Dynamical Approach to Multi-Equilibria Problems Considering the Debye-Hückel Theory of Electrolyte Solutions: Concentration Quotients as a Function of Ionic Strength


We recently described a dynamical approach to the equilibrium problem that involves the formulation of the kinetic rate equations for each species. The equilibrium concentrations are determined by evolving the initial concentrations via this dynamical system to their steady state values. This dynamical approach is particularly attractive because it can be extended easily to very large multi-equilibria systems and the effects of ionic strength also are easily included. Here we describe mathematical methods for the determination of steady state concentrations of all species with the consideration of their activities using several approximations of Debye-Hückel theory of electrolyte solutions. We describe the equations for a system that consists of a triprotic acid H3A and its conjugate bases. With these equations, two types of multi-equilibria systems were studied and compared to experimental data. The first system is exemplified by case studies of solutions of acetate-buffered acetic acid and the second system is exemplified by the hydroxide titration of citric acid. The discussion focuses on the effect of ionic strength on pH and on the amplification of acidity by ionic strength. Ionic strength effects are shown to cause significant deviations from the widely used Henderson-Hasselbalch equation.




Petroleum Research Fund
National Science Foundation (U.S.)


Acknowledgement is made to the donors of the American Chemical Society Petroleum Research Fund for partial support of this research PRF-53415-ND4. This research was supported by NSF-PRISM grant Mathematics and Life Sciences (MLS, #0928053).

Keywords and Phrases

Acids/Bases; Activity Coefficient; Dynamical Approach; Equilibrium; Ionic Strength; Ordinary Differential Equations

International Standard Serial Number (ISSN)

0095-9782; 1572-8927

Document Type

Article - Journal

Document Version


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© 2017 Springer Verlag, All rights reserved.

Publication Date

01 Mar 2017