Comparison of the Debye–Hückel and the Mean Spherical Approximation Theories for Electrolyte Solutions

Abstract

The thermodynamics of electrolyte solutions has been investigated by many scientists throughout the last century. While several theories have been presented, the most popular models for the electrostatic interactions are based on the Debye–Hückel and mean spherical approximation (MSA) theories. In this paper we investigate the differences between the Debye–Hückel and the MSA theories, and comparisons of the numerical results for the Helmholtz energy and its derivatives with respect to temperature, volume and composition are presented. The investigation shows that the nonrestricted primitive MSA theory performs similarly to Debye–Hückel, despite the differences in the derivation. We furthermore show that the static permittivity is a key parameter for both models and that in many cases it completely dominates the results obtained from the two models. Consequently, we conclude that the simpler Debye–Hückel theory may be used in connection with electrolyte equations of state without loss of accuracy.

Basic Remarks on Acidity

“…Them ain difference between the two is that the Debye-Hückel theory treats all ions as point charges,w hile the MSA treats ions as hard spheres with individual diameters. [8]…”

“…This value equates to the standard potential of the proton in the respective solvent [Eq. (8)] and allows the construction of the absolute-acidity scale.…”

“…(8) allows the connection of the chemical potential of solvated protons H + (solv) ,which is m abs H þ ; S ðÞ ,toany medium pH S value [and via Eq. (4) to the respective proton activites] and thus to the unified pH abs value [Eq.…”

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

“…In the case of the primitive model, one of two classical theories is typically used to resolve the corresponding residual free energy: either the Debye-Hückel theory [1] or the mean spherical approximation (MSA) [6,55]. As shown by Maribo-Mogensen et al [56], both approaches lead to a similar representation of the macroscopic thermodynamic properties of electrolyte solutions; the material difference between the two is the parametrisation procedure for the corresponding models. In our current paper, the MSA theory is applied following the formulation of Blum [5,6], as laid out in previous work [21].…”

Prediction of thermodynamic properties of aqueous electrolyte solutions using equation of state

“…In our previous work, the primitive MSA was used for long range interaction. Recent investigations showed that the primitive MSA performs similarly to the DH theory . Since prediction of derivative properties is the main purpose of this study and temperature and density derivative of the Helmholtz free energy of each term is required, the DH theory is utilized because of its simplicity without loss of accuracy.…”