Comparison between Heterogeneous and Homogeneous MASS Action Models in the Prediction of Ternary Ion Exchange Equilibria

Abstract

In this paper two models for the prediction of multicomponent ion exchange equilibria were compared: one, a heterogeneous model, based on the mass action law in which ideal behavior for both the solution and the solid phase and the heterogeneity of ion exchange sites has been assumed, and the other a homogeneous model, based on the same mass action law in which nonideal behavior for both the solution and the solid phase has been taken into account. Considering counterions with different valences, the optimum value of the fraction of functional groups was obtained from binary systems data. It was shown that the energy distribution was practically symmetric. Likewise, a procedure for decreasing the number of adjustable parameters, based on the determination of the minimum linearly independent equilibria considering each equilibrium as a heterogeneous reaction, was developed. The adjustable parameters (namely, the equilibrium constants forced to satisfy the triangle rule) were used in the prediction of the ternary equilibrium data. In all cases the prediction of the heterogeneous model was in good agreement with experimental data. However, although the homogeneous model was somewhat superior to the heterogeneous model in the prediction of ternary systems, the comparison between both models did not allow us to distinguish statistically between them.

Thermodynamic Modeling of Cl−, NO3− and SO42− Removal by an Anion Exchange Resin and Comparison with Dubinin−Astakhov Isotherms

“…The change in Gibbs standard free energy (Δ G 0 , J mol −1 ) during the ion exchange reaction is calculated as follows normalΔ G 0 = − R T .25em ln nobreak.25em K AB where T is the temperature (K) and R is the ideal gas constant (8.314 J mol −1 K −1 ). The values calculated for the ion exchange systems under study are in the range of cationic ion exchange systems involving a strong cation exchange resin …”

“…In addition, the selectivity coefficients deduced from the model are particularly valuable for further industrial applications. It is often considered as a theoretical model in opposition to the empirical models represented by the adsorption isotherms. − Recently, several studies have compared the results of Langmuir and Freundlich modeling with the thermodynamic ion exchange model, mainly focusing on cationic species ion exchange on zeolite materials. − …”

Determination of Intraparticle Diffusivities of Na+/K+ in Water and Water/Alcohol Mixed Solvents on a Strong Acid Cation Exchanger

“…It was observed that the models based on the law of mass action best represented the ion-exchange equilibrium. [10][11][12][13][14][15][16][17] In a more recent paper, 18 we reported ion-exchange equilibrium isotherms in pure methanol, ethanol, 2-propanol, 1-butanol, and 1-pentanol and mixtures of these solvents. Experimental equilibrium data were satisfactorily correlated using a homogeneous mass action law model in which the Wilson and Debye-Huckel equations were used to calculate the activity coefficients in the solid and liquid phases, respectively.…”

Swelling behavior of ion exchange resins incorporated in tri-calcium silicate cement matrix: I. Chemical analysis

“…Thus, with this hypothesis, the average volume Vl SCH of one continuous shell of portlandite might be calculated with the following equation. (18) where N IER is the average number of IER in the sample C 3 S/IER and Vm CH is the molar volume of portlandite.…”