Standard Reduction (Half-Cell) Potentials Cell EMF Standard Reduction (Half-Cell) Potentials Consider Zn(s)  Zn2+(aq) + 2e-. We measure Ecell relative to the SHE (cathode): Ecell = Ered(cathode) + Eox (anode) 0.76 V = 0 V + Eox(anode). Therefore, Eox(anode) = +0.76 V. Standard reduction potentials must be written as reduction reactions: Zn2+(aq) + 2e-  Zn(s), Ered = -0.76 V.

2Zn2+(aq) + 4e-  2Zn(s), Ered = -0.76 V. Since Ered = -0.76 V we conclude that the reduction of Zn2+ in the presence of the SHE is not spontaneous. The oxidation of Zn with the SHE is spontaneous. Changing the stoichiometric coefficient does not affect Ered. Therefore, 2Zn2+(aq) + 4e-  2Zn(s), Ered = -0.76 V. Reactions with Ered > 0 are spontaneous reductions relative to the SHE.

Reactions with Ered < 0 are spontaneous oxidations relative to the SHE. The larger the difference between Ered values, the larger Ecell. In a voltaic (galvanic) cell (spontaneous) Ered(cathode) is more positive than Ered(anode). Recall

Examples – Balance the following equations, and calculate E°cell for each: Cr3+ + Cl2 (g)  Cr2O72- + Cl- Cu2+ + Mg (s)  Mg2+ + Cu (s) IO3- + Fe2+  Fe3+ + I2 Zn (s) + Ag+  Zn2+ + Ag

Oxidizing and Reducing Agents The more positive Ered the stronger the oxidizing agent on the left. The more negative Ered the stronger the reducing agent on the right. A species on the higher to the left of the table of standard reduction potentials will spontaneously oxidize a species that is lower to the right in the table. That is, F2 will oxidize H2 or Li; Ni2+ will oxidize Al(s).

Spontaneity of Redox Reactions In a voltaic (galvanic) cell (spontaneous) Ered(cathode) is more positive than Ered(anode) since Or More generally, for any electrochemical process A positive E indicates a spontaneous process (galvanic cell). A negative E indicates a nonspontaneous process.

Examples – Sketch the cells containing the following reactions Examples – Sketch the cells containing the following reactions. Include E°cell, the direction of electron flow, direction of ion migration through salt bridge, and identify the anode and cathode: Cr3+ + Cl2 (g)  Cr2O72- + Cl- Cu2+ + Mg (s)  Mg2+ + Cu (s) IO3- + Fe2+  Fe3+ + I2

EMF and Free-Energy Change We can show that G is the change in free-energy, n is the number of moles of electrons transferred, F is Faraday’s constant, and E is the emf of the cell. We define Since n and F are positive, if G > 0 then E < 0.

Examples – Balance, and calculate E°cell and ΔG° for each reaction: Mg (s) + Au3+  Mg2+ + Au (s) Al (s) + Ag+  Al3+ + Ag (s) Cu2+ + Na (s)  Cu (s) + Na+

Cell EMF and Chemical Equilibrium A system is at equilibrium when G = 0. From the Nernst equation, at equilibrium and 298 K (E = 0 V and Q = Keq):

Batteries A battery is a self-contained electrochemical power source with one or more voltaic cell. When the cells are connected in series, greater emfs can be achieved.

Cathode: PbO2 on a metal grid in sulfuric acid: Lead-Acid Battery A 12 V car battery consists of 6 cathode/anode pairs each producing 2 V. Cathode: PbO2 on a metal grid in sulfuric acid: PbO2(s) + SO42-(aq) + 4H+(aq) + 2e-  PbSO4(s) + 2H2O(l) Anode: Pb: Pb(s) + SO42-(aq)  PbSO4(s) + 2e-

The overall electrochemical reaction is PbO2(s) + Pb(s) + 2SO42-(aq) + 4H+(aq)  2PbSO4(s) + 2H2O(l) for which Ecell = Ered(cathode) + Eox (anode) = (+1.685 V) + (0.356 V) = +2.041 V. Wood or glass-fiber spacers are used to prevent the electrodes from touching.

2NH4+(aq) + 2MnO2(s) + 2e-  Mn2O3(s) + 2NH3(aq) + 2H2O(l) Alkaline Battery Anode: Zn cap: Zn(s)  Zn2+(aq) + 2e- Cathode: MnO2, NH4Cl and C paste: 2NH4+(aq) + 2MnO2(s) + 2e-  Mn2O3(s) + 2NH3(aq) + 2H2O(l) The graphite rod in the center is an inert cathode. For an alkaline battery, NH4Cl is replaced with KOH.

Anode: Zn powder mixed in a gel: Zn(s)  Zn2+(aq) + 2e- Cathode: reduction of MnO2.

Direct production of electricity from fuels occurs in a fuel cell. Fuel Cells Direct production of electricity from fuels occurs in a fuel cell. On Apollo moon flights, the H2-O2 fuel cell was the primary source of electricity. Cathode: reduction of oxygen: 2H2O(l) + O2(g) + 4e-  4OH-(aq) Anode: 2H2(g) + 4OH-(aq)  4H2O(l) + 4e-