Elovich Plot

In some systems, e.g., Ha on ZnO, ZnO-CrOg, ZnO-MoOg, NiMgO, WSa Ha on Pt, Pd, Rh, Ir Oa on NiO and Ag, the plot of q against log( + to) has been closely approximated by two or more linear segments, with different values of a and b over limited ranges of t and so 

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A plot of (qt) vs (Inf) should give a linear relationship if the Elovich model is applicable, with a slope of (1//J) and an intercept of [(1 Iff). ln(a/J)]. Some investigators have suggested that multiple linear segments in Elovich plots could indicate a changeover from one type of binding site to another however, Sparks [23] questioned the correctness of such mechanistic interpretations. 

Some investigators have also suggested that breaks or multiple linear segments in a q versus In t Elovich plot [Eq. (2.48)] could indicate a changeover from one type of binding site to another (Atkinson et al., 1970 Chien and Clayton, 1980). However, one should be cautious about making such mechanistic conclusions from a plot of an empirical equation. 

Normally, with increase of temperature, a increases and b decreases (13) in some systems, e.g., Hg on Ni, Ru, Ir, Pd, Ph ZnO-CraOg, WS2, more precise relationships have been obtained, e.g., both b and In a being proportional to the reciprocal of the temperature (5). The presence of discontinuities in the Elovich plots, however, often obscure such dependences. Nevertheless, even in their absence, complex changes are often evident, e.g., a temperature increase may cause b to pass through maximum or minimum values as for H2 on ZnO, ZnO-MoOa O2 on ZnO, or the variation of a with T may be changed by altering the ambient pressure. 

The choice of a particular value of will not affect the "Elovich plot," i.e.. 0, plotted against In t. It will only shift it on the time axis. Therefore, in presenting our illustrative model calculations, we plot 8, against lnK,p. Figure 8 shows three such Elovich plots for various values of the parameter Kp. 

Although this relationship is often obeyed, in many cases it is not and the slope changes abruptly [1]. Each different slope has been interpreted to represent a different set of adsorption sites with its own values for Eq and a. However, an alternative perspective of time-dependent adsorption was proposed more recently by Ritchie [15], which in many cases removed the non-linearity observed in Elovich plots. His approach did not necessitate the assumption of a variable activation energy, and he simply assumed that more than one site may be required in the adsorption process. Therefore, the rate of change of surface coverage could be written as ... 

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

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)...

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 ... 

Some investigators have used Elovich parameters to estimate reaction rates. Chien and Clayton (1980) suggested that a decrease in Y and/ or an increase of X would increase reaction rate. However, this may be questionable. The slope of plots using an equation like Eq. (2.48) changes with the... 

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)]. 

The conclusions to be drawn are (i) On introduction of the mixed adsorbates to a clean adsorbent surface, component 1 is adsorbed preferentially ( 001 < 002) af R rate independent of the presence of component 2 in the gas phase, (ii) Over the time interval t o to hm (corresponding to an energy range Eso to E m) the slope dqild log t) of the against log t plot decreases, and the corresponding slope dg2/d(log t) increases the Elovich equation is not obeyed, (iii) After a time > tmoi>... 

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