A Linear Model for Fitting Data of the Effect of pH on the Adsorption of Metal Ions onto Activated Carbon and Kaolinite

A Linear Model for Fitting Data of the Effect of pHon the Adsorption of Metal Ions onto ActivatedCarbon and Kaolinite

Bassam El-EswedZarka University College, Al-Balqa Applied University, Zarka, Jordan

The aim of this work was to develop a simple linear model (LPH)that could be used to fit the huge amount of data available in theliterature concerning the effect of pH on the adsorption of metal ions.A total of 52 datasets of available published data dealing with twodifferent adsorbents, activated carbon and kaolinite, were analyzed.The equilibrium constants (log K) and coordination numbers (n) ofthe complexes of metal ions with the surface (�S�) were determinedfrom linear plots of log Kd (partition coefficient) versus log[�S�].The values of log K and n increased with the decrease of initial metalions concentration. When compared with the state-of-the-art surfacecomplexation model, the model developed in this study (LPH) wasfound to be simpler and have more predictive abilities.

Keywords activated carbon; kaolinite; linear model; metal ions;pH dependent adsorption

INTRODUCTION

Heavy metals released into the water environment aretoxic to human beings if their concentrations exceed the toler-ance level. The problem associatedwith heavymetal pollutioncan be reduced by several methods such as precipitation,coagulation, reverse osmosis, adsorption, electrode depo-sition, and solvent extraction. Adsorption has been foundto be an effective and an economic method with high poten-tial for the removal, recovery and recycling of metal ions fromwastewater. Substances like activated carbon and kaolinitehave assumed a wide application as adsorbents in this regard.This is clear from the large amount of available data studyingthe adsorption of metal ions onto these adsorbents (1,2,3).

Many simple models are available in the literature forfitting data concerning the effect of metal ions concen-tration on the amount of metal ions adsorbed (4). The mostcommon of these models are Langmuir and Freundlichmodels. These models provide simple linear equations thatcan be used to calculate adsorption parameters (adsorption

capacity and affinity constants). These parameters havebeen widely used for evaluation and comparison of adsorp-tion behavior of metal ions onto different adsorbents. Onthe other hand, there is no simple linear model availablefor fitting the data concerning the effect of pH on theamount of metal ions adsorbed. The major part of these datais presented in the literature without any treatment. So, thereis a great demand for a simple model that can systematizethese data. However, plots of log Kd (partition coefficient)against pH were sometimes used to linearize pH-adsorptioncurves (5), and thus to compare the adsorption behavior ofdifferent soils toward metal ions (6,7). These plots, which aredependent on the assumption that the surface site density ofthe adsorbent, are not affected by pH, and were abandonedsince the advent of surface complexation (SC) model (5).During the last three decades, the comprehensive SC modelhas been extensively applied to modeling pH dependentadsorption data of metal ions. However, appreciable dataand experience are needed to exploit SC model effectively(5), and the equilibrium constants determined by SC modelare sensitive to uncertainty in determination of surface sitedensity (8). Furthermore, the electrostatic models incorpor-ated in the SC model have some weaknesses in assumptionsabout capacitance values (9), and there is no universal con-sensus as to which of the electrostatic models is the preferredone (5). Finally, the large number of variables in the compre-hensive SC model makes it difficult to compare the results ofdifferent workers on the adsorption of metal ions onto dif-ferent adsorbents.

The aim of the present article was to develop a simplelinear model for fitting selected reported data concerningthe effect of pH on the adsorption of Zn(II), Cd(II), Co(II),Cu(II), Pb(II), and Ni(II) onto activated carbon [10-150],and adsorption of Zn(II), Cd(II), Cu(II), Pb(II), Ni(II),and Cr(III) onto kaolinite (16–19). The model was evalu-ated according to the following aspects:

i. The dependence of the determined equilibrium con-stants and stoichiometries on the nature of metal ionsand their initial concentrations

Received 18 March 2011; accepted 23 November 2011.Address correspondence to Bassam El-Eswed, Zarqa Univer-

sity College, Al-Balqa Applied University, P. O. Box 313, Zarka,Jordan. E-mail: [email protected], [email protected]

Separation Science and Technology, 47: 1080–1089, 2012

Copyright # Taylor & Francis Group, LLC

ISSN: 0149-6395 print=1520-5754 online

DOI: 10.1080/01496395.2011.644611

1080

ii. The relationship between the determined equilibriumconstants and those obtained from SC model

iii. The sensitivity of the determined equilibrium constantsto the change in the site density of adsorbent

iv. A comparison between the model of the present workand the classical log Kd - pH model.

DATA COLLECTION

Following a review of the available published data dealingwith thepHdependent adsorptionofmetal ionsontoactivatedcarbon and kaolinite, a total of 52 datasets were investigated,representing over 380 individual experimental measurements.They included adsorption of 7 different metal ions onto fouractivated carbons and three kaolinite adsorbents. The datawere transcribed from published tables or digitized fromprinted Figures. The experimental conditions and the charac-teristics of adsorbents for each dataset are given in Table 1.

MODEL DERIVATION

The model proposed in the present study (LPH model)was derived from the equilibrium expression of the reactionof metal ions with a number (n) of surface negativelycharged groups (�S�):

Mmþ þ n � S� $� SnMm�n ð1Þ

Neglecting the activity coefficients, the equilibrium con-stant for this reaction is:

K ¼ ½� SnMm�n�

½Mmþ�½� S��n ð2Þ

The distribution coefficient Kd can be defined as:

Kd ¼ ½� SnMm�n�

½Mmþ� � V

W¼ C� � Ce

Ce� V

Wð3Þ

Where Co and Ce are the initial and equilibrium concen-trations of metal ions, respectively, V is the volume of thesolution, and W is the mass of the adsorbent. SubstitutingEq. 3 in Eq.2:

K ¼ Kd

½� S��n �W

Vð4Þ

Taking the common logarithm of Eq. 4 yields:

logKd ¼ logK � logW

Vþ n log½� S�� ð5Þ

The plot of logKd versus log[�S�] should give a straightline with a slope equal to n (the average reaction coefficientor stoichiometry) and an intercept equal to logK � logW

V .

The value of [�S�] can be calculated at different pHvalues from the equilibrium expressions of the acid-basereactions of the amphoteric surface of activated carbonand kaolinite:

� SHþ2 $� SH þHþ

Ka1 ¼½� SH�½Hþ�½� SHþ

2 �ð6Þ

� SH $� S� þHþ

Ka2 ¼½� S��½Hþ�½� SH�

ð7Þ

Thus, the concentration of the total surface sites [Sites]tcan be expressed as:

½Sites�t ¼ ½� S�� þ ½� SH� þ ½� SHþ2 � ð8Þ

Substituting Eq. 6 and 7 for [�SH] and [�S�] in Eq. 8:

½Sites�t ¼Ka2½� SH�

½Hþ� þ ½� SH� þ ½� SH�½Hþ�Ka1

ð9Þ

Rearranging leads to:

½� SH� ¼ ½Sites�tKa2½Hþ� þ 1þ ½Hþ�

Ka1

n o ð10Þ

So the value of [�SH] can be calculated as a functionof pH using Eq. 10 when the adsorbent characteristics([Sites]t, Ka1, Ka2) are known. Consequently, the valueof [�S�] can be calculated as a functions of pH fromEq. 7 for each point in the dataset.

RESULTS AND DISCUSSION

The LPH model plots of log Kd versus log[�S�] (Eq. 5)for all the datasets investigated were linear. Some of theseplots are given in Fig. 1. The values of the LPHmodel para-meters n, log K and R2 calculated from these plots for all thestudied data are given in Tables 2 and 3. These values wereanalyzed in the following sections of this article.

Correlation of Log K with n Values

An interesting correlation (Fig. 2) was found betweenthe LPH parameters, log K and n, for AC4, AC5, K1,K2, and K3 datasets. These datasets belonged to differentmetal ions with different initial concentrations (see Table 2and 3). The parameter n was considered as the stoichi-ometry or coordination number of metal ions in their com-plexes with the surface sites of adsorbent. So as the value ofn increased, the strength of interaction of metal ions withthe surface (log K) also increased. This relationship may

pH EFFECT ON METAL ION ADSORPTION 1081

TABLE 1Description of adsorption experiments and characteristics of adsorbents for the investigated datasets

Initial metalion

concentration,M (number of

points)

Characteristics of adsorbentMass of

adsorbent tovolume of

solution ratioW=V g=L

Datasetcode adsorbent [Sites]t mol=L pKa

Specificsurfaceaream2=g

Ionicstrength

Sourcereference

AC1Cu1 3.15� 10�4(7) Activatedcarbon cloth,

2.2� 10�3 pKa1¼ 6.26pKa2¼ 9.33pHpzc¼ 7.5

1689 0.0 2.0 (10)

AC1Cu2 6.30� 10�4(7) Actitex Co.,Levallois,France(CS1501)

(11)

AC2Cu1 3.15� 10�4(5)AC2Cu2 6.30� 10�4(5)AC3Cu1 3.15� 10�4(6) Activated

carbon cloth,1.6� 10�3 pKa1¼ 3.90

pKa2¼ 11.90pHpzc¼ 9.53

1460 0.0 2.0 (11)

AC3Cu2 6.30� 10�4(6) Actitex Co.,Levallois,France(RS1301)

AC4Cu1 3.15� 10�4(4) Activatedcarbon cloth,

2.2� 10�3 pKa1¼ 6.26pKa2¼ 9.33pHpzc¼ 7.5

1689 0.0 2.0 (11)

AC4Cu2 6.30� 10�4(5) Actitex Co.,Levallois,France(CS1501)

AC4Pb1 9.66� 10�5(4)AC4Pb2 1.93� 10�4(4)AC4Ni1 3.41� 10�4(5)AC4Ni2 6.81� 10�4(5)AC5Zn1 4.88� 10�5(8) Activated

carbon Darco12-20 mesh,Aldrich

8.02� 10�3 pKa1¼ 2.80pKa2¼ 9.40pHpzc¼ 6.1

590 0.0 10 (12)

AC5Zn2 9.65� 10�5(8)AC5Zn3 2.20� 10�4(6)AC5Zn4 3.99� 10�4(6)AC5Cd1 5.66� 10�5(7)AC5Cd2 1.09� 10�4(6)AC5Cd3 2.28� 10�4(6)AC5Cd4 4.61� 10�4(5)AC6Zn 1.00� 10�5(5) Activated

carbon15.3� 10�3 (a) pKa1¼ 1.9

pKa2¼ 11.5pHpzc¼ 7.0

1125 0.0 2.5 (13)

AC6Cd 1.00� 10�5(8) Viscose rayoncloth,

(Continued )

1082 B. EL-ESWED

TABLE 1Continued

Initial metalion


points)






Ionicstrength

Sourcereference

YugoslaviaAC7Zn 1.00� 10�4(16) Activated

carbonFiltrasorb

13.7� 10�3 (b) pKa1¼ 1.9pKa2¼ 11.5pHpzc¼ 7.0

(c)

1009 0.005 10 (14)

AC7Co 1.00� 10�4(10) 200H-type,Calgon,

AC7Cu 1.00� 10�4(16) PittsburghAC8Zn 4.88� 10�5 (6) Activated

carbon Darco12-20 mesh,ldrich,granular

8.02� 10�3 pKa1¼ 2.80pKa2¼ 9.40pHpzc¼ 6.10

590 0.01 10 (15)

AC8Cd 5.66� 10�5 (6)

K1Zn 4.88� 10�5(12) Kolinite fromMacon,Georgia

3.92� 10�4 pKa1¼ 4.63pKa2¼ 7.54pHpzc¼ 6.85

22.4 0.001 7.8 (16)

K1Pb 4.88� 10�5(8)K1Cu 4.88� 10�5(12)K1Cd 4.88� 10�5(15)K1Ni 4.88� 10�5(17)K2Ni1 4.26� 10�3(5) Kaolin from

AmericanClay Society

9.37� 10�3(d) pKa1¼ 3.80pKa2¼ 9.40pHpzc¼ 6.60

24 0.1 100 (17)

K2Ni2 1.70� 10�3(5)K2Ni3 8.52� 10�4(4)K2Ni4 5.11� 10�4(4)K2Cd1 2.22� 10�3(4)K2Cd2 8.90� 10�3(5)K2Cd3 4.45� 10�3(4)K2Cd4 2.67� 1�4(4)K2Cd5 1.33� 10�4(4)K2Cr1 4.81� 10�3(4)K2Cr2 1.92� 10�3(4)K2Cr3 9.62� 10�4(4)K2Cr4 5.77� 10�4(4)K2Cr5 2.88� 10�4(4)K3Pb 1.33� 10�4(6) Kaolinite

supplied byAjaxChemicalSydney,Australia

6.67� 10�4(e) pKa1¼ 3.81pKa2¼ 6.16pHpzc¼ 4.88

14.4 0.01 6.7 (18)

(Continued )


be attributed to the chelate effect which is very common incoordination chemistry.

Effect of Initial Metal Ions Concentration on theEquilibrium Constant

The effect of initial metal ions concentration on thevalues of log K determined from LPH model could bededuced from Table 2 and 3. The values of log K increasedwith the decrease of initial metal ions concentration. Thiseffect was obvious for adsorption of Zn and Cd onto acti-vated carbon (datasets AC5) and for adsorption of Cd, Cr,and Ni onto kaolin (datasets K2).

A similar observation was reported for adsorption ofmetal ions onto activated carbon (11), iron, aluminum,and manganese oxides (20–22), where log KSC decreasedwith the increase of initial metal ions concentration. Inthe literature, this observation was attributed to the exist-ence of an array of oxides surface sites of variable strength(heterogeneous surface) toward metal ions (21). This expla-nation was inconsistent with the implicit assumption madein calculating K that all surface sites are energeticallyequivalent (as in Eq. 2). However, in the present article, adifferent explanation could be proposed depending on the

TABLE 1Continued

Initial metalion


points)






Ionicstrength

Sourcereference

K3Cu 1.33� 10�4(6)K3Cd 1.33� 10�4(10)K3Zn 1.33� 10�4(8)K4Cu 1.00� 10�4(17) Kaolinite

supplied byAjaxChemicalSydney,Australia

3.25� 10�4 (f) pKa1¼ 3.96pKa2¼ 7.24pHpzc¼ 5.60

14.7 0.005 6.8 (19)

a : estimated using the following relation: ([Sites]t of AC6)=([Sites]t of AC5)¼ (surface area of AC6=surface area of AC5).b: estimated as in a.c: assumed to equal that of dataset 6.d : calculated from data given in the original article¼ (2.35� 1018 site.m�2)(24m2.g)(1=6.02� 1023mol.site-1)(100 g.L�1).e: calculated from data given in the original article¼ (6.93� 10�6mol.m�2)(96.3m2.L�1).f : calculated from data given in the original article¼ (3.25� 10�6mol.m�2)(100m2.L�1).

FIG. 1. Plots of log Kd versus log[�S�] for some of the datasets accord-

ing to LPH model (Eq. 5).

1084 B. EL-ESWED

concept of coordination number (n) determined by theLPH model. As the concentration of metal ions increased,the coordination number (n) decreased because the chanceto find vacant sites (that were assumed to have the sameenergy) decreased. Consequently, the interaction betweenthe metal ions and the surface sites became weaker andso the log K values decreased. Thus, depending on theLPH model, the decrease of log K with the increase ofinitial metal ions concentration was attributed to thedecrease of coordination number of the complexes ofmetal ions with homogenous surface sites. This expla-nation was consistent with the assumption made in calcu-lating K that all surface sites were energetically equivalent(Eq. 2).

Correlation of Log K with Log KSC

The LPH model developed in the present work was sim-pler than the SC model because it had fewer variables.Nevertheless, the log K values calculated depending onthe LPH model correlated well (Fig. 3) with the logKSC

values determined by the authors of the original articlesof the datasets.

Dependence of Log K on the Nature of Metal Ions

In order to make a comparison between the log K valuescalculated from the LPH model for different metal ions,their initial concentrations should be the same because ofthe significant effect of the initial metal ions concentration

TABLE 2Equilibrium constants and coordination numbers for metal ions adsorption onto activated carbon

MODEL LPH LPHDSC

codeInitial metal ionconcentration n

logK R2

RSD� ofslope

RSD�� ofintercept log K0

RSD�� ofintercept

logKSC

��

AC1Cu1 3.150� 10�04 0.341 3.846 0.9819 6.1 4.2 0.661 5.2AC1Cu2 6.300� 10�04 0.359 3.786 0.9588 9.3 6.8 0.433 12.7AC2Cu1 3.150� 10�04 0.299 3.393 0.9983 2.4 3.8 0.602 1.6AC2Cu2 6.300� 10�04 0.261 2.675 0.9952 4.0 7.2 0.243 6.0AC3Cu1 3.150� 10�04 0.288 3.314 0.9768 7.7 14.0 �0.107 24.8AC3Cu2 6.300� 10�04 0.261 2.678 0.9625 9.9 20.1 �0.423 7.3AC4Cu1 3.150� 10�04 0.281 3.165 0.9937 5.6 9.3 0.546 4.9 2.909AC4Cu2 6.300� 10�04 0.259 2.650 0.995 4.1 7.4 0.233 6.3 2.102AC4Pb1 9.660� 10�05 0.765 9.384 0.9622 14.0 33.7 2.249 9.3 4.137AC4Pb2 1.930� 10�04 0.416 4.348 0.9911 6.7 11.9 0.468 10.1 2.545AC4Ni1 3.410� 10�04 0.126 0.606 0.951 13.1 28.0 �0.569 6.6 0.068AC4Ni2 6.810� 10�04 0.145 0.587 0.866 22.7 57.5 �0.762 9.8 �0.02AC5Zn1 4.880� 10�05 0.631 3.643 0.9892 4.3 12.1 �2.286 11.6AC5Zn2 9.650� 10�05 0.631 3.429 0.987 4.7 13.1 �2.498 9.9AC5Zn3 2.200� 10�04 0.476 2.412 0.9957 3.3 12.2 �2.063 8.1AC5Zn4 3.990� 10�04 0.443 2.028 0.9882 5.5 23.3 �2.137 11.9AC5Cd1 5.660� 10�05 0.476 2.617 0.9831 5.9 14.1 �1.855 19.1AC5Cd2 1.090� 10�04 0.399 2.047 0.9518 11.3 33.5 �1.700 34.7AC5Cd3 2.280� 10�04 0.418 1.964 0.9836 6.5 15.3 �1.968 14.7AC5Cd4 4.610� 10�04 0.309 1.159 0.9808 8.1 29.2 �1.742 16.6AC6Zn 1.000� 10�05 0.912 7.212 0.9585 12.0 35.5 �3.278 20.0AC6Cd 1.000� 10�05 0.399 3.125 0.9565 8.1 7.9 �1.466 9.5AC7Zn 1.000� 10�04 0.515 3.852 0.9942 2.0 2.3 �2.071 0.9AC7ZCo 1.000� 10�04 0.386 2.948 0.9753 5.6 7.2 �1.495 3.3AC7Cu 1.000� 10�04 0.567 5.522 0.9787 3.9 5.1 �0.994 2.7AC8Zn 4.880� 10�05 0.656 3.861 0.9642 9.6 43.9 �2.307 41.8AC8Cd 5.660� 10�05 0.543 2.989 0.9972 2.7 7.4 �2.116 3.9

�Relative standard deviation of slope¼ (standard deviation of slope=value of slope)� 100%.�Relative standard deviation of intercept¼ (standard deviation of intercept=value of intercept)� 100%.��Reported by reference of dataset (see Table 1).


on the value of log K (section titled ‘‘Effect of Initial MetalIons Concentration . . . ’’). Thus, the data sets selected forthis comparison had the same initial metal ions concen-tration as shown in Table 4. For activated carbon, theorder of decreasing the value of log K was:Pb(II)>Cu(II)>Zn(II)>Co(II)>Cd(II), and for kaolinitethe order was: Pb(II)>Cu(II)>Zn(II)>Cd(II)>Ni(II). Thehydrolysis constants (log Kh) followed the same order(Table 4), which supports the idea that adsorptionoccurred by the reaction between metal ions and surfacehydroxyl groups (19).

A Comparison Between Activated Carbon and Kaolinite

The log K values in Table 4 indicated that kaolinite isless selective toward metal ions than activated carbon. Thismay be due to the fact that activated carbon and kaolinitehave completely different structures. The sheet structure of

kaolinite is more open than the porous structure of acti-vated carbon and this may be the cause of the lower selec-tivity of the former toward metal ions. The adsorption ofmetal ions onto iron hydroxide (a-FeOOH) was reportedto have the same behavior of kaolinite, where the ironhydroxide (20) showed no selectivity toward metal ions(see values of equilibrium constants in Table 4).

Sensitivity of Log K Value to the Change in Surface SiteDensity

Different methods were reported to determine the sur-face site density of activated carbon and kaolinite (5). Sincethese methods gave different values, it was necessary tocheck the sensitivity of the LPH model parameters to thechange in surface site density. As shown in Fig. 4, the valueof n was completely insensitive to the change of [Sites]t.Furthermore, the value of log K increased slightly by the

TABLE 3Equilibrium constants and coordination numbers for metal ions adsorption onto kaolinite

MODELLPH LPHD

SC

codeInitial metal ionconcentration n

logK R2

RSD� ofslope

RSD�� ofintercept log K00

RSD�� ofintercept

logKSC

��

K1Zn 4.88� 10�5 0.303 2.061 0.9845 4.0 4.7 �0.221 3.3 �2.85K1Pb 4.88� 10�5 0.382 3.148 0.973 6.8 14.4 0.267 4.0 �0.64K1Cu 4.88� 10�5 0.269 2.079 0.9743 5.1 6.0 0.053 15.1 �1.96K1Cd 4.88� 10�5 0.262 1.768 0.9789 4.1 4.5 �0.207 3.3 �3.23K1Ni 4.88� 10�5 0.250 1.692 0.9446 6.3 5.0 �0.192 5.8 �3.43K2Ni1 4.26� 10�3 0.174 1.191 0.9884 6.3 12.8 �0.448 5.5 �2.6K2Ni2 1.7� 10�3 0.177 1.198 0.973 9.6 20.0 �0.465 5.2 �2.6K2Ni3 8.52� 10�4 0.245 1.589 0.9772 10.8 22.9 �0.714 7.0 �2.6K2Ni4 5.11� 10�4 0.260 1.734 0.9943 5.4 13.9 �0.713 5.0 �2.6K2Cd1 2.22� 10�3 0.227 1.015 0.9993 1.8 5.6 �1.117 0.7 �3.3K2Cd2 8.90� 10�3 0.245 1.348 0.9975 2.9 7.4 �0.956 1.1 �3.3K2Cd3 4.45� 10�3 0.278 1.624 0.9911 6.7 19.8 �0.948 4.8 �3.3K2Cd4 2.67� 10�4 0.250 1.516 0.9998 1.0 2.2 �0.837 0.5 �3.3K2Cd5 1.33� 10�4 0.313 1.624 0.9521 15.9 52.6 �1.314 9.6 �3.3K2Cr1 4.81� 10�3 0.362 3.630 0.9793 10.3 20.0 0.223 19.6 5K2Cr2 1.92� 10�3 0.341 3.560 0.9817 10.0 18.0 0.356 10.9 5K2Cr3 9.62� 10�4 0.540 5.662 0.9387 18.1 30.3 0.588 21.6 5K2Cr4 5.77� 10�4 0.591 6.294 0.9759 11.1 15.1 0.740 14.4 5K2Cr5 2.88� 10�4 0.557 6.119 0.9831 9.3 12.2 0.880 9.5 5K3Pb 1.33� 10�4 0.928 3.805 0.9807 7.0 17.2 �1.912 7.4K3Cu 1.33� 10�4 0.651 2.737 0.9537 11.0 26.9 �1.275 6.8K3Cd 1.33� 10�4 0.648 2.349 0.9466 8.4 14.1 �1.641 7.8K3Zn 1.33� 10�4 0.528 2.199 0.9559 8.8 14.6 �1.051 6.2K4Cu 1.00� 10�4 0.573 3.191 0.953 5.7 6.3 �0.954 2.4K4Pb 1.00� 10�4 0.445 2.558 0.9353 6.6 5.7 �0.666 2.8

�Relative standard deviation of slope¼ (standard deviation of slope=value of slope)� 100%.�Relative standard deviation of intercept¼ (standard deviation of intercept=value of intercept)� 100%.��Reported by reference of dataset (see Table 1).

1086 B. EL-ESWED

change of [Sites]t in the range from 2� 10�3 to 1.4� 10�2

mol=L (Figure 4).

Other Related Models

The ability of LPH model to make reasonable predic-tions (like those in sections 4.1–4.5) was compared withthat of classical log Kd – pH model (13). The latter was

based on the following ion exchange reaction:

Mmþþ � SH $� SMm�n þ nHþ ð11ÞDepending on this reaction, Eq. 12 was derived in the

literature (10):

logKd ¼ logK ‘� logW

Vþ log½� SH� þ npH ð12Þ

FIG. 2. Correlation of log K with n values determined from LPH model.

FIG. 3. Correlation of log K calculated from the LPH model with log

KSC obtained from surface complexation model (by authors of original

articles of datasets).

TABLE 4Comparison of equilibrium constants for adsorption of metal ions onto different adsorbents

Code (activated carbon) AC4Pb1 AC7Cu AC7Zn AC5Zn2 AC5Cd2 AC7Co

Metal ion Pb(II) Cu(II) Zn(II) Cd(II) Co(II)Initial metal ion concentration 9.66� 10�5 1.00� 10�4 1.00� 10�4 9.65� 10�5 1.09� 10�4 1.00� 10�4

Log K 9.348 5.522 3.852 3.429 2.047 2.948

Log K0 �1.898 0.684 �0.290 �1.724 �0.436 0.494Log K00 2.249 �0.994 �2.071 �2.498 �1.700 �1.495Code (kaolinite) K1Pb K1Cu K1Zn K1Cd K1NiMetal ion Pb(II) Cu(II) Zn(II) Cd(II) Ni(II)Initial metal ion concentration 4.88� 10�5 4.88� 10�5 4.88� 10�5 4.88� 10�5 4.88� 10�5

Log K 3.148 2.079 2.062 1.768 1.692

Log K0 0.980 1.884 1.413 1.776 1.837Log K00 0.267 0.053 �0.221 �0.207 �0.992Log Kh

� �7.7 �8.0 �9.0 �9.6 �9.7 �9.9Log K�� a-FeOOH 6.9 6.6 5.9 5.9 5.9 –

�Reference (18,19).��Reference (20).


Actually, Eq. 12 resulted from employing derivations ofEq. 2 through Eq. 5 on Eq. 11 instead of Eq. 1. As it washandled in the literature, this model assumed that [�SH] isindependent on pH (which is not true). Then from a plot oflog Kd versus pH, the values of log K0 and n could be cal-culated (the values are not given here). This model will bereferred to as the LPHI model.

We can develop the LPHI model by taking the change of[�SH] with pH into consideration. The values of [�SH] asa function of pH can be calculated from Eq.10. Rearrang-ing Eq. 12 leads to:

logKd ¼ logK 00 � logW

V� n log

½Hþ�½� SH� ð13Þ

From a plot of log Kd versus � log ½Hþ�½�SH�, the values of

log K00 and n can be calculated (Tables 2 and 3). Thismodel will be referred to as LPHD model.

Both LPHI and LPHD models gave inconclusive resultsand the correlations discussed in sections 4.1–4.5 were inap-plicable. There was no correlation between log K0 or log K00

and n values, initial metal ions concentration or log KSC.The LPH model proposed in the present article was superiorto LPHI model because the former took the change of [�SH]with pH into consideration. However, both LPH and LPHDmodels supposed the same adsorption mechanism becausethey assumed the same product (�SnM

m�n). Both modelshad given similar values of n, R2 and errors of slope(Tables 2 and 3). Therefore, there was a straightforward deri-vation of the relationship between the log K obtained fromLPH model and the log K00 obtained from LPHD model:

K ¼ K 00

ðKa2Þnð14Þ

However, both LPH and LPHD models had differentequilibrium constants and different errors in intercepts(Tables 2 and 3). The superiority of the LPH model overLPHD in giving more systematic results may be due tothe observation that the LPH model gave greater valuesof equilibrium constants than the LPHD model (Tables 2and 3).

CONCLUSION

The model developed in this article offered a simplemethod (linear plots of logKd- log [�S�]) for the treatmentof pH adsorption data. This made it possible to compareadsorption affinity (logK) and coordination number (n) ofdifferent metal ions and adsorbents. The model had fewervariables than the surface complexation model, and it wasslightly sensitive to the surface site density of adsorbent.

As the initial concentration of metal ions increased, thecoordination number (n) of metal ion with surface sitesdecreased, and consequently, the affinity constant (logK)decreased. Kaolinite was less selective toward metal ionsthan activated carbon due to the fact that the sheet struc-ture of kaolinite is less selective than the porous structureof activated carbon.

ABBREVIATIONS

SC: surface complexation model.LPH: model developed in the present article, Linear

plots of log Kd versus log[�S�].LPHI: classical model, plots of log Kd versus pH.LPHD: classical model modified to take the effect of

pH on [�SH] into consideration, plots of logKd versus � log ½Hþ�

½�SH�.n: coordination number of metal ions in their

complexes with the surface of activated carbonand kaolinite.

Log K: equilibrium constant derived from LPH model.Log K0: equilibrium constant derived from LPHI

model.Log K00: equilibrium constant derived from LPHD

model.Log KSC: equilibrium constant derived from surface

complexation model.

REFERENCES

1. Bhattacharyya, K.G.; Gupta, S.S. (2006) Kaolinite, Montmorillonite

and their modified derivatives as adsorbents for removal of Cu(II)

from aquous solution. Sep. Purif. Technol., 50 (5): 388.

2. Bhattacharyya, K.G.; Gupta, S.S. (2008) Adsorption of a few heavy

metals on natural and modified kaolinite and montmorillonite: A

review. Adv. Colloid. Interface Sci., 140 (2): 114.

3. Alfarra, A.; Frackowiak, E.; Beguin, F. (2004) The HSAB concept as

a means to interpret the adsorption of metal ions onto activated car-

bons. Apl. Surf. Sci., 228: 84.

4. Foo, K.Y.; Hameed, B.H. (2010) Insights into the modeling of

adsorption isotherm systems. Chem. Eng. J., 156: 2.

FIG. 4. The influence of surface site density on log K and n, calculated

from LPH model for dataset AC7Zn.

1088 B. EL-ESWED

5. Jenne, E.A. (1998) Adsorption of Metals by Geomedia Data Analysis,

Modeling, Controlling Factors and Related Ussues, In: Adsorption of

Metals by Geomedia: Variables, Mechanisms and Model Applications.

Jenne, E.A., ed.; Elsevier.

6. Allen, H. E.; Chen, Y.; Li, Y.; Huang, P. (1995). Soil partition coeffi-

cients for Cd2þ by column desorption and comparison to batch

adsorption measurements. Environ. Sci. Technol., 29: 1887.

7. Lee, S.; Allen, H. E.; Huang, C. P.; Sparks, D.L.; Sanders, P.F.;

Peijnenburg, W.J. G.M. (1996). Predicting soil-water partition coeffi-

cients for cadmium. Environ. Sci. Technol., 30: 3418.

8. Goldberg, S. (1991) Sensitivity of surface complexation modeling to

the surface site density parameter. J. Colloid and Interface Sci., 145: 1.

9. Goldberg, S. (1995) Adsorption models incorporated into chemical

equilibrium models. In: Chemical Equilibrium and Reaction Models.

Soil Science Society of America, American Society of Agronomy, 677

S. Segoe Rd., Madison, W1 53711, SSSA special publication 42.

10. Kadirvelu, K.; Faur-Brasquet, C.; Le Cloirec, P. (2000) Removal of

Cu(II), Pb(II), Ni(II) by adsorption onto activated carbon cloths.

Langmuir., 16: 8404.

11. Faur-Brasquet, C.; Reddad, Z.; Kadirvelu, K.; Le Cloirec, P. (2002)

Modeling the adsorption of metal ions (Cu2þ, Ni2þ, Pb2þ) onto ACCs

using surface complexation models. Applied Surface Science, 196: 356.

12. Marzal, P.; Seco, A.; Gabaldon, C. (1996) Cadmium and zinc adsorp-

tion onto activated carbon: influence of temperature, pH and metal=

carbon ratio. J. Chem. Tech. Biotechnol., 66: 279.

13. Babic, B.M.; Milonjic, S.K.; Polovina, M.J.; Cupic, S.; Kaludjerovic,

B.V. (2002) Adsorption of zinc, cadmium and mercury ions from

aqueous solutions on activated carbon cloth. Carbon, 40: 1109.

14. Chen, J.P.; Lin, M. (2000) Comprehensive investigation of important

factors governing metal-ion adsorption by H-type granular activated

carbon. Sep. Sci. Technol., 35: 2063.

15. Gabaldon, C.; Marzal, P.; Ferrer, J.; Seco, A. (1996) Single and com-

petitive adsorption of Cd and Zn onto granular activated carbon.

Water Research., 30: 3050.

16. Gu, X.; Evans, L.J. (2008) Surface complexation modeling of Cd(II),

Cu(II), Ni(II), Pb(II) and Zn(II) adsorption onto kaolinite. Geochim.

Cosmochim. Acta., 72: 267.

17. Al-Hamdan, A.Z.; Reddy, K.R. (2005) Surface speciation modeling of

heavy metals in kaolin: Implications for electrokinetic soil remedation

processes. Adsorption, 11: 529.

18. Srivastava, P.; Singh, B.; Angove, M. (2005) Competitive adsorption

behavior of heavy metals on kaolinite. J. Colloid and Interface Sci.,

290: 28.

19. Ikhsan, J.; Johnson, B.B.; Wells, J.D. (1999) A comparative study of

the adsorption of transition metals on kaolinite. J. Colloid and Inter-

face Sci., 217: 403.

20. Smith, R.W.; Jenne, E.A. (1991) Recalculation, evaluation and predic-

tion of surface complexation constants for metal adsorption on iron

and manganese oxides. Environ. Sci. Technol., 25: 525.

21. Benjamin, M.M.; Leckie, J.O. (1981) Multiple-site adsorption of Cd,

Cu, Zn and Pb on amorphous iron oxyhydroxide. J. Colloid and Inter-

face Sci., 79: 209.

22. Davis, J.A.; Leckie, J.O. (1978) Surface ionization and complexation

at the oxide=water interface, II surface properties of amorphous iron

hydroxide and adsorption of metal ions. J. Colloid and Interface Sci.,

67: 90.


Documents

A Linear Model for Fitting Data of the Effect of pH on the Adsorption of Metal Ions onto Activated Carbon and Kaolinite