Mixed Surface Reaction and Diffusion-Controlled Kinetic Model for Adsorption at the Solid/Solution Interface Monireh Haerifar and Saeid Azizian* Department of Physical Chemistry, Faculty of Chemistry, Bu-Ali Sina University, Hamedan, 65174, Iran *S Supporting Information ABSTRACT: The effects of diffusion and surface reaction mechanisms have been considered conjointly to investigate the kinetics of adsorption. A new model has been proposed for the modeling of adsorption kinetics at the solid/solution interface in batch systems. Based on generated data points (t, q) by using of the new model, it was found that there is a deviation from linearity as a downward curvature at initial times of adsorption in usual t/q vs time plot, when diffusion contributes to the rate-controlling step of adsorption. Moreover, results of nonlinear fitting to the different experimental data show that the mixed surface reaction and diffusion-controlled model can be useful for kinetics modeling of adsorption in which pure surface reaction or mixed surface reaction and diffusion contribute to the rate-controlling step of adsorption. 1. INTRODUCTION Purification of industrial wastewaters including colors, organic compounds, heavy metals, and other impurities is an important technology to solve serious environmental and public problems. Among the various treatment techniques, adsorption is one of the most efficient and economic methods that has been widely investigated from equilibrium and kinetic aspects. The equilibrium isotherms have been applied to describe sorption equilibrium data; however, studying the time dependency of adsorption processes is crucial to predict kinetic parameters and to design the reactors. According to the literature 1,2 the sorption mechanism can be divided into four consecutive steps: (i) transport of solute in the bulk solution; (ii) diffusion of solute through the liquid film surrounding the adsorbent particles; (iii) diffusion of solute in the pores of the sorbent (intraparticle diffusion); and (iv) chemical reaction as adsorption and desorption on the solid surface. The overall rate of the sorption process may be controlled by any of these steps or in some cases by combination of two steps. Various kinetic models have been used for solid/solution adsorption batch systems. For example, Langmuir, 3,4 statistical rate theory (SRT), 5−7 pseudo first-order (PFO), 8,9 pseudo second-order (PSO), 9,10 Elovich, 11 and intraparticle diffusion model (IDM) 12,13 are the most well-known sorption kinetic models. The other adsorption rate equations such as modified pseudo first-order (MPFO), 7,14 modified pseudo second-order (MPSO), 15 pseudo n-order (PnO), 16 modified pseudo n-order (MPnO), 15 two-site pseudo second-order (TS-PSO), 17 mixed 1,2-order equation (MOE), 18 exponential kinetic model (Exp), 19 and so on 1,4,15,20−22 have been recently presented to describe kinetic data in adsorption systems. An overview of the literature show that, among the mentioned equations, the intraparticle diffusion model is applicable when the rate determining step is the mass transfer of adsorbate to the solid surface sites (step iii), whereas the other ones are used for description of adsorption kinetics when the overall sorption rate is controlled by the rate of surface reaction (step iv). 1,2,23 Since both surface reaction and diffusion models were used extensively in literature for modeling of adsorption kinetics, in this work we are going to present a new adsorption kinetic model which includes both surface reaction and diffusion simultaneously. The obtained new equation can be used for modeling of adsorption kinetics in which both diffusion and surface reaction steps control the overall rate of this process at the solid/solution interface. 2. ADSORPTION KINETIC MODELS As mentioned before, there are several models for the description of the adsorption rate at the solid/solution interface. Despite the diversity of kinetic equations and their capability to simulate kinetic data in different sorption systems, it seems that pseudo-first-order, intraparticle diffusion model, and especially pseudo-second-order equations are still the most popular and renowned kinetic models. 2.1. Pseudo-First-Order Equation (PFO). The PFO or the so-called Lagergren equation 8,9 has the following differential form: = − q t k q q d d ( ) 1 e (1) Received: February 13, 2013 Revised: April 4, 2013 Published: April 5, 2013 Article pubs.acs.org/JPCC © 2013 American Chemical Society 8310 dx.doi.org/10.1021/jp401571m | J. Phys. Chem. C 2013, 117, 8310−8317