Equilibria, surface complex formation

The central ion of a mineral surface (in this case we take for example the surface of a Fe(lll) oxide and S-OH corresponds to =Fe-OH) acts as Lewis acid and exchanges its stuctural OH against other ligands (ligand exchange). Table 2.1 lists the most important adsorption (= surface complex formation) equilibria. The following criteria are characteristic for all surface complexation models (Dzombak and Morel, 1990.)... 

Table 2.1 Adsorption (Surface Complex Formation Equilibria)...

The Langmuir equation is derived here from application of the mass law, in a similar way as the surface complex formation equilibria were derived in Chapter 2. In principle at a constant pH there is no difference between a Langmuir constant and a surface complex formation constant. 

Surface protonation and deprotonation are experimentally directly accessible from alkalimetric or acidimetric surface tritrations. The surface concentrations (sMOH ) or <=MO") are nonlinearly related to H+ by surface complex formation equilibria or by semi-empirical relations in other words,... 

We will illustrate that surface complex formation equilibria permit us to predict quantitatively the extent of adsorption of H", OH of metal ions and ligands as a function of pH and solution variables and of surface characteristics. 

Table 9.1 presents the most important adsorption (= surface complex formation) equilibria. The following criteria are characteristic of all surface com-plexation models (Dzombak and Morel, 1990) ... 

List II summarizes schematically the type of surface complex formation equilibria that characterize the adsorption of H+, OH, cations, and ligands at a hydrous oxide surface. The various surface hydroxyls formed at a hydrous oxide surface may not be fully equivalent structurally and chemically. However, to facilitate the schematic representation of reactions and of equilibria, we will consider the chemical reaction of < a> surface hydroxyl group, S-OH. The following surface groups can be envisaged. 

Figure 7. The effect of ligands and metal ions on surface protonation of a hydrous oxide is illustrated by two examples (1). Part a Binding of a ligand (pH 7) to hematite, which increases surface protonation. Part h Adsorption of Pb2+ to hematite (pH 4.4), which reduces surface protonation. Part c Surface protonation of hematite alone as a function of pH (for comparison). All data were calculated with the following surface complex formation equilibria (1 = 5 X 10"3 M >. Electrostatic correction was made by diffuse double layer model.

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-... 

The arrows show the isotherm evolution for continual addition of dissolved Me. The initial isotherm with the slope of 1 (in the double logaritmic plot) corresponds to a Langmuir isotherm (surface complex formation equilibrium). [Me]S0 = solubility concentration of Me for the stable metal oxide [Me]p = solubility concentration of Me for a metastable precursor (e.g., a hydrated Me oxide phase). 

In order to evaluate the two important variables which - in addition to pH - affect the residual concentrations of a metal ion, we use a simple equilibrium approach to assess the effect of these two variables. We assume a constant pH and characterize the effect of particle ligands, =L, by the surface complex formation equilibrium. 

Figure 13.29. Schematic sorption isotherms of a metal ion (Me) on an oxide (XO ) at constant pH (a) adsorption only (H) adsorption and surface precipitation via ideal solid solution (c) adsorption and heterogeneous nucleation in the absence of a free energy nucleation barrier (AG 0) adsorption and heterogeneous nucleation of a metastable precursor (e) same as in (3) but with transformation of the precursor into the stable phase. The arrows show the isotherm evolution for continual addition of dissolved Me. The initial isotherm with the slope of 1 (in the double logarithmic plot) corresponds to a Langmuir isotherm (surface complex formation equilibrium). [Me]s , = solubility concentration of Me for the stable metal oxide [Me]p = solubility concentration of Me for a metastable precursor (e.g., a hydrated Me oxide phase). (From Van Cappellen, 1991.)...

The conditions for the validity of a Langmuir type adsorption equilibrium are i) thermal equilibrium up to the formation of a monolayer, 0 = 1 ii) the energy of adsorption is independent of 0, (i.e., equal activity of all surface sites). There is no difference between a surface complex formation constant and a Langmuir adsorption... 

We have argued that (inner-sphere) surface complex formation of a metal ion to the oxygen donor atoms of the functional groups of a hydrous oxide is in principle similar to complex formation in homogeneous solution, and we have used the same type of equilibrium constants. How far can we apply similar concepts in kinetics ... 

The phenomena of surface precipitation and isomorphic substitutions described above and in Chapters 3.5, 6.5 and 6.6 are hampered because equilibrium is seldom established. The initial surface reaction, e.g., the surface complex formation on the surface of an oxide or carbonate fulfills many criteria of a reversible equilibrium. If we form on the outer layer of the solid phase a coprecipitate (isomorphic substitutions) we may still ideally have a metastable equilibrium. The extent of incipient adsorption, e.g., of HPOjj on FeOOH(s) or of Cd2+ on caicite is certainly dependent on the surface charge of the sorbing solid, and thus on pH of the solution etc. even the kinetics of the reaction will be influenced by the surface charge but the final solid solution, if it were in equilibrium, would not depend on the surface charge and the solution variables which influence the adsorption process i.e., the extent of isomorphic substitution for the ideal solid solution is given by the equilibrium that describes the formation of the solid solution (and not by the rates by which these compositions are formed). Many surface phenomena that are encountered in laboratory studies and in field observations are characterized by partial, or metastable equilibrium or by non-equilibrium relations. Reversibility of the apparent equilibrium or congruence in dissolution or precipitation can often not be assumed. 

Since this step is fast in comparison to the subsequent ones, this reaction can be considered as a pre-equilibrium, is the surface complex formation (equivalent to the Langmuir) constant. 

Assuming unit partition of the uncharged ligand between the equilibrium and interlamellar solution allows one to determine the overall surface complex formation constant g from the... 

Figure 9.13. Surface complex formation with ligands (anions) as a function of pH. (a) Binding of anions from dilute solutions (5 x 10 M) to hydrous ferric oxide [TOTFe= 10 M]. Based on data from Dzombak and Morel (1990). I = 0.1. (b) Binding of phosphate, silicate, and fluoride on goethite (a-FeOOH) the species shown are surface species. (6 g FeOOH per liter, Pj = 10 M, Si/ = 8 x 10 M.) The curves are calculated with the help of experimentally determined equilibrium constants (Sigg and Stumm, 1981).

Data for surface complex formation on hydrous ferric oxide (Q) are from Dzom-bak and Morel (5), data for goethite (marked g) are from Sigg and Stumm ( ), and data for y-Al203 ( j are from Kummert and Stumm (8). These data are intrinsic equilibrium constants (i.e., extrapolated to zero surface charge). At the ordinate and abscissa a few relevant surface complex formation constants and solute equilibrium constants, respectively, are listed for which the constants in solution or at the surface are not known they may be used to estimate the corresponding unknown constant. 

Figure 9. The relative dissolution rate, R/Rf)J as a function of pH. Dashed lines were calculated by using the equilibrium and surface complex formation constants for pH 2S at 10r2 atm = /SO/ / = 10 1 M and--------------= /H2P047 =...

Inner- or outer-sphere surface complex formation is a. necessary prerequisite for most surface chemical redox reactions. (ESR may provide important information regarding the nature of the precursor complex.) When electron transfer is fast k2 ArJArOH]), overall rates of reaction are influenced by rates of organic reductant adsorption. When electron transfer is slow kl < ArJArOH]), Eq. [18] can be modeled as a pseudoequilibrium reaction, using the equilibrium constant... 

SOLUTION 1) with this surface and contains the instruction -no edl, which turns off all electrostatic calculations, those necessary for the electrostatic double layer theory. It also defines the total number of L sites. There is no explicit mention of Langmuir isotherm because, as mentioned above, there is no difference between a Langmuir isotherm equilibrium constant and a single-site surface complex formation constant, which phreeqc understands. 

Figure 9. The relative dissolution rate, R/Rf>, as a function of pH. Dashed lines were calculated by using the equilibrium and surface complex formation con-...

Kinetics evaluation software generates the values of ka (rates of complex formation) and kd (rates of complex dissociation) by fitting the data to interaction models. In a sensorgram, if binding occurs as sample passes over a prepared sensor surface, the response increases and is registered upon equilibrium, a constant signal is reached. The signal decreases when the sample is replaced with buffer, since the bound molecules dissociate. 

In a typical SPR experiment real-time kinetic study, solution flows over the surface, so desorption of the guest immobilized on the surface due to this flow must be avoided.72 In the first stage of a typical experiment the mobile reactant is introduced at a constant concentration ([H]0) into the buffer flowing above the surface-bound reactant. This favors complex association, and the progress of complex formation at the surface is monitored. The initial phase is then followed by a dissociation phase where the reactant is removed from the solution flowing above the surface, and only buffer is passed over the surface to favor dissociation of the complex.72 74 The obtained binding curves (sensograms) contain information on the equilibrium constant of the interaction and the association and dissociation rate constants for complex formation (Fig. 9). 

We return to the complex formation equilibria described in Chapter 2 (Eqs. 2.1 -2.10). The equilibrium constants as given in these equations are essentially intrinsic constants valid for a (hypothetically) uncharged surface. In many cases we can use these constants as apparent constants (in a similar way as non-activity corrected constants are being used) to illustrate some of the principal features of the interdependent variables that affect adsorption. Although it is impossible to separate the chemical and electrical contribution to the total energy of interaction with a surface without making non-thermodynamic assumptions, it is useful to operationally break down the interaction energy into a chemical and a Coulombic part ... 

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