Macroscopic proton coefficient microscopic subreactions

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. 

In surface-complexation models, the relationship between the proton and metal/surface-site complexes is explicitly defined in the formulation of the proposed (but hypothetical) microscopic subreactions. In contrast, in macroscopic models, the relationship between solute adsorption and the overall proton activity is chemically less direct there is no information given about the source of the proton other than a generic relationship between adsorption and changes in proton activity. The macroscopic solute adsorption/pH relationships correspond to the net proton release or consumption from all chemical interactions involved in proton tranfer. Since it is not possible to account for all of these contributions directly for many heterogeneous systems of interest, the objective of the macroscopic models is to establish and calibrate overall partitioning coefficients with respect to observed system variables. 

Non-integer, net proton coefficients are reasonable considering the complexity of heterogeneous systems (q.v., Table I). Although integer stoichiometric coefficients are appropriate for microscopic subreactions, arbitrarily extending stoichiometric relationships used in microscopic reactions to macroscopic partitioning expressions is unwarranted. 

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