A theoretical treatment of cation exchangers - III. The hydration of cations in polystyrene sulphonates

Abstract

The adsorption of water by the polystyrene sulphonates of cations has been investigated at 0 and 25° C, using an isopiestic method. The adsorption isotherm and the heats (enthalpies) and entropies of hydration have been obtained for the monovalent cations H, Li, Na, K, Cs, NH4, Ag and for the divalent cations Be, Mg, Ca, Sr, Ba, Hg. With the exception of H, which gives a smooth enthalpy-water-content curve, all monovalent cations show a more or less marked step in the differential enthalpy of adsorbed water between the first and second water molecule adsorbed per ion, thereafter the steps are less clearly defined. The differential entropies show similarities to those calculated for a B. E. T. isotherm, except that the curves show two minima which correspond to approximately 0.15 and 1.5 molecules of water/ion. The adsorption isotherms follow more or less the model of the B. E. T. isotherm, with several significant differences: ( a ) the volatility of the second and further water molecule/ion is not that of liquid water, but only tends to reach this value after several molecules/ion are adsorbed, and the energy levels of the first successive water molecules, though rising rapidly, differ substantially from that of liquid water; ( b ) the adsorption process of the first water molecule is significantly different from a Langmuir mechanism, and varies approximately as the one-half power of the water activity. The knowledge of the free energies, enthalpies and entropies permits a fair analysis of the hydration mechanism into its individual steps, which then permits a calculation of the standard state enthalpies and entropies of the first hydration steps. Both functions show a markedly linear relationship with the ionic radius of the unhydrated ion when summed up for the first two water molecules adsorbed. The knowledge of the adsorption isotherms permits one to differentiate between water adsorbed with zero free energy (swelling water) and the excess adsorbed water (cationic and anionic hydration water). The amount of hydration water associated with the cations has been obtained in this way both for mono- and divalent ions. The amount varies both with the water activity and with temperature. It is clear from the small free energies of hydration of all monovalent ions that the association of almost all water molecules is very loose, and is not related to the co-ordination number of the ions.