Electrochemistry
Electrochemistry tests the quantitative link between cell potential, free energy, conductance and practical cells. Numericals on the Nernst equation and molar conductivity are standard.
Nernst equation and thermodynamics
For aA + bB → cC + dD, E_cell = E°_cell − (0.0591/n) log Q at 298 K, where Q = [C]^c[D]^d/[A]^a[B]^b. ΔG = −nFE and ΔG° = −nFE°. A positive E_cell means a spontaneous cell reaction. Concentration cells have E° = 0 and a potential from the concentration ratio only.
Conductance
Conductivity κ is the conductance of a 1 cm cube; molar conductivity Λm = 1000κ/M, with κ in S cm−1 and M in mol L−1, giving S cm2 mol−1. For weak electrolytes Λm rises steeply on dilution; α = Λm/Λ°m. Kohlrausch's law of independent migration gives Λ°m for weak electrolytes from strong-electrolyte data.
Electrolysis and batteries
Faraday's first law: mass deposited ∝ charge, m = ZIt; one mole of electrons is 96500 C. In electrolysis, oxidation occurs at the anode and reduction at the cathode regardless of cell type. Primary cells (dry cell, alkaline cell) are not rechargeable; lead-acid and Li-ion are secondary. In rusting, iron is the anode and oxygen reduction at cathodic sites completes the electrochemical cell.
Worked example
For Zn|Zn2+(0.10 M)||Cu2+(0.010 M)|Cu with E° = 1.10 V: Q = [Zn2+]/[Cu2+] = 0.10/0.010 = 10. E = 1.10 − (0.0591/2) log 10 = 1.10 − 0.0296 = 1.07 V. Write the cell reaction first so Q is oriented products over reactants.
Mark-losing traps
Reversing Q, using n = 1 for a two-electron cell, applying 0.0591 at temperatures other than 298 K, and confusing conductivity with molar conductivity cost marks. Remember that a salt bridge maintains electrical neutrality, not electron flow.