DebyeHückelGesetz

Debye-Hückel-Gesetz is a relation in physical chemistry that describes how the activity coefficients of ions in dilute electrolyte solutions depend on ionic strength. It quantifies deviations from ideal behavior caused by electrostatic interactions among ions in a solvent, typically water.

The law was formulated by Peter Debye and Erich Hückel in the early 1920s. It rests on the picture of ions as charged particles embedded in a continuous dielectric medium, surrounded by an ionic atmosphere that screens the electrostatic field. The model makes simplifying assumptions, such as treating ions as point charges and neglecting specific ion–solvent interactions and finite ion sizes. It is valid primarily for low ionic strengths, where interactions are weak and the solution is sufficiently dilute.

Two closely related forms are used. The Debye-Hückel limiting law (for very dilute solutions) states that log10 γi = −A zi^2 √I, where γi is the activity coefficient of ion i, zi is its charge, I is the ionic strength, and A is a temperature- and solvent-dependent constant. A and, in more general form, the extended Debye-Hückel equation introduce a size parameter ai for ion i: log10 γi = − (A zi^2 √I) / (1 + B ai √I). Here B is another constant dependent on temperature and solvent. The ionic strength is I = 1/2 Σ ci zi^2 with ci the molar concentrations.

For water at 25 °C, typical values are A ≈ 0.509 (mol/L)−1/2 and B ≈ 3.290 Å−1 (mol/L)−1/2. The Debye-Hückel framework remains a foundational tool in electrochemistry and solution chemistry, though its accuracy diminishes at higher ionic strengths where more advanced models are needed.