Film-Pore Diffusion Control for the Batch Sorption of Cadmium Ions from Effluent onto Bone Char

Journal of Colloid and Interface Science 234, 328–336 (2001) doi:10.1006/jcis.2000.7281, available online at http://www.idealibrary.com on

Film-Pore Diffusion Control for the Batch Sorption of Cadmium Ions from Effluent onto Bone Char C. W. Cheung, C. K. Chan, J. F. Porter, and G. McKay1 Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Received March 22, 2000; accepted October 16, 2000

The sorption equilibrium and kinetics of cadmium ions from aqueous solution onto bone char have been studied. Equilibrium isotherms for the sorption system were correlated by Langmuir and bi-Langmuir equations. The application of the bi-Langmuir equation was developed because the mechanistic analysis in this research indicated that cadmium removal occurs ion exchange and physical adsorption onto different surface sites. The bi-Langmuir equation provides a better fit to the experimental data. In addition, the removal rates of cadmium ions based on the Langmuir models have been investigated. The effective diffusivity was calculated using the effects of initial metal ion concentration and bone char mass. Two mass-transport models based on film-pore diffusion control have been applied to analyze the concentration decay curves. The film and pore diffusion coefficients using an analytical equation are equal to 1.26 × 10−3 cm/s and 5.06 × 10−7 cm2 /s, respectively. The pore diffusion coefficient obtained from the numerical method is 4.89 × 10−7 cm2 /s. A sensitivity analysis showed that the film-pore diffusion model and constant effective diffusivity could be used to describe the mass-transport mechanism of the sorption system with a high degree of correlation. °C 2001 Academic Press Key Words: bone char; cadmium; calcium hydroxyapatite; filmpore diffusion; ion exchange.

INTRODUCTION

Adsorption is widely recognized as an effective treatment process for the removal of pollutants from aqueous effluents. The presence of cadmium ions in effluents from various industries, including organics, chloralkali, electronics, metal, inorganic, fertilizer, and petroleum, is of particular concern because of its toxicity. Several studies on the removal of cadmium by sorption systems are reported in the literature. Salim et al. (1) studied the uptake of cadmium from water by beech leaves. The results showed that the various concentrations of cadmium agreed with the empirical Freundlich adsorption isotherm. Holan and Volesky (2) studied the accumulation of cadmium, lead, and nickel by fungal and wood biosorbents. The cadmium uptake by the materials examined was summarized in the decreasing qmax sequence for native biomass type: Penici1 To whom correspondence should be addressed. Fax: (852) 2358 0054. E-mail: [email protected].

0021-9797/01 $35.00

C 2001 by Academic Press Copyright ° All rights of reproduction in any form reserved.

llium chrysogenum > Absidia Orchidis > Rhizopus arrhizus > Rhizopus nigricans. Namasivayam and Ranganathan (3) used the waste Fe(III)/Cr(III) hydroxide to remove the cadmium ions from wastewater. The adsorption capacity of cadmium increased when the adsorption temperature increased. The authors explained that the enhancement of the adsorption capacity of Fe(III)/Cr(III) hydroxide at higher temperatures may be attributed to the enlargement of pore size and/or activation of the adsorbent surface. Leusch et al. (4) used marine algae to remove the heavy metals (cadmium, copper, nickel, lead, and zinc). The Langmuir, Freundlich, and Dubinin-Radushkevich models were used for experimental data modeling. Allen et al. (5) used bone char, lignite, peat, and Norit carbon to remove the cadmium ions from aqueous solution. The most effective sorbent tested by these authors was bone char with a capacity of over 100 mg cadmium uptake per gram of bone char, followed by Bord na Mona peat with a capacity of 60 mg/g. Other good performers were activated carbon (Norit) and lignite (e.g., Crumlin), all with capacities around 40 mg/g of adsorbent sample. The poorest performers were the peat char (1 mg/g) and lignite char (5 mg/g). No kinetic or mass-transfer studies were carried out to analyze the data from this study. McKay and Porter (6) studied the equilibrium sorption of copper, cadmium, and zinc onto peat. Most metal ion sorption system models in the literature are based on reaction kinetics using pseudo-first-order kinetics (7–8), pseudo-second-order kinetics (9–10), Ritchie kinetics (11), or Elovich kinetics (11–13). These models result in an individual best fit pseudo-rate constant for each set of experimental data; therefore the application of these rate constants to sorber design is restricted to the systems studied. Another modeling approach has been through solution complexation theory (14–19). These models, although successful, require the prediction of equilibrium constants and activity coefficients for application to the models. Therefore, the application in this research to develop a model for metal ion sorption based on diffusion mass transfer and incorporating global or system diffusion coefficients is novel and relatively simple. Only a limited number of diffusion applications to metal ion sorption are reported (20–24). In this research, the sorption of cadmium ions onto bone char in an agitated batch sorber has been studied. The objective of the present work is to assess whether one value of diffusiontransport parameter can describe a range of experimental

328

329

FILM-PORE DIFFUSION CONTROL

conditions for each metal ion–bone char system. Ranges of initial metal ion concentration values, sorbent masses, and solution temperatures have been selected for testing the model. MATERIALS AND METHODS

The bone charcoal used in the studies was Brimac 216, 20/60 Tyler Mesh supplied by Tate & Lyle Process Technology. A typical analysis of Brimac 216 provided by the manufacturer is shown in Table 1. The adsorbents were rinsed three times with deionized water. Finally, the adsorbents were dried at 103– 105◦ C for 24 h and then allowed to cool in a desiccator. Analytical-grade cadmium(II) sulfate (3CdSO4 · 8H2 O) used in the experiments was supplied by Riedel-de Ha¨en Chemicals. Stock solution of metal ions was prepared using deionized water. All solutions were adjusted to pH 4.8 ± 0.1 using dilute sulfuric acid. Equilibrium Sorption Isotherms A fixed mass of bone charcoal was weighed into 120-ml test bottles. Cadmium ion solutions were prepared and then pipetted into the test bottles. The initial pH of the solutions was adjusted to 4.8 ± 0.1 by the addition of dilute sulfuric acid. The test bottles were put in the shaker bath for 72 h, which was sufficient time to reach equilibrium. The quantities of metal ion sorbed at equilibrium (qe , mg/g) or at time t (qt , mg/g) were calculated from qt =

(Co − Ct )V M

[1]

where Co and Ct are the initial concentration and solution concentration at time t (mg/dm3 ), V is the volume of solution (dm3 ), and M is the sorbent mass (g). Batch Contact Time Studies The standard tank configuration was used to derive the relative dimensions of the vessel and its components. The configuration of the vessel with respect to the inside diameter, Di , is shown in Fig. 1. The adsorber vessel used was a 2-dm3 plastic beaker of internal diameter 0.13 m holding a volume of 1.7 dm3 metal ion solution. Mixing was provided by a six-bladed, flat plastic impeller of 0.065-m diameter and 0.013-m blade height. A TABLE 1 Physical and Chemical Properties of Bone Char Chemical composites

Physical properties

Items

Limits

Items

Limits

Acid-Insoluble ash Calcium carbonate Calcium sulfate Carbon content Hydroxyapatite Iron as Fe2 O3

3 wt% max 7–9 wt% 0.1–0.2 wt% 9–11 wt% 70–76 wt% <0.3 wt%

Bulk density (dry) Carbon surface area Moisture Pore size distribution Pore volume Total surface area

640 kg/m3 50 m2 /g 5 wt% max 7.5–60,000 nm 0.225 cm3 /g 100 m2 /g

FIG. 1. Standard tank configuration.

Heidolph variable motor was used to drive the impeller using a 0.005-m-diameter plastic shaft. Six plastic baffles were evenly spaced around the circumference of the vessel, positioned at 60◦ intervals and held securely in place on top of the vessel. The adsorption vessel was used to obtain kinetic data, and the effects of initial metal ion concentration, sorbent mass, and temperature were studied. RESULTS AND DISCUSSION

Equililbrium Isotherms The isotherm equilibrium data were analyzed using the Langmuir and bi-Langmuir equilibrium equations. The Langmuir, Eq. [2], is widely used in the sorption of sorbate onto single homogeneous sites. The bi-Langmuir, Eq. [3], can be used in the sorption of sorbates on homogeneous sites, which contain two type of sorption site on the sorbent. This equation was used in the sorption of lead(II) and zinc(II) onto goethite (25); however, these authors reported only the equilibrium data, and their data were not used to model contact time data. qe =

q m aL C e 1 + aL C e

[2]

qe =

qm,1 aL,1 Ce qm,2 aL,2 Ce + 1 + aL,1 Ce 1 + aL,2 Ce

[3]

330

CHEUNG ET AL.

where qm,i (mg/g) and aL,i (dm3 /mg) are the parameters of the Langmuir and bi-Langmuir equations. Since the hydroxyapatite compound (CaHOAP), which is the main component of bone char, was reported to adsorb metal ions by adsorption and ion exchange, the bi-Langmuir equation was used to correlate the experimental data. Although the bi-Langmuir equation has been found to fit data over a wide range of concentrations, this does not imply that the surface comprises just two types of surface sites. In fact, the Langmuir two-site equation can represent any experimental sorption isotherm that is a smooth, concave function of the adsorbate concentration and approaches a maximum value asymptotically (25). Therefore, the bi-Langmuir equation may be used in multisite systems. The sorption mechanisms are proposed to follow Eqs. [4a], [4b], and [4c]. The calcium hydroxyapatite (CaHOAP) and carbon (C) in bone char adsorb and act as “physical” sorption sites to a part of the cadmium ions. The other part of the cadmium ions is exchanged by the calcium ions in the hydroxyapatite lattice. Adsorption: mCd2+ (aq) + Cax (PO4 ) y (OH)z(s) + → mH+ (aq) + Cax (PO4 ) y (OH)z−m (OCd )m(s) + + Cd2+ (aq) + Carbon-H(s) → Carbon-Cd(s) + H(aq)

[4a] [4b]

Ion exchange:

TABLE 2 The Constants and SAEs of Langmuir Equation Temperature (K)

dp (µm)

aL (dm3 /mg)

qm (mg/g)

SAE

283.2 293.2 313.2 333.2

500–710 500–710 500–710 500–710

0.788 0.788 0.788 0.788

43.56 58.50 86.60 98.98

17.30 92.06 13.60 8.16

cient of cadmium ions in the hydroxyapatite is 3.8 × 10−19 cm2 /s (29). The parameters of the equations were determined by minimizing the sum of the absolute errors (SAE). SAE =

[4c]

The sorptions of cadmium ions onto hydroxyapatite and carbon (Eqs. [4a] and [4b]) are simplified equations. The actual sorption mechanism on hydroxyapatite is ≡POH + Cd2+ = ≡POCd+ + H+ ≡PO + Cd

≡CaOH + Cd

[4a,i]

+

= ≡POCd

2+

[5]

Film-Pore Diffusion Model

→ kCa2+ (s) + Cax−k Cdk (PO4 ) y (OH)z(s)

2+

|qexp,i − qcalc,i |

Tables 2 and 3 show the constants and SAE of the Langmuir and bi-Langmuir equations. The parameters aL,1 and qm,1 of the bi-Langmuir equation are calculated from the cationic exchange capacity (CEC) of calcium. The adjustable parameters from Eq. [3] are aL,2 and qm,2 . However, the Langmuir equation can correlate the experimental data better than the bi-Langmuir equation can by evaluating the SAE of the equations. Figure 2 shows the experimental results and Langmuir isotherms at different temperatures.

kCd2+ (aq) + Cax (PO4 ) y (OH)z(s)

−

X

[4a,ii] +

+

= ≡CaOCd + H .

[4a,iii]

The sorption mechanism of cadmium ions onto hydroxyapatite surface was suggested by Xu and Schwartz (26). The authors also used the Langmuir isotherm to correlate the adsorption isotherm. The sorption of cadmium ions onto carbon can be interpreted to mean that cadmium ions are sorbed by the functional groups of carbon such as the carboxylic group on the carbon surface (27, 28): ≡COOH + Cd2+ = ≡COOCd+ + H+ .

[4b,i]

In addition, the salt inclusion effect occurs in the ion-exchange process (Eq. [4c]). The cadmium ions exchange with the calcium ions on the surface and slowly diffuse in the crystal lattices, but the rate of salt inclusion is very slow. The solid diffusion coeffi-

Model 1 (Analytical Method) The reaction occurs first at the outer skin of the bone char particle. The zone of reaction then moves into the solid, leaving behind completely converted sorbent. Therefore, at any time during reaction, there exists an unreacted core of sorbent that shrinks in size as the adsorption process continues. The model assumes that there is irreversible adsorption, that the adsorption rate is controlled by an external and internal mass-transfer resistance, and that this linked transport mechanism could be described using well-known equations. The analysis is based on work by Keinath and Weber (30) and Neretnieks (31) and on the unreacted core theory (32). Calculation of adsorption rate. The sorption rate onto bone char is determined as follows: TABLE 3 The Constants and SAEs of bi-Langmuir Equation Temperature (K)

dp (µm)

aL,1 (dm3 /mg)

qm,1 (mg/g)

aL,2 (dm3 /mg)

qm,2 (mg/g)

SAE

283.2 293.2 313.2 333.2

500–710 500–710 500–710 500–710

0.177 0.177 0.177 0.177

13.63 18.60 41.97 50.49

0.322 0.322 0.322 0.322

30.15 40.00 47.28 50.05

26.28 79.45 29.18 35.64

331

FILM-PORE DIFFUSION CONTROL

FIG. 2. Sorption of cadmium ions onto bone char at different temperatures: 3, T = 283.15 K; h, T = 293.15 K; 1, T = 313.15 K; s, T = 333.15 K; ——, Langmuir equation; ---, cation exchange capacity.

1. The mass transfer from the external water phase, dn/dt (mg/s), is dn = kf 4π R 2 (Ct − Ce,t ), dt

[6]

where kf is the film-diffusion coefficient (cm/s), Ct and Ce,t are the concentration of sorbate at bulk solution and sorbent surface (mg/dm3 ), and R is the mean radius of sorbent (cm). 2. The diffusion in the pore water according to Fick’s law is 4π De Ce,t dn = , dt 1/r − 1/R

[7]

FIG. 3. Connection between bulk and surface concentrations during batch the adsorption in the batch: h, (Ct , qt ); 1, (Ce,t , qe,t ); ——, operating line; ---, tie lines.

expressed as a function of adsorbate concentration ξ in the water phase, adsorbate concentration η in the adsorbent phase, and the Biot number Bi. The adsorption rate is represented by 3(1 − Ch η)(1 − η)1/3 dη = dτ 1 − (1 − 1/Bi)(1 − η)1/3

[10]

or in general by dη = ξ f(η)Bi, dτ

[11]

where the dimensionless parameters are defined as where r and R are the radius of sorbent at time t and initial, and De is the effective diffusion coefficient (cm2 /s). The relationships of Ct and Ce,t are shown in Fig. 3. The average sorption capacity of sorbent at time t is increased along the operating line to reach equilibrium. In fact, the sorption capacity is the adsorbed core of sorbent. 3. The velocity of the concentration front is obtained from the mass balance on a spherical element, dr dn = −4πr 2 qh ρs , dt dt

τ =

C o De t ρs qh R 2

[8]

where qh is hypothetical equilibrium solid-phase concentration (mg/g) and ρs is particle density (g/cm3 ). 4. The average concentration in the sorbent is given by ·

µ ¶3 ¸ r . qt = qh 1 − R

[9]

The concentration profile in bone char is shown in Fig. 4. By considering these conditions and introducing dimensionless parameters, the adsorption rate for a single particle can be

FIG. 4. Concentration profile in bone char particle.

[12]

332

CHEUNG ET AL.

η=

qt qh

[13]

ξ =

C1 Co

[14]

kf R . De

[15]

Bi =

Batch studies with the equilibrium driving for qe,t − qt projecting onto the monolayer can be treated with a “pseudoirreversible” isotherm approximation and so qe,t − qt = qh − qt .

[16]

This allows us to integrate Eq. [10] to give Eq. [16], τ =

ª 1 © ln[X 3 + a 3 ]2(1−1/Bi)−1/a + ln[X + a]3/a 6Ch ¶ µ 2X − a 1 , [17] arctan √ −√ 3aCh 3a

where X = (1 − η)1/3

[18]

and µ a=

1 − Ch Ch

¶1/3 ,

[19]

where Ch is the capacity factor in the pore diffusion model [Ch = (qh M)/(Co V )]. The limits for Eq. [17] are τ = 0, η = 0, and

X =1

τ = τ, η = η, and

X = X,

Hypothesis for the prediction of the adsorption rate. Bone char is a porous material. The sorption rate may be controlled by the diffusion of adsorbate in liquid film and pore. The use of film-pore diffusion is based on the following assumptions: 1. The adsorbate is transferred within the pores of the bone char by means of molecular diffusion. 2. The deposition rate of the metal ion in the pore liquid onto the bone char is taken to be much higher than the rate of diffusion. 3. The adsorption of metal ions onto bone char is irreversible. Therefore, the equilibrium concentration at the surface, qe,t, can be replaced by a hypothetical equilibrium concentration, qh = constant. 4. The quantity of adsorbate in the pore water is much lower than that on the bone char and therefore is neglected. Similar assumptions were suggested by Spahn and Schl¨under (33) for the sorption of phenyl acetic acid onto activated carbon. Based on these assumptions, the hypothetical equilibrium concentration is assumed to be equal to the equilibrium capacity of the Langmuir equation (qh = qe,∞ ). However, the correlation of film-pore diffusion using (qh = qe,∞ ) is poor. If qh = qm = 58.5 mg/g (i.e., monolayer capacity), the curve fitting will be greatest improved. Figure 5 shows the effect of the initial concentration and the volume to mass ratio (i.e., V /M ratio) for the adsorption isotherm of cadmium ions onto bone char. The equilibrium capacities, qe,∞ , are changed at different initial concentrations and the volume to mass ratios change for different sorbent masses. Therefore, the film and pore diffusion coefficients of the analytical Eq. [20] were calculated by minimizing the objective function Eq. [21] for all sets of data. Figures 6 and 7 show that the film-pore diffusion model can be used for all concentration and V /M ratios. The external mass transfer coefficient and the effective diffusivity are equal to 1.26 × 10−3 cm/s and 5.06 × 10−7 cm2 /s, respectively.

and inserting these limits we find that ( ¯ ¯ ) ¯ ¯ ¯ X + a ¯3/a ¯ X 3 + a 3 ¯2(1−1/Bi)−1/a 1 ¯ ¯ + ln¯¯ ln¯¯ τ = 6Ch 1 + a3 ¯ 1+a ¯ ½ µ ¶ µ ¶¾ 2−a 1 2X − a arctan √ +√ − arctan √ .[20] 3aCh 3a 3a Therefore by converting dimensionless time τ into real time it is possible to compare experimental and theoretical concentration decay curves. The diffusivity in model 1 is derived from minimizing the sum of the SAE. Therefore, the diffusivity obtained by model 1 is a constant based on Eq. [20], SAEtotal =

n X j=1

(

m X j=1

) |texp,i − tcalc,i |

. j

[21]

FIG. 5. Langmuir isotherm and operating lines for the adsorption of cadmium ions onto bone char (effect of initial concentration and mass of sorbent): ——, effect of initial concentration; ---, effect of mass of sorbent.

333

FILM-PORE DIFFUSION CONTROL

The Langmuir equation is used to relate equilibrium concentrations on the solid phase surface, qe,t =

qm aL Ce,t . 1 + aL Ce,t

[24]

The solid phase/liquid mass balance from Eq. [1] becomes M[qe,t (1 − (r/R)3 )] = V (Co − λCe,t ).

[25]

In the previous model, a rapid analytical solution was developed by assuming that qe,t is a constant equal to qh . In this model, the tie lines and time-dependent values for Ce,t and hence qe,t can be obtained. Combining Eqs. [23]–[25] and putting Rm = (1 − (r/R)3 )(M/V ), we obtain the quadratic equation FIG. 6. Sorption of cadmium ions onto bone char (effect of initial concentration-analytical method). 3, Co = 242 mg/dm3 ; h, Co = 302 mg/dm3 ; 1, Co = 356 mg/dm3 ; ×, Co = 356 mg/dm3 ; s, Co = 356 mg/dm3 ; ——, analytical method.

2 + (λ + aL qm Rm − aL Co )Ce,t − Co = 0. aL λCe,t

From Eq. [26], Ce,t can then be obtained, as Ce,t (r )

Model 2 (Numerical Method) The mass transfer from the bulk solution across the liquid film is equal to intraparticle diffusion of sorbate. Therefore, combining Eqs. [6] and [7], we obtain · Ct = 1 +

De r kf R(R − r )

¸ Ce,t

[26]

=

−(λ + aL qm Rm − aL Co ) +

p

(λ + aL qm Rm − aL Co )2 + 4aL λCo . 2aL λ

[27] The mass transfer rate, dn/dt, is given by

or Ct = λCe,t ,

dn dr = −4πr 2 qe,t ρs . dt dt

[22]

[28]

Combining Eqs. [7] and [28], the rate equation becomes

where λ(r ) = 1 +

De r . kf R(R − r )

[23]

dr De (1 + aL Ce,t )R = . dt qm aLr (r − R)ρs

[29]

Since Ce,t is known as a function of r, Eq. [27] can be solved for an specified time period by a numerical method, with dr corresponding to increments dt to achieve analytical stability. The optimum De , as a function of t, can be found by minimizing the SAE between the experimental and the theoretical time for experimental Ct values, as SAEtotal =

( n m X X j=1

FIG. 7. Sorption of cadmium ions onto bone char (effect of mass of sorbentanalytical method): 3, M = 6.5 g; h, M = 7.5 g; 1, M = 8.5 g; ×, M = 9.5 g; s, M = 10.5 g; ——, analytical method.

i=1

) |(Ct )exp,i − (Ct )calc,i |

.

[30]

j

The best single average value for De can also be determined by optimization and used for comparison with previous models. Figures 8 and 9 show that the pore diffusion model can be correlated to the experimental data very well. The sorption rate control is independent of initial concentration and the mass of sorbent (Fig. 5). Nine sets of kinetic data were substituted into the film-pore diffusion model to get the film diffusion coefficient (1.82 × 10−3 cm/s) and pore diffusion coefficient (4.89 × 10−7 cm2 /s), respectively.

334

CHEUNG ET AL.

Therefore, the molecular diffusion in a liquid-pore is equal to DM (T ) = DMO

µo T µ To

[32]

where DMO and µo are the molecular diffusivity and the viscosity of the solution in the pore-liquid at a reference temperature (i.e., To = 293.2 K). As the viscosity of solution is a function of temperature, the Eyring equation (Eq. [33]) will be used to predict the temperature effect of the viscosity in the solution (34), µ∼ =

FIG. 8. Sorption of cadmium ions onto bone char (effect of initial concentration-numerical method): 3, Co = 242 mg/dm3 ; h, Co = 302 mg/dm3 ; 1, Co = 356 mg/dm3 ; ×, Co = 356 mg/dm3 ; s, Co = 356 mg/dm3 ; ——, numerical method.

Pore size and pore diffusivity. From Table 1, the pore size distribution of bone char is around 7.5–60,000 nm. According to the IUPAC definition of pore diameters (dh , nm), the bone char only contains mesopore (2 < dh < 50 nm) and macropore (dh > 50 nm) regions. Therefore, the constant effective diffusivity represents the mean of the molecular diffusivity of cadmium ions in the mesopores and macropores. The constant effective diffusivity (i.e., De = 4.89 × 10−7 cm2 /s) was calculated by using model 2. Since the molecular diffusivity in the pore-liquid is a function of temperature, the increase of temperature will also increase the diffusion rate of cadmium ions in pores. The Stokes–Einstein relationship was used to incorporate the temperature effect into the effective diffusivity as ¶ µ DM µ = Constant. [31] T

FIG. 9. Sorption of cadmium ions onto bone char (effect of mass of sorbentnumerical method): 3, M = 6.5 g; h, M = 7.5 g; 1, M = 8.5 g; ×, M = 9.5 g; s, M = 10.5 g; ——, numerical method.

N˜ h exp(3.8(Tb /To )), V˜

[33]

where N˜ , h, Tb , and V˜ are Avogadro’s number (mole−1 ), Planck’s constant (g cm2 /s), the boiling point of liquid (K), and the volume of a mole of liquid (cm3 /mole), respectively. Since this equation is used only to approximately calculate the viscosity of liquid (µo , g/cm/s), the predicted diffusivity is only an approximate method. The effective diffusivity at different temperatures can be expressed by combining Eqs. [32] and [33] to yield ½µ De (T ) = Deo

T To

¶·

¶¶¸¾ µ µ 1 1 − , [34] exp 3.8Tb To T

where Tb is the boiling point of liquid. In this research, the boiling point of dilute cadmium(II) sulfate was assumed to be equal to the boiling point of water (i.e., T ≈ 373.2 K). Therefore, Eq. [34] is used to predict the temperature effect of the experimental data. Figure 10 showed the sorption of cadmium ions onto bone char with a different temperature effect. The predicted curves are closed to the experimental data at T = 313.2 K and T = 333.2 K. The best-fit curves are obtained by optimizing the pore diffusion model for the individual sets of data. The

FIG. 10. Sorption of cadmium ions onto bone char (effect of initial concentration-numerical method). 3, T = 283.15 K; h, T = 293.15 K; 1, T = 313.13 K; ×, T = 313.15 K; ——, best-fit correlation; ---, theoretical predication.

FILM-PORE DIFFUSION CONTROL

FIG. 11. Prediction of constant effective diffusivity (temperature effect): 1, best-fit correlation; ---, theoretical prediction.

theoretical and experimental constant effective diffusivities are plotted in Fig. 11. Discussion of Sorption Mechanism Since bone char contains 70–76 wt% of hydroxyapatite, the chemical properties (equilibrium) are comparable with the sorption of metal ions onto calcium hydroxyapatite. However, bone char is a porous material. The sorption mechanism (rate) is similar to that of activated carbon. Generally speaking, the adsorption rate onto the surface is a very fast process and diffusion is a slow process. Therefore, the sorption rate is controlled mainly by intraparticle diffusion. In recent research, Abdel Raouf and Daifulah (27) used bone char to remove the antimony and europium radioisotopes from radioactive wastes. The authors suggested that chemisorption of europium ions occurs through specific sorption with the basic surface of bone charcoal. The lone pair of electrons associated with the oxygen atoms chemisorbed onto the surface would be coordinated to the inner transition metal vacant d-orbitals of the europium ion to form a type of coordination bond. In contrast, there is a lack of any vacant d-orbitals in the electronic configuration of antimony; hence antimony ions will undergo preferential physical sorption with the bone char surface. Since, in the cadmium ion, the d-orbitals are full, the sorption of cadmium ions onto the carbon surface component may be physical sorption according to these authors. However, the authors did not discuss the possibility of the sorption of metal ions onto hydroxyapatite. Table 1 shows that bone char is composed of calcium hydroxyapatite, carbon, and calcium carbonate. Since the calcium hydroxyapatite and calcium carbonate are active components and are involved, it is speculated that the sorption of cadmium ions onto these compounds may also be involved in rate controlling the sorption mechanism. Suzuki and co-workers (35) reported the sorption of metal ions, including cadmium ions, onto hydroxyapatite. The authors suggested that the cadmium uptake

335

phenomenon is not simply an adsorption effect but rather an ion-exchange reaction between cadmium ions in solution and calcium ions in the sample. Suzuki et al. (36) suggested that calcium hydroxyapatite contains two sorption sites, Ca(1) and Ca(2). The radii of easily removed ions such as cadmium fall ˚ and the metal with the range of the radius of Ca(2) (0.9–1.3 A), ions have large electronegativity values. Chen et al. (37) also reported the possible involvement of adsorption and ion-exchange effects of calcium sites in the removal of cadmium ions. The adsorption mechanisms of cadmium ions onto hydroxyapatite are still not clear. Fedoroff et al. (29) investigated the sorption of cadmium ions onto different sorption sites by controlling the temperature. The authors found that the cadmium ions only replaced the calcium ions at the Ca(2) site at T = 18 and 28◦ C. When the temperature increased to T = 75◦ C, the cadmium ions exchanged exclusively with the Ca(1) site. Therefore, the ionexchange effect of cadmium ions onto bone char is to replace the calcium ions in Ca(2) site on hydroxyapatite at T = 20◦ C. However, the calcium carbonate in the bone char may enhance the sorption of cadmium. Suzuki et al. (35) reported that the ion-exchange characteristics of the carbonate apatites for zinc, cadmium, and lead ions were discovered with increasing carbonate ion content. Therefore, the sorption mechanism of bone char becomes quite complex. In this study, the sorption of cadmium ions onto bone char at pH 4.0 was conducted. The ion-exchange effect was measured using different initial concentrations of cadmium ions in solution. Figure 12 shows that increasing the initial concentration of cadmium ions in solution will increase the quantity of calcium ions in solution. Therfore, ion exchange is one of the sorption mechanisms for removing cadmium ions using bone char. Figure 13 shows the ratio of physical sorption to total sorption

FIG. 12. Total adsorption capacity and ion-exchange capacity for the sorption of cadmium ions (at pH = 4.0): 3, Co = 238 mg/dm3 ; h, Co = 294 mg/dm3 ; 1, Co = 353 mg/dm3 ; ×, Co = 452 mg/dm3 ; s, Co = 550 mg/dm3 ; ——, sorption capacity for cadmium ions; ---, ion exchange capacity for calcium ions.

336

CHEUNG ET AL.

FIG. 13. The ratio of physical adsorption to total adsorption of cadmium ions (at pH = 4.0): 3, Co = 238 mg/dm3 ; h, Co = 294 mg/dm3 ; 1, Co = 353 mg/dm3 ; ×, Co = 452 mg/dm3 ; s, Co = 550 mg/dm3 .

of cadmium ions. The cadmium ions are highly adsorbed after the first two hours, and after that, the physical sorption rates of cadmium ions decrease. Therefore, cation exchange is the main sorption mechanism after 2 h. CONCLUSIONS

The Langmuir and bi-Langmuir equations were used to correlate the experimental data of the equilibrium isotherm. The Langmuir equation can correlate the experimental data better than the bi-Langmuir equation by evaluation the SAE of the equations. In addition, the Langmuir equation was incorporated into the mass balance equation to set up the film-pore diffusion model. The constant effective diffusion coefficients obtained by using model 1 and 2 are close to 4.89 × 10−7 cm2 /s. The film-pore diffusion is the main mass-transport rate-controlling process for the sorption of cadmium ions to bone char, even though the sorption mechanism involves ion-exchange reaction processes and physical sorption processes. ACKNOWLEDGMENT C. W. Cheung thanks R.G.C. and D.A.G. for support during this research.

REFERENCES 1. Salim, R., Al-Subu, M., and Sahrhage, E., J. Environ. Sci. Health A27(3), 603 (1992). 2. Holan, Z. R., and Volesky, B., Appl. Biochem. Biotechnol. 53, 132 (1995).

3. Namasivayam, C., and Ranganathan, K., Water Res. 29(7), 1737 (1995). 4. Leusch, A., Holan, Z. R., and Volesky, B., J. Chem, Tech. Biotechnol. 62, 279 (1995). 5. Allen, S. J., Whitten, L. J., Murray, M., and Duggan, O., J. Chem. Tech. Biotechnol. 68, 442 (1997). 6. McKay, G., and Porter, J. F., J. Chem. Tech. Biotechnol. 69, 309 (1997). 7. Mishra, S. P., and Singh, V. K., Radiochimica Acta 68, 251 (1995). 8. Lee, C. K., Low, K. S., and Kek, K. L., Bioresource Tech. 54, 183 (1995). 9. Ho, Y. S., and McKay, G., Trans. IChemE 76(Part B), 332 (1998). 10. Quek, S. Y., Al-Duri, B., Wase, D. A. J., and Forster, C. F., Trans. IChemE. 76, 50 (1998). 11. Ritchie, A. G., J. Chem. Society-Faraday Trans. 73, 1650 (1977). 12. Aharoni, C., and Ungarish, M., J. Chem. Society-Faraday Trans. I 72, 456 (1977). 13. Taylor, R. W., Hassan, K., Mehadi, A. A., and Shuford, J. W., Commun. Soil Sci. Plant Analyt. 26(11, 12), 1761 (1995). 14. Dzombak, D. A., and Morel, F. M. M., J. Colloid Interface Sci. 67, 90 (1987). 15. Van Riemsdijk, W. H., Bolt, G. H., Koopal, L. K., and Blaakmeer, J., J. Colloid Interface Sci. 109, 219 (1986). 16. Van Riemsdijk, W. H., De Wit, J. C. M., Koopal, L. K., and Bolt, G. H., J. Colloid Interface Sci. 116, 511 (1987). 17. Hayes, K. F., and Leckie, J. O., J. Colloid Interface Sci. 115, 564 (1985). 18. Sparks, D. L., “Kinetics of Soil Chemical Process,” Academic Press, San Diego, 1989. 19. Yiacoumi, S., and Tien, C., “Kinetics of Metal ion Adsorption from Aqueous Solutions,” Kluwer Academic Publishers, New York, 1995. 20. Petrazzelli, D., Helfferich, F., Liberti, L., Millar, J. R., and Passino, R., React. Polymer 7, 1 (1987). 21. Helfferich, F., React. Polymer. 13, 191 (1990). 22. Fernandez, A., Rodrigues, A., and Diaz, M., Chem. Eng. J. 57, 17 (1995). 23. Allen, S. J., and Brown, P. A., J. Chem. Tech. Biotechnol. 62, 17 (1995). 24. Ar´evalo, E., Rendueles, A., Fern´andez, A., Rodrigues, A., and Diaz, M., Separ. Purif. Tech. 13, 37 (1998). 25. Rodda, D. P., Johnson, B. B., and Wells, J. D., J. Colloid Interface Sci. 184, 365 (1996). 26. Xu, H., and Schwartz, F., J. Environ. Sci. Technol. 28, 1472–140 (1994). 27. Abdel Raouf, M. W., and Daifullah, A. A. M., Adsorp. Sci. Technol. 15(8), 559–569 (1997). 28. Jia, Y. F., and Thomas, K. M., Langmuir 16, 1114–1122 (2000). 29. Fedoroff, M., Jeanjean, J., Rouchaud, J. C., Mazerolles, L., Trocellier, P., Maireles-Torress, P., and Jones, D. J., Solid State Sci. 1, 71 (1999). 30. Keinath, T. M., and Weber, W. J., J. Water Pollu. Control Federation 40, 741 (1968). 31. Neretnieks, I., Chem. Eng. Tech. 46, 1 (1974). 32. Levenspiel, O., “Chemical Reaction Engineering,” John Wiley & Sons, New York, 1962. 33. Spahn, H., and Schl¨under, E. U., Chem. Eng. Sci. 30, 529 (1975). 34. Bird, R. B., Stewart, W. E., and Lightfoot, E. N., “Transport Phenomena,” John Wiley & Sons, New York, 1960. 35. Suzuki, T., Hatsushika, T., and Miyake, M., International Conference on Ion Exchange (1991; Tokyo, Japan) 401, 1991. 36. Suzuki, T., Hatsushika, T., and Hayakawa, Y., J. Chem. Society-Faraday Trans. 1(78), 3605 (1982). 37. Chen. X., Wright, J. V., Conca, J. L., and Peurrung, L. M., J. Environ. Sci. Technol. 31(3), 624 (1997).