Rate Freundlich isotherm

Recent reports on biosorbents based on diverse types of macrophytes are found widely in the literature. Free-floating aquatic plants from the genera Salvinia, Azolla, Eichhornia, Lemna, and Pistia have been described the most. S. natans biomass was able to uptake As(V) at low initial concentrations from 0.25 to 2 mg/L (74.8% and 54%, respectively). The experimental data fitted well to both Langmuir and Freundlich isotherms. The effect of pH and biomass quantities on sorption rate has also been investigated along with some metabolic parameters.105... 

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

Loukidou et al. (2005) fitted the data for the equilibrium sorption of Cd from aqueous solutions by Aeromonas caviae to the Langmuir and Freundlich isotherms. They also conducted, a detailed analysis of sorption rates to validate several kinetic models. A suitable kinetic equation was derived, assuming that biosorption is chemically controlled. The so-called pseudo second-order rate expression could satisfactorily describe the experimental data. The adsorption data of Zn on soil bacterium Pseudomonas putida were fit with the van Bemmelen-Freundlich model (Toner et al. 2005). 

The variation of rate with a fractional power of the silver ion concentration can be explained if adsorption of the silver ions by the silver occurs prior to reaction and if the adsorption follows a Freundlich isotherm. The reaction rate then would be directly proportional to the concentration - of adsorbed silver ions, since the concentration of adsorbed ions would be related to that in solution by the equation... 

Isotherms. When a fiber is immersed in a dyebath, dye moves from the external phase into Lhe fiber. Initially the rate is quick but with time this slows and eventually an equilibrium is reached between the concentration of dye in the fiber and the concentration of dye in the dyebath. For a given initial dyebath concentration of a dye under given dyebath conditions, e.g.. temperature, pH, and conductivity, there is an equilibrium concentration of dye in fiber, D, and dye in the dyebath external solution, D,. Three models describe this relationship simple partition isotherm. Freundlich isotherm, and Langmuir isotherm. 

Equation (150) is the well-known equation for adsorption rate found by Zel dovich and Roginskil (45) (sometimes it is erroneously called the Elo-vich equation )- This equation was experimentally confirmed for many cases of chemisorption. It follows from (135) and (146) that on a surface where the Freundlich isotherm is valid, the adsorption rate is proportional to P/6m. Inverse proportionality between r+ and a fractional power of 6 was found by Bangham (46). 

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... 

Rate-limited sorption can also be modeled assuming a kinetic rate expression coupled with a nonlinear equilibrium expression. If we assume a Freundlich isotherm and a first-order rate expression, we can use the following equation to model sorption kinetics [21] ... 

The surface area of Black Pearls 2 carbon was sufficiently large (850 m2g 1) for the rates and extents of adsorption to be easily determined from the initial decreases in either optical rotation (see Fig. 2) or optical absorbance. The equilibrium amounts of Co(en)3+ and of I adsorbed per gram of carbon fitted Freundlich isotherms. The rates of adsorption exhibited first-order behaviour and led to half-lives of adsorption of 2 min for Co(en)3+ and of 3min for I" [223], These were much faster than the rate of racemisation or the rate of the slow accompanying carbon-catalysed redox reaction. 

In the cases of Langmuir and Freundlich isotherms, it has been assumed that the total disappearance rate of substrate per imit surface area, Vj, follows a pseudo-first-order kinetics with respect to the substrate concentration which is expressed by its fractional coverage. The same assumption is made for R-P isotherm however, as the R-P isotherm relates an adsorbed amount (and not a fractional coverage) with the equilibrium concentration... 

In a kinetically controlled separation system using CMS or zeolite 4A as adsorbents, it is necessary to use more accurate rate model. Therefore, concentration dependent diffusivity model based on Darken equation combined with Langmuir-Freundlich isotherm was applied and each result was compared with the experimental data. 

Finite-difference techniques were used to compute numerical solutions as column-breakthrough curves because of the nonlinear Freundlich isotherm in each transport model. Along the column, 100 nodes were used, and 10 nodes were used in the side-pore direction for the profile model. A predictor-corrector calculation was used at each time step to account for nonlinearity. An iterative solver was used for the profile model whereas, a direct solution was used for the mixed side-pore and the rate-controlled sorption models. 

We therefore believe that the Elovich equation may be used as a basis for a quantitative interpretation of rates of adsorption and desorption both from the single-gas phase, and from binary mixtures, and that it is a useful expression, like that for a Freundlich isotherm in equilibrium adsorption studies, as a means of describing the heterogeneous nature of many rate processes. We have not attempted to describe, in detail, the extensive experimental data that are available in the literature since this has been thoroughly and critically assessed up to 1960 by Low (5) who has written an excellent and comprehensive review in which he provides references to the original papers. 

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-... 

Result of a linearisation of the associated Freundlich isotherm with respect to Tantamount to rate of easy accessible sorption sites (approximated via ratio of inner and outer grain surface). 

Figure 5. Schematic representation and equations defining the 2-box (top) and 3-box (bottom) kinetic models. X = dissolved metal Y, Yi and Y2 = reversibly sorbed metal on Freundlich sorption sites f = fraction of Freundlich sorption sites reaching equilibrium instantaneously K and n are the Freundlich-isotherm constants r and k are the reversible and irreversible rate constant, respectively Z = irreversibly sorbed metal. The subscript 0 in the mass balance equations denotes concentrations at time zero, and Cp = particle concentration. (Adapted from ref. 15)...

The SEM images of PANI and PANI/silica composite are illustrated in Fig 11.4. The PANI was 100-300 nm in diameter and 2-40 pM in length with easily visual cavities. Instead, the PANI/silica composite appeared as cluster spot and enhanced surface area, which helped to increase the adsorption rate toward acid green [36]. The adsorption process was revealed to be pseudo-second-order kinetic model and Langmuir isotherm, as shown in Figure 11.4. The regression constants were 0.9894,0.9995,0.9961, and 0.9945 for pseudo-first-, pseudo-second-order kinetic models, the Langmuir and Freundlich isotherms, respectively. 

Experimental studies for the removal of dissolved TBP in aqueous solutions by adsorbing on a fixed bed containing Amberlite XAD-4 resin were conducted. Break through curves were established for different flow rates and feed concentrations of TBP in aqueous solutions. Break through capacity, saturation capacity and mass transfer zone length (MTZ) were estimated and the MTZ length was correlated. The distribution data of TBP on resin were measured and the equilibrium data were fitted to Freundlich isotherm model. 

Line QP on Fig. 10.5.8 represents Eq. (40). The curve represents the equilibrium for this system. Adsorption rates are generally fast, and the system reaches equilibrium rapidly. When the Freundlich isotherm applies and xi is zero, Eq. (40) becomes... 

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