Extension of classical adsorption rate equations using mass of adsorbent: A graphical analysis
Graphical abstract
Introduction
Surface reactions play critical roles in a wide range of the industrial applications, involving: petroleum, oil, wastewater treatment and so on [1]. The knowledge of kinetic of these reactions is a paramount of importance in design and operation of the chemical reactors. Therefore, it is really vital and significant to find a simple method to investigate the kinetic of these reactions [2]. Blackmond et al. presented a graphical method RPKA (reaction progress kinetic analysis), for analysis of kinetic of the surface catalytic reactions [3], [4]. Recently, Burés presented an interesting graphical approach to find the catalyst order in a catalytic reaction [5]. Although, adsorption is mechanistically different with the catalytic surface reactions, it can be considered as another noticeable and important example of the surface reactions [6], [7], [8], [9]. A systematic search among the published articles shows that there are more than twenty thousand research papers about kinetic of adsorption. Although, there are a lot of studies, which tried to explain kinetic of adsorption [10], [11], [12], [13], [14], [15], [16], a little attention has been given to the very important parameter i.e. the adsorbent concentration. Only some studies have been devoted to the detailed analysis of the adsorbent dosage effect on kinetic of adsorption [17]. Ho and McKay proposed an empirical complex function to show how the adsorbent dosage affects the rate of adsorption [5].
The aim of this study is to introduce a simple graphical method to determine the order of the adsorbent dosage in the adsorption rate equation. By finding the order of the adsorbent dosage, it is possible to extend the classical adsorption rate equations. Therefore, the mass of adsorbent can be one of the descriptive parameters of kinetic of adsorption.
Section snippets
Normalized time scale approach
The analysis of kinetic of adsorption is often according to the investigation of the change of the adsorbed amount with time as follow:where is the amount of the adsorbed species per unit mass of the adsorbent, and is the reaction time. Moreover, is the rate constant and is a function of . It should be noticed that the most popular forms of are and in pseudo first order[18] and pseudo second order [17], [19] models, respectively, where is the
Conclusions
In summary, a powerful methodology for elucidating the order of the adsorbent dosage in the adsorption rate equation has been presented. Being fast and easy to use are the significant advantages of the presented method. Furthermore, the fewer experiments are needed to analyze the effect of the adsorbent dosage on kinetic of adsorption. Also, based on our proposed extended kinetic model, it is possible to find the adsorption rate coefficient, which is independent of the adsorbent mass.
Acknowledgements
Authors gratefully acknowledge financial support of Bu Ali Sina University, (Grant number (32-12-67)).
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