Kinetics, Equilibrium, and Comparision of Multistage Batch Adsorber

The Langmuir isotherm assumes a saturated monolayer of lead ions on the ..... h1, and the intraparticle diffusion rate were formed to follow the trend...
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Kinetics, Equilibrium, and Comparision of Multistage Batch Adsorber Design Models for Biosorbent Dose in Metal Removal from Wastewater A. E. Ofomaja* and E. B. Naidoo Biosorption and Water Treatment Research Laboratory, Department of Chemistry, Vaal University of Technology, P. Bag X021, Vanderbiljpark, 1900, South Africa S Supporting Information *

ABSTRACT: Kinetics of lead(II) adsorption onto increasing masses of raw and Ca(OH)2-treated pine cone powder was evaluated. The first rapid stage in the adsorption profile was found to be controlled by film and intraparticle diffusion while the second slow stage was influenced by slow movement of lead(II) through longer diffusion paths created by particle aggregation especially at higher dose. Slight changes in surface properties due to base activation was observed which lead to greater contribution of the diffusion processes to the rate-controlling step. On the basis of the Langmuir isotherm, three multistage batch adsorber models were compared.

1. INTRODUCTION Separation of dissolved pollutants from aqueous solution, removal of impurities from targeted chemical substances, chemical recovery, and catalysis are examples of unit processes in industry that apply adsorption techniques. The adsorption technique has been successfully and extensively applied to industrial and domestic wastewater purification. Activated carbon is the most popular adsorbent for industrial use, having many advantages over most adsorbents applied in separation methods. In recent times, biosorbents from different sources including microbial,1 bacterial fungal, or algal biomass,2 yeast,3 and lignocellulosic materials4 have been studied and applied for water purification. Batch absorbers applied in adsorption processes often yield important kinetic and equilibrium data useful for further fixed bed studies and for predicting industrial adsorber performance.5 In batch adsorber design, optimization of the amount of adsorbent required to remove a given percentage of pollutant from fixed volume of aqueous solution is important to increase the efficiency of the adsorber and reduce the size of the batch adsorber and its cost. In most investigations, biosorbent dose is simply optimized by varying the amount of adsorbent in contact with a given volume of pollutant solution, and then, the capacity of the adsorbent for the pollutant and the percentage removal with changing adsorbent dose is determined. The adsorbent dose that then corresponds with highest percentage pollutant removal is considered to be the optimum dose for the particular adsorbent. The equilibrium relationship between the amount of pollutant in the aqueous phase and that on the adsorbent surface at a given temperature (isotherm) has been shown to be an important tool for the prediction of optimum process parameters in batch adsorption such as volume and mass of adsorbent for single stage batch adsorber.6 In this method, the best fitting isotherm model for the pollutant removal is determined and the isotherm model parameters such as the © 2013 American Chemical Society

capacity is used in setting up the model equation from which the various parameters are optimized.7 In this study, the effect of biosorbent dose on the kinetics and equilibrium uptake of lead(II) onto raw and Ca(OH)2treated pine cone powder will be examined. Equilibrium modeling of the effect of pine cone powder dose will be performed using the Langmuir, Freundlich, and BET isotherm models. Comparison of several batch adsorber design models for optimization of biosorbent dose will also be carried out.

2. MATERIALS AND METHODS 2.1. Materials. Pine cone powder was prepared as described in ref 8 in a procedure where 50 g of the powder was contacted with 0.15 mol dm−3 Ca(OH)2 solution and the slurry stirred overnight. The mass of pine cone was then rinsed with distilled water to remove excess Ca(OH)2. The above procedure was repeated twice ensure removal of Ca(OH)2 from the powder. The residue was then dried overnight at 90 °C. The chemicals, Ca(OH)2 and lead(II) nitrate, were bought from Aldrich Chemicals Germay. 2.2. Methods. 2.2.1. Point of Zero Charge. The pH at point zero charge (pHPZC) of the pine cone powder was determined by the solid addition method.9 To a series of 100 cm3 conical flasks, 45 cm3 of 0.01 mol dm−3 of KNO3 solution was transferred. The pHi values of the solutions were roughly adjusted to pH 2 and 12 by adding ether 0.10 mol dm−3 HCl or NaOH with a pH meter (Crison Basic 20+). The total volume of the solution in each flask was made up to 50 cm3 by adding the KNO3 solution of the same strength. The pHi of the each solution was accurately noted, and 0.10 g of pine cone powder was added to each flask, which were securely capped Received: Revised: Accepted: Published: 5513

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t 1 t = + 2 qt qe k1qe

immediately. The suspensions were then manually shaken and allowed to equilibrate for 48 h with intermittent manual shaking. The pH values of the supernatant liquids were noted. The difference between the initial and final pH values (pH = pHi − pHf) was plotted against the pHi. The point of intersection of the resulting curve at which pH = 0 gave the pHPZC. 2.2.2. Determination of Acid and Basic Groups on Pine Cone Powder Surface. Acidic and basic sites on both raw and modified pine cone powder were determined by the acid−base titration method proposed by Boehm.10 The total acid sites matching the carboxylic, phenolic, and lactonic groups were neutralized using 0.10 mol dm−3 NaOH solution while the basic sites were neutralized with 0.10 mol dm−3 HCl solution. The carboxylic and lactonic sites were titrated with 0.05 mol dm−3 Na2CO3 solution, the carboxylic sites were determined with 0.10 mol dm−3 NaHCO3 solution, and the phenolic sites were estimated by difference.10 2.2.3. Fourier Transformed Infrared (FTIR) Spectroscopy. The FTIR spectra of pine cone powder before and after base washing were recorded on a Fourier transform infrared spectrometer, Perkin-Elmer model 337 (USA) to elucidate the functional groups present on the pine cone powder before and after base washing. 2.2.4. Scanning Electron Microscope (SEM). SEM images were obtained on a LECO 1430 (Japan) instrument that has a tungsten filament as an electron source. Imaging was done at 3 kV to further alleviate charge build-up. On each sample about 10 images were obtained at 75× magnification and a further 5 images at 150× magnification in order to provide a representative overview of each sample. 2.2.5. Kinetics of the Effect of Biosorbent Dose. Batch experiments were performed by agitating known weights (0.4, 0. 5, 0.6, 0.7, and 0.8 g) of raw pine and Ca(OH)2-treated cone powder in 250 cm3 beakers containing 100 cm3 of 579.15 mmol dm−3 solution at pH 5.0. The flasks were agitated at 160 rpm and 291 K for 15 min. Samples was withdrawn out at different time intervals, centrifuged, and the concentration of lead(II) analyzed using an atomic absorption spectrophotometer. 2.2.6. Equilibrium Studies of the Effect of Biosorbent Dose. A volume of 100 cm3 of lead(II) solution with concentrations ranging from 289.58 to 579.15 mmol dm−3 were placed in 250 cm3 conical flasks and set at pH 5.0. Accurately weighed amounts (0.4 g) of the raw pine and Ca(OH)2-treated pine cone was added to the solutions. The conical flasks were then agitated at a constant speed of 160 rpm in a water bath set at 291 K. After agitating the flasks for 30 min, a known quantity of sample was withdrawn and filtered through micropore sand, and the filtrate analyzed with atomic absorption spectrophotometry (AAS). The experiment was repeated with 0.4, 0.5, 0.6, 0.7, and 0.8 g of raw and Ca(OH)2-treated pine cone powder.

where k2 (g mmol−1 min−1) is the rate constant of the pseudosecond-order adsorption. Double-Exponential Model. The double-exponential model is a mathematical solution that describes a two-step mechanism and is shown below: qt = qe −

k1 t 2.303

D1 D exp( −K D1t ) − 2 exp( −K D2t ) mads mads

(3)

where D1 and D2 are sorption rate parameters (mmol dm−3) of the rapid and the slow step, respectively, and KD1 and KD2 are parameters (min−1) controlling the mechanism. When the exponential term corresponding to the rapid process is assumed to be negligible considering the overall kinetics of the reaction system (KD1 much greater than KD2), eq 3 can be simplified to allow for the determination of KD1 and KD2: qt = qe −

D2 exp( −K D2) mads

(4)

The linearization then gives ln(qe − qt ) = ln

D2 − K D2t mads

(5)

Knowing the values of the constants D2 and KD2, the parameters D1 and KD1 can therefore be obtained from the plot of the following equation: ⎛ ⎞ D D ln⎜qe − qt − 2 exp( −K D2t )⎟ = ln 1 − K D1t mads mads ⎝ ⎠

(6)

3.3. Adsorption Isotherm. The Freundlich isotherm considers the adsorption process for lead ions to proceed by multilayer arrangement of the adsorbate on the adsorbent surface. The isotherm constants, 1/n and KF, can therefore be calculated for lead(II) ion adsorption according to eq 7: log qe = log KF +

1 log Ce n

(7)

The Freundlich constant KF from the above equation indicate the adsorption capacity of the adsorbent, while Freundlich the constant n is a measure of the deviation from linearity of the adsorption or the adsorption affinity of the adsorbent for the adsorbate. The Langmuir isotherm assumes a saturated monolayer of lead ions on the adsorbent, which can be represented as Ce C 1 = + e qe K aqm qm

(8) −3

where Ce is the equilibrium concentration (mmol dm ); qe is the amount of metal ion biosorbed (mmol g−1); qm is qe for a complete monolayer (mmol g−1); Ka is biosorption equilibrium constant (dm3 mmol−1). The BET isotherm12 is a special form of the Langmuir isotherm where constants, KB and qm, were calculated for lead ion adsorption according to eq 9:

3. THEORIES 3.1. Kinetic Models. The pseudo-first-order model suggested by for the adsorption from solid/liquid systems has been applied by many authors1 log(qe − qt ) = log(qe) −

(2)

(1)

⎛ K − 1 ⎞⎛ C ⎞ Ce 1 ⎟⎟⎜ e ⎟ = + ⎜⎜ B (Cs − Ce)q KBqm K q ⎝ B m ⎠⎝ Cs ⎠

where k1 (min−1) is the rate constant of the adsorption. The pseudo-second-order adsorption 5514

(9)

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Figure 1. Schematic diagram for a multistage batch adsorber.

where qm is the amount of solute adsorbed per unit weigh of adsorbent in forming a complete monolayer on the surface (mmol/g) and KB is the constant expressive of energy of interaction with the surface. Ce is the concentration of solute remaining in solution equilibrium (mmol dm−3), Cs is the saturation concentration of solute (mmol dm−3), q is the amount of solute adsorbed per unit weigh of adsorbent (mmol g−1), Therefore a plot of Ce/(Cs − Ce)q against (Ce/Cs) should give a straight line and from the slope and intercept the values of KB and qm can be calculated. 3.3. Batch Adsorber Design Models. Studies have shown that adsorption isotherm parameters can be applied in predicting the design of batch adsorption systems weather single or multistage.6 Figure 1 shows an effluent containing a volume of V dm3 of water with initial concentration of pollutant, C0, which will be reduced to C1 in the adsorption process. In the initial treatment stage, the pollutant concentration on the pollutant free adsorbent solid of mass W kg changes from q0 = 0 (initially) to qn. The mass balance that equates the pollutant removed from the liquid effluent to that accumulated by the solid is V (Cn − 1 − Cn) = W (qn − q0)

Adsorption system number one therefore consists of a series of equilibrium pollutant concentration from Cn−1 to Cn in a number of x decrement in the first stage. The objective in this design is to reduce the initial pollutant concentration from Cn−1 to Cn−1 − x, Cn−1 − 2x, Cn−1 − 3x, Cn−1 − 4x, Cn−1 − 5x, up to Cn mmol dm−3. In the second stage of the design, the equilibrium pollutant concentration in stage 1 will then be reduced to Cn′ (mmol dm−3), while in the third stage, the pollutant concentration in stage 2 will be reduced to Cn″ (mmol dm−3). Therefore, a plot of the total amount of adsorbent mass required at all stages versus the adsorption systems number to reduce the pollutant concentration from Cn−1 to Cn″ can be made. This plot can then be used to predict the minimum adsorbent mass required to reduce the pollutant concentration from Cn−1 to Cn″ for a constant concentration and volume of pollutant solution. Batch Adsorber Model 2. The batch adsorber model proposed by Unuabonah et al.14 is described below: In the use of this model, the authors applied Henry’s law given by qe = KCe

(10)

Where qe is the amount of adsorbate on the adsorbent (mmol g−1) at equilibrium, Ce is the concentration of adsorbate left in solution at equilibrium (mmol dm−3), and K is the equilibrium constant (dm3 mmol−1). It was then assumed that adsorption of water is negligible, adsorbate concentration is low and that the volume of the solution does not change. Therefore the mass balance for the adsorbate is as follows:

If fresh adsorbent is added to the system at each stage, the amount of pollutant adsorbed on a unit mass of adsorbent for a desired percentage of pollutant removal can be obtained by rearranging eq 10 as follows: qn =

V (Cn − 1 − Cn) W

(11)

V (C0 − Ce) = Mqe

Batch Adsorber Model 1. The batch adsorber model proposed by Basha et al.13 is described below: If the equilibrium pollutant uptake follows the Langmuir isotherm, then the amount of pollutant removed to the solid phase can be evaluated using the eq 10. On combing of eqs 10 and 13, the amount of adsorbent required for the desired pollutant removal to the solid adsorbent can be predicted using eq 12 as follows: V (Cn − 1 − Cn)(1 + K aCn) W= (K aqmCn)

(13)

(14)

For an adsorbent which is not initially free from the adsorbate but had been regenerated to a residual loading of q0, it will be necessary to replace the right-hand side of eq 14 with M(qe − qo). Simultaneous solution of eqs 13 and 14 will give the mass of the adsorbent required to effect the desired purification: M=

(12)

V ⎛ C0 ⎞ ⎜ ⎟−1 K ⎝ Ce ⎠

(15)

Equation 15 shows that it is possible to reduce the mass of adsorbent required to reduce the pollutant concentration in solution if an adsorbent with a higher equilibrium constant is applied. Equation 15 can therefore be rearranged to give a linear relationship between qe and Ce.

Therefore, eq 12 can be applied in the determination of the amount of adsorbent required for the removal any given pollutant concentration from aqueous solution in a multistage system. The design of this model is such that, to treat a given volume, V0, of pollutant solution of initial concentration Cn−1 mmol dm−3, the first stage involves the reduction of the pollutant concentration from Cn−1 to Cn mmol dm−3.

qe = 5515

V (C0 − Ce) M

(16)

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If the adsorbent was regenerated before reuse then the linear relationship would be: V qe = (C0 − Ce) = q0 M

(Cn − 1 − Cn) =

⎞ V ⎛ C0 − 1⎟ ⎜ K ⎝ Ce ⎠

m

⎞ V ⎛ C1 − 1⎟ ⎜ K ⎝ Ce ⎠

n−1

WqmK aCn V (1 + K aCn)

100WqmK aCn 100(Cn − 1 − Cn) = C0 V (1 + K aCn)

m n−1

(25)

(26)

100 C0V

m

∑ n−1

qmWK aCn (1 + K aCn)

(27)

For the nth stage, the relationship between Cn and C0 can be written as m

Cn = (1 −

(18)

∑ R n)C0

(28)

n−1

And substituting eq 28 into eq 27, we obtain m

100 ∑ Rn = C 0V n−1

m

∑ n−1

m

qmWK a(1 − ∑ni − 1 R n)C0 m

1 + K a(1 − ∑n − 1 R n)C0

(29)

Applying eqs 27, 28, and 29, the removal percentage of pollutant at any given initial pollutant concentration can be predicted and the minimum amount of biosorbent needed for multistage systems can also be evaluated.

(19)

4. RESULTS AND DISCUSSION 4.1. Properties of Raw Pine and Ca(OH)2-Treated Pine Cone. The percentages of compounds like carbohydrate and lignin in Ca(OH)2-treated pine cone were found to reduce as compared with the raw pine cone (see Supporting Information Table S1). Reports by other researchers11,15 has shown that extraction of sugars, resin acids, and a small fraction of lignin occurring during base treatment is likely responsible for the reduction in these chemical compounds. Bulk densities of the raw and Ca(OH)2-treated pine cone samples was also observed to reduce due to extraction of base soluble organic compounds and pigments leading to discoloration of the treatment solution. Ofomaja et al.8 reported a reduction in negatively charged components of the treated pine cone as compared to the raw pine cone powder due to reduction in sugars and resin acid content of the pine cone. The total acidic functional groups of Ca(OH)2-treated pine cone was observed to decrease from 3.20 to 2.49 mmol g−1 as compared with the raw sample. This reduction can be attributed to extraction of sugars and resin acids.8 Total basic groups were also found to decrease from 4.27 to 1.04 mmol g−1. Carboxylic functions reduced from 0.80 to 0.50 mmol g−1, phenolics reduced from 1.07 to 0.69 mmol g−1, while lactonics increased from 1.33 to 1.67 mmol g−1. 4.2. FTIR Analysis. The complex nature of the FTIR spectra reveals that pine cone is composed of various functional groups (see Supporting Information Figure S1). First, unbound −OH can be identified at 3418.47 cm−1by the broad band.16

(20)

(21)

(22)

Batch Adsorber Model 3. The batch adsorber model proposed by Ofomaja and Naidoo11 is described below: When the relationship between qe and Ce is best described by the Langmuir isotherm, the adsorption equilibrium at nth stage is given by eq 8: Therefore combining eqs 8 and 11 will yield the following: q K aCn V (Cn − 1 − Cn) = m 1 + K aCn W

n−1

∑ Ri =

Therefore for a multistage process involving N stages, the general result for a linear isotherm is 1/ N ⎡ ⎤ NV ⎢⎛ c0 ⎞ ∑ (M1 + M2 + M3 ... MN ) = ⎢⎜ ⎟ − 1⎥⎥ K ⎣⎝ ce ⎠ ⎦

∑

Therefore the total pollutant removal percentage is obtained from the following equation:

Substitution of C1 from eq 10 into eqs 18 and 19 shows that the minimum amount of adsorbent for the purification can be obtained when ⎤ ⎡ ⎛ ⎞0.5 V C M1 = M 2 = ⎢ ⎜ 0 ⎟ − 1⎥ ⎥⎦ ⎢⎣ K ⎝ Ce ⎠

m

∑ (Cn− 1 − Cni) =

Rn =

To obtain a minimum total mass of the adsorbent, the differential of (M1 + M2) with respect to the intermediate concentration C1 needs to be zero. Therefore, it can be shown that C1 = (C0·Ce)

(24)

Pollutant removal percentage in each adsorption stage, Ri, can be calculated using the following equation:

where q1 (amount adsorbed after stage 1) is in equilibrium with intermediate concentration C1. Simultaneous solution of the adsorbate mass balance with the equilibrium relationship for the second batch vessel yields M2: M2 =

V (1 + K aCni)

The evaluation of the total amount of pollutant removed can be made by

(17)

It is necessary to consider the use of multistage batch systems when attempting to purify polluted water using large amounts of adsorbent. Batch adsorption systems involving multiple steps as shown in Figure 1 may then be necessary to achieve this goal. This multistep batch adsorption system will involve splitting of the total weight of the adsorbent into several parts M1, M2, ..., Mn. The procedure then involves first contacting the pollutant solution with fresh batch of adsorbent which reduces the adsorbate concentration to Cn. After separation of the pollutant solution from the adsorbent in the initial stage, the pollutant solution is then contacted with a further fresh portion of adsorbent. In this system, subsequent batch of the adsorbent removes less and less amount of the adsorbate as the adsorbate concentration decreases. Simultaneous solution of the adsorbate mass balance with the equilibrium relationship for the first batch vessel yields M1:

M1 =

Wq i mK aCn

(23) 5516

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The peak observed at 2925.90 cm−1 is likely due to aliphatic C−H group, while the 1647.08 cm−1 peaks corresponds to the C−O stretch. The −C−C− and −CN stretching can be observed between 1058.81 and 559.32 cm−1 respectively.17 Both FTIR spectra of the raw and Ca(OH)2-treated pine cone powder samples were observed to be similar, but some differences can be identified in the intensities of the broad bands at 3418.47 (OH) and 1647.08 cm−1 (CO) accounting for reduction in acid and hydroxyl groups due to extraction of sugars and resin acids (see Supporting Information Figure S1). Peak reduction observed at 559.32 cm−1 (CN) can be accounted for by the decrease in basic groups as observed in the determination of basic groups using Boehm’s titration. 4.3. Scanning Electron Microscopy. Scanning electron microscopy was applied in the determination of the surface morphologies of raw and Ca(OH)2-treated pine cone powder (see Supporting Information Figure S2). The pine cone surface is smooth, flat, and consists of multiple layers. Small numbers of pore spaces can be identified on the surface indicating that the material presents good characteristics to be employed as a natural adsorbent for metallic ions taken up, as previously reported.18 It is believed that these pores provide ready access and large surface area for the sorption of metals at the binding sites. When pine cone was treated with Ca(OH)2 solution, the number of pores on the pine cone powder surface is seen to have increased in number. 4.4. Kinetics of Effect of Adsorbent Dose. The effect of increasing the mass of raw and Ca(OH)2-treated pine cone powder in contact with a fixed volume of solution in the removal of lead(II) from aqueous solution was determined in simple batch contact experiments using different adsorbent masses. Increase in the adsorbent dose was shown to reduce the amount of lead(II) adsorbed per unit mass of adsorbent, while the percentage lead(II) removed increased.19 The amount of lead(II) ions removed from solution at any given time by Ca(OH)2-treated adsorbent at all doses applied was shown to be more than that removed for raw pine cone powder. But the equilibrium uptake times seemed to be the same for both adsorbents (15 min). The plots of amount of lead(II) adsorbed per unit mass versus time revealed an initial rapid uptake of lead(II) ions in the first 5 min of contact followed by a slower equilibrium stage up to 15 min of contact. Two reasons may be advanced for the shape observed: (1) a two-step adsorption mechanism which involves a rapid metal uptake taking place through external and internal diffusion during the first step and a slow stage where intraparticle diffusion controls the adsorption rate and finally the metal uptake reaches equilibrium during the second step20 and (2) during adsorption, binding of metal ions on two different types of adsorption sites on the adsorbent surface may occur.21,22 To determine the actual mechanism of adsorption of lead(II) onto these adsorbents, five kinetic models where applied to analyze the kinetic data. 4.4.1. Pseudo-first-Order Kinetic Model. The pseudo-firstorder kinetic model proposed by Lagergren23 was applied in modeling the kinetic data. Values of the pseudo-first-order rate constant, equilibrium capacity, and correlation coefficients for pine cone and Ca(OH)2 modified pine cone powder are shown in Supporting Information Tables S1 and S2. Although the predicted pseudo-first-order equilibrium capacities reduced in the same trend as the experimentally determined values for both adsorbents, the values of equilibrium capacities were not

close to those observed experimentally. The pseudo-first-order plots showed that there were deviations of the pseudo-firstorder model from the straight line of the experimental data after 5 min of initial contact for both adsorbents. The implication of this is that ether a change in adsorption mechanism had occurred at that point or a switch of metal binding site from one type of site to another had occurred. The rate constant, k1, of pseudo-first-order were observed to be higher for Ca(OH)2 pine cone powder than for the raw adsorbent and there was an increase in the rate constant, k1, with increasing biosorbent dose for both samples. The correlation coefficient, r2, values suggests that there is a stronger deviation from the straight line for the Ca(OH)2treated samples than for the raw samples. 4.4.2. External Mass Transfer Model. The external mass transfer rate constant was obtained from the plot of Ct/C0 against time for different pine cone and Ca(OH)2-treated pine cone powder dose at the beginning of the adsorption period (0−5 min). The procedure involved fitting second-order polynomials to the data, and d(Ct/C0)/dt were calculated from the first derivative of the polynomials at t = 0. The values of the mass transfer constants, ks, are shown in Table S2 in the Supporting Information. It was observed that mass transfer constant, ks, increased with increasing adsorbent dose and where higher for the Ca(OH)2-treated absorbent than for the untreated sample (the mass transfer rate for the raw pine cone sample was almost constant). As the adsorbent dose increased at a fixed lead(II) solution concentration, the amount of surface available for solid-solution contact increased for both samples. The treated sample with lower bulk density had a larger surface than the raw sample, therefore the large surface of the treated sample led to an increase in the mass transfer of lead(II) to its surface than that of the raw sample. 4.4.3. Pseudo-Second-Order Kinetic Model. Values of the pseudo-second-order rate parameters for the kinetics of lead(II) adsorption onto raw and Ca(OH)2 modified pine cone powder along with the correlation coefficient are determined (see Supporting Information Tables S1 and S2). It was observed that the predicted pseudo-second-order equilibrium capacities were quite close to the experimentally determined equilibrium capacities for both samples. Increase in adsorbent dose increased the initial sorption rate, h, and pseudo-second-order rate constant, k2, while the equilibrium capacity, qt, reduced. The values of correlation coefficient, r2, were fairly high for all adsorbent doses and for both samples. 4.4.4. Intraparticle Diffusion. The effect of dose on intraparticle diffusion of lead(II) into both pine cone and Ca(OH)2-treated pine cone powder was investigated using the intrapartcle diffusion model. The intraparticle diffusion rate constant, ki, was calculated from the slopes and intercepts of the plots of lead(II) capacity at different time intervals against square root of time for both samples at different adsorbent doses. The experimental results indicates that intraparticle diffusion rate constants decreased with increasing adsorbent dose from 2.9504 to 0.5550 mmol g−1 min−1 for the untreated sample and from 1.1681 to 0.4308 mmol g−1 min−1 for the Ca(OH)2-treated sample. As explained previously, the surface of the treated sample is larger than that of the raw sample as seen from the bulk density and BET surface area. As the adsorbent dose increases in a fixed concentration of lead(II), the change in surface area is higher for the treated sample. The higher surface area therefore increases the migration of lead(II) onto its surface, reduces internal diffusion, and increases mass 5517

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internal surface of the treated sample (higher surface area) means that longer diffusion paths may have been formed which increases the percentage of lead(II) entering the internal surface. Therefore the mechanism for the slow step of adsorption can be attributed to internal diffusion of lead(II) ions into pores in the adsorbent surface. 4.5. Equilibrium Studies of Effect of Adsorbent Dose. In the optimization equilibrium isotherms to experimental data, it is necessary to define an error function so as to evaluate the fit of the isotherm equation to the experimental data. The use of two error functions which are (1) the linear coefficient of determination, r2, and (2) the nonlinear chi-square, χ2, were employed in this investigation. The coefficient of determination, r2, is given by

transfer resistance, which limits migration of lead(II) into the internal surface. 4.4.5. Double Exponential Model. The parameters D1, D2, KD1, and KD2 of the double exponential model were calculated and presented in Supporting Information Table S2 for both adsorbents. The values of the double exponential model parameters D1 and D2 were found to be similar for both adsorbents in the removal of lead(II) from solution. This result suggests that there is likely one type of adsorption site participating in the adsorption process. The values of the diffusion parameters controlling the overall kinetics, KD1 and KD2 were not similar; therefore, two diffusion mechanisms may be involved in the adsorption process accounting for the fast and slow steps as seen in the kinetic plots. It is assumed that, during the fast stage, a rapid metal uptake involves a combination of external and internal diffusion and then a slow stage later emerges in which intraparticle diffusion controls the adsorption rate and finally the metal uptake reaches equilibrium.24 The values for KD1 (fast step) were found to decrease with increasing adsorbent dose for both samples, and its values were higher for the treated than for the untreated sample. KD1, the rapid stage sorption coefficient, takes into account both external and internal diffusion. The pseudo-second-order rate constant, k2, the initial rate, h2, the pseudo-first-order rate constant, k1, and mass transfer diffusion rate, ks, all increased with increasing adsorbent dose which does not follow the trend in the relationship between amount of lead(II) adsorbed at equilibrium with the various adsorbent doses for both samples (see Supporting Information Tables S1 and S2). On the other hand, both the pseudo-first-order initial rate constant, h1, and the intraparticle diffusion rate were formed to follow the trend in the relationship between equilibrium removal and adsorbent dose. This suggests that the fast stage of the sorption process is controlled by film diffusion and intraparticle diffusion. Lo and Leckie25 suggested that about 30% of the total internal surface area of an adsorbent is near the outer region of the adsorbent particle, and this part of the particle is known as the external surface area. The higher values of KD1 (fast step) displayed by the treated sample over the untreated may be attributed to the higher rates of film diffusion and intraparticle diffusion. The values of KD2 (slow step) on the other hand were formed to increase with increasing adsorbent dose for both samples. It was noticed that higher adsorbent dose reduced the equilibrium concentrations of lead(II) in solution and that the treated samples had lower equilibrium concentrations than the untreated. Michard et al.24 reported that increasing particle size of Merck silica gel resulted in the reduction in the concentration of uranium ion in solution, and the authors attributed this to diffusion. In our study, it was observed that at 5 min of adsorption the percentage of lead(II) removed in solution for a fixed lead(II) concentration and volume, increased with adsorbent dose and that the equilibrium lead(II) concentration also decreased with dose. The increase in KD2 (slow step) with increasing dose may therefore be attributed to an increase in the diffusion path length, which increases with adsorbent dose. As diffusion path length increases, lead(II) ions will diffuse slowly through a longer path length causing more lead(II) ions to enter into the internal surface, reducing equilibrium lead(II) concentration in solution. Also the greater

r2 =

∑ (qm − qt̅ )2 ∑ (qm − qt̅ ) + ∑ (qm − qt )2

(30)

where qm is amount of 4-nitrophenol on the surface of the sawdust at any time, t, (mg g−1) obtained from the pseudosecond-order kinetic model; qt is the amount of 4-nitrophenol on the surface of the sawdust at any time, t, (mg g−1) obtained from experiment; and qt̅ is the average of qt (mg g−1). The chi-square, χ2, test statistic is based on the sum of the squares of the difference between the experimental data and data obtained by calculation using models, with each squared difference divided by the corresponding data obtained by calculating from models. The equivalent mathematical statement is 2

χ =

∑

(qe − qe,m)2 qe,m

(31)

where qe,m is the equilibrium adsorption capacity obtained by calculation from models (mmol g−1), qe is the equilibrium adsorption capacity of experimental data (mmol g−1). If the data from the model is close to the experimental data, χ2 will give a small number, and if they are far apart in value, χ2 will be a larger number. The ability of the predicted values of the individual isotherm models to correlate with the experimental data obtained was accessed by plotting theoretical points from each isotherm along with the experimental data for adsorption of lead(II) ions onto raw and Ca(OH)2-treated pine cone at the 299 K (see Supporting Information Figure S3). A comparison of the coefficient of determination, r2, and the nonlinear chi-square, χ2, of four isotherms for lead(II) ion adsorption onto raw and Ca(OH)2-treated pine cone was made and listed in Supporting Information Table S2. It was be observed that both Langmuir and BET isotherm models have similar values for coefficient of determination, r2, for all adsorbent doses (raw and Ca(OH)2-treated). It will also be noticed that the Freundlich isotherm had the least values for coefficient of determination, r2. On examination of the plots (Supporting Information S3a and b), it will be noticed that the Freundlich isotherm actually was further away from the experimental data indicating that this isotherm model gave the least fitting to the experimental data. For the raw pine cone powder, the BET isotherm model line was observed to be closer to the experimental data than the Langmuir isotherm, while the opposite is the case for Ca(OH)2-treated pine cone where the Langmuir isotherm model gave a closer fitting than the BET isotherm. These observations are in line with the 5518

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Table 1. Minimum Total Amount of Raw and Ca(OH)2-Treated Pine Cone Needed to Achieve Various 95% Removals for Multistage Biosorption Systems Using Different Models and a Single-Stage Biosorption System model Unuabonah et al. (2009) Ofomaja and Naidoo (2010) Basha et al. (2009) single-stage

adsorbent

no. of stages

S1 (kg)

S2 (kg)

S3 (kg)

S4 (g)

S5 (kg)

Stotal (kg)

raw Ca(OH)2-treated raw Ca(OH)2-treated raw Ca(OH)2-treated raw Ca(OH)2-treated

4 4 2 2 2 2 1 1

1.71 1.21 1.97 1.45 2.84 1.98

1.71 1.21 1.78 1.71 1.76 0.88

1.71 1.21

1.71 1.21

1.71 1.21

6.83 4.83 3.75 3.16 4.60 2.86 17.36 12.26

prediction of the nonlinear chi-square, χ2, error determination method. This therefore makes the nonlinear chi-square, χ2, error method a better method of evaluating the fit of the isotherm equation to the experimental data in this study. 4.5.1. Isotherm Models. The Freundlich isotherm constants, 1/n and KF, calculated for lead(II) ion adsorption according to eq 9 were determined by the Freundlich isotherm plots (see Supporting Information Table S4). The values of the Freundlich constant KF provides insight to the biosorption capacity of the biosorbent while Freundlich constant n measures the deviation from linearity of the adsorption or the adsorption affinity of the adsorbent for the adsorbate. The values of n for raw pine cone was in the range of 2.458−3.280, while for Ca(OH)2-treated pine cone, values of n were between 2.275 and 2.853. The observed values for n in this study were all are greater than unity indicating that lead(II) removal at all adsorbent doses applied is feasible. There was no obvious trend in the values of n with increasing dose in both samples. The values of KF on the other hand for both raw and Ca(OH)2treated pine cone were found to decrease with increased adsorbent dose. As raw pine cone dose increased from 4 to 8 g dm−3, the values of KF for raw and Ca(OH)2-treated samples decreased from 5.922 to 4.522 and 13.632 to 5.504. These results therefore suggest that adsorption capacity decreases with increasing adsorbent dose and Ca(OH)2-treated samples have higher capacities than the raw samples. The heat of adsorption of lead(II) onto raw and Ca(OH)2treated pine cone powder can be predicted from the magnitude of Langmuir constant, Ka. The higher magnitude of Langmuir constant, Ka, the higher heat of adsorption and the stronger the bond formed. The monolayer capacity of the adsorbent for the lead(II) ion is predicted by the value of qm (mmol g−1). The good fit of the Langmuir model to the experimental data indicates the homogeneity of the actives sites on the biosorbent surface. As adsorbent dose is increased from 4 to 8 g dm−3, the Langmuir constant, qm, decreased from 79.37 to 38.91 mmol g−1 for raw pine cone and from 112.35 to 69.93 mmol g−1 for Ca(OH)2-treated pine cone. The results in Supporting Information Table S4 show that monolayer capacities for Ca(OH)2-treated pine cone are much higher than does of the raw pine cone. On the other hand, the equilibrium constant, Ka, values for raw pine cone was found to increase with increasing raw pine and Ca(OH)2-treated pine cone dose. The results suggest the heat of adsorption increases with dose and stronger bonds are formed at higher adsorbent dose than lower dose. The logarithmic relationship between the Langmuir constants and adsorbent dose, ms, for raw and Ca(OH)2-treated pine cone for uptake lead(II) adsorption can be represented by a straight line curve with correlation coefficient, r2, as high as 0.960 and mathematically represented as

Raw pine cone qm = 352.21ms−1.0357 K a = 5.44 × 10−3ms 0.2566

(r 2 = 0.967) (r 2 = 0.992)

(32) (33)

Ca(OH)2-treated pine cone qm = 298.74ms−0.6901 K a = 1.58 × 10−2ms 0.031

(r 2 = 0.987) (r 2 = 0.992)

(34) (35)

The BET model is assumed to be an extension of the Langmuir model for multilayer adsorption. This isotherm model is therefore based on the assumption that each adsorbate in the first adsorbed layer serves as adsorption site for the second layer and so on. The values of saturation capacity, qm, obtained using the BET isotherm model was exactly the same as for the Langmuir model, which signifies that monolayer adsorption of lead(II) ions on the adsorbents surfaces actually occurred. The energy of interaction with the surface expressed by the constant, KB, was higher for Ca(OH)2-treated samples than for the raw samples at all adsorbent doses as predicted by the Langmuir isotherm. Energy of interaction and bond strength between lead(II) and Ca(OH)2-treated samples were higher than between lead(II) and raw pine cone. The effect of increasing the adsorbent dose also increased the bond strengths and energies of interaction between adsorbent particles. The logarithmic relationship were also drawn between BET constant, KB, and adsorbent dose, ms, for raw and Ca(OH)2treated pine cone for uptake lead(II) adsorption which can be represented by a straight line curve with correlation coefficient, r2, as high as 0.967 and mathematically represented as Raw pine cone KB = 1.57 × 104ms 0.1598

(r 2 = 0.996)

(36)

(r 2 = 0.995)

(37)

Ca(OH)2-treated pine cone KB = 3.35 × 104ms 0.1500

4.6. Multistage Batch Adsorber Optimization for Adsorbent Mass. An idea of the total amounts of adsorbent and the minimum amounts required for the adsorption process of each stage of a multistage system is critical both in the design of the adsorption equipment and its application on a large scale. In this study, we intend to consider the minimum adsorbent mass of adsorbent required for the removal of 95% lead(II) from 2.5 m3 of 579.15 mmol dm−3 of the metal in a multistage batch adsorption process. Three models of multistage adsorbent mass optimization were applied to the equilibrium data obtained. Therefore, the amount of adsorbent required to reduce the concentration of lead(II) from 571.15 to 28.05 5519

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Figure 2. Comparison of methods for the optimization of adsorbent amount of raw pine cone powder in the removal of lead(II) from aqueous solution. Models by (a) Unuabonah et al.,14 (b) Ofomaja and Naidoo,11 and (c) Basha et al.13

mmol dm−3 (95% lead(II) removal) with the raw and Ca(OH)2-treated pine cone were determined using the parameters of the Langmuir isotherm, since it best described the adsorption process. The values of the Langmuir monolayer capacity (qm) and equilibrium constant (Ka) for the raw pine cone were 79.37 mmol g−1 and 0.0078 dm3 g−1 and 112.36 mmol g−1 of 0.0165 dm3 g−1 for the Ca(OH)2-treated pine cone. The optimization model for adsorbent mass proposed by Unuabonah et al.14 has the advantage of predicting both the total adsorbent mass and the number of stages that the adsorbent mass can be divided into. This model also takes into account the Langmuir constant, Ka, and the monolayer capacity, qm, of the adsorption system. From the results in Table 1, it is observed that the total amount of adsorbent needed for the raw pine/lead(II) system and the Ca(OH)2-treated pine/lead(II) system is 6.38 and 4.38 kg, respectively. The Ca(OH)2-treated pine cone is needed in lower amount to reduce the concentration of lead(II) in solution from 517.15 to 28.05 mmol dm−3. This result is different from that predicted when optimum adsorbent mass is predicted from contacting different amounts of raw pine and treated pine cone with a fixed concentration of lead(II) solution.6 The model also predicted that the optimum number of stages for both systems is five, meaning that both systems will need a five-stage process where the adsorbent mass will be 1.71 kg in each stage for raw pine cone and 1.21 kg of Ca(OH)2 in each of the five stages. The model described by Ofomaja and Naidoo7 was derived using the Langmuir isotherm model and takes into account the Langmuir parameters, qm and Ka. For the reduction of the concentrations of lead(II) ions in solution from 517.15 to 28.08 mmol dm−3 in a 2.5 m3 solution, the total amounts of raw and Ca(OH)2-treated pine cone masses required were 3.75 and 3.16 kg, respectively (Figure 2). The optimum number of stages was found to be two for both the raw pine/lead(II) and Ca(OH)2-treated pine cone/lead(II) systems. For the raw pine cone/lead(II) system, the amounts required for each stage was 1.97 and 1.78 kg, while that of Ca(OH)2-treated pine cone was 1.45 and 1.71 kg, respectively. This results again shows that optimum adsorbent masses needed in the case of raw pine cone and Ca(OH)2-treated pine cone were not the same. Basha et al.13 proposed an adsorbent mass optimization model also based on the Langmuir adsorption isotherm which takes into account the Langmuir isotherm parameters qm and Ka. The difference between this model and the previous model

is that in their model the amount of lead(II) removed was assumed to be equal (25 mmol dm−3) for each system number. Therefore to reduce the concentration of lead(II) from 517.15 to 28.08 mmol dm−3 in a 2.5 m3 solution, the total amounts of raw and Ca(OH)2-treated pine cone masses required were 4.60 and 2.86 kg, respectively. The optimum number of stages was found to be 2 for both the raw pine/lead(II) and Ca(OH)2treated pine cone/lead(II) systems (Figure 2). For the raw pine cone/lead(II) system, the amounts required for each stage was 2.84 and 1.76 kg, while that of Ca(OH)2-treated pine cone was 1.98 and 0.88 kg, respectively. The Ofomaja and Naidoo7 model gave values that are closer to the Basha et al.13 model than the Unuabonah et al. model. For examples, both Ofomaja and Naidoo7 and Basha et al.13 models predicted an optimized two-stage process, while the Unuabonah et al.14 model predicted an optimized five-stage process for both adsorbents. The masses of the adsorbents at the first stage for raw and Ca(OH)2-treated pine cone for the Ofomaja and Naidoo7 and Basha et al.13 models were 1.97 and 2.84 kg (raw pine cone) and 1.45 and 1.98 kg (Ca(OH)2treated pine cone). Comparing the results of multistage adsorbent dose optimization to the single stage process, it was observed that the single-stage process will require 17.36 and 12.26 kg of raw and Ca(OH)2-treated pine cone to reduce the concentration of lead(II) from 517.15 to 28.08 mmol dm−3 in a 2.5 m3 solution. The amounts are quite larger than those predicted for a multistage system although the results also show that the amounts needed for the raw pine cone/lead(II) system is more than for the Ca(OH)2 pine cone/lead(II) system.

4. CONCLUSION Base treatment and effect of adsorbent mass on adsorption mechanism was examined in this study, and both the fast and slow stages of the process were found to be controlled by film and intrapaticle diffusion. The surface area of the pine cone and the effect of aggregation of adsorbent particles played a major role in modifying the rate-determining steps. Equilibrium isotherm was best described by Langmuir and Freundlich isotherms while at different adsorbent masses. Optimization of adsorbent mass using three different models showed that lesser amounts were needed for the treated than the raw pine cone. 5520

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(19) Ofomaja, A. E. Sorptive removal of Methylene blue from aqueous solution using palm kernel fibre: Effect of fibre dose. Biochem. Eng. J. 2008, 40, 8. (20) Chiron, N.; Guilet, R.; Deydier, E. Adsorption of Cu(II) and Pd(II) onto grafted silica: isotherm and kinetic models. Wat. Res. 2003, 37, 3079. (21) Benjamin, M. N.; Leckie, J. O. Multi-site adsorption of Cd, Cu, Zn, and Pn on amorphous iron oxyhydroxide. J. Colloid Interface Sci. 1981, 79, 209. (22) Dzombak, D. A.; Fish, W.; Morel, F. M. M. Metal-humate interactions. I. Discrete ligand and continuous distribution models. Environ. Sci. Technol. 1986, 20, 669. (23) Lagergren, S. Zur theorie der sogenannten adsorption gelöster stoffe; The Royal Swedish Academy of Sciences: Stockholm, Sweden, 1989; Vol. 24, p 1. (24) Michard, P.; Guibal, E.; Vincent, P.; Le Cloirec, P. Sorption and desorption of uranyl ions by silica gel: pH, particle size and porosity effects. Microp. Mater. 1996, 5, 309. (25) Lo, K. S. L.; Leckie, J. O. Kinetic studies of adsorption− desorption of Cd, Zn onto Al2O3/solution interfaces. Wat. Sci. Technol. 1993, 28, 39.

ASSOCIATED CONTENT

S Supporting Information *

Further details regarding data obtained and plots. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] or [email protected]. Phone: +27 768202689, +27 738126830, or +234 80715034. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Vaal University of Technology research unit for funding this research project.

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REFERENCES

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