Removal of copper(II) ions from aqueous solution by biosorption onto agricultural waste sugar beet pulp

Process Biochemistry 40 (2005) 3031–3044 www.elsevier.com/locate/procbio

Removal of copper(II) ions from aqueous solution by biosorption onto agricultural waste sugar beet pulp Zu¨mriye Aksu *, I˙. Alper ˙Is¸og˘lu Hacettepe University, Department of Chemical Engineering, 06532 Beytepe, Ankara, Turkey Received 21 September 2004; received in revised form 13 January 2005; accepted 14 February 2005

Abstract Dried sugar beet pulp, an agricultural solid waste by-product, was used as an biosorbent for the removal of copper(II) from aqueous solution. A series of experiments were conducted in a batch system to assess the effect of the system variables, i.e. initial pH, temperature and initial metal ion concentration. The results indicated that at 250 mg l
1 initial copper(II) concentration dried sugar beet pulp exhibited the highest copper(II) uptake capacity of 28.5 mg g
1 at 25 8C and at an initial pH value of 4.0. The equilibrium data were analyzed using the Freundlich, Langmuir, Redlich–Peterson and Koble–Corrigan isotherm models depending on temperature. The Langmuir model was found to best describe the data in the concentration and temperature ranges studied. Simple mass transfer and kinetic models were applied to the experimental data to examine the mechanisms of biosorption and potential rate-controlling steps such as external mass transfer, intraparticle diffusion and biosorption process. It was found that the intraparticle diffusion played an important role in the biosorption mechanisms of copper(II), and biosorption kinetics followed pseudo first- and pseudo second-order kinetic models rather than the saturation type kinetic model for all temperatures studied. The activation energy of biosorption (EA) was determined as
58.47 kJ mol
1 using the Arrhenius equation. Using the thermodynamic equilibrium coefficients obtained at different temperatures, the thermodynamic constants of biosorption (DG8, DH8 and DS8) were also evaluated. # 2005 Elsevier Ltd. All rights reserved. Keywords: Biosorption; Copper(II); Dried sugar beet pulp; Equilibrium; Kinetics; Thermodynamics

1. Introduction Copper is a widely used industrial metal used for electrical wiring, plumbing, air conditioning tubing and roofing. The properties of copper, which make it suitable for these applications, include high electrical and thermal conductivity, good corrosion resistance, ease of fabrication and installation, attractive appearance, ready availability, and high recyclability. Additionally, copper, which is an essential nutrient to humans and other life forms, is biostatic/ biocidal to certain organisms. However, copper(II) is known to be one of the heavy metals most toxic to living organisms and it is one of the more widespread heavy metal contaminants of the environment. The potential sources of copper in industrial effluents include metal cleaning and plating baths, pulp, paper board mills, wood pulp produc* Corresponding author. Tel.: +90 312 2977434; fax: +90 312 2992124. E-mail address: [email protected] (Z. Aksu). 1359-5113/$ – see front matter # 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2005.02.004

tion, and the fertilizer industry, etc. Consequently, wastewaters of these industries contain high levels of copper(II) ions and in order to avoid water pollution treatment is needed before disposal [1–6]. The most widely used method for removing heavy metal ions including copper(II) ions is coagulation and precipitation. Heavy metals, for example, can be precipitated as insoluble hydroxide at high pH or sometimes as sulfides. A major problem with this type of treatment is the disposal of the precipitated waste. Moreover, the precipitation itself cannot reduce the contaminant far enough to meet current water-quality standards. Ion exchange treatment is the second most widely used method for metal removal. This method does not present a sludge disposal problem and has the advantage of reclamation of metals. It can reduce the metal ion concentration to a very low level. However, ion exchange does not appear to be practicable to wastewater treatment from a cost stand point. Adsorption with activated carbon can also be highly efficient for the removal of

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Z. Aksu, I˙.A. I˙s¸og˘lu / Process Biochemistry 40 (2005) 3031–3044

numerous trace elements from water, but the high cost of activated carbon inhibits its large-scale use as adsorbent. Then, the need for effective and economical removal of heavy metal ions resulted in a research for unconventional methods and materials that might be useful in this field [1– 6]. Biosorption is an alternative technology to remove heavy metals from dilute aqueous solutions using inactive and dead biomasses, such as agricultural and fermentation wastes, various kinds of microorganisms, to bind and accumulate these pollutants by different mechanisms such as physical adsorption, complexation, ion exchange and surface microprecipitation [1,4–6]. In the past few years, extensive research has been undertaken to develop alternative and economic adsorbents. An economic sorbent is defined as one which is abundant in nature, or is a by-product or waste from industry and requires little processing. Agricultural waste biosorbents generally used in biosorption studies are also inexhaustible, low-cost and non-hazardous materials, which are specifically selective for heavy metals and easily disposed by incineration. Agricultural by-products as a whole exceed 320,000,000,000 kg/year. Most of these by-products are considered to be low value products. The agricultural byproducts such as peat, wood, pine park, banana pith, rice bran, wheat bran, peanut shells, wool, rice milling byproducts (hulls and bran), sunflower and grape stalks wastes, sugar beet pulp, olive mill solid residue, sawdust and leaves have been demonstrated to remove heavy metal ions from wastewater. Many examples are available in the literature concerning the direct or activated use of these materials as adsorbents [2,7–25]. One of these low-cost sorbents particularly suited to biosorption is sugar beet pulp, a by-product of the sugarrefining industry, which exhibits a large capacity to bind metals. This material is very cheap and is mainly used as animal feed. Sugar beet pulp is a natural polysaccharide and is composed of 20% and more than 40% of cellulosic and pectic substances, respectively. The pectic substances, which account for more than 40% of the dry matter, are complex heteropolysaccharides containing galacturonic acid, arabinose, galactose and rhamnose as the major sugar constituents. Due to the carboxyl functions of galacturonic acid, pectic substances are known to strongly bind metal cations in aqueous solution [22–25]. There are some reports of heavy metal biosorption by sugar beet pulp, but little attention has been paid to the investigation of temperature dependence of biosorption process and evaluating equilibrium, kinetic and thermodynamic parameters of the system, which are important in the design of treatment systems. This paper presents the study of biosorption characteristics of dried sugar beet pulp for removing copper(II) from aqueous solutions. The binding capacity of dried sugar beet pulp for copper(II) was shown as a function of initial pH, temperature and initial copper(II) concentration in this study. The biosorp-

tion equilibrium were expressed by the Langmuir, Freundlich, Redlich–Peterson and Koble–Corrigan adsorption models and the effect of temperature on the model constants was investigated. Batch studies were carried out to identify the rate-controlling steps and determining external mass transfer and intraparticle diffusion rate coefficients. Only a limited number of studies have so far been focused on the kinetic analysis of biosorption of copper(II) in the literature so the experimental data were also analyzed using three different adsorption kinetic models and kinetic constants were calculated depending on temperature. The activation energy of biosorption process, which is an indicator of adsorption type, was also evaluated by using a first-order saturation type kinetic model constant. Since the evaluation of the heat change of the biosorption process is very important for reactor design, the thermodynamics of the adsorption process was also investigated.

2. Materials and methods 2.1. Adsorbent In this study, the waste pulp of sugar beet remaining from extraction of sugar was used as metal biosorbent. The pulp was obtained from the Ankara Sugar Mill, Turkey. Wet sugar beet pulp was dried at 100 8C until constant weight, grounded and sieved. The adsorbent particle size is an important factor in adsorption kinetics because it determines the time required for transport of sorbate within the pore to adsorption sites. The diffusional resistance to mass transfer is greater for large particles but, the smallest size allows very fast removal kinetics if the adsorption is to be primarily a surface phenomenon. Moreover, increasing the surface area due to small particle size also increases the number of sites, or indirectly increases the adsorption capacity, so the preliminary batch biosorption experiments were carried out using three different particle sizes of 250, 350 and 500 mm. Since the adsorbent of the particle size 500 mm has a poor adsorption capacity, the adsorbent of the particle size 250 mm was selected for adsorption studies due to its higher adsorption capacity. 2.2. Chemicals Stock solutions of copper(II) were prepared by dissolving accurately weighed amount of analytical grade CuSO45H2O (Merck) in 1 l double-distilled water. The test solutions were prepared by diluting 1 g l
1 of stock solution of copper(II) to the desired concentrations. The range of concentrations of prepared copper(II) solutions was 25–250 mg l
1. Before mixing the adsorbent, the pH of each test solution was adjusted to the required value with diluted and concentrated H2SO4 and NaOH solutions, respectively.

Z. Aksu, I˙.A. I˙s¸og˘ lu / Process Biochemistry 40 (2005) 3031–3044

Insignificant decreases in the final equilibrium pH were recorded, so during the uptake pH was assumed constant. 2.3. Adsorption studies Sorption studies were conducted in a routine manner using a batch technique. A number of stoppered Pyrex glass Erlenmeyers containing a definite volume (100 ml in each case) of solutions of copper(II) of desired concentration, pH and temperature were placed in a thermostatic rotary shaker. For the studies, 0.1 g of dried sugar beet pulp was treated with 100 ml of copper(II) bearing solution at a defined pH and temperature. The flasks were agitated at a 150 rpm constant shaking rate for 24 h to ensure equilibrium was reached. Samples (5 ml) were taken before mixing the biosorbent and copper(II) bearing solution and at pre-determined time intervals and the copper(II) solution was separated from the biosorbent by centrifugation at 5000 rpm for 5 min. Uptake values were determined as the difference between the initial copper(II) concentration and the one in the supernatant. All the experiments were carried out in duplicates and the average values were used for further calculations. 2.4. Analysis of copper(II) The concentration of residual copper(II) in the biosorption medium was determined spectrophotometrically. 0.2 ml of 1% (w/v) sodium diethyl dithiocarbamate solution, and 20 ml of 1.5N NH3 solution was added to the sample (1 ml) containing lower than 60 mg l
1 of copper(II) ions and diluted to 25 ml with double-distilled water. The absorbance of the yellow–brown coloured solution was read at 460 nm [1].

3. Results and discussion

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the surface charge of the adsorbent, but also the degree of ionization and speciation of the heavy metal in solution. The metal cations in aqueous solution convert to different insoluble hydrolysis products due to pH. The hydrolysis products of copper(II) are also a function of pH. The dominant species of copper in the pH range 3–4 are Cu2+ and CuOH+, while the copper at above 5.0 occurs as insoluble Cu(OH)2. Fig. 1 indicates the effect of initial solution pH on the biosorption of copper(II) on dried sugar beet pulp at 100 mg l
1 initial metal ion concentration and at 25 8C. Copper(II) removal was strongly dependent on pH and almost constant from pH 2.0 to 3.0 and increased significantly with further increase in pH. The equilibrium uptake of copper(II) increased from 10.8 to 24.6 mg g
1 with increasing pH from 2.0 to 4.0. The drastic decrease in copper biosorption above pH 4.5 was probably due to the precipitation of copper(II) ions as insoluble Cu(OH)2 precipitate and not due to biosorption. It was verified that the raw sugar beet pulp is dominated by negatively charged sites that are largely carboxylate groups with some weaker acidic groups. The copper(II) ions are mainly fixed on these acid sites. At low pH, the surface of biosorbent would also be surrounded by hydronium ions which decrease the copper interaction with binding sites of the dried sugar beet pulp by greater repulsive forces. The smaller biosorption values observed at low pH have been attributed to the competition between the protons and the ions released, i.e. sodium(I), phosphorus(III), calcium(II), etc. by pulp into the solution. At pH 2, most of the potential fixation sites are protonated and prevent copper(II) ions to be fixed. Moreover, ion exchange with calcium(II) ions neutralizing the carboxyl groups of the polysaccharide may be the other predominant mechanism. As expected, the capacities of fixation increase with pH. As the pH increased, the overall surface on the dried sugar beet pulp became negative and biosorption increased making true sorption studies impossible. When the pH increases, fixation

Analysis of biosorption data is important for developing equilibrium, kinetic and thermodynamic equations that can be used for design purposes. The equilibrium, kinetic and thermodynamic results obtained in the biosorption of copper(II) on to dried sugar beet pulp are given as the units of adsorbed copper(II) quantity per gram of adsorbent at any time and at equilibrium [q = (C0
C)/X and qeq = (C0
Ceq)/X] (q; qeq: mg g
1), respectively, unadsorbed copper(II) concentration in solution at any time and at equilibrium (C; Ceq: mg l
1), respectively, adsorbed copper(II) concentration in solution at equilibrium (Cad,eq: mg l
1) and biosorption yield [Ad% = 100  (C0
Ceq)/ C0]. 3.1. Effect of initial pH on copper(II) biosorption pH is an important factor influencing heavy metal biosorption on agricultural by-products. pH affects not only

Fig. 1. The effect of initial pH on the equilibrium copper(II) sorption capacity of dried sugar beet pulp (T: 25 8C; C0: 100 mg l
1; X: 1.0 g l
1; agitation rate: 150 rpm).

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capacities are improved due to the lower competition between the protons and copper(II) ions [22–25]. As a result the working pH value for copper(II) biosorption was chosen as 4.0 and the other biosorption experiments were performed at this pH value. 3.2. Effect of temperature on copper(II) biosorption In most cases, biosorption decreases with increasing temperature. The equilibrium uptake of copper(II) by dried sugar beet pulp was also affected by temperature and decreased notably with increasing temperature up to 45 8C (Table 1). At 100 mg l
1 initial copper(II) concentration the equilibrium uptake capacity of sorbent decreased from 24.6 to 12.3 mg copper(II) per gram of adsorbent with increasing temperature from 25 to 45 8C. Copper(II) biosorption was exothermic thus the extent of biosorption increased with decreasing temperature so the sorption of copper(II) by dried sugar beet pulp may involve mainly physical sorption. The decrease in biosorption capacity of dried sugar beet pulp at higher temperature may be attributed to the deactivation of the adsorbent surface or the destruction of some active sites on the adsorbent surface due to bond rupture.

Fig. 2. The biosorption curves of copper(II) obtained at 100 and 200 mg l
1 initial copper(II) concentrations and at different temperatures (initial pH 4.0; X: 1.0 g l
1; agitation rate: 150 rpm).

equilibrium copper(II) uptake as shown in Table 1. With the change in temperature from 25 to 45 8C, the uptake capacity decreased from 28.5 to 16.1 mg g
1 at 250 mg l
1 initial copper(II) concentration. However, the removal percentage of copper(II) showed an opposite trend and decreased with increasing initial metal ion concentration. The biosorption yield of copper(II) decreased from 45.9 to 11.0% at 25 8C with increasing initial copper(II) concentration from 25.6 to 258.8 mg l
1. In the case of lower concentrations, the ratio of initial number of metal ions to the available sorption sites is low and subsequently the fractional biosorption becomes independent of initial concentration. At higher concentrations, however, the available sites of biosorption become fewer and subsequently the removal of metals depends on the initial concentration. As a result, the purification yield can be increased by diluting the wastewaters containing high metal ion concentrations.

3.3. Effect of initial copper(II) concentration on temperature-dependent copper(II) biosorption The initial concentration provides an important driving force to overcome all mass transfer resistance of copper(II) between the aqueous and solid phases, hence a higher initial concentration of copper(II) will increase the biosorption rate. The equilbrium copper(II) uptake values at different initial metal ion concentrations are given in Table 1 with respect to temperature. It is clear that the equilibrium sorption capacity of dried sugar beet pulp for copper(II) increased with increasing initial copper(II) concentration up to 250 mg l
1, and decreased with increasing temperature up to 45 8C. Then, the equilibrium uptake did not change with further increase in initial metal ion concentration at any of the temperature studied showing a saturation trend at higher copper(II) concentrations due to a finite number of surface binding sites. At 25 8C, when the initial copper(II) concentration increased from 25.6 to 258.8 mg l
1, the loading capacity of dried sugar beet pulp increased from 11.8 to 28.5 mg g
1. The temperature also influenced

3.4. Biosorption kinetics Fig. 2 shows the results of kinetic experiments conducted to determine the equilibrium time required for the uptake of

Table 1 Effect of initial copper(II) concentration and temperature on the equilibrium uptake capacity and biosorption yield of dried sugar beet pulp 25 8C

35 8C
1


1

45 8C
1


1

C0 (mg l )

qeq (mg g )

Ad%

C0 (mg l )

qeq (mg g )

Ad%

C0 (mg l
1)

qeq (mg g
1)

Ad%

25.6 52.9 106.1 153.9 198.2 258.8

11.8 19.6 24.6 27.6 28.1 28.5

45.9 37.1 23.9 17.9 14..2 11.0

26.7 48.2 100.9 143.4 212.3 258.0

8.8 11.9 16.7 19.7 21.1 21.2

32.9 24.6 16.5 13.8 9.9 8.2

25.1 49.5 104.4 150.0 205.3 252.9

5.3 8.8 12.3 14.5 15.8 16.1

21.0 17.7 11.8 9.6 7.7 6.3

Z. Aksu, I˙.A. I˙s¸og˘ lu / Process Biochemistry 40 (2005) 3031–3044

copper(II) ions by the dried sugar beet pulp. The curves at 25, 35 and 45 8C were obtained by plotting the copper(II) uptake capacity, q, versus time at 100 and 200 mg l
1 initial copper(II) concentrations. For the given concentrations and temperatures the amount of copper(II) adsorbed by dried sugar beet pulp increased linearly with time in the beginning, then non-linearly at a slower rate and finally attained saturation called the equlibrium time which was dependent on time and temperature. The data showed that a contact time ranging from about 1 to 3 h depending on temperature was sufficient to achieve equilibrium and biosorption did not change subsequently up to 24 h (data not shown). For both initial copper(II) concentrations the biosorption capacity of dried sugar beet pulp decreased significantly with increasing temperature. In general, as the concentration of copper(II) increased, although the time to reach equilibrium did not change notably, copper(II) removal increased without regard to temperature. For all initial copper(II) concentrations initial sorption of copper(II) occurred rapidly and the majority of copper(II) uptake occurred within the first 30 min (Fig. 2). At 25 8C, 71.3 and 78.4% of total adsorbed amount of copper(II) was removed by biosorbent in the first 30 min of contact at 100 and 200 mg l
1 initial metal ion concentrations, respectively. At 35 8C, dried sugar beet pulp adsorbed up to 74.4 and 83.1% of the total sorbed quantity of copper(II) within the initial 30 min at the same initial metal ion concentrations, respectively. At 45 8C, about 85.7 and 88.9% of the total metal ion sorption was achieved within 30 min at 100 and 200 mg l
1 initial metal ion concentrations, respectively, with little further biosorption over the next 30 min. The rapid uptake of copper(II) in all cases indicates that the uptake of metal ion occurs predominantly by surface binding and that available sites on the biosorbent are the limiting factor for the biosorption. 3.5. Modelling of biosorption equilibrium depending on temperature Equilibrium data, commonly known as adsorption isotherms, are basic requirements for the design of adsorption systems. In order to discover the sorption capacity of beet pulp the experimental data points were fitted to the Freundlich, Langmuir, Redlich–Peterson and Koble–Corrigan equations applicable to sorption process. For each isotherm initial copper(II) concentrations were varied while the adsorbent weight in each sample was held constant. The Langmuir equation which is valid for monolayer sorption onto a completely homogeneous surface with a finite number of identical sites and with negligible interaction between adsorbed molecules is given by Eq. (1). qeq ¼

Q0 bCeq 1 þ bCeq

(1)

where Q0 is the maximum amount of the copper(II) per unit weight of dried sugar beet pulp to form a complete mono-

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layer on the surface bound at high Ceq, and b is a constant related to the affinity of the binding sites. Q0 represents a practical limiting biosorption capacity when the surface is fully covered with copper(II) and assists in the comparison of biosorption performance, particularly in cases where the sorbent did not reach its full saturation in experiments [26]. The empirical Freundlich equation based on a monolayer adsorption by the adsorbent with a heterogeneous energy distribution of active sites is given below by Eq. (2). 1=n qeq ¼ KF Ceq

(2)

where KF and n are the Freundlich constants characteristic on the system. KF and n are indicators of biosorption capacity and biosorption intensity, respectively. The Freundlich isotherm is also more widely used but provides no information on the monolayer biosorption capacity, in contrast to the Langmuir model [27]. The three-parameter Redlich–Peterson equation has been proposed to improve the fit by the Langmuir or Freundlich equation and is given by Eq. (3). It has a linear dependence on concentration in the numerator and an exponential function in the denominator. qeq ¼

KRP Ceq b 1 þ aRP Ceq

(3)

where KRP, aRP and b are the Redlich–Peterson parameters. b lies between 0 and 1. For b = 1 Eq. (3). converts to the Langmuir form [28]. Koble–Corrigan model is another three-parameter empirical model for the representing equilibrium biosorption data. It is a combination of the Langmuir and Freundlich isotherm type models and is given by qeq ¼

n ACeq n 1 þ BCeq

(4)

where A, B and n are the Koble–Corrigan parameters. This model is valid when n > 1 [29]. Fig. 3 shows the experimental isotherm data of copper(II) on dried sugar beet pulp at three different temperatures. In the copper(II) concentration range examined, the resulting isotherms were positive, regular, concave to the concentration axis, indicating an affinity for biosorption, and showed a saturation trend at higher copper(II) concentrations; indicating a complete monolayer of copper(II) covering the surface of sorbent. The uptake of the metal ions decreased with an increase in temperature thereby indicating the process to be exothermic. The criteria for selection of the most suitable isotherm model were average percentage error and deviation from experimental value. The corresponding Langmuir, Freundlich, Redlich–Peterson and Koble–Corrigan parameters at different temperatures are obtained by non-linear regression analysis and listed in Table 2 along with the average percentage errors. The average percentage errors between the experimental and predicted values are calculated using

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Fig. 3. Non-linearized adsorption isotherms (experimental equilibrium data) of copper(II) obtained at 25, 35 and 45 8C (initial pH 4.0; X: 1.0 g l
1; agitation rate: 150 rpm).

Eq. (5). In Eq. (5), the subscripts ‘exp’ and ‘calc’ show the experimental and calculated values and N the number of measurements. PN e% ¼

i¼1

jqeq;i;exp
qeq;i;calc =qeq;i;exp j  100 N

(5)

Fig. 4 depicts the comparison of experimental and predicted amounts of copper(II) adsorbed on dried sugar beet pulp obtained from these adsorption models at the Table 2 Comparison of the Freundlich, Langmuir, Redlich–Peterson and Koble– Corrigan biosorption constants obtained from the Freundlich, Langmuir, Redlich–Peterson and Koble–Corrigan adsorption isotherms of copper(II) at different temperatures Temperature ( 8C)

KF [(mg g
1)(mg l
1)
1/n]

n

e (%)

Freundlich model 25 35 45

3.94 3.30 1.52

2.41 2.32 2.23

11.98 4.57 6.86

Temperature ( 8C)

Q0 (mg g
1)

b (mg g
1)

e (%)

Langmuir model 25 35 45

31.4 24.6 19.9

0.043 0.028 0.019

1.98 3.35 1.82

Temperature ( 8C)

aRP [(l mg
1)b]

Redlich–Peterson model 25 0.043 35 0.035 45 0.022 Temperature ( 8C)

A (ln mg1
n g
1)

Koble–Corrigan model 25 1.28 35 1.92 45 1.24

KRP (l g
1)

b

e (%)

1.36 0.69 0.37

1.000 0.963 0.973

1.98 3.17 1.88

B (l mg
1)n

n

e (%)

0.041 0.060 0.014

1.025 0.639 0.505

1.74 2.75 8.13

temperatures of 25, 35, 45 and 55 8C. Basically, if most of the data are distributed around the 458 line, this indicates that the model represent well the experimental data of the system so as shown in the figure. On this basis, the Langmuir model could reasonably fit the data well with an average percentage error in the range 1.82–3.35 suggesting that the monolayer sorption, mainly due to ion-exchange, would not be disturbed by lateral interactions between cations sorbed with similar sorption energies. The other two-parameter model of Freundlich could fit the equilibrium data with an average percentage error more than 4.57. In order to further minimize error and hence to get better representation of data, Redlich–Peterson and Koble–Corrigan three-parameter models were tried and compared. Again, Redlich–Peterson model could fit the data of copper(II) well. Morever, the Koble–Corrigan model also seemed to agree well with the experimental data of copper(II) considering that obtained percentage error values are lower than 8.13% in all cases. Adsorption model constants, the values of which express the surface properties and affinity of the adsorbent, can be used to compare the adsorptive capacity of dried sugar beet pulp for copper(II). KF, one of the Freundlich constants has been used as a relative measure of biosorption capacity (KF reaches the value of qeq when the equilibrium concentration Ceq approaches to unity, thus can be considered as an indicative parameter of the adsorption strength). n, the other Freundlich constant is related to intensity of biosorption. From Table 2, the magnitude of KF showed a high copper(II) adsorptive capacity of dried sugar beet pulp from aqueous solution at all temperatures studied and decreased with the rise in temperature. The highest KF value was found as 3.94 at 25 8C. Table 2 also indicated that n is greater than unity, indicating that copper(II) is favourably adsorbed by dried sugar beet pulp at all the temperatures studied. Values of Q0 and b calculated from the Langmuir model at different temperatures are also tabulated in Table 2. While the Freundlich model does not describe the saturation behaviour of the biosorbent, Q0, the mono-component Langmuir constant represents the monolayer saturation at equilibrium or the total capacity of the adsorbent for copper(II). The biosorption capacity of sorbent also decreased with increasing the temperature. The value of Q0 obtained at 25 8C (i.e. maximum uptake and equal to 31.37 mg g
1) appears to be higher in comparison with the uptakes obtained at the other temperatures. The other monocomponent Langmuir constant b, is related to the free energy of biosorption, DG (b / e
DG/RT) and indicates the affinity for the binding of copper(II). Its value is the reciprocal of the concentration at which half of the saturation of the adsorbent is attained (or copper(II) amount of Q0/2 is bound). A high b value indicates a high affinity. The higher value of b obtained at 25 8C also implied strong bonding of copper(II) to the dried sugar beet pulp at this temperature. Related biosorption parameters were also calculated according to the three-parameter isotherm of Redlich–

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Fig. 4. Comparison of the experimental qeq values with the theoretical qeq values obtained from the Langmuir, Freundlich, Redlich–Peterson and Koble– Corrigan adsorption models at different temperatures for copper(II) biosorption.

Peterson using non-linear regression method for copper(II) and are tabulated in Table 2 at different temperatures. Redlich–Peterson constant KRP indicated that the adsorption capacity of biosorbent also decreased with increasing temperature. It is noted that b normally lies between 0 and 1, indicating favourable biosorption. The corresponding Koble–Corrigan parameters of A, B and n for different temperatures along with percentage errors are also given in Table 2. Koble–Corrigan constant A indicated that the biosorption capacity and affinity of biosorbent to copper(II) ions also decreased with increasing temperature. 3.6. Modelling of biosorption kinetics depending on temperature Adsorption on an adsorbent from the aqueous phase involves three steps: (1) the transport of the adsorbate from the bulk phase to the exterior surface of the adsorbent (film diffusion); (2) the transport into the adsorbent by either pore diffusion and/or surface diffusion (intraparticular diffusion); and (3) the adsorption on the surface of the adsorbent. The slowest of these steps determines the overall rate of the adsorption process. When removing copper(II) from aqueous solution by dried sugar beet pulp, these steps are possible. Sorption kinetics show a large dependence on the physical and/or chemical characteristics of the sorbent material which also influences the sorption mechanism. In order to investigate the mechanism of sorption and potential

rate-controlling steps such as external mass transfer, intraparticle diffusion and adsorption processes and also for design purposes, mass transfer and kinetic models have been used to test the experimental data and attempts were made to calculate the coefficients of these models. In the first step of adsorption, the film diffusion is an important rate-controlling step. The change of copper(II) concentration with respect to time can be written as follows: dC ¼
kL AðC
CS Þ dt

(6)

where C is the bulk liquid phase concentration of copper(II) at a time t, CS the surface concentration of copper(II), kL the external mass transfer coefficient and A the specific surface area for mass transfer. It is assumed that during the initial stages of adsorption, the intraparticle resistance is negligible and the transport is mainly due to film diffusion mechanism. At t = 0 the surface concentration of copper(II), CS, is negligible and C = C0. With these assumptions Eq. (6) can be simplified as   dðC=C0 Þ (7) ¼
kL A dt Since it was not possible to determine the specific surface area A, due to the poor porosity of particles, it is approximated as the external surface area. Assuming the adsorbent particles are spherical, A is calculated from Eq. (8) as 0.2575 cm
1.

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A¼

6X dp r p

(8)

where X is the sorbent mass concentration in the solution, dp average particle diameter and rp the density of the sorbent. By plotting C/C0 against t, the value of kL may be determined from the slope at t = 0 [30–33]. External mass transfer is characterized by the initial rate of solute diffusion for the system studied. The effect of initial copper(II) concentration and temperature on the external diffusion rate was given by a plot of C/C0 versus time for 100 and 200 mg l
1 initial copper(II) concentrations and at 25, 35 and 45 8C temperature values (Fig. 5). It was seen that the concentration of copper(II) falls very fast during the initial uptake before intraparticular diffusion could begin to control the adsorption kinetics for all cases. The kinetic data presented in the figure were fitted to Eq. (7) for the initial uptake phase and the external mass transfer coefficients were determined from the slopes as t
0 and presented in Table 3. The results show that both the increasings in initial copper(II) concentration and temperature resulted in a decrease in the initial rate, respectively. It is clear that, as expected, external mass transfer resistance cannot be neglected even for a high agitation speed, although this resistance is only significant for the initial period of biosorption time. Weber and Morris [30] have concluded that, for processes which are controlled by external diffusion, the initial rate will be directly proportional to the solute concentration. The non-proportionality shown in Fig. 6, therefore, indicates that external mass transfer is not the rate-controlling step.

Fig. 5. C/C0 vs. t plots obtained at 100 and 200 mg l
1 initial copper(II) concentrations and at different temperatures (initial pH 4.0; X: 1.0 g l
1; agitation rate: 150 rpm).

Fig. 6. Variation of kL with C0 with respect to temperature.

In the model developed by Weber and Morris [30], the rate of intraparticular diffusion is a function of t0.5 and can be defined as follows: !0:5 Dt q¼ f 2 ¼ Kt0:5 (9) rp where rp is particle radius, D is the effective diffusivity of solutes within the particle, and K is intraparticular diffusion rate constant. If intraparticle diffusion occurs, then q versus t0.5 will be linear and if the plot of q versus t0.5 passes through the origin, then the rate-limiting process is only due to the intraparticle diffusion. Otherwise, some other mechanism along with intraparticle diffusion is also involved. If such types of plots present a multi-linearity, imply that two or more steps occur. The first, sharper portion is the external surface adsorption stage. The second linear portion is the gradual adsorption stage, where the intraparticle diffusion is rate-limited. The third portion is final equilibrium stage where the intraparticle diffusion starts to slow down due to extremely low solute concentration in the solution and surface. A good correlation of rate data in this model can justify the mechanism and K values can be obtained by linearizing the curve q = f(t0.5) [30–33]. Fig. 7 shows the effect of initial copper(II) concentration and temperature on intraparticular diffusion at 100 and 200 mg l
1 initial copper(II) concentrations and at 25, 35 and 45 8C temperatures. As seen from the figure all the plots have the same general feature. They all have an initial curved portion, followed by an intermediate linear portion and a plateau. The initial portion of these plots which extent is related to initial copper(II) concentration is due to external mass transfer and the intermediate linear part is due to intraparticle diffusion. At a certain time limit (between 5 and 60 min at all initial copper(II) concentrations and at all temperatures studied) the curves revealed a linear characteristic. The values of K evaluated from these linear parts of q versus t0.5 plots are also tabulated in Table 3. These are rate parameters with units mg g
1 min
0.5 and as such, are

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Table 3 Effect of initial copper(II) concentration and temperature on the external mass transfer coefficients (kL) and intraparticle diffusion rate constants (K) 25 8C

35 8C 2

45 8C 2

C0 (mg l
1)

kL  10 (cm min
1)

K (mg g
1 min
0.5)

C0 (mg l
1)

kL  10 (cm min
1)

K (mg g
1 min
0.5)

C0 (mg l
1)

kL  102 (cm min
1)

K (mg g
1 min
0.5)

25.6 52.9 106.1 153.9 198.2 258.8

17.7 12.7 7.3 6.3 5.3 4.1

1.99 2.76 3.54 4.04 4.26 4.38

26.7 48.2 100.9 143.4 212.3 258.0

11.8 8.0 4.9 4.1 3.5 3.1

1.44 1.89 2.65 3.10 3.45 3.52

25.1 49.5 104.4 150.0 205.3 252.9

7.0 5.9 4.1 3.4 2.8 2.2

0.83 1.23 1.96 2.40 2.72 2.84

not a direct quantification of the rates. Nevertheless, they can be interpreted in relative terms. Examined in this way, the data show the rate of diffusion increased with a raise in initial copper(II) concentration and decreased with increasing temperature of solution. This may be due to a greater driving force with increasing C0. At all temperatures when C0 is increased from 25 to 200 mg l
1 there is a marked effect on the rate of intraparticular copper(II) diffusion. Above C0 200 mg l
1 the effect is small. It is also observed that the higher the value of K the more rapid is the uptake of copper(II). The linear plots at each concentration and temperature did not pass through the origin and this indicated that the intraparticle diffusion is not only ratecontrolling step. Moreover, according to the theoretical equations for diffusion, when intraparticle diffusion is the only rate-determining step, the rate parameter is also directly related to the square root of the initial concentration (C00:5 ). Such a plot given in Fig. 8 also confirmed that intraparticle diffusion is not the only operative mechanism [30]. These two results show that increasing the copper(II) concentration

in the solution seems to reduce the diffusion of metal ions in the boundary layer and to enhance the diffusion in the solid. On the other hand the biosorption kinetics may be described by pseudo first-order [34], pseudo second-order [35] and saturation type kinetic models [36,37]. These three models basically include all steps of adsorption such as external film diffusion, adsorption, and internal particle diffusion, so they are pseudo-models. The pseudo first-order rate expression based on solid capacity is generally expressed as follows: dq ¼ k1;ad ðqeq
qÞ dt

(10)

where k1,ad is the rate constant of first-order biosorption. After integration and applying boundary conditions, t = 0 to t and q = 0 to qeq; the integrated form of Eq. (10) becomes: logðqeq
qÞ ¼ logqeq


k1;ad t 2:303

(11)

A straight line of log(qeq
q) versus t suggests the applicability of this kinetic model. In order to fit Eq. (11) to experimental data, the equilibrium sorption capacity, qeq, must be known. In many cases qeq is unknown and as biosorption tends to become unmeasurably slow, the amount sorbed is still significantly smaller than the equilibrium amount. For this reason, it is necessary to obtain the real

Fig. 7. q vs. t0.5 plots obtained at 100 and 200 mg l
1 initial copper(II) concentrations and at different temperatures (initial pH 4.0; X: 1.0 g l
1; agitation rate: 150 rpm).

Fig. 8. Variation of K with C00:5 with respect to temperature.

Z. Aksu, I˙.A. I˙s¸og˘ lu / Process Biochemistry 40 (2005) 3031–3044

3040

rad ¼

equilibrium sorption capacity, qeq, by extrapolating the experimental data to t = 1 or by using a trial and error method. Furthermore, in most cases the first-order kinetic model does not fit well for the whole range of contact time and is generally applicable over the initial 20–30 min of the sorption process. The pseudo second-order equation is also based on the sorption capacity of the solid phase and is expressed as: (12)

where k2,ad is the rate constant of second-order biosorption. For the same boundary conditions the integrated form of Eq. (12) becomes t 1 1 ¼ þ t 2 q k2;ad qeq qeq

(15)

where kad is the first-order rate constant of saturation type 0 biosorption. The expression of kad/kad defines the zero-order rate constant (k0,ad). A straight line of 1/rad versus 1/C0 suggests the applicability of this kinetic model and kad and k0,ad can be determined from the slope and intercept of the plot. This model predicts the biosorption behaviour over the whole studied concentration range of copper(II) at a constant temperature. The first-order rate constant of the saturation type biosorption reaction (kad) is expressed as a function of temperature by the following Arrhenius type relationship:  
EA kad ¼ A0 exp (16) RT

Fig. 9. Variation of rad with C0 with respect to temperature.

dq ¼ k2;ad ðqeq
qÞ2 dt

kad C0 0 C 1 þ kad 0

(13)

If second-order kinetics are applicable, the plot of t/q against t of Eq. (13) should give a linear relationship, from which qeq and k2,ad can be determined from the slope and intercept of the plot and there is no need to know any parameter beforehand. The plot of q versus time can be used to find the initial biosorption rate (rad) by differentiating the plot at t = 0 as defined in Eq. (14).  dq ¼ rad (14) dt t¼0 From experimental data, it was shown that the initial biosorption rate is proportional to the first power of the initial copper(II) concentration at lower bulk copper(II) concentrations (first-order kinetics) and at higher copper(II) concentrations, the rate becomes independent of initial copper(II) concentration (zero-order kinetics) (Fig. 9). Eq. (15) can be used to describe the rate of biosorption very accurately in both situations. This kind of rate equation is also defined as ‘saturation type’.

where A0 is the frequency factor, EA is the activation energy of sorption, R is the gas constant and T is the solution temperature. When ln kad is plotted versus 1/T, a straight line with slope
EA/R is obtained. The magnitude of activation energy may give an idea about the type of sorption. The validity of all models can be checked from the linear plots. The first-order rate constant (k1,ad) and qeq values were determined from the plots of linearized form of the pseudo first-order model at all concentrations and at all temperatures studied for the initial 30 min (data not shown) and are presented in Table 4 along with the correlation coefficients. The first-order rate constants decreased slightly with increasing both the initial concentration of copper(II) and temperature. As seen from the table, besides very high regression coefficients (>0.992), experimental qeq values agreed very well with qeq values obtained from Lagergren plots. This indicated that pseudo first-order kinetic model describes the kinetics adequately in the studied concentration and temperature range. Using Eq. (13), t/q was plotted against t at 25, 35 and 45 8C, and second-order adsorption rate constants (k2,ad) and equilibrium uptake values (qeq) were determined from the slope and intercept of the plots (data not shown). The values of the parameters k2,ad and qeq and of correlation coefficients are also presented in Table 4. The results indicated that second-order rate constants were also affected by both the initial copper(II) concentration and temperature and diminished with increasing these parameters. The correlation coefficients of all temperatures and concentrations studied were also found very high in this case. Moreover, the theoretical qeq values found from the second-order kinetic model also agreed very well with the experimental qeq values. This showed that the adsorption of copper(II) also follows the pseudo-second-order kinetic model. The saturation type kinetic model was also applied to the experimental data at different temperatures changing from 25 to 45 8C to describe the batch biosorption kinetics. The

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Table 4 Comparison of the first- and second-order reaction rate constants and experimental and calculated qeq values obtained at different initial copper(II) concentrations and temperatures Temperature (8C)

C0 (mg l
1)

qeq,exp (mg g
1)

First-order kinetic model

Second-order kinetic model

k1,ad  102 (min
1)

qeq,cal (mg g
1)

R2

k2,ad  103 (g mg
1 min
1)

qeq,cal (mg g
1)

R2

25

25.6 52.9 106.1 153.9 198.2 258.8

11.8 19.6 24.6 27.6 28.1 28.5

7.09 5.90 5.09 4.72 4.35 3.96

11.8 19.5 24.3 27.4 27.2 27.1

1.000 1.000 1.000 1.000 0.996 0.996

66.61 44.86 34.10 21.45 15.85 15.12

11.8 19.7 24.7 27.7 28.3 28.7

1.000 1.000 1.000 1.000 1.000 1.000

35

26.7 48.2 100.9 143.4 212.3 258.0

8.8 11.9 16.7 19.7 21.1 21.2

6.86 5.23 4.35 3.82 2.92 2.35

8.9 11.8 16.5 19.5 21.1 20.6

1.000 1.000 1.000 1.000 1.000 0.992

42.87 32.39 25.49 19.16 11.46 11.28

8.8 12.0 16.8 19.8 21.1 21.0

1.000 1.000 1.000 1.000 1.000 1.000

45

25.1 49.5 104.4 150.0 205.3 252.9

5.3 8.8 12.3 14.5 15.8 16.1

6.13 4.95 3.98 3.02 2.46 2.10

5.3 8.8 12.3 14.4 15.7 15.3

1.000 1.000 1.000 1.000 1.000 0.998

28.59 22.80 17.25 14.17 9.21 9.05

5.3 7.3 12.3 14.5 15.8 16.0

1.000 1.000 1.000 1.000 1.000 1.000

values of kad and k0,ad were determined from the plots of linearized form of the saturation type kinetic model at all temperatures studied (data not shown). The plots indicated that such saturation type kinetic expression is not so valid to the present system (R2 < 0.982 for all temperatures). However, the values of kad and k0,ad at 25, 35 and 45 8C are still listed in Table 5 for reference. Table 5 shows that both the biosorption rate constants were affected with increase in temperature and decreased notably with increasing temperature. These suggest that the biosorption of copper(II) at 25, 35 and 45 8C is not a saturation type reaction and may be best described by the pseudo first- and second-order kinetic models with fairly high correlation coefficients. The change of rate constant due to temperature also showed that one of the rate-controlling steps is biosorption reaction. Applying the Weber and Morris principles to the variation in the initial rate with C0 (Fig. 9) indicated that the rate was not directly proportional to C0 and also confirmed that sorption process was not the only rate-limiting step. The data also confirmed that both mass transfer and pore diffusion are important in determining the biosorption rates and that their relative significance depends on the initial copper(II) concentration and temperature.

The activation energy for the biosorption system of copper(II) onto dried sugar beet pulp was found as
58.47 kJ mol
1 from the slope of ln kad against 1/T linear plot with a correlation coefficient of 0.939 in the temperature range studied (data not shown). Since negative value of activation energy have no obvious physical significance, the biosorption study of this metal ion should be performed at much more lower solution temperatures to obtain biosorption activation energy.

Table 5 Comparison of the saturation type kinetic rate constants obtained at different temperatures

KC0 ¼

Temperature ( 8C)

kad  102 (l g
1 min
1)

k0ad  102 (l mg
1)

R2

25 35 45

4.35 2.61 1.39

2.32 1.87 1.16

0.982 0.951 0.972

3.7. Thermodynamic parameters of biosorption The thermodynamic parameters reflect the feasibility and spontaneous nature of the process. Thermodynamic parameters such as free energy change, enthalpy change and entropy change can be estimated using equilibrium constants changing with temperature. The biosorption process of copper(II) can be summarized by the following reversible process which represents a heterogeneous equilibrium. copperðIIÞin solution $ copperðIIÞ-biosorbent

(17)

The apparent equilibrium constant (KC0 ) of the biosorption is defined as: Cad;eq Ceq

(18)

where Cad,eq is the concentration of copper(II) on the biosorbent at equilibrium. In this case the activity should be used instead of concentration in order to obtain the standard thermodynamic equilibrium constant (KC0 ) of the biosorption system. If infinite dilute value of KC0 can be

Z. Aksu, I˙.A. I˙s¸og˘ lu / Process Biochemistry 40 (2005) 3031–3044

3042

found by calculating the apparent equilibrium constant (KC0 ) at different initial concentrations of copper(II) and extrapolating to zero, this value will give KC0 . When 1 g l
1 of adsorbent is used, this value can be taken equal to the opposite value of intercept of Ceq/qeq versus Ceq plot (=bQ0), which shows the linearized form of Langmuir equation. The Kc0 value is used in the following equation to determine the free energy change of the biosorption reaction (Gibbs free energy) (DG8) at 25 8C. DG ¼
RT ln KC0

(19)

where R the universal gas constant and T the absolute temperature. The free energy change indicates the degree of spontaneity of the biosorption process and the higher negative value reflects a more energetically favourable adsorption. The equilibrium constant may be expressed in terms of enthalpy change of biosorption (DH8) and entropy change of biosorption (DS8) as a function of temperature. The relationship between the KC0 and temperature is given by the van’t Hoff equation: lnKC0 ¼

DS DH
R RT

(20)

DH8 and DS8 can be obtained from the slope and intercept of a van’t Hoff plot of ln KC0 versus 1/T. The KC0 value at 25 8C evaluated from the Cad,eq/Ceq versus Ceq plot (data not shown) as 1.35 was used to find the DG8 value. The standard Gibbs free energy for the biosorption process was obtained as
0.74 kJ mol
1 using Eq. (19). A negative value of DG8 confirms the feasibility of the process and spontaneous nature of biosorption at 25 8C. The standard enthalpy and entropy changes of biosorption determined from the ln KC0 versus 1/T plot (R2 = 0.976) were
66.3 kJ mol
1 and
0.22 kJ mol
1 K
1, respectively. The negative value of DH8 indicates an exothermic biosorption reaction while negative DS8 confirms the decreased randomness at the solid– solution interface during biosorption. 3.8. Comparison of results with the literature The copper(II) adsorption capacity of dried sugar beet pulp was compared to the adsorption capacities of some other adsorbents reported in literature. Differences of metal uptake are due to the properties of each adsorbent such as structure, functional groups and surface area. Namasivayam and Kadirvelu [10] examined the adsorption of copper(II) by coirpith carbon and found a 39.7 mg g
1 copper(II) uptake capacity. Sun and Shi [12] used the sunflower stalks as an adsorbent for the removal of heavy metal ions and found a 29.3 mg g
1 uptake capacity for copper(II). Gupta and Ali [14] studied with the bagasse fly ash for the biosorption of copper(II); the biosorption capacity of sorbent was only 2.26 mg g
1 at 30 8C and at optimum pH of 4.0. Yu et al. [14] indicated that sawdust has a distinctly lower uptake capacity for copper(II)

(1.8 mg g
1). Ho and McKay [3] used peat for the biosorption of copper(II) and they found that at 200 mg l
1 1 initial copper(II) concentration 14.3 mg copper(II) was adsorbed per gram of sorbent. Pagnanelli et al. [17] tested olive mill solid residue for copper(II) adsorption and found 13.5 mg g
1 uptake capacity at pH 5.0. Ho [19] reported the biosorption capacity of tree fern for copper(II) as 10.6 mg g
1. Basci et al. [20] observed that wheat shell adsorbed copper(II) from aqueous solutions to a maximum of approximately 10.8 mg g
1. Villaescusa et al. [21] also studied the sorption of this metal ion by grape stalks wastes achieving an uptake of 10.1 mg g
1 dry mass. Ozer et al. [7] investigated the biosorption of copper(II) on dehydrated wheat bran. At 100 mg l
1 initial copper(II) concentration and at 1 g l
1 biosorbent concentration they found the biosorption capacity of sorbent as 51.5 mg g
1 at an optimum pH value of 5.0 and at 60 8C. Dronnet et al. [22] and Gerente et al. [23] used washed and activated sugar beet pulp and they found that 21.1 and 17.1 mg copper(II) was adsorbed per gram of sorbent, respectively, at 20 8C and at pH 4.0. The comparison of results of this work with the others found in the literature showed that copper(II) uptakes found in this work were similar to those obtained using sunflower stalks wastes and washed sugar beet pulp and much more higher than the reported ones by the other referred wastes except that coirpith carbon and dehydrated wheat bran.

4. Conclusions In this work, dried sugar beet pulp has been used successfully as an adsorbing agent for the removal of copper(II) ions from aqueous solutions. Adsorption was influenced by various parameters such as initial pH, temperature and initial copper(II) concentration. The maximum uptake of copper(II) by dried sugar beet pulp occurred at an initial pH of 4.0 and adsorption increased with increasing copper(II) concentration up to 250 mg l
1 and decreased with temperature. The maximum copper(II) uptake capacity of biosorbent was 28.5 mg g
1; this value is comparable to other sorbent media tested for copper(II) biosorption. The Freundlich, Langmuir, Redlich–Peterson and Koble– Corrigan adsorption models were used for the mathematical description of the adsorption equilibrium of copper(II) on to dried sugar beet pulp depending on temperature and the isotherm constants evaluated from the isotherms were used to compare the adsorptive capacity of the dried sugar beet pulp. The biosorption of copper(II) on to dried sugar beet pulp was found to exhibit non-linear favorable biosorption behaviour that could be characterized well by the Langmuir, Redlich–Peterson and Koble–Corrigan isotherm models in the studied concentration range at all the temperatures studied. Assuming the batch adsorption as a single-staged equilibrium operation, the separation process can be

Z. Aksu, I˙.A. I˙s¸og˘ lu / Process Biochemistry 40 (2005) 3031–3044

mathematically defined using these isotherm constants to estimate the residual concentration of copper(II) or amount of adsorbent for desired purification. The adsorption process rate and dynamic behaviour of the system are very important factors for the process design and operation control. The rate of diffusion may be valid in many realistic situations. Three simplified models including pseudo first-order, pseudo second-order and saturation type kinetic models were used to test the adsorption kinetics. It was shown that the adsorption of copper(II) on to dried sugar beet pulp could be best fitted by the pseudo first- and second-order models. A film diffusion model and an intraparticle diffusion model developed by Weber and Morris were used to find both the boundary and intraparticle diffusion rate constants. The sorption data indicated that the mechanism of copper(II) biosorption by dried sugar beet pulp is rather complex and is probably a combination of external mass transfer, intraparticle diffusion and sorption process. The obtained kinetic parameters can be used for reactor design. It may be suitable to apply such simple kinetic models to a wellagitated batch biosorption system. Thermodynamic constants were also evaluated using equilibrium constants changing with temperature. The negative value of DG8 indicated the spontaneity and the negative values of DH8 and DS8 showed the exothermic nature and increase in order of copper(II) biosorption, respectively. We believe that application of biosorption by dried sugar beet pulp in purification of wastewater for the removal of copper(II) from industrial wastewaters can be suitable for the fabrication and designing of wastewater treatment plants by using these kinetic parameters. Since sugar beet pulp, an agricultural solid waste, used in this investigation, is freely, abundantly and locally available, the sorbent is expected to be economically viable for wastewater treatment.

Appendix A aRP A A0 b B C C0 Cad,eq Ceq dp EA DG8 DH8

Redlich–Peterson adsorption constant [(l mg
1)b] Koble–Corrigan adsorption constant (ln mg1
n g
1) frequency factor Langmuir adsorption constant (l mg
1) Koble–Corrigan adsorption constant (l mg
1)n residual copper(II) concentration at any time (mg l
1) initial copper(II) concentration (mg l
1) adsorbed copper(II) concentration at equilibrium (mg l
1) residual copper(II) concentration at equilibrium (mg l
1) particle diameter (cm) activation energy of sorption (kJ mol
1) The Gibbs free energy of biosorption (kJ mol
1) Enthalpy change of biosorption (kJ mol
1)

k, k0 k1 k2 kL K KC0 KC0 KF KRP n q qeq Q0 rad R R2 DS8 T X

3043

rate constants of saturation type adsorption (l g
1 min
1; l mg
1) first-order rate constant (min
1) second-order rate constant (g mg
1 min
1) external mass transfer coefficient (cm min
1) intraparticular diffusion rate (mg g
1 min
0.5) standard thermodynamic equilibrium constant of the adsorption system apparent equilibrium constant of the biosorption system Freundlich adsorption constant [(mg g
1) (mg l
1)n] Redlich–Peterson adsorption constant (l g
1) Freundlich and Koble–Corrigan adsorption constants adsorbed copper(II) quantity per gram of dried sugar beet pulp at any time (mg g
1) adsorbed copper(II) quantity per gram of dried sugar beet pulp at equilibrium (mg g
1) Langmuir adsorption constant (mg g
1) initial adsorption rate (mg g
1 min
1) gas constant (=8.314 J mol
1 K
1) correlation coefficient Entropy change of biosorption (kJ mol
1) solution temperature (8C, K) dried sugar beet pulp concentration (g l
1)

Greek letters b Redlich–Peterson biosorption constant rp particle density (g ml
1)

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