Elovich equation applications

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... 

Thus if Eq is small compared with q, the adsorption follows the Elovich Equation. Melnick points out that the Elovich Equation agrees with experiment only if q is large, the adsorption rate being much too high for small q. Thus the model of Fig. 5 is in agreement with the Elovich Equation over approximately the range of its application. 

Equation (2.48) is a simplified Elovich equation that several investigators have used to study the rates of soil chemical processes. An application of this equation to P04 sorption on soils is shown in Fig. 2.4, and one sees a... 

In conclusion, the explicit form of the Elovich equation as follows from the combined application of the CA and ACA is therefore... 

In diffusion in a heterogeneous medium the intermediate linear part in (he Z(0 plot is dominant, and this similarly applies to the plot of q vs. In / the range of applicability of the Elovich equation is very wide and often all the measured data are in that range (Fig. 1-3). We expect the slope of q/qgreater than 10 [the actual value cannot be estimated as q is not reached, (Aharoni et al., unpublished data)]. 

Aharoni, C., and Y. Suzin. 1982a. Application of the Elovich equation to the kinetics of occlu-... 

Aharoni, C., and Y. Suzin. 1982b. Application of the Elovich equation to the kinetics of occlusion. Part 2. Analysis of experimental data from the literature. J. Chem. Soc., Faraday Trans. 1, 78 2321-2327. 

Fig. 1. Establishment of desorption profile. The Elovich equation is applicable after an interval of time,. ...

For an immobile adsorbate, the Elovich equation is obeyed for any variation of —AH with coverage when heterogeneity comprises both site and induced effects. For a mobile adsorbate, the Elovich equation is applicable when —AH decreases linearly with increase of patch number and also with increase of coverage on each patch, i.e., [cf. Eq. (47)]. 

Systems for which the Elovich equation applies in a limited range of temperatures and pressures, or to a portion of the amount adsorbed, are ineluded in the table. The range of applicability is not specified. 

References marked contain original adsorption measurements that have been tested for the applicability of the Elovich equation by Taylor and Thon (13). References marked f have been tested by Low (5) and the reference marked J by Porter and Tompkins (M). 

That equation and its integral form soon gained enormous popularity among scientists investigating the kinetics of gas adsorption on solid surfaces. Correlations of experimental data usually started with the application of that equation, and the frequently noted deviations from "Elovich behavior" were the form of analysis in dozens of published papers. Even reviews followed that general trend, discussing the Elovich equations and "deviations" from it. 

According to the latter authors the rationalization of the Elovich equation is simple. It is based on the application of the absolute rate theory (ART) to adsorption on an energetically heterogeneous surface with a rectangular distribution of activation energies for adsorption. An implicit assumption is then made that the adsorption process is at quasi-equilibrium, that the process proceeds in a stepwise fashion, and that the activation energy for adsorption increases linearly with surface coverage. 

The other way of investigations of adsorption/desorption kinetics on solids is connected with the famous and commonly used empirical expression known, in literature as the Elovich equation [390,391]. The excellent work on application of this formula for describing single-component adsorption/desorption kinetics on heterogeneous surfaces was presented recently by Cerofolini [392]. 

Although first-order models have been used widely to describe the kinetics of chemical reactions on natural materials, a number of other simple kinetic models, such as zero-order, second-order, Elovich, power function, and parabolic diffusion models have also been employed. The final forms of these equations are given in Table 5.1. Complete details and applications of these models can be obtained in work by Sparks (1990, 1999, 2003). 

---