Adsorption isotherm generalized Freundlich

In the case of multilayer formation, it is useful to express the coverage degree by 6 = V/Vm where denotes the volume of the adsorbed substance in a monolayer. Adsorption and desorption can be described as well as the kinetic and equilibrium process. Equilibrium is described by the general condition /( , p, T) = 0. The process is described either at a constant pressure (adsorption isobar) or constant temperature (adsorption isotherm). The most simple adsorption isotherm after Freundlich and Langmuir is based on the equilibrium... 

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... 

Freundlich adsorption isotherm — The empirical adsorption isotherm 0 = bcn (0 surface coverage, b and n are constant, 0 < n < 1, and c is the solution concentration) was initially proposed by Boedecker in 1895 [i], however it was popularized by -> Freundlich [ii], and today is generally referred to as the Freundlich adsorption isotherm [iii]. 

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. 

Of the equilibrium adsorption isotherms observed on real surfaces, three hold particular positions. They are the Temkin isotherm, the Freundlich isotherm, and the Dubinin-Ra-dushkevich isotherm, and are reviewed in Refs. [22, 23]. The analysis carried out in Ref. [24] of several previously reported, often quoted, adsorption systems has shown that the Freundlich and the Dubinin-Radushkevich isotherms are the high-pressure and low-pressure limits, respectively, of a unique isotherm referred to as FDR. In turn, the FDR isotherm is a special case of a more general isotherm proposed by Jajoniec [25] on the basis of a previous idea of Heer [26],... 

Empirical adsorption equilibrium models like Langmuir and Freundlich can generally be used to describe type I pure water vapour adsorption isotherms on aluminas [6] ... 

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 foregoing procedure will suffice to serve the needs of most general routine. In any fundamental study, however, it can be very helpful to know and fully understand a principle of measuring adsorption that is embodied in the Freundlich adsorption isotherm.1 6 This isotherm expresses the fact that for data on adsorption... 

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]. 

Liquid adsorption isotherms have many different shapes and may be quite complex. It is difficult to generalize over the whole range of possible concentrations. In dilute solutions, the common application in the chlor-alkali industry, the Freundlich isotherm fiequendy applies ... 

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... 

The Gibbs adsorption isotherm is vaUd generally for each phase boundary, but is used mainly for mobile phase interfaces (gas Uquid and liquid-hquid systems). Solid phase-gas phase systems do not use the variable F (as surface energy is not constant), but the amount of gas adsorbed (a), which depends on temperature and pressure. It represents the amount of adsorbate to the amount of solid adsorbent and is expressed mostly in moles or mass units. Adsorption can then be characterised, for example, by an empirical Freundlich isotherm a = (or in linearised form In [Pg.488]

The Freundlich adsorption isotherm is a special type of equilibrium relation of the general form ... 

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],... 

The linear equilibrium isotherm adsorption relationship (Eq. 11) requires a constant rate of adsorption, and is most often not physically valid because the ability of clay solid particles to absorb pollutants decreases as the adsorbed amount of pollutant increases, contrary to expectations from the liner model. If the rate of adsorption decreases rapidly as the concentration in the pore fluid increases, the simple Freundlich type model (Eqs. 8 and 9) must be extended to properly portray the adsorption relationship. Few models can faithfully portray the adsorption relationship for multicomponent COM-pollutant systems where some of the components are adsorbed and others are desorbed. It is therefore necessary to perform initial tests with the natural system to choose the adsorption model specific to the problem at hand. From leaching-column experimental data, using field materials (soil solids and COMs solutions), and model calibration, the following general function can be successfully applied [155] ... 

The early experimental data of Freundlich Eapillarchemie) indicated that the adsorption of a solute from a solution followed the general laws governing the adsorption of vapours by solids, i.e. the Freundlich isotherm... 

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