are realreal in electrochemistry in electrochemistry

Galvanic CellsGalvanic Cells

• One ½ cell rxn. One ½ cell rxn. occurs in each occurs in each compartment.compartment.

• Zn Zn ZnZn2+2+ + 2e + 2e–– in in the anode.the anode.

• CuCu2+2+ + 2e + 2e–– Cu in Cu in cathode.cathode.

• But not without a But not without a connection.connection.

Zn

Zn2+ Cu2+

Zn + CuZn + Cu2+2+ Zn Zn2+2+ + Cu + Cu

SO42– SO4

2–

Cu

Anode=Oxidation

Cathode=Reduction

Ion (“salt”) BridgeIon (“salt”) Bridge

• But even with a But even with a connection of the connection of the electrodes, no electrodes, no current flows.current flows.

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

Zn

Zn2+ Cu2+

Zn + CuZn + Cu2+2+ Zn Zn2+2+ + Cu + Cu

SO42– SO4

2–

Cu

2e– 2e–

Standard Reduction Standard Reduction Potentials, Potentials, EE°°

– The voltage generated by the Zn/Cu The voltage generated by the Zn/Cu galvanic cell is +1.1V under galvanic cell is +1.1V under standard standard conditionsconditions..

• Standard conditions are:Standard conditions are:– T = 25°C and P = 1 bar for gases.T = 25°C and P = 1 bar for gases.– Solids and liquids are pure.Solids and liquids are pure.– Solutions are 1 Solutions are 1 MM in all species. in all species.

• EE°°cellcell is sum of ½ cell is sum of ½ cell EE° values.° values.

½ cell Reduction ½ cell Reduction PotentialsPotentials

• All ½ cells are catalogued as All ½ cells are catalogued as reduction reactions & assigned reduction reactions & assigned reduction potentials, reduction potentials, EE°.°.– The The lowerlower reduction potential ½ rxn is reduction potential ½ rxn is

reversedreversed to become the oxidation. to become the oxidation. EE°°oxidationoxidation = – = –EE°°reductionreduction

• That makes spontaneous That makes spontaneous EE°°cellcell > 0. > 0.

– But But EE°°redred can’t be found w/o can’t be found w/o EE°°oxox!!

Origin for Reduction Origin for Reduction PotentialsPotentials

– We had the same problem for S°We had the same problem for S°ionsions and solved it by making Hand solved it by making H++ special. special.

• 2H2H++((aqaq) + 2e) + 2e–– H H22(1 bar) (1 bar) EE° ° 0 V 0 V

– 1 bar H1 bar H22 flows over a Pt electrode, and flows over a Pt electrode, and the full the full EE°°cellcell is is assignedassigned to the to the otherother electrode. electrode. EE°°SHESHE = 0 V. = 0 V.

– E.g., standard E.g., standard calomelcalomel electrode: electrode:– HgHg22ClCl22((ss) + 2e) + 2e–– 2 Hg( 2 Hg(ll) + Cl) + Cl–– EE°°SCE SCE = +0.27V= +0.27V

– a more physically convenient reference.a more physically convenient reference.

Active Metal SeriesActive Metal Series

• AgAg++ + e + e– – Ag .80V Ag .80V• CuCu2+ 2+ + 2e+ 2e– – Cu .34 Cu .34

• 2H2H+ + + 2e+ 2e– – H H22 .00 .00

• FeFe2+ 2+ + 2e+ 2e– – Fe Fe ––.44.44• ZnZn2+2+ + 2e + 2e– – Zn Zn ––.76.76• MgMg2+2+ + 2e + 2e– – Mg Mg ––2.372.37• Etc.Etc.

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

• A cursory glance A cursory glance at the standard at the standard reduction reduction EE°s at °s at left tells us why left tells us why Cu is immune to 1 Cu is immune to 1 MM HCl while HCl while metals with lower metals with lower EE° merrily bubble ° merrily bubble off Hoff H22..

Corroding CopperCorroding Copper

• Cu isn’t immortalCu isn’t immortal• HH++ doesn’t do it. doesn’t do it.

– We fried that We fried that penny penny notnot with HCl with HCl but with HNObut with HNO33..

• So HNOSo HNO33 isn’t isn’t merely acid but merely acid but oxidizingoxidizing acid! acid!

• CuCu2+2+ + 2e + 2e– – Cu Cu– has has EE° = +0.34V° = +0.34V

• NONO33–– + 4H + 4H++ + 3e + 3e––

NO + HNO + H22OO– has has EE° = + 0.96V° = + 0.96V

• So So reversingreversing the the Cu and adding Cu and adding HNOHNO33 gives a cell gives a cell EE° = ° = ++ 0.62 V 0.62 V

Galvanic Line NotationGalvanic Line Notation

• ShorthandShorthand for a complete redox for a complete redox cell is of the form:cell is of the form:

• Anode | anodic soln. || cathodic Anode | anodic soln. || cathodic soln. | Cathodesoln. | Cathode

• but written all on the same line.but written all on the same line.• So making a cell of Cu corrosion,So making a cell of Cu corrosion,

• Cu | CuCu | Cu2+2+ || NO || NO33––, NO(, NO(gg), H), H++ |Pt |Pt

• where all ions should be suffixed (where all ions should be suffixed (aqaq) and ) and both metals should have (both metals should have (ss).).

Free Energy and WorkFree Energy and Work

• Were all (aq) concentrations in the Cu Were all (aq) concentrations in the Cu corrosion cell at 1 corrosion cell at 1 MM, the cell potential , the cell potential would be would be ++ 0.62V ( 0.62V (spontaneousspontaneous).).

• Spontaneous reactions have Spontaneous reactions have negativenegative GG° = max ° = max (non-PV)(non-PV) work. work.– Electrical work = chargeElectrical work = chargepotentialpotential

– nnee moles of e moles of e–– carry carry nnee FF Coulombs. Coulombs.

GG° = ° = –– nnee F EF E°° J ( J = C V ) J ( J = C V )

• FF = 96,485 C mol = 96,485 C mol–1–1, the , the FaradayFaraday const. const.

Temperature Dependence Temperature Dependence of of EE°°

• Since Since EE° = – ° = – GG° ° // n n FF, , – and and EE = – = –G G // n n FF for that matter, for that matter,

• ddEE / / ddTT = ( –1 / = ( –1 / n n F F ) d) dG G / / ddTT– But dBut dGG = = VVddPP – – SSddTT, so d, so dGG/d/dTT = – = – SS

• Or dOr dEE / d / dTT = + = + SS / / n n FF SS° / ° / n n FF – where we’ve presumed that neither where we’ve presumed that neither S nor S nor H H

will change much with moderate will change much with moderate T.T.– Since Since SS° = + 124 J/mol K for a car battery, it’s ° = + 124 J/mol K for a car battery, it’s

harder to start in winter. For 0°C, the 6 cell harder to start in winter. For 0°C, the 6 cell battery puts out 0.1V less than at 25°Cbattery puts out 0.1V less than at 25°C

Nernst Eqn: Potentials and Nernst Eqn: Potentials and ConcentrationsConcentrations

– Both Both GG° and ° and EE° refer to unit ° refer to unit (standard) concentrations.(standard) concentrations.

– But at But at equilibriumequilibrium, , GG = 0 and the cell = 0 and the cell potential potential EE = 0 as well = 0 as well (see no (see no °°))..

GG = = GG° + RT ln(Q)° + RT ln(Q) – – nneeFEFE = – = – nneeFEFE° + RT ln(Q)° + RT ln(Q)

EE = = EE° – ° – 2.3032.303 (RT/ (RT/nneeFF) ) loglog(Q)(Q)

• EE = = EE° – (59.1 mV/° – (59.1 mV/nnee) log(Q) ) log(Q) @ 25°C@ 25°C

K from K from EE°°

• Just as Just as GG = = GG° + R° + RT T ln(K) = 0 ln(K) = 0 implies implies GG° = – R° = – RT T ln(K),ln(K),

• – – nnee F EF E° = – R° = – RTT ln(K) implies ln(K) implies

•K = eK = e++nnee F EF E° / R° / RTT

• where, as before, where, as before, nnee = moles of electrons = moles of electrons involved in the overall reaction as written!involved in the overall reaction as written!

• Very large K can be calculated.Very large K can be calculated.

Confession TimeConfession Time

– On slide 9, I touted the HgOn slide 9, I touted the Hg22ClCl22/Hg /Hg couple as a convenient standard and couple as a convenient standard and drew its drew its EE° from the table.° from the table.

• But S.C.E. stands for But S.C.E. stands for “saturated”“saturated” calomel electrode and calomel electrode and E E = 0.241 = 0.241 not not EE° = 0.268 V ° = 0.268 V (with saturated Cl(with saturated Cl––)) . .– Since Q = [ClSince Q = [Cl––], by inverting Nernst, ], by inverting Nernst,

we find [Clwe find [Cl––]]sat’dsat’d = 2.86 = 2.86 MM. Cool.. Cool.

Potential from a Potential from a SINGLESINGLE ½ ½ Reaction?!?Reaction?!?

• Don’t we need an oxidation as well Don’t we need an oxidation as well as a reduction?as a reduction?

• YesYes, but they , but they cancan be the be the samesame reaction reaction (but for a reversal)!(but for a reversal)!

– ConcentrationsConcentrations mustmust differ between differ between the anode and cathode.the anode and cathode.• I.e., Q must less be than 1 so log(Q) is I.e., Q must less be than 1 so log(Q) is

negative; then although negative; then although EE°=0 still °=0 still E E >0.>0.• The cell brings Q to 1 at equilibrium by The cell brings Q to 1 at equilibrium by

equalizing concentrations in ½ cells.equalizing concentrations in ½ cells.

Ion-selective ElectrodesIon-selective Electrodes

• [Ag[Ag++] can be obtained by ] can be obtained by EE from from simple Ag wire referred to SCE.simple Ag wire referred to SCE.

• [H[H++]] is much more important! is much more important!– pH electrodes, enclosed in glass, swap pH electrodes, enclosed in glass, swap

HH++ for Na for Na++ at silicate surface. at silicate surface.– Potential difference thus induced is Potential difference thus induced is

calibrated for [Hcalibrated for [H++]]externalexternal..

– See your See your HarrisHarris § 15.4 for details. § 15.4 for details.

Assaulted with BatteriesAssaulted with Batteries

• ““Battery” refers to a Battery” refers to a seriesseries of of Galvanic cells whose Galvanic cells whose EE add. add.

• (Parallel hookup adds current, I, not (Parallel hookup adds current, I, not EE.).)

• Rechargeable NiCad reactions:Rechargeable NiCad reactions:Cd + 2 OHCd + 2 OH–– Cd(OH) Cd(OH)22 + 2e + 2e––

NiONiO22 + 2H + 2H22O + 2eO + 2e–– Ni(OH) Ni(OH)22 + 2 OH + 2 OH––

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

Better BatteriesBetter Batteries

• NiCad, though rechargeable, will NiCad, though rechargeable, will accept progressively smaller accept progressively smaller charges; charges; “battery memory.”“battery memory.”

• NiMH replaces anode rxn withNiMH replaces anode rxn with– MH + OHMH + OH–– M + H M + H22O + eO + e––

– with a with a muchmuch longer recharge life. longer recharge life.

– M might be MgM might be Mg22Ni with Ni with = 4.1 and = 4.1 and effective H effective H densitydensity twicetwice H H22(liquid)(liquid)

Best BatteryBest Battery

• OK, I’m prejudiced.OK, I’m prejudiced. EE°°

2 H2 H22 + 4 OH + 4 OH–– 4 H 4 H22O + 4 eO + 4 e–– +0.83V +0.83V

OO22 + 2 H + 2 H22O + 4 eO + 4 e–– 4 OH 4 OH–– +0.40V +0.40V

• Is nothing more than hydrogen Is nothing more than hydrogen combustion; no Greenhouse gas.combustion; no Greenhouse gas.

• Best example of “fuel cell” Best example of “fuel cell” – so called because Hso called because H22 and O and O22 are not built into the are not built into the

battery but battery but suppliedsupplied externally. externally.– Notice that [OHNotice that [OH––] is again unchanging.] is again unchanging.

CorrosionCorrosion

• A battery is electrochemistry A battery is electrochemistry happening where you want it.happening where you want it.

• CorrosionCorrosion is where you is where you don’tdon’t..– All M/MOAll M/MOxx couples at couples at E° E° < 0.4V are < 0.4V are

corroded corroded eveneven in caustic solutions: in caustic solutions:

– OO22 + 2 H + 2 H22O + 4 eO + 4 e–– 4 OH 4 OH–– EE° = 0.40° = 0.40

– OO22 + 4 H + 4 H++ + 4 e + 4 e–– 2 H 2 H22O O EE° = 1.23° = 1.23• So acid does even better. Q effect!So acid does even better. Q effect!

Metal CorrosionMetal Corrosion

• Metal oxides are lower density Metal oxides are lower density (higher (higher

volume)volume) than their metals. than their metals.– So oxide formation opens blossoms of So oxide formation opens blossoms of

corrosion and spreads. corrosion and spreads. – Salt spray is worst; it’s electrolytic!Salt spray is worst; it’s electrolytic!

– Some oxides (e.g., CrSome oxides (e.g., Cr22OO33) form ) form impervious oxide coats, slowing further impervious oxide coats, slowing further OO22 attack. attack.

Sacrificial AnodesSacrificial Anodes

• Structural metals like Fe are Structural metals like Fe are perfectly protected by more active perfectly protected by more active (lower (lower EE°) metals like Mg.°) metals like Mg.– If conductive contact is made, OIf conductive contact is made, O22 gets gets

reduced (to Hreduced (to H22O) O) onon Fe by e Fe by e–– released released fromfrom Mg instead. Mg instead.

– Replacing the active metal plate is Replacing the active metal plate is cheaper than a rusted ship!cheaper than a rusted ship!

Mg Mg2+ + 2e–

O2 + 2H2O + 4e– 4 OH–

Electromotive Force as a Electromotive Force as a “Chemical Reactant”“Chemical Reactant”

– If instead of doing work If instead of doing work withwith a a Galvanic cell potential, you Galvanic cell potential, you supplysupply a a reverse potential, you run the reaction reverse potential, you run the reaction in the in the nonnon-spontaneous direction! -spontaneous direction! Uphill. Uphill. EndoEndoergically.ergically.

• This is This is electrolysiselectrolysis, a synthesis., a synthesis.– You supply You supply EE not e not e––; the e; the e–– are taken are taken

from a cathode reaction, but from a cathode reaction, but anodeanode and and cathodecathode have have swaswappppeded..

Electrolysis CellElectrolysis Cell

• Electrolysis can Electrolysis can only proceed with only proceed with a potential more a potential more negative than –negative than –EE°.°.– Then the cell runs Then the cell runs

in reverse.in reverse.– External work External work

supplies needed supplies needed GG..

Zn

Zn2+ Cu2+

Zn + CuZn + Cu2+2+ Zn Zn2+2+ + Cu + Cu

SO42– SO4

2–

Cu

2e– 2e–+

Electrolytic StoichiometryElectrolytic Stoichiometry

• Charge ( current Charge ( current time = I time = I t t ) ) determines amount of product.determines amount of product.

• (Coulombs = Amperes (Coulombs = Amperes Seconds) Seconds)

– Electrons are the limiting reactant in Electrons are the limiting reactant in electrolysis.electrolysis.

– Moles electrons = Moles electrons = nnee = = QQ // FF = I = Itt // FF

– The usual stoichiometric ratios The usual stoichiometric ratios convert between convert between nnee and moles of and moles of product.product.

Concentration Concentration Electrolysis?Electrolysis?

• Does it make any sense to run a Does it make any sense to run a concentration cell concentration cell backwards?backwards?

• All you seem to do is to create a All you seem to do is to create a concentration differenceconcentration difference rather than rather than exploiting one that tends to uniformity.exploiting one that tends to uniformity.

– This is the way we This is the way we purify metalspurify metals!!• Force impure metals to be anodes.Force impure metals to be anodes.• They shed ions that are “plated” as pure They shed ions that are “plated” as pure

metal on the cathodes!metal on the cathodes!

Making Active MetalsMaking Active Metals

• You can’t “plate” You can’t “plate” NaNa, say, out of an , say, out of an aqueous solution!aqueous solution!

• It will simply redox react with HIt will simply redox react with H22O to O to make NaOH(aq).make NaOH(aq).

• We We electrolyzeelectrolyze active metals from active metals from their melts their melts (which conduct)(which conduct)..– 2 NaCl(2 NaCl(liqliq) ) 2 Na( 2 Na(liqliq) + Cl) + Cl22((gg))

– AlAl22OO33((liqliq) + 3C ) + 3C 2 Al( 2 Al(liqliq) + 3 CO) + 3 CO22((gg))• 5% of all U.S. electricity goes here!5% of all U.S. electricity goes here!

Recharging your CarRecharging your Car

• As the engine runs, a As the engine runs, a dynamodynamo (i.e., (i.e., reverse motorreverse motor) generates a voltage to ) generates a voltage to reverse battery drain from ignition.reverse battery drain from ignition.

• 2PbSO2PbSO44 + 2H + 2H22O O Pb + PbO Pb + PbO22 + 2H + 2H22SOSO44

• And it takes about 20 km of driving to And it takes about 20 km of driving to recharge after an average ignition.recharge after an average ignition.

– With many shorter trips, the battery will die, With many shorter trips, the battery will die, necessitating an external recharge whose necessitating an external recharge whose voltage will reduce Hvoltage will reduce H++ ion to H ion to H22 too. too.

– Sparks from disconnect may Sparks from disconnect may detonatedetonate H H22!!