The statistics of the Debye–Hückel limiting law

The Debye–Hückel Limiting Law (DHLL) correctly predicts the thermodynamic behavior of dilute electrolyte solutions. Most articles and books explain this law using Peter Debye Erich Hückel’s original formalism linearizing Poisson–Boltzmann equation for a simple model. Brilliant in its own right, approach does not fully which microstates contribute range theory. Notably, establish Energy Multiplicity Distribution (EMD), is energy distribution system’s microstates. This work establishes an analytical expression EMD that satisfies DHLL. Specifically, proportional to [Formula: see text] DHLL monovalent solution. Here, U el effective electrostatic due ion–ion interactions. proposed proportionality shows quantitative agreement with simulated EMDs Coulomb lattice gas corresponds aqueous sodium chloride solution at concentration 3.559 × 10 −4 M. used incorporate solvent molecules, but interactions are scaled through permittivity emulates solvent—similar Moreover, explains by partitioning into set contributions minimal spanning graphs. discussion on new field. It widens scope theory could lead parameterization option developing equations state.