Adsorption isotherms generalized Freundlich equation

The special forms of the MJ isotherm (61) have been frequently used to study adsorption from solution generalized Freundlich equation [199], Langmuir-Freundlich isotherm [170,200-205],... 

Equation 10.27 is generally known as Freundlich equation. Equation 10.27 with concentration replaced by pressure was also used to describe the adsorption isotherms of gases on solids, suggesting the incorrect idea that adsorption from solution by a solid could be paralleled with gas or vapor adsorption on the same adsorbents. Whereas in some cases the restriction to dilute solutions was imposed by the solubility of solids (e.g., benzoic acid in water or stearic acid in benzene) it was not imposed on the investigation of mixtures of completely miscible liquids, e.g., acetic acid in water. 

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... 

The variation of adsorption with pressure at a given constant temperature is generally expressed graphically as shown in the figure given above. Each curve is known as adsorption isotherm for a particular temperature. The relation ship between the magnitude of adsorption and pressure can be expressed mathematically by a empirically equation commonly known as Freundlich adsorption isotherm, viz. 

In the theories of gas adsorption the applicability of Freundlich equation was long ago associated with the energetic heterogeneity of the adsorption sites on the actual solid surfaces. It was also known, that Freundlich equation is a simplified form of a more general isotherm equation which is now commonly called Langmuir-Freundlich isotherm. Thus, in 1980 Sposito [13] suggested that it was high time it were used also in the case of ion adsorption at water/oxide interfaces. 

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. 

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 isotherms are used for determining the sorption of organic chemicals by wetland soil. Sorption data are generally described by using either the Freundlich or the Langmuir equation. 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

The Freundlich equation is very popularly used in the description of adsorption of organics from aqueous streams onto activated carbon. It is also applicable in gas phase systems having heterogeneous surfaces, provided the range of pressure is not too wide as this isotherm equation does not have a proper Henry law behaviour at low pressure, and it does not have a finite limit when pressure is sufficiently high. Therefore, it is generally valid in the narrow range of the adsorption data. 

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... 

Though the suggestions of Sips were received well, by Sips himself who proposed a generalized Freundlich isotherm, by Misra who considered a kind of generalized DR equation, by Rudzinski and co-workers who extended the method to multilayer adsorption, and by Toth et who... 

A plot of log(A /m) against log c should be linear, with an intercept of log a and slope of Xjn-, it is generally assumed that, for systems that obey this equation, adsorption results in the formation of multilayers rather than a single monolayer. Figure 6.17 shows Freundlich isotherms for the adsorption of local anaesthetics on activated carbon the method of calculating the constants a and jn from these plots is given in Example 6.5. 

Equation 2.66 shows that the velocity of a chemical solute concentration Vq is slower than the solution (water) velocity v by a retardation factor Rq. The retardation is caused by the adsorption of the chemical on the solid. Adsorption can be defined using the Freundlich isotherm or Langmuir isotherm. The general form of the Freundlich isotherm is... 

The BET model has been generalized by using of various monolayer isotherms for heterogeneous surfaces Langmuir-Freundlich [94], Toth [95], generalized Freundheh (GF) [94], Dubinin-Radushkevich [67,95,96], and others [5]. These equations have been apphed to the interpretation of experimental data [5,6]. The above-discussed procedure has also extended to the adsorption with lateral interactions on randomly heterogeneous surfaces also [5]. 

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