Electrochemistry

2.1 Core concepts

• An electrochemical cell has two electrodes dipped in electrolyte(s); a galvanic/voltaic cell converts the chemical energy of a spontaneous redox reaction into electrical energy while an electrolytic cell uses electrical energy to drive a non-spontaneous reaction (NCERT §2.1, p. 32).
• The Daniell cell (Zn|ZnSO4 || CuSO4|Cu) is built on Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s) and delivers 1.1 V when [Zn2+] = [Cu2+] = 1 mol dm−3; if an opposing external voltage of exactly 1.1 V is applied the current is zero, below 1.1 V it works as a galvanic cell, above 1.1 V it functions as an electrolytic cell with reversed reaction (NCERT §2.1, Fig. 2.2, p. 32).
• A galvanic cell is built from two half-cells (redox couples); each half-cell has a metal electrode in its electrolyte and the two electrolytes are linked internally by a salt bridge and externally by a wire and voltmeter (NCERT §2.2, p. 33).
• IUPAC convention: anode on the left, cathode on the right, single vertical bar between metal and electrolyte, double vertical bar for the salt bridge; Ecell = Eright − Eleft and is positive for a spontaneous cell (NCERT §2.2, p. 34).
• The potential of a single electrode cannot be measured; the standard hydrogen electrode (SHE), Pt(s)|H2(g, 1 bar)|H+(aq, 1 M), is assigned zero potential at all temperatures and serves as the reference (NCERT §2.2.1, p. 34, Fig. 2.3).
• IUPAC standard electrode potentials are reduction potentials measured at unit activity; a positive E° indicates the species is reduced more easily than H+, a negative E° indicates the reverse — so F2/F− (+2.87 V) is the strongest oxidising agent and Li+/Li (−3.05 V) places Li as the strongest reducing agent in aqueous solution (NCERT §2.2.1, Table 2.1, p. 37).
• Nernst equation for a half-cell Mn+ + ne− → M is E = E° − (RT/nF) ln(1/[Mn+]); for a general cell aA + bB → cC + dD, Ecell = E°cell − (RT/nF) ln Q, which at 298 K becomes Ecell = E°cell − (0.059/n) log Q (NCERT §2.3, eqns 2.8–2.13, pp. 36–38).
• At equilibrium Ecell = 0 and Q = Kc, giving E°cell = (0.059/n) log Kc at 298 K; for the Daniell cell E°cell = 1.1 V yields log Kc = 37.288, Kc ≈ 2 × 1037 (NCERT §2.3.1, p. 39).
• The Gibbs energy change of a cell reaction is ΔrG = −nFEcell and at standard state ΔrG° = −nFE°cell; ΔrG° is extensive (depends on n), Ecell is intensive (NCERT §2.3.2, eqns 2.15–2.16, p. 40).
• Resistance R = ρ(l/A); the reciprocal ρ−1 is conductivity κ (S m−1), measured in S m−1 or S cm−1 (1 S cm−1 = 100 S m−1); conductivity of metals depends on the metal and decreases with temperature, whereas electrolytic (ionic) conductance depends on the electrolyte, ion size and solvation, solvent viscosity, concentration and increases with temperature (NCERT §2.4, eqns 2.17–2.18, pp. 41–43).
• Cell constant G* = l/A is determined by measuring R for a KCl solution of known κ; conductivity of an unknown solution is then κ = G*/R; resistance is measured on a Wheatstone bridge with an AC source to avoid electrolysis (NCERT §2.4.1, eqns 2.18–2.20, pp. 43–44, Fig. 2.5).
• Molar conductivity Λm = κ/c (S m2 mol−1 if c is in mol m−3); 1 S m2 mol−1 = 104 S cm2 mol−1 (NCERT §2.4.1, eqn 2.21, pp. 44–45).
• Conductivity κ always decreases on dilution; molar conductivity Λm always increases on dilution; for a strong electrolyte Λm rises slowly per Λm = Λ°m − Ac1/2, while for a weak electrolyte Λm rises steeply near infinite dilution as α increases (NCERT §2.4.2, eqn 2.23, Fig. 2.6, pp. 46–47).
• Kohlrausch's law of independent migration of ions: Λ°m = ν+λ°+ + ν−λ°−; this lets us compute Λ°m for weak electrolytes (e.g. Λ°m(HAc) = Λ°m(HCl) + Λ°m(NaAc) − Λ°m(NaCl)) and from there α = Λm/Λ°m and Ka = cα2/(1 − α) (NCERT §2.4.2, eqns 2.24–2.27, pp. 49–50).
• In an electrolytic cell the cation discharging at the cathode and the species oxidised at the anode are decided by E° values (modified by overpotentials and Nernst effects); e.g. molten NaCl gives Na and Cl2 whereas aqueous NaCl gives H2 (at cathode, from H+/H2O) and Cl2 (at anode, due to O2 overpotential) (NCERT §2.5/2.5.1, eqns 2.28–2.39, pp. 51–54).
• Faraday's first law: amount of substance produced at an electrode ∝ quantity of electricity passed (Q = It); second law: amounts of different substances produced by the same Q are in the ratio of their chemical equivalent weights; one Faraday F = NA·e = 96487 C mol−1 (≈ 96500 C mol−1) is the charge per mole of electrons (NCERT §2.5, pp. 51–52).
• Primary batteries (one-shot): Leclanche dry cell uses Zn anode, MnO2 + C cathode, NH4Cl + ZnCl2 paste electrolyte, ~1.5 V; mercury cell uses Zn–Hg amalgam anode, HgO + C cathode, KOH/ZnO paste, ~1.35 V constant during life (NCERT §2.6.1, pp. 54–55).
• Secondary batteries (rechargeable): lead storage cell (Pb anode, PbO2-on-Pb-grid cathode, 38% H2SO4 electrolyte; discharge: Pb + PbO2 + 2H2SO4 → 2PbSO4 + 2H2O); Ni–Cd cell (longer life but more expensive; discharge: Cd + 2Ni(OH)3 → CdO + 2Ni(OH)2 + H2O) (NCERT §2.6.2, pp. 55–56).
• A fuel cell converts the combustion energy of a fuel (H2, CH4, CH3OH, etc.) directly into electricity; the H2–O2 cell used in the Apollo programme has porous carbon electrodes (Pt/Pd catalysts) in conc. NaOH, with cathode O2 + 2H2O + 4e− → 4OH− and anode 2H2 + 4OH− → 4H2O + 4e−, giving 2H2 + O2 → 2H2O at ~70% efficiency, pollution-free (NCERT §2.7, p. 56).
• Corrosion of iron (rusting) is an electrochemical phenomenon: at the anodic spot Fe → Fe2+ + 2e− (E° = −0.44 V) and at the cathodic spot O2 + 4H+ + 4e− → 2H2O (E° = 1.23 V), overall E°cell = 1.67 V; Fe2+ is further oxidised by atmospheric O2 to hydrated Fe2O3·xH2O (rust); prevention: painting/coating, electroplating with Sn or Zn, or using a sacrificial electrode of Mg/Zn (NCERT §2.8, Fig. 2.13, p. 57).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 2.1 (p. 32): Daniell cell — Zn rod in ZnSO4, Cu rod in CuSO4, salt bridge linking the two beakers, voltmeter showing 1.1 V.
• Fig. 2.2 (p. 32): three modes when an external Eext is applied to a Daniell cell — Eext < 1.1 V (galvanic, current flows Cu→Zn outside), Eext = 1.1 V (no current, no reaction), Eext > 1.1 V (electrolytic, reaction reversed).
• Fig. 2.3 (p. 34): SHE — Pt black electrode in 1 M HCl with H2 at 1 bar bubbled over it; reference half-cell with E° = 0.
• Table 2.1 (p. 37): standard electrode potentials at 298 K from F2/F− (+2.87 V) down to Li+/Li (−3.05 V); oxidising power decreases and reducing power increases top to bottom.
• Fig. 2.5 (p. 44): Wheatstone-bridge setup for measuring resistance of an electrolytic solution with an AC oscillator and detector.
• Fig. 2.6 (p. 47): Λm vs c1/2 — straight line for KCl (strong electrolyte) with intercept Λ°m, steep rise near zero concentration for acetic acid (weak electrolyte).
• Fig. 2.8 (p. 54): commercial Leclanche dry cell — Zn container (anode), central graphite rod (cathode) packed in MnO2 + C, with moist NH4Cl + ZnCl2 paste.
• Fig. 2.9 (p. 55): mercury cell with Zn–Hg amalgam anode and HgO + C cathode in KOH/ZnO paste.
• Fig. 2.10 (p. 55): lead storage battery — alternating Pb plates and PbO2-on-Pb grids immersed in 38% H2SO4.
• Fig. 2.12 (p. 56): H2–O2 fuel cell with porous carbon electrodes in concentrated NaOH, H2 fed to anode and O2 to cathode.
• Fig. 2.13 (p. 57): corrosion of iron — anodic and cathodic spots on the same iron surface, water film acting as the electrolyte, with the overall rust formation reaction.

2.4 Common confusions / NTA trap points

• Sign of Ecell vs ΔrG: spontaneous cell has Ecell > 0 AND ΔrG < 0 (because ΔrG = −nFEcell). NTA loves to flip the sign convention or quote "negative emf ⇒ spontaneous".
• Standard electrode potentials in Table 2.1 are reduction potentials. For an oxidation half-reaction the sign is reversed — but Ecell is still computed as E°cathode − E°anode using reduction potentials of both, never adding oxidation and reduction potentials.
• Daniell cell at Eext = 1.1 V gives I = 0 (no current and no reaction); only when Eext > 1.1 V does the cell run as an electrolytic cell with reversed reaction.
• Conductivity κ decreases on dilution but molar conductivity Λm increases on dilution — students often invert the two.
• For a weak electrolyte Λ°m cannot be obtained by extrapolating Λm vs c1/2 (the curve is too steep near zero); it must be calculated from Kohlrausch's law using strong-electrolyte data.
• In aqueous NaCl electrolysis the anode product is Cl2 (not O2) despite O2 having a lower E° — because of the overpotential of oxygen. A favourite distractor.
• The Faraday constant 96487 C mol−1 is the charge per mole of electrons, not per mole of any ion; for Al3+ → Al you need 3F per mole of Al, for Cu2+ → Cu you need 2F.