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

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. ■ INTRODUCTION Solutions containing electrolytes are encountered in many important industrial processes, such as postcombustion CO2 capture, acid gas scrubbing, purification of proteins and pharmaceuticals, and corrosion in wet gas pipelines. To describe the phase equilibrium of mixtures containing electrolytes, it is necessary to account for the long-range electrostatic forces between charged molecules. The thermodynamics of electrolyte solutions has been studied by many researchers by adding the long-range electrostatic forces to an existing model for the short-range forces in activity coefficient models such as UNIQUAC and NRTL and to equations of state such as SRK or CPA and a range of SAFT models. The most commonly used models for the electrolyte interactions are the Debye−Hückel model and the electrostatic part of the mean spherical approximation (MSA). Both models use Coulomb’s law to describe the force between two charges qi and qj: