Macroscopic proton coefficient

Macroscopic Descriptions of Solute Adsorption and the Net Proton Coefficient. The macroscopic proton coefficient plays two important roles in our macroscopic descriptions of surface processes. First,... 

Figure 1. Log concentration-pH diagram showing the effect of the macroscopic proton coefficient on metal adsorption onto two hypothetical solids in separate, single adsorbent systems. Both adsorbents are present at the same site concentration top,...

Figure 2. Shift in system equivalence points (pH of 50% fractional metal adsorption) as a function of site concentration and macroscopic proton coefficient. Initial equivalence point of pH 8 and SOH. = 10 M are arbitrary reference conditions.

In their description of metal ion adsorption, Benjamin and Leckie used an apparent adsorption reaction which included a generic relationship between the removal of a metal ion from solution and the release of protons. The macroscopic proton coefficient was given a constant value, suggesting that x was uniform for all site types and all intensities of metal ion/oxide surface site interaction. Because the numerical value of x is a fundamental part of the determination of K, discussions of surface site heterogeneity, which are formulated in terms similar to Equation 4, cannot be decoupled from observations of the response of x to pH and adsorption density. As will be discussed later, It is not the general concept of surface-site heterogeneity which is affected by what is known of x> instead, it is the specific details of the relationship between K, pH and T which is altered. 

To what extent are assumptions of a constant x valid Table II shows the observed macroscopic proton coefficients for cation and anion adsorption in a variety of heterogeneous systems. The coefficients were determined by Kurbatov plots ( 6) or by isotherm analysis ( 7), unless otherwise indicated. In all cases, x is not an integer. 

The macroscopic proton coefficient may be determined by graphical analysis of observed system variables according to two different procedures fractional adsorption edge linearization (6) and isotherm analysis (7 ). The procedures for calculating the macroscopic proton coefficients according to these two methods are discussed in detail below, as are their relative advantages and disadvantages for use in semi-empirical descriptions of adsorption. 

The observation that the macroscopic proton coefficient is a function of adsorption density and pH has several implications for macroscopic modeling of cation and anion adsorption. The dependency of x on pH and T affects 1) the relationship of the macroscopic partitioning coefficient to pH and adsorption density, 2) the notion of metal ion preferences for a particular surface in systems with multiple solid phases, 3) the accuracy of predictive models when used over a range of adsorption density and pH values, and 4) conclusions about site heterogeneity based upon partitioning expressions which use constant proton coefficients. 

Microscopic Subreactions and Macroscopic Proton Coefficients. The macroscopic proton coefficient may be used as a semi-empirical modeling variable when calibrated against major system parameters. However, x has also been used to evaluate the fundamental nature of metal/adsorbent interactions (e.g., 5). In this section, macroscopic proton coefficients (Xj and v) calculated from adsorption data are compared with the microscopic subreactions of the Triple-Layer Model ( 1 ) and their inter-relationships are discussed. 

A specific example of the relationship between the microscopic subreactions required to model experimental observations of metal removal and the macroscopic proton coefficient is shown for the case of Cd(II) adsorption onto a-A f (Figure 3). One variation of the surface coordination concept is used to describe the system subreactions the Triple Layer Model of Davis et al., (1,20). The specific subreactions which are considered, the formation constants and compact layer capacitances, are shown in Table IV. Protons are assigned to the o-plane (the oxide surface) and Cd(II) surface species and electrolyte ions to the 8-plane located a distance, 8, from the o-plane. 

To what extent is the macroscopic proton release the direct expression of the metal/surface site reactions Table V compares the macroscopic proton coefficients (Xp ) ) with the coefficient expected if only the Cd(II) surface reactions are considered is the proton coefficient determined by considering the mole fraction of Cd(II) surface species and their formation reactions (Figure 14b). For example, when pSOH is 2.84, y = 0.11 x 1 + 0.89 x 2 = 1.89. At high alumina concentrations pSOH 2.14-2.53) the single surface reaction required to fit the data sets a limiting proton release of 2.0. 

It is clear, for the CdCl /a-Al O system at pH 7, that other reactions are not negligible in their contribution to the macroscopic proton coefficient at low surface coverage, when SO—CdOH"1" is the only postulated metal-containing surface species, the macroscopic proton coefficient is less than 2. Xp however, does approach 2.0 at low pH and high T (Figure 7). 

THE MATHEMATICAL DEVELOPMENT OF ISOTHERM ANALYSIS FOR THE MACROSCOPIC PROTON COEFFICIENT, Xp... 

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