Magnetic chitosan nanoparticles for removal of Cr(VI) from aqueous solution

Materials Science and Engineering C 33 (2013) 1214–1218

Contents lists available at SciVerse ScienceDirect

Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec

Magnetic chitosan nanoparticles for removal of Cr(VI) from aqueous solution Nguyen Ngoc Thinh a, Pham Thi Bich Hanh b, Le Thi Thanh Ha a, Le Ngoc Anh c, Tran Vinh Hoang a, Vu Dinh Hoang a, Le Hai Dang d, Nguyen Van Khoi b, Tran Dai Lam e,⁎ a

School of Chemical Engineering, Hanoi University of Science and Technology, 1, Dai Co Viet Road, Hanoi, Viet Nam Institute of Chemistry, Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet Road, Hanoi, Viet Nam Institute of Marine Geology and Geophysics, Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet Road, Hanoi, Viet Nam d Hanoi National University of Education,136 Xuan Thuy, Hanoi, Viet Nam e Institute of Materials Science, Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet Road, Hanoi, Viet Nam b c

a r t i c l e

i n f o

Article history: Received 28 April 2012 Received in revised form 29 August 2012 Accepted 3 December 2012 Available online 9 December 2012 Keywords: Fe3O4 Magnetic chitosan nanoparticles Adsorption isotherm Cr(VI)

a b s t r a c t A simple method was introduced to prepare magnetic chitosan nanoparticles by co-precipitation via epichlorohydrin cross-linking reaction. The average size of magnetic chitosan nanoparticles is estimated at ca. 30 nm. It was found that the adsorption of Cr(VI) was highly pH-dependent and its kinetics follows the pseudo-second-order model. Maximum adsorption capacity (at pH 3, room temperature) was calculated as 55.80 mg·g−1, according to Langmuir isotherm model. The nanoparticles were thoroughly characterized before and after Cr(VI) adsorption. From this result, it can be suggested that magnetic chitosan nanoparticles could serve as a promising adsorbent for Cr(VI) in wastewater treatment technology. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Contamination of water by toxic heavy metals through the discharge of industrial wastewater is a worldwide environmental problem. Rapid industrialization has seriously contributed to the release of toxic heavy metals to water streams. Among the various heavy metals, chromium (Cr) is one of the most toxic pollutants generated by the electroplating, leather tanning, metal finishing, steel fabrication, textile industries and chromate preparation. The most common oxidation states of Cr in nature are Cr(III) and Cr(VI). Chromium(VI) is more hazardous than Cr(III) as it can diffuse as CrO42− or HCrO4− through cell membranes and oxidize biological molecules [1]. A wide range of physical and chemical processes are available for the removal of chromium from wastewater such as filtration [2], electrochemical precipitation [3], adsorption [4,5], electrodeposition [6] and membrane systems or ion exchange process [7–9]. Among these methods, adsorption is one of the most economically favorable while being technically easy [10–12]. Chitosan has excellent properties for the adsorption of heavy metal ions, principally due to the presence of amino groups (–NH2) in the polymer matrix, which interact with metal ions in solution by ion exchange and complexation reactions [13–15]. Most of the chitosan-based adsorbents are submicron to micron-sized and need large internal porosities to ensure adequate surface area for adsorption. However, the diffusion limitation within the particles leads to the decrease in the

adsorption rate and available capacity. Compared to the traditional micron-sized supports used in separation process, nano-sized adsorbents display better performance due to high specific surface area and the absence of internal diffusion resistance. The nano-adsorbents cannot be separated easily from aqueous solution by filtration or centrifugation [16]. The application of magnetic adsorbent technology to solve environmental problems has received considerable attention in recent years [16–18]. In this paper, magnetic chitosan nanoparticles were prepared, characterized and applied for the removal of Cr(VI) in the water solution. Afterwards, thermodynamic and kinetic aspects of the adsorption process were considered. The improved magnetic and high adsorption uptake properties are two main features of the synthesized nanoparticles that can be advantageously used in water treatment. 2. Experimental 2.1. Chemicals FeCl3·6H2O, FeSO4·7H2O, K2Cr2O7, CH3COOH, NaOH and NH3 were of analytical grade. Chitosan (MW= 400,000, DA=70%) was purchased from Nha Trang Aquatic Institute (Vietnam) and re-characterized by viscometry and IR measurements at our laboratory [18]. Double distilled water was used in the preparation of all solutions. 2.2. Preparation of magnetic chitosan nanoparticles

⁎ Corresponding author. Tel.: +84 4 37564129; fax: +84 438360705. E-mail address: [email protected] (T.D. Lam). 0928-4931/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msec.2012.12.013

Magnetic chitosan nanoparticles were prepared by co-precipitation method [18–20], with several modifications. Experiments were carried

N.N. Thinh et al. / Materials Science and Engineering C 33 (2013) 1214–1218

out in inert gas (N2). Fe3O4 nanoparticles were synthesized by co-precipitation of ferric and ferrous salts. The amount 6.4795 g of FeCl3·6H2O and 3.3339 g of FeSO4·7H2O were dissolved into 150 mL of deoxygenated distilled water. After stirring for 30 min, chemical precipitation was achieved at 30 °C under vigorous stirring by adding 20 mL of NH3·H2O solution (28%, v/v). During the reaction process, pH was maintained at about 10. The reaction system was kept at 70 °C for 1 h. 1 g chitosan flake was dissolved in a 150 mL CH3COOH solution 2% (w/v). The chitosan solution was then dropped into the obtained magnetic fluid in the flask through a dropper. Afterwards, 2 mL of pure epichlorohydrin was added into reaction flask and stirred at 85 °C for 3 h, before the flask was cooled down to room temperature. The precipitate was washed with distilled water to remove all existing in the effluents. Silver nitrate (AgNO3) was used to detect residue of Cl−. The precipitate was then washed with ethanol and dried at 50 °C, in the vacuum oven.

1215

of solutions was adjusted by using diluted solution of NaOH and HCl. The temperature of the solutions (25 °C, 35 °C, 45 °C) was controlled with the thermostatic bath. The adsorbed amount of Cr(VI) per unit weight of magnetic chitosan nanoparticles, qt (mg·g−1), was calculated from the mass balance equation as: qt ¼

ðC 0 −C t Þ⋅V m

ð1Þ

where C0 and Ct (mg/L) are the initial Cr(VI) concentration and the Cr(VI) concentrations at any time t, respectively; V (L) is the volume of the Cr(VI) solution; and m (g) is the mass of the magnetic chitosan nanoparticles. Samples of the Cr(VI) solution were collected at predetermined time intervals and analyzed using a UV–Vis Spectrophotometer (model UV-PC1600, Shimadzu), at λmax =540 nm, according to the 1,5-diphenyl-carbazide method [21]. All measurements were conducted triplicate.

2.3. Adsorption experiments 2.4. Characterization methods The sorption experiments were performed by batch method. Samples of 0.1 g of magnetic chitosan nanoparticles were equilibrated with 50 mL of solution containing various amount of Cr(VI). The pH value

X-ray diffraction (XRD) patterns were obtained at room temperature by D8 Advance, Bruker ASX, using CuKα radiation (λ = 1.5406 Å)

Fig. 1. Camera pictures (a, b); FE-SEM images (c, d) and TEM images (e, f) of magnetic chitosan nanoparticles.

1216

N.N. Thinh et al. / Materials Science and Engineering C 33 (2013) 1214–1218

in the range of 2θ = 10°–60°, and a scanning rate of 0.02°·s −1. Morphology of magnetic chitosan nanoparticles was analyzed by Field Emission Hitachi S-4500 Scanning Electron Microscope (FE-SEM) and Transmission Electron Microscope (TEM, JEOL, Voltage: 80 kV). Absorbance measurements were carried out using Shimadzu UV-PC1600 spectrophotometer in the range of 400–800 nm. The magnetic properties were measured with home-made vibrating sample magnetometer (VSM) and evaluated in terms of saturation magnetization and coercivity. Chemical composition of samples was determined by JEOL Scanning Electron Microscope and Energy Dispersive Spectroscopy (SEM/EDS) JSM-5410 Spectrometer. 3. Results and discussion 3.1. Characterization of magnetic chitosan nanoparticles TEM and SEM micrograph of magnetic chitosan particles provides information on their size and morphology. It can be observed from Fig. 1 that the magnetic particles have a spherical shape with a diameter of about 30 nm. XRD pattern of magnetic chitosan nanoparticles shows six characteristic peaks for Fe3O4 corresponding to (220), (311), (400), (422), (511) and (440) (JCPDS file, PDF No. 65-3107) (Fig. 2). Quite weak diffraction lines of composite indicated that Fe3O4 particles have been coated by amorphous chitosan, which did not affect the phase and structure of Fe3O4. Particle size of magnetic chitosan nanoparticles can be estimated approximately as 30 nm, via line broadening in the pattern, using Debye–Scherrer equation (d =kλ/ βcos θ). Typical magnetization loops were recorded by VSM and shown on Fig. S1 (supporting information). From the plot of magnetization vs. magnetic field and its enlargement near the origin, the saturation magnetization, remanence magnetization, coercivity and squareness could be calculated. Because of no remanence and coercivity, it can be suggested that the beads are superparamagnetic. It can also be observed from this figure that magnetization moment of Fe3O4 nanoparticles decreases very little after chitosan surface coating, meaning that chitosan does not affect magnetic properties of these magnetic chitosan nanoparticles. Therefore, maintaining such a high saturation magnetization value (Ms) after coating these nanoparticles is advantageous and susceptible to the external magnetic field for magnetic separation.

regard, the chemical modification of chitosan by using crosslinking reaction offers an important pathway for producing chemically more stable chitosan derivatives, extending the potential applications of this biopolymer. In our study, the crosslinking approach with epichlorohydrin to block/crosslink via hydroxyl (OH) group is expected to improve chemical stability, mechanical resistance and adsorption/desorption properties, compared to that with glutaraldehyde (to block amino (NH2) group respectively), when keeping reactive amino groups intact for complexing reaction with heavy metal ions [14,16,19]. Next, selecting an optimum pH is very important for the adsorption process, since pH affects not only the surface charge of adsorbent, but also the degree of ionization and the speciation of the adsorbate during the reaction. The effect of pH on the adsorption process was investigated over the range from 2 to 6. As indicated in Fig. 3, the maximum capacity of Cr(VI) absorption occurred at pH of 3. The explanation would be addressed as the pH of the aqueous solution affects to stability of chromium speciation and the surface charge of the adsorbent. At pH 1, the chromium ions exists in the form of H2CrO4, while in the pH range of 1–6, different forms of chromium 2− such as Cr2O72−, HCrO4−, and Cr3O10 coexist while HCrO4− predominates. As the pH increases, those form shifts to Cr2O42− and Cr2O72− [11]. Cr(VI) exists predominantly as HCrO4− in aqueous solution below pH 4 and the amino groups (–NH2) of magnetic chitosan nanoparticles would be in protonated cationic form (–NH3+) to a higher extent in acidic solution. This results in the stronger attraction for negatively charged ions. Electrostatic interaction between the sorbent and HCrO4− ions also contributes to the high chromium removal. However, at the pH lower than 3, decrease in uptake capacity is observed as the predomination of H2CrO4 and the strong competition for adsorption sites between H2CrO4 and protons. The decreasing of the adsorption capacity at higher pH values may be explained by the dual competition of CrO42− and OH− for adsorption [11]. Thus, pH 3 was selected as the optimum pH value for the following adsorption experiment. 3.3. Adsorption isotherms Equilibrium experimental data were successfully fitted to the Langmuir isotherm whose equation can be expressed as q¼

qm ⋅K L ⋅C e 1 þ K L ⋅C e

ð2Þ

3.2. Effect of initial pH on the adsorption process It is well known that some metals are preferentially adsorbed in acidic media while chitosan can dissolve under this acidic condition. In this

where qm (mg·g−1) is the maximum sorption capacity (corresponding to complete monolayer coverage), Ce is the equilibrium concentration in the solution (mg/L), qe is the equilibrium Cr(VI) concentration in

85

(311)

80 75

R(%)

Intensity

(440)

(511)

(220)

(400)

70 65 60

(422)

55 50 2

20

30

40

50

60

2θ Fig. 2. XRD pattern of magnetic chitosan nanoparticles.

70

3

4

5

6

pH Fig. 3. The influence of initial pH value on the adsorption of the Cr(VI) on magnetic chitosan nanoparticles.

N.N. Thinh et al. / Materials Science and Engineering C 33 (2013) 1214–1218 Table 1 Adsorption equilibrium constants obtained from Langmuir isotherm in the adsorption of Cr(VI) onto magnetic chitosan nanoparticles (volume: 50 mL; absorbent dose: 0.1 g; initial concentrations: 60, 80 and 180 mg·L−1; pH value: 3.0; temperature: 298,308, 318 K). qmax (mg·g−1)

KL

R2

298 308 318

55.80 46.71 43.29

0.366 0.119 0.138

0.993 0.997 0.994

3.4. Thermodynamic and kinetic studies In this section, thermodynamic and kinetic aspects of the adsorption process will be considered. The experimental data obtained at Table 2 Comparison of adsorption capacities of Cr(VI) with other adsorbents. Adsorbents

Adsorption capacity (mg·g−1)

pH Ref.

Tires activated carbon Rubberwood activated carbon Coconut shell activated carbon Hazelnut shell activated carbon Beech sawdust Sugarcane bagasse Coconut shell charcoal Coconut tree sawdust Chitosan Non-cross linked chitosan Cross linked chitosan Magnetic chitosan nanoparticles (this study)

58.50 44.05 20.00 17.70 16.10 13.40 10.88 3.60 22.09 78.00 50.00 55.80

2.0 2.0 2.0 2.0 1.0 2.0 4.0 3.0 3.0 5 5 3

[23] [3] [24] [25] [26] [27] [28] [29] [30] [31] [31]

17

90

0.6

9 0.

=

,R

5x

0.5 0.4

1 81

3

4.

9+

6 20

9

3.

-1

−1

the sorbent (mg·g ), and KL is the sorption affinity constant related to the binding energy of sorption (L·mg−1). The experimental data (Table 1) fitted well with Langmuir model (R2 > 0.99), confirming that the adsorption process is monolayer adsorption. The results of adsorption studies by Langmuir model, indicating improved Cr(VI) uptake properties of magnetic chitosan nanoparticles (55.80 mg·g−1, pH 3, room temperature, compared to the other adsorbents (Table 2)), probably relates to the smaller loss of amine groups of chitosan, involved in the cross-linking reaction when using epichlorohydrin as a cross-linker. Cr(VI) removal by adsorbent as a function of contact time with different initial concentrations (40, 80 and 180 mg·L −1) of Cr(VI) is shown in Fig. 4, where the adsorption rate of metal uptake was quite slow and the maximum uptake was observed within 100 min.

C=80 mg/L

0.7

Ln(qe/Ce)

Temperature (K)

0.8

1217

y=

0.3 0.2 0.1 3.20

3.22

3.24

3.26

3.28

3.30

3.32

3.34

3.36

1/T*10-3 (1/K) Fig. 5. Thermodynamic plot of ln (qe/Ce) vs. 1/T.

different temperatures were used in calculating the thermodynamic parameters such as Gibbs free energy (ΔG), enthalpy (ΔH) and entropy (ΔS) according to the following equations: ΔG ¼ ΔH−T  ΔS

ð3Þ

lnK ¼ lnðqe =C e Þ ¼ −ΔH=RT þ ΔS=R:

ð4Þ

Where K is the equilibrium constant, obtained from Langmuir isotherms at different temperature and R is the universal gas constant. ΔH and ΔS were obtained from the slope and intercept of the plot log (qe/Ce) vs. 1/T (Fig. 5), namely: ΔH ¼ −0:6853

    −1 −1 −1 and ΔS ¼ −115:7366 J⋅mol ⋅K : kJ⋅mol

Table 3 Thermodynamic data of Cr(VI) adsorption process. T (K)

ΔG (kJ·mol−1)

ΔH (kJ·mol−1)

ΔS (J·mol−1·K−1)

298 303 307 312

−35.164 −35.742 −36.205 −36.784

−0.6853

−115.7366

70

4 40mg/L 80mg/L 180mg/L

65 60

3

40mg/L 80mg/L 180mg/L

2

55

1

50

ln(qe-qt)

q(mg/g)

0 45 40 35

-1 -2 -3

30

-4

25

-5

20

-6

15

-7

10 0

50

100

150

200

250

300

350

400

t(min) Fig. 4. Effect of contact time on Cr(VI) adsorption (volume: 50 mL; absorbent dose: 0.1 g; initial concentrations: 40, 80 and 180 mg·L−1; pH value: 3.0; temperature: 298 K).

-50

0

50

100

150

200

250

300

350

t(min) Fig. 6. Kinetic pseudo-first order sorption kinetics of Cr(VI) (volume: 50 mL; absorbent dose: 0.1 g; initial concentrations: 40, 80 and 180 mg·L−1; pH value: 3.0; temperature: 298 K).

1218

N.N. Thinh et al. / Materials Science and Engineering C 33 (2013) 1214–1218

18 40mg/L 80mg/L 180mg/L

16 14

t/qt(min.g/mg)

indicating the occurrence of monolayer adsorption process. Thermodynamically, the adsorption of Cr(VI) is spontaneous (in term of ΔG) and exothermic (in term of ΔH) process. Kinetically, the adsorption of Cr(VI) onto magnetic chitosan nanoparticles obeyed the pseudo-second-order model. Compared to the other adsorbents, magnetic chitosan nanoparticles shows greatly improved uptake properties of Cr(VI), probably due to high concentration of remaining active sites on the surface of magnetic chitosan nanoparticles. The improved magnetic and adsorption uptake properties are two main features of the synthesized nanoparticles that can be advantageously used in water treatment.

12 10 8 6 4

Acknowledgments

2

Funding of this work was provided by Vietnam Ministry of Science and Technology (grant 08/2011/HÐ-NÐT).

0 0

50

100

150

200

250

300

350

t(min)

Appendix A. Supplementary data

Fig. 7. Kinetic pseudo-second order sorption kinetics of Cr(VI) (volume: 50 mL; absorbent dose: 0.1 g; initial concentrations: 40, 80 and 180 mg·L − 1 ; pH value: 3.0; temperature: 298 K).

Supplementary data to this article can be found online at http:// dx.doi.org/10.1016/j.msec.2012.12.013.

The negative value of ΔG obtained from Eq. (3) reflects a spontaneous (favorable) adsorption process of Cr(VI) (Table 3), while the negative value of ΔH indicates that the adsorption reaction is exothermic and the adsorption of Cr(VI) is more effective at lower temperatures. Kinetically, in order to understand the behavior of the adsorbent and to examine the controlling mechanism of the adsorption process, the pseudo-first-order and the pseudo-second-order were applied to the experimental data (Figs. 6 and 7). The pseudo-first-order rate expression of Lagergren is given as: ln(qe −qt)=ln(qe)−k1 ⋅t where qe and qt are the amounts of Cr(VI) (mg·g−1) adsorbed on the adsorbent at equilibrium and at time t, respectively and k1 is the rate constant of first-order adsorption (min−1). The slopes and intercepts of plots of ln(qe −qt) vs. t were used to determine the first-order rate constant k1. The pseudo1 1 second-order kinetic model is expressed as: qt ¼ k ⋅q 2 þ q  t where k2 t 2 e e (g·mg−1·min−1) is the rate constant of second order adsorption. The slopes and intercepts of plots of t/qt vs. t were used to calculate the second-order rate constant k2 and qe [22]. Adsorption rate constants were summarized in Table 4. The values of regression coefficient for pseudo-second-order model were close to 1 for all initial Cr(VI) concentrations. The calculated values qe,cal were very close to obtained qe,exp values. Hence, the adsorption of Cr(VI) onto magnetic chitosan nanoparticles could obey the pseudo-second-order kinetic model.

References

4. Conclusion In this work, cross-linked with epichlorohydrin magnetic chitosan nanoparticles were prepared and characterized. The Cr(VI) adsorption behavior on the prepared magnetic chitosan nanoparticles has been studied under various conditions of different solution pH values and adsorption contact times. Optimal adsorption conditions of Cr(VI) were found at pH 3, and contact time of 100 min, with maximum adsorption capacity of 55.80 mg·g − 1. The Langmuir model was found to fit well with the experimental data (correlation coefficient R 2 > 0.99),

[1] P.G. Krishna, J.M. Gladis, U. Rambabu, T.P. Rao, G.R.K. Naidu, Talanta 63 (2004) 541–546. [2] C. Das, P. Patel, S. De, S. DasGupta, Sep. Purif. Technol. 50 (2006) 291–299. [3] N. Kongsricharoern, C. Polprasert, Water Sci. Technol. 34 (9) (1996) 109–116. [4] E.S. Abdel-Halim, S.S. Al-Deyab, Carbohydr. Polym. 86 (2011) 1306–1312. [5] Q. Li, Y. Qian, H. Cui, Q. Zhang, R. Tang, J. Zhai, Chem. Eng. J. 173 (2011) 715–721. [6] Junxi Liu, Chuan Wang, Jianying Shi, Hong Liu, Yexiang Tong, J. Hazard. Mater. 163 (1) (2009) 370–375. [7] R. Güell, E. Anticó, V. Salvadó, C. Fontàs, Sep. Purif. Technol. 62 (2008) 389–393. [8] F. Gode, E. Pehlivan, J. Hazard. Mater. B119 (2005) 175–182. [9] T. Sardohan, E. Kir, A. Gulec, Y. Cengeloglu, Sep. Purif. Technol. 74 (2010) 14–20. [10] Lulu Fan, Chuannan Luo, Zhen Lv, Lu. Fuguang, Huamin Qiu, Colloids Surf. B: Biointerfaces 88 (2011) 574–581. [11] T. Karthikeyan, S. Rajgopal, L.R. Miranda, J. Hazard. Mater. B124 (2005) 192–199. [12] K.C. Justi, V.T. Fávere, M.C.M. Laranjeira, A. Neves, R.A. Peralta, J. Colloid Interface Sci. 291 (2005) 369–374. [13] W.S. Wan Ngah, L.C. Teong, M.A.K.M. Hanafiah, Carbohydr. Polym. 83 (4) (2011) 1446–1456. [14] Feng-Chin Wu, Ru-Ling Tseng, Ruey-Shin Juang, J. Environ. Manage. 91 (4) (2010) 798–806. [15] Choong Jeon, Wolfgang H. Höll, Hydrometallurgy 71 (3–4) (2004) 421–428. [16] Y.C. Chang, S.W. Chang, D.H. Chen, React. Funct. Polym. 66 (2006) 335–341. [17] A.A. Atia, A.M. Donia, A.E. Shahin, Sep. Purif. Technol. 46 (2005) 208–213. [18] H.V. Tran, L.D. Tran, T.N. Nguyen, Mater. Sci. Eng. C 30 (2010) 304–310. [19] Guolin Huang, Hongyan Zhang, Jeffrey X. Shi, Tim A.G. Langrish, Ind. Eng. Chem. Res. 48 (5) (2009) 2646–2651. [20] Jingmiao Qu, Guang Liu, Yiming Wang, Ruoyu Hong, Adv. Powder Technol. 21 (4) (2010) 461–467. [21] APHA AWWA WPCF, Standard Methods for the Examination of Water and Wastewater, 21st ed., American Public Health Association, Washington, DC, 2005. [22] Y.S. Ho, Scientometrics 59 (2004) 171–177. [23] N.K. Hamadi, X.D. Chen, M.M. Farid, M.G.Q. Lu, Chem. Eng. J. 84 (2001) 95–105. [24] G.J. Alaerts, V. Jitjaturant, P. Kelderman, Water Sci. Technol. 21 (1989) 1701–1704. [25] G. Cimino, A. Passerini, G. Toscano, Water Res. 34 (2000) 2955–2962. [26] F.N. Acar, E. Malkoc, Bioresour. Technol. 94 (2004) 13–15. [27] D.C. Sharma, C.F. Forster, Bioresour. Technol. 47 (1994) 257–264. [28] S. Babel, T.A. Kurniawan, Chemosphere 54 (2000) 951–967. [29] K. Selvi, S. Pattabhi, K. Kadirvelu, Bioresour. Technol. 80 (2001) 87–89. [30] Y.A. Aydin, N.D. Aksoy, Chem. Eng. J. 151 (2009) 188–194. [31] R. Schmuhl, H.M. Krieg, K. Keizer, Water SA 27 (2001) 1–7.

Table 4 Comparison of the first-order and second-order adsorption rate constants, calculated qe,cal and experimental qe,exp values for different initial Cr(VI) concentrations. C0 (mg·L−1)

qe,exp (mg/g)

First-order kinetic model −1

k1 (min 40 80 180

19.42 37.05 53.8

0.029 0.030 0.025

)

Second-order kinetic model −1

qe,cal (mg·g 5.59 25.43 22.04

)

R

2

0.946 0.876 0.956

k2(g·mg−1·min−1) −3

8.38 × 10 2.08 × 10−3 2.16 × 10−3

qe,cal (mg·g−1)

R2

19.94 38.46 55.55

0.994 0.992 0.996