The equilibrium electrode potential depends on concentration via the Nernst equation:
where R = 8.314 J/mol·K, F = 96485 C/mol (Faraday's constant), n = electrons transferred, Q = [Ox]/[Red] (reaction quotient). The slope RT/nF = 25.7 mV / n at 298 K — this is the thermal voltage.
Applications: pH meters (H⁺ electrode, 59.16 mV/decade at 25°C), membrane potentials (Goldman equation is a generalization), batteries (Li-ion discharge curves follow Nernst-like behavior), corrosion (Pourbaix diagrams plot E vs pH). At equilibrium: E = 0 → ln(K_eq) = nFE°/RT, linking electrochemistry to thermodynamics.