Determination of the thermodynamic equilibrium constants of ion exchange processes

Abstract

Ion exchange reactions are considered on the basis of chemical equivalents (i), where n and m are nM⁺+nm(N/n) R ⇌mNⁿ⁺+nm(M/m)R (i) the valencies of the respective ion, Nⁿ⁺ and M^m+, R^– represents the negative ion of the resin framework. The corresponding thermodynamic equilibrium constant expression is rearranged in the form (ii). Plotting experimental data as log (a_N^m/a_Mⁿ)versus equivalent fraction of the ion log (a_N^m/a_Mⁿ)= log K+nmlog (a_NR/a_MR)(ii) exchanged leads to the appearance of an inflexion point. It is mathematically found that the quotient a_NR/a_MR, from the equilibrium constant expression, may be substituted by the ratio of equivalent fraction of (N/n)R over equivalent fraction of (M/m)R at the inflexion point. The calculated thermodynamic ion exchange constants are in very good agreement with the values obtained by other methods.