Competitive Langmuir adsorption

Figure 4.6 shows the competitive adsorption of mephobarbital by activated carbon in the presence of phenobarbital. It clearly illustrates that the extent of mephobarbital adsorption decreases in the presence of phenobarbital. This result shows that the two solutes are competing for the same adsorption sites on the activated carbon. The extent of mephobarbital adsorption in the presence of phenobarbital can be predicted by the competitive Langmuir adsorption isotherm. 

Competitive Langmuir Adsorption Isotherm When two or more substances can be adsorbed on a surface, the so-called competitive isotherms are applied. The Langmuir isotherm was improved for the adsorption of two gases by Markham and Benton (1931). Of course, the four assumptions of Langmuir isotherms are valid here, too. The surface-adsorbed quantity of component 1 is... 

The values for the concentration or occupancy 0 must be determined from the competitive Langmuir adsorption isotherm ... 

The form of the competitive Langmuir adsorption isotherm will not be derived here, but it has been derived by Adamson (1976) for two competing gases on a surface. 

Various functional forms for / have been proposed either as a result of empirical observation or in terms of specific models. A particularly important example of the latter is that known as the Langmuir adsorption equation [2]. By analogy with the derivation for gas adsorption (see Section XVII-3), the Langmuir model assumes the surface to consist of adsorption sites, each having an area a. All adsorbed species interact only with a site and not with each other, and adsorption is thus limited to a monolayer. Related lattice models reduce to the Langmuir model under these assumptions [3,4]. In the case of adsorption from solution, however, it seems more plausible to consider an alternative phrasing of the model. Adsorption is still limited to a monolayer, but this layer is now regarded as an ideal two-dimensional solution of equal-size solute and solvent molecules of area a. Thus lateral interactions, absent in the site picture, cancel out in the ideal solution however, in the first version is a properly of the solid lattice, while in the second it is a properly of the adsorbed species. Both models attribute differences in adsorption behavior entirely to differences in adsorbate-solid interactions. Both present adsorption as a competition between solute and solvent. 

The knowledge of these adsorption isotherms allows quantification of the respective affinity for the stationary phase with respect to the different solutes. Many different isotherm equations have been described in the literature, and experimental methods allowing their determination are reviewed by [58]. As a first approximation, modified competitive Langmuir isotherms can often he used ... 

In a more general form of equation 8.4-21 or -22, a AT c, term appears in the denominator for each adsorbing species i in competition for the adsorption sites. Furthermore, if the species dissociates into nt fragments, the appropriate term is (Kici)lln as in equation 8.4-15 for n = 2. Therefore, in the most general case, the expression for Langmuir adsorption of species i from a multispecies gas mixture is ... 

The multicomponent Langmuir adsorption isotherm given in Eq. (7) is the simplest model for the description of non-linear, multicomponent, adsorption equilibrium. At high concentration, the model predicts saturation of the stationary phase and overload of the chromatographic column. At low concentration (high dilution) the behavior can be correctly described by the non-competitive linear adsorption isotherm ... 

A number of classic rate expressions are commonly used to characterize heterogeneous reactions. These include expressions for the Langmuir adsorption isotherm, competitive... 

From the discussion of the Langmuir adsorption isotherm above, it is easy to write the analogous reaction-rate expressions for such competitive adsorption ... 

Theory of Vapor-Particle Partitioning of PAH Compounds in the Atmosphere. Yamasaki et al. (64) treated semivolatile PAHs as inherently vapor-phase materials, existing in the particle phase only because of their tendency to sorb on nonvolatile materials. Under this assumption, the proportion in each phase should vary with the available surface area for sorption and with the ambient temperature. They assumed that sorption followed a Langmuir adsorption isotherm, requiring that there be only a low fractional coverage of the particulate matter with semivolatile material. In this case, competition for sorption sites can be ignored. At equilibrium, the rate of sorption equals the rate of evaporation. They derived this relationship ... 

This equation can be interpreted in terms of Langmuir adsorption isotherms. It is assumed (see 1.5.4) that both reactants must be adsorbed in order to react and that KA and KB are the respective Langmuir adsorption equilibrium constants. The denominator allows for competition for sites between... 

Mg2+ influences calcite dissolution rates the same way, but not to the same extent as Ca2+. The inhibition effects of Mg2+ can be described in terms of a Langmuir adsorption isotherm. Sjoberg (1978) found he could model results for the combined influences of Ca2+ and Mg2+ in terms of site competition consistent with ion exchange equilibrium. The inhibition effects of Mg2+ in calcite powder runs increase with increasing Mg2+ concentration and as equilibrium is approached. 

This effect is relatively small until the total magnesium ion concentrations reach about 1000 ppm. o The effect of Mg2+ concentration on limestone dissolution rate can be explained by a surface adsorption model. The adsorption of Mg2+ reduces the limestone dissolution rate because the surface is partially blinded by the adsorbed magnesium ions. The competitive adsorption of calcium and magnesium ions was described by a mathematical model based on the Langmuir adsorption isotherm. The model was used to explain the sensitivity of limestone dissolution rate to magnesium ion concentration under limestone DA operating conditions. 

Let us first focus on a nonreactive system with constant separation factors. Typical examples are distillation processes with constant relative volatilities or adsorption processes described by competitive Langmuir isotherms. For nonreactive systems with constant separation factors, the constant pattern waves and spreading waves are... 

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