Freundlich equation adsorption isotherm

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... 

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. 

An adsorbed film obeys a modified Amagat equation of state, t(t = qkT (see Eq. ni-107). Show that this corresponds to a Freundlich adsorption isotherm (Eq. XI-12) and comment on the situation. 

The adsorption coefficients (K) were determined using the equation for the Freundlich adsorption isotherm ... 

Adsorption from liquids is less well understood than adsorption from gases. In principle the equations derived for gases ought to be applicable to liquid systems, except when capillary condensation is occurring. In practice, some offer an empirical fit of the equilibrium data. One of the most popular adsorption isotherm equations used for liquids was proposed by Freundlich 21-1 in 1926. Arising from a study of the adsorption of organic compounds from aqueous solutions on to charcoal, it was shown that the data could be correlated by an equation of the form ... 

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. 

Equation (135) is the well-known Freundlich adsorption isotherm. In a number of instances this isotherm accurately describes experimental data. The interpretation of the Freundlich adsorption isotherm as resulting from exponential nonuniformity of surface is due to Zel dovich 43). 

Experimental studies of the partitioning of sodium into aragonite, calcite, and dolomite have been carried out by White (1977, 1978), who concluded that the mode of substitution was as Na2CC>3 rather than as Na bicarbonate or hydroxide. The behavior of Na+ does not follow that normally described by a simple partition coefficient, but rather coprecipitation is better described by a Freundlich-type adsorption isotherm equation, implying that adsorption is important. 

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. 

Molecular or ion-pair adsorption The adsorption of potassium bromate on the surface of barium sulfate appears to involve the simultaneous occupation of adjacent sites on the crystal surface by potassium ions and bromate ions this is called an equivalent adsorption because equal amounts of the two ions are adsorbed. Such adsorptions, and in fact many molecular adsorption processes, follow an empirical equation known as the Freundlich adsorption isotherm ... 

Figure 6.2. Fit of the Freundlich adsoiption isotherm equation to copper adsorption by two soils. (From Kurdi and Doner, 1983.)...

If the Freundlich adsorption isotherm is valid than the adsorption rate is proportional to pressure and inversely proportional to a fractional power of surface coverage, giving the Bangham 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 relation between minimum anion activity necessary to inhibit pitting of 18-8 stainless steel in a solution of given CT activity follows the relation log (CT) = k log (anion) -i- const. The same relation apphes to inhibition of pitting of aluminum. The equation can be derived assuming that ions adsorb competitively in accord with the Freundlich adsorption isotherm [26]. 

The adsorption on a solid surface, the types of adsorption, the energetics of adsorption, the theories of adsorption, and the adsorption isotherm equations (e.g., the Langmuir equation, BET equation, Dubinin equation, Temkin equation, and the Freundlich equation) are the subject matter of Chapter 2. The validity of each adsorption isotherm equation to the adsorption data has been examined. The theory of capillary condensation, the adsorption-desorption hysteresis, and the Dubinin theory of volume fllhng of micropores (TVFM) for microporous activated carbons are also discussed in this chapter. 

In 1909, Freundlich gave an empirical expression representing the isothermal variation of quantity of gas adsorbed by unit mass of solid adsorbent with pressure. This equation is known as the Freundlich adsorption isotherm. The Freundlich adsorption isotherm is mathematically expressed for gas-phase adsorption as... 

The so-called Freundlich adsorption isotherm was also proposed by Boedecker in 1895 [109] as an empirical equation. This equation is known in literature as the Freundlich s equation, because Freundlich [110] assignated great importance to it and popularized its use. 

As already mentioned, the Freundlich adsorption isotherm, unlike the other ones in Table 4.2, does not become linear at low concentrations, but remains convex to the concentration axis. Moreover, it does not show saturation or limiting value. Hence, for the Freundlich adsorption isotherm in Table 4.2 F is a parameter scaling the adsorption (rather than saturation adsorption). This isotherm can be derived assuming that the surface (as a rule solid) is heterogeneous [18,19], Consequently, if the data fit the Freundlich equation, this is an indication, but not a proof, that the surface is heterogeneous [6]. 

It is possible to treat the adsorption of a liquid onto a solid surface in a manner analogous to that given for the solid-gas system. However, in the liquid state it is usually a solute which is removed by adsorption onto the solid surface. The Langmuir equation is applicable in most cases. In other cases where the surface is heterogeneous the Freundlich adsorption isotherm... 

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. 

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