Langmuir isotherm, solid-aqueous

Figure 11.20 Comparison of calculated (solid line) and experimental (s5nnbols) individual band profiles. Mixtures of N-benzoyl-L-(l) and D-(2)-alanine on a Resolvosil-BSA-7 column. Mobile phase 10 mM buffer aqueous solution (pH 6.7) with 3% 1-propanol (v/v) at Fn = 1 mL/min. L = 15 cm, d = 4 mm N = 700 plates. Binary competitive Langmuir isotherm selective site ai i = 14.16, fli p = 35.09, qs,i,L - 0.0019 mol/L, = 0.0020 mol/L nonselective site 2 = 4.41, = 0.01995 mol/L. (Left) Racemic mixture, sample sizes 0.26...

Many empirical equations have been proposed to describe sorption behavior of aqueous species on solid surfaces. The most conventional methods of plotting sorption data are the Freundlich and Langmuir isotherms (7). Both isotherms were developed for the sorption of gases by solid surfaces. However, they often, but not always, describe the sorption of nonelectrolytes and other species from liquid solution onto solid... 

In the case of dextran (0.1-1%) and amyiopectin (0.05%) the potentiometric measurements do not indicate any interaction with NaDS, the activity of NaDS solutions is the same with and without these polymers. An amylose solution of 0.025% was turbid and it did not clear up even in the presence of 20 mmoLkg" NaDS. However, the potentiometric measurements showed binding of NaDS according to a Langmuir isotherm with a saturation value of 0.27 mmol/g amylose. The binding of NaDS on amylose is regarded as an adsorption on solid amylose particles and not as an interaction between them in solution. It is concluded that the investigated polysaccharides do not interact with NaDS in aqueous solution. 

Hydrophilic surfactants adsorb best on aqueous phases, whereas hydrophobic surfactants adsorb best on lipophilic surfaces (oils). Data on adsorption at constant temperature are usually plotted as a function of the surfactant equilibrium concentration plots for solid substrates are termed Langmuir isotherms. From such isotherms the maximum surfactant concentration at the interface (Fmax) can be derived and the maximum area occupied by the surfactant at the interface ( max) can be calculated. In addition, the Gibbs adsorption equation can be extracted. 

This isotherm is similar to the Langmuir model, to which it becomes identical for t = 1. The parameters b and t permit independent adjustment of the initial slope and curvature of the isotherm. This model has been used successfully to account for experimental isotherm data regarding gas-solid adsorption [33]. It was used to account for the adsorption behavior of theophylline on a Kromasil Cig column eluted with an aqueous solution of methanol [11]. It is frequently used to account... 

Experiments to determine constants for the isotherms are usually performed in laboratory batch tests, that is in vessels that contain a known total amount of sorbent solid mixed with a known total amount of a potentially sorbing aqueous species. The approach is often to systematically vary sorbent and/or sorbate concentrations and pH, for example, in a series of centrifuge tubes. After centrifugation the amount sorbed is then deterimined by its difference from the total sorbate added (cf. Catts and Langmuir 1986). 

This equation is similar to the backward reaction terms of Eq. 11 if it is remembered that the product u0h —aHco, is related to aCQ2 by an equilibrium condition. There is, however, a fundamental difference in that the activities of HCO 3 and OH in Eq. 24 are those at the surface of the mineral and not in the bulk of the solution. The relations between the activities of these ions at the surface of the solid and in the aqueous solution are given by Langmuir or Freundlich isotherms. 

Several models have been developed to describe reactions between aqueous ions and solid surfaces. These models tend to fall into two categories (1) empirical partitioning models, such as distribution coefficients and isotherms (e.g., Langmuir and Freundlich isotherms), and (2) surface-complexation models (e.g., constant-capacitance, diffuse-layer, or triple-layer model) that are analogous to solution complexation with corrections for the electrostatic effects at the solid-solution interface (Davis and Kent, 1990). These models have been described in numerous articles (Westall and Hohl, 1980 Morel, Yeasted, and Westall, 1981 James and Parks, 1982 Barrow, 1983 Westall, 1986 Davis and Kent, 1990 Dzombak and Morel, 1990). Travis and Etnier (1981) provided a comprehensive review of the partitioning and kinetic models typically used to define sorption of ions by soils. The reader is referred to the cited articles for details of the models. 

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