1relation of the equilibrium constant and standard free Gibbs energy change
$\Delta G^0 = -RT \ln{K}$
2affinity
free energy change
3total standard Gibbs free energy change upon adsorption
$\Delta \tilde{G}^0 = \Delta G^0 + zF \psi_0 = \Delta G^0_{ch} + \Delta G^0_{el}$
4electrochemical potential and standard Gibbs free energy relation
$\tilde{\mu}_i = \left( \frac{\partial \tilde{G}}{\partial n_i} \right)_{T,P,n_j}$
5intrinsic contribution to ion sorption
the chemical, nonelectrostatic contribution
6two main approaches to model ion sorption to soil colloidal particles
chemical modeling
adsorption modeling
7chemical modeling of ion sorption
the sorption is treated as a chemical reaction, with the free surface sites considered as a reactant, and a chemical equilibrium expression in terms of the bulk activities is written
8adsorption modeling of ion sorption
an appropriate adsorption isotherm is employed, related to the activity at the outer Helmholtz plan $a_{i,2}$ (at the limit of the diffuse double layer)
9typical surface reactions on oxides
$\text{X-OH}+\text{H}^+ \rightleftharpoons \text{X-OH}^+_2$
$\text{X-OH} \rightleftharpoons \text{X-O}^- + \text{H}^+$
where X represents a cationic, Lewis acid, lattice species (Al(III), Fe(III), etc.)