Part V: Electrochemistry
Electrochemistry connects thermodynamics and kinetics at charged interfaces — from galvanic and electrolytic cells through electrode reaction mechanisms to ion transport in solution. This part develops the Nernst equation, Butler-Volmer kinetics, Debye-Hückel theory, and ionic conductivity from first principles.
Part Overview
Electrochemistry underpins batteries, fuel cells, corrosion science, electrolysis, and biological membrane potentials. We begin with the thermodynamics of electrochemical cells — relating cell EMF to Gibbs free energy and the Nernst equation. We then move to electrode kinetics, deriving the Butler-Volmer equation that governs how current depends on overpotential. Finally, we study transport phenomena in electrolyte solutions: the Debye-Hückel model of ionic atmospheres, conductivity, and diffusion.
Key Topics
- • Galvanic and electrolytic cells, standard electrode potentials, cell notation
- • Nernst equation and its thermodynamic derivation from chemical potentials
- • Butler-Volmer equation, Tafel plots, exchange current density
- • Debye-Hückel theory of electrolyte solutions and activity coefficients
- • Ionic conductivity, transference numbers, and the Onsager equation
- • Diffusion in electrolytes, Nernst-Planck equation, and limiting currents
3 chapters | Cells, Kinetics & Transport | From Nernst to Butler-Volmer
Key Equations
Nernst Equation: $E = E^\circ - \frac{RT}{nF}\ln Q$
Butler-Volmer: $j = j_0 \left[ \exp\!\left(\frac{\alpha_a F \eta}{RT}\right) - \exp\!\left(-\frac{\alpha_c F \eta}{RT}\right) \right]$
Debye-Hückel Limiting Law: $\ln \gamma_\pm = -A |z_+ z_-| \sqrt{I}$
Ionic Conductivity: $\Lambda_m = \Lambda_m^\circ - K\sqrt{c}$
Cell EMF & Gibbs Energy: $\Delta G = -nFE$
Tafel Equation: $\eta = a + b \ln j$
Chapters
Chapter 1: Electrochemical Cells
Galvanic cells convert chemical energy into electrical work; electrolytic cells drive non-spontaneous reactions. We derive the relationship between cell EMF and Gibbs free energy, establish the standard hydrogen electrode as reference, and build the Nernst equation from chemical potentials. Applications include pH measurement, concentration cells, and battery thermodynamics. The temperature dependence of EMF yields reaction entropy, connecting electrochemistry to calorimetry.
Chapter 2: Electrode Kinetics
At equilibrium, anodic and cathodic currents balance at the exchange current density. Away from equilibrium, the Butler-Volmer equation describes how net current depends on overpotential through transfer coefficients. In the high-overpotential limit, the Tafel equation provides a linear relationship between overpotential and the logarithm of current. We discuss Marcus theory's molecular picture of electron transfer, the role of the electrical double layer, and practical implications for corrosion, electrocatalysis, and fuel cell design.
Chapter 3: Transport Phenomena
Ions in solution experience electrostatic interactions screened by the ionic atmosphere. The Debye-Hückel theory predicts activity coefficients from ionic strength, explaining deviations from ideal behavior. Ionic conductivity depends on ion mobilities and is described by Kohlrausch's law at low concentrations. The Nernst-Planck equation combines diffusion and migration, governing mass transport to electrodes. We derive limiting current densities and discuss transference numbers, the Onsager reciprocal relations, and their application to electrolyte transport.