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

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Abstract

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.

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Acknowledgements

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). M.A.D. has been supported as an MLS Fellow. EZ was supported by the Honors College Discovery Fellowship and the Arts & Sciences Undergraduate Research Mentorship Program.

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Authors and Affiliations

  1. Department of Chemistry, University of Missouri, Columbia, MO, 65211, USA

    Ethan Zars, Joseph Schell, Marco A. Delarosa & Rainer Glaser

  2. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Marco A. Delarosa & Carmen Chicone

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  1. Ethan Zars
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  2. Joseph Schell
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  3. Marco A. Delarosa
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Correspondence to Rainer Glaser.

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Zars, E., Schell, J., Delarosa, M.A. et al. Dynamical Approach to Multi-Equilibria Problems Considering the Debye–Hückel Theory of Electrolyte Solutions: Concentration Quotients as a Function of Ionic Strength. J Solution Chem 46, 643–662 (2017). https://doi.org/10.1007/s10953-017-0593-z

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