The sorption of lead(II) ions on peat

PII: S0043-1354(98)00207-3 Wat. Res. Vol. 33, No. 2, pp. 578±584, 1999 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/98 $19.00 + 0.00 RESEARCH NOTE THE SORPTION OF LEAD(II) IONS ON PEAT Y. S. HO* and G. MCKAY Department of Chemical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong (First received January 1998; accepted in revised form April 1998) AbstractÐThe sorption of lead ions from aqueous solution onto peat has been studied. Kinetic studies have been carried out using an agitated batch and the e€ect of varying process parameters has been investigated; these include initial lead ion concentration, peat particle size, solution temperature and agitation speed. The data were analyzed using a pseudo-®rst order Lagergren equation and the data were correlated using a two-step ®rst order reaction mechanism. # 1998 Elsevier Science Ltd. All rights reserved Key wordsÐsorption, ®rst order, kinetics, lead, peat INTRODUCTION The ®rst order rate equation of Lagergren (1898) has long been widely applied. The earlier application of the ®rst order rate equation of Lagergren to the sorption of cellulose triacetate from chloroform on calcium silicate was undertaken by Trivedi et al. (1973). Numerous studies report ®rst order Lagergren kinetics for the sorption of metals, such as the sorption of nickel(II) from aqueous solutions by Wollastonite and China clay (Sharma et al., 1990, 1991), the sorption of chromium(VI) traces by bismuth trioxide (Bhutani and Kumari, 1994) and the sorption of lead(II) onto kaolinitic clay (Orumwense, 1996). However, it is often incorrect to apply simple kinetic models such as ®rst- or second-order rate equations to a sorption system with solid surfaces which are rarely homogeneous and because the e€ects of transport phenomena and chemical reactions are often experimentally inseparable (Sparks, 1989). Singh et al. (1996) reported that the sorption of mercury(II) by kaolinite obeyed multiple ®rst order kinetics. This investigation studies the kinetics of the sorption of lead(II) by peat under various initial lead (II) concentrations, solution temperatures, peat particle size ranges and agitation speeds. THEORY The Lagergren rate equation (Lagergren, 1898) was the ®rst rate equation for the sorption of *Author to whom all correspondence should be addressed at: Dahin Group, 9F, No. 99, Chang An E. Road, Sec. 2, Taipei, Taiwan, R.O.C. 578 liquid/solid system based on solid capacity. The Lagergren rate equation is one of the most widely used sorption rate equations for the sorption of a solute from a liquid solution. It may be represented: dqt ˆ k qe ÿ qt † dt 1† Integrating equation 1 for the boundary conditions t = 0 to t = t and qt=0 to qt=qt, gives:   qe k log ˆ t 2† 2:303 qe ÿ qt which is the integrated rate law for a pseudo-®rst order reaction, where qe is the amount of dye sorbed at equilibrium (mg/g); qt is amount of dye sorbed at time t (mg/g); k is the equilibrium rate constant of pseudo-®rst sorption (1/min). Equation 2 can be rearranged to obtain a linear form log qe ÿ qt † ˆ log qe † ÿ k t 2:303 3† The equation applicable to experimental results generally di€ers from a true ®rst order equation two ways (Aharoni and Sparks, 1991). . The parameter k(qeÿqt) does not represent the number of available sites. . The parameter log(qe) is an adjustable parameter, often it is found not equal to the intercept of a plot of log(qeÿqt) against t, whereas in a true ®rst order process log(qe) should be equal to the intercept of a plot of log(qeÿqt) against t. In order to ®t equation 3 to experimental data, the equilibrium sorption capacity, qe, must be Research Note known. In most cases in the literature, the pseudo®rst order equation of Lagergren does not ®t well for the whole range of contact time. In equation 3, one has to ®nd some means of extrapolating the experimental data to t = 1, or treat qe as an adjustable parameter to be determined by trial and error. For this reason, it is necessary to use a trial and error method to obtain the equilibrium sorption capacity, qe. The results of the equilibrium sorption capacity, qe, from equation 3 using a trial and error method cannot agree with the value determined from intercept of equation 3, log(qe) in this study. A time constant, t0, therefore can be considered for a pseudo®rst order process as shown in equation 4: log qe ÿ qt † ˆ log qe † ÿ k t ‡ t0 † 2:303 4† where t0 is an adjustable parameter that makes the equilibrium sorption capacity, qe, suitable for use in the kinetic expression. Its value may be determined by plotting equation 4, the intercept gives qe with an extremely high correlation coecient in all studies. EXPERIMENTAL PROCEDURE All contact investigations were carried out using a ba‚ed agitated 2 dm3 sorber vessel. Samples (3 ml) were withdrawn at suitable time intervals, ®ltered through a 0.45 mm membrane ®lter and then analyzed with an inductively coupled plasma atomic emission spectrophotometer 579 (ICP-AES) for all of studies. Unless a process parameter was the system variable, the following conditions were used a 6.8 g sample of peat (500±710 mm) was added to each 1.7 dm3 volume of lead(II) solution using an agitation speed of 400 rpm at room temperature (24228C). DISCUSSION AND RESULTS Equilibrium isotherm The equilibrium isotherm for the sorption of lead(II) on peat was determined by agitating 0.25 gm peat (500±710 mm) with 50  10ÿ3 dm3 of lead(II) solutions of various concentrations. The systems were agitated in a constant temperature shaking water bath for seven days. The experimental points are shown in Fig. 1 and compared with a solid Langmuir isotherm line, having a correlation coecient 0.99 and equation: qe ˆ 45:6Ce : 1 ‡ 0:374Ce 5† E€ect of initial concentration Several experiments were undertaken to study the e€ect of varying the initial lead(II) concentration on the rate of lead(II) removal from solution. A range of lead(II) concentrations from 100 to 500 mg/dm3 were used and agitation was carried out for four hours. The e€ect of initial concentration on the sorption of lead(II) on peat is shown in Fig. 2. The curves Fig. 1. Isotherm for the sorption of lead(II) using peat. 580 Research Note Fig. 2. E€ect of concentration on the sorption of lead(II) by peat at various initial concentrations. indicate that the rate of sorption is very fast initially and reaches a plateau at equilibrium. When the initial lead(II) concentration is 209 mg/dm3, sat- uration was obtained in less than 120 min. The change in the sorption capacity with time is found to ®t the ®rst order relationship as de®ned by Fig. 3. Pseudo-®rst order sorption kinetics of lead(II) onto peat at various initial concentrations. Research Note 581 Table 1. Kinetic parameters for the sorption of lead(II) on peat at 0±20 min C0 (mg/dm3) 504 410 309 209 101 k1 (1/min) ÿ2 8.08  10 9.29  10ÿ2 9.12  10ÿ2 0.129 0.494 qe (mg/g) t0 (min) r2 q20 (mg/g) 71.7 69.3 64.8 51.2 25.2 4.03 3.90 4.42 3.91 0.947 0.998 0.999 0.994 0.992 0.997 61.5 61.8 58.0 48.9 25.3 q240 (mg/g) 101 94.6 75.3 52.3 ÿ Table 2. Kinetic parameters for the sorption of lead(II) on peat at 20±90 min C0 (mg/dm3) k2 (1/min) ÿ2 504 410 309 209 2.79  10 2.52  10ÿ2 4.09  10ÿ2 5.99  10ÿ2 qe (mg/g) t0 (min) r2 95.2 92.6 93.4 52.1 17.0 23.7 18.2 25.8 0.999 0.999 1.00 0.999 equation 4 and the results indicate that the lead(II) sorption in these systems obeyed a two-step ®rst order kinetics, because the regression analysis of equation 4 revealed two distinct rate curves. The values of the rate constants for the ®rst two steps can be obtained from the slopes of the lines in Fig. 3. The constants of k1, k2, t0 and equilibrium sorption capacity, qe, evaluated from equation 4 for the four di€erent initial concentrations are presented in Tables 1 and 2. The rate constants for the ®rst step, k1, is higher than the second step for each initial concentration of lead(II). E€ect of temperature A series of experiments were undertaken to study of e€ect of temperature by performing experiments q240 (mg/g) 101 94.6 75.3 52.3 at 6, 15, 25, 35 and 458C. In all the experiments the particle size range of peat was 500±710 mm, the initial lead(II) concentration was 300 mg/dm3 and an agitation speed of 400 rpm was used. The in¯uence of temperature on the sorption of lead(II) is shown in Fig. 4. The rate of sorption increased with decreasing temperature and the constants from equation 4 are shown in Tables 3 and 4. The e€ect of temperature on the sorption rate in the ®rst and second regions is shown in Fig. 5. The values of k1 and k2 increase with decreasing temperature. The activation energy for the sorption of lead(II) was calculated and for the ®rst step it is 6.39 kJ/mol and for the second step is 11.4 kJ/mol using the Arrhenius equation. Fig. 4. E€ect of temperature on the sorption of lead(II) by peat at various temperatures. 582 Research Note Table 3. Kinetic parameters for the sorption of lead(II) on peat at 0±20 min T (8K) k1 (1/min) qe (mg/g) t0 (min) r2 q20 (mg/g) q240 (mg/g) 279 288 298 308 318 0.129 9.72  10ÿ2 9.23  10ÿ2 8.97  10ÿ2 8.85  10ÿ2 72.2 68.9 63.4 57.5 51.2 4.04 4.72 4.01 3.71 3.65 0.999 0.997 0.997 0.999 0.997 69.0 62.9 56.6 50.7 45.0 76.2 76.2 75.8 74.6 73.0 Table 4. Kinetic parameters for the sorption of lead(II) on peat at 20±90 min T (8K) k2 (1/min) qe (mg/g) t0 (min) r2 q240 (mg/g) 75.8 75.3 74.1 72.4 70.8 33.4 21.8 22.9 17.0 20.0 0.991 1.00 0.998 1.00 1.00 76.2 76.2 75.8 74.6 73.0 ÿ2 279 288 298 308 318 4.67  10 4.36  10ÿ2 3.41  10ÿ2 3.27  10ÿ2 2.53  10ÿ2 Table 5. Kinetic parameters for the sorption of lead(II) on peat at 0±20 min dp (mm) 500±710 355±500 250±355 150±240 k1 (1/min) ÿ2 8.77  10 0.125 0.179 0.261 qe (mg/g) t0 (min) r2 q20 (mg/g) q240 (mg/g) 65.5 70.9 75.9 77.0 3.91 3.34 3.72 3.08 0.998 0.998 0.995 0.997 57.6 67.1 74.9 76.8 78.2 78.8 79.3 79.3 E€ect of particle size The in¯uence of contact time on four particle size ranges of peat was investigated using the size ranges listed in Table 5. The e€ect of uptake was studied using an initial lead(II) concentration of 300 mg/ dm3, an agitation speed of 400 rpm, a solution temperature of room temperature (242 28C) and 1.7 dm3 volume lead(II) solution with 6.8 g of peat. The in¯uence of particle size on the sorption of lead(II) is shown in Fig. 6. The measured values of sorption capacity at time of 20 and 240 min, q20 and q240, are listed in Tables 5 and 6. The equilibrium sorption capacities, qe, and ®rst order rate constants, k1, k2, were determined from the equation 4. E€ect of agitation A series of experiments were performed using agitation speeds of 280, 350, 390, 430, 470 and Fig. 5. Plot of In(k) against (1/T). Research Note 583 Fig. 6. E€ect of particle size on the sorption of lead(II) by peat at various particle sizes. 510 rpm, and a particle size range of 500±710 mm. The initial lead(II) concentration was 300 mg/dm3. From the contact time results the ®rst order rate constant, k1 and k2 can be obtained using equation 4. The k1 and k2 values and equilibrium sorption capacity, qe, determined using trial and error method are compared in Tables 7 and 8. Figure 7 illustrates a plot of sorption capacity against time. The constants of k1, k2, t0 and equili- brium sorption capacity, qe, evaluated from equation 4 for the six di€erent agitation speeds are presented in Tables 7 and 8. The in¯uence of agitation speed on the rate constant, k, is very slight. Since t0 has been considered as a pre-sorption time, the equilibrium sorption capacity, qe, can be evaluated by equation 4 using a trial and error method were closer to the experimental data (q240) which are shown in Tables 1±8. Table 6. Kinetic parameters for the sorption of lead(II) on peat at 20±90 min dp (mm) 500±710 355±500 250±355 150±240 k1 (1/min) qe (mg/g) t0 (min) r2 q240 (mg/g) 76.3 77.9 78.6 78.7 18.8 29.0 48.7 67.4 0.999 0.997 1.00 0.990 78.2 78.8 79.3 79.3 ÿ2 3.66  10 4.15  10ÿ2 4.40  10ÿ2 4.18  10ÿ2 Table 7. Kinetic parameters for the sorption of lead(II) on peat at 0±20 min S (rpm) k1 (1/min) qe (mg/g) t0 (min) r2 q20 (mg/g) q240 (mg/g) 510 470 430 390 350 280 0.115 0.108 9.37  10ÿ2 9.89  10ÿ2 0.102 0.120 67.5 66.1 65.6 63.7 61.7 56.5 4.24 3.45 4.33 4.05 3.38 1.80 0.998 0.999 0.997 0.997 0.998 0.998 63.5 60.8 59.0 57.9 56.2 52.3 77.7 76.8 76.6 76.7 77.2 77.0 Table 8. Kinetic parameters for the sorption of lead(II) on peat at 20±90 min S (rpm) k2 (1/min) qe (mg/g) t0 (min) r2 q240 (mg/g) 510 470 430 390 350 280 4.77  10ÿ2 4.27  10ÿ2 4.03  10ÿ2 3.69  10ÿ2 3.89  10ÿ2 3.43  10ÿ2 76.5 75.0 75.0 74.9 74.8 74.8 17.7 19.2 18.9 20.6 15.9 16.2 0.996 1.00 1.00 0.999 1.00 0.999 77.7 76.8 76.6 76.7 77.2 77.0 584 Research Note Fig. 7. E€ect of agitation speed on the sorption of lead(II) by peat at various agitation speeds. CONCLUSION The kinetics of sorption of lead ions onto peat has been well correlated by a pseudo-®rst order two step reaction mechanism. The ®rst reaction stage appears to be di€usion controlled and the second stage is chemisorption controlled. The two disadvantages of the model are ®rstly, that a value for the equilibrium sorption capacity, qe, has to be incorporated into the kinetic equation and solved by trial and error. REFERENCES Aharoni C. and Sparks D. L. (1991) Kinetics of soil chemical reactions ± A theoretical treatment. 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