Elovich kinetics

We should point out that the Langmuir kinetics given by expressions (1.11) and (1.12) which is often observed in experiment is as often violated. In numerous cases the data on adsorption kinetics follows the well-known Roginsky-Zeldovich-Elovich kinetics isotherm [47, 48]... 

Indeed, assuming that the surface of adsorbent is characterized by homogeneous distribution in adsorption activation energy we arrive to the Zeldovich - Roginsky - Elovich kinetic isotherm of In (f + + providing the validity of function (2.50) in case of direct in-... 

The adsorption of oxygen onto most types of coal follow Elovich kinetics i.e. a rapid uptake followed by a much more gradual uptake (9)... 

The chemisorption data determined gravimetrically were analyzed according to Elovich kinetics (J5). These kinetics are based on the assumption that the rate of chemisorption (dg/dt) declines as the more reactive sites are quenched according to the equation ... 

A time-logarithm behaviour can be recognized neither in Eq. (55) nor (56), so that the Elovich kinetics cannot be understood in terms of chemisorption kinetics on ideally homogeneous surfaces. 

Arsenate adsorption on ferrihydrite consisted of a period of rapid uptake followed by slow adsorption for at least 8 days 43). The rate of the slow adsorption reaction is considered to be limited by diffusion into the ferrihydrite aggregates. Slow adsorption kinetics similar to those for phosphate are expected for arsenate because of the similar chemistry of these two anions. Arsenate adsorption data adhere to the Elovich kinetic model indicating a diffusion limited reaction. Arsenate desorption rates were much slower than arsenate adsorption rates, also consistent with a diffusion limited process. A model was developed that assumes that 63% of adsorbing sites are located at the exteriors of aggregates and reach arsenate equilibrium rapidly, while 37% of adsorbing sites are located in the interiors of aggregates with access being diffusion limited. 

In order to minimize contact time, it is necessary to use a contact time model, which may be a kinetic model (first order, second order, Elovich kinetics, etc.) or a mass transport diffusion model (film, pore, surface, pore-surface). The present case study is based on a pseudo-second order kinetic model (Ho and McKay, 1998), and the kinetic equation is ... 

In practice the kinetics are usually more complex than might be expected on this basis, siace the activation energy generally varies with surface coverage as a result of energetic heterogeneity and/or sorbate-sorbate iateraction. As a result, the adsorption rate is commonly given by the Elovich equation (15) ... 

Kinetics of Adsorption and Desorption and the Elovich Equation C. Aharoni and F. C. Tompkins... 

Note that besides the kinetics of the change of electric conductivity (2.44) - (2.47) considered, the logarithmic kinetics similar to that of Zeldovich - Roginsky - Elovich is often observed in experiment (see Section 1.10) [30, 65, 82, 83] ... 

The two-constant equation and the simple Elovich equation efifect-tively described the change of Co in the main source, the ERO fraction in both soils (Fig. 6.30). This suggests that the diffusion processes controlled the rate of Co transformation. It is noted above that the kinetics of Mn transformation in the three main fractions (EXC, CARB, and ERO), in the... 

Figure 6.30. Kinetics of transformation of Co in the ERO fraction in two Israeli soils according to the two-constant rate model (a) and the simple Elovich model (b), respectively. Soils were incubated under the saturation paste regime (modified after Han et al., 2002b. Reprinted from J Environ Sci Health, Part A, 137, HanF.X., Banin A., Kingery W.L., Li Z.P., Pathways and kinetics of transformation of cobalt among solid-phase components in arid-zone soils, p 192, Copyright (2003), with permission from Taylor Francis)...

Fig. 7. Kinetics of arsenate (AsO,) sorption onto ferrihydrite (A) or Al(OH)x (B) at pH 5.0 in the absence or presence of phosphate (P04) or phosphate and malate (Mai). Initial PO4/ASO4 molar ratio of 1 (AsO, + PO,) and AsO, + POyMal molar ratio of 1 (As04+P04 +2Mai). Arsenate was added at 50% of surface coverage. The fit for the sorption data was obtained best using Elovich model (authors unpublished data, 2007).

Reaction kinetics. The time-development of sorption processes often has been studied in connection with models of adsorption despite the well-known injunction that kinetics data, like thermodynamic data, cannot be used to infer molecular mechanisms (19). Experience with both cationic and anionic adsorptives has shown that sorption reactions typically are rapid initially, operating on time scales of minutes or hours, then diminish in rate gradually, on time scales of days or weeks (16,20-25). This decline in rate usually is not interpreted to be homogeneous The rapid stage of sorption kinetics is described by one rate law (e.g., the Elovich equation), whereas the slow stage is described by another (e.g., an expression of first order in the adsorptive concentration). There is, however, no profound significance to be attached to this observation, since a consensus does not exist as to which rate laws should be used to model either fast or slow sorption processes (16,21,22,24). If a sorption process is initiated from a state of supersaturation with respect to one or more possible solid phases involving an adsorptive, or if the... 

While first-order models have been used widely to describe the kinetics of solid phase sorption/desorption processes, a number of other models have been employed. These include various ordered equations such as zero-order, second-order, fractional-order, Elovich, power function or fractional power, and parabolic diffusion models. A brief discussion of these models will be provided the final forms of the equations are given in Table 2. 

The Elovich model was originally developed to describe the kinetics of heterogeneous chemisorption of gases on solid surfaces [117]. It describes a number of reaction mechanisms including bulk and surface diffusion, as well as activation and deactivation of catalytic surfaces. In solid phase chemistry, the Elovich model has been used to describe the kinetics of sorption/desorption of various chemicals on solid phases [23]. It can be expressed as [118] ... 

The Elovich equation was developed to determine the kinetics of heterogeneous chemisorption of gases on sohd surfaces. This equation assumes a heterogeneous distribution of adsorption energies, where the energy of activation E) increases linearly with surface coverage (Rao et al. 1989). A simplified Elovich equation used to study the rate of soil chemical processes is given by... 

Cells R, Cox L, Hermosin MC, Cornejo J (1996) Retention of metamitron by model and natural particulate matter. Intern J Environ Anal Chem 65 245-260 Chaney RL (1989) Toxic element accumulation in soils and crops protecting soil fertility and agricultural food chains. In Bar Yosef B, Barrow NJ, Goldschmid J (eds) Inorganic contaminants in the vadose zone Springer, Heidelberg, pp 140-159 Charlatchka R, Cambier P (2000) Influence of reducing conditions on solubility of trace metals in contaminated soils. Water, Air Soil PoUut 118 143-167 Chien SH, Clyton WR (1980) Application of Elovich equation to the kinetics of phosphate release and sorption in soils. Soil Sci Am J 44 265-268... 

Polysopoulos NA, Keramidas VZ, Pavlatou A (1986) On the limitation of the simplified Elovich equation in describing the kinetics of phosphate sorption and release from soils. J Soil Sci... 

In the cases of Cr203, NiO, and Fe2Ch it was possible (24) to follow the kinetics of the adsorption of 02 at constant pressures around 6 cm. It was found that the uptake q followed the Elovich equation ... 

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