Available online at www.sciencedirect.com ScienceDirect IERI Procedia 5 (2013 ) 232 237 Linearized Equations of Pseudo Second-order Atlantica a Kinetic for the Adsorption of Pb( (II) on Pistacia Shells Nahid Ghasemi a *, Parya Tamri a, Ali Khademi a, Naser Sareban nezhad b, Sharifah Rafidah Wan Alwi c c P 2013 International Conference on Agricultural and Natural Resources Engineering a Department of Chemistry, Sciencse Faculty,Islamic Azad University, Arak Branch, Arak, Iran b The Aeine Nasim Company- Arak, Iran Process Systems Engineering Centre (PROSPECT), Faculty of Chemical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia Abstract In the present study, four forms of pseudo second (PS) order kinetic linearized equations for the adsorption of Pb(II) by pistacia atlantica shells were investigated. Kinetic parameters determined for all forms of linearized equations and results obtained from this study show that not only the parameters obtained can be differed but also based on the kinetic parameters obtained is recommended to calculate the PS-order parameters by the linearized equation 1, because this form has the maximum amount of adsorbed of Pb( (II) at equilibrium(q e =50.000 mgg -1 ) and coefficient of determination (R 2 =0.996). 2013 013. The Published Authors. Published by Elsevier by Elsevier B.V. B.V. Open access under CC BY-NC-ND license. Selection ection and and peer pee review r review under responsibility under responsibilit of Information ty of Engineering Information Research Engineer Institute ing Research Institute Keywords: Pseudo-second-order, Kinetics, Pb(II), Adsorption * Corresponding author. Tel.: +98 8613670017; fax: +988613670017. E-mail address: n-ghasemi@iau-arak.ac.ir 2212-6678 2013 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license. Selection and peer review under responsibility of Information Engineering Research Institute doi:10.1016/j.ieri.2013.11.097
Nahid Ghasemi et al. / IERI Procedia 5 ( 2013 ) 232 237 233 Introduction Removal of heavy metals in treatment of wastewater has long been considered. The research of adsorption is important because it provides noteworthy viewpoint into the reaction trajectory and the mechanism of sorption reactions, also demonstrates the solute adsorbed rate[1]. According to Ho studies on sorption is provided PS-order rate expression[2]. Also, Azizian reported the analysis of a theoretical model of PS-order [3]. For low initial concentration from a solute, the Azizian s extraction has advantage because the sorption process will follow the PS-order model. The first advantage of PS-order equation is that it doesn t have any problem to assign a capacity of effective sorption. Also the rate of initial sorption, the capacity of sorption and the PS-order constant rate can be determined from the equation with unknown parameter. The final advantage is that by using batch reactions at various concentrations of initial sorption, different particle sizes, speeds of agitation, doses of sorbent, values of ph and different temperatures, the type of sorbent and sorbate, the kinetic studies can be carried out. In this research, the pistacia atlantica shells was applied for the adsorption of Pb (II) ions from wastewater as adsorbent. The research focuses on adsorption kinetics studies of the prepared adsorbent and four PS-order kinetic linear equations have been applied to test. 1. Experimental 1.1. Materials and methods The experiments were conducted using pistacia atlantica shells obtained from Eilam-Iran. At first it was washed five times with hot deionized water to take the impurities, and was then dried at 105 o C for 24 h in an oven, and was after screened with a sieve (120 mesh). The sieved pistacia atlantica shells was soaked with H 2 SO 4 at 1:1 ratio for overnight. The acidic solution was then removed, and the pistacia atlantica shells was rinsed until the ph=7 with distilled water to remove excess H 2 SO 4. The powder obtained from the pistacia atlantica shells become dry for 2 h at 105 C. The main solution of Lead nitrate (1000 mg L -1 ) was ready with purified water using Lead nitrate salt. Different concentrations of solutions of Pb (II) are ready from the main solution when necessary. The pistacia atlantica shells (0.1 gr) was added to a 120 ml Erlenmeyer containing 70 ml of 100 mg L -1 of Pb(II) with ph =4, stirred at 150 rpm and at temperature 298 K. Samples were taken at proper time intervals (5-120 minutes) and the filtrate analysed by Atomic Absorption Spectrophotometer (AAS). By using HNO 3 or NaOH (0.1N), initial ph was adjusted. PS- order The PS-order kinetic rate equation [4] which is generally extracted in Equation (1): Where k(gmg -1 min -1 ) is PS-order rate constant of adsorption, q e and q t (mgg 1 ) are named the adsorption capacity at time of equilibrium and t. Integrating Equation (1) with applying border conditions t=0 and t=t, q t =0and q t =q t, gives: (1) (2)
234 Nahid Ghasemi et al. / IERI Procedia 5 ( 2013 ) 232 237 In general, due to its simplicity, the PS-order kinetic has been widely applied in the designing of very adsorption methods[5]. Sinc the PS-order which explained by Equation (2) is non linear, seem that appraising the value of q e and the rate constant of adsorption k needs adjusting the equation to empirically results by non linear of regression applying methods of numeric optimization. A proper choice for non-linear of regression is to apply linearized variants of the equations that the PS-order kinetic could be linearized to four versions (Table 1) for the calculation of parameters of q e and k [6]. Table 1. PS-order kinetic linearized forms [6] linearized versions 1 = equation 2 3 4 (Fig. 1) and (Fig. 2), linearized versions 1 and 2 of the PS-order kinetic equations have t/q and 1/q on their Y axis, that amounts of numeric low of Y whereas q is great. As observed in linearized versions equations 2 and 3 (Fig. 3), in t and q, the errors of the experimental distribution, if the axises be the versus 1/t or 1/q will change. There is also a difficulty in incorrect relation in linearized versions 1, 3 and 4(Fig. 4). It often takes place that the proportional relation of variables was applied to make of a variable relationship among the variables their selves [6]. An empirical error was presented in the X axis variable, as in linearized versions 3 and 4 observed, if the axis of X is (q/t or q), many experimental methods have unimportant errors in measuring t. Fig. 1. linearized versions-1 equation of PS-order obtained during the adsorption of Pb(II) by using pistacia atlantica shells
Nahid Ghasemi et al. / IERI Procedia 5 ( 2013 ) 232 237 235 1/q 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 y = 0.049x + 0.022 R² = 0.723 0 0.05 0.1 0.15 0.2 0.25 1/t Fig. 2. linearized versions-2 equation of PS-order obtained during the adsorption of Pb(II) by using pistacia atlantica shells 60 50 40 y= 2.283x + 44.91 R² = 0.646 q 30 20 10 0 0 2 4 6 8 q/t Fig. 3. linearized versions-3 equation of PS-order obtained during the adsorption of Pb(II) by using pistacia atlantica shells All of parameters for four linearized versions of PS-order kinetic equations included q e and k and the coefficient of determination, R 2 listed in Table 2. These parameters were determined from the slope time and the intercept of a straight line according to equations that given in Table 1.
236 Nahid Ghasemi et al. / IERI Procedia 5 ( 2013 ) 232 237 Fig. 4. linearized versions-4 equation of PS-order obtained during the adsorption of Pb(II) by using pistacia atlantica shells Table 2. Parameters of PS-order kinetic determined by using the linearized versions equations Parameters linearized versions q e (mgg -1 ) k(g mg -1 min -1 ) R 2 1 50.000 0.00333 0.996 2 45.454 0.0098 0.723 3 44.914 0.0097 0.646 4 47.243 0.0059 0.647 2. Conclusions The experimental outcome were analysed and determined according to the four PS-order kinetic linearized versions equations. Based on the outcome of this research, it is not recommended to calculate the parameters of PS-order by using the linearized versions of 2, 3 and 4. The PS-order linearized version equation 1 provided accurate evaluates in very cases. According to the evaluation using the all PS-order linear kinetic kinetic linearized versions equations, the sorption capacity were obtained 49.751, 45.454, 44. 914, 47.138 mggg -1,respectively(Table 2). The results also showed a good fit between linearized version equation 1 with the experimental dataa (q e.exp =48.575 mgg -1 ) (Fig. 5). Acknowledgements The authors are special thankful to Mr Naser Sareban nezhad for the financial support of this study.
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