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Kinetic and Pseudo-Second-Order Modeling of Lead Biosorption onto Pine Cone Powder A. E. Ofomaja,* E. B. Naidoo, and S. J. Modise Department of Chemistry, Vaal UniVersity of Technology, P. bag X021, Vanderbiljpark 1900, South Africa
The sorption of lead(II) onto pine cone powder (PCP) and 0.15 mol/L NaOH treated pine cone powder (PCP 0.15), an abundant agricultural waste from the wood industry, was studied to evaluate the effect of NaOH treatment on the kinetics of lead(II) uptake by performing batch kinetic sorption experiments. Batch biosorption kinetics was performed by varying biosorbent dose and initial lead(II) concentration and the kinetic data modeled using the pseudo-first, pseudo-second intraparticle, and Bangham diffusion models. The results revealed that NaOH treatment changed the pattern of the biosorption kinetics, the biosorption kinetic parameters, and influenced the rate-limiting step. The pseudo-second-order kinetic model gave a better fitting of the kinetic data for both PCP and PCP 0.15. The batch biosorption model, based on the pseudo-second-order mechanism, was applied to predict the rate constant of biosorption, the equilibrium capacity, the initial sorption rate, the effects of biosorbent dose, and initial lead(II) concentration. Equilibrium concentrations were evaluated with the equilibrium capacity obtained from the pseudo-second-order rate equation. In addition, pseudo-isotherms were obtained by changing initial lead(II) concentration using the equilibrium concentration and equilibrium capacity obtained based on the pseudo-second-order constants. 1. Introduction The rate of pollutant removal from aqueous solution onto the surface of an adsorbent of biological origin, the study of factors that influence these rates, and the development of theories, which can be used to predict them, is termed biosorption kinetic studies. A biosorption rate law can only be determined experimentally and is not inferred by examining the chemical equation representing the biosorption process.1 Polar acidic organic groups of lignin and cellulose, which are major constituents of biological materials of plant origin including aldehydes, ketones, carboxylic, phenolic, and ether groups, are usually responsible for pollutant uptake on the biosorbent surface.2 The high affinity of the biosorbent for the pollutant species leads to the biosorption of pollutants on the biosorbent by different mechanisms. Several biosorption kinetic models have been developed for analyzing kinetic biosorption data, and these include first-order3 and second-order4 reversible reactions, first-order5 and secondorder6 irreversible reactions, pseudo-first-order7 and pseudosecond order8 reactions based on solution concentration, the Elovich model,9 and Lagergren’s first-order10 and Ho’s secondorder11 reactions based on the capacity of the biosorbent. The pseudo-second-order kinetic expression described by Ho12 is by far the most widely applied kinetic model for sorption systems in recent years. Most biosorption kinetics have been found to be well-described by the pseudo-second-order kinetic model. Examples of these are the following: biosorption of cadmium(II) on to pectinrich fruit wastes;13 biosorption of chromuim(III) and lead(II) from aqueous solution by yellow passion-fruit shell;14 biosorption of cadmium on coconut copra meal;15 and biosorption of lead(II) and copper(II) on palm kernel fiber.16,17 The ability of the pseudo-second-order model to accurately predict the biosorption kinetics has been tested by Ho and Wang,1 Ho,18 and Ho and Ofomaja.19 The authors used the * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +27768202689; +27738126830.
equilibrium capacities obtained from the pseudo-second-order expression to evaluate equilibrium concentration and generated pseudo-isotherms by changing initial concentration, Co,1,18 or sorbent dose, ms,19 and obtained equilibrium capacities based on the pseudo-second-order constants. These pseudo-isotherms have been found to represent the measured sorption data well. In the present investigation, the variation caused by the 0.15 mol/L NaOH modification of pine cone powder on the kinetics and diffusion of lead(II) ions onto the pine cone powder surface was investigated. The aim being to understand the impact of the change in the surface charges on the kinetics and diffusion processes. The ability of the pseudo-first- and pseudo-secondorder, intraparticle, and Bangham diffusion models to describe the biosorption data for varying biosorbent dose and initial lead(II) concentration was tested. Confirmation of the ability of the pseudo-second-order model to completely describe experimental data of lead(II) uptake of both biosorbents using pseudo-isotherm was also examined. 2. Materials and Methods 2.1. Materials. Pine tree cones were obtained from a plantation in Sasolburg, Free State, South Africa. Pine tree cones were collected between August and September 2007. The cones were washed to remove impurities such as sand and leaves, the washed cones were then dried at 90 °C for 48 h in an oven. The scales on the cones were then removed and blended in a food processing blender. The resultant powder was sieved, and particles below 300 µm were collected and used for NaOH washing and subsequent analysis. Pine cone powder (50 g) was soaked in 500 mL of 0.15 mol/L solution of NaOH (purchased from Sigma (St. Louis, MO)) and stirred overnight at 160 rpm. The base solution was decanted, and the excess base was removed by washing with distilled water several times.27 The powder was then dried at 90 °C for 48 h and stored in an airtight container. The raw pine cone powder was coded PCP while the 0.15 mol/L NaOH treated pine cone powder was coded PCP 0.15.
10.1021/ie901150x 2010 American Chemical Society Published on Web 02/10/2010
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A stock solution of lead(II) nitrate (Pb(NO3)2) purchased from sigma (St. Louis, MO) was prepared by dissolving an accurately weighed amount of the salt in deionized water. The experimental solutions were prepared by diluting the stock solution with distilled water when necessary. Other chemicals such as Na2CO3, HCl, iodine crystal, and potassium iodide were purchased from Sigma (St. Louis, MO). 2.2. Methods. 2.2.1. Scanning Electron Microscopy (SEM). SEM images were obtained on a LEO 1430 instrument (carl ZesisSMT AG, Germany) that has a tungsten filament as the electron source. Sample preparation was done by scooping a small amount of the powder with a spatula onto an aluminum stub covered with double-sided carbon tape. The excess powder was removed by tapping the stub firmly against the bench. In order to prevent charge buildup on the sample surface, the surface conductivity of the sample was improved by sputtering a thin layer of Au-Pd onto the sample. Imaging was done at 3 kV to further alleviate charge buildup. 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. 2.2.2. Determination of Surface Negative Charge. A modification of the method used by Boehm20 was used to determine total negative charge. The “total” negative charge could be obtained only on samples at pH 2.5. At this pH, even the most easily ionizable negative groups (i.e., carboxyl groups) were fully protonated as indicated by no change in titratable negative charge when the pH was at 2.5. For a fully protonated surface, the presence of a strong base (NaOH) deprotonated both strongly and weakly ionizable groups which contribute to the total negative charge. A mass of 1.5 g of pine cone powder, which had pH value 2.5, was suspended in 25 mL of 0.1 mol/dm3 NaOH and stirred at 300 rpm for 16-20 h in glass stoppered 100 mL Erlenmeyer flasks. The flasks were kept stoppered during stirring to minimize the dissolution of carbon dioxide gas in the NaOH and the subsequent formation of Na2CO3. The flask contents were filtered by vacuum filtration through Whatman no. 4 filter paper, and 10 mL of the filtrate was added to 15 mL of 0.1 mol/dm3 HCl. The addition of excess HCl prevented any possible adsorption of carbon dioxide by the base and was particularly important if the solutions were required to stand for extended time periods before analysis. The solution was titrated with 0.1 mol/dm3 NaOH until an end point. The results were expressed in millimoles H+ neutralized by excess OHper gram of pine cone powder. 2.2.3. Point of Zero Charge. The pH at the point zero charge (pHPZC) of the pine cone powder was determined by the solid addition method.21 To a series of 100 mL conical flasks, 45 mL 0.01 mol/L of KNO3 solution were transferred. The pHi values of the solution were roughly adjusted from pH 2 to 12 by adding ether 0.1 mol/L HCl or NaOH using a pH meter (Crison Basic 20+, Barcelona, Spain). The total volume of the solution in each flask was made up to 50 mL by adding the KNO3 solution of the same strength. The pHi of the solution was accurately noted, and 0.1 g of pine cone powder was added to the flask, which was securely capped 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 ) pHf - pHi) was plotted against the pHi. The point of intersection of the resulting curve at which ∆pH ) 0 gave the pHPZC.
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2.2.4. Iodine Number Determination. In this experiment, 25 mL of iodine solution of 0.05 mol/L was added to eight flasks, which contained different amounts of pine cone powder ranging from 0.031 to 0.500 g. The flasks were then shaken for 24 h to ensure equilibrium adsorption of iodine onto pine cone powder. The iodine number (mg/g) (or adsorption capacity) was determined from the titration of the residual solution of 10 mL with 0.1 mol/L sodium thiosulfate in the presence of 1 mL of 1 wt % starch solution as an indicator. The iodine adsorption capacity was determined from the adsorbed iodine/unit mass of the adsorbent at the residual iodine concentration. 2.2.5. Effect of Biosorbent Dose. The experiments were performed by agitating known weights (0.10, 0.15, 0.20, and 0.25 g) of pine cone powder in 250 mL beakers containing 100 mL of 120 mg/dm3 solution at pH 5.0. The flasks were shaken at 160 rpm and 291 K for 15 min. Samples (3 mL) were withdrawn out at different time intervals, centrifuged, and the concentration of lead(II) analyzed using an atomic absorption spectrophotometer. 2.2.6. Effect of Concentration. Kinetic experiments were carried out by agitating 100 mL of lead(II) solution of concentration ranging from 50 to 120 mg/dm3 with 0.4 g of pine cone powder in 250 mL beakers at 291 K at an optimum pH of 5.0 and at a constant agitation speed of 160 rpm for 15 min. Samples (3.0 mL) were pipetted out at different time intervals and centrifuged, and the concentration of lead(II) was analyzed using an atomic absorption spectrophotometer. 2.3. Theory. In the case of sorption preceded by diffusion through a boundary, the kinetics most likely follows the pseudofirst-order equation of Lagergren:22 dqt ) k1(qe - qt) dt
(1)
where qt and qe are the amount sorbed at time t and at equilibrium and k1 is the rate constant of the pseudo-first-order sorption process. The integrated rate law, after applying the initial conditions of qt ) 0 at t ) 0, is log(qe - qt) ) log(qe) -
k1 t 2.303
(2)
Plots of log (qe - qt) versus t give a straight line for pseudofirst-order kinetics, which allows computation of the sorption rate constant, k1. If the experimental results do not follow eqs 1 and 2, they differ in two important aspects: (i) k1(qe - qt) then does not represent the number of available sites, and (ii) log(qe) is not equal to the intercept of the plot of log(qe - qt) against t. The pseudo-second-order chemisorption kinetics may be expressed as9 dqt ) k2(qe - qt)2 dt
(3)
where k2 is the rate constant of sorption and qe and qt have the same definition as above. Separating the variables in eq 3 gives dqt (qe - qt)2
) k2 dt
(4)
Integrating this for the boundary conditions t ) 0 to t ) t and qt ) 0 to qt ) qt gives: 1 1 ) + k2t (qe - qt) qe
(5)
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which is the integrated rate law for a pseudo-second-order reaction. Equation 5 can be rearranged to obtain qt )
t 1 t + 2 q k2qe e
(6)
which has a linear form of t 1 1 ) + t qt qe k2qe2
(7)
If the initial sorption rate is h ) k2qe2
(8)
then eqs 7 and 8 become qt )
t t 1 + h qe
(9)
and t 1 1 ) + t qt h qe
(10)
Figure 1. SEM picture of pine cone powder.
the constant can be determined experimentally by plotting of t/qt against t. The intraparticle diffusion model can be expressed as follows23 qt ) kit0.5 + C
(11)
where ki is the intraparticle diffusion constant (mg/(g min)) and C is the intercept. In this model, due to the porous nature of the adsorbent, pore diffusion is expanded to be surface sorption. Therefore, the rate constant of intraparticle transport (ki) is estimated from the slope of the linear portion of the plot of amount sorbed (mg/g) against square root of time. 2.4. Error Analysis. In this study, both the linear coefficient of determination, r2, and the nonlinear χ-square error analysis method were used to test the best fit of the isotherm model to the experimental data. The coefficient of determination, r2, is given by r ) 2
∑ (q
m
∑ (q
m
- qjt)2 +
- qjt)2
∑ (q
m
- qt)2
(12)
where qm is amount of lead(II) on the surface of the pine cone powder at any time, t, (mg/g) obtained from the pseudo-secondorder kinetic model; qt is the amount of lead(II) ion on the surface of the pine cone powder at any time, t, (mg/g) obtained from experiment; and qjt is the average of qt (mg/g). The χ-square, χ2, is given as follows: The χ-square test statistic is basically the sum of the squares of the difference between the experimental data and data obtained by calculating from models, with each squared difference divided by the corresponding data obtained by calculating from models. The equivalent mathematical statement is χ2 )
∑
(
qe - qe,m qe,m
)
(13)
where qe,m is the equilibrium capacity obtained by calculating from the model (mg/g) and qe is the experimental data of equilibrium capacity (mg/g). 3. Result and Discussion 3.1. Surface Morphology of Pine Cone Powder. The surface morphology of pine cone powder determined by SEM
Figure 2. (a) Percentage removal of lead(II) from aqueous solution using PCP: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K. (b) Percentage removal of lead(II) from aqueous solution using PCP 0.15: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K.
is shown in Figure 1. Pine cone is made up of a smooth flat multilayer surface. This surface can be seen to contain small pores indicating that this material presents good characteristics to be employed as a natural adsorbent for metallic ion uptake, as previously reported.24 It is believed that these pores provide
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Table 1. Parameters of Kinetic Models (a) For lead(II) Biosorption on Pine Cone Powder at Different Pine Cone Powder Dose model
parameters
0.4 g/L
0.5 g/L
0.6 g/L
0.7 g/L
0.8 g/L
0.9 g/L
10 g/L
pseudo-first
qe (exp) qe1 (cal) k1 r2 χ2
8.46 6.04 0.2856 0.993 1.4426
7.03 4.21 0.2994 0.988 2.7415
5.95 3.01 0.3086 0.982 4.0986
5.15 2.23 0.3293 0.981 5.3211
3.31 1.71 0.3362 0.978 6.4677
4.04 1.33 0.3455 0.976 5.6200
3.67 1.04 0.3316 0.967 9.3105
pseudo-second
qe (exp) qe2 (cal) h k2 r2 χ2
8.46 9.34 6.01 0.689 0.996 8.2210-5
7.03 7.53 7.02 0.1238 0.997 0.0053
5.95 6.26 7.88 0.2091 0.998 3.92 × 10-5
5.15 5.36 8.93 0.3109 0.998 4.96 × 10-5
3.31 4.68 9.64 0.4401 0.999 5.99 × 10-5
4.04 4.15 10.51 0.6102 0.997 1.76 × 10-5
3.67 3.75 11.14 0.7122 0.999 2.02 × 10-5
Bangham diffusion
Ri k0 r2
0.3941 0.0030 0.935
0.3202 0.0037 0.920
0.2655 0.0043 0.907
0.2197 0.0048 0.896
0.1887 0.0052 0.888
0.1615 0.0055 0.881
0.1426 0.0051 0.876
intraparticle diffusion
ki C r2 χ2
0.6115 6.12 0.980 0.4318
0.368 5.62 0.983 0.4195
0.238 5.03 0.982 0.3389
0.159 4.54 0.981 0.1500
0.115 4.09 0.981 0.1731
0.084 3.72 0.980 0.0773
0.065 3.42 0.980 0.0929
(b) For Lead Biosorption on 0.15 mol/L NaOH Treated Pine Cone Powder at Different Pine Cone Powder Dose model
parameters
0.4 g/L
0.5 g/L
0.6 g/L
0.7 g/L
0.8 g/L
0.9 g/L
1.0 g/L
pseudo-first
qe (exp) qe1 (cal) k1 r2 χ2
24.71 8.73 0.3316 0.974 50.6600
21.01 5.50 0.3431 0.969 60.7633
18.07 3.52 0.3501 0.964 83.1583
pseudo-second
qe (exp) qe2 (cal) h k2 r2 χ2
24.71 25.45 56.47 0.0876 0.998 1.11 × 10-6
21.01 21.43 71.87 0.1564 0.998 0.0082
18.07 18.32 88.62 0.2640 0.992 4.47 × 10-6
Bangham diffusion
Ri k0 r2
0.1687 0.0147 0.870
0.1327 0.0174 0.873
0.0967 0.0194 0.846
0.0677 0.0208 0.857
0.0575 0.0206 0.834
0.0474 0.0227 0.831
0.0396 0.0299 0.828
intraparticle diffusion
ki C r2 χ2
0.581 22.48 0.981 0.5471
0.334 19.73 0.969 0.3421
0.201 17.30 0.980 0.1509
0.134 15.27 0.979 0.0867
0.094 13.70 0.979 0.0529
0.069 12.52 0.979 0.0002
0.051 11.22 0.979 0.0252
a
15.79 2.39 0.3455 0.957 19.6851 15.79 15.95 102.11 0.4014 0.995 5.33 × 10-6
14.06 1.79 0.3685 0.963 115.3934 14.06 14.18 115.33 0.5736 0.998 6.17 × 10-6
12.80 1.36 0.3777 0.964 96.1592 12.80 12.88 129.41 0.7801 0.997 6.90 × 10-6
11.42 1.08 0.4076 0.971 99.0601 11.42 11.48 140.71 1.0631 0.997 7.22 × 10-6
qe, qe1 and qe2 ) mg g-1; k1 ) min-1; k2 ) gm g-1 min-1; h ) mg g-1 min-1; ki ) mg g-1 min-0.5.
ready access and large surface area for the sorption of metals on the binding sites. 3.2. Surface Negative Charge. Availability of negatively charged groups at the biosorbent surface is necessary for the biosorption of metals to proceed.25 There is an observed relationship between metal biosorption and the magnitude of negative charge on the surface of the biosorbent, which is related to the surface functional groups.26 The magnitude of negative charge was determined by protonating all ionizable functional groups and titrating the replacable hydrogen (H+) ions on the biosorbent. The magnitude of negative charge on the surface of the pine cone and 0.15 mol/L NaOH treated pine cone powder were 3.82 and 2.88 mmol/g. Base extraction removes plant pigments as the extraction liquid becomes brown. The pigment fraction may contain negatively charged compounds, such as tannins, which, upon removal could reduce the total negative charge.27 Marshall et al.27 showed that base-treated samples had a total negative charge that was more efficient in binding copper ions with respect to copper ion uptake. 3.3. Point Zero Charge. The pH at point zero charge (pHPZC) is the pH at which the amount of negative charges on the
biosorbent surface just equals the amount of positive charges. The organic functional groups on the biosorbent surface may acquire a net negative or positive charge depending on the solution pH. For pH values greater than the pKa of acidic groups, the sites are mainly in the dissociated form and acquire a negative charge, while at pH values lower than pKa, these groups will be associated with a proton to become positively charged. The pHPZC for pine cone powder was determined to be 7.49. This pHPZC value is much higher than that for corncob (6.2),28 untreated coffee waste (4.4),29 mustard husk (6.0),30 and yellow passion fruit wastes (3.7).31 The high value of pHPZC may be attributed to the higher amount of basic groups present on the pine cone powder (4.27 mmol/g). Treatment of pine cone powder with 0.15 mol/L NaOH solution led to the reduction in pHPZC from 7.49 to 2.55. The fall in pHPZC can be attributed to the unblocking of potential biosorption sites which are exposed after base washing and the possible saponification of functional groups that may have been in the condensed state. 3.4. Iodine Number. The total surface area of an adsorbent is made up of both an external and internal surface. The iodine
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Figure 3. (a) Pseudo-first-order kinetics for the removal of lead(II) from aqueous solution using different PCP doses: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K. (b) Pseudofirst-order kinetics for the removal of lead(II) from aqueous solution using different PCP 0.15 doses: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K.
number gives information on the internal surface of an adsorbent.32 The iodine number for the pine cone powder and NaOH treated pine cone powder were obtained from the isotherm plot of the amount of iodine biosorbed versus that remaining in solution. The iodine number for the pine cone powder was obtained to be 15.46 mg/g. This value is quite low compared to iodine values obtained for some agricultural wastes in the literature. For example, the iodine number for HCl treated rice husks32 is 68.00 mg/g, that for sugar cane Baggase33 is 75 mg/ g, and that for Tendu leaf refuse34 is 128 mg/g. The low iodine number as attributed to the high lignin and other plant cell wall content in pine cone. Treatment of pine cone powder with 0.15 mol/L NaOH solution increased the iodine number. The iodine number is found to 16.7 mg/g suggesting that the extraction of plant components would have opened up pore spaces and increased internal surface area of the pine cone. 3.5. Effect of Biosorbent Dose. The effect of varying the pine cone powder dose, ms, for a fixed volume (0.1dm3) of lead(II) solution at constant concentration (120 mg/L) is shown in Figure 2 for both PCP and PCP 0.15. Figure 2a and b shows the percentage of lead(II) removed with time for both biosorbents at different doses. A rapid increase in the percentage removal was seen at the initial stage of biosorption which reduced to a much slower rate after 5 min where equilibrium is
Figure 4. (a) Pseudo-second-order kinetics for the removal of lead(II) from aqueous solution using different PCP doses: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K. (b) Pseudosecond-order kinetics for the removal of lead(II) from aqueous solution using different PCP 0.15 doses: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K.
assumed to have been reached. Equilibrium capacities for lead(II) of other biosorbents reported includes macrofungus (Lactarius Scrobicus) biomass:35 60 min, green alga (Ulva lacttuca) biomass;36 60 min, lichen (Parmelina tiliaceae) biomass;37 90 min. It will also be observed from Figure 2a and b that increasing the pine cone powder dose, ms, from 4.0 to 10 g/L decreased the amount of lead(II) biosrbed from aqueous solution from 9.34 to 3.75 mg/g for PCP and from 25.45 to 11.48 mg/g for PCP 0.15. This has been attributed to two reasons. The increase in biosorbent dose at constant lead(II) concentration and volume will lead to saturation of sorption sites through the biosorption process38-40 and may also be due to particulate interaction such as aggregation resulting from high biosorbent dose.40 Such aggregation would lead to decrease in total surface area of the sorbent and an increase in the diffusion path length.38 It can also be observed from Figure 2 that the gradients of the curves differ. The curve for PCP 0.15 had a higher gradient than that of PCP, i.e., the change in biosorption capacity for PCP 0.15 was greater than for PCP when the biosorbent dose was increased from 4 to 10 g/L. The difference may likely explain the change in the physical and chemical nature of the powder surface brought about by NaOH treatment. The base
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Figure 5. (a) Bangham’s diffusion plots for the removal of lead(II) from aqueous solution using different PCP doses: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K. (b) Bangham’s diffusion plots for the removal of lead(II) from aqueous solution using different PCP 0.15 doses: initial lead(II) conc ) 120 mg/L; pH ) 5.0, agitation speed ) 160 rpm; temp ) 291 K.
treatment has been shown to remove organic pigments from the pine cone powder, and the effect of this was shown in the increase of point zero charge and iodine number. Therefore, it can be said that the higher surface area and increased negative charge on PCP 0.15 would have led to higher capacity as the amount of PCP 0.15 added increased. PCP on the other hand has lower surface area and lower point zero charge which led to only a small increase in capacity when its mass in solution was increased. The optimum biosorbent dose was obtained as 4 g/L for both samples. The optimum biosorbent dose of other biosorbents reported includes macrofungus (Lactarius Scrobicus) biomass,35 4 g/L; green alga (UlVa lacttuca) biomass,36 20 g/L; lichen (Parmelina tiliaceae) biomass,37 4 g/L. 3.6. Sorbent Dose Effect on Biosorption Kinetics. Chemical reaction may occur between the organic functional groups on the pine cone surface and the lead(II) cation in aqueous solution via complexation or cation exchange due to the negative charges on the sorbent surface. Chemical reaction may therefore control the reaction rate. Other processes present, which may also control sorption process, include the following: transport in the bulk liquid phase, diffusion across the liquid film surrounding the solid particles, diffusion in liquid-filled macropores. 3.6.1. Pseudo-First-Order Kinetics. The modeling of the effect of biosorbent dose using the pseudo-first-order kinetics proposed by Lagergren,22 by plotting log (qe -qt) versus time for the various biosorbent dose allows for the calculations of
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pseudo-first-order parameters, k1 and qe. The results of these calculations are displayed in Table 1a and b for PCP and PCP 0.15. Similar trend in the pseudo-first-order plots were observed for both PCP and PCP 0.15 (Figure 3 a and b). A deviation from the straight line can be noticed after 5 min of biosorption for all pine cone dose applied with both samples. This may signify that the pseudo-first-order kinetics is only applicable for the first 5 min of sorption. This observation also supports the explanation for the initial rapid sorption due to the absence of sorbate-sorbate interaction at the initial stage. The values for rate constant, k1, increased while equilibrium sorption capacity, qe, was found to decrease with increase in sorbent dose (Table 1a and b). The model values for equilibrium capacity, qe mod, and experimental values for equilibrium capacity, qe exp, were very different from each other for both PCP and PCP 0.15. The values for r12 were in the range of 0.990-0.967 for PCP and 0.974-0.957 for PCP 0.15. This observation again suggests that the sorption of lead(II) by PCP and PCP 0.15 is not diffusion controlled and the processes does not follow the pseudo-first-order sorption rate expression of Lagergren. 3.6.2. Pseudo-Second-Order Kinetics. The kinetic data for lead(II) sorption onto PCP and PCP 0.15 were plotted according to the pseudo-second-order kinetic model (Figure 4a and b), and the rate parameters were calculated and shown in Table 1a and b. From Table 1a and b, there was an increase in rate constants, k2, and the initial sorption rate, h, with increase in pine cone powder dose. This can be attributed to the fact that increasing biosorbent mass for a fixed volume and concentration of sorbate increases surface area for sorption and these results in an increase in the available sites for biosorption. The values of these constants were higher for PCP 0.15 than PCP due to the larger surface and lower point zero charge value of PCP 0.15. The equilibrium biosorption, qe, decreased with increasing sorbent dose. This is because increasing the biosorbent mass increases the surface area for biosorption, and hence, the rate of lead(II) biosorption is increased while the initial lead(II) concentration remains constant. The model values of equilibrium sorption, qe mod, were found to be very close to the experimental values of equilibrium sorption, qe exp, indicating that pseudosecond-order kinetics sufficiently described the biosorption of lead(II) onto pine cone powder for the range of pine cone powder dose used. Correlation coefficient values, r22, were all higher than 0.995. The corresponding linear regression of the values of qe, k, and h against ms, for PCP and PCP 0.15, were regressed to obtain expression for these values in terms of the pine cone powder dose, ms, parameters with correlation coefficients greater than 0.994 respectively, as follows: PCP qe ) 38.1154ms-1.01
(14)
h ) 2.3057ms-0.6904
(15)
k2 ) 0.0016ms2.7096
(16)
qe ) 88.6543ms-0.8858
(17)
h ) 15.3780ms0.9621
(18)
k2 ) 0.0020ms2.7336
(19)
PCP 0.15
3.6.3. Bangham Diffusion Model. Since the uptake of lead(II) on PCP and PCP 0.15 slowed down during the later
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Table 2. Pseudo-second Order Parameters for Lead Biosorption (a) On Raw Pine Cone Powder at Different Lead Concentrations model
parameters
60 mg/L
70 mg/L
80 mg/L
90 mg/L
100 mg/L
110 mg/L
120 mg/L
pseudo-second
qe (exp) qe (cal) h k2 r2 χ2 Ce Re
5.78 6.07 8.12 0.2204 0.998 1.03 × 10-5 35.72 40.47
6.56 6.96 7.63 0.1575 0.997 8.44 × 10-6 42.16 39.77
7.20 7.71 7.25 0.1220 1.000 7.22 × 10-6 49.16 38.55
7.68 8.30 6.96 0.1002 1.000 6.41 × 10-6 56.80 36.89
8.09 8.82 6.54 0.0841 1.000 5.76 × 10-6 64.72 35.28
8.39 9.22 6.23 0.0733 0.999 5.50 × 10-6 73.12 33.52
8.46 9.34 6.01 0.0689 1.000 5.12 × 10-6 82.64 31.13
(b) On 0.15 mol/L NaOH Treated Pine Cone Powder at Different Lead Concentrations model
parameters
60 mg/L
70 mg/L
80 mg/L
90 mg/L
100 mg/L
110 mg/L
120 mg/L
pseudo-second
qe (exp) qe (cal) h k2 r2 χ2 Ce Re
14.66 14.73 204.34 0.9418 0.998 6.23 × 10-6 1.08 98.20
16.99 17.12 146.63 0.5003 0.997 5.13 × 10-6 1.52 97.83
19.21 19.43 114.35 0.3029 1.000 4.35 × 10-6 2.28 97.15
21.22 21.54 94.23 0.2031 1.000 3.74 × 10-6 3.84 95.73
22.92 23.38 77.54 0.1419 1.000 3.29 × 10-6 6.48 93.52
24.22 24.84 64.22 0.1041 0.999 2.95 × 10-6 10.64 90.33
24.71 25.45 56.74 0.0876 1.000 2.79 × 10-6 18.20 84.83
Table 3. Comparison of the Best Kinetic Model and Equilibrium Amounts of Lead(II) Removal metal ion
kinetic model
equili capacity (mg/g)
biosorbent
ref
lead (II)
pseudo-second pseudo-second pseudo-second pseudo-second pseudo-second pseudo-second pseudo-second pseudo-second pseudo-second
19.76 35.22 7.70 34.00 5.32 0.89 52.16 8.46 24.71
Ficus religiosa leaves cotton waste seed of Strychnos potatorum L. tea waste Syzygium cumini L. NaOH-treated Rubber leaves powder NaOH-treated sawdust (Acacia arabica) PCP PCP NaOH
42 43 44 45 46 47 48 this study this study
stages of the sorption reaction, Bangham’s equation, as suggested by Aharoni et al.,41 of the following form was used:
(
log log
) (
)
C0 k0m ) log + Rlog t C0 - q t m 2.303V
(20)
where C0 is the initial concentration of lead(II) in solution (mg/ L), V is the volume of solution (L), m the mass of biosorbent used per liter of solution (g/L), qt is the amount of lead(II) retained at time t (mg/g), and R (
