Freundlich isotherm Equation

Data for adsorption isotherms can often be correlated by the Freundlich Isotherm Equation. For adsorption from... 

Table 21.2 The parameters of Langmuir and Freundlich isotherm equations for the adsorption of eateehol and resoreinol...

There exists an equilibrium at the interface between a charged suspension and its solution consisting of a dynamic interchange of both cation and anion. If the suspension be positively charged the adsorption of the positive ion is greater than that of the negative at that particular concentration. On application of the Freundlich isotherm equation to each ion... 

Freundlich Adsorbents that follow the Freundlich isotherm equation are assumed to have a heterogeneous surface consisting of sites with different adsorption potentials, and each type of site is assumed to adsorb molecules, as in the Langmuir equation (Perry and Green, 1999) ... 

Sorption is measured by recording sorption isotherms, which themselves are a way to express the amount of surfactant sorbed as function of the concentration of the compound in the solution. The Freundlich isotherm (Equation II) is a general sorption isotherm which describes sorption behavior and often is used in studies of surfactant sorption. KF is the Freundlich sorption coefficient which expresses the affinity of a surfactant for a given solid... 

This equation has been successfully applied to many sorption and desorption reactions of dissolved metals and organic compounds. In the case of irreversible sorption (hysteresis), sorption and desorption isotherms are not identical. However, both sorption and desorption Freundlich isotherm equations can be substituted into the transport equation(2) ... 

Figure 2.3 Freundlich isotherm [Equation (2.12)] plots for Xe and Kr adsorption on volcanic ash shale. Reproduced from Fanale and Cannon (1971).

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],... 

Equation 4.27 has the form of the generalized Freundlich isotherm equation.11 If the product A[C]cb < < 1, it reduces to the van Bemmelen-Freundlich isotherm equation and, ifb 1, it becomes the Langmuir isotherm equation (cf. Eq. 3.50b).M Thus Eq. 4.18 and a gamma distribution of the two rate coefficients it contains are sufficient to generate three very common adsorption... 

Generalize the derivation of Eq. 4.27 to include the dissociable species QzQ(aq) in Eq. 4.3. Show that the result is the generalized competitive Freundlich isotherm equation ... 

Modifications to the Langmuir and Freundlich isotherm equations have been made to extend their flexibihty for accomodating the effects on As adsorption of pH variability (Anderson et al., 1976) and ionic competition (Kingston et al., 1971 Roy et al., 1986a). However, even these modified equations are limited in their abihty to simulate As adsorption in complex natural environments. 

The simplest mathematical models to describe sorption from solution are the so-called isotherm equations. The simplest of these is the Freundlich isotherm equation, which may be written ... 

I.2. Freundlich Adsorption Isotherm Equation The Freundlich adsorption isotherm equation is the oldest of the nonlinear isotherms, and its use implies heterogeneity of adsorption sites. The Freundlich isotherm equation is... 

As in the single-stage analysis, and assuming a Freundlich isotherm. Equations... 

At equilibrium, the uptake of a dissolved compound can often be expressed in the simple terms of the Freundlich isotherm equation. 

Equations (3.75) and (3.76) are valid only if the partition coefficient Kr, does not depend on the contents of the sorbate proper and water composition, i.e., corresponds with Henry s adsorption isotherm. This is possible at very low concentrations of an adsorbed component. At high concentrations, when adsorption corresponds with Freundlich, Langmuir isotherms or depends on ion exchange with another component, the retardation factor is expressed much more complexly. For Freundlich isotherm (equation (2.177)), the retardation factor may be estimated from equation... 

This is required by the integration procedure of Eq. (2)m calculating the spreading pressure. For example, the Freundlich isotherm equation,... 

The Freundlich isotherm equation, which is empirical, often approximates data for many physical adsorption systems and is particularly useful for liquids. 

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... 

Urano et al. combined the generalizations of the Polanyi potential theory and the Freundlich isotherm equation to derive a relationship that these workers claimed could successfully predict the adsorption isotherms for several organic compounds from aqueous solutions on active carbons. Their adsorption equation is represented as... 

Kitagara ° nsed two commercial granular activated carbons for the adsorption of phenol, p.nitrophenol, and 2,4 dichlorophenol from aqueous solutions, and found that the adsorption data could be explained by the Freundlich isotherm equation. The adsorption at a given concentration decreased with increase in the temperature of adsorption, although the rate of adsorption increased with increase in the adsorption temperature. Scharifov derived a mathematical model for the adsorption of phenols by activated carbons from aqueous solutions and obtained an equation for the static adsorption isotherm, which could help in the calculation of adsorption of phenol at any concentration. Chakravorti and Weber used batch and fixed-bed systems for the removal of phenol from aqueous solutions by activated carbons. The pore-diffusion model and a homogenous solid model were used to explain the results. 

The Freundlich isotherm equation is a limiting form of the Langmuir isotherm and is applicable only in the middle ranges of vapor pressure. The equation is of greater significance for chemisorption, although some physical adsorption data have also been found to fit this equation. 

Free gel was added to definite concentrations of the MB solutions (2-20 mg/1) at room temperature and was noted for its adsorption. It is clear from Figure 13.3 that the dye adsorption increases sharply with an increase in the initial dye concentration. When Cq was reached at 5 ppm and 10 ppm, the was reached at 10.04 and 20.81 respectively, which were much higher than reported Qe values of other adsorbents (Table 13.3). Equilibrium adsorption isotherm is an important criterion to determine the mechanism of dye adsorption on hydrogel. The Langmuir and Freundlich models are widely used to examine the adsorption isotherms. Freundlich isotherm models are based on the assumption that the surface of the adsorbent is not homogeneous. The experimental data in Figure 13.3 was also analyzed with the Freundlich isotherm model, which describes a heterogeneous system with multilayer adsorption. The linear form of Freundlich isotherm equation... 

The Freundlich isotherm [equation (4)] is perhaps the simplest such equation (see Section 1). It may be written in the generalized form as presented by Sips -" ... 

The Freundlich isotherm equations do not have the surface area explicitly as a parameter in the equations. Therefore, the surface area cannot be determined using these equations. 

This is a purely empirical formula, where the term Vads represents the adsorbed amount, p the adsorptive pressure, whereas k and n are suitable empirical constants for a given adsorbent-adsorbate pair at temperature T. The adsorbed amount are normalized either to the mass of the adsorbent or to the exposed surface area. As an example see. Fig. 1.6a, where the adsorption volumetric isotherms of H2O on H—BEA zeolite are reported the experimental points were interpolated by the Freundlich isotherm equation. The Freundlich isotherm assumes that the adsorption enthalpy AaH (per site) varies exponentially with increasing equilibrium pressure. In fact, the experimental points in the correspondent heat of adsorption versus coverage plot were properly interpolated by an exponential fitting, as illustrated in Fig. 1.15 (vide infra Sect. 1.4.2.3). 

---