Freundlich maximum adsorption

Sorption and desorption are usually modeled as one fully reversible process, although hystersis is sometimes observed. Four types of equations are commonly used to describe sorption/desorption processes Langmuir, Freundlich, overall and ion or cation exchange. The Langmuir isotherm model was developed for single layer adsorption and is based on the assumption that maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, that the energy of adsorption is constant, and that there is no transmigration of adsorbate on the surface phase. 

The main limitation of the Freundhch equation is that it does not predict a maximum adsorption capacity, because linear adsorption generally occurs at very low solute concentration and low loading of the sorbent. However, in spite of this limitation, the Freundlich equation is used widely for describing contaminant adsorption on geosorbents. 

The frequent good fit of adsorption data to the Freundlich equation is influenced by the insensitivity of log-log plots and by the flexibility afforded curve fitting by the two empirical constants K and n. This flexibility does not guarantee accuracy, however, if the data are extrapolated beyond the experimental range. The Freundlich equation has the further limitation that it does not predict a maximum adsorption capacity, however mythical the adsorption maximum may be. Despite its shortcomings, the Freundlich equation is a common adsorption equation and is included in several models for predicting pesticide behavior in soil. 

The Freundlich isotherm has no definite maximum adsorption or saturation value therefore, when 0 approaches a monolayer, the Freundlich equation necessarily breaks down. For high coverages the exponential distribution function is conveniently replaced by a linear distribution... 

Beside kinetic and thermodynamic studies, equilibrium studies were done in order to determine the influence of the initial concentration of the metals ions upon the efficiency of the adsorption process and in order to determine the maximum adsorption capacities of the phosphorylated chitin and chitosan materials in the removal process of various metal ions from aqueous solutions. The experimental equilibrium data were fitted to the Langmuir and Freundlich isotherms. In all the cases the experimental results showed a better fit to the Langmuir than to the Freundlich equation. The maximum adsorption capacities obtained from the Langmuir isotherm plot in the... 

It can be shown that when 0 = noQadm> this corresponds to maximum adsorption, i.e., 0 = 1, so this equation can be normalized to (KoP) " , which is the form of the empirical Freundlich isotherm given by equation 5.56. 

We wUl now touch upon some of these factors. First, let s look at what we mean by system isotherm. Freundlich liquid phase isotherm studies can be used to establish the adsorptive capacity of activated carbon over a range of different concentrations. Under standard conditions, the adsorptive capacity of activated carbon increases as the concentration increases, until we reach a point of maximum saturation capacity. An example of an isotherm for phenol is shown in Figure 8. 

The Freundlich liquid phase isotherm can be used to determine the effect of solubility on the adsorptive capacity of activated carbon over a range of different concentrations. Phenol is highly soluble due to its polar nature whilst, in comparison, tetrachloroethylene (PCE) has a low solubility due to being non-polar. In the isotherms illustrated, the concentration of phenol is low relative to its solubility limit and consequently, the adsorptive capacity peaks at 18% maximum (see Figure 9). In comparison the concentration of tetrachloroethylene is relatively close to its solubility limit and, accordingly, the adsorptive capacity is exceptionally good. 

A plot of C/-SC versus C will produce a straight line with slope 1/ST and y intercept of 1/KlSt (Fig. 4.21). Such a plot will allow one to determine the so-called adjustable parameters, ST and KL. Note that both the Freundlich equation and the Langmuir equation produce a surface adsorption affinity constant, but the latter (Langmuir) also produces the often-sought adsorption maximum (ST). 

The Freundlich isotherm and the distribution coefficient K,i) adsorption models assume an infinite number of sorption sites are available, whereas the Langmuir i.sotherm and ion-exchange models assume a limited or maximum number ol sorption sites. Write sorption reactions that correspond to each of these models and explain the above statements in terms of those reactions. 

Henry and Freundlich isotherms did not provide for C. value growth limit. Irving Langmuir (1881-1957) in 1916 introduced such limit C and proposed a more complex but more accurate equation. He viewed the adsorption balance as a result of the competition between the rates of adsorption and desorption. If maximum adsorbent capacity relative component i is j> it may be assumed that the adsorption rate is proportion-... 

Doping dodecyl benzene sulfonic acid (DBSA) into PANI/carbon nanotube composite can fabricate PANI/carbon nanotube-DBSA nanocomposite [56]. The preparation, as well as the adsorption to Cr(VI), is depicted in Figure 11.11 with the pseudo-second-order kinetics and Freundlich isotherm model with maximum monolayer adsorption capacity of 55.55 mg/g. Electrostatic interactions between PANI and Cr(VI) anions are the predominant driving forces for this adsorption process. 

Adsorption from solutions was fully studied by G. C. Schmidt. He first showed that the adsorbed amount reaches a maximum, when the surface is saturated, and does not then increase if the concentration of the solution is increased (1910). He proposed an adsorption formula (1911) taking this into account, which he later modified (1916). Extensive researches carried out from 1906 by Freundlich showed that a thermodynamic theory given by J. W. Gibbs (1877, see p. 742) could be used as a guide. A modification of the adsorption equation (5), viz. xlm=kc f (6), applies to solutions, where adsorbed amount, m=mass of adsorbent, equilibrium concentration of solution, k and n are constants (i/n varies from o i to o-8). It was apparently first used by C. H. D. Bodeker, then by W. Biltz, and Freundlich. 

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