Development of a Two Parameter Temperature-Dependent Semi

Apr 18, 2007 - Development of a Two Parameter Temperature-Dependent Semi-Empirical ... To ensure that all experiments were conducted on purely binary ...
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3766

Ind. Eng. Chem. Res. 2007, 46, 3766-3773

Development of a Two Parameter Temperature-Dependent Semi-Empirical Thermodynamic Ion Exchange Model Using Binary Equilibria with Amberlite IRC 748 Resin Kathryn A. Mumford,† Kathy A. Northcott,*,† David C. Shallcross,† Geoff W. Stevens,† and Ian Snape‡ Particulate Fluids Processing Centre, Department of Chemical and Biomolecular Engineering, UniVersity of Melbourne, ParkVille, Victoria 3010, Australia, and EnVironment, Protection and Change Program, Australian GoVernment Antarctic DiVision, Channel Highway, Kingston, Tasmania 7050, Australia

A chelating ion-exchange resin, Rhom and Haas Amberlite IRC 748, was investigated for the exchange of copper and sodium from aqueous solutions at four different temperatures. A two-parameter temperaturedependent, semiempirical thermodynamic ion exchange model was used to describe binary systems involving the ions Cu2+, Na+, and H+. To ensure that all experiments were conducted on purely binary systems, the resin was preconditioned into the hydrogen form. All experiments were conducted with Cl- as the nonexchanging anion and at temperatures of 4.0, 12.0, 20.0, and 40.0 ( 0.1 °C. The semiempirical thermodynamic ion exchange model was shown to predict the shape of the equilibrium ion exchange curves accurately, despite the low concentrations of copper used in this study (0.001 57-0.007 87 N). There was a consistent increase in selectivity of the resin toward copper with an increase in temperature. 1. Introduction Ion exchange is a well proven technology for the removal of low concentrations of toxic metals from contaminated waters.1,2 Exchange resins with chelating functional groups such as iminodiacetic acid (IDA), aminophosphonic acid, and amidoxime have a particularly high selectivity for transition metals and so are specially suited to remove metal ions from multimetal mixtures.3 Resins containing the IDA functional group, such as Chelex 100, Amberlite IRC 748, Purolite S930, and Lewatit TP 207, have been used successfully for a range of treatment processes including fly ash leachate,4 mineral processing,5 and contaminated groundwater.6 The work described in this paper follows from a successful attempt to use the chelating resin Amberlite IRC 748 to treat contaminated ground- and surface water from an abandoned landfill site in Antarctica.7 An important consideration for application of ion exchange technologies in cold regions such as Antarctica is the impact of low temperature on the selectivity of the resin and its ion exchange equilibrium characteristics. A wide range of models have been proposed to predict ion exchange equilibrium behavior. However, no fully theoretical model has been developed that does not utilize some experimental data. Even less work has been conducted to explore the effects of temperature on ion exchange equilibria. In this work a semiempirical ion exchange model developed by Mehablia et al.8 is applied to the H-Cu and H-Na binary exchange systems on Amberlite IRC 748. The model, which links the solid-phase concentration of the exchanging ion to the solution-phase concentrations, is extended to incorporate the effect of temperature. The thermodynamic equilibrium constant is calculated independently using the approach of Argensinger et al.9 Nonidealities in both phases are considered by applying Pitzer’s electrolyte solution theory10 and the Wilson model.11 The model * Corresponding author. Telephone: 61 3 8344 0466. Fax: 61 3 8344 4153. E-mail: [email protected]. † University of Melbourne. ‡ Australian Government Antarctic Division.

also takes into account the formation of ion pairs of the electrolytes in the solution which limit the free ions available for ion exchange.12,13 Temperature effects are modeled through use of generally accepted thermodynamic functions such as Gibbs free energy. 2. Modeling Ion Exchange Equilibria 2.1. Model Development for a Binary System. The exchange of two ions between a solution phase and an exchanger phase may be represented by the stoichiometric equation of the type

zbA(za + zaB(zb a zbA(za + zaB(zb

(1)

where za and zb are the valencies of ionic species A and B, respectively, and the underline denotes that the ion is in the exchanger phase. The equilibrium constant for such an exchange may be written in terms of the activities of the ions.

KAB )

( )( ) RA RA

zb

RB RB

za

(2)

where Ri and Ri are the activities of ionic species i, either A or B, in the solution and exchanger phases, respectively. The equilibrium constant, KAB, is defined in terms of activities rather than concentrations because of the nonideal behavior generally exhibited by ions in both the solution and the exchanger phases. Before the activity coefficients of the ionic species present within the solution may be calculated, the free ion concentrations of each of the species must be determined. When an ionic compound, MX, is introduced into an aqueous solution, at moderate to high concentrations, it will not fully dissociate into its separate constituent ions. Instead an equilibrium will be established between the associated and the dissociated forms corresponding to the equation

MX(aq) a M+(aq) + X-(aq)

10.1021/ie0615436 CCC: $37.00 © 2007 American Chemical Society Published on Web 04/18/2007

(3)

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007 3767 Table 1. Stability Constant Expressions Used in This Investigation compound a

CuCl2 CuCl+a NaClb HClb a

Table 2. AO Values at Various Temperatures15

KS (I, ionic strength)

temperature (°C)

Aφ

temperature (°C)

Aφ

0.4966 1.105 exp(-0.537 - 1.002I) exp(-1.179 - 0.982I)

4 12

0.3788 0.3832

20 40

0.3881 0.4022

b is an empirical parameter equal to 1.2 at 25 °C.14 I is the ionic strength of the solution:

b

Reference 26. Reference 12.

I)

The method of Kester and Pykowicz12 may be used to calculate the free ion concentrations. The stability constant is defined as

KMX S )

[MX] +

(4)

-

[M ]f[X ]f

[M]t ) [M+]f(1 + KMX S [X ]f)

[N]t ) [N ]f(1 +

+ KNX S [X ]f

+

(5)

+ - 2 2 NX KNX S KS [X ]f )

(6)

Solving these equations enables the free ion concentrations of the exchanging ions to be calculated. The activity of ion Mm+ is related to the free ion concentration by

RMm+ ) γM[Mm+]f

(11)

Aφ is defined as

1 2πN0Fw Aφ ) 3 1000

( ) e2 kT

1.5

(12)

where N0 is Avogadro’s number, Fw and  are the density and the static dielectric constant of the pure solvent, respectively, k is Boltzmann’s constant, T is the absolute temperature, and e is the electron charge. Pitzer produced a table of Aφ values at temperatures between 0 and 300 °C.15 On the basis of this data an empirical correlation to describe the variation was formulated. This correlation calculates the Aφ values listed to within 1%.10

Aφ ) 0.134 22[4.172 533 2 - 0.148 128 1T0.5 + (1.518 850 5 × 10-5)T2 - (1.801 631 7 × 10-8)T3 + (9.381 644 × 10-10)T3.5] (13) where T is the temperature expressed in K, with the applicable range being 273 e T e 373 K. The values of Aφ used in this investigation are presented in Table 2. Cca is derived from Cφca as

(7)

In Pitzer’s model the activity coefficients of cations (γM) are calculated as follows, where the subscripts M and c refer to cations and a and a′ refer to anions: Na

ln γM ) zM2F +

mizi2 ∑ 2 i

0.5

Here KMX S is the stability constant and subscript f refers to free of the compound MX for ion concentrations. Values for KMX S all compounds investigated in this study are presented in Table 1. Material balance equations may be written for the free ion concentration with respect to the total concentration. Equations 5 and 6 describe the material balance for a monovalent cation M+ and divalent cation N2+, respectively, both in the presence of a single monovalent anion X-. The subscript t refers to the total concentration of the ion present.

2+

1

∑ma(2ΒMa + ZCMa) + c)1 ∑mc(2ΦMc +

a)1

Na

Cca )

Cφca 2x|zcza|

(14)

Parameters ΒMa and ΒMa ′ of eqs 8 and 10 describe the interaction of pairs of oppositely charged ions, representing measurable combinations of the second virial coefficients. They are defined as explicit functions of ionic strength:

Na

∑maψMca) + ∑a a′)a+1 ∑ mama′ψaa′M + |zM|c)1 ∑ a)1 ∑ mcmaCca

(0) (1) (2) + β Ma g(RMaxI) + β Ma g(RMa ′ xI) ΒMa ) β Ma

(15)

a)1

(8) Here zi and mi are the charge and molality of species i, respectively. Z is calculated as

′ ) ΒMa

∂ΒMa g′(aMaxI) g′(aMa ′ xI) (1) (2) ) β Ma + β Ma (16) ∂I I I

where N

Z)

∑|zk|mk

(9)

k)1

and F is given by

F ) -Aφ

(

xI

2

1 + bxI

∑ ∑

c)1 c′)c+1

)

g′(x) )

+ ln(1 + bxI) + b

mcmc′Φ′cc′ +

∑ ∑

g(x) )

mama′Φ′aa′ +

a)1 a′)a+1 Nc

Na

∑ ∑ mcmaB′ca

c)1 a)1

(10)

2(1 - (1 + x)e-x) x2

-2(1 - (1 + x + (x2/2))e-x x2

(17)

(18)

(0) (1) (2) Here, x denotes RMaxI or RMa ′ xI, and βMa , βMa , βMa , and RMa are temperature-dependent ion-interaction parameters. The applicable values used for this study are presented in Table 3. For instances where one or both ions of a salt are of univalent type, only the first two terms in eq 15 and only the first term in eq 16 are used, and aMa ) 2.

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Table 3. Single Salt Pitzer Model Parametersa (0) βMa

(1) βMa

φ CMa

0.2966 0.18729 0.16968 × 10-3(T - 298.15) + 0.18566 × 10-4(T - 298.15)2/2 -656.81518/T + 24.879183 2.1552731 × 10-5P + 5.0166855 × 10-8P2 4.4640952 ln(T) + (0.011087099 6.4479761 × 10-8P 2.3234032 × 10-10P2)T + (-5.2194871 × 10-6 + 2.4445210 × 10-10P + 2.8527066 × 10-13P2)T2 + (-1.5696232 + 2.2337864 × 10-3P 6.3933891 × 10-7P2 4.5270573 × 10-11P3)/(T - 227) + 5.4151933/(680 - T)

1.3910 0.29697 + 0.55795 × 10-3(T - 298.15) 0.11218 × 10-4(T - 298.15)2/2 119.31966/T - 0.48309327 + 1.4068095 × 10-3T 4.2345814/(T - 227)

-0.03602 -0.33328 × 10-3 0.31969 × 10-4(T - 298.15) 0.124427069 × 10-5(T - 298.15)2/2 -6.1084589/T + 0.40743803 6.8152430 × 10-6P 0.075354649 ln(T) + (1.2609014 × 10-4 + 6.2480692 × 10-8P)T + (1.8994373 × 10-8 1.0731284 × 10-10P)T2 + (0.32136572/(T - 227)) (2.5382905 × 10-4P)/(T - 227)

MX b

CuCl2 HClc NaCld

a

T is the absolute temperature expressed in K, and P is pressure expressed in bar. b Reference 27. c Reference 28. d Reference 15.

Table 4. Mixed Electrolyte Pitzer Model Parameters A

B

X

θAB

ψABX (T in K)

Cu2+ Na+

H+ H+

ClCl-

-0.24120a 0.123228 1.1538 × 10-6T2 b

Cu2+

Na+

Cl-

0.000a

0.030492a 0.48045 3.6329 × 10-3T + 6.938137 × 10-6T2 b -0.014a

a

Reference 27. b Reference 28.

In eqs 8 and 10, Φcc, Φcc ′ , and Φaa ′ are interaction parameters for like sign ionic pairs. They are temperature and ionic strength dependent.

Φij ) θij + Eθij(I)

(19)

′ θij′ ) Eθij(I)

(20)

and Eθij(I) ′ are functions of the ionic charges between the pair and solution ionic strength. These functions are defined by Pitzer10 and can normally be ignored in moderately concentrated solutions of ionic strength less than 10 molal (for all like ′ ) 0). Also, θij are temperaturesign pairs, Eθij(I) ) 0 and Eθij(I) dependent fitting parameters. Parameters and ψcca and ψaa′c, appearing in eq 8, are the temperature-dependent interaction coefficients of ternary terms, and the applicable values for use in this study are presented in Table 4. The equilibrium constant, KAB, may be calculated from experimental binary equilibria data using the Gaines and Thomas16 approach where

Elprince and Babcock17 first proposed applying the Wilson18 model to estimate the exchanger phase activity coefficients. The Wilson equation is

∆GE

Na

)

RT

∫01 ln(λAB) dyA

(21)

and yi is the equivalent ionic fraction of species i in the exchanger phase. Here λAB is the equilibrium quotient, a quantity that may be determined relatively easily from experimental data. It is defined as

λAB )

( )( ) yA γ Ax A

zB

γBxB yB

zA

(22)

Here xi is the equivalent ionic fraction of species i in the solution phase.

ymi ln(∑Λijymi) ∑ i)1 j)1

(23)

where Na is the number of exchanging counterion species and Λij are the Wilson binary interaction parameters, ∆GE is the change in Gibbs free energy, R is the universal gas constant, and T is the absolute temperature. Differentiation of the above equation with respect to the number of moles of species i in the resin phase yields the equation from which the resin phase activity coefficient, γi, may be calculated if the parameters, Λij, are known M

ln γi ) 1 - ln[

Eθ ij(I)

ln KAB ) (zB - zA) +

Na

M

ymiΛij] - ∑ ∑ j)1 k)1

[ ] ymkΛki

(24)

M

Λkj ∑ j)1

In this equation Λii ) 1, and for nonideal systems Λij * 1. For a single binary system the above equation reduces to

ln γi ) 1 - ln(ymi + ym2Λ12) ym2Λ21 ym1 + (25) ym1 + ym2Λ12 ym1Λ21 + ym2

(

)

Smith and Woodburn19 proposed that values for the Wilson binary interaction parameters may be calculated along with the equilibrium constant using equilibrium data from a single binary system such that

[

ln λAB ) ln KAB M

∑

k)1

wk 1 - ln(

M

∑ l)1

M

ymlΛkl) -

∑

n)1

( )] ymnΛnk

M

(26)

ymlΛnl ∑ l)1

where wk is the stoichiometric coefficient of species k in the exchanger phase. Smith and Woodburn,19 along with other workers such as Shallcross et al.,20 successfully used this formulation to deter-

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007 3769

mine the equilibrium constant and two binary interaction parameters via nonlinear least-squares regression algorithms. This method enables the model to produce a close fit to the experimental data. However, the parameters obtained (KAB, ΛAB, ...) are very sensitive to slight variations in experimental data.21,22 2.2. Incorporation of the Mehablia Et al. Model. In this study, the approach of Mehablia et al.8 is utilized. The Gaines and Thomas16 approach (refer to eq 21) is used to first determine the equilibrium constant, followed by substitution into eq 26. This method decouples the effect of variations on the equilibrium constant from variations in the Wilson binary interaction parameters. A two parameter regression, to minimize a slightly modified form of the object function F′, is then performed to determine the Wilson binary interaction parameters.

(

N

(xi(1 - xi)yi(1 - yi)) ∑ i)1 F′ )

2

)

λiexp - λifit λiexp

N

(27)

[xi(1 - xi)yi(1 - yi)] ∑ i)1

2

This form of the objective function recognizes that when one of the phase compositions approaches an extreme (i.e., xi f 0 or xi f 1, or yi f 0 or yi f 1) then the experimental error associated with obtaining the data point will be much higher. The regression process produces a three-dimensional plot of the minimum objective function versus the binary interaction parameters. The surface of this plot forms a deep trough, through which a curve is fitted. This curve represents the combinations of ΛAB and ΛBA with which the objective function produces the lowest minima. To select the final ΛAB and ΛBA value for each binary equilibrium set, the Ha´la23 constraint or reciprocity relation is implemented. Two Wilson interaction binary parameters can be obtained starting from the equation

ΛAB )

VLiq B VLiq A

e(-(δAA-δBA)/RT)

(28)

Liq where VLiq A and VB are the pure liquid molar volumes and the δAB ()δBA) are proportional to the intermolecular interaction energies. The reciprocity relation can be described as follows:

ΛABΛBA ) e((δAA+δBB-2δAB)/RT)

(29)

The δAB term may be approximated by the following equations:

δAB ) (δAAδBB)1/2

(30)

δAA + δBB 2

(31)

or

δAB )

Via substitution it may be shown that

ΛABΛBA ) e0 ) 1

(32)

Therefore, the values for ΛAB and ΛBA were selected so that they fall on the lowest minima of the objective function and that their product is equal to one.

2.3. Incorporation of Temperature Dependance of Exchange. A two parameter temperature-dependent model for ion exchange may be developed by studying the effect of temperature on the equilibrium constant and interaction parameters and associating it with thermodynamic functions. The Gibbs free energy is defined as

∆GAB ° ) -RT ln KAB

(33)

As noted previously the Wilson interaction parameters vary according to eq 28, where subscripts A and B are replaced with and VLiq are the pure liquid molar volumes i and j. Hence, VLiq i j and the δij ()δji) are proportional to the intermolecular interaction energies. These relations imply that ln KAB and ln ΛAB vary linearly with the inverse of absolute temperature. The two parameter temperature-dependent model proposes use of this linear relation between the two extreme temperatures investigated in this study (277 K and 313 K). 2.4. Evaluation of Error. To evaluate and quantify the accuracies of the predictions of the ion exchange equilibrium model and the temperature dependence model, this work uses the relative residue (RR), which is defined as follows: Q

RR )

[( P

∑ ∑ i)1 j)1

)]

χmodel - χexpt χ expt

2

j

i

QP - 1

(34)

P is the number of the set of equilibrium data, Q is the number of cationic species, and χ is the quantity of interest. 3. Experimental Material, Apparatus, and Procedures 3.1. Resins and Solutions. The ion exchange medium used in the experimental study was the commercial chelating resin Amberlite IRC 748 (Rhom and Haas). The opaque, beige, spherical beads had a particle size of 0.50-0.65 mm (dry). The copper chloride and sodium chloride used were of analytical grade (Sigma Aldrich), and Milli-Q water was used for all solution preparation. To ensure all experiments were conducted on pure binary systems and because of the relatively high selectivity of Amberlite IRC 748 for hydrogen over sodium (see results section), the resin was preconditioned into the hydrogen form. Before the first use, the resin was subjected to a preconditioning process that washed it of any water soluble residues and left it in the desired hydrogen (H) form. This involved washing the resin in 0.5 mol L-1 hydrochloric acid and then rinsing with a large amount of distilled water until an effluent pH of 6 was achieved. 3.2. Cation Exchange Capacity. The cation exchange capacity of the resin was determined for the H-Na and the H-Cu binary systems using two methods. To determine the capacity of the resin for Na+ in the H-Na binary system, the hydrogen form resin was contacted with a NaCl solution for 72 h. The tests were conducted by weighing 2.5 g of NaCl into 250 mL Erlenmeyer flasks. A total of 0.25 g of hydrogen form resin was then weighed into each of the flasks. After weighing out the resin, 100 mL of Milli-Q water containing varying amounts of 0.1 mol L-1 NaOH solution was added, and the flasks were then gently agitated at 100 rpm and 20 °C for 72 h. Samples were tested for pH of the aqueous solution, and the sodium capacity was calculated by converting the pH values to hydrogen concentrations in solution (mol L-1), which can be

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directly related to the amount of hydrogen exchanged with sodium on the resin. When this process was repeated several times, the Na+ exchange capacity of the H+ form of the resin was found to be 1.29 ( 0.011 mmol g-1 of dry resin. For the H-Cu system the hydrogen form resin was contacted with a CuCl2 solution for 72 h. Tests were conducted by weighing 0.02 g of resin into 250 mL flasks. After weighing out the resin, 100 mL of CuCl2 solution at three concentrations (100, 250, and 500 mg L-1 as Cu) was added to the conical flasks and gently agitated at 100 rpm and 20 °C for 72 h. The copper concentrations in the initial and final solutions were analyzed by atomic adsorption spectrophotometry (AAS). The Cu2+ capacity was calculated by plotting the equilibrium concentration of copper on the resin with respect to the equilibrium concentration of the copper in solution. The result was a straight line through the data at constant solid-phase concentration which corresponds to the Cu2+ capacity of the resin. When this process was repeated several times, the Cu2+ exchange capacity of the H+ form of the resin was found to be 2.70 ( 0.22 mmol g-1 of dry resin. There is a significant difference between the copper and sodium adsorption/exchange capacity of Amberlite IRC 748. This behavior is not unusual for IDA adsorbents.24,25 A study by Gao and co-workers24 looked at the adsorption capacities for column pretreating chelating resins with various metals species in aqueous solutions. A cross-linked chitosan functionalized with IDA groups was investigated; it was found that the adsorption capacities for Cu(II), Pb(II), and La(III) were 0.90, 0.65, and 0.34 mmol g-1, respectively. It is thought that the difference in exchange capacity can be related to a number of resin and solution characteristics. Examples are the valence of the ion in solution, the predominant adsorption mechanism (ion exchange versus chelation), and addition of a spacer arm to the IDA containing molecule, creating an adsorbent with characteristics closer to those of free IDA in solution. 3.3. Batch Equilibrium Experiments. The equilibrium experiments were performed by placing a previously unused sample of resin of known form and mass into a 250 mL Erlenmeyer flask with precisely 100.0 mL of a solution of known composition and concentration. Preliminary tests had confirmed that 72 h was sufficient to ensure that equilibrium was attained. At the conclusion of this period, the solution was separated from the resin, and its concentration was determined by AAS. Once the equilibrium composition of the solution phase was determined, the equilibrium composition of the exchanger or resin phase was inferred by use of a simple material balance. The amount of the resin used and the composition and concentration of the solution phases were varied to ensure that a wide range of equilibrated compositions were measured. For the copper exchange experiments the initial concentrations of copper in solution were 50, 100, and 250 mg L-1 (0.001 57, 0.003 15, and 0.007 87 N), and the tests were conducted at 4, 12, 20, and 40 °C. For the sodium exchange experiments the initial concentrations of sodium in solution were 250, 450, and 1000 mg L-1 (0.0105, 0.0195, and 0.0445 N), and the tests were conducted at 4 °C and 20 °C. 3.4. Moisture Tests. As a result of the hydrophilic nature of the resin, all samples used in the equilibrium experiments were divided into two portions immediately prior to the experiments, with one portion being used for the equilibrium experiments and the other for moisture analysis. The moisture content sample of the resin was weighed and placed inside an oven at 105 °C for 24 h. This process drove off all of the interstitial as well as some of the structural moisture. The resin was then reweighed

Figure 1. Binary isotherm data and model prediction for the Cu-H system at three different concentrations and 4 °C.

immediately upon removal from the oven. The moisture content was then determined from the difference in mass before and after heating. Because heating the resin samples to 105 °C leads to irreversible changes in its properties, all samples that had been heated in this way were discarded once they had been reweighed. 4. Results 4.1. Application of the Two Parameter Thermodynamic Ion Exchange Model to Batch Equilibrium Data. As described earlier, the two parameter thermodynamic ion exchange model requires information on the stability of different compounds in solution as well as a number of empirical fitting parameters established by previous researchers. Table 1 gives the stability constants for the compounds utilized in this study.12,26 Tables 2-4 provide all of the modeling parameters required for application of Pitzer’s electrolyte solution theory, including both single salt and mixed electrolyte parameters.15,27,28 The experimental data along with the model predictions for copper-hydrogen exchange on Amberlite IRC-748 at three initial copper concentrations (0.001 57, 0.003 15, and 0.007 87 N) at four temperatures (4, 12, 20, and 40 °C) are presented in Figures 1-4. As depicted in Table 5, a single set of equilibrium constants, KAB, and Wilson interaction parameters, ΛAB, are regressed at each temperature. These regression parameters were used to describe all of the ion exchange equilibria, at the various initial solution concentrations, undertaken at that temperature. As expected, the experimental results showed there was a trend toward lower selectivity for copper over hydrogen by Amberlite IRC 748 with an increase in copper concentration in the aqueous phase, as shown by the change in the position of the ion exchange curve. This trend was consistent across the entire temperature range investigated. For all initial solution concentrations and temperatures investigated, the model predicted the relative positions and shapes of the experimental equilibria curves with a high degree of accuracy. The model was able to account for the characteristic S-shape for the experiments conducted at 4 °C, indicative of possible selectivity reversal, as well as the more typical favorable selectivity curve for the ion exchange isotherms at 40 °C.

Ind. Eng. Chem. Res., Vol. 46, No. 11, 2007 3771

Figure 2. Binary isotherm data and model prediction for the Cu-H system at three different concentrations and 12 °C.

Figure 3. Binary isotherm data and model prediction for the Cu-H system at three different concentrations and 20 °C.

The effect of temperature on the copper-hydrogen exchange is depicted in Figure 5. This figure shows the copper-hydrogen exchange system at an initial copper concentration of 0.003 15 N at the four temperatures investigated. There is a consistent increase in selectivity toward copper as temperature increases. This is confirmed by the calculated equilibrium constants presented in Table 5. There is a steady increase in the equilibrium constant with respect to temperature for copperhydrogen exchange. This is in agreement with the results obtained by other workers. Valverde et al.29 found an increase in selectivity for Cu2+, Cd2+, and Zn2+ on Amberlite IR-120, with an increase in temperature for the range of 283-303 K. Lin and Juang3 also found an increase in selectivity toward Cu2+ with an increase in temperature (15-45 °C), but this work did not fully incorporate a semiempirical thermodynamic model to the results. Similar experiments were conducted for sodium exchange onto the hydrogen form of Amberlite IRC-748. Figure 6 depicts the experimental data points and model predictions for sodiumhydrogen exchange at three exchanging concentrations (0.0105,

Figure 4. Binary isotherm data and model prediction for the Cu-H system at three different concentrations and 40 °C.

Figure 5. Effect of temperature on copper-hydrogen exchange at an initial copper concentration of 0.003 15 N. Table 5. Equilibrium Constants and Interaction Parameters, along with Calculated Relative Residues for Each of the Equilibrium Systems system (A-B)

temperature (°C)

KAB

ΛAB

Cu2+-H+ Cu2+-H+ Cu2+-H+ Cu2+-H+ Na+-H+ Na+-H+

4 12 20 40 4 20

0.051 0.063 0.084 0.111 0.000307 0.000210

3.83 2.03 2.30 1.92 0.22 0.19

model prediction RR

temperature model RR

0.052 0.0359 0.1804 0.085

0.0978 0.3187

0.0195, and 0.0445 N), at 4 °C. Figure 7 depicts a plot of the logarithm of the equilibrium quotient against the equivalent ionic fraction of sodium in the resin phase, used to determine the equilibrium constants, while Table 5 depicts the equilibrium constants obtained. The experimental and model results show that the resin is significantly more selective for hydrogen over sodium at the temperatures and concentrations investigated. The equilibrium constants for the Cu-H system are greater than the Na-H system by 3 orders of magnitude. As the resin is so

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Figure 6. Binary isotherm data and model prediction for the Na-H system at three concentrations and at 4 °C.

Figure 8. ln(equilibrium constant) versus inverse absolute temperature for the copper-hydrogen system.

Figure 7. ln(equilibrium quotient) versus equivalent ionic fraction in the exchanger phase.

Figure 9. Use of the two parameter temperature-dependent model for copper-hydrogen exchange on Amberlite IRC-748.

unselective for sodium it was not possible to determine an increase or decrease of selectivity with respect to temperature with any degree of certainty. 4.2. Evaluation of the Model and Error Analysis. A graphical representation of ln KAB versus inverse absolute temperature for the copper-hydrogen system is presented in Figure 8, and a similar plot may also be presented for ln ΛAB verses inverse absolute temperature. This figure depicts a linear relation, as suggested by the Gibbs free energy function. A linear equation to describe the variation in the regression parameters, ln KAB and ln ΛAB, with changes in the inverse of absolute temperature was then evaluated. This equation only utilized the data points taken at the temperature extremes (4 °C and 40 °C). As the experimental data points suggest the relation to be linear, this equation may be used to describe the regression parameters at temperatures between the extreme temperatures. The two equations are

These equations were then used to calculate new values for the equilibrium constant and the interaction parameters for the intermediate temperatures (12 °C and 20 °C) and then applied to the semiempirical thermodynamic model, to produce new predictions for the equilibrium curves. Such a prediction for 20 °C is represented in Figure 9, and the relative residues for the 20 °C and 12 °C predictions are presented in Table 5. The model prediction results in relative residues for 12 and 20 °C of 0.0359 and 0.1804, respectively. Using the straight line relation between 4 and 40 °C to determine the equilibrium constant and interaction parameters at 12 and 20 °C, the relative residues are 0.0978 and 0.3187, respectively. These results show that while the temperature model based on the highest and lowest predictions is not as accurate for prediction of equilibrium curves than if actual equilibrium data for the intermediate temperatures is utilized, a reasonable result can still be obtained. The error analysis found that the model prediction was most accurate at the highest and lowest temperatures, with a relative residue of 0.052 for the 4 °C data and a relative residue of 0.085 for the 40 °C data (see Table 5). The model predictions for the

ln KAB ) -1853.8(1/T) + 3.7236

(35)

ln ΛAB ) 1658.9(1/T) - 4.6471

(36)

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intermediate temperatures were somewhat less accurate; however, these results do not account for the possibility of experimental error which may have played a role in the intermediate temperature results. Overall the relative residue and absolute errors of the model predictions to the equilibrium data sets are thought to be reasonable considering the extremely low concentrations of copper utilized in this study. 5. Conclusions The temperature-dependent behavior of two binary systems (H-Cu and H-Na) were investigated using the chelating cation exchange resin, Amberlite IRC 748. A semiempirical thermodynamic model incorporating temperature dependence showed good agreement with experimental equilibrium data for all systems, concentrations, and temperatures investigated. The resin was found to have high selectivity for copper, which increased with increasing temperature but decreased with increasing copper concentration in solution. The selectivity of the resin for sodium over hydrogen was highly unfavorable, and it was not possible to determine a strong trend with increasing temperature for the H-Na system. The quality of the predictions were confirmed using relative residue techniques, and the relative residue values of the model predictions were found to be low over the concentration and temperature ranges investigated. Acknowledgment The authors would like to thank Jeremy Lane, University of Melbourne, for his assistance with the ion exchange experiments. In addition the authors would like to acknowledge funding support provided by the Particulate Fluids Processing Centre, a Special Research Centre of the Australian Research Council, as well as funding support from the Australian Antarctic Science (AAS) grant program (ASAC 1300, 2570) through the Australian Antarctic Division. Literature Cited (1) Da¸ browski, A.; Hubicki, Z.; Podkos´cielny, P.; Robens, E. Selective removal of the heavy metal ions from waters and industrial wastewaters by ion-exchange method. Chemosphere 2004, 56, 91. (2) Woinarski, A. Z.; Stevens, G. W.; Snape, I. A natural zeolite permeable reactive barrier to treat heavy-metal contaminated waters in Antarctica. Kinetic and Fixed-bed studies. Process Saf. EnViron. Prot. 2006, 84 (B2), 109. (3) Lin, L.-C.; Juang, R.-S. Ion-exchange equilibria of Cu(II) and Zn(II) from aqueous solutions with Chelex 100 and Amberlite IRC 748 resins. Chem. Eng. J. 2005, 112, 211. (4) Seggiani, M.; Vitolo, S.; D’Antone, S. Recovery of nickel from Orimulsion fly ash by iminodiacetic acid chelating resin. Hydrometallurgy 2006, 81, 9. (5) Mendes, F. D.; Martins, A. H. Selective sorption of nickel and cobalt from sulphate solutions using chelating resins. Int. J. Miner. Process. 2004, 74, 359. (6) Vilensky, M. Y.; Berkowitz, B.; Warshawsky, A. In Situ Remediation of Groundwater Contaminated by Heavy- and Transition-Metal Ions by Selective Ion-Exchange Methods. EnViron. Sci. Technol. 2002, 36, 1851. (7) Woodberry, P.; Stevens, G.; Northcott, K.; Snape, I.; Stark, S. Field trial of ion-exchange resin columns for removal of metal contaminants,

Thala Valley Tip, Casey Station, Antarctica. Cold Reg. Sci. Technol. 2007, 48, 105. (8) Mehablia, M. A.; Shallcross, D. C.; Stevens, G. W. Prediction of Multicomponent Ion Exchange Equilibria. Chem. Eng. Sci. 1994, 49, 2277. (9) Argensinger, W. J.; Davidson, A. W.; Bonner, O. D. Thermodynamics and Ion Exchange Phenomena. Trans. Kansas Acad. Sci. 1950, 53, 404. (10) Pitzer, K. S. ActiVity Coefficients in Electrolyte Solutions; CRC Press: Boca Raton, 1991. (11) Wilson, G. M. Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127. (12) Kester, D. R.; Pytkowicz, R. M. Sodium, Magnesium and Calcium Sulphate Ion-Pairs in Seawater at 25°C. Limnol. Oceanogr. 1969, 14, 686. (13) Johnson, K. S.; Pytkowicz, R. M. Ion Association of Cl- with H+, Na+, K+, Ca2+ and Mg2+ in Aqueous Solutions at 25°C. Am. J. Sci. 1978, 278, 1428. (14) Pitzer, K. S.; Mayorga, G. J. Thermodynamics of Electrolytes. II Activity and osmotic coefficients for strong electrolytes with one or both ions univalent. J. Phys. Chem. 1973, 77, 2300. (15) Pitzer, K. S.; Peiper, K. S.; Busey, R. H. Thermodynamic properties of aqueous sodium chloride solutions. J. Phys. Chem. Ref. Data 1984, 13, 1. (16) Gaines, G. L.; Thomas, H. C. Adsorption studies on clay minerals. II. A formulation of the thermodynamics of exchange adsorption. J. Chem. Phys. 1952, 21, 714. (17) Elprince, A. M.; Babcock, K. L. Prediction of Ion Exchange Equilibria in Aqueous Systems with more than two counter-ions. Soil Sci. 1975, 120, 332. (18) Wilson, G. M. Vapor-liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127. (19) Smith, R. P.; Woodburn, E. T. Prediction of multicomponent ion exchange equilibria for the ternary system SO42- - NO3- - Cl- from data of binary systems. AIChE J. 1978, 24, 577. (20) Shallcross, D. C.; Herrmann, C. C.; McCoy, B. J. An improved model for the prediction of multicomponent ion exchange equilibria. Chem. Eng. Sci. 1988, 43, 279. (21) Allen, R. M.; Addison, P. A.; Dechapunya, A. A. The characterization of binary and ternary ion exchange equilibria. Chem. Eng. J. 1989, 40, 151. (22) Mehablia, M. A.; Shallcross, D. C.; Stevens, G. W. The Wilson equation applied to the non-idealities of the resin phase of multicomponent ion exchange equilibria. Presented at IEX ’92, Cambridge, July 1992. (23) Ha´la, E. Letter to the editor. AIChE J. 1972, 18, 876. (24) Gao, Y.; Oshita, K.; Lee, K.-Y.; Oshima, M.; Motomizu, S. Development of column pretreatment chelating resins for matrix elimination/ multi-element determination by inductively coupled plasma-mass spectrometry. The Analyst 2002, 127, 1713. (25) Chen, C.-Y.; Chiang, C.-L.; Huang, P.-C. Adsorptions of heavy metal ions by a magnetic chelating resin containing hydroxy and iminodiacetate groups. Sep. Purif. Technol. 2006, 50, 15-21. (26) Dean, J. A. Lange’s handbook of chemistry; McGraw-Hill Professional Publishing: New York, 1992. (27) Haung, H. H. Estimation of Pitzer’s ion interaction parameters for electrolytes involved in complex formation using a chemical equilibrium model. J. Solution Chem. 1989, 18, 1069. (28) Clegg, S. L.; Whitfield, M. A chemical model of seawater including dissolved ammonia and the stoichiometric dissociation constant of ammonia in estuarine water and seawater from -2 to 40 degrees C. Geochim. Cosmochim. Acta 1995, 59, 2403. (29) Valverde, J. L.; de Lucas, A.; Gonza´lez, M.; Rodriguez, J. F. Equilibrium Data for the Exchange of Cu2+, Cd2+, and Zn2+ Ions for H+ on the Cationic Exchanger Amberlite IR-120. J. Chem. Eng. Data 2002, 47, 613-617.

ReceiVed for reView November 30, 2006 ReVised manuscript receiVed February 25, 2007 Accepted March 19, 2007 IE0615436