Adsorption isotherms Langmuir-Freundlich equation

The adsorption capacity of activated carbon may be determined by the use of an adsorption isotherm. The adsorption isotherm is an equation relating the amount of solute adsorbed onto the solid and the equilibrium concentration of the solute in solution at a given temperature. The following are isotherms that have been developed Freundlich Langmuir and Brunauer, Emmet, and Teller (BET). The most commonly used isotherm for the application of activated carbon in water and wastewater treatment are the Ereundlich and Langmuir isotherms. The Freundlich isotherm is an empirical equation the Langmuir isotherm has a rational basis as will be shown below. The respective isotherms are ... 

Table 1. The constants for adsorption isotherm in Freundlich and Langmuir equations.

The Mo adsorption process can be studied by using adsorption isotherms. Langmuir and Freundlich equations are the two major types of isotherms used to describe the Mo adsorption process. The Langmuir equation is based on the kinetic theory of gaseous adsorption onto solids, but is often used to model the adsorption of ions from solution (Ellis and Knezek, 1972). A common form of the Langmuir equation is... 

Fig. 14 Isotherms of pyridine adsorption on Li-ZSM-5 (sample No. 5) at various temperatures Ty and described by a Langmuir-Freundlich equation solid lines)...

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). 

For the reader s convenience, some of the most frequently used adsorption isotherms and surface equations of state (that of Henry, Langmuir, Freundlich, Volmer, Frumkin, and van der Waals) [35,49-51] are summarized in Table 1 the respective expressions for dT/ dc and the Gibbs elasticity, stemming from the various isotherms are also given F, Bf, and m are characteristic parameters of the Freundlich adsorption isotherm. 

Sorption and desorption are usually modeled as one fully reversible process, although hystersis is sometimes observed. Four types of equations are commonly used to describe sorption/desorption processes Langmuir, Freundlich, overall and ion or cation exchange. The Langmuir isotherm model was developed for single layer adsorption and is based on the assumption that maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, that the energy of adsorption is constant, and that there is no transmigration of adsorbate on the surface phase. 

Predominantly, Freundlich s fitted adsorption isotherms computed by means of simple linear regression were proposed for the mathematical description of the process studied. Unlike the Langmuir equation, the Freundlich model did not reduce to a linear adsorption expression at very low nor very high solute concentrations, as above resulted. 

Abstract Removal of the pesticide metobromuron from aqueous solutions by adsorption at the high area activated carbon cloth was investigated. Kinetics of adsorption was followed and adsorption isotherms of the pesticide was also be determined. In kinetic studies a special V-shaped cell with an UV cuvette attached to it was used for adsorption processes. With this cell it was possible to follow the concentration of pesticide molecule by in situ UV spectroscopy as it is adsorbed at the activated carbon cloth. The obtained absorbance vs time data were converted into concentration vs time data and these data were treated according to pseudo-first-order and psendo-second-order kinetic models. Adsorption of that pesticide was fonnd to follow second-order kinetic model with k 87.35 g mol min. Adsorption isotherms were derived at 25°C on the basis of batch analysis. Isotherm data were treated according to Langmuir and Freundlich models. The fits of experimental data to these equations were examined and founded that the adsorption isotherm was well represented by Frenndlich model. 

It will be noted that the universal isotherm equation as written here has formal similarity to pressure explicit forms of Langmuir, Langmuir-Freundlich and LRC models. One key advantage of the universal form is that the heat of adsorption and the adsorption equilibrium are bound to be self-consistent. 

Fig. 5.2 Typical adsorption isotherms described by (a) Langmuir, (b) Freundlich and (c) BET equations (Yaron et al. 1996)...

The adsorption data is often fitted to an adsorption isotherm equation. Two of the most widely used are the Langmuir and the Freundlich equations. These are useful for summarizing adsorption data and for comparison purposes. They may enable limited predictions of adsorption behaviour under conditions other than those of the actual experiment to be made, but they provide no information about the mechanism of adsorption nor the speciation of the surface complexes. More information is available from the various surface complexation models that have been developed in recent years. These models represent adsorption in terms of interaction of the adsorbate with the surface OH groups of the adsorbent oxide (see Chap. 10) and can describe the location of the adsorbed species in the electrical double layer. 

The Freundlich equation proved to be applicable to the adsorption of liquids with only limited ranges of concentration. It was replaced by the Langmuir equation (see later on) and others which had a theoretical basis in the kinetic theory of gases. It is clear that neither the Freundlich nor the Langmuir equation can describe isotherms of the shape shown in Figure 10.5. 

Note that this Kid value is significantly smaller than the Kjd obtained in the linear part of the isotherm (i.e., at low 1,4-DNB concentrations). Furthermore, as can be seen from Fig. 2, the Freundlich equation overestimates C(S (and thus Kid) at both the low and the high end of the concentration range considered. In fact, inspection of Fig. 2 reveals that at very high concentrations, the K+-illite surface seems to become saturated with 1,4-DNB, which is not surprising considering that only limited adsorption sites are available. In such a case, the sorption isotherm can also be approximated by a Langmuir equation (Eq. 9-3). 

Adsorption isotherm An equation or distribution on a graph representing the concentration of an adsorbed chemical species as a function of its concentration in an associated aqueous solution. Adsorption isotherms are measured in systems that are at equilibrium and where temperature, pressure, and possibly other conditions are held constant. Isotherms are often described with linear, Freundlich, or Langmuir equations. 

Freundlich isotherm An equation for an adsorption isotherm in the form of Cads = Kf(Cso n)n (if n = 1, the distribution is linear, see Chapter 2 for details), which describes the distribution of a chemical species between an adsorbent and an associated solution under equilibrium conditions. Some adsorption isotherms are better described with the Langmuir isotherm. 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

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],... 

There have been numerous attempts to assign mathematical isothermal adsorption relations to various experimental data. Among the most frequently used isotherm equations are Langmuir, Freundlich, and BET. 

The more desirable approach is to determine f(Q) from an assumed 0(P,T,Q) and the experimental adsorption isotherm. Sips (16) showed that Equation 1 could be treated by a Stieltjes transform, so that in principle an explicit function could be written for f(Q), provided the experimental isotherm function, 0, could be expressed in analytical form. Subsequently, Honig and coworkers (10, 11, 12) investigated this approach further. The difficulty is that only for certain types of assumed functions 0 and 0 is the approach practical. As a consequence the procedure has been first to restrict the choice of 0 to the Langmuir equation, and second to assume certain simple functions for 0 such as the Freundlich and Temkin isotherm equations. The system is thus forced into an arbitrary mold and again it is not certain how much reliance should be placed on the site energy distributions obtained. 

The best results to describe the adsorption isotherm by the selected isotherm equations were achieved by the Toth model. The Freundlich model showed in some cases a lack of flexibility in describing the region were the linear behaviour changed to saturation behaviour (22 MPa) and the Langmuir-model in some cases had difficulties in describing the region were the adsorbate is saturated (16 MPa). 

The Freundlich equation, unlike the Langmuir one, does not become linear at low concentration but remains concave to the concentration axis, nor does it show a saturation or limiting value. Roughly speaking krf gives a measure of the adsorbent capacity and slope n, of intensity of adsorption. The shape of isotherm is such that n is less than unity. 

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. 

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