Qualitative analysis of physical factors that determine activity coefficients of electrolytes. III. Mixtures of electrolytes
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Abstract
In the paper we propose a model describing interaction characteristics of hydrated ions in the mixtures of uni-univalent electrolytes with a common ion. The main factor taken into consideration is a variation of the hydrate shell size in the mixture from its value in the binary solution. Account of this factor gives a possibility to calculate the corresponding variation of the potential describing the mutual ions interaction. The potential is the sum of the electrostatic potential of ions and potential resulted from deformation of approaching hydrated shells. On this basis it is possible to explain the behavior of curves describing the activity coefficients in the mixtures of electrolytes in the range of concentrations from zero to several moles per liter. The results obtained by a numerical modelling are verified by comparing with the available experimental data.
Keywords
Activity coefficients Simulation Uni-univalent electrolytes MixturesList of symbols
- a (or b)
The radius of a stable part of the hydrate shell around the ion \(A^{+}\) (or \(B^{+}\)) in the statistical model; approximately corresponds to the distance of the closest approach of ions (Å)
- \(\bar{{a}}\) (or \(\bar{{b}}\))
The radius in the binary solution (Å)
- \(C_a \) (or \(C_b \))
The concentration of the substance \(A^{+}D^{-}\) (or \(B^{+}D^{-}\)) in the mixture (mol/l)
- C
The concentration of the component in a binary solution or \(C=C_a +C_b \) in the mixture (mol/l)
- \(\gamma \)
The activity coefficient in the binary solution (dimensionless)
- \(\gamma _a\) (or \(\gamma _b \))
The activity coefficient of the component \(A^{+}D^{-}\) (or \(B^{+}D^{-})\) in the mix solution of \(A^{+}D^{-} \hbox { and } B^+D^-\) (dimensionless)
- \(\nu \)
The volume of attraction zones around ions \(D^{-}\), \(\nu _0 =\mathop {\hbox {lim} }\limits _{C\rightarrow 0} \nu \) (l/mol)
- U
The difference of the average potential energies in the attraction zone and free zone divided by kT, \(U_0 =\mathop {\hbox {lim} }\limits _{C\rightarrow 0} U\) (dimensionless)
- \(\varepsilon \)
The local value of the dielectric permittivity (dimensionless)
- \(\alpha _a \) (or \(\alpha _b\))
The function which reflects size variation of the radius a (or b) in the mix solution against its value in the binary solution (dimensionless)
- \(\rho (t)\)
The distance of minimal approaching of an ion \(B^{+}\) to the fixed ion \(D^{-}\) in the mixture. The distance changes due to short-lived variation of a hydrate shell of an ion \(D^{-}\) on time (Å)
- \(t_1 \)
The typical time, which takes to rebuild the shell of ion \(D^{-}\) under its interaction with \(A^{+}\) (s)
- \(t_2 \)
The typical time, which takes to return \(\rho (t)\) to the \(\overline{b} \) value (s)
- \(\tau _A \)(or \(\tau _B \))
An average time between approaches \(D^{-}\) and \(A^{+}\) (or \(B^{+})\) (s)
Mathematics Subject Classification
93A30References
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