Chapter 2: Electrochemistry | Summary

A galvanic cell converts the Gibbs energy of a spontaneous redox reaction into electrical work. Each galvanic cell consists of two half-cells (redox couples). The half-cell where oxidation occurs is the anode (negative electrode) and the half-cell where reduction occurs is the cathode (positive electrode). The two half-cells are connected internally by a salt bridge.

Electrode potential arises due to the tendency of metal ions to deposit on the electrode and metal atoms to dissolve into solution. When concentrations of all species are unity, the potential is the standard electrode potential (E°). According to IUPAC convention, standard reduction potentials are referred to as standard electrode potentials. The Standard Hydrogen Electrode (SHE) is assigned zero potential at all temperatures. The cell EMF is given by E°cell = E°right − E°left.

The Nernst equation describes the dependence of electrode and cell potential on concentration. For the general electrode reaction Mn+(aq) + ne− → M(s), the electrode potential is E = E° − (RT/nF) ln(1/[Mn+]). For a cell reaction aA + bB → cC + dD, the cell potential is E(cell) = E°(cell) − (RT/nF) ln Q, where Q is the reaction quotient.

At 298 K, the Nernst equation simplifies to E(cell) = E°(cell) − (0.059/n) log Q. At equilibrium, E(cell) = 0 and the Nernst equation gives the relationship E°(cell) = (0.059/n) log Kc, allowing calculation of equilibrium constants from standard electrode potentials. This is extremely useful for reactions difficult to study by direct methods.

The reversible work done by a galvanic cell equals the decrease in its Gibbs energy. The relationship is ΔrG = −nFE(cell), where n is the number of moles of electrons transferred and F is the Faraday constant (96487 C mol−1). Under standard conditions, ΔrG° = −nFE°(cell).

Since ΔrG° = −RT ln K, all three quantities — standard cell potential, standard Gibbs energy, and equilibrium constant — are interrelated. Measurement of E°(cell) thus provides an important thermodynamic route to ΔrG° and Kc for the reaction occurring in the cell.

Electrical resistance R is measured in ohms (Ω) and is proportional to length l and inversely proportional to cross-sectional area A: R = ρ(l/A). The constant ρ is called resistivity (SI unit: Ω m). The inverse of resistance is conductance G (SI unit: siemens, S). The inverse of resistivity is conductivity κ (SI unit: S m−1). The cell constant G* = l/A is used to calculate conductivity as κ = G*/R.

Molar conductivity Λm = κ/c relates conductivity to concentration. It increases with dilution because the total volume containing one mole of electrolyte increases. For strong electrolytes, the Debye-Hückel-Onsager equation gives Λm = Λ°m − A√c. For weak electrolytes, Λm increases steeply at very low concentrations and Λ°m cannot be obtained by extrapolation but must be calculated using Kohlrausch's law.

Kohlrausch's law of independent migration of ions states that the limiting molar conductivity of an electrolyte is the sum of the individual contributions of its cation and anion: Λ°m = ν+λ°+ + ν−λ°−. This law was derived from the observation that the difference in Λ°m between electrolytes sharing one common ion is nearly constant.

Applications of Kohlrausch's law include: calculation of Λ°m for any electrolyte from tabulated ionic conductivities, determination of Λ°m for weak electrolytes (like acetic acid) which cannot be obtained by extrapolation, and calculation of the degree of dissociation α = Λm/Λ°m and dissociation constant Ka of weak electrolytes at any concentration c.

An electrolytic cell uses an external voltage to drive non-spontaneous chemical reactions. The products of electrolysis depend on the nature of the electrolyte, type of electrodes (inert or reactive), and the standard electrode potentials of competing electrode reactions. Overpotential can also influence which reaction occurs preferentially.

Faraday's first law states that the amount of chemical reaction at an electrode is proportional to the quantity of electricity passed (Q = It). Faraday's second law states that amounts of different substances liberated by the same charge are proportional to their equivalent weights. One Faraday (F ≈ 96500 C mol−1) deposits one mole of a univalent ion. Metals like Na, Mg, and Al are industrially produced by electrolysis of their molten salts or oxides.

Primary batteries are non-rechargeable. The dry cell (Leclanche cell) uses a zinc anode, carbon-graphite cathode, MnO2 and NH4Cl/ZnCl2 paste, producing about 1.5 V. The mercury cell uses a zinc-mercury amalgam anode, HgO cathode and KOH/ZnO electrolyte, producing a constant 1.35 V — suitable for hearing aids and watches.

Secondary batteries can be recharged by reversing the current. The lead storage battery (used in automobiles) operates on the reaction Pb + PbO2 + 2H2SO4 → 2PbSO4 + 2H2O during discharge; charging reverses this. The nickel-cadmium cell has a longer life but is more expensive. Both are examples of secondary cells where the electrode reactions are reversible.

Fuel cells are galvanic cells designed to convert the chemical energy of combustion of fuels (hydrogen, methane, methanol, etc.) directly into electrical energy. They are more efficient (about 70%) compared to thermal plants (about 40%). The hydrogen-oxygen fuel cell, used in the Apollo space programme, produces water as the only product.

In the H2-O2 fuel cell, hydrogen is bubbled at the anode (2H2 + 4OH− → 4H2O + 4e−) and oxygen at the cathode (O2 + 2H2O + 4e− → 4OH−), both through porous carbon electrodes in concentrated NaOH. Catalysts like finely divided platinum or palladium are used. Fuel cells are pollution-free and represent the basis of the Hydrogen Economy.

Corrosion is the oxidation of metals by loss of electrons to oxygen, forming oxides or other salts. Iron rusting is an electrochemical process: anodic spots oxidise Fe to Fe2+ (E° = −0.44 V) while cathodic spots reduce O2 in the presence of H+ (E° = +1.23 V), giving E°cell = 1.67 V. The Fe2+ ions are further oxidised to Fe3+ which forms hydrated ferric oxide (rust).

Prevention methods include covering metal surfaces with paint, chemicals like bisphenol, coating with less reactive metals (Sn, Zn), or using a sacrificial electrode of a more reactive metal (Mg, Zn) that corrodes preferentially. Corrosion causes enormous economic damage to infrastructure, and its prevention is of prime importance in engineering and industry.

Electrochemistry is a unifying branch of chemistry that connects thermodynamics, kinetics, and practical applications. The core concepts — electrode potential, Nernst equation, Gibbs energy relationships, Faraday's laws, conductance, and Kohlrausch's law — form an interconnected framework for understanding how chemical reactions and electrical energy are interconverted. Batteries, fuel cells, and industrial electrolysis are direct consequences of these principles.

From a board examination perspective, this chapter is highly scoring and concept-dense. Numerical problems based on the Nernst equation, calculation of cell EMF, Gibbs energy, equilibrium constant, molar conductivity, and Faraday's laws are regularly asked. Qualitative questions on galvanic vs electrolytic cells, electrode reactions in lead storage and dry cells, corrosion mechanism, and Kohlrausch's law applications are equally important. Mastery of this chapter requires understanding both theory and quantitative problem-solving.