Extension of classical adsorption rate equations using mass of adsorbent: A graphical analysis

https://doi.org/10.1016/j.seppur.2017.02.021Get rights and content

Highlights

  • A new graphical method has been proposed for analyzing the effect of adsorbent mass.

  • The proposed method can determine the adsorbent mass order in adsorption rate equations.

  • Adsorption rate equations can be extended using this approach.

Abstract

A simple and interesting method is presented for analyzing the effect of adsorbent mass on the rate of adsorption process. In this approach, a graphical method is applied for determination the adsorbent mass order in the rate equation. The proposed analysis is according to the plot of the normalized adsorbed amount qe-qqe, versus the normalized time scale t[m]n. In comparison with the limited available methods for describing the adsorbent dosage effect on the adsorption rate, this method needs fewer experiments. The classical adsorption kinetic models were extended by considering mass of adsorbent which provides unique rate coefficient for all experiments.

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:dqdt=kf(q)where q is the amount of the adsorbed species per unit mass of the adsorbent, and t is the reaction time. Moreover, k is the rate constant and f(q) is a function of q. It should be noticed that the most popular forms of f(q) are (qe-q) and (qe-q)2 in pseudo first order[18] and pseudo second order [17], [19] models, respectively, where qe 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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