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Biochemical Engineering Journal 12 (2002) 143153

Kinetic studies on sorption of Cr(VI) and Cu(II) ions bychitin, chitosan and Rhizopus arrhizus

Yesim Sag, Ycel AktayDepartment of Chemical Engineering, Faculty of Engineering, Hacettepe University, 06532 Beytepe, Ankara, Turkey

Received 17 July 2001; accepted after revision 16 May 2002

Abstract

This work focuses on Cr(VI), Cu(II) sorption kinetics by chitin, a naturally occurring material, chitosan, the deacetylated form of chitin,and Rhizopus arrhizus, a filamentous fungus containing chitin and chitosan as a main cell wall component. The aim of this study is tounderstand the mechanisms that govern Cr(VI) and Cu(II) removal, and find an appropriate model for the kinetics of removal in a batchreactor. In order to investigate the mechanism of sorption and potential rate controlling steps, the pseudo-first, first, pseudo-second orderkinetic models and the Elovich equation have been used to test experimental data. For all of the metalbiosorbent systems studied, thepseudo-second order rate expression provided the best fitting kinetic model. 2002 Elsevier Science B.V. All rights reserved.

Keywords: Sorption; Cr(VI)Cu(II); Chitin; Chitosan; Rhizopus arrhizus; Kinetic models

1. Introduction

Today, environmental conservation is of increasing so-cial and economic importance. A particularly intractablepollution problem is that of the contamination of waters byheavy metals. Heavy metals produce undesirable effects,even if they are present in trace quantities. Traditionaltreatment methods such as chemical precipitation as metalhydroxide, electrodeposition, ion exchange, membrane sep-aration have been applied [1]. Sorption however seemsto be a good alternative. Many sorbents have been testedfor the sorption of various heavy metals. Sorption on rub-ber tyres, human hair and coconut husks has been studied[24]. New research shows effective sorption of heavymetals using agricultural products and by-products, suchas walnut expeller meal, peanut skins, wool, rice straw,plumpit shells, peanut hulls, sugar cane bagasse, tea leavesand coffee powder [57]. Intra-particle diffusion, externalmass transfer and chemical binding reactions can take partin the rate controlling steps; the precise mechanisms ofmetal ion binding however has not been established formany of the sorbents. There is no direct evidence on whichone of the adsorption processes mentioned is more efficientand has the greatest industrial perspective. Some of these

Corresponding author. Tel.: +90-312-297-7444;fax: +90-312-299-2124.E-mail address: [email protected] (Y. Sag).

sorbents such as ion exchange resins and activated carbonare effective but expensive. Fly ash, clay and sawdust areinexpensive but poor sorbents. Some materials fail for otherreasons, for instance activated alumina is effective in re-moving heavy metals, but is readily soluble under extremepH conditions.

While microorganisms were first used for studies ofresistance to metal contamination, the abilities of microor-ganisms to remove metal ions in solution have been exten-sively studied. In fact, the overall sorption is located in thecell wall of microorganisms, through passive phenomena,which include sorption, complexation, chelation, coordina-tion or precipitation processes [812]. In the case of fungalbiomass, the cell wall can be regarded as a mosaic of differ-ent functional groups where coordination complexes withmetals can be formed. Among those groups are carboxyl(COOH), amide (NH2), thiol (SH), phosphate (PO43),and hydroxide (OH). Phosphate groups are present mainlyin glycoproteins and are believed to play an important rolein biosorption because they can exhibit a negative chargeabove pH 3 [13]. In fungal cells, metal ions can bind to theamino groups of chitin (R2NH) and chitosan (RNH2).Chitin and its associated proteins contain many carboxylategroups. Aspartate, glutamate, and cysteine are also believedto play an important role in metal chelation [1416].

Most of these studies investigated possible uses of suchsorbents to remove heavy metals. Although several ap-proaches exist pertaining to the evaluation of the chelating

1369-703X/02/$ see front matter 2002 Elsevier Science B.V. All rights reserved.PII: S1 3 6 9 -703X(02 )00068 -2

144 Y. Sag, Y. Aktay / Biochemical Engineering Journal 12 (2002) 143153

ability of the natural polymers, few rigorous worksrelated to kinetic studies have been examined. Equilibriumconsiderations of the sorption process have been extensivelyinvestigated [12,1719]. In addition to equilibrium studies,the kinetics of the sorption has to be determined in orderto establish the time course of the metal uptake. Rapid up-take of the metal by the biosorbent is desirable providingfor a short solutionbiosorbent contact time in the actualprocess. The kinetics describes the solute uptake rate whichin turn controls the residence time of sorbate uptake at thesolidsolution interface. It is important to be able to pre-dict the rate at which pollutant is removed from aqueoussolutions in order to design appropriate sorption treatmentplants. The study of sorption kinetics in wastewater treat-ment is also important as it provides deep understanding ofthe reaction pathways and the mechanism of sorption reac-tions. A knowledge of the rate law describing the sorptionsystem is needed in order to develop sorption kinetics [20].

Four sorption kinetic models were tested in this study forthe sorption of Cr(VI) and Cu(II) ions onto chitin/chitosanand the biosorption of Cr(VI) and Cu(II) ions on Rhizo-pus arrhizus. In order to investigate the mechanism ofCr(VI)Cu(II) sorption, characteristic constants of sorp-tion were determined using a pseudo-first order equationof Lagergren [21] based on solid capacity, a first orderequation of Bhattacharya and Venkobachar [22] based onsolution concentration, a pseudo-second order equation [20]based on solid phase sorption, and the Elovich equation[23], respectively.

2. Materials and methods

2.1. Materials

Chitin prepared from crab shells [poly(N-acetyl-1,4--d-glucopyranosamine)] (C8H13NO5)n (Fluka 22720) andchitosan [2-amino-2-deoxy-(1 4)--d-glucopyranan;poly(1,4--d-glucopyranosamine)] (Fluka 22742) wereused for chromium and copper removal. Before utilizationof the sorbent, the raw chitin and chitosan were groundand sieved into three fractions as a function of particle di-ameter dp(m) 250 < dp < 420, 420 < dp < 595 and595 < dp < 841. Before and after sorption experiments, thechitin and chitosan particles were weighed and no weightloss of the sorbent was observed at the optimum pH valuedetermined for each metalsorbent system.

R. arrhizus, a filamentous fungus, was obtained from theUS Department of Agriculture Culture Collection. R. ar-rhizus was grown aerobically in batch culture at 30 C andprepared for biosorption as described previously [24].

2.2. Preparation of sorption media

Cu(II) and Cr(VI) solutions were prepared by diluting0.02 M stock solutions of copper(II) and chromium(VI),

obtained by dissolving anhydrous CuSO4 or K2Cr2O7 indistilled water, respectively. Initial concentrations of Cr(VI)and Cu(II) ions were varied over the 0.4814.808 and0.3934.721 mmol l1 ranges, respectively, while the drysorbent weight in each sample was constant at 1.0 g l1.To obtain the same molar ratios, the chosen initial con-centration range for Cr(VI) and Cu(II) ions correspondsto 25250 and 25300 mg l1, respectively on the basis ofweight. Before mixing with the chitin or chitosan flakes orfungal suspension, the pH of each solution was adjusted tothe optimum value (pH = 4.0) for the sorption of Cu(II)ions, by adding 1 mol l1 H2SO4. The optimum pH forCr(VI) sorption by chitin and R. arrhizus was reached atpH around 2 and kinetic studies were performed at thispH value. This occurs because when the pH increasesthe electrostatic attraction diminishes. In chitin and chi-tosan sorbents, degree of deacetylation (DD), a proportionbetween amine and acetylamino groups, could be a keyparameter in controlling sorption and desorption of sor-bates. Since a high DD of chitosan brings instability instrongly acidic solutions owing to the increased solubil-ity, Cr(VI) sorption kinetics onto chitosan was studiedat pH 3.0.

2.3. Batch sorption experiments

Batch kinetic experiments were conducted at a con-stant temperature (25 C), in a batch baffled and mag-netically stirred reactor. The working volume of thereactor was 100 ml. The stirring rate was varied be-tween 150 and 800 rpm. The effect of stirring speed (n)on the external and intraparticular diffusion was evalu-ated in terms of the Reynolds number (NRe = nD2a/)calculated from the diameter (Da) and peripheral speedof the impeller (nDa). Increasing the Reynolds numberfrom 2900 to 11 600 resulted in slightly increased initialsorption rates of Cr(VI) and Cu(II) ions onto chitin andchitosan. This means that the external film mass transferwas not the only rate-limiting step in a well-agitated ves-sel [25]. Before mixing the chitin or chitosan flakes withthe metal-bearing solution, 3 ml samples were taken fromthe sorption media. Subsequently, samples were takenat 25 min intervals at the beginning of sorption and at153060 min intervals before equilibrium was reached.Batch type contact studies were continued for 72 h. Fungalbiosorption studies were carried out as described previously[24].

2.4. Measurement of heavy metal ions

The concentration of unadsorbed Cr(VI) and Cu(II)ions in the sorption medium was determined spectropho-tometrically. The colored complexes of Cr(VI) ions withdiphenyl carbazide and Cu(II) ions with sodium diethyldithiocarbamate were read at 540 and 460 nm, respectively[26].

Y. Sag, Y. Aktay / Biochemical Engineering Journal 12 (2002) 143153 145

3. Kinetic models applied to the sorption of Cr(VI) andCu(II) ions onto chitin/chitosan and on R. arrhizus

3.1. Pseudo-first order rate equation of Lagergren

The pseudo-first order equation of Lagergren [21] is gen-erally expressed as follows:dqdt= ks1(qeq q) (1)

where qeq and q are the amount of metal sorbed per unitweight of sorbent at equilibrium and at any time t, respec-tively (mmol g1) and ks1 the rate constant of pseudo-firstorder sorption (l min1). After integration and applyingboundary conditions, for t = 0, q = 0, the integrated formof Eq. (1) becomes [20]

log(qeq q) = log(qeq) ks12.303 t (2)

3.2. First order equation of Bhattacharyaand Venkobachar

A reversible first order rate expression based on solutionconcentration [22] may be represented by Eq. (3):dCBdt

=dCAdt

= CAi dXAdt = k1CA k2CB= k1(CAi CAiXA) k2(CBi CAiXA) (3)

where CB is the concentration of metal on the sorbent at anytime, CA the concentration of metal in solution at any time,CAi and CBi the initial concentrations of metal in solutionand on the sorbent, respectively, XA the fractional conversionof soluted metal, and k1 and k2 the first order rate constants.

After necessary rearrangements, elimination, factorizationand integration of Eq. (3) gives

ln(

1 XAXAeq

)= ((CBi/CAi)+ 1)k1t

(CBi/CAi)+XAeq (4)

where XAeq is the fractional conversion of soluted metal atequilibrium:

XAeq =Keq (CBi/CAi)

Keq + 1 (5)

where Keq is the equilibrium constant. A plot of ln(1 XA/XAeq) versus time gives a straight line and from theslope k1 can be obtained. Eq. (4) may be considered as apseudo-first order irreversible reaction. Therefore Eq. (4) isanalogous to Eq. (2) [20].

3.3. Pseudo-second order rate equation

If the rate of sorption is a second order mechanism, thepseudo-second order chemisorption kinetic rate equation isexpressed as [20]dqdt= k(qeq q)2 (6)

where k is the rate constant of pseudo-second order sorption(g mmol1 min1).

Integrating this equation for the boundary conditions fort = 0, q = 0 givest

q= 1

kq2eq+ 1qeq

t (7)

The intercept of the linearized pseudo-second order rateequation gives the second order rate constant, k.

3.4. The Elovich equation

The Elovich equation is given as follows [23]:dqdt= exp(q) (8)

where q is the sorption capacity at time t and the ini-tial sorption rate (mmol g1 min1) and the desorptionconstant (g mmol1). To simplify the Elovich equation, itis assumed that t 1 and by applying the boundaryconditions q = 0 at t = 0, this equation becomesq = ln()+ ln t (9)Thus, the constants can be obtained from the slope andintercept of a straight line plot of q versus ln t.

4. Results and discussion

Fig. 1. shows contact time curves for sorption of Cr(VI)ions onto chitosan. The sorption equilibrium was reachedafter 24 h, depending on the initial metal ion concentrationand particle size. At lower initial metal ion concentrationsor lower particle sizes, the variation of the unadsorbedCr(VI) concentration in the solution was negligible after360420 min of contact time. The adsorbed amounts ofCr(VI) ions by chitosan continued to increase after the equi-librium stage, and it is suggested that chemisorption, a subse-quent slow, often irreversible uptake, is responsible for muchof the Cr(VI) uptake. This type of adsorption is specific andinvolves forces much stronger than in physical adsorption.An important feature of chemisorption is that its magnitudewill not exceed that corresponding to a monomolecularlayer. The pattern of sorption of Cu(II) ions from aqueoussolutions by chitosan was the same as the Cr(VI) situation(Fig. 2). The sorption equilibrium between Cu(II) and activesites of chitinchitosan occurred within 24 h and significantincreases in the sorbed amounts were not observed after thisstage. The biosorption pattern of Cr(VI) and Cu(II) ions byR. arrhizus was the same as the chitin/chitosan situation.

Fig. 3 shows a plot of the linearized form of thepseudo-first order model (Eq. (2)) for the sorption of Cr(VI)ions onto chitin at various initial Cr(VI) ion concentrationsfor contact times of 360 min. The rate of sorption wasassumed to be proportional to the difference between thecapacity, qeq, at equilibrium and the capacity at any time,


Fig. 1. The sorption curves for Cr(VI) sorption onto chitosan (pH, 3.0; sorbent concentration, 1.0 g l1; particle size, 250420m; agitation rate, 150 rpm).

t, of the sorbed in a first order. The linearized form of thepseudo-first order model for the sorption of Cu(II) onto chi-tosan is also given in Fig. 4. The pseudo-first order modeldid not adequately describe the sorption results of Cr(VI)and Cu(II) ions onto chitinchitosan. For the sorption ofCr(VI) ions onto chitin and chitosan, correlation coefficients(R2) between the predicted and the experimental values forthe entire data set ranged between 0.837 and 0.955. For thesorption of Cu(II) ions onto chitin and chitosan, correlationcoefficients ranged between 0.859 and 0.986. Correlationcoefficients for the biosorption of Cr(VI) and Cu(II) ions onR. arrhizus were lower than those for the sorption of Cr(VI)

Fig. 2. The sorption curves for Cu(II) sorption onto chitosan (pH, 4.0; sorbent concentration, 1.0 g l1; particle size, 250420m; agitation rate, 150 rpm).

and Cu(II) ions onto chitin/chitosan, and ranged between0.798 and 0.961, and 0.827 and 0.975, respectively.

The pseudo-first order sorption rate expression differsfrom a true first order equation in two ways: (i) the parame-ter ks1(qeq q) does not represent the number of availablesites; (ii) the parameter log(qeq) is an adjustable parameterwhich is often not found equal to the intercept of a plot oflog(qeq q) versus t, whereas in a true first order sorptionreaction log qeq should be equal to the intercept of a plotof log(qeq q) versus t [23]. Since chemisorption tends tobecome unmeasurably slow, the amount sorbed is still sig-nificantly smaller than the amount sorbed at equilibrium.


Fig. 3. Pseudo-first order sorption kinetics of Cr(VI) onto chitin at variousinitial concentrations (pH, 2.0; sorbent concentration, 1.0 g l1; particlesize, 250420m; agitation rate, 150 rpm).

One suggestion for the differences in experimental and the-oretical qeq values is that there is a time lag, possibly dueto a boundary layer or external resistance controlling at thebeginning of the sorption. This time lag is also difficult toquantify. For this reason, it is necessary to use a trial and er-ror method in order to obtain the equilibrium uptake, qeq. Tofind qeq, the experimental data were extrapolated to t = .Another disadvantage of this model is that the pseudo-firstorder sorption rate expression of Lagergren does not fit wellthe experimental data for the whole range of contact time andthe plots are only linear over the first 30 min, approximately.However, in the case of Cr(VI)Cu(II)/chitinchitosanR.arrhizus, the Lagergren equation seems to characterize thewhole range of contact time.

The pseudo-first order sorption rate expression of Lager-gren has been widely used for the sorption of metals, such as

Fig. 4. Pseudo-first order sorption kinetics of Cu(II) onto chitosan at various initial concentrations (pH, 4.0; sorbent concentration, 1.0 g l1; particle size,250420m; agitation rate, 150 rpm).

Fig. 5. First order sorption kinetics of Cr(VI) onto chitin at various initialconcentrations (pH, 2.0; sorbent concentration, 1.0 g l1; particle size,250420m; agitation rate, 150 rpm).

the sorption of Cr(VI) by fly ash and wollastonite [27], thesorption of Cu(II) by fly ash [28], the sorption of Fe(II) bywollastonite [29], the sorption of Cd(II) and Ni(II) by peanuthull carbon [30,31], the sorption of Cr(III) and Cr(VI) bymoss and copper-coated moss [32], the sorption of Pb(II) bykaolinitic clay [33], the sorption of Cr(VI) by chitosan [34],the sorption of Cu(II) by chitin [35]. The pseudo-first ordermodel was also used for the sorption of dyes, such as thesorption of Rhodamine-B by biogas residual slurry [36], thesorption of Congo Red, Procion Orange and Rhodamine-Bby Orange peel [37] and the sorption of Acid Blue 29 and Re-active Blue 2 by chrome sludge [38]. Multiple pseudo-firstorder kinetics was also represented in some sorption sys-tems such as -lactoglobulin and hemoglobin sorption bysilica [39] and bisphenol A sorption by kaolinite [40]. In


Fig. 6. First order sorption kinetics of Cu(II) onto chitin at various initialconcentrations (pH, 4.0; sorbent concentration, 1.0 g l1; particle size,250420m; agitation rate, 150 rpm).

a multiple pseudo-first order process, a plot of ln(qeq-q)versus time can be divided into two or three linear sections.Each linear section represents a pseudo-first order reactionmechanism. In the case of two kinetic steps, the first step ofsorption is more rapid than the second one.

The linearized form of the first order model for the sorp-tion of Cr(VI) onto chitin is presented in Fig. 5. The exper-imental data deviate considerably from the theoretical dataof the first order model. For the sorption of Cr(VI) ions ontochitin and chitosan, correlation coefficients between the ex-perimental values and the predicted values using the first or-der model for the entire data set ranged between 0.716 and0.935. A plot of the linearized form of the first order modelfor the sorption of Cu(II) onto chitin is also given in Fig. 6.

Fig. 7. Pseudo-second order sorption kinetics of Cr(VI) onto chitin at various initial concentrations (pH, 2.0; sorbent concentration, 1.0 g l1; particlesize, 250420m; agitation rate, 150 rpm).

For the sorption of Cu(II) ions onto chitin and chitosan, cor-relation coefficients ranged between 0.747 and 0.928. It isalso interesting to note that the sorption of Cr(VI) and Cu(II)ions onto chitinchitosan can be considered as an irreversibleprocess. No release of Cr(VI) and Cu(II) ions occurred spon-taneously. They were only released when a special eluentwas used, after the metal uptake and equilibrium stages. Onthe other hand, chemisorption may be a reversible adsorptionprocess. A chemical change of the adsorbate during desorp-tion is good evidence indeed that chemisorption has been oc-curred. Especially Cr(VI) ions were removed with difficultyfrom chelating molecules by pH manipulation and the totalamount of the bound metal ions could not be eluted from thebiomass. On the other hand, Cr(VI) in the form of dichro-mate is anionic and a strong oxidizing agent, the propertiesof which may account for a number of observations, such asits irreversible binding to the biomass. By treating with analkaline solution, elution of the bound Cr(VI) can be accom-plished. In the case of R. arrhizus, there was no correlationbetween the experimental data and the predicted values us-ing the first order reversible kinetic model. This model hasbeen applied to several sorption systems, such as the sorp-tion of Cd(II) by both Giridih coal and coconut shell [22],the sorption of Cr(VI), Cd(II) and Al(III) by waste tea, Turk-ish coffee, exhausted coffee, nut shell and wallnut shell [7].

The linearized form of the pseudo-second order model(Eq. (7)) for the sorption of Cr(VI) onto chitin at variousinitial Cr(VI) concentrations is given in Fig. 7. The cor-relation coefficients for the linear plots of t/q versus timefrom the pseudo-second order rate law ranged between 0.922and 0.995 for contact times of 360 min. Figs. 812 alsoshow plots of the linearized form of the pseudo-second or-der model for Cr(VI)/chitosan, Cu(II)/chitinchitosan andCr(VI) or Cu(II)/R. arrhizus sorption systems. The values


Fig. 8. Pseudo-second order sorption kinetics of Cr(VI) onto chitosan atvarious initial concentrations (pH, 3.0; sorbent concentration, 1.0 g l1;particle size, 250420m; agitation rate, 150 rpm).

of the correlation coefficients for the sorption of Cr(VI)ions onto chitosan were all extremely high and ranged be-tween 0.976 and 0.998. The best fit model for the sorptionof Cu(II) by chitin and chitosan was also the pseudo-secondorder sorption rate expression. The correlation coefficientsbetween experimental and predicted values for the sorp-tion of Cu(II) by chitin and chitosan ranged between 0.912and 0.979, and 0.946 and 0.979, respectively. The corre-lation coefficients between experimental and predicted val-ues for the biosorption of Cr(VI) and Cu(II) by R. arrhizusranged between 0.952 and 0.990, and 0.945 and 0.999, re-spectively. Since the effects of mass transfer and sorptionare often experimentally inseparable, it is generally incorrect

Fig. 9. Pseudo-second order sorption kinetics of Cu(II) onto chitin at various initial concentrations (pH, 4.0; sorbent concentration, 1.0 g l1; particle size,250420m; agitation rate, 150 rpm).

Fig. 10. Pseudo-second order sorption kinetics of Cu(II) onto chitosan atvarious initial concentrations (pH, 4.0; sorbent concentration, 1.0 g l1;particle size, 250420m; agitation rate, 150 rpm).

to apply simple kinetic models such as pseudo-first, first orpseudo-second rate models to a biosorption with solid sur-faces which are rarely homogeneous such as microorganismsurfaces. However, the pseudo-second order kinetic model,in contrast to the pseudo-first or first order models, provideda good correlation for the biosorption of Cr(VI) and Cu(II)ions on R. arrhizus.

Some studies published in the literature also reportpseudo-second order kinetics for sorption reactions, suchas the sorption of Cu(II), Cd(II), Ni(II) and Zn(II) by peat[41], the sorption of Cr(VI) by peat, leaf mould and gran-ular activated carbon [4244]. The sorption of Cu(II) andNi(II) using peat and the sorption of Cr(VI) using corncob


Fig. 11. Pseudo-second order sorption kinetics of Cr(VI) on R. arrhizusat various initial concentrations (pH, 2.0; sorbent concentration, 1.0 g l1;agitation rate, 150 rpm).

Fig. 12. Pseudo-second order sorption kinetics of Cu(II) on R. arrhizusat various initial concentrations (pH, 4.0; sorbent concentration, 1.0 g l1;agitation rate, 150 rpm).

were reported to follow a similar second order reactionmechanism [5,45,46]. Although much research work hasbeen conducted using chitin/chitosan as an effective metalscavenger, chitin/chitosanmetal sorption kinetics has stillnot yet been fully explained. Kim et al. in 1997 [47] re-ported that the sorption kinetics of Acid Blue 193, AcidBlue 40, Direct Yellow 44 and Direct Blue 78 onto chitinfollows a second order rate expression. Ho and McKay [20]

Table 1Change of the pseudo-second order rate constants with particle size

Particle size(m)

Cr(VI) sorption onto chitin Cr(VI) sorption onto chitosan Cu(II) sorption onto chitin Cu(II) sorption onto chitosank (g mmol1 min1) R2 k (g mmol1 min1) R2 k (g mmol1 min1) R2 k (g mmol1 min1) R2

250420 0.3828 0.9622 0.1238 0.9977 0.2702 0.9741 0.0489 0.9792420595 0.3114 0.9362 0.1200 0.9793 0.3114 0.9725 0.0539 0.9860595841 0.2630 0.9768 0.1104 0.9756 0.3521 0.9548 0.0405 0.9817

Fig. 13. Pseudo-second order sorption kinetics of Cu(II) onto chitosan atvarious particle sizes (pH, 4.0; sorbent concentration, 1.0 g l1; particlesize, 250420m; agitation rate, 150 rpm).

tested 11 sorption system including Ni(II)/wollastonite,Cr(VI)/Bi2O3, Cu(II)/peanut hull carbon, Cu(II)/granularactivated carbon, Cd(II)/beech leaves, Pb(II)/cypress leaves,Cu(II) and Pb(II)/bottom ash, Cd(II)/reed leaves, previouslyreported as first order kinetics and one system, Cu(II)/peat,previously reported as a second order process. They showedthat in all 12 systems, the highest correlation coefficientswere obtained for the pseudo-second order kinetic model.

The pseudo-second order kinetic model is based on theassumption that the rate-limiting step may be chemisorp-tion involving valency forces through sharing or exchangeof electrons between sorbent and sorbate. In our previousstudy, the heats of biosorption of Cr(VI) and Cu(II) ionsby R. arrhizus were shown to be of the same order ofmagnitude as the heat of chemisorption [48]. Chitin is acopper-chelating agent that binds the metal by amine andhydroxyl groups. Chitosan has already been described asa suitable natural polymer for the collection of metal ionsthrough chelation, due to the presence of an amino groupof the 2-amino-2-deoxy-d-glucose (glucosamine) unit. Al-though there is a disagreement in the literature regardingthe coordination modes for the chitosancopper complex,it has been recently confirmed by the technique of elec-trospray mass spectrometry that the Cu(II) is coordinatedto the C(1)-alkoxide, the four amine nitrogens of chitosantetrasaccharide and an anion. The solution equilibria for thechitosan tetrasaccharides with Cu(II) are given elsewhere

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.Aktay/Biochemical

EngineeringJo

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al12(2002)

143153151


[23]. Chromium forms stable complexes such as Cr2O72,HCrO4, CrO42 and HCr2O7 and the fraction of any par-ticular species is dependent upon chromium concentrationand pH. A lower pH will cause the functional groups of chitinto be protonated to a higher extent and result in a strongerattraction for a negatively charged ion in the solution. Ini-tially, this leads to the electrostatic interaction between thesorbent and the sorbate. Then sorption of chromium appearsto occur by precipitation onto chitin/chitosan with the for-mation of nodules of metal, a mechanism referred to theEidenJewell effect [49].

The Elovich equation was also applied to the sorption ofCr(VI) and Cu(II) ions by chitin/chitosan/R. arrhizus. Thelinearization of the equation giving the rate of reaction al-lows to obtain the initial sorption rate, (mmol g1 min1)from the intercept of a straight line plot of q versus ln t. How-ever, the experimental initial sorption rates were substan-tially lower than the predicted initial sorption rates whichhave no physical sense.

Fig. 13 shows a plot of t/q versus time for sorption ofCu(II) onto chitosan at different particle sizes. A mean-ingful change of pseudo-second order rate constants withparticle size was not observed for the sorption of Cu(II)ions onto chitin/chitosan. In the case of Cr(VI) sorptiononto chitin/chitosan, the pseudo-second order rate constantsslightly changed with increasing particle size (Table 1).If film diffusion is rate controlling, the constant of thepseudo-second order equation will vary inversely with theparticle size; if the process is sorption rate controlled,the constant of the equation will be independent of particlediameter and will depend only on the concentrations of themetal ions in solution and the temperature (Table 2).

5. Conclusion

The kinetics of sorption of Cr(VI) and Cu(II) ions ontochitin/chitosan and on R. arrhizus was tested using fourdifferent kinetic models. All findings presented in this studysuggest that Cr(VI)Cu(II)/chitinchitosanR. arrhizus sys-tems cannot be described by a first order reaction and theElovich equation. The pseudo-first order kinetic model hasbeen used extensively to describe the sorption of metalions onto sorbents. The main disadvantages of this modelare (i) that the linear equation (2) does not give theoreticalqeq values which agree with experimental qeq values, and(ii) the plots are only linear over the initial 2030 min ofthe sorption process. The pseudo-second order equation isbased on the sorption capacity on the solid phase and isin agreement with a chemisorption mechanism being therate controlling step. For all of the systems examined, thepseudo-second order kinetic model provided the best corre-lation of the experimental data. Since qeq and k can be de-termined from the slope and intercept of the linear form ofthe pseudo-second order rate equation, contrary to the othermodels there is no need to know any parameter beforehand.

Another advantage of the pseudo-second order rate model isthat it predicts the behavior over the whole range of studies,whereas the pseudo-first order model generally fits sorptiondata well for an initial period of the first reaction step only.The sorption kinetics of Cr(VI) and Cu(II) ions was studiedas a function of initial metal ion concentration and particlesize. While the latter parameter has no meaningful effecton sorption kinetics, chemisorption seems significant in therate controlling step.

Acknowledgements

The authors wish to thank TBITAK, the Scientificand Technical Research Council of Turkey, for the partialfinancial support of this study (project no. YDABAG,199Y095).

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Kinetic studies on sorption of Cr(VI) and Cu(II) ions by chitin, chitosan and Rhizopus arrhizusIntroductionMaterials and methodsMaterialsPreparation of sorption mediaBatch sorption experimentsMeasurement of heavy metal ions

Kinetic models applied to the sorption of Cr(VI) and Cu(II) ions onto chitin/chitosan and on R. arrhizusPseudo-first order rate equation of LagergrenFirst order equation of Bhattacharya and VenkobacharPseudo-second order rate equationThe Elovich equation

Results and discussionConclusionAcknowledgementsReferences

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