Antagonistic Competitive Equilibrium Modeling for the Adsorption of

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Ind. Eng. Chem. Res. 2008, 47, 3129-3137

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Antagonistic Competitive Equilibrium Modeling for the Adsorption of Ternary Metal Ion Mixtures from Aqueous Solution onto Bagasse Fly Ash Vimal Chandra Srivastava,* Indra Deo Mall, and Indra Mani Mishra Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India

The present study reports the simultaneous adsorption of cadmium (Cd(II)), nickel (Ni(II)), and zinc (Zn(II)) ions from aqueous solution onto bagasse fly ash (BFA). BFA is a waste material collected from the particulate collection equipment attached to the flue-gas line of bagasse fired boilers in sugar mills. The equilibrium adsorption data were obtained with a BFA dosage of 10 g/dm3 at varying initial concentrations (C0 ) 10100 mg/dm3), 5 h contact time, 30 °C temperature, and initial pH 6. The single metal ion equilibrium adsorption data were fitted to the noncompetitive Langmuir, Freundlich and Redlich-Peterson (R-P) models. The R-P and Freundlich models represent the equilibrium data better than the Langmuir model over 10 e C0 e 100 mg/dm3. The adsorption capacity of Zn(II) is found to be higher than that of Ni(II) or Cd(II) for the ternary metal solutions, and is in agreement with the single-component adsorption data. The equilibrium metal removal decreases with an increase in the concentration of the other metal ion and the combined action of Cd(II), Ni(II), and Zn(II) ions on BFA is generally found to be antagonistic. Equilibrium isotherms for the ternary adsorption of Cd(II), Ni(II), and Zn(II) ions on BFA have been analyzed by using nonmodified, modified, and extended Langmuir models; nonmodified and modified R-P models; and the Sheindorf-RebuhnSheintuch (SRS) model. The competitive SRS model fits the ternary adsorption equilibrium data satisfactorily and adequately, and has been used to simulate the equilibrium sorption behavior of the ternary metal ion system through three-dimensional plots. 1. Introduction Adsorption as a separation process has aroused considerable interest during recent years. In wastewater treatment, adsorption is regarded as one of the most potent techniques for the removal of metal ions. A considerable amount of work on the adsorption of heavy metal ions has focused on the uptake of single metals by various kinds of adsorbents. Since industrial effluents can contain several metals simultaneously, it is necessary to study the simultaneous multicomponent sorption of metal ions and also to quantify the interactive influence of metals on the sorption of one another. Thus the studies on equilibrium and kinetics of adsorption of heavy metals from ternary systems are very important. Commercially, activated carbon is regarded as the most effective adsorbent for the removal of the organic and inorganic pollutants from wastewater. However, due to its high cost and about 10-15% loss during regeneration, unconventional adsorbents such as bagasse fly ash (BFA), rice husk ash, corncob, red mud, fly ash, baker’s yeast cells, akaganeite, river bed sediments, animal bones, oil shale ash, etc. have attracted the attention of several investigators.1-5 BFA is a waste collected from the particulate collection equipment attached upstream to the stacks of bagasse-fired boilers. Its potential as an adsorbent has been investigated in wastewater treatment for the removal of COD and color from sugar mills,6 paper mills,7 and chemical manufacturing units for the removal of pyridine and its derivatives,8-10 heavy metals,11-12 phenolic compounds,13 and dyes.14-16 Most of the sugar mills spend money for the collection, transportation and disposal of BFA as a landfill material. It is abundantly available, and therefore, its use as an adsorbent will not entail any expenditure, except that on its transportation and sieving, as it * To whom correspondence should be addressed. Tel.: +91-1332285889. Fax: +91-1332-276535, 273560. E-mail: [email protected], [email protected].

can be used without any treatment. Thus, BFA may prove to be a much cheaper substitute to activated carbon as an adsorbent. Cadmium (Cd(II)), nickel (Ni(II)), and zinc (Zn(II)) are among the most commonly found metals in industrial effluents.17 The toxicity of these metal ions on living beings and the environment has been detailed by many researchers.11-12,17-19 The Ministry of Environment and Forests, Government of India, has prescribed Minimal National Standards, MINAS, of 0.2, 2.0, and 5.0 mg/dm3, respectively, for the discharge of Cd(II), Ni(II), and Zn(II) in the effluents to be discharged into surface waters.20 The permissible Cd(II), Ni(II), and Zn(II) concentrations in potable waters have been set as 0.003, 0.02, and 3 mg/ dm3, respectively.21 The experimental data on the adsorption of metal ions from binary metal ion liquid mixtures by BFA have been reported recently.11,22 Only a few adsorption studies are reported in the literature on the adsorption of metal ions from ternary metal ion aqueous solutions.23-30 The single-component adsorption isotherm equations are generally extended and modified to represent the ternary and multicomponent adsorption equilibria. The aim of the present paper is to (i) study the feasibility of using BFA as an adsorbent for the simultaneous removal of Cd(II), Ni(II), and Zn(II) metal ions from aqueous solutions; (ii) gather experimental adsorption equilibrium data for the ternary system of Cd(II), Ni(II), and Zn(II) ions in aqueous solution; (iii) determine the applicability of noncompetitive adsorption isotherm models (i.e., Freundlich, Langmuir, and Redlich-Peterson (R-P)) for single components; and (iv) to examine the applicability of the multicomponent adsorption isotherm equations to the competitive adsorption equilibria of the metals in a ternary system. 2. Single-Component and Multicomponent Adsorption Modeling Designing an optimized adsorption system requires establishment of the best correlation representing the equilibrium data.

10.1021/ie0709842 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/26/2008

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Ind. Eng. Chem. Res., Vol. 47, No. 9, 2008

Table 1. Mono- and Multicomponent Isotherm Models ref Freundlich

Monocomponent Isotherm Models qe ) KFC1/n e

Langmuir Redlich-Peterson

31

qmKLCe qe ) 1 + K L Ce KRCe qe ) 1 + aRCβe

32 33

Multicomponent Isotherm Models qm,iKL,iCe,i qe,i ) nonmodified Langmuir N

1+

∑K

L,jCe,j

the single-component Langmuir equation to give extended Langmuir isotherm for multicomponent systems. Sheindorf et al.36 derived a Freundlich-type multicomponent adsorption isotherm known as the Sheindorf-Rebuhn-Sheintuch (SRS) equation, to represent the multicomponent experimental data. The competition coefficient aij in the SRS model describes the inhibition to the adsorption of component i by component j, and can be determined from the thermodynamic data or, more likely, from the experimental data of multicomponent systems. The SRS equation assumes that (i) each component individually obeys the Freundlich isotherm, (ii) there exists an exponential distribution of site adsorption energies for each component in a multicomponent adsorption system

j)1

modified Langmuir

qe,i )

qm,iKL,i(Ce,i/ηL,i)

Ni(Q) ) Ri exp(-βiQ/RT)

N

1+

∑K

where Ri and βi are constants, and (iii) that the surface coverage by each adsorbate molecule (or ion) at each energy level Q is given by the multicomponent Langmuir isotherm equation:

L,j(Ce,j/ηL,j)

j)1

N

extended Langmuir

qe,i ) KF,iCe,i(

∑a C

(1/ni)-1 ij e,j)

35

j)1

Sheindorf-Rebuhn-Sheintuch (SRS)

qe,i )

1+

36

∑K

KiCe,i

θi(Q) )

qmaxKEL,iCe,i N

1+

EL,jCe,j

KR,iCe,i

qe,i )

(2)

N

j)1

nonmodified Redlich-Peterson

(1)

34

KjCe,j ∑ j)1

where

N

1+

∑a

Kj ) K0j exp(Q/RT)

β,j R,jCe,j

(3)

j)1

modified Redlich-Peterson

KR,i(Ce,i/ηR,i)

qe,i )

N

1+

∑a

β,j R,j(Ce,j/ηR,j)

j)1

Therefore, the equilibrium adsorption data for Cd(II), Ni(II), and Zn(II) ions from single and ternary systems onto BFA have been used to test the applicability of various single-component and multicomponent isotherm equations. These isotherm equations are given in Table 1. The theory associated with these isotherm equations has already been discussed by Srivastava et al.11,22 Various isotherm equations such as the Freundlich, Langmuir, and Redlich-Peterson (R-P) equations have been extensively used to describe the equilibrium characteristics of monocomponent adsorption. The Freundlich isotherm31 is derived by assuming a heterogeneous surface with a nonuniform distribution of heat of adsorption over the surface, whereas in the Langmuir theory,32 the basic assumption is that the sorption takes place at specific homogeneous sites within the adsorbent. The R-P isotherm33 incorporates three parameters and can be applied to both the homogeneous and heterogeneous systems. The multicomponent isotherm equations are basically extensions of single-component isotherm equations. In the nonmodified competitive Langmuir model, the individual adsorption constants may not define exactly the multicomponent adsorption behavior of metal ions. Therefore, an interaction term, ηL,i, which is a characteristic of each species present in the solution and depends on the concentrations of the other components, has been added in the competitive Langmuir to formulate the modified competitive Langmuir isotherm.34 Similarly, the competitive nonmodified R-P model is modified, using an interaction term ηR,i, to get the modified competitive R-P model. Assuming that the surface sites are uniform, and that all the adsorbate molecules (ions) in the solution compete for the same surface sites, Yang35 extended

Integration of Ni(Q) θi(Q) over energy levels in the range of -∞ to +∞ yields eq 2 and the competition coefficient is defined as aij ) K0j/K0i; thus aji ) 1/aij. The isotherm parameters of all the multicomponent models can be found by using Microsoft Excel 2002 for Windows by minimizing Marquardt’s percent standard deviation (MPSD).37 This error function is given as

MPSD ) 100

x ( 1

n

∑

nm - np i)1

N

∑ i)1

(

N

∑ i)1

qe,i,exp) - (

)

2

qe,i,cal)

N

qe,i,exp ∑ i)1

(4)

i

In the above equation, the subscripts “exp” and “calc” represent the experimental and calculated values; nm is the number of measurements and np is the number of parameters in the model. The adsorptive uptake (qe,i), individual adsorption yield (Adi (%)), and the total adsorption yield (AdTot (%)) can be calculated by using the following expressions:

qe,i ) (C0,i - Ce,i)V/w (mg of adsorbate/g of adsorbent) (5) Adi (%) ) 100(C0,i - Ce,i)/C0,i AdTot (%) ) 100

∑(C0,i - Ce,i)/∑C0,i

(6) (7)

where V is the volume of the adsorbate-containing solution (dm3) and w is the mass of the adsorbent (g). 3. Experimental Section 3.1. BFA. BFA was obtained from a nearby sugar mill (Deoband sugar mill, U.P., India) and was sieved, and the

Ind. Eng. Chem. Res., Vol. 47, No. 9, 2008 3131

maintained at 6.0. This pH0 was found to be the optimum pH0 on the basis of batch tests carried out to determine the effect of pH0 on the adsorption capacity of BFA for these metal ions. The concentration of each metal ion in a sample was determined by a flame atomic absorption spectrophotometer (AAS) (GBC Avanta, Australia) with the detection limits of 0.009, 0.040, and 0.008 mg/dm3 at wavelengths 228.8, 232, and 213.9 nm, for Cd(II), Ni(II), and Zn(II), respectively. Airacetylene flame was used in the AAS. Before the analysis, the sample was diluted, if necessary, with DDW to a concentration in the range of 0.2-1.8 mg/dm3 for Cd(II), 1.8-8 mg/dm3 for Ni(II), and 0.4-1.5 mg/dm3 for Zn(II). 4. Results and Discussion

Figure 1. Equilibrium adsorption isotherms for individual adsorption of Cd(II), Ni(II), and Zn(II) ions onto bagasse fly ash. Experimental data points given by the symbols and the lines predicted by the Freundlich and RedlichPeterson models.

material with an average particle size of 167.35 µm was used as an adsorbent without any pretreatment. Detailed physicochemical characteristics of the BFA have already been presented elsewhere.11,12 3.2. Chemicals. All the chemicals used in the study were of analytical reagent grade. Nickel chloride hexahydrate (NiCl2‚ 6H2O) was procured from Qualigens Fine Chemicals, Mumbai, India. Cadmium sulfate octahydrate (3CdSO4‚8H2O), zinc sulfate heptahydrate (ZnSO4‚7H2O), NaOH, HCl, HNO3, H2SO4, and CH3COOH were obtained from S.D. Fine Chemicals, Mumbai. Stock solutions of 1 g/dm3 strength of Cd(II), Ni(II), and Zn(II) metal ions were prepared by dissolving 2.282, 4.05, and 4.40 g of 3CdSO4‚8H2O, NiCl2‚6H2O, and ZnSO4‚7H2O separately in 1 dm3 of double-distilled water (DDW). The stock solution for each metal salt was diluted with DDW to give the initial metal ion concentration (C0) in the range of 10-100 mg/ dm3 for use in the experiments. 3.3. Batch Adsorption Studies. For each experimental run, 0.1 dm3 of aqueous solution of a known concentration of Cd(II), Ni(II), or Zn(II) or a ternary mixture of these components was taken in a 0.25 dm3 glass-stoppered conical flask containing 1 g of BFA. These flasks were agitated at a constant shaking rate of 150 rpm in a temperature-controlled orbital shaker (Remi Instruments, Mumbai) maintained at 30 °C. For single metal-BFA systems, C0was varied from 10 to 100 mg/dm3 and the adsorbent dosage was kept at m ) 10 g/dm3. In ternary metal ion mixture-BFA systems, for C0 of Cd(II) solution, viz., 10, 20, 30, 50, and 100 mg/dm3, the Ni(II) and Zn(II) C0’s were varied in the range of 10-100 mg/dm3 (viz., 10, 20, 30, 50, and 100 mg/dm3). The adsorbent dose was kept at m ) 10 g/dm3. In all cases, the pH0 of the solution was

4.1. Single-Component Adsorption of Metal Ions. The equilibrium uptakes and the adsorption yields obtained for single-component adsorption at pH0 6.0 are shown in Figure 1 and Table 2. An increase in the C0 up to 100 mg/dm3 results in an increase in the equilibrium uptake and a decrease in the adsorption yield of all the components. When the C0 increases from 10 to 100 mg/dm3, the loading capacity of BFA increases from 0.89 to 5.18 mg/g for Cd(II), from 0.95 to 5.78 mg/g for Ni(II), and from 0.96 to 6.27 mg/g for Zn(II). C0 provides the necessary driving force to overcome the resistances to the mass transfer of metal ions between the aqueous bulk phase and the solid phase. An increase in the C0 also enhances the interaction between the metal ions in the aqueous phase and the BFA. Therefore, an increase in the C0 enhances the adsorption uptake of the metal ions. The adsorption capacity of the BFA for the metal ions was in the order Zn(II) > Ni(II) > Cd(II). This trend is according to the increasing size of the metal ions: Zn(II) (1.53 Å) < Ni(II) (1.62 Å) < Cd(II) (1.71 Å). Smaller metal ions have better accessibility to the surface and pores than bigger metal ions, resulting in the higher adsorption capacity of the smaller metal ions. 4.2. Single-Component Adsorption Isotherm. The experimental equilibrium adsorption data were obtained by varying the concentrations of individual metal ions with a fixed adsorbent dosage of 10 g/dm3. These data were fitted to the isotherm models. The isotherm parameters for each metal ion and the MPSD values as obtained from the fitting of different isotherm models with the experimental data are listed in Table 3. BFA has a heterogeneous surface for the adsorption of metal ions. Therefore, it is expected that the Freundlich and R-P isotherm equations can better represent the equilibrium sorption data than the Langmuir isotherm equation. The MPSD error values are least for the R-P model followed by those for the Freundlich and Langmuir models. Therefore, the equilibrium adsorption data of Cd(II), Ni(II), and Zn(II) ion adsorption on BFA can be represented appropriately by the R-P and the Freundlich models for 10 e C0 e 100 mg/dm3. The single-component Freundlich constants, KF and 1/n, indicate the adsorption capacity and adsorption intensity, respectively. The lower the value of 1/n, the more nonlinear is the adsorption isotherm, and as 1/n becomes less than 0.1, the

Table 2. Comparison of Individual Adsorption Equilibrium Uptakes and Yields of Cadmium(II), Nickel(II), and Zinc(II) Ion Adsorption onto Bagasse Fly Ash C0,Cd

Ce,Cd

qe,Cd

AdCd (%)

C0,Zn

Ce,Zn

qe,Zn

AdZn (%)

C0,Ni

Ce,Ni

qe,Ni

AdNi (%)

10 20 30 50 100

1.10 3.98 7.46 17.10 48.24

0.89 1.60 2.25 3.29 5.18

89.00 80.10 75.13 65.80 51.76

10 20 30 50 100

0.40 1.80 4.00 11.00 37.30

0.96 1.82 2.60 3.90 6.27

96.00 91.00 86.67 78.00 62.70

10 20 30 50 100

0.48 2.12 5.41 13.30 42.16

0.95 1.79 2.46 3.67 5.78

95.20 89.39 81.98 73.40 57.84

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Table 3. Isotherm Parameter Values for the Removal of Cadmium(II), Nickel(II), and Zinc(II) Ions by Bagasse Fly Ash Langmuir Constants adsorbate

KL (dm3/mg)

qm (mg/g)

MPSD

Cd(II) Ni(II) Zn(II)

0.09 0.15 0.18

6.19 6.49 7.03

23.89 35.07 32.61

Freundlich Constants adsorbate

KF ((mg/g)/(mg/L)1/n)

1/n

MPSD

Cd(II) Ni(II) Zn(II)

0.85 1.29 1.43

0.47 0.40 0.42

2.39 2.40 2.19

Redlich-Peterson Constants adsorbate

KR (dm3/g)

aR (dm3/mg)

β

MPSD

Cd(II) Ni(II) Zn(II)

10.44 306.79 22.09

11.36 237.39 14.36

0.55 0.59 0.61

2.19 2.39 2.19

adsorption approaches a so-called rectangular or irreversible isotherm. The higher the value of the exponent 1/n, the higher will be the affinity and the heterogeneity of the adsorbent sites. It is found from Table 3 that the BFA shows the greatest heterogeneity for Cd(II) followed by that for Zn(II) and Ni(II) ions. Since 1/n < 1, both metal ions are favorably adsorbed by BFA at pH0 6.0. The KF value indicates the highest uptake of Zn(II) followed by that of Ni(II) and Cd(II) in that order. The value of the R-P constant 0 e β e 1 indicates favorable adsorption. The β values for Zn(II), Ni(II), and Cd(II) ions were found to be 0.61, 0.60, and 0.55, respectively. Therefore, all the metal ions are adsorbed favorably by BFA. Thus, both isotherm models, viz., Freundlich and R-P, indicate the same conclusion. The comparison of the experimental and predicted equilibrium uptakes (qe) from the single-component Freundlich and R-P models for the individual adsorption of Cd(II), Ni(II), and Zn(II) from aqueous solution of 10 e C0 e 100 mg/dm3 onto BFA at pH0 6.0 is presented in Figure 1. This figure shows that the Freundlich and R-P isotherms represent the equilibrium sorption of individual metal ions adequately and satisfactorily. Table 2 also shows that the MPSD values for the two isotherm models are similar and much lower than that for the Langmuir model. Thus, either of the Freundlich and R-P models can be used to represent the experimental adsorption data. 4.3. Ternary Adsorption of Metal Ions. The simultaneous adsorption of Cd(II), Ni(II), and Zn(II) ions from ternary systems was also investigated. A total of 125 experiments were conducted to check the interactive effect of C0 of metal ions (Cd(II), Ni(II), and Zn(II)) with respect to each other for C0 ) 10, 20, 30, 50, and 100 mg/dm3. Representative adsorption equilibrium data are shown in Table 4. It was found that the equilibrium Cd(II) uptake increases with an increase in the C0 of Cd(II) up to 100 mg/dm3 for the same concentrations of Ni(II) and Zn(II) ions in the solution. The equilibrium uptake of Cd(II), however, decreases with an increase in the C0 values of Ni(II) and Zn(II). The individual and total adsorption equilibrium uptakes by BFA and the adsorption yields of Cd(II), Ni(II), and Zn(II) ions at various C0 values of each metal ion is listed in Table 4. In general, an increase in C0 of Ni(II) and/or Zn(II) ions decreases the individual adsorption yields and equilibrium uptake of Cd(II) and the total adsorption yields for each experimental run. At C0 ) 100 mg/dm3 for the single-component Cd(II) ion adsorption, the equilibrium uptake is found to be 5.18 mg/g (Table 2). However, with C0 ) 100 mg/dm3 Ni(II) ions and 10 mg/

Table 4. Comparison of Individual and Total Adsorption Equilibrium Yields at Different Cadmium(II) Concentrations in the Presence of Increasing Concentrations of Nickel(II) and Zinc(II) Ions on Bagasse Fly Ash C0,Cd qe,Cd AdCd (%) C0,Ni qe,Ni AdNi (%) C0,Zn qe,Zn AdNi (%) AdTot (%) 10 10 10 10 10 10 10 20 20 20 20 20 20 20 30 30 30 30 30 30 30 50 50 50 50 50 50 50 100 100 100 100 100 100 100

0.79 0.49 0.47 0.42 0.39 0.73 0.36 1.40 0.87 0.74 0.68 0.56 1.28 0.43 2.00 1.30 1.21 1.11 1.03 1.91 0.90 2.83 1.97 1.79 1.60 1.38 2.68 1.20 4.99 3.52 3.40 3.26 3.20 4.45 3.01

78.90 49.00 46.70 42.00 39.00 72.70 35.70 70.05 43.30 37.00 33.85 27.75 63.85 21.65 66.70 43.17 40.40 36.87 34.40 63.63 30.00 56.66 39.34 35.72 32.04 27.60 53.68 24.00 49.89 35.22 34.00 32.60 31.95 44.54 30.09

10 10 20 30 50 100 100 10 10 20 30 50 100 100 10 10 20 30 50 100 100 10 10 20 30 50 100 100 10 10 20 30 50 100 100

0.83 0.52 0.97 1.28 2.01 5.21 3.75 0.82 0.52 0.92 1.17 1.80 5.10 3.65 0.81 0.51 0.84 1.09 1.58 4.89 3.13 0.81 0.50 0.80 1.00 1.31 4.70 3.00 0.80 0.49 0.71 0.91 1.10 4.52 2.76

82.50 52.20 48.30 42.57 40.20 52.06 37.54 81.90 51.50 46.10 38.87 36.00 51.00 36.54 81.40 50.80 42.20 36.47 31.50 48.89 31.33 80.70 50.20 39.80 33.47 26.10 46.96 30.00 80.00 49.00 35.65 30.17 21.96 45.21 27.58

10 100 100 100 100 10 100 10 100 100 100 100 10 100 10 100 100 100 100 10 100 10 100 100 100 100 10 100 10 100 100 100 100 10 100

0.85 5.70 5.44 5.16 4.72 0.52 4.07 0.84 5.59 5.40 5.11 4.67 0.50 3.87 0.82 5.52 5.36 5.07 4.61 0.48 3.33 0.81 5.50 5.31 5.05 4.56 0.46 3.10 0.80 5.50 5.28 4.98 4.46 0.43 2.48

84.60 57.00 54.35 51.60 47.19 51.80 40.70 83.70 55.89 54.00 51.13 46.68 50.00 38.66 82.10 55.24 53.56 50.69 46.05 47.60 33.27 81.20 55.02 53.12 50.46 45.55 45.70 31.00 80.20 55.00 52.79 49.77 44.60 43.00 24.80

82.00 55.93 52.83 48.98 44.49 53.76 38.96 76.43 53.62 50.44 46.37 41.31 52.90 36.15 72.72 52.34 49.41 45.43 40.07 51.96 32.00 63.60 49.82 46.44 42.51 36.20 48.98 29.20 54.93 45.30 42.69 39.75 35.01 44.79 27.49

dm3 Zn(II) ions and 100 mg/dm3 initial Cd(II) ions, the total uptake of Cd(II) ions was only 4.45 mg/g. Further increase in C0 of Ni(II) and Zn(II) ions to 100 mg/dm3 each adversely affected the uptake of Cd(II) ions with qe reduced to 3.01 mg/ g. In general, a mixture of different adsorbates may exhibit three possible types of behavior: synergism (the effect of the mixture is greater than that of each of the individual adsorbates in the mixture), antagonism (the effect of the mixture is less than that of each of the individual adsorbates in the mixture), and noninteraction (the mixture has no effect on the adsorption of each of the adsorbates in the mixture). The combined effect of the three components, viz., Cd(II), Ni(II), and Zn(II), seems to be antagonistic. To analyze the antagonistic adsorption interaction of the three metal ions, the adsorption yields of the singlecomponent and ternary systems were also compared. For instance, using Table 2, it was expected that the total adsorption yield must be equal to 57.43% for the total C0 ) 300 mg/dm3 of all metal ions in equal proportions [calculated AdTot (%) ) 57.43 ) 100[{51.76 mg/dm3 Cd(II) + 57.84 mg/dm3 Ni(II) + 62.70 mg/dm3 Zn(II) ion)}/300 mg/dm3 total C0]]. However, the total experimental adsorption yield was only 27.49% [experimental AdTot (%) ) 27.49 ) 100[{30.09 mg/dm3 Cd(II) + 27.58 mg/dm3 Ni(II) + 24.80 mg/dm3 Zn(II) ion}/300 mg/ dm3 total C0]]. This shows that the ternary metal solution exhibited inhibitory (antagonistic) adsorption for each of the other two components. This results in a lower sorption yield. 4.4. Multicomponent Adsorption Models. The simultaneous adsorption data of Cd(II), Ni(II), and Zn(II) from the ternary system have been fitted to the multicomponent isotherm models, viz., nonmodified, modified, and extended Langmuir models; nonmodified and modified R-P models; and the SRS model.

Ind. Eng. Chem. Res., Vol. 47, No. 9, 2008 3133 Table 5. Ternary Equilibrium Isotherm Parameters for the Simultaneous Removal of Cd(II), Ni(II), and Zn(II) Metal Ions for the BFA nonmodified Langmuir nodel MPSD

60.46

extended Langmuir model

nonmodified R-P nodel MPSD

98.16

modified Langmuir model

adsorbate

ηL,i

KEL,i

qmax

Cd(II) Ni(II) Zn(II)

0.79 0.99 1.15

0.036 0.048 0.086

9.11

MPSD

54.35

46.71

adsorbate

aij

SRS model aij

aij

modified R-P model ηR,i

Cd(II) Ni(II) Zn(II)

1 0.05 0.01

0.01 1 4.46

4.39 3.66 1

0.01 10.37 0.01

MPSD

41.03

52.40

The parametric values of all the multicomponent adsorption models are given in Table 5. The MPSD values between the experimental and calculated qe values for the entire data set of Cd(II), Ni(II), and Zn(II) are also given in Table 5. A comparison of MPSD values for different isotherm models shows that the SRS model best fits the experimental adsorption data of ternary systems in comparison to other models. Metal ion adsorption for the ternary system showed an MPSD value of 41.026 for the fitting of the experimental data to the SRS model. This MPSD value for the respective systems was lowest in comparison to those for other models. The multicomponent nonmodified Langmuir model shows a poor fit to the experimental data with an MPSD value of 60.462 for all the metal ions. The values of the modified Langmuir coefficient (ηL,i) deviate from 1, indicating that the nonmodified multicomponent Langmuir model related to the individual isotherm parameters cannot be used to predict the ternary system adsorption. However, the use of the interaction term, ηL,i, improved the fit of the modified Langmuir model as shown by the lowering of MPSD value (54.349) of the modified Langmuir model in comparison to nonmodified Langmuir model. The multicomponent extended Langmuir model, however, has been found to adequately describe the adsorption equilibria of the ternary system of Cr(VI), Cu(II), and Cd(II) for a biosorbent Rhizopus arrhizus.38 However, the use of this model in the present study shows its inadequacy to represent the experimental data (MPSD values are large) owing to the heterogeneity of the BFA surface. The KEL,i values, reflecting the affinity between the adsorbent and the metals in the ternary systems, are 0.036 dm3/mg for Cd(II), 0.048 dm3/mg for Ni(II), and 0.086 dm3/ mg for Zn(II). The overall total metal ion uptakes (qmax) by BFA is 9.106 mg/g. This value is considerably lower than the sum of the maximum total capacities of Cd(II), Ni(II), and Zn(II) ions resulting from the single-component adsorption systems. For that reason, the adsorption sites of Cd(II), Ni(II), and Zn(II) in ternary systems on BFA may likely be partially overlapped. It may also imply that there may be a variety of binding sites on the adsorbents showing partial specificity to the individual metal ions. The information obtained from the maximum capacity seems to violate the basic assumptions of the Langmuir model; i.e., the entire adsorbent surface is homogeneous and there is no lateral interaction between the adsorbate molecules. Thus the affinity of each binding site for the adsorbate molecules should be uniform.39 Nonmodified Redlich-Peterson (R-P)

model gave very high MPSD values; however, modified R-P model improved the fit considerably. The fit of the modified R-P model (MPSD ) 52.398) is comparably better than that of the single-component-based modified Langmuir model. The multicomponent SRS model applies to systems where each component individually obeys the single-component Freundlich isotherm. The isotherm coefficients can be determined from the single-component isotherm except for the adsorption competition coefficient, aij, which has to be determined experimentally. The competition coefficient, aij, describes the inhibition to the adsorption of component i by component j. The three components individually were found to obey the singlecomponent Freundlich model. The individual isotherm constants, KF,i and 1/ni, were determined by using nonlinear regression of three single-component isotherms of Cd(II), Ni(II), and Zn(II) ions. The main assumptions incorporated in the derivation are that, for each component in a multicomponent adsorption, adsorption energies of sites are exponentially distributed and that the coverage by each adsorbate at each energy level is given by the multicomponent Langmuir isotherm. The competition coefficients aij and aji were estimated from the competitive adsorption data of Cd(II), Ni(II), and Zn(II) ions by using MS Excel 2002 program. The optimal parameters of the multicomponent SRS model were evaluated by minimizing the MPSD. The satisfactory agreement between the experimental data and predictions from the proposed isotherm equation was demonstrated for Cd(II), Ni(II), and Zn(II) ion sorption onto BFA, and by the observation that the product of the competition coefficients aij and aji is close to unity for the ternary system Cd(II)-Ni(II)-Zn(II) for sorption onto BFA. Furthermore, according to the SRS model

a13a21a32 )

K03 K01 K02 K01 K02 K03

should be 1. For the simultaneous adsorption of Cd(II), Ni(II), and Zn(II) onto BFA, the product of a12, a13, and a23 is found to be 1.036. Thus, the SRS model satisfactorily represents the ternary sorption data for the three metal ions. The competitive Sheindorf-Rebuhn-Sheintuch (SRS) model is found to best represent the simultaneous sorption phenomena of Cd(II), Ni(II), and Zn(II) ions on BFA. Therefore, the sorption of Cd(II), Ni(II), and Zn(II) ions onto BFA from a ternary metal ion mixture is represented by the following equations:

qe,Cd ) 0.8545Ce,Cd(Ce,Cd + 0.01Ce,Ni + 4.3909Ce,Zn)(0.4693-1) (8) qe,Ni ) 1.2865Ce,Ni(0.053Ce,Cd + Ce,Ni + 3.6549Ce,Zn)(0.4016-1) (9) qe,Zn ) 0.8545Ce,Zn(0.01Ce,Cd + 4.4568Ce,Ni + Ce,Zn)(0.415-1) (10) A comparison of the competition coefficients in the adsorption isotherm equation for BFA shows that the uptake of the strongly adsorbed Zn(II) was almost unaffected by the presence of Cd(II) (a31 ) 0.010), while the inhibition exerted in the reverse situation was strong (a13 ) 4.391). On the other hand, Ni(II) and Zn(II) ions significantly inhibited the adsorption of each other onto BFA (a23 ) 3.655 and a32 ) 4.457). The adsorption of Cd(II) and Ni(II) ions was almost unaffected by the presence

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Figure 2. Three-dimensional adsorption isotherm surfaces created by using multicomponent SRS model for the Cd(II) + Ni(II) + Zn(II) system with Ce,Cd as a parameter. (a) Effect of Zn(II) concentration on the equilibrium uptake of Ni(II); (b) effect of Ni(II) concentration on the equilibrium uptake of Zn(II); (c) effect of Ni(II) and Zn(II) concentrations on the equilibrium total uptake of Ni(II) + Zn(II) ions by BFA.

of each other (a12 ) 0.010 and a21 ) 0.053). The competition coefficients seem to suggest that the sorption of Zn(II) ions onto BFA was inhibited by the presence of Ni(II) ions, while the sorption of Cd(II) and Ni(II) ions was inhibited mainly by the presence of Zn(II) ions. For the SRS model, the BFA shows different capacities, KF,i, for Cd(II), Ni(II), and Zn(II) and competition coefficients during their coexistence. This tends to suggest that the surface sites of the adsorbents are heterogeneous, and some of the sites show specificity to certain metals.39 4.5. Three-Dimensional Adsorption Isotherm Surfaces. Three-dimensional (3-D) adsorption isotherm surfaces are used to evaluate the performance of the binary metal ion adsorption system.11,22,40,41 This method is extended to represent the adsorption equilibria for ternary metal ion system by a series of 3-D plots. The residual concentration of one of the metals is taken as a parameter in these plots. The multicomponent SRS model can be used to simulate the equilibrium sorption behavior of the ternary metal ion system through 3-D plots. A 3-D diagram is plotted on the basis of the randomly generated data, and the experimental data are fitted to a smooth surface according to the appropriate input equation. The adsorption isotherm surfaces of Zn(II) and Ni(II) for BFA, as shown in Figure 2, were created by using the multicomponent SRS model given by eqs 8-10, and smoothed and fitted to the experimental adsorption data. Randomly selected initial concentrations of Cd(II) were chosen as para-

meters. Depending on the qe,i value calculated and used, there could be three different adsorption isotherm surface plots: (a) for the uptake of Ni(II), yielding the effect of Zn(II) on Ni(II) (Figure 2a); (b) for the uptake of Zn(II), yielding the effect of Ni(II) on Zn(II) (Figure 2b); and (c) for the total uptake (Ni(II) + Zn(II)) (Figure 2c). When both Zn(II) and Ni(II) ions were present in the solution and the effect of Cd(II) was ignored, some reduction of the Zn(II) uptake was observed with increasing Ni(II) concentration (Figure 2b). The uptake of Ni(II) ions also decreased with increasing equilibrium Zn(II) concentration. The inhibition effect of Zn(II) ions on Ni(II) ions increased with an increase in the equilibrium Ni(II) concentration. Figure 3 shows the plots of residual solution concentrations of Cd(II) and Zn(II) ions at equilibrium against the Cd(II), Zn(II), and total metal uptakes by the BFA. The C0 of Ni(II) ions was taken as a parameter. It is found that the Cd(II) ion uptake by the BFA was moderately affected by the presence of Zn(II) ions compared to Ni(II) ions in Figure 3a. The predicted data points for the Cd(II) uptake using the multicomponent SRS model are least accurate followed by those of Zn(II) and Ni(II) in that order. The deviations of the predicted data from the experimental data for Zn(II) ions were much more pronounced in the 3-D adsorption isotherm plots (Figure 3b). Since the expected increases in the inhibitory effects caused by the presence of the other metal ions at increasing concentrations were not observed, the predicted equilibrium uptake values for Zn(II) ions were higher than the experimental values.

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Figure 3. Three-dimensional adsorption isotherm surfaces created by using multicomponent SRS model for the Cd(II) + Ni(II) + Zn(II) system with Ce,Ni as a parameter. (a) Effect of Zn(II) concentration on the equilibrium uptake of Cd(II); (b) effect of Cd(II) concentration on the equilibrium uptake of Zn(II); (c) effect of Cd(II) and Zn(II) concentrations on the equilibrium total uptake of Cd(II) + Zn(II) ions by BFA.

There is a marked difference between the shapes of the two isotherm surfaces for the binary systems Ni(II) + Zn(II) and Cd(II) + Zn(II), as illustrated in Figures 2c and 3c, respectively. Since the uptake of Ni(II) ions was severely affected by the increase in the concentrations of Zn(II) ions and vice versa, the Ni(II) + Zn(II) adsorption surfaces (Figure 2c) were curved concavely downward. On the other hand, the Zn(II) uptake was not affected much by the presence of Cd(II), and the Cd(II) + Zn(II) adsorption surfaces (Figure 3c) were curved convexly upward. 5. Conclusion The present study shows that BFA is a rational adsorbent for the single and ternary sorbate system adsorption for Cd(II), Ni(II), and Zn(II) metal ions from aqueous solution. Freundlich and Redlich-Peterson isotherms show very good fits with the single-component experimental adsorption equilibrium data. In the ternary metal ion systems, the affinity of BFA for Zn(II) ions was marginally greater than that for Ni(II) or Cd(II), for both the single-component and ternary systems under the same experimental conditions. The net interactive effect of Cd(II), Ni(II), and Zn(II) ions on the adsorption of Cd(II) ions by BFA was found to be antagonistic. Based on Marquardt’s percent standard deviation (MPSD) error function, the simultaneous adsorption phenomena of Cd(II), Ni(II), and Zn(II) ions on BFA can be satisfactorily and adequately represented by the SRS model.

Nomenclature aij ) competition coefficients of component i by component j, dimensionless aR ) constant of Redlich-Peterson isotherm, dm3/mg BFA ) bagasse fly ash C0 ) initial concentration of adsorbate in solution, mg/dm3 C0,i ) initial concentration of each component in solution, mg/ dm3 Ce ) unadsorbed concentration of the single component at equilibrium, mg/dm3 Ce,i ) unadsorbed concentration of each component in the ternary mixture at equilibrium, mg/dm3 kA ) adsorption rate constant for adsorption equilibrium kd ) desorption rate constant for adsorption equilibrium Ki ) individual extended Langmuir isotherm constant of each component, dm3/mg KF ) monocomponent (noncompetitive) constant of Freundlich isotherm of the single component, (mg/g)/(dm3/mg)1/n KF,i ) individual Freundlich isotherm constant of each component, (mg/g)/(dm3/mg)1/n KL ) constant of Langmuir isotherm, dm3/mg KL,i ) individual Langmuir isotherm constant of each component, dm3/mg KR ) constant of Redlich-Peterson isotherm, dm3/g m ) mass of adsorbent per liter of solution, g/dm3 nm ) number of measurements np ) number of parameters

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n ) monocomponent (noncompetitive) Freundlich heterogeneity factor of the single component, dimensionless ni ) individual Freundlich heterogeneity factor of each component, dimensionless N ) number of data points Ni(Q) ) number of sites having energy Q, dimensionless pH0 ) initial pH of the solution MPSD ) Marquardt’s percent standard deviation qe ) equilibrium single-component solid-phase concentration, mg/g qe,i ) equilibrium solid-phase concentration of each component in ternary mixture, mg/g qe,cal ) calculated value of solid-phase concentration of adsorbate at equilibrium, mg/g qe,exp ) experimental value of solid-phase concentration of adsorbate at equilibrium, mg/g qm ) maximum adsorption capacity of adsorbent, mg/g qmax ) constant in extended Langmuir isotherm, mg/g Q ) adsorption energy, J R ) universal gas constant, 8.314 J/K mol t ) time, min T ) absolute temperature, K XAe ) fraction of the adsorbate adsorbed on the adsorbent under equilibrium Greek Symbols Ri ) constant in SRS model for each component, dimensionless β ) constant of Redlich-Peterson isotherm (0 < β < 1) βi ) constant in SRS model for each component, dimensionless ηi ) multicomponent (competitive) Langmuir adsorption constant of each component, dimensionless θi(Q) ) coverage of each component at energy level Q, dimensionless Literature Cited (1) Apak, R.; Guclu, K.; Turgut, M. H. Modeling of copper(II), cadmium(II), and lead(II) adsorption on red mud. J. Colloid Interface Sci. 1998, 203, 122. (2) Bayat, B. Comparative study of adsorption properties of Turkish fly ashes II. The case of chromium(VI) and cadmium(II). J. Hazard. Mater. 2002, B95, 275. (3) Deliyanni, E. A.; Matis, K. A. Sorption of Cd ions onto akaganeitetype nanocrystals. Sep. Purif. Technol. 2005, 45, 96. (4) Goksungur, Y.; Uren, S.; Guvenc, U. Biosorption of cadmium and lead ions by ethanol treated waste baker’s yeast biomass. Bioresour. Technol. 2005, 96, 103. (5) Leyva-Ramos, R.; Bernal-Jacome, L. A.; Acosta-Rodriguez, I. Adsorption of cadmium(II) from aqueous solution on natural and oxidized corncob. Sep. Purif. Technol. 2005, 45, 41. (6) Mall, I. D.; Mishra, N.; Mishra, I. M. Removal of organic matter from sugar mill effluent using bagasse fly ash activated carbon. Res. Ind. 1994, 39, 115. (7) Srivastava, V. C.; Mall, I. D.; Mishra, I. M. Treatment of pulp and paper mill wastewaters with polyaluminium chloride and bagasse fly ash. Colloids Surf., A: Physicochem. Eng. Aspects 2005, 260, 17. (8) Lataye, D. H.; Mishra, I. M.; Mall, I. D. Removal of pyridine from aqueous solution by adsorption on bagasse fly ash. Ind. Eng. Chem. Res. 2006, 45, 3934. (9) Lataye, D. H.; Mishra, I. M.; Mall, I. D. Adsorption of 2-picoline onto bagasse fly ash from aqueous solution. Chem. Eng. J. 2008, http:// dx.doi.org/10.1016/j.cej.2007.05.043. (10) Lataye, D. H.; Mishra, I. M.; Mall, I. D. Pyridine sorption from aqueous solution by rice husk ash (RHA) and granular activated carbon (GAC). J. Hazard. Mater. 2008, http://dx.doi.org/10.1016/j.jhazmat. 2007.10.111. (11) Srivastava, V. C.; Mall, I. D.; Mishra, I. M. Equilibrium modelling of single and binary adsorption of cadmium and nickel onto bagasse fly ash. Chem. Eng. J. 2006, 117, 79.

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ReceiVed for reView July 19, 2007 ReVised manuscript receiVed January 11, 2008 Accepted January 30, 2008 IE0709842