Relationship of the Permittivity with the Activity Coefficients of Water and Ions in Aqueous Solutions of Lithium and So
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ICAL CHEMISTRY OF SOLUTIONS
Relationship of the Permittivity with the Activity Coefficients of Water and Ions in Aqueous Solutions of Lithium and Sodium Sulfates I. Yu. Shilova, * and A. K. Lyashchenkob aMoscow
State University Department of Chemistry, Moscow, 119991 Russia Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow, 119991 Russia *e-mail: [email protected]
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Received February 25, 2020; revised March 12, 2020; accepted March 27, 2020
Abstract—The activity coefficients in aqueous solutions of lithium and sodium sulfates at 298 K were calculated by the generalized Debye–Hückel theory using the experimental values of the static permittivity of the solutions. The effect of the hydration and ion association on the dielectric and thermodynamic properties of the electrolyte solutions was considered. Keywords: electrolyte solutions, ion pairs, hydration DOI: 10.1134/S003602362008015X
INTRODUCTION The generalized Debye–Hückel theory (GDHT) developed in 2015 [1] takes into account the dependence of the static permittivity of electrolyte solutions on their concentration and thus allows one to analyze the relationship of their dielectric and thermodynamic properties. Because the static permittivity is experimentally determined by dielectric spectroscopy methods [2, 3], GDHT can be used to predict the activity coefficients in concentrated solutions and study the laws obeyed by the thermodynamic properties of electrolyte solutions [4–6]. The calculations for aqueous solutions of uni-univalent electrolytes showed that, in particular cases, there is quantitative agreement with the experimental data to a concentration of 6–7 mol/kg [1, 4, 5]. In many cases, the deviation from the experimental values correlates with the formation of ion pairs in the studied solutions [4, 5], which enables one to analyze not only the contributions of the long-range Coulomb and solvation interactions, but also the manifestation of the ion association in the activity coefficients. The purpose of this work was to investigate the relationship of the permittivity and the activity coefficients in aqueous solutions of lithium and sodium sulfates at 298 K, in which various physicochemical methods determined the formation of ion pairs separated by water molecules.
CONCENTRATION DEPENDENCE OF PERMITTIVITY The dielectric properties of solutions of lithium sulfate [7–11] and sodium sulfate [7–10, 12] were studied previously. For using in calculations of the activity coefficients, the permittivity of solutions was approximated by analytical expressions presented in Table 1. The value of the permittivity of pure water was taken from the literature [13]. Figure 1 compares the concentration dependences of the permittivity from various sources. They differ because of the differences in experimental conditions and data processing methods. The complex permittivity ε*(ω) of solutions of lithium and sodium sulfates was determined [7] in the frequency range Δν = 7–25 GHz and was approximated by the Cole–Cole equation
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