Ion activity models: the Debye-Hückel equation and its extensions

Thermodynamic properties of electrolyte solutions are relevant for the study of ion channel transport, control of scale formation in oil pipelines, design and optimization of industrial processes, and quality assessment of natural waters and soils, to name only a few examples. However, despite their clear relevance, the thermodynamic properties of electrolyte solutions are only briefly discussed in most of the physical chemistry textbooks. Moreover, a more detailed discussion about the ionic cloud theory and its implications for the development of ion activity models is frequently left for advanced books of chemical thermodynamics and electrochemistry. Given this scenario, in this article, the Debye-Hückel equation and its most common extensions are comprehensively discussed, as well as their limitations and ranges of applicability. To this end, the foundations of the ionic cloud theory are thoroughly discussed by emphasizing the close linkage between the ions distribution and the ion–ion interactions in solution. Hence, the aim of this work is twofold: discuss in a didactic way how the development of the ionic cloud theory culminated in the Debye-Hückel equation and introduce other relevant ion activity models to undergraduate and graduate students of chemistry and chemical engineering.