Zumdahl’s Chapter 17

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

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 • 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

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

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° • 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.

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 • 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.

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 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

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 • 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 • 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° • 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 • 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° • 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 • 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 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 • [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 • “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 • 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 • 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 • 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 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 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” • 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 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 • 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? • 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 • 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 • 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!

Zumdahl’s Chapter 17