Mass action equations surface complexation calculations

Methods for measurement of parameters used in SCM s have been described in the literature. Only a brief summary is presented here. Surface complexation model parameters that can be measured directly include, (1) the solid concentration, (2) surface site density, (3) surface area, and (4) equilibrium constants for the mass action equations describing all relevant adsorption reactions. The relation between surface charge and potential is calculated in geochemical equilibrium models. 

Of course, the ion exchange and surface complexation reactions can be easily included in this step of the model in a similar manner to the precipitation reactions. Likewise, the concentration of electron as a master species (pe value) is needed to calculate the concentration of the aqueous species involved in a redox couple. The mass action equation for each of these redox couples is combined to remove the concentration of the electron from the equations, as if a set of redox couple was in a redox equilibrium. 

As in Section III.B for divalent cation adsorption, Eq. (268) allows calculation of the mean surface site electrostatic charge, v, once the fraction of surface sites complexed with a cation, bJa, has been determined. Also, as for divalent eations, Eq. (268) can be used to calculate activity coefficient quotients found in mass action equations iteratively by (1) calculation of sA under ideal adsorption conditions where Z = 1, (2)... 

Using surface complexation models is another way to quantitatively describe the ion-exchanges processes. Surface complexation models also apply the law of mass action, combined with surface electric work (Table 1.7). However, there are some theoretical problems with the calculations, namely, that the equations of intrinsic stability use concentrations instead of activities, without discussing... 

Equation (100) is a rigorous adsorption equation which allows calculation of SM> fraction of surface sites complexed with the cation, M, from a knowledge of the activity coefficients, the equilibrium molar solution concentration, Xy, of cation M, and the mass action constants for proton and cation surface complexation. 

Hence, the proper mass action treatment can be expected to provide an excellent fit between experimental and predicted adsorption data. In addition, adsorption equations expanded to include more than one adsorbed complex are based on mass action thermodynamics in which the only unknown variables introduced are mass action constants no parameters are introduced or needed to specify the fraction of each type of surface complex. Instead, once the mass action constants are determined for the respective surface complexes, the fraction of each surface complex can be calculated directly from a knowledge of the interfacial system, such as pH, initial mole fraction of each solute added, mole fraction of solute added, etc. 

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