This work presents a simple solution for the diffuse double layer model, applicable to calculation of surface speciation as well as to simulation of ionic adsorption within the diffuse layer of solution in arbitrary salt media. Based on Poisson-Boltzmann equation. the Gaines-Thomas selectivity coefficient for uni-bivalent exchange on clay, K-GT(Me2+/M+)=(Q(Me)(0.5)/Q(M)){M+}/(Me2+)(0.5), (Q is the equivalent fraction of cation in the exchange capacity, and {M+} and {Me2+} are the ionic activities in solution) may be calculated as [surface charge, mu eq/m(2)]/0.61. The obtained solution of the Poisson-Boltzmann equation was applied to calculation of ionic exchange on clays and to simulation of the surface charge of ferrihydrite in 0.01-6 M NaCl solutions. In addition, a new model of acid-base properties was developed. This model is based on assumption that the net proton charge is not located on the mathematical surface plane but diffusely distributed within the subsurface layer of the lattice. It is shown that the obtained solution of the Poisson-Boltzmann equation makes such calculations possible, and that this approach is more efficient than the original diffuse double layer model. (c) 2008 Elsevier Inc. All rights reserved.