Equilibrium surface protonation equation

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

The next step in describing the importance of surface adsorption in this model involves the exchange affinity of the surface sites for metal ions as well as protons. In other words, metals in solution compete with protons for the oxide surface sites. Equations for this process are exactly analogous to those for similar solution reactions. Again it was demonstrated (see, for example, Schindler and Stumm, 1987) that the equilibrium constants determined for the competition between protons and metals for the metal oxide surface are linearly... 

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 ... 

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

Here k is the rate constant, and Kj is the equihbrium constant for an exchange reaction between protons and the metal M, at the surface. Oelkers argues that when the term Kfa +la Y is small, significant M, remains in the surface leached layer, and the rate equation simplifies in that the denominator becomes unity. For such a case, the logarithm of the far-from-equilibrium rate becomes linearly related to the logarithm of the activity of the aqueous species M, and is dependent only upon pH and activity of M,. Oelkers (2001b) has used this simplified rate equation to describe dissolution of basalt glass... 

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. 

L]o is known for solution studies, and as regards the surface the information on the amount and nature of adsorption sites is mostly absent. The methods for determining of their number by interaction with certain substances including a titration and evaluation of capacity by metal ion sorption are also based finally on surface equilibria and hence require account of equilibrium (1) and an equation of a type (3). For example, in the case of proton adsorption Eq. (3) has the following form ... 

Consider an adsorbing variable-charge mineral with a concentration of reactive surface hydroxyl groups, (St), defined earlier in this chapter (section 4.1c). As before, at any particular pH these groups can be protonated, uncharged, or deprotonated, so that equation 4.15 applies. The association and dissociation reactions of the groups are defined as before (reactions 4.7 and 4.8) using the equilibrium constants, and Ki. The assumptions and weaknesses inherent to this approach are described in section 4.1c. 

However, in these cases the proton exchange occurs at the surface of the particle(s) and this must be related to the concentration (or activity) of the protons in the equilibrium solution. This may be done by applying the Boltzmann equation, which states... 

Formulation of Eq. 9 is consistent with transition-state theory, where the rate of the reaction far from equilibrium depends solely on the activity of the activated transition-state complex (Wieland et al., 1988). Equations 8 and 9 are equivalent to Eq. 2 for proton attack, where C, is equal to the surface concentration of activated complex. 

The adsorption of silicic acid on a-FeOOH tends to release protons (a) and causes a decrease in surface charge (b). The extent of adsorption as a function of pH can be predicted by an equilibrium model that considers the equilibrium constants given in Equations 22 and 23 and the acidity constant of H SiO and =FeOH, (IS). 

It should be noted that this is not a simple adsorption of the alkyl ammonium ion on the surface of the iron sulfide but can be considered as an ionic reaction in which a proton is being set free. It is now reasonable to consider the factors which may influence the concentration of the surface complex formed from iron sulfide and the alkyl ammonium ion. Going through a simple series of equilibrium calculations, it is found that the concentration of the surface complex equals the product of a series of equilibrium constants times the proton concentration of the medium, as shown in equation 34. 

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