Adsorption Freundlich equation applied

The Langmuir and Freundlich equations (see page 128) are frequently applied to adsorption from solution data, for which they take the form... 

The modeling of the obtained isotherms was carried out by applying the Freundlich equation. This is an empirical relationship based on the assumption of a logarithmic decrease in adsorption heat with adsorption surface coverage. The Freundlich equation is commonly used in the form ... 

Due to the effects of molecular size and shape and pore structure on the kinetics, the model cannot be used for general predictive purposes. In practice, in order to predict PAC adsorption, a series of experiments must first be carried out using the compound of interest, the activated carbon to be applied, and the water in which it is to be used. Equilibrium parameters, determined from the Freundlich adsorption isotherm equation, are used as input into a computer-based HSDM, which uses the method of least squares to minimize the difference between the experimental kinetic data points and the HSDM fit of the data [10]. When the best fit is achieved, the resultant kinetic parameters (liquid film mass transfer coefficient, k(, and the surface diffusion coefficient, DJ can then be used for the prediction of adsorption behavior under different conditions. 

Ion exchange differs from adsorption and chromatography in that one sorbate (a counterion) is exchanged for a solute ion, and the exchange is governed by a reversible, stoichiometric, chemical-reaction equation. For ion exchange, the law of mass action is applied to obtain an equilibrium ratio rather than to fit data to a sorption isotherm such as the Langmuir or Freundlich equation. 

To illustrate the linearity of this plot, we apply the Freundlich equation to the adsorption data of propane onto a sample of activated carbon at 10, 30 and 60 °C. The data are shown in Table 3.2-1 and Figure 3.2-2. This activated carbon is a typical commercial activated carbon, having a BET surface area of 1100 mVg, and a porosity of 0.7 (including macropores and micropores)... 

The Redlich-Peterson equation only differs from the Langmuir-Freundlich equation by the absence of exponent on at the numerator part of the equation (Ng et al, 2002). Meanwhile, the Dubinin-Radushkevitch (D-R) isotherm describes the adsorption on a single type of uniform pores and can be applied to distinguish between physical and chemical adsorption. This isotherm does not assume a homogeneous surface or a constant adsorption potential (Unlu and Ersoz, 2006). 

The classical Freundlich equation has been proposed by Cerofolini [60]. This isotherm corresponds to a decreasing-exponential adsorption energy distribution function [5]. The various forms of the Freundlich equation were applied to approximate experimental isotherms [56-65,69]. 

Ai lication of the Freundilch equation The Freundlich equation can frequently be applied to adsorption of this type, particularly since small adsorbable solute concentrations are usually involved This can be written in the following form for the concentration units used here. 

Equilibria The equilibrium distribution of an ion between an exchange solid and a solution can be described graphically by plotting isotherms in much the same manner used for ordinary adsorption. Various empirical equations for these isotherms, such as the Freundlich equation (11.3), have sometimes been applied to them. It is also possible to apply equations of the mass-action type to the exchange reaction. For example, for the cationic exchange... 

The Freundlich isotherm applies to the situation where dye adsorption onto the fibre is not limited by a number of specific adsorption sites and the fibre does not become saturated with dye. A typical system is one for which the dye ion and the fibre surface have the same type of electrical charge. The empirical equation describing this isotherm is shown in Eqs 2.5a or 2.5b ... 

At this point, it is feasible to correlate the liquid-phase adsorption equilibrium single component data, with the help of isotherm equations developed for gas-phase adsorption, since, in principle, it is feasible to extend these isotherms to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [92], These equations are the Langmuir, Freundlich, Sips, Toth, and Dubinin-Radushkevich equations [91-93], Nevertheless, the Langmuir and Freudlich equations are the most extensively applied to correlate liquid-phase adsorption data. [2,87],... 

Also, the linear regression analysis can be carried out applying a commercial regression software, which can as well be used for the nonlinear regressing analysis of each set of experimental data using directly the Freundlich isotherm equation for liquid-phase adsorption [95,96],... 

In the past, much attention was given to the study of dye and iodine adsorption by active carbons (Bmnauer, 1945 Orr and Dalla Valle, 1959). Many studies have been made with dye molecules of well-known size, shape and chemical properties, but the results have not been easy to interpret (Giles et al., 1970 McKay, 1982, 1984). In a systematic study of iodine adsorption (from aqueous solution) on a carbon black and four activated carbons (Femandez-Colinas etal., 1989b), it was found that the iodine isotherms could be analysed by the as-method. In this way it was possible to assess values of the available volume in pores of effective width of 0.5-1.5 nm. The adsorption of iodine was also featured in a recent study by Ziolkowska and Garbacz (1997), who applied the Langmuir, Freundlich and other isotherm equations. 

In conclusion, the QCM-technique has been applied to study the process of a HRP layer formation on a PEI/PSS coated quartz crystal resonator from enzyme aqueous solutions. It has been shown, that adsorption of HRP can be described by the Freundlich and Langmuir equations. 

The mathematical models that have been applied to the physical adsorption from liquid solutions are generally extensions of the theories that have been developed to describe the sorption of gases on solid surfaces with modifications to account for the competition between the solute and solvent for the adsorption sites. Two of these models have been applied to the adsorption isotherms of nonelectrolytes from solution they are the Langmuir model and the Brunauer, Emmett, and Teller (BET) model in addition the Freundlich empirical equation has also been used. In the Langmuir model it is assumed that the adsorbed species forms a monolayer on the surface of the adsorbent, that the adsorbed molecules... 

Adsorption from solutions was fully studied by G. C. Schmidt. He first showed that the adsorbed amount reaches a maximum, when the surface is saturated, and does not then increase if the concentration of the solution is increased (1910). He proposed an adsorption formula (1911) taking this into account, which he later modified (1916). Extensive researches carried out from 1906 by Freundlich showed that a thermodynamic theory given by J. W. Gibbs (1877, see p. 742) could be used as a guide. A modification of the adsorption equation (5), viz. xlm=kc f (6), applies to solutions, where adsorbed amount, m=mass of adsorbent, equilibrium concentration of solution, k and n are constants (i/n varies from o i to o-8). It was apparently first used by C. H. D. Bodeker, then by W. Biltz, and Freundlich. 

Adsorption isotherms on microcrystalUne carbons, which include charcoals, carbon blacks, and active carbons, from solutions of solids and liquids have been found to be of the forms shown in Figure 3.1. The Freundlich isotherm equation could be applied to isotherm 1(c), which is for solutions of solids of limited solubility. The other three forms of isotherms show a maximum in each case that could not be... 

Of the adsorption isotherms discussed above, the Langmuir equation is important because of its theoretical and conceptual contribution to the studies of adsorption and the kinetics of surface reactions. The Freundlich isotherm has found a wide use in correlating experimental data the Temkin isotherm is obeyed by certain systems [62-64], but it is expected to apply only in the intermediate range of coverage due to the simplifying assumptions made in its derivation. 

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