Macroscopic proton coefficient determination

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. 

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. 

Ross and Riley (11) determined the macroscopic dissociation constants for lomefloxacin using UV spectrophotometric measurements at 266 nm. Takacs-Novak et al. used UV spectrophotometry to determine octanol/water partition coefficients for lomefloxacin and related quinolones and related them to their protonation equilibria (18). 

As for effective kinetic parameters of the ORR that should be used in macroscopic models, it seems reasonable to assume that the reaction order for oxygen concentration will be yo2 = 1 for conditions of interest. The effective transfer coefficient of the ORR, ac, will transition through a sequence of discrete values between 1 and 0.5, as a function of electrode potential. The reaction order for proton concentration, yh+, depends strongly on the adsorption regime and, therefore, a prediction of the value is not trivial. The difference ac - yh+ is a key determinant of electrostatic effects in water-filled nanopores inside of catalyst layers, as discussed in the section ORR in Water-Filled Nanopores Electrostatic Effects. ... 

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