A unified model for predicting the mononuclear first- to fifth-order and the polynuclear hydrolysis constants of metal cations

Abstract

This contribution introduces a quite simple method to establish a universal equation for quantitatively estimating the cationic hydrolysis tendency in water. The unified model is constructed on the basis of the general from of the hydrolysis reaction of metal cations: mMe Z+ + nH 2O→Me m (OH) n ( mZ− n)+ + nH +. According to this general form, the metal cation (Me Z+ ) and water molecule (H 2O) are properly regarded as the main reactants of a hydrolysis reaction of metal cations. The universal predicting equation for the thermodynamic hydrolysis constants ( log K mn) can then be obtained as: log K mn=Ω R− S ×(n/m)×(m IE+n BE)−(m+n) log 55.51+(− ΔG° Extra /2.303RT)(n+1)/2. The parameter IE is the total ionization energy of metal atoms. The parameter BE can be calculated from the energy change of the following reaction: oxygen atom+2 hydrogen atom→water molecule. The enthalpy for stabilizing the hydrolysis reactants in an aquatic system is defined as Ω R− S ×(n/m)×(m IE+n BE). Here Ω R− S is the reactant-stabilizing enthalpy coefficient, which equals the inverse of (2.303 RT×dielectric constant of water). The entropy contribution for stabilizing the hydrolysis reactants in an aquatic system can be represented by the total molar numbers of the hydrolysis reactants, ( m+ n), multiplied with − log 55.51. The remaining free energy term, (−Δ G° Extra/2.303 RT), accounts for the extraneous effects arisen from adjacent solvent molecules interacting with the metal cation. This unified model finds out a physically meaningful coefficient (i.e. reactant-stabilizing enthalpy coefficient, Ω R− S ) and proposes a novel free energy partioning procedure to make the universal prediction for cationic hydrolysis constants become possible.