Freundlich’s isotherm

Next we consider Freundlich s isotherm. In this case it makes sense to suppose that k — k k Rc and ki and k of order 1. Then we get once more Equation (26) but with 0(m) = k U. ... 

The parameter La is also called the separation factor and provides a quantitative description of the equilibrium regions La = 0 for irreversible, La< 1 for favorable, La = 1 for lineal-, and La > 1 for unfavorable adsorption. The same holds for Fr in Freundlich s isotherm. 

It was stated, that macroporous carbons of plant origin show better properties in dynamic than in static conditions. It is cormected with relationship of quantity of macropores and diffusion rate. Greater differences in classsification are observed at lower equilibrium concentrations (0,1 and 0,01 mg/dm ) in static adsorption. Therefore direct factors of Freundlich s isotherms influencing adsorption capacities at different concentrations should be considered. It was stated that angle of slope, adsorption rate in static conditions, shape of breaktrough curves in dynamic conditions... 

Table IV. Parameters of Freundlich s Isotherm for Sevin, 1-Naphthol, Baygon, Pyrolan, and Dimetilan on Kaolinite and Bentonite...

The study of the phosphorus adsorption in the Changjiang River Estuary sediments showed that the sediments were buffers to phosphate and the balance time of phosphorus adsorption (desorption) was about 6 h. The saturated adsorption quantity of phosphorus was about 600 pg/g and the saturated desorption was about 126.37 pg/g. The apparent adsorption heat of fine sediments (AH) was 47.59 kJ/mol. The adsorption of phosphate was in accordance with Freundlich s isothermal equilibrium and it was a heat absorption reaction. The contents of sand and mud in sediments had some influence on adsorption and the adsorption would decrease with the increase in sand or mud content. In general, the increase in pH favors adsorption. Moreover, the increase in salinity does not favor adsorption but favors desorption. The research shows that the release of phosphorus in the sediments of the Changjiang River Estuary... 

Predominantly, Freundlich s fitted adsorption isotherms computed by means of simple linear regression were proposed for the mathematical description of the process studied. Unlike the Langmuir equation, the Freundlich model did not reduce to a linear adsorption expression at very low nor very high solute concentrations, as above resulted. 

Numerous examples of adsorption isotherms are to be found in Freundlich s Kapillarchemie. 

In this case it is difficult to separate isotherms that belong to certain centers. Adsorption isotherms of an empirical character are described by Freundlich s equation4,81,82) ... 

It is of interest to examine what equation of state of the adsorbed film would follow if the relation between the amount adsorbed and the vapour pressure or activity in solution obeyed Freundlich s adsorption isotherm (Chap. VII,... 

The Adsorption isotherm . The relation between the amount adsorbed and the pressure in the gas, the adsorption isotherm is a complicated one, and depends on the nature of the solid surface, on its homogeneity or otherwise (and few, if any, solid surfaces are homogeneous), and of course on the forces between gas molecules and solid, which depend on the chemical nature of the gas. For many porous, and some other, solids, a first approximation is given by Freundlich s well-known equation if x is the amount of gas adsorbed, and p the pressure of the gas,... 

Two functions, Freundlich s and Langmuir s adsorption isotherms, are used to describe adsorption (see Figure 8.7). The former is more often used ... 

Figure 8.7 Two adsorption isotherms according to Freundlich s formula with (1) k = 3 and n = 0.8 and (2) k = 5 and n = 0.3. A Langmuir s isotherm is shown by line 3, with a = 0.2 and b = 30. The scales have arbitrary units. Experiments must be done in order to find the best relation.

Type I isotherms can be approximated by simple equations. The two most common ones are Freundlich s [19] and Langmuir s [20,21] (see also any textbook on physical chemistry) ... 

Isotherms for propene adsorption on NiO, vanadium pentoxide, and cuprous oxide at 100° are shown in Fig. 2. All isotherms are described by Freundlich s equation and correspond to a heterogeneous surface with exponential distribution as to heats of adsorption. 

The determination of adsorption capacities in multicomponent solutions requires an appropriate description of the single solute isotherm. Freundlich s model may be selected, with the division of isotherms into linear concentration ranges introduced 1 Tien [3],... 

Equations (3.75) and (3.76) are valid only if the partition coefficient Kr, does not depend on the contents of the sorbate proper and water composition, i.e., corresponds with Henry s adsorption isotherm. This is possible at very low concentrations of an adsorbed component. At high concentrations, when adsorption corresponds with Freundlich, Langmuir isotherms or depends on ion exchange with another component, the retardation factor is expressed much more complexly. For Freundlich isotherm (equation (2.177)), the retardation factor may be estimated from equation... 

Uptake experiments were carried out on cultures of a planctonic alga, Scenedesmus obliquus, exposed to i Ag at different stages of development . The accumulation of the radionuclide was rapid and intense, and equilibrium was reached in an exposure time of less than 24 hours. The uptake kinetics showed the algal concentration level to be dependent only on the medium concentration and on the cell development at the time of 0 Ag addition. Passive uptake was described by Freundlich adsorption isotherms. During the depuration phase the Ag retention by S. obliquus developed in accordance with an exponential model based on the existence of two biological half-hves i.e. a very short one of a few seconds and a longer one of 115 h. In a similar study the radioactivity of sea water was determined by studying the concentration of metals in squid livers and the distribution of Ag in them. 

Umpleby II, R.J. Baxter, S.C. Bode, M. Berch, J.K. Shah, R.N. Shimizu, K.D. Application of the Freundlich adsorption isotherm in the characterization of molecularly imprinted polymers. Anal. Chim. Acta 2001, 435, 35-42. 

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. 

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