Equations Elovich

SO that at a given temperature, the rate should vary according to f(6)e ° . Equation XVIII-19 is a form of what is known as the Elovich equation 129. 

We have seen various kinds of explanations of why may vary with 6. The subject may, in a sense, be bypassed and an energy distribution function obtained much as in Section XVII-14A. In doing this, Cerefolini and Re [149] used a rate law in which the amount desorbed is linear in the logarithm of time (the Elovich equation). 

Show whether a plot of d versus log t should be linear (a form of the Elovich equation). 

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... 

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... 

Elovich equation, 1 595 Elution, in ion exchange, 14 410—412 Elution buffer, in affinity chromatography, 6 392... 

Although Eq. (4.32) can be derived as a general rate law expression under the assumption of an exponential decrease in number of available sorption sites with r and/or a linear increase in activation energy of sorption with T, the Elovich Equation is perhaps best regarded as an empirical one for the characterization of rate data (Sposito, 1984). 

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... 

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... 

Fig. 5.4 Plot of Elovich equation for phosphate (PO ) sorption on two soils, where is the initial concentration added at time zero and C is the concentration in the soil solution at time t (Chien and Clayton, 1980)...

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... 

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. 

Taylor and Thon (36), using the results of Taylor and Sickman (29), have recently applied the Elovich Equation to the adsorption of hydrogen by zinc oxide. The results indicate that there are two types of adsorption at 184°C, and one at 110°C. 

At higher temperatures and initial doses of TMS the reaction proceeds with a steady increase in pressure over 1000 min (Figure 2). However, at high dose number (> 5) the isotherms resemble those for reaction at lower temperatures. For doses 1-4 at 550°, and 1-3 at 450°, increase in pressure (Ap) vs. time plots obey the Elovich equation for activated adsorption ... 

A number of relations between rate of activated adsorption and coverage have been proposed. Of these, one has been particularly frequently used, the Roginskii-Zeldovich equation sometimes called the Elovich equation,... 

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