JEE Chemistry Electrochemistry Notes Set 05

Electrochemical Cells

A galvanic (voltaic) cell converts the chemical energy of a spontaneous redox reaction into electrical energy; an electrolytic cell uses electrical energy to drive a non-spontaneous reaction. In both, oxidation takes place at the anode and reduction at the cathode. In a galvanic cell the anode is negative and the cathode positive; in an electrolytic cell the anode is positive and the cathode negative.
In the Daniell cell, zinc in ZnSO₄ solution is the anode and copper in CuSO₄ solution is the cathode. Electrons flow through the wire from zinc to copper. The salt bridge (a gel containing KNO₃ or KCl, chosen because the ions have nearly equal mobilities) completes the circuit by letting ions migrate and keeps each half cell electrically neutral.
Cell notation: anode on the left, cathode on the right, a single line for a phase boundary and a double line for the salt bridge, for example Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s).

Electrode Potential and the Electrochemical Series

Each half cell has a tendency to gain electrons, measured by its reduction potential relative to the standard hydrogen electrode (SHE, taken as 0.00 V; Pt, H₂ at 1 atm in 1 M H⁺). The standard electrode potential E° is measured with all species at 1 M (or 1 atm) and 298 K.
Arranged in order of E°, the metals form the electrochemical series. A species with a higher E° is a stronger oxidising agent; one with a lower E° is a stronger reducing agent. A metal displaces from solution any metal with a higher E°, and metals with negative E° liberate hydrogen from dilute acids.
The cell EMF is \( E^\circ_{cell}=E^\circ_{cathode}-E^\circ_{anode} \) (both as reduction potentials). E° is an intensive property, so it does not change if the half reaction is multiplied by a coefficient; it is not additive when electron numbers differ (add ΔG° instead).

Nernst Equation and Thermodynamics of Cells

For the reaction aA + bB → cC + dD with n electrons transferred, at 298 K: \( E=E^\circ-\frac{0.0591}{n}\log Q \), where Q is the reaction quotient. For an electrode Mⁿ⁺ + ne⁻ → M, \( E=E^\circ+\frac{0.0591}{n}\log[M^{n+}] \).
Links with thermodynamics: \( \Delta G^\circ=-nFE^\circ,\quad \Delta G=-nFE,\quad \log K=\frac{nE^\circ}{0.0591} \), with F = 96500 C mol⁻¹. At equilibrium E = 0 and Q = K. A spontaneous cell has E > 0 and ΔG < 0.
A concentration cell has identical electrodes with different concentrations, so E° = 0 and \( E=\frac{0.0591}{n}\log\frac{C_{cathode}}{C_{anode}} \); the half cell with the more dilute solution is the anode.
Combining half reactions with different numbers of electrons: E° = (n₁E₁° ± n₂E₂°)/n (add the ΔG° values), as in the Fe³⁺/Fe²⁺ and Cu⁺/Cu examples.

Worked Example 1. Find E° and K for Zn + Cu²⁺ → Zn²⁺ + Cu, given E°(Zn²⁺/Zn) = −0.76 V and E°(Cu²⁺/Cu) = +0.34 V.
Answer:
E° = 0.34 − (−0.76) = 1.10 V.
log K = 2 × 1.10/0.0591 = 37.2, so K ≈ 1.6 × 10³⁷ and ΔG° = −2 × 96500 × 1.10 = −212.3 kJ.

Electrolysis and Faraday's Laws

Products of electrolysis depend on the electrolyte, the electrodes and the concentration. At the cathode, the species with the higher reduction potential is discharged first; at the anode, the species that is more easily oxidised is discharged first. Examples: molten NaCl gives Na and Cl₂; aqueous NaCl with inert electrodes gives H₂ at the cathode, Cl₂ at the anode and NaOH in solution; aqueous CuSO₄ with Pt electrodes gives Cu and O₂; with copper electrodes copper dissolves from the anode and deposits on the cathode (purification of copper); dilute H₂SO₄ gives H₂ and O₂ in the ratio 2 : 1 by volume.
Faraday's first law: the mass deposited is proportional to the charge passed, \( m=ZQ=ZIt \), where the electrochemical equivalent Z = E/96500 and E is the equivalent mass. Second law: for the same charge, the masses of different substances deposited are proportional to their equivalent masses.
One faraday (96500 C) is the charge of one mole of electrons and deposits one gram equivalent of any substance. Moles of metal deposited = \( \frac{It}{nF} \).

Conductance of Electrolytic Solutions

Resistance R and conductance G = 1/R (siemens). Resistivity ρ and conductivity κ = 1/ρ are related by \( \kappa=G\times\frac{l}{A}=G\times G^* \), where l/A is the cell constant (cm⁻¹), found by measuring the conductance of a standard KCl solution.
Molar conductivity: \( \Lambda_m=\frac{1000\,\kappa}{C} \) (κ in S cm⁻¹, C in mol L⁻¹, Λm in S cm² mol⁻¹). Equivalent conductivity uses normality instead of molarity.
Conductivity κ falls on dilution (fewer ions per unit volume) while molar conductivity Λm rises on dilution. For a strong electrolyte Λm varies linearly with √C (Debye-Hückel-Onsager equation, \( \Lambda_m=\Lambda_m^\circ-A\sqrt C \)). For a weak electrolyte Λm rises steeply at low concentration because the degree of ionisation increases, and \( \alpha=\frac{\Lambda_m}{\Lambda_m^\circ} \).
Kohlrausch's law of independent migration: at infinite dilution each ion contributes a definite amount, \( \Lambda_m^\circ=\nu_+\lambda_+^\circ+\nu_-\lambda_-^\circ \). It is used to find Λ° of weak electrolytes, for instance Λ°(CH₃COOH) = Λ°(CH₃COONa) + Λ°(HCl) − Λ°(NaCl), and to calculate solubility and degree of dissociation. Electrolytic conductance falls with decreasing temperature and rises with temperature, unlike metallic conductance.

Batteries, Fuel Cells and Corrosion

A primary cell cannot be recharged (dry cell: Zn anode, graphite cathode with MnO₂ and NH₄Cl paste; mercury cell, with a steady 1.35 V). A secondary cell can be recharged. The lead-acid storage battery has a Pb anode and a PbO₂ cathode in about 38% H₂SO₄. Discharge: Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O, so the acid is used up and its density falls. Charging reverses the reaction. The nickel-cadmium cell is another rechargeable cell.
A fuel cell converts the energy of combustion of a fuel directly into electricity. In the H₂–O₂ fuel cell, the anode reaction is H₂ + 2OH⁻ → 2H₂O + 2e⁻ and the cathode reaction is O₂ + 2H₂O + 4e⁻ → 4OH⁻; the net reaction is 2H₂ + O₂ → 2H₂O. It is efficient (about 70%) and pollution free.
Corrosion is an electrochemical process. At one spot of the iron surface, Fe → Fe²⁺ + 2e⁻ (anode); at another spot O₂ + 4H⁺ + 4e⁻ → 2H₂O (cathode). Fe²⁺ is further oxidised to hydrated Fe₂O₃, rust. Prevention: paint, galvanising (zinc coating), sacrificial anodes of Mg or Zn, and alloying.