Freundlich adsorption equation

The dissolution of passive films is, in the main, controlled by a chemical activation step in contrast to film-free conditions at. Many protective anodic films are oxides and hydroxides whose dissolution depends upon the hydrogen ion concentration, and the rate follows a Freundlich adsorption equation ... 

The isosteric heats of adsorption, AH so, were calculated as a function of nitrogen loading for each of the samples tested. For each sample, the AHiS0 was found to decrease logarithmically with increased loading and this functionality is consistent with the assumptions of the Freundlich adsorption equation. As before, the brevity of presentation, the heat of adsorption data were curve fitted to an equation of the form ... 

Bacterial sorption of some metals can be described by the linearized Freundlich adsorption equation log S = log K+n log C, where S is the amount of metal absorbed in pmol g, C is the equilibrium solution concentration in pmol L, and K and n are the Freundlich constants. 

Phosphate behavior is also described by Langmuir and Freundlich adsorption equations, although these models may be too simple to accurately explain soil phosphate behavior. Kinetic models of phosphate retention by soils are also being employed. Although kinetics can suggest retention mechanisms, the complexity of soil-phosphate behavior makes this prospect difficult to achieve. 

Discussion. The adsorption isotherms obtained for Sevin, baygon, pyrolan, and dimetilan on bentonite and kaolinite conformed with the Freundlich adsorption equation. 

Freundlich adsorption equation, although successful to explain many solution adsorption data, has failed to explain the data at very high and low concentrations. This is perhaps due to the fact that the Freundlich equation is empirical in nature and thermodynamically inconsistent at high and low concentrations. Thus, a theoretical analysis of adsorption from solution and the derivation of a suitable equation have been comparatively difQcult as both the components of the solution compete with each other for the available surface. Moreover, the thermal motion of the molecules in the liquid phase and their mutual interactions are much less well understood. It is, therefore, difQcult to correctly assess the nature of the adsorbed phase, whether monomo-lecular or multimolecular. The nature of the phase is usually determined by the nature of the carbon as well as by the nature of the components of the solution, the concentration of the solution, and the mutual solubility of the components. 

Ashley et al. studied the adsorption of S.triazines and their metabolites on granulated and powdered activated carbons at pH 7 and 9. The equilibrium adsorption data followed the Freundlich adsorption equation. The adsorption of S.triazine, and its metabolites diethyl atrazine and diisopropyl atrazines, was different on GAC and PAC and at different pH values. 

Usmani and Wahab ° determined the adsorption of lower aliphatic and some organic unsaturated fatty acids from their aqueous solutions on activated carbons prepared from wood, rice husk, and lignite coal. The adsorption depended on the porosity and the chemical stfucture of the carbon surface. It was also found that for a given acid the adsorption depended on the polarity of the carboxylic group, the length of the side chain, and the nature of the type of bonding. The adsorption followed both the Langmuir and the Freundlich adsorption equations. 

In a special case, when the variation in b is attributed entirely to the variation in the heat of adsorption, the solution to the Langmuir adsorption equation can be reduced to the Freundlich adsorption equation [12] ... 

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. 

In a study of adsorption of organic herbicides by montmorillonite, Bailey and colleagues138 found that none of the compounds conformed to the Langmuir adsorption equation. Of the 23 compounds tested, only a few did not conform well to the Freundlich equation. 

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

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

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) ... 

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). 

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... 

Freundlich,1 Rideal,2 and Hiickel3 have summarized the results of adsorption measurements on porous substances. Very roughly, it may be said that the ease of adsorption is proportional to the ease with which the gases can be liquefied, a fact which has been held to indicate that there is sometimes actual condensation of vapour in the smallest pores. Numerous empirical formulae, of which Freundlich s equation ( 9) is the best known, have been developed, but. none seem to fit the data with any accuracy over a considerable range of pressures. 

The treatment of Freundlich adsorption also becomes tractable only by making the assumption that the extents of adsorption are small. This leads to the kinetic equations... 

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. 

Equation 6.9 is the same as the Freundlich empirical equation 6.1. This agreement was taken as a proof for the theory of monomolecular adsorption advanced by Langmuir. 

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