11: Modeling Ion Binding (Gen Concepts)

$\Delta G^0 = -RT \ln{K}$

free energy change

$\Delta \tilde{G}^0 = \Delta G^0 + zF \psi_0 = \Delta G^0_{ch} + \Delta G^0_{el}$

$\tilde{\mu}_i = \left( \frac{\partial \tilde{G}}{\partial n_i} \right)_{T,P,n_j}$

the chemical, nonelectrostatic contribution

chemical modeling
adsorption modeling

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

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)

$\text{X-OH}+\text{H}^+ \rightleftharpoons \text{X-OH}^+_2$
$\text{X-OH} \rightleftharpoons \text{X-O}^- + \text{H}^+$
where X represents a cationic, Lewis acid, lattice species (Al(III), Fe(III), etc.)