Equilibrium constant surface reflecting

The surface complexation models used are only qualitatively correct at the molecular level, even though good quantitative description of titration data and adsorption isotherms and surface charge can be obtained by curve fitting techniques. Titration and adsorption experiments are not sensitive to the detailed structure of the interfacial region (Sposito, 1984) but the equilibrium constants given reflect - in a mean field statistical sense - quantitatively the extent of interaction. 

Extensive tabulations on experimentally determined surface equilibrium constants (Schindler and Stumm, 1987 Dzombak and Morel, 1990) reflecting the acid-base characteristic of surface hydroxyl groups and the stability of surface metal com-... 

As every surface complex formation equilibrium constant can be converted into an equivalent Langmuir adsorption constant (Stumm et al., 1970), every FFG equation reflects the surface complex formation constant corrected with the interaction coeffi-... 

These surface acid equilibrium constants differ from their solution counterparts in that they reflect both an intrinsic reactivity of the particular O-H bond and an electrostatic free energy of moving H+ to and from a charged surface ... 

The Langmuir model describes, for a uniform surface and a non-self-interacting adsorbate, the relationship between amount adsorbed and exposure concentration. The parameters of the model are the maximum amount adsorbed as a full monolayer and the equilibrium constant for the adsorption-desorption process which indirectly reflects the strength of the adsorbate-substrate interaction. For the present situation the analysis is modified in the following ways ... 

Accurate predictions of the transport of As in groundwater requires site specific data to model adsorption/desorption reactions. In complex mixtures of minerals, it may not be possible to quantify the adsorption properties of individual minerals. Therefore, it has been suggested that adsorption properties of composite materials should be characterized as a whole (Davis and Kent, 1990). Previously published data for adsorption by pure mineral phases such as the surface complexation database for adsorption by ferrihydrite (Dzombak and Morel, 1990) can be a useful starting point for modeling adsorption of solutes in groundwater however, these equilibrium constants may not reflect the adsorption properties of composite oxide coatings on aquifer solids. For example, incorporation of Si, and to a lesser extent, A1 into Fe oxyhydroxides has been shown to decrease adsorption reactivity towards anions (Ainsworth et al., 1989 Anderson and Benjamin, 1990 Anderson et al, 1985). Therefore, equilibrium constants will likely need to be modified for site-specific studies. 

Sp represents a site of fixed charge arising from isomorphous substitution r other structural defects. Because the intrinsic equilibrium constants for equations 30 and 31 reflect solute concentrations at the surface of the sorbent, vhich depend in turn on the surface potential, a coulombic term must be included in the mass law expression... 

Walden and Birr showed that for isomeric picrates the thermal expansion coefficients of the primary, secondary, and tertiary ammonium salts are greater than for the quaternary salts. Presumably the larger expansion coefficients occur in sustems which are less ionic because of the dissociation of the salt into amine and picric acid. This explanation is in agreement with the comparison of the isoelectronic salts and hydrocarbons in Section 2.2. For them the nonelectrolyte has the greater thermal expansion coefficient when the comparison is made at constant pressure and temperature, in agreement with Walden and Birr, while for a comparison at constant volume and temperature the salt has a greater coefficient. Thus nonelectrolyte components are in equilibrium with the primary through tertiary ammonium salts and the shifts in this equilibrium will be reflected in the thermal expansion coefficient and produce unreasonable estimates of the surface tension. 

However, we have to reflect on one of our model assumptions (Table 5.1). It is certainly not justified to assume a completely uniform oxide surface. The dissolution is favored at a few localized (active) sites where the reactions have lower activation energy. The overall reaction rate is the sum of the rates of the various types of sites. The reactions occurring at differently active sites are parallel reaction steps occurring at different rates (Table 5.1). In parallel reactions the fast reaction is rate determining. We can assume that the ratio (mol fraction, %a) of active sites to total (active plus less active) sites remains constant during the dissolution that is the active sites are continuously regenerated after AI(III) detachment and thus steady state conditions are maintained, i.e., a mean field rate law can generalize the dissolution rate. The reaction constant k in Eq. (5.9) includes %a, which is a function of the particular material used (see remark 4 in Table 5.1). In the activated complex theory the surface complex is the precursor of the activated complex (Fig. 5.4) and is in local equilibrium with it. The detachment corresponds to the desorption of the activated surface complex. 

---