Equilibrium adsorption isotherm Freundlich

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],... 

Figure 6. Coupled hydrology and geochemistry of the adsorption and displacement of U(VI) through the Plio-Pleistocene Unit, (a) Equilibrium adsorption isotherm showing both Freundlich and linear fits, (b) Observed (points) and modeled (lines) of the displacement of nonreactive tracer Br and U through repacked sediments, (c) Observed (points) and modeled (lines) of the displacement of multiple nonreactive tracers through the intact core, under saturated and unsaturated conditions. The displacement of U occurred under...

Free gel was added to definite concentrations of the MB solutions (2-20 mg/1) at room temperature and was noted for its adsorption. It is clear from Figure 13.3 that the dye adsorption increases sharply with an increase in the initial dye concentration. When Cq was reached at 5 ppm and 10 ppm, the was reached at 10.04 and 20.81 respectively, which were much higher than reported Qe values of other adsorbents (Table 13.3). Equilibrium adsorption isotherm is an important criterion to determine the mechanism of dye adsorption on hydrogel. The Langmuir and Freundlich models are widely used to examine the adsorption isotherms. Freundlich isotherm models are based on the assumption that the surface of the adsorbent is not homogeneous. The experimental data in Figure 13.3 was also analyzed with the Freundlich isotherm model, which describes a heterogeneous system with multilayer adsorption. The linear form of Freundlich isotherm equation... 

For different acceptor particle adsorption isotherms expressions (1.85) - (1.89) provide various dependencies of equilibrium values of <7s for a partial pressure P (ranging from power indexes up to exponential). Thus, in case when the logarithmic isotherm Nt InP is valid the expression (1.85 ) leads to dependence <75 P" often observed in experiments [20, 83, 155]. In case of the Freundlich isotherm we arrive to the same type of dependence of - P" observed in the limit case described by expression (1.87). 

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 ... 

A number of attempts have been made to modify the IAS model (Eqs. 22-29) to improve its accuracy and reduce computational efforts. Using the IAS model, DiGiano et al. [80] derived a Simplified Competitive Equilibrium Adsorption Model (SCAM). This model, which is based on the Freundlich isotherm, assumes the single-solute isotherms of all the components are equal and it utilizes average isotherm constants when this assumption is not valid. The IAS model equations have been reduced to a single expression ... 

Of the various equilibrium and non-equilibrium sorption isotherms or sorption characteristics models, the most popular are the Langmuir and Freundlich models. The correct modeling of an adsorbate undergoing both transport and adsorption through a clay soil-solid system necessitates the selection of an adsorption isotherm or characteristic model which best suits the given system. The use of an improper or inappropriate adsorption model will greatly affect the... 

When measured adsorption data are plotted against the concentration value of the adsorbate at equilibrium, the resulting graph is called an adsorption isotherm. The mathematical description of isotherms invariably involves adsorption models described by Langmuir, Freundlich, or Brauner, Emmet and Teller (known as the BET-model). Discussion of these models is given in Part 111, as conditions relevant to chemical-subsurface interactions are examined. 

Estimate the equilibrium concentration of the solution. An adsorption isotherm of the Freundlich type is given as... 

It can be easily seen that if adsorption equilibrium follows the Freundlich isotherm, then r will be proportional to 0". According to (143), (145), and (160),... 

Manganese oxides As(lll) and As(V) removal by Mn02(s) is similar, up to 5 mmol As mol-1 Mn at micromolar As equilibrium solution concentrations. Freundlich isotherm obeyed. As(lll) oxidized to As(V). Rapid oxidation (minutes) and adsorption of As(lll). Monitored Mn release and effect of pH, Ca, phosphate, and sulfate Driehaus, Seith and Jekel (1995)... 

Adsorption isotherm An equation or distribution on a graph representing the concentration of an adsorbed chemical species as a function of its concentration in an associated aqueous solution. Adsorption isotherms are measured in systems that are at equilibrium and where temperature, pressure, and possibly other conditions are held constant. Isotherms are often described with linear, Freundlich, or Langmuir equations. 

Freundlich isotherm An equation for an adsorption isotherm in the form of Cads = Kf(Cso n)n (if n = 1, the distribution is linear, see Chapter 2 for details), which describes the distribution of a chemical species between an adsorbent and an associated solution under equilibrium conditions. Some adsorption isotherms are better described with the Langmuir isotherm. 

The adsorption capacity of activated carbon may be determined by the use of an adsorption isotherm. The adsorption isotherm is an equation relating the amount of solute adsorbed onto the solid and the equilibrium concentration of the solute in solution at a given temperature. The following are isotherms that have been developed Freundlich Langmuir and Brunauer, Emmet, and Teller (BET). The most commonly used isotherm for the application of activated carbon in water and wastewater treatment are the Ereundlich and Langmuir isotherms. The Freundlich isotherm is an empirical equation the Langmuir isotherm has a rational basis as will be shown below. The respective isotherms are ... 

Secondly, the adsorption equilibrium on a sparsely covered surface is approximately proportional to the square root or to the cube root of the equilibrium pressure, tending, however, to follow a lesser power of the equilibrium pressure at higher coverage. This nearly corresponds to the Freundlich type of adsorption isotherm. From this Kwan suggests... 

The co-ordinates of the adsorption isotherms, i.e. C, the equilibrium concentration of adsorbate in the solution phase (p ml) and X, the equilibrium concentration of adsorbate in the adsorbed phase (pg/g), were inserted into the Freundlich... 

As described earlier, the relation between the amount of substance adsorbed by an adsorbent and the equilibrium pressure or concentration at constant temperature is called the adsorption isotherm. The adsorption isotherm is the most important and by far the most often used of the various equilibria data that can be measured. To represent the variation of the amount of adsorption per unit area or unit mass with pressure, Freundlich proposed the equation... 

Adsorption isotherms are typically used to describe the equilibrium relationship between the bulk aqueous phase activity (concentration) of the adsorbate and the amount adsorbed on the interface at a given temperature. The more common models used are empirical models such as the linear model and the Freundlich model. First principles models such as the Langmuir model are also used. 

Experiments were performed on the removal of Cu" from aqueous solution at pH 1.5 and 25 C with the Dowex XFS 4195.02. These data allowed the development of a mathematical equation describing the isotherm equilibrium adsorption of Cu, using the Freundlich equation. These results are shown in Figure 1. 

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 adsorption isotherm for Chrysophenine G, which is shown in Fig. 16.1 and is typical of that obtained with most direct dyes, corresponds with the Freundlich equilibrium. This indicates that with the direct dyes opportunity for hydrogen bonding and Van der Waals forces to bind the dye are, for practical purposes, almost unlimited. The limitation which is imposed is the available surface for attachment, but this does not terminate... 

An adsorption isotherm relates the amount of the substance adsorbed at thermodynamic equilibrium to the amount present in the liquid or gas stream (concentration or partial pressure) at a constant temperahue. Langmuir and Freundlich isotherms are the most common adsorption isotherms. 

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