Casteel-Amis-equation

If the conductivity of an electrolyte in a polar solvent is measured up to high concentrations, the conductivity-concentration relation usually shows a maximum as in Fig. 7.3. Such a relationship is explained by the competition between the increase in the number of charge carriers and the decrease in ionic mobilities, mainly due to the strengthening of ion-ion interactions. Various empirical equations have been reported to express such a relation. The Casteel-Amis equation [21] for the relation between k and the molal concentration m is... 

The use of soft rules to estimate ideal solvent blend composition and the empirical Casteel-Amis-equation can be helpful to reduce the number of measurements [433]. Another more general approach is the use of the well-established simplex algorithm, which is applied in optimization of technical and economic processes. The most important advantage is that no theoretical assumption has to be made because it is based only on a simple geometric approach (the relation of the control variables to the response variables is unimportant). A second advantage is its efficiency, when many control variables have to be scanned. 

Conductivities of concentrated solutions are usually expressed by empirical equations with parameters having no physical meaning. A widely used the Casteel and Amis equation for specific conductivity curves, k(c) or tc(m), have four adjustable parameters a, b, and or maximum of specific... 

The data analysis with the help of Eqs. (83), (84), (87), and (88) where association constants are used with MSA activity coefficients [Eqs. (90), (91), (92)] yields a good reproduction of experimental data up to molar concentrations. As an example. Fig. 9 shows the conductivity of BU4NCIO4 in the mixed solvent system acetonitrile-propylene carbonate. Comparison is made of measured data with MSA and the Amis-Casteel equation, which both exactly reproduce the conductivity maximum at every solvent composition. 

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