Class 12 Chemistry · Chapter 2 NotesElectrochemistry

An electrochemical cell has two metallic electrodes dipping in electrolytic solutions. A galvanic cell converts the chemical energy of a spontaneous redox reaction into electrical energy. In the Daniell cell, zinc dissolves at the anode and copper deposits at the cathode, giving a cell potential of 1.1 V when both ion concentrations are 1 mol dm⁻³. If an external opposing voltage greater than 1.1 V is applied, the reaction reverses and the cell works as an electrolytic cell. Each half-cell develops an electrode potential at the metal–solution interface. The standard hydrogen electrode is assigned zero potential, and standard electrode potentials of other half-cells are measured against it. The cell potential is E(cell) = E(right) − E(left), where the right electrode is the cathode and the left is the anode.

• Galvanic cellspontaneous redox reaction produces electricity
• Electrolytic cellelectrical energy drives a non-spontaneous reaction
• Standard electrode potential of SHE is 0.00 V at all temperatures
• E°(cell) = E°(cathode) − E°(anode)
• ExampleE°(cell) for Daniell cell = 0.34 V − (−0.76 V) = 1.10 V

The electrical work done by a galvanic cell equals the decrease in Gibbs energy of the cell reaction. For n electrons transferred and cell potential E(cell), the relation is ΔrG = −nFE(cell). When all species are in their standard states, ΔrG° = −nFE°(cell). A positive cell potential means a negative Gibbs energy change, so the reaction is spontaneous. The standard Gibbs energy is also related to the equilibrium constant by ΔrG° = −RT ln K. Combining these gives E°(cell) = (2.303RT/nF) log K, which at 298 K becomes E°(cell) = (0.059 V/n) log K. This allows equilibrium constants to be calculated from standard cell potentials.

• ΔrG = −nFE(cell)
• ΔrG° = −nFE°(cell)
• ΔrG° = −RT ln K
• At 298 KE°(cell) = (0.059 V/n) log K

The Nernst equation gives the electrode or cell potential when concentrations are not unity. For the electrode reaction Mⁿ⁺(aq) + ne⁻ → M(s), the electrode potential is E = E° − (RT/nF) ln (1/[Mⁿ⁺]). For a general cell reaction aA + bB → cC + dD with n electrons, E(cell) = E°(cell) − (RT/nF) ln Q, where Q = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ. At 298 K, the equation simplifies to E(cell) = E°(cell) − (0.059 V/n) log Q. For the Daniell cell, E(cell) = E°(cell) − (0.059 V/2) log ([Zn²⁺]/[Cu²⁺]). The cell potential increases when the concentration of the cathode ion increases or the anode ion decreases.

• Nernst equation for electrodeE = E° − (RT/nF) ln (1/[Mⁿ⁺])
• Nernst equation for cellE(cell) = E°(cell) − (0.059 V/n) log Q at 298 K
• For Daniell cellE(cell) = E°(cell) − (0.059 V/2) log ([Zn²⁺]/[Cu²⁺])

The resistance R of a conductor is proportional to its length l and inversely proportional to its area of cross-section A: R = ρl/A, where ρ is resistivity. Conductance G is the inverse of resistance, G = 1/R = κA/l, where κ is conductivity. The cell constant G* = l/A is determined using a KCl solution of known conductivity. Conductivity is the conductance of a solution of unit length and unit area of cross-section. Molar conductivity Λm is defined as Λm = κ/c, where c is the concentration in mol m⁻³. Conductivity decreases with dilution because the number of ions per unit volume decreases. Molar conductivity increases with dilution because the total volume containing one mole of electrolyte increases. For strong electrolytes, Λm = Λ°m − A√c; for weak electrolytes, Λm increases steeply near infinite dilution.

• R = ρl/A, G = 1/R, κ = 1/ρ
• Cell constant G* = l/A = κ × R
• Molar conductivity Λm = κ/c
• Λm = Λ°m − A√c for strong electrolytes
• Kohlrausch lawΛ°m = ν₊λ°₊ + ν₋λ°₋

In an electrolytic cell, electrical energy drives a non-spontaneous reaction. Faraday's first law states that the amount of chemical reaction at an electrode is proportional to the quantity of electricity passed. The second law states that the amounts of different substances liberated by the same quantity of electricity are proportional to their chemical equivalent weights. The quantity of electricity Q = It, where I is current in amperes and t is time in seconds. One mole of electrons carries a charge of 96487 C, called one Faraday (F). The mass of substance deposited can be calculated using the stoichiometry of the electrode reaction. For example, Cu²⁺ + 2e⁻ → Cu requires 2F to deposit 1 mol of copper. The products of electrolysis depend on the electrode material and the relative standard electrode potentials, and overpotential can affect which reaction occurs.

• Faraday's first lawamount of reaction ∝ quantity of electricity
• Faraday's second lawamounts ∝ chemical equivalent weights
• Q = It; 1F = 96487 C mol⁻¹
• Mass deposited = (molar mass × Q) / (nF)

Batteries are galvanic cells used as practical sources of electrical energy. Primary batteries, such as the dry cell and mercury cell, cannot be recharged. The dry cell has a zinc anode, a carbon cathode surrounded by MnO₂ and carbon, and a moist paste of NH₄Cl and ZnCl₂; its potential is about 1.5 V. The mercury cell uses zinc–mercury amalgam as anode and HgO as cathode with KOH paste, giving about 1.35 V. Secondary batteries can be recharged, such as the lead storage battery (lead anode, PbO₂ cathode, 38% H₂SO₄ electrolyte) and the nickel–cadmium cell. Fuel cells convert the energy of combustion of fuels directly into electricity; the hydrogen–oxygen fuel cell produces water and has an efficiency of about 70%.

• Primary batteriesdry cell (≈1.5 V), mercury cell (≈1.35 V)
• Secondary batterieslead storage battery, nickel–cadmium cell
• Fuel cellH₂ and O₂ react to form water, efficiency about 70%

Corrosion is an electrochemical process in which a metal is oxidised by loss of electrons. Rusting of iron occurs in the presence of water and air. At an anodic spot, iron is oxidised: Fe → Fe²⁺ + 2e⁻. The electrons travel through the metal to a cathodic spot where oxygen is reduced in the presence of H⁺: O₂ + 4H⁺ + 4e⁻ → 2H₂O. The overall reaction is 2Fe + O₂ + 4H⁺ → 2Fe²⁺ + 2H₂O with E°(cell) = 1.67 V. Ferrous ions are further oxidised to hydrated ferric oxide, Fe₂O₃·xH₂O, which is rust. Corrosion can be prevented by coating the surface with paint or chemicals, by covering with a more inert metal such as Sn or Zn, or by using a sacrificial electrode of a more active metal like Mg or Zn.

• AnodeFe → Fe²⁺ + 2e⁻
• CathodeO₂ + 4H⁺ + 4e⁻ → 2H₂O
• Overall2Fe + O₂ + 4H⁺ → 2Fe²⁺ + 2H₂O, E°(cell) = 1.67 V
• Preventionpainting, coating with Sn/Zn, sacrificial electrode