Kinetic modeling of the adsorption of basic dyes by kudzu

Kinetic modeling of the adsorption of basic dyes by kudzu

Journal of Colloid and Interface Science 286 (2005) 101–109 www.elsevier.com/locate/jcis Kinetic modeling of the adsorption of basic dyes by kudzu St...

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Journal of Colloid and Interface Science 286 (2005) 101–109 www.elsevier.com/locate/jcis

Kinetic modeling of the adsorption of basic dyes by kudzu Stephen J. Allen a,∗ , Quan Gan a , Ronan Matthews a , Pauline A. Johnson b a School of Chemical Engineering, Queen’s University of Belfast, Stranmillis Road, Belfast BT9 5AG, UK b Department of Civil and Environmental Engineering, The University of Alabama, Tuscaloosa, AL, USA

Received 19 October 2004; accepted 16 December 2004 Available online 11 February 2005

Abstract The use of kudzu, a rapidly growing, high-climbing perennial leguminous vine, for the adsorption of basic dyes from aqueous solution has been investigated at various initial dye concentrations, masses of kudzu, and agitation rates. The extent and rate of adsorption of the three basic dyes (Basic Red 22, Basic Yellow 21, and Basic Blue 3) were analyzed using a pseudo-first-order and a pseudo-second-order kinetic model. While both rate mechanisms provided an acceptable degree of correlation with the experimental sorption rate data, the pseudo-second-order model gave a much higher degree of correlation, suggesting that this model could be used in design and simulation applications.  2005 Elsevier Inc. All rights reserved. Keywords: Adsorption; Kudzu; Dye; Kinetics; First order; Second order

1. Introduction A major problem facing the textile industry is the cleanup of wastewaters that contain visible concentrations of colored effluent. Though not always toxic, dyes do have a considerable adverse aesthetic effect because they are visible pollutants. The presence of color in water will reduce aquatic diversity by blocking the passage of light through the water. Colored agents interfere with the transmission of light through water and hinder photosynthesis [1], resulting in ecological imbalance. This is possibly the most serious consequence of the presence of dye in the water. In some cases less than 1 ppm of dye concentration produces obvious water coloration. It is estimated that around 70,000 tonnes of dyes are used annually, with a variable loss to the environment in textile manufacturing and processing of up to 50% [2]. Coloration of the liquid effluent results from wastage and washing during dyeing, with the degree of coloration being dependent on the color/shade dyed and the type of dye used. Another important reason for the use of adsorption as * Corresponding author. Fax: +44(0)2890-381753.

E-mail address: [email protected] (S.J. Allen). 0021-9797/$ – see front matter  2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.12.043

a technique for removal of dyes is the failure of conventional physicochemical coagulation/flocculation methods [3]. A number of references outline the applicability of adsorbents for removing dyes. Activated carbons and synthetic clays show a high adsorption capacity for dyes [4]. A number of biological adsorbents have also been investigated for the removal of reactive dyes; these include, among others, maize cobs, wood, and rice hulls [5]. These biological sorbents were found to be efficient in binding with basic dyes rather than acid dyes. This was attributed mainly to the coulombic attraction between the negative surface of the adsorbent and the positively charged ions of basic dyes. The removal of colored organic material by adsorption onto low-cost materials is reported by Boucher et al. [6]. Various waste biomasses have been investigated. Many lower cost materials, such as reed char [7], bone char [8], chemically modified algae [9], and peanut hull char [10], have proved successful, to a varying degree, in the removal of heavy metals from wastewater. Materials such as charred sawdust [11], carbonized wool waste [12], charred plant material [13], quaternized rice husk [14], and cassava peel char [15], have been found to be effective in the removal of a variety of dyes from water. Materials that have been used in their natural state to adsorb dyes from solution in-

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clude pine bark [16], lignite [17], linseed cake [18], sunflower stalks [19], banana peel [20], orange peel [21], chitosan [22,23], and eucalyptus bark [24]. Reviews of equilibrium and kinetic studies of dye adsorption by eggshell membranes [25,26], Rhizopus oryzae [27], peat and lignite [28], lignite-based activated carbons [29], and commercial activated carbon [30] have been are reported. Neem leaf powder is reported to be an effective adsorbent of a brilliant green dye [31]. Jain et al. [32] described the use of industrial waste products as adsorbents of anionic dyes. Janos et al. [33] tested brown coal fly ashes as adsorbents of both basic (cationic) and acid (anionic) dyes and reported that both classes of dye are adsorbed to a similar extent by the fly ash. Mesoporous materials such as sepiolite and zeolite, which are highly porous materials, have been used to adsorb dyes [34]. Ozdemir et al. [34] went on to suggest that modification of the sepiolite and zeolite surfaces by quaternary amine surfactants will enhance the adsorption capacity. Kudzu (Pueraria lobata) is a rapidly growing, highclimbing perennial leguminous vine native to eastern Asia. It was exported from Japan in 1876 to be exhibited in the Japanese pavilion at the Philadelphia Centennial Exposition in the United States. Because of its decorative dense foliage and attractive, crushed-grape-like fragrant flowers, kudzu rapidly gained popularity as an ornamental shade plant [35]. In 1970 this once helpful plant was classified as a weed and most information on it has come from attempts to eradicate it [36,37]. This has led to increased interest in finding a use for the plant. There has also been some research into the use of kudzu as an adsorbent of heavy metals. Clark et al. [36] found kudzu to have significantly greater capacity for copper than granular activated carbon. Brown et al. [38] found kudzu to be an effective adsorbent for the removal of copper, cadmium, and zinc from aqueous solution, though not as effective as a commercial grade ion-exchange resin. A study of the adsorption of basic dyes by kudzu has been reported by Matthews [39]. Allen et al. [40] compared optimized adsorption isotherm models for Basic Blue 3, Basic Yellow 21, and Basic Red 22 adsorption. Kudzu demonstrated a good capacity for basic dyes, although the capacity was not as high as for a commercial activated carbon. Adsorption capacity for basic dyes on kudzu was reduced upon mixing in multicomponent solutions. The adsorption capacity of the individual dye from any mixture was lower than sorption from a single component system for all dyes studied. In this work, the adsorption kinetics for three cationic or basic dyes, namely Basic Red 22 (Maxillon Red BL-N., Bayer), Basic Yellow 21 (Astrazone Yellow 7 GL., CibaGeigy), and Basic Blue 3 (Astrazone Blue BG., Bayer) were evaluated for their adsorption by kudzu. The focus of the present research was to investigate the effect of a number of process variables on the rate of adsorption and the applicability of two kinetic models in predicting the adsorption kinetic profiles.

Table 1 Physical properties of kudzu Property

Value

Monolayer volume Specific surface area Total absorbed volume Bulk density Sample porosity

2.31 cm3 g−1 10.05 m2 g−1 8.95 cm3 g−1 0.64 g cm−3 3.2%

2. Methods 2.1. Adsorbents Kudzu was collected in Tuscaloosa, AL, air-dried, and sieved in accordance with American Society for Testing and Materials Method D422. The particle size range used in these investigations was 0.71–0.85 mm. The prepared adsorbent was a uniformly mixed sample containing all plant components including leaf and stem. An analysis of the kudzu is given in Table 1. 2.2. Adsorbates The three basic dyes were used in single-component aqueous solutions to assess typical experimental behavior during equilibrium adsorption studies. Basic dyes possess an overall positive charge because of ionization in solution. The molar volume and molecular diameter of the dyes were 337.6 cm3 mol−1 (Basic Red 22) and 1.13 nm (Basic Red 22) and 419.3 cm3 mol−1 (Basic Yellow 7) and 1.24 nm (Basic Yellow 7), respectively [40]. 2.3. Analysis Dye concentrations in aqueous solution were determined by comparison with standard solutions in the visible range of the spectrum. A Perkin–Elmer Model 550S double-beam spectrophotometer with a 1-cm path length was used. Deionized water was used as the reference sample. The maximum wavelengths λmax (nm) for the basic dyes studied were determined to be 417 and 538 nm for the yellow and red dye, respectively. 2.4. Methodology A 2-dm3 glass beaker of internal diameter 0.13 m was used and a volume of 1.7 dm3 of solution. A six-blade flat stainless steel impeller extending vertically into the solution at a distance of 0.065 m from the bottom of the beaker provided good mixing in the vessel. The impeller was powered by a Heidolph Type 5011 variable speed motor using a 0.013-m-diameter aluminum shaft. Eight baffles were spaced evenly around the vessel circumference to prevent the formation of a vortex, the consequent reduction in relative motion between liquid and solid particles, and power losses due to air entrainment at the impeller. The baffles

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Fig. 1. The effect of adsorbent mass on pseudo-first-order model curves for the adsorption of Basic Red 22 onto kudzu.

used were flat strips of aluminum 0.2 m long and 0.013 m wide, positioned 0.008 m from the bottom of the adsorber vessel. The mixing characteristics and performance of this agitation configuration have been described and discussed previously [41]. A volume of 1.7 dm3 of dye solution of known concentration was added to the adsorber vessel and the impeller switched on at a fixed speed. An initial sample was taken before a known weight of adsorbent was added to the solution. Samples were then extracted at selected time intervals using a syringe until the system reached equilibrium. The samples were then filtered through 50-µm Millipore filters and analyzed using the spectrophotometer.

3. Results and discussion 3.1. First-order kinetic model The sorption of basic dyes onto kudzu may involve chemical adsorption, which can control the reaction rate. In order to investigate the mechanism of adsorption, the sorption kinetics can be described by a pseudo-first-order equation [42,43], dqt = k1 (qe − qt ), (1) dt where k1 is the adsorption constant. Integrating Eq. (1) for the boundary conditions t = 0 to t = t and qt = 0 to qt = qe and rearranging yields the linear time-dependent function k1 (2) t. 2.303 The intercept of the straight-line plots of log(qe − qt ) against t should equal log(qe ). However, if the intercept does not equal qe , then the reaction is not likely to be first-order, irrespective of the magnitude of the correlation coefficient. The pseudo-first-order equation (2) was used to correlate the experimental data for the adsorption of the three basic dyes onto kudzu. In order to obtain the rate constants, the straight-line plots of log(qt ) against t for the different dyes have been tested. Fig. 1 is typical of the plots for the dyes log(qe − qt ) = log(qe ) −

adsorbing onto kudzu. The k1 values, the correlation coefficients, R 2 , and the predicted and experimental qe values for all sorbent/dye combinations are given in Table 2. Although correlation coefficients, R 2 , for the application of the first-order model are reasonably high in some cases, all of the intercepts of the straight-line plots do not yield predicted qe values equal, or even values reasonably close to experimental qe values (Table 2). Any reaction occurring is therefore not likely to be a first-order reaction. 3.2. Second-order kinetic model A pseudo-second-order model may also describe the kinetics of adsorption. According to Hamadi et al. [44], the differential equation for this reaction is dqt = k2 (qe − qt )2 . dt Separating the variables in Eq. (3) gives dqt = k2 dt. (qe − qt )2

(3)

(4)

Integrating Eq. (4) for the boundary conditions t = 0 to t = t and qt = 0 to qt = qe gives 1 1 = + k2 t, (qe − qt ) qe

(5)

which is the integrated rate law for a pseudo-second-order reaction. Equation (5) can be rearranged to obtain qt =

t 1 k2 qe2

+

t qe

,

(6)

which has a linear form of 1 1 t =  2 + t. qt qe k2 q e

(7)

If the initial sorption rate is h = k2 qe2 ,

(8)

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Table 2 The effect of process variables on pseudo-first-order model constants Basic Blue 3 k1

qe mod

Initial concentration (mg dm−3 ) 25 50 100

0.031 0.028 0.022

Mass of kudzu (g) 1 2 3 5 Agitation rate (rpm) 100 200 300 400 500

Basic Red 22 qe exp

R2

k1

qe mod

4.1 9.4 19.1

13 23 49

0.877 0.906 0.852

0.020 0.015 0.019

0.027 0.023 0.027 0.021

45.1 16.9 9.4 4.2

69 35 23 14

0.951 0.946 0.906 0.864

0.029 0.035 0.039 0.037 0.032

11.8 11.0 12.2 8.9 8.5

22 23 23 23 24

0.945 0.942 0.910 0.898 0.855

Basic Yellow 11 qe exp

R2

k1

qe mod

qe exp

R2

3.6 7.9 17.1

9 16 28

0.935 0.907 0.987

0.018 0.015 0.016

3.2 5.3 8.8

6 9 20

0.918 0.953 0.900

0.013 0.012 0.015 0.016

15.6 12.4 7.9 3.7

26 20 16 10

0.932 0.940 0.907 0.938

0.019 0.017 0.015 0.012

9.9 6.6 5.3 2.5

17 12 9 7

0.964 0.966 0.953 0.904

0.027 0.028 0.029 0.036 0.027

12.4 11.5 11.9 11.8 10.3

15 15 16 15 16

0.987 0.974 0.968 0.983 0.968

0.029 0.028 0.038 0.033 0.031

7.4 6.8 7.7 7.0 6.7

9 9 9 10 10

0.977 0.956 0.967 0.962 0.953

Fig. 2. The effect of adsorbent mass on pseudo-second-order model curves for the adsorption of Basic Red 22 onto kudzu.

then Eq. (7) becomes t qt = 1 t + h qe

(9)

and 1 1 t = + t. (10) qt h qe The constants can be determined experimentally by plotting t/qt against t. The lower values of R 2 (Table 2) suggest that the degree of fit of the experimental data by the pseudo-first-order equation was not great; hence the second-order model equations were applied to the data points for the adsorption of the three basic dyes by kudzu. The rate constants were calculated from the intercept and slope of straight line plots of t/qt against t for the different dyes and under varying process conditions. Figs. 2 and 3 are typical of the straightline plots obtained for all the sorbent/dye combinations for each of the process variables.

Table 3 lists the rate constants, k2 , the predicted equilibrium sorption capacities, qe model , and the initial sorption rates, h, determined from the straight-line plots for each adsorbent/sorbate system. Figs. 4–6 show typical curves calculated from the constants. The experimental points are shown, together with the theoretically generated curves. The agreement between the experimental and predicted curves is very good. It can be seen from Table 3 that the values of the initial sorption rates, h, increased with an increase in the initial dye concentration. It has been shown elsewhere [39] that the initial rate of adsorption calculated from the single-externalresistance-to-mass-transfer model decreased with increasing initial dye concentration. The accuracy of the pseudosecond-order model in predicting the experimental data confirms that the external resistance model failed to describe the adsorption mechanism adequately and that boundary layer resistance is not the rate-controlling step. It is clear that the increase in h values can be attributed to the increase in the

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105

Fig. 3. The effect of agitation speed on pseudo-second-order model curves for the adsorption of Basic Yellow 21 onto kudzu.

Table 3 The effect of process variables on pseudo-second-order model constants Basic Blue 3

Basic Red 22

Basic Yellow 11

k2

h

qe mod

qe exp

k2

h

qe mod

qe exp

k2

h

qe mod

qe exp

Initial concentration (mg dm−3 ) 25 50 100

0.022 0.008 0.003

3.61 4.53 8.71

12.9 23.6 50.5

13 23 49

0.017 0.005 0.003

1.35 1.34 2.29

9.0 16.4 29.1

9 16 28

0.013 0.007 0.005

0.47 0.73 2.28

6.1 9.9 21.2

6 9 20

Mass of kudzu (g) 1 2 3 5

0.001 0.004 0.008 0.018

7.03 4.86 4.53 3.79

72.5 35.7 23.6 14.4

69 35 23 14

0.002 0.002 0.005 0.015

1.564 1.159 1.344 1.709

27.8 21.6 16.4 10.5

26 20 16 10

0.004 0.007 0.007 0.019

1.37 1.09 0.73 0.92

17.9 12.9 9.3 6.9

17 12 9 7

Agitation rate (rpm) 100 200 300 400 500

0.006 0.008 0.008 0.012 0.011

3.33 4.67 4.52 6.63 6.76

23.1 23.7 23.6 23.9 24.4

22 23 23 23 24

0.003 0.004 0.005 0.006 0.006

0.92 1.10 1.27 1.45 1.54

16.5 16.2 16.7 16.1 16.5

15 15 16 15 16

0.005 0.006 0.008 0.009 0.01

0.474 0.601 0.758 0.914 1.077

10.1 10.1 9.8 10.3 10.6

9 9 9 10 10

Fig. 4. Comparison of experimental and pseudo-second-order predicted data for the adsorption of Basic Yellow 21 onto kudzu with varying initial dye concentration.

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Fig. 5. Comparison of experimental and pseudo-second-order predicted data for the adsorption of Basic Blue 3 onto kudzu with varying mass.

Fig. 6. Comparison of experimental and pseudo-second-order predicted data for the adsorption of Basic Red 22 onto kudzu with varying agitation speed.

driving force for mass transfer, allowing more dye molecules to reach the surface of the adsorbents in a shorter period of time. The values of the rate constant, k2 , were found to decrease with increasing initial dye concentration. The corresponding linear plots of the values of qe , k2 , and h against C0 were regressed to obtain expressions for these values in terms of the initial dye concentration (Table 4). The terms qe , k2 , and h can be expressed as a function of C0 as follows [45,46]: C0 , Aq C0 + Bq C0 k2 = , Ak C0 + Bk C0 . h= Ah C0 + Bh qe =

(11) (12) (13)

Substituting the values of qe and h from Table 3 into Eqs. (11) and (13) and then into Eq. (9) derives the rate law for pseudo-second order and the relationship of qt , C0 , and t: Basic Blue 3

qt =

C0 t , (2.007)t + 0.053C0 + 6.713

(14)

Basic Red 22 C0 t , (15) (0.009C0 + 2.585)t + 0.306C0 + 15.27 Basic Yellow 21 C0 t qt = (16) . (0.006C0 + 4.238)t − 0.175C0 + 65.36 Equations (14)–(16) represent generalized predictive models for the amounts of the three basic dyes adsorbed at any contact time and initial dye concentration within the given range onto kudzu. The equations indicate that the amount of dye adsorbed at any contact time is higher for a greater initial dye concentration. This can be attributed to the more efficient utilization of the sorptive capacities of both adsorbents due to an increase in driving force for adsorption. These equations can be used to derive the amount of dye adsorbed at any given dye concentration and reaction time. Fig. 5 shows typical sorption curves for the effect of the adsorbent mass on the sorption kinetics of the three dyes. It is clear that the data also showed good compliance with the pseudo-second-order equation. Table 3 shows that there was a decrease in h, the initial rate parameter, with adsorbent mass. However, the values of the rate constant, k2 , qt =

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Table 4 Empirical parameters for predicted qe , k2 , and h Aq

Process variable

Bq

Ak

Bk

Ah

Bh

Initial concentration (mg dm−3 ) 0.000 0.009 0.006

Basic Blue 3 Basic Red 22 Basic Yellow 11

72.0 35.02 18.47

Mass of kudzu (g) −1.004 0.001 1.633 −0.243 0.001 0.530 −0.586 0.004 0.868

0.041 0.061 0.094

Agitation rate (rpm) 0.366 66.89 11100 0.040 142.1 17888 1.173 73.8 16239

Basic Blue 3 Basic Red 22 Basic Yellow 11

2.007 2.585 4.238

387.5 481.1 240.1

−10400 −11940 −4500

Basic Blue 3 Basic Red 22 Basic Yellow 11

0.053 0.306 −0.175 6.770 1.265 1.292 0.105 0.527 0.612

6.71 15.27 65.36 −0.375 0.044 −0.304 23.07 67.24 184.9

were found to increase with increasing adsorbent mass. An increase in the sorbent mass results in an increase in the surface area for adsorption and an increase in the available sites for adsorption. The decrease in qe values with increasing mass is due to the fact that increasing the adsorbent mass increases the surface area for sorption and hence the rate of dye sorption is increased while the initial dye concentration remains constant. It was found that qe , k2 , and h can be expressed as a function of adsorbent mass, M, as follows: qe = Aq M

Bq

,

(17)

k2 = Ak M Bk ,

(18)

h = Ah M

(19)

Bh

.

The corresponding linear plots of the values of qe , k2 , and h against M were regressed to obtain expressions for these values in terms of the adsorbent mass (Table 4). Substituting the values of qe and k2 from Table 3 into Eqs. (17) and (18) and then into Eq. (9) derives the rate law for pseudo-second order and the relationship of qt , C0 , and t: Basic Blue 3 qt =

t 1 0.001M 1.633 (72.00M −1.004 )2

+

t 72.00M −1.004

+

t 35.02M −0.243

+

t 18.47M −0.586

,

(20)

,

(21)

.

(22)

Basic Red 22 qt =

t 1 0.001M 0.530 (35.02M −0.243 )2

Basic Yellow 21 qt =

t 1 0.004M 0.868 (18.47M −0.586 )2

These equations can be used to derive the amount of dye adsorbed at any given reaction time for any sorbent mass within the given range. Fig. 6 shows typical adsorption curves for the effect of the agitation speed on the sorption kinetics of the three dyes onto both adsorbents. Again, the data showed good compliance with the pseudo-second-order equation. Table 3 shows that both the initial rate parameters h and the rate constants

107

k2 increased with an increase in agitation speed. This is due to the very small effects of the decrease in the boundary layer resistance to mass transfer, allowing more dye to reach the surface of the adsorbent in a shorter period of time. As expected, the qe values remain virtually constant when the adsorbent mass and initial dye concentration are constant, so agitation speed can only affect the initial rate of dye uptake and not the final extent of uptake. It was found that qe , k2 , and h can be expressed as a function of agitation speed, S, as follows: S , Aq S + Bq S , k2 = Ak S + Bk S h= . Ah S + Bh

qe =

(23) (24) (25)

The corresponding linear plots of the values of qe , k2 , and h against S were regressed to obtain expressions for these values in terms of the agitation speed (Table 4). Substituting the values of qe and h from Table 3 into Eqs. (23) and (25) and then into Eq. (9) derives the rate law for pseudo-second order and the relationship of qt , C0 , and t: Basic Blue 3 St , (0.041S + 0.366)t + 0.105S + 23.07 Basic Red 22 St , qt = (0.061S + 0.040)t + 0.527S + 67.24 Basic Yellow 21 St qt = . (0.094S + 1.173)t + 0.612S + 184.9 qt =

(26)

(27)

(28)

These equations can be used to derive the amount of dye adsorbed at any given reaction time for any agitation speed within the given range, and under the test conditions used. It is clear from the accuracy of the model that the sorption kinetics of the basic dyes are described by a pseudo-secondorder chemical reaction and that this reaction is significant in the rate-controlling step. Physical adsorption and chemisorption may be indistinguishable in certain situations, and in some cases a degree of both types of bonding can be present, as with covalent bonds between two atoms having some degree of ionic character and vice versa. Although dyes are considered to be organic compounds, basic dyes ionize in solution to form positive ions. The structure of kudzu is cellulose-based, and the surface of cellulose in contact with water is negatively charged, so it is likely that a chemical reaction may be taking place, which appears to be the main rate-determining factor in the adsorption process. Kudzu is cellulose-based, and the surface of cellulose is negatively charged when in contact with water. In the adsorption of basic dyes onto kudzu, the cationic dyes carry charge opposite to that of the adsorbent, aiding the adsorption process. The kudzu has a low porosity of only 3.2%

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and a surface area of 10 m2 g−1 ; an activated carbon can have a surface area of 1100 m2 g−1 and a porosity of 47%. Hence the kudzu does not have a well-developed microporous structure. This accounts for the F400 activated carbon adsorbing 670 and 800 mg g−1 of the red and yellow dyes, respectively, compared to 210 and 150 mg g−1 for the kudzu. The mechanism of adsorption can also be described as chemisorption, involving valency forces through sharing or the exchange of electrons between sorbent and sorbate as covalent forces [45]. This can be tested using chemisorption pseudo-kinetic models. Low et al. [47] reported that the sorption of two basic dyes onto water hyacinth roots was described by pseudo-first-order kinetics. Ho and McKay [42] tested the application of pseudo-first- and -second-order equations for the description of the sorption kinetics of two dyes onto peat, finding the pseudo-second-order equation to be more suitable and stating that the chemical reaction was important and significant in the rate-controlling step. Cheung et al. [8] and Hamadi et al. [44] also found that the pseudo-second-order chemical reaction model provided the best correlation between experimental and predicted curves for adsorption of metal ions onto used tires, sawdust, and bone char. The sorption of the basic dyes onto kudzu may involve chemical adsorption, which can control the reaction rate. To investigate the mechanism of adsorption, the sorption kinetics can be described by a pseudo-first-order equation. However, if the intercept does not equal qe , then the reaction is not likely to be first-order, irrespective of the magnitude of the correlation coefficient. According to the values in Tables 2 and 3 the optimum results are those for the second-order model. These results suggest that the pseudo-second-order mechanism is predominant and that chemisorption might be the rate-limiting step that controls the adsorption process. Both of the models describe the adsorption processes to an extent; however, they cannot predict the rapid rate of adsorption that occurs during the first few minutes of the adsorption process. The ratecontrolling mechanism may vary during the course of the sorption process. Three possible mechanisms may be occurring. There is an external surface mass transfer or film diffusion process that controls the early stages of the sorption process. This may be followed by a reaction or constant-rate stage, and finally by a diffusion stage, where the adsorption process slows down considerably. Again the pseudo-second-order model is slightly better. This sharp rise in solid phase concentration in the early stages of the sorption process is considered to be indicative of a fast initial external-mass-transfer step. The concentration of the adsorbate on the adsorbent may be regarded as an adsorption density that increases with a decrease in the adsorbent dosage because there is a proportionately larger amount of dye in contact with a lower unit mass of kudzu. The internal diffusion rate decreases with an increase in mass, perhaps due to the increased external surface for sorption, the consequent rapid fall in dye con-

centration in solution, and a consequent reduction in the concentration difference driving force for the mass transfer.

4. Conclusion Certain variables that influence the kinetics of the adsorption process have been investigated. Increased initial dye concentration resulted in an increase in the amount of dye adsorbed per gram of adsorbent for all sorbent/dye combinations. The initial uptake of dye was found to be more rapid from solutions with lower concentrations. The rate of dye adsorption increased with increasing adsorbent mass and agitation speed. A pseudo-first-order model was used to correlate the experimental data for the adsorption of the three basic dyes. Although correlation coefficients were reasonably high, the model did not predict qe values equal, or even reasonably close, to experimental qe values. Any reaction occurring is therefore not likely to be a first-order reaction. A pseudo-second-order model was also applied to the experimental data, assuming that the external-mass-transfer limitations on the system could be neglected and that sorption was chemisorption-controlled. The correlation coefficients and the accuracy of the model in predicting experimental data strongly suggest that the rate-limiting step may be chemical sorption involving valence forces through sharing or exchange of electrons between sorbent and sorbate. Equations were developed using the pseudo-second-order model that accurately predict the amounts of the three basic dyes adsorbed at any contact time, initial dye concentration, adsorbent mass, and agitation speed within the given range.

Appendix A. Nomenclature Ce C0 Ct h k1 k2 M qe qe mod qe exp qt S t

Equilibrium liquid-phase concentration (mg dm−3 ) Initial liquid-phase concentration (mg dm−3 ) Liquid-phase concentration at time t (mg dm−3 ) Initial sorption rate (mg−1 min−1 ) Rate constant of first-order sorption (min−1 ) Rate constant of pseudo-second-order sorption (g mg−1 min−1 ) Mass of adsorbent (g) Equilibrium solid-phase concentration (mg g−1 ) Model-predicted dye equilibrium solid-phase concentration (mg g−1 ) Measured dye equilibrium solid-phase concentration (mg g−1 ) Dye solid-phase concentration at time t (mg g−1 ) Agitation rate (rpm) Time (min)

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