Equilibrium surface protonation constants

Predictive equations for the equilibrium surface protonation constants derived using the approach of Sverjensky and Sahai (1996) are... 

Sverjensky, D.A. Sahai, N. (1996) Theoretical prediction of single-site surface protonation equilibrium constants for oxides and silicates in water. Geochem. Cosmochim. Acta 60 3773-3797... 

Typical values of pK[nt and pfor a humic acid are 2.67 and 4.46. The introduction of the electrostatic factor into the equilibrium constant is analogous to the coulombic term used in the definition of the intrinsic surface complexation constants. In addition another binding site (WAH) is recognised which is thought to behave as a weak acidic phenolic functional group. Although this site does not contribute to the titratable acidity and, therefore, no pK is needed for proton dissociation, it is involved in metal complexation reactions. The total number of the three monoprotic sites is estimated from titratable acidity and then paired to represent the humic substance as a discrete non-interacting mixture of three dipro-tic acids, which act as the metal complexation sites. The three sites are... 

In natural waters, other surface reactions will be occurring simultaneously. These include protonation and deprotonation of the >FeOH site at the inner o-plane and complexation of other cations and anions to either the inner (o) or outer (IS) surface planes. Expressions similar to Equation (5) above can be written for each of these reactions. In most studies, the activity coefficients of surface species are assumed to be equal to unity thus, the activities of the surface sites and surface species are equal to their concentrations. Different standard states for the activities of surface sites and species have been defined either explicitly or implicitly in different studies (Sverjensky, 2003). Sveijensky (2003) notes that the use of a hypothetical 1.0 M standard state or similar convention for the activities of surface sites and surface species leads to surface-complexation constants that are directly dependent on the site density and surface area of the sorbent. He defines a standard state for surfaces sites and species that is based on site occupancy and produces equilibrium constants independent of these properties of the solids. For more details about the properties of the electrical double layer, methods to calculate surface specia-tion and alternative models for activity coefficients for surface sites, the reader should refer to the reference cited above and other works cited therein. 

The intrinsic equilibrium constants for the diffuse layer model are similar to those for the constant capacitance model where P is replaced by Equations (6.10) and (6.11) describe surface protonation and dissociation, respectively. Metal surface complexation is described by two constants similar to tliat defined in Eq. (6.12) for strong and weak sites ... 

Using these new standard states for the sorbent sites and sorbate species, the equilibrium constant for the surface protonation reaction, Eq. (6.6), is given by... 

The experimentally observed pH after addition of a reagent (e.g., in potentiometric titration) does not reach a constant value, but changes at a variable rate even over very long times. Some arbitrary assumption is necessary to establish the equilibrium value. A few examples of kinetic experiments of surface protonation are briefly presented in this section. 

Machesky, M.L. et al.. On the temperature dependence of intrinsic surface protonation equilibrium constants An extension of the revised MUSIC model, J. Colloid Interf. Sci., 239, 314, 2001. 

Recalling the reaction schemes (Equation 8.102) representing the surface proton exchange, we find the following equilibrium constants ... 

Here, and are protonation and deprotonation constants at the interface, and is electric potential of the formed charge. Equilibrium constants in these reactions characterize acid-alkali properties of the mineral surface as amphoteric substance and are called surface acidity constants. 

Kinetics of Selenium Adsorption. Zhang and Sparks 4G) examined selenate and selenite adsorption and desorption on goethite using pressure jump relaxation techniques. Selenate produced a single relaxation, that was interpreted as outer-sphere complexation with surface protonation based on fitting to the triple layer model. The forward rate constant was 10 L mol s Selenite adsorption was proposed to occur via two steps, an initial outer-sphere complex and subsequent replacement of a water molecule by formation of inner-sphere complexes of both HSeOj and SeOj, based on optimized fits using the triple layer model. The model optimized fit for the pK, of the surface species was approximately 8.7. Forward rate constants for the first step were on the order of 10 L -mor -s for HSeOj and 10 L -mor -s for SeOj. Forward rate constants for the formation of the inner-sphere complexes were 100 and 13 s respectively for HSeOj and SeOj. Agreement between the equilibrium constant obtained from batch and kinetic studies was taken as confirmation of the proposed reactions. 

Only a few attempts have been made to use computational methods for the silanol acidities. Sverjensky and Sahai have developed a method for estimating surface protonation equilibrium constants from the surface dielectric constant and an average Pauling bond strength. Rustad and coworkers [319] have used molecular dynamics methods to estimate the pK, for the reaction >SiOH — >SiO + H+ at 8.5. Tossell [320] used several quantum chemical levels of theory to establish correlations between calculated gas-phase AE and AH values and experimental aqueous solution pK s. Liu et al. [308] have employed both experimental and computation methods to study the gas-pha.se properties of organic silanols. ... 

Sveijensky DA, Sahai N (1996) Theoretical prediction of single-site surface protonation equilibrium constants for oxides and silicates in water. Geochim Cosmochim Acta 60 3773-3797 Tasker PW (1979) Stability of ionic crystal surfaces. J Physics C Solid State Physics 12 4977-4984 Toukan K, Rahman A (1985) Molecular-dynamics study of atomic motions in water. Phys Rev B- Con Mat 31 2643-2648... 

The exchange of protons between water and an amphoteric metal oxide interface will produce three different types of surface sites (1) unprotonated anionic sites each with a unit negative valence, (2) monoprotonated nonionic sites each with a zero valence, and (3) diprotonated cationic sites each with a unit positive valence. Given sufficient time to reach equilibrium, the proton exchange will produce a S—MO interface in which the number of each type of site and the number of protons in solution becomes constant. To specify the stochiometry of this equilibrium proton distribution, the total number of siuface sites will be designated as nj with the number of each specific type of siuface site designated as (1) n Q, unprotonated anionic sites, (2) soH monoprotonated nonionic sites, and (3) for diprotonated cationic sites. 

The critical hydrogen content for the ductility loss increased with increasing hydrogen solubility in the alloy. The fracture surfaces were not characteristic of those found under conditions of SCC. In terms of hydrogen and deuterium solubility in a similar series of bcc alloys, the equilibrium constants were determined at infinite dilution as a function of temperature The free energy function was expressed in terms of the bound-proton model. 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

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