Activation energies of ion exchange processes

Abstract

The temperature dependences of the electrical conductivity of MK-41 heterogeneous cation-exchange membranes and MA-41 anion-exchange membranes in the form of ions of different charges were measured by the contact-difference method. The measurements were carried out in the temperature range of 20-50оС and exponentially increasing dependences of electrical conductivity on temperature were obtained. The activation energies were calculated based on the measured values using the Arrhenius equation.

For the calculation of the activation energies, we assumed that they are the sum of the energy of the Coulomb interaction of counterions with fixed ions and the energy of breaking hydrogen bonds formed by hydrated water molecules of counterions and fixed ions. The breaking energies of hydrogen bonds were calculated using non-empirical method of quantum chemistry and by Planck equation for the bending vibrations of the water molecule. The electrostatic interaction of counterions and fixed ions was calculated using the integral form of Coulomb's law. The results of quantum chemical calculations were used for the calculation of the distances between fixed ions and counterions, the effective values of the charges of the ions, and Debye’s theory of polar molecules was used for the calculation of permittivity. The analysis of the obtained results showed that, in the case of ion exchange of singly charged ions, the factor determining the values of activation energies is the energy of breaking hydrogen bonds. It was established that as the charges of counterions increased, the Coulomb interaction of counterions and fixed ions increased, and for triply charged ions, the values of the Coulomb interaction energies were comparable with the energies of breaking hydrogen bonds. The calculated activation energies were in satisfactory agreement with the experimental results.