Kinetics and Thermodynamics of Alkaline Earth and Heavy Metal Ion

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Kinetics and Thermodynamics of Alkaline Earth and Heavy Metal Ion Exchange under Particle Diffusion Controlled Phenomenon Using Polyaniline-Sn(IV)iodophosphate Nanocomposite Md. Dilwar Alam Khan,* Arshia Akhtar, and Syed Ashfaq Nabi Analytical Research Laboratory, Department of Chemistry, Aligarh Muslim University, Aligarh, India 202002 S Supporting Information *

ABSTRACT: The polyaniline-Sn(IV)iodophosphate nanocomposite (PANI-SnIP) has been synthesized, and its various kinetic and thermodynamic parameters for alkaline earth and heavy metal ion exchange were evaluated. Above 0.03 M solution of metal ions, the particle diffusion controlled phenomenon is found to be predominant (R2 > 0.98). The kinetic and thermodynamic parameters like diffusion coefficient (Do), energy of activation (Ea), enthalpy of activation (ΔH*), entropy of activation (ΔS*), and free energy of activation (ΔG*) were evaluated under particle diffusion controlled phenomenon. The fractional attainment of equilibrium was faster at an elevated temperature, and the rate of exchange is predominated by Hg(II) ions in the case of multicomponent systems. The positive values of the standard enthalpy change (ΔH*) indicate the endothermic nature of the ion exchange process. The ion exchange follows an associative mechanism as indicated by ΔS* < −130 J mol−1 K−1. The comparatively fast kinetics of ion exchange by the nanocomposite depicts its applicability for environmental remediation.

1. INTRODUCTION The rapid industrialization, mining, and manifold increase in automobile exhaust has brought the level of pollution to an alarming situation. The continuous discharge of toxic heavy metals, radionuclide, and dyes by the power plant, textile, paper, paint, and automobile industries is adversely affecting both the aquatic and terrestrial life. Toxic metals such as Cd, Pb, Hg, Zn, As, Co, etc. are continuously discharged into the water streams and lakes, which leads to their bioaccumulation in living organisms, thereby causing health disorders in plants, animals, and human beings.1,2 The industrial effluents containing these toxic heavy metal ions and dyes need to be treated before their discharge into water streams as they are refractory and nonbiodegradable in nature. Adsorbents like red mud, bottom ash, activated carbon, etc. are being employed for the removal of reactive dyes, namely, methylene blue, Rhodamine-B, and fast green from industrial wastewater.3,4 The applications of conventional methods like coagulation, flocculation, precipitation, membrane separation, solvent extraction, and adsorption are not efficient enough to treat industrial effluent.5 Sometimes they lack selectivity for a particular heavy metal ion. Among the available heavy metal removal processes, ion exchange process is very effective in qualitative as well as quantitative separation of various heavy metals. Also, the ion exchange material can be easily recovered and reused by a regeneration process.6 The past few years have witnessed the synthesis of organic−inorganic composite ion exchange materials and their application in removal of heavy metal ions from industrial effluents and wastewater treatment.7−10 These materials have received wide attention owing to their significantly high thermal and chemical stability, ease of synthesis, reproducibility, selectivity, and cost effectiveness. © 2014 American Chemical Society

Although these materials possess better stability, selectivity, regenerability, etc., their practical utility depends on their ease of synthesis and ion exchange kinetics. The kinetics of ion exchange gives an idea about the viability of an ion exchange material in separation technology. Moreover, the evaluation of ion exchange kinetics and thermodynamic parameters, such as diffusion coefficient, energy and entropy of activation, or free energy change, is essential to understand the mechanism, ratedetermining step, rate laws, and ease of the ion exchange process. Most of the earlier studies11−14 involved the kinetic studies of alkaline earth and transition metal ion exchange, but no significant work has been done to evaluate the kinetic and thermodynamic parameters involving toxic heavy metal ions such as Hg(II) and Pb(II). Also, the ion exchange material has been employed for selective removal of Cs(I), Hg(II), and Cd(II)15−17 from the solution with only one counterion species, but a multicomponent system involving competing ionic species is rarely considered for kinetic studies, thus limiting their application to complex ion exchange systems. Therefore, the present work deals with the study of kinetics and thermodynamic behavior of alkaline earth as well as heavy metal ion exchange on a nanocomposite ion exchanger under the particle diffusion controlled phenomenon. The effects of metal ion concentration, temperature, contact time, etc. were also studied to assess the viability of the ion exchange process using the polyaniline-Sn(IV)iodophosphate (PANI-SnIP) nanocomposite. The removal of Hg(II) from aqueous solution under competitive environment is also studied to evaluate the Received: June 9, 2014 Accepted: July 10, 2014 Published: July 17, 2014 2677

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Figure 1. Simultaneous TGA-DTA curves of the PANI-SnIP nanocomposite.

diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) analyses were carried out to characterize the composite material. The infrared (IR) spectra were recorded on a FTIR spectrometer from PerkinElmer (1730, USA) using the KBr disc method. Simultaneous TGA-DTA measurements were carried out on a DTG-60 H; C305743 00134, (Schimadzu, Japan) analyzer. An X’Pert PRO analytical diffractometer (PW-3040/60, The Netherlands) with Cu Kα radiation, λ = 1.5418 Å, was used for XRD measurement. A SEM instrument (LEO, 435 VF) was used for capturing SEM images. TEM analysis was carried out on a Jeol H-7500 microscope. 2.4. Kinetic Measurements. A water bath incubator shaker having a temperature variation of ±0.5 °C was used for all equilibrium studies. The ion exchange material in H+ form having particles with a mean radii of ∼ 125 μm (80−120 mesh) was considered for the evaluation of kinetic parameters. The limited batch technique was employed to investigate the effects of operational parameters such as initial metal ion concentration, contact time, and temperature on the ion exchange process and to determine the rate of ion exchange. Twenty milliliter fractions of the metal ion solutions (0.03 M each) of Mg(II), Ca(II), Sr(II), Hg(II), Cd(II), and Zn(II) were shaken with 200 mg of the nanocomposite cation exchanger in H+ form in several stopper conical flasks at temperatures of 25 °C, 35 °C, 45 °C, and 55 °C for different time intervals (1 min, 2 min, 3 min, 4 min, and 5 min). The optimum agitation speed of 250 rpm was maintained for all experimental test runs. The supernatant liquid was removed immediately, and residual metal ion concentrations were determined usually by EDTA titrations.18 Each set was repeated three times, and the mean values were taken for calculations. For competitive ion exchange processes, the binary viz. Hg(II) + Mg(II), Hg(II) + Zn(II) and ternary viz. Hg(II) + Mg(II) + Zn(II), Hg(II) + Sr(II) + Cd(II) systems were considered with equal initial concentration of each competing ionic species. In each case, Hg(II) is commonly considered as it is found to be more selectively exchanged by the nanocomposite. The experiment was carried out at room temperature (25 ± 2 °C), and the same procedure was employed as mentioned above. The metal ion concentrations in the solution

kinetic behavior of the separation approaching a more realistic scenario.

2. EXPERIMENTAL SECTION 2.1. Reagents and Chemicals. The reagents used for the synthesis were stannic chloride, SnCl4·5H2O (CDH, India), potassium iodate, KIO3 (SDFCL, India), ortho-phosphoric acid, H3PO4 (E-Merck, India), ammonium persulfate, (NH4)2S2O8, and aniline, C6H5NH2 (CDH, India). The rest of the chemicals used were of analytical grade. Potassium iodate (0.1 M) and ortho-phosphoric acid (0.1 M) were prepared in demineralized water, whereas stannic chloride (0.1 M) was prepared in 1 M HCl solution. Solutions of double distilled aniline (10 % v/v) and ammonium persulfate (0.1 M) were prepared in 1 M HCl solution. 2.2. Synthesis of Polyaniline-Sn(IV)iodophosphate Nanocomposites. The sol−gel method was employed for the synthesis of nanocomposite material. First, the inorganic precipitate of Sn(IV)iodophosphate was prepared at room temperature (25 ± 2 °C) by gradually adding a mixture of potassium iodate and ortho-phosphoric acid to the solution of stannic chloride with constant stirring for 2 h at pH 1. The polymerization of aniline was initiated at 5 ± 2 °C by mixing an equal volume ratio of aniline and ammonium persulfate where the latter acts as an oxidizing agent. The green colored polyaniline gel so formed was added to the white inorganic precipitate of Sn(IV)iodophosphate with constant stirring for 2 h. The resultant blackish green colored slurry was kept for 24 h at room temperature (25 ± 2 °C) in mother liquid for complete digestion. The material was then filtered under suction and washed thoroughly with demineralized water to remove excess reagents. After the compound is dried in an oven at 50 °C, it is crushed into granules for column and batch experiments. Finally, the material was converted into H+ form upon treatment with 1 M HNO3 solution for 6 h. The material was then dried and sieved to obtain the particles of desired size, that is, mean radii ∼ 125 μm (80−120 mesh). 2.3. Characterization of Nanocomposite. The physicochemical properties such as ion exchange capacity, functionality behavior, and stability were evaluated for the nanocomposite cation exchanger. The Fourier transform infrared (FTIR), X-ray 2678

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to 1210 cm−1 corresponds to the phosphate group of the inorganic part.23 The X-ray diffraction spectrum (Figure 3) shows the presence of some low intensity peaks at 2θ values of 37, 43, and 77, indicating the semicrystalline nature of the nanocomposite. The SEM image (Figure 4a) taken at the magnification of 1000× shows the intermixing of both inorganic and organic phases with the absence of any impure phases. Similarly, the TEM image (Figure 4b) of the composite depicts the formation of nano-sized particles with chain-like conformations, which may facilitate the sorption of metal ions. 3.1. Kinetics of Ion Exchange. The kinetic measurements were carried out under conditions favoring the particle diffusion controlled ion exchange phenomenon for the exchange of Mg(II)−H(I), Ca(II)−H(I), Sr(II)−H(I), Hg(II)−H(I), Cd(II)−H(I), and Zn(II)−H(I). The particle diffusion controlled phenomenon is favored by a high metal ion concentration, a relatively large particle size of the exchanger, and vigorous shaking of the exchanging mixture.24 The effect of contact time shows that the exchange of metal ions increases with time and occurs in two distinct phases: a relatively quick exchange in the first stage followed by a relatively slower one until the equilibrium is reached. The infinite time of exchange is the time necessary to obtain equilibrium in an ion exchange process. The rate of ion exchange becomes independent of time after this interval. It is evident from Figure 5 that 40 min was required to establish the equilibrium for Mg(II)−H(I) exchange at 25 °C. The Ca(II)−H(I), Sr(II)−H(I), Hg(II)−H(I), Cd(II)−H(I), and Zn(II)−H(I) exchange system behaved in a similar fashion. Therefore, 40 min was assumed to be infinite time of exchange for this particular system under consideration. It is now a well-established25 fact that the rate of exchange is governed by the exchange of ions either through the liquid film surrounding the exchanger material or through the exchanger particles. The former is considered to control the rate process in dilute solution and the latter at higher concentrations of the exchanging ions. This behavior may be due to ion concentration where the transition is getting stronger mass with greater emphasis.26 Therefore, a plot of “τ”, a dimensionless parameter obtained from U(τ) (discussed later) versus time t

phase were analyzed by FAAS. A comparative analysis of singlecomponent and multicomponent systems of ion exchange has been done to have an insight into the effect of competing ionic species on the exchange of a particular metal ion of interest.

3. RESULTS AND DISCUSSION The newly synthesized polyaniline-Sn(IV)iodophosphate nanocomposite cation exchanger possesses an ion exchange capacity of 1.48 mequiv g−1 for the K+ ion. The ion exchange capacity for alkali and alkaline earth metal ions increases with decreasing hydrated ionic radii of the metal ion (Supporting Information). The pH titration curves for alkali metal ions with their corresponding salt using the nanocomposite show bifunctional behavior of the cation exchanger (graphs omitted). Simultaneous TGA-DTA curve (Figure 1) of the nanocomposite shows a continuous weight loss of about 10.7% up to 190 °C, which is due to the removal of free external water molecules.19 Further weight loss in the region of 190 °C to 545 °C may be attributed to the condensation of a phosphate group to pyrophosphate and IO3 group into I2O5.20,21 The FTIR spectrum of the PANI-SnIP nanocomposite (Figure 2) shows the intermixing of polyaniline and Sn(IV)iodophosphate with characteristic sharp bands at ∼1600 cm−1 and ∼1510 cm−1 corresponding to N−H bending vibration while the bands at 1270 cm−1 to 1300 cm−1 of medium intensity accounts for C−N stretching vibration of the polyaniline.22 A strong broad band at 900 cm−1

Figure 2. FTIR spectrum of the PANI-SnIP nanocomposite.

Figure 3. XRD spectrum of the PANI-SnIP nanocomposite. 2679

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Figure 6. Effect of metal ion concentration on M(II)−H(I) exchange at 25 °C using the PANI-SnIP nanocomposite.

phenomenon and initial rate of exchange is proportional to metal ion concentration. Below the concentration of 0.03 M, film diffusion controlled phenomenon is found to be more prominent. Therefore, a metal ion concentration of 0.03 M is considered for further studies. For an ion exchange process, the fractional attainment of equilibrium is given by the expression U (τ ) =

amount of metal ion exchanged at time t amount of metal ion exchanged at infinite time (1)

The plots of U(τ) versus time t at different temperature for a constant metal ion concentration of 0.03 M (Figure 7) shows that the fractional attainment of equilibrium is faster at a higher temperature. This may be due to an increase in the mobility of the ions through the thermally enlarged interstitial positions of the ion exchange matrix at elevated temperature. In the case of ion uptake by the PANI-SnIP from a competitive environment, it has been found that the exchange of a particular metal ion is affected by the presence of other competing ionic species of the same charge in the solution. The rate of fractional attainment of equilibrium is slower in the case of binary and ternary systems for each of the metal ions than their corresponding single-component system at the same temperature (Figures 8 and 9). It may be due to the competition among the metal ions for binding sites or cavities present on the nanocomposite material. Further, it may be noted that in each case the fractional attainment of equilibrium is faster for the Hg(II) ion, and its uptake is negligibly affected by the presence of other ions in the solution. For the ternary system, the uptake of ions follows the order Hg(II) > Mg(II) > Zn(II) and Hg(II) > Sr(II) > Cd(II). This is in accordance with their diffusion coefficient Do value. The comparatively fast and selective uptake of Hg(II) ion reflects the affinity of the nanocomposite for the Hg(II) ion, a hazardous water pollutant. For each value of U(τ), there is a corresponding value of τ, a dimensionless time parameter. On the basis of the Nernst− Planck equation, the numerical results can be expressed by explicit approximation27−29

Figure 4. (a) Scanning electron micrograph image and (b) transmission electron micrograph image of the PANI-SnIP nanocomposite.

Figure 5. Plot of U(τ) versus time (t) for Mg(II)−H(I) exchange at 25 °C on the PANI-SnIP nanocomposite.

U (τ ) = {1 − exp[π 2(f1 (α)τ + f2 (α)τ 2 + f3 (α)τ 3)]}1/2

shows the effect of exchanging metal ion concentration on the rate of ion exchange (Figure 6). The rate of exchange increases with the increase in concentration of metal ion (0.01 M to 0.05 M) at the solution phase. The straight line passing through the origin for the metal ion concentration at 0.03 M and above shows that the predominance of particle diffusion controlled

where τ is the half-time of exchange = α is the mobility ratio = D H+/ D M2+ , ro is the particle radius, D H+ and D M2+ are the interdiffusion coefficients of counterions H+ and M2+, respectively, in the exchanger phase. The three functions f1(α), f 2(α), and f 3(α) depend upon the mobility ratio (α) and the charge ratio (ZH+/ZM2+) of the exchanging ions and have

(2)

D H+ t/r2o,

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Figure 7. Plots of U(τ) versus time (t) for different M(II)−H(I) exchanges at different temperatures on the PANI-SnIP nanocomposite cation exchanger.

Figure 8. Plots of fractional attainment of equilibrium as a function of time for ion exchange in the binary system.

The value of τ corresponding to each U(τ) value has been evaluated using eq 2. The plots of τ versus time (t) for each M(II)−H(I) exchange system at four different temperatures (Figure 10) give straight lines passing through the origin, confirming particle diffusion controlled phenomenon at a metal ion concentration of 0.03 M. 3.2. Activation Energy and Thermodynamic Functions. The slopes (S) of various τ versus time (t) graph presented in Table 1 are related to D̅ H+ as

expression as given below. For M(II)−H(I) type ion exchange reaction with 1 ≤ α ≤ 20 as in the present case, the three functions have the values f1 (α) = −

1 0.64 + 0.36α 0.668

f2 (α) = −

1 0.96 − 2.0α 0.4635

f3 (α) = −

1 0.27 + 0.09α1.140

S = D H+ /ro2 2681

(3)

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Figure 9. Plots of fractional attainment of equilibrium as a function of time for ion exchange in the ternary system.

Figure 10. Plots of τ vs time (t) for M(II)−H(I) exchange at various temperature (◆) 25 °C, (■) 35 °C, (△) 45 °C, and (●) 55 °C on the PANI-SnIP nanocomposite cation exchanger.

Figure 11. Arrhenius plots of −ln D̅ H versus 1/T for the metal ion exchange on the PANI-SnIP nanocomposite cation exchanger. 2682

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intercept and slope of the −ln D̅ H+ versus 1/T graph at 273 K. The diffusion coefficient Do gives the entropy of activation ΔS* as30

Table 1. Slopes of Various τ vs Time (t) Plots and Related D̅ H+ Values for Metal Ion Exchange on PANI-SnIP Nanocomposites at Different Temperatures metal ion

temp (°C)

slope × 10−4 (s−1)

R2

D̅ H+ × 10−12 (m2 s−1)

Mg(II)

25 35 45 55 25 35 45 55 25 35 45 55 25 35 45 55 25 35 45 55 25 35 45 55

5.00 5.66 6.67 7.67 4.17 4.67 5.17 6.00 3.67 4.33 5.00 5.67 6.83 8.00 9.33 10.16 2.33 2.67 3.17 3.67 2.17 2.67 3.00 3.33

0.997 0.998 0.998 0.998 0.997 0.996 0.998 0.997 0.995 0.998 0.995 0.997 0.996 0.998 0.997 0.995 0.996 0.998 0.998 0.998 0.999 0.998 0.999 0.999

7.812 8.843 10.421 11.984 6.515 7.296 8.078 9.375 5.734 6.765 7.812 8.859 10.671 12.500 14.578 15.875 3.640 4.171 4.953 5.734 3.390 4.171 4.687 5.203

Ca(II)

Sr(II)

Hg(II)

Cd(II)

Zn(II)

⎛ kT ⎞ ⎛ ΔS* ⎞ ⎟ Do = 2.72d 2⎜ ⎟exp⎜ ⎝ h ⎠ ⎝ R ⎠

where k, h, and R are the Boltzmann, Planck, and gas constants, respectively, d is the average distance between the successive exchange sites and is taken as 5 Å.31 T (=273 K) is the temperature in Kelvin scale. The enthalpy of ion exchange reaction ΔH* was calculated using its relationship with Ea as ΔH * = Ea − nRT

(6)

The free energy of activation ΔG* corresponding to four different temperatures was evaluated using the following relationship.32 (7)

ΔG* = ΔH * − T ΔS*

The values of diffusion coefficient (Do), energy of activation (Ea), enthalpy of activation (ΔH*), entropy of activation (ΔS*), and free energy of activation (ΔG*) are summarized in Table 2. The magnitude of diffusion coefficient depends upon the nature of interactions between the ions and the exchanger. For physical adsorption, the value of diffusion coefficient ranges from 10−6 m2 s−1 to 10−9 m2 s−1, whereas for chemical sorption, the value ranges from 10−9 m2 s−1 to 10−17 m2 s−1.33 In the present investigation, the values of diffusion coefficient were found to be on the order 10−12 m2 s−1, which infers a chemisorption phenomenon or specifically an ion exchange process where the molecules after the exchange get strongly bound and localized. The energies of activation (Ea) for the ion exchange process under consideration are in the order Hg(II) < Mg(II) < Ca(II) < Sr(II) < Zn(II) −10 J mol−1 K−1 generally imply a dissociative mechanism, whereas a high negative value or < −10 J mol−1 K−1 indicate an associative mechanism.34 In the present study, a high negative value of ΔS* (−130 J mol−1 K−1 to −155 J mol−1 K−1) shows that the ion exchange by the PANI-SnIP nanocomposite cation exchanger follows an associative mechanism, and there is no significant change in the internal structure of the nanocomposite. Figure 12 shows the relationship between Ea and ΔS* values for two different sets of the metal ion exchange on the nanocomposite cation exchanger. The plots of Ea versus ΔS* give a linear relationship indicating that the Ea − ΔS* compensation mechanism holds in the ion exchange process. Normally it is found in the acid variety of processes and reaction equilibrium. The physicochemical origin of the Ea − ΔS* compensation is probably related to an intrinsic property of hydration.35 This process favored the M(II)−H(I) ion exchange with greater ease.

4. CONCLUSION An insight into the ion exchange kinetics and thermodynamics shows that the polyaniline-Sn(IV)iodophosphate nanocomposite cation exchanger can be applied successfully for the removal of toxic heavy metal ions from wastewater. The concentration of metal ion, contact time, and temperature of the solution has a pronounced effect on the ion exchange behavior of the nanocomposite. The fractional attainment of equilibrium was found to be faster at higher temperature. The evaluation of various kinetic and thermodynamic parameters under particle diffusion controlled phenomenon for alkaline earth and heavy metal ions shows that the exchange of Hg(II) is comparatively fast and selective with high diffusion coefficient (Do) and low energy of activation (Ea). The ion exchange followed an associative mechanism as revealed by high negative values of entropy of activation (ΔS*). All of these characteristics reflect the viability of the ion exchange process using the the PANI-SnIP nanocomposite.

■

ASSOCIATED CONTENT

S Supporting Information *

Ion exchange capacity table. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are thankful to the Chairman, Department of Chemistry, Aligarh Muslim University, Aligarh (India) for providing necessary research facilities, and University Grants Commission, India, for providing UGC-BSR Faculty fellowship to S.A.N.

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REFERENCES

(1) Mustafa, K. Removal of Pb(II) from water by natural zeolitic tuff: Kinetics and thermodynamics. J. Hazard. Mater. 2012, 199−200, 383. 2684

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(23) Davies, M. Infrared Spectroscopy and Molecular Structures; Elsevier Publishing Company: Amsterdam, 1963; p 318. (24) Khan, A. A.; Akhtar, T. Cation-exchange kinetic studies on polyo-toluidine Ce(IV) phosphate: a nano-composite and electrical conducting material. Appl. Polym. Sci. 2012, 47, 3241. (25) Aboul-Magd, A. S.; Kamal, F. H.; Salem, A. M.; Hassan, E. A. Kinetics and mechanism of exchange sorption of Mg(II) in aqueousacetone on Dowex HCR. Indian J. Technol. 1985, 26, 354. (26) Han, R.; Zou, W.; Li, H.; Li, Y.; Shi, J. Copper(II) and Pb(II) removal from aqueous solution in fixed-bed columns by Mn-oxide coated Zeolite. J. Hazard. Mater. 2006, 137, 934. (27) Hall, K. R.; Eagleton, L. C.; Acrivos, A.; Vermeulen, T. Poresolid-diffusion kinetics in fixed-bed adsorption under constant-pattern conditions. Ind. Eng. Chem. Fundam. 1966, 5, 212. (28) Helfferich, F.; Plesset, M. S. Ion exchange kinetics. A nonlinear diffusion problem. J. Chem. Phys. 1958, 28, 418. (29) Plesset, M. S.; Helfferich, F.; Franklin, J. N. Ion exchange kinetics. A non-linear diffusion problem. II. Particle diffusion controlled exchange of univalent and bivalent ions. J. Chem. Phys. 1958, 29, 1064. (30) McKay, H. A. C. Kinetics of exchange reactions. Nature 1998, 147, 927. (31) Helfferich, F. Ion Exchange; McGraw-Hill: New York, 1962; p 256. (32) Jencks, P. Catalysis in Chemistry and Enzymology; McGraw-Hill: New York, 1969. (33) Walker, G. M.; Weatherley, L. R. Kinetics of acid dye adsorption on GAC. Water Res. 1999, 33, 1895. (34) El-Naggar, I. M.; Zakaria, E. S.; Ali, I. M.; Khalil, M.; El-Shahat, M. F. Kinetic modeling analysis for the removal of cesium ions from aqueous solutions using polyaniline titanotungstate. Arabian J. Chem. 2012, 5, 109. (35) El-Naggar, I. M.; Zakaria, E. S.; Shady, S. A.; Aly, H. F. Diffusion mechanism and ion exchange equilibria of some heavy metal ions on cerium(IV) antimonate as cation exchanger. Solid State Ionics 1999, 122, 65.

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