Potentiometric and solubility studies of association quotients of aluminum malonate complexation in...

transcript

PII S0016-7037(98)00143-4

Potentiometric and solubility studies of association quotients of aluminum malonatecomplexation in NaCl media to 75°C

MOIRA K. RIDLEY,1,* DONALD A. PALMER,2 DAVID J. WESOLOWSKI,2 and RICHARD M. KETTLER1

1Department of Geology, University of Nebraska, Lincoln, Nebraska 68588-0430, USA2Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6110, USA

(Received September10, 1997;accepted in revised form March26, 1998)

Abstract—A potentiometric method was used to determine the formation quotients for aluminum-malonate(Al(Ma)y

322y, Ma [ CH2(CO2)222) complexes from 5 to 75°C at four ionic strengths from 0.1 to 1.0 molal in

aqueous NaCl media. Two mononuclear aluminum-malonate species, Al(Ma)1 and Al(Ma)22, were identified,

and the formation quotients for these species were modeled by empirical equations to describe theirtemperature and ionic strength dependencies. Differentiation of the two empirical equations with respect totemperature provided thermodynamic quantities for the Al-malonate complexes. The thermodynamic quan-tities obtained for Al(Ma)1 at 25°C and infinite dilution are: log K1 5 7.496 0.18,DH°1 5 196 5 kJ z mol21,DS°1 5 2086 18 J z K21 z mol21 andDC°p1 5 3316 120 Jz K21 z mol21; whereas the values for Al(Ma)2

are: log K2 5 12.626 0.40,DH°2 5 29 6 10 kJ z mol21, DS°2 5 3406 36 J z K21 mol21 andDC°p2 5 5756 230 Jz K21 mol21. These thermodynamic values indicate that Al(Ma)1, a chelate complex, is much morestable than the equivalent monodentate Al-diacetate complex (Al(Ac)2

1) (Palmer and Bell, 1994). A solubilitystudy, which was undertaken to verify the 50°C potentiometric data, was performed by reacting powderedgibbsite (Al(OH)3) with malonic acid solutions at 0.1 molal ionic strength in aqueous NaCl media. The resultsof the solubility study are in excellent agreement with the potentiometric data.Copyright © 1998 ElsevierScience Ltd

1. INTRODUCTION

The potential for carboxylic and dicarboxylic acids to complexmetal ions (Drever and Vance, 1994; Fein, 1991, 1994; Gior-dano, 1994; Kawamura and Kaplan, 1987; Kharaka et al., 1993;Pittman and Lewan, 1994; Shock, 1995; Shock and Koretsky,1993, 1995; Surdam et al., 1984) has generated considerableinterest in the geochemical role of these acids in a variety ofprocesses, including: (1) transporting metals in hydrothermalsystems and sedimentary basins (Barth et al., 1989; Giordano,1994; Hennet et al., 1988; Shock, 1995; Shock and Koretsky,1993, 1995); (2) the development and preservation of second-ary porosity in aluminosilicate minerals (Fein, 1994; Harrisonand Thyne, 1992; Kharaka et al., 1993; Surdam et al., 1984);(3) enhancing mineral dissolution and weathering rates(Carothers and Kharaka, 1978; MacGowan and Surdam, 1990;Welch and Ullman, 1993); (4) increasing contaminant transport(Bennet and Siegel, 1987; Bennet et al., 1988; Fein et al.,1995); (5) biogeochemical cycling of metals (Fein and Brady,1995); and (6) buffering the pH and Eh of natural aqueousfluids (Kharaka et al., 1993). Despite this diverse interest in thecarboxylic acids, the thermodynamic data required to evaluateand quantify the role of these acids in such varied geochemicalprocesses are limited at elevated temperatures.

Equilibrium data have been determined experimentally forfew metal-dicarboxylic acid complexes (Athavale et al., 1967;Fein and Hestrin, 1994; Fein et al., 1995; Harrison and Thyne,1992; Marklund and O¨ hman, 1990; Marklund et al., 1989; Nairand Nancollas, 1961; O¨ hman, 1988, 1991; Sedeh et al., 1992;Shock and Koretsky, 1993, 1995; Sjo¨berg and O¨ hman, 1985;

Tedesco and Gonza´lez Quintana, 1974). Although thermody-namic data for metal-dicarboxylate and metal-carboxylate com-plexes have been estimated empirically by Harrison and Thyne(1992), discrepancies were noted between this database andother works (Kettler et al., 1995). Despite interest in the role ofAl-malonate complexes in the formation of secondary porosityand other geochemical processes, equilibrium data for the for-mation of these complexes have been determined over re-stricted ranges of temperature and ionic strength (Table 1).

This paper presents the results of a potentiometric studyundertaken to determine the speciation and association quo-tients for the complexation of Al with malonate and to provideempirical equations that describe the temperature and ionicstrength dependencies of the formation quotients. Solubilityexperiments performed at 50°C were undertaken to validate thepotentiometric data and to examine the effect of malonic acidon the solubility of gibbsite (and by analogy, other Al-bearingminerals). The thermodynamic data and empirical equationspresented in this paper provide the necessary information toassess the role of Al-malonate complexes in geochemical pro-cesses such as those outlined above and may be used to modelAl-malonate speciation at geochemically relevant conditions.

2. EXPERIMENTAL

2.1. Potentiometric Titrations

2.1.1. Materials

Three solutions at each ionic strength (0.1, 0.3, 0.5, and 1.0 molal)were prepared by diluting concentrated stock solutions of HCl, NaOH,NaCl, AlCl3, and malonic acid with distilled, deionized water. Theprocedures followed for the preparation, standardization, and storage ofthe HCl, NaOH, NaCl, and AlCl3 stock solutions were described byPalmer and Wesolowski (1993). The malonic acid was prepared bydrying crystalline solid (Aldrich lot # 03903 AG) in a vacuum oven at

*Present address:Chemical and Analytical Sciences Division, OakRidge National Laboratory, Oak Ridge, Tennessee 37831-6110, USA.

Pergamon

0016-7037/98 $19.001 .00

50°C for at least 2 h, dissolving it in purified water, then standardizingit against the NaOH stock solution by acidimetric titration.

The compositions of the test, reference and titrant solutions usedin each titration are given in Table 2. All test and reference solutionswere prepared with a hydrogen ion concentration greater than 1023

molal in order to minimize Al-hydrolysis. The hydrogen ion con-centration and ionic strength of corresponding test and referencesolutions were matched as closely as possible, whereas the ionic

strength of the titrant solutions was slightly higher. By increasingthe ionic strength of the titrant solutions, it was possible to maintaina near constant ionic strength throughout the titrations. Titrantsolutions were prepared with a malonic acid to bimalonate ratio of1:3 calculated using the acid dissociation quotients of Kettler et al.(1992), thus fixing pH at approximately 3. (Note that throughout thisstudy pH 5 2log[H1] in molal concentration as discussed byMesmer, 1991).

2280 M. K. Ridley et al.

2.1.2. Equipment and procedure

Titrations were performed at four temperatures (5, 25, 50, and 75°C)with the upper temperature limit constrained by the thermal stability ofmalonic acid, which thermally decomposes below 100°C (Hall, 1949;Kettler et al., 1992). The hydrogen-electrode concentration cell andauxiliary equipment used, and the titration procedures followed inperforming the potentiometric titrations have been described previously(Giordano and Drummond, 1991; Kettler et al., 1991; Mesmer et al.,1970; Palmer and Bell, 1994). In this study, the configuration of theconcentration cell prior to the addition of titrant was

Pt, H2 u HCl, AlCl3, NaCl uu HCl, NaCl u H2, Pt

Test Reference

The experiments proceeded by the addition of titrant into the Al-testsolution in aliquots increasing in size from 0.2 mL to 2.0 mL over thecourse of a titration. As in earlier studies (Palmer and Bell, 1994;Palmer and Wesolowski, 1993), the cell potential was recorded bysignal averaging, which included fifty readings taken over a 2-minperiod, providing an accuracy of60.05 mV. After an addition oftitrant, the cell potential was considered stable when a constant poten-tial (60.01 mV) was recorded for three consecutive readings (ca. 6min). Performing the titrations by adding a malonic acid titrant to anAl-test solution (rather than the reverse) allowed the concentration ofmalonate to be changed over a broad range. For example, during atypical titration the ratio of total Al to total malonic acid changed from1:0 to 1:4. The broad range in the concentration of malonic acidprovided a wide variation in the degree of association, which wasfavorable in accurately constraining the association quotients and re-action stoichiometry when more than one complex was formed, i.e.,Al(Ma)y

322y, y 5 0–2. In contrast to the broad range in malonic acidconcentrations, the maximum range in pH was from 3.02 to 2.02; whichminimized the formation of Al-hydrolysis species (Palmer and Wes-olowski, 1993).

2.2. Solubility Experiments

2.2.1. Materials

A set of four solutions were prepared from the concentrated NaOH,NaCl, and malonic acid stock solutions used for the potentiometrictitrations. In addition, acetic acid prepared from glacial acetic acid(Mallinckrodt analytical reagent, lot 3121 KAHH) and standardizedagainst the NaOH stock solution by acidimetric titration, was includedin the experimental solutions. The experimental solutions were pre-pared at 0.1 molal ionic strength, an initial hydrogen ion concentrationof 1023.5 molal, and total molal malonate concentrations (includingprotonated and complexed forms) between 0.004 and 0.04 molal; thecomposition of each experimental solution is given in Table 3. Aceticacid was added to the experimental solutions in order to buffer pH and,therefore, constrain the pH to a limited range as the solubility experi-ments progressed. The narrow range in pH minimized the formation ofAl-hydrolysis species. The ionic strength of each solution was recal-culated at the end of the solubility experiment, based on the reaction

with gibbsite (no significant changes were observed except at thehighest malonate concentrations).

The gibbsite used in these experiments is from the same batch ofpure, synthetic gibbsite (Alcoa composition C–31) as that used inearlier studies performed in this laboratory (Ridley et al., 1997; We-solowski, 1992; Wesolowski and Palmer, 1994). Wesolowski (1992)described the pre-treatment and characterization of the gibbsite follow-ing the procedure of Bloom and Weaver (1982).

2.2.2. Experimental procedure and analytical method

In duplicate experiments, approximately 4 g of gibbsite and 40 g ofexperimental solution were loaded into 50 mL, disposable, sterile,polypropylene/polyethylene syringes. The syringes were then mountedon a rotating rack, in a thermostated water bath at 50°C6 0.05°C andallowed to react for four days, at which point the solution was dis-carded, replaced with fresh starting solution, and then the syringes werereturned to the water bath. The syringes were sampled after 21, 30, 44,51, 69, 111, and 184 days. At each sampling the syringes were fittedwith a 0.2 mm poly(vinylidene fluoride) (PVDF) membrane filterthrough which a small volume of solution was initially dispensed anddiscarded. A filtered aliquot of each experimental solution was imme-diately diluted by weight-addition with 0.01N HCl for analysis of thetotal dissolved Al content, by ion chromatography. All Al analyzeswere completed within two days of sampling.

In addition to measuring the total dissolved Al concentration of theexperimental solutions, the pH of the solutions was also measured at50°C during the course of the study, following the procedure describedby Wesolowski and Palmer (1994). After sampling the syringes for Alanalysis, an additional filtered sample was collected in a 5 mLdispos-able, polypropylene/polyethylene syringe and placed in a second ther-mostated water bath at 50°C. A Ross glass pH electrode was equili-brated at 50°C, then standardized with four solutions containing 0.001to 0.03 molal HCl in NaCl media at 0.1 molal ionic strength. Acalibration curve was established by recording the potential reading (inmillivolts) of each standard solution. The potential of each sample wasthen measured at 50°C and the H1 concentration calculated from thecalibration curve. No drift in the potential readings of the standards wasobserved during the period required to measure the eight samples.

3. RESULTS

The effectiveness of the potentiometric technique as appliedin this study relies on the competition between H1 and Al31 forassociation with the malonate anions, providing the acid/basechemistry of malonate and Al are known (Kettler et al., 1992;Wesolowski and Palmer, 1994). The concentration of hydrogenions in the test solution ([Htest

1 ]), therefore, provides an accuratemeasure of the degree of complexation between Al31 andmalonate. The molal concentration of hydrogen ions in the test

Table 3. Summary of the starting molal (molzkg21) solution compo-sitions for the dissolution of gibbsite at 50°C and 0.1 molal ionicstrength.

2281Auminum-malonate complexation

solution can be related to the observed cell potential by apply-ing the Nernst equation

2log [Htest1 ] 5

2.303F

RT(E 1 ELJ) 2 log [Href

1 ] (1)

where F is the Faraday constant; R the universal gas constant;T is temperature in Kelvin; [Href

1 ] the known hydrogen ionconcentration of the reference solution; and E and ELJ representthe measured cell potential and calculated liquid junction po-tential, respectively (Ridley, 1997). The liquid junction poten-tial was calculated using the full Henderson equation (Eqn.[2–12] in Baes and Mesmer, 1976), which is considered to beaccurate to within 25% if the limiting equivalent conductancesof the relevant species are known (Mesmer and Holmes, 1992).Limiting equivalent conductance data are known for H1, Na1,and Cl2 (Quist and Marshall, 1965), but data for the Al31,malonate and Al-malonate species have not been measuredover the temperature ranges considered in this study. Thelimiting equivalent conductance of the univalent, negatively-charged malonate species (bimalonate and Al-dimalonate(Al(Ma)2

2) were, therefore, modeled using the conductancedata for bisulphate, whereas malonate was modeled as sulphate(Quist and Marshall, 1965), and Al-malonate (AlMa1) as Na1.Conductance values for Al31 were assumed equivalent to val-ues for La31 (Robinson and Stokes, 1959). These and similarassumptions have been used previously by this laboratory(Giordano and Drummond, 1991; Kettler et al., 1991, 1992;Palmer and Bell, 1994; Palmer and Drummond, 1988; Palmerand Wesolowski, 1993) and contribute little to the uncertaintyassigned to the liquid junction potential. For all titrations, thecalculated liquid junction potentials were small, particularly atthe higher ionic strengths. A maximum calculated liquid junc-tion potential of21.485 mV was calculated at an ionic strengthof 0.1 molal and 75°C, which contributes an uncertainty of,0.014 in the pH of the test solution, assuming that theHenderson equation predicts ELJ to within 25% (Mesmer andHolmes, 1992).

The hydrogen ion ([Htest1 ]), free malonate ([Ma22]), and free

aluminum ([Al31]) concentrations were calculated using aniterative process involving the Nernst expression (Eqn. 1), thedissociation quotients of malonic acid and water (Kettler et al.,1992; Busey and Mesmer, 1978, respectively), and a stepwiserefinement of the ELJ and the ionic strength terms. A summaryof the results for each titration (E, ELJ, n# , pH, SAl and SMa)were presented by Ridley (1997). The degree of complexationbetween Al31 and malonate is defined conventionally (Baesand Mesmer, 1976) in terms of n# ; which is calculated from

n# (obs) 5Sy[Al(Ma)y

SAl 2 S[Al(OH)p32p]

5SMa 2 ([Ma22] 1 [HMa2] 1 [H2Ma])

SAl 2 S[Al(OH)p32p] (2)

SMa 2 [Ma22]S11[H1]2

SAl 2 S[Al(OH)p32p]

when assuming the formation of only mono-aluminum speciesand no mixed complexes. The numerator of Eqn. 2 reflects all

malonate bound to Al31; and the denominator is the totalstoichiometric aluminum concentration, corrected for the pres-ence of Al-hydrolysis species. The concentration of associatedmalonate is given by the initial stoichiometric concentration ofmalonic acid,SMa, minus the calculated molality of malonate,bimalonate, and malonic acid; [H1], Q1 and Q2 represent thecalculated molality of hydrogen ions and the dissociation quo-tients of malonic acid (Kettler et al., 1992), respectively.

The correction applied to the denominator of Eqn. 2 wasneeded in order to preserve the conventional definition of n#(Baes and Mesmer, 1976) as the average number of ligandsbound perfree metal ion in the solution. By this convention n#would then approach unity if the only significant species insolution were Al(Ma)1 and Al(OH)p

32p, p . 0, regardless ofpH. Assuming the formation of Alm(OH)pMaq complexes werenegligible at the pH conditions employed in this study then

[Al 31] 1 S[Al(Ma)y322y] [ SAl 2 S[Al(OH)p

32p] (3)

The concentration Al-hydrolysis species,S[Al(OH)p32p], were

computed iteratively using the well established Al-hydrolysisformation quotients of Wesolowski and Palmer (1994). In alltitrations the concentration of Al(OH)21 was low and de-creased rapidly during the course of a titration (Fig. 1). Withthe exception of one titration,SAl present as Al(OH)21 com-prised less than 5.5% of the total Al concentration. For a singletitration at an ionic strength of 0.1 molal and 75°C, Al(OH)21

contributed 8.25% to the total Al concentration at the start ofthe titration.

All n# values computed for a given titration were regressedusing a simultaneous non-linear least-squares fitting routine(Busing and Levy, 1962) to establish the appropriate speciationand formation quotients of complexes formed between Al31

and malonate according to Eqn. 4.

n# (calc) 5SyQy[Al 31][Ma22]y

(Al 2 S[Al(OH)p32p] (4)

Equation 4 is derived from Eqn. 2 by substituting [Al(Ma)y322y]

for the formation quotient, Qy, which is defined as

Fig. 1. The progress of a typical titration is shown on the ordinate asthe concentration of total Al3 103m; free Al31 3 103m; free malonate3 103m; AlOH21 3 103m; pH; and the ligand number (n# ), vs. the totalconcentration of malonate. The titration results shown in the plot are fora titration performed at 50°C and 0.5 m ionic strength.

Qy 5[Al(Ma)y

[Al 31][Ma22]y 5 Ky

gAl 31gMa22y

gAl(Ma)y322y

where Ky is the corresponding equilibrium constant at infinitedilution and gi are the individual ionic activity coefficients(Giordano and Drummond, 1991; Palmer and Bell, 1994;Palmer and Drummond, 1988). Two mononuclear Al-malonatecomplexes, AlMa1 and Al(Ma)2

2, were identified and are de-scribed by the reaction

Al31 1 yCH2C2O422º Al(CH2C2O4)y

322y (6)

where y is# 2. Agreement between the experimental n# values(n#obs, Eqn. 2) and the modeled n# values (n#calc, Eqn. 4)calculated from the least-squares fitting routine was good(Giordano and Drummond, 1991; Palmer and Bell, 1994;Palmer and Drummond, 1988). Examples of the agreementbetween n#obs and n#calc are shown in Fig. 2 for a selection oftitrations at 1.0 molal ionic strength. Ion pairing, includingNa-malonate°, NaCl°, HCl°, etc., is not assumed, but isimplicitly incorporated into the stoichiometric molal activitycoefficient model.

The formation of Al-malonate species other than AlMa1 andAl(Ma)2

2 was expected to be negligible, as good agreement wasobserved between the experimental and modelled n# values.Experiments were, however, performed to test for the possibleformation of polynuclear Al-malonate (AlyMa3y22) species.The total Al concentration was increased by a factor of 4 in a1.0 molal ionic strength test solution (Table 2), in order to favorthe formation of multiple Al ion complexes. Agreement be-tween n#obs and the n# values calculated from the least-squaresfitting routine (n#calc) was good, which attests to the absence ofpolynuclear species. In addition, it was necessary to determinewhether Al-bimalonate complexes (Al(HMa)y

32y) formed. Astudy by Tedesco and Gonza´lez Quintana (1974) reported that

under low pH conditions, such as used in this study, Al-bimalonate complexation predominates. Tedesco and Gonza´lezQuintana (1974) suggest that Al-malonate species would onlyform at higher pH conditions (i.e., [CH2C2O4

22] .[CH2C2O4H

2]). Therefore, a titration was performed using a1.0 molal ionic strength test solution in which the initial pH wasincreased from 2.3 to 3.7 (Table 2), thus favoring the formationof Al-malonate species. As before, the AlMa1 and Al(Ma)2

complexes were considered when regressing the n# values com-puted for this titration, and agreement between the n#obs andn#calc values was good. The correct identification of the AlMa1

and Al(Ma)22 species was confirmed by the consistency be-

tween the 1.0 molal ionic strength titrations, in which either theAl concentration or pH of the test solutions were varied. Thisagreement also indicates that Al-hydrolysis species were cor-rectly accounted for. The molal formation quotients resultingfrom this least-squares fitting procedure are listed for eachtitration in Table 4.

The total Al concentrations at each sampling, and the mea-sured pH values are shown in Table 5, and plotted as a functionof time in Fig. 3. As apparent from Fig. 3, the malonatesolutions closely approached equilibrium with the gibbsite bythe first sampling (21 days). Variations observed in the con-centration of measured Al from the first sampling until the endof the study are within the precision of the sampling technique(Wesolowski and Palmer, 1994). The results of samples 1 to 6showed a covariance (standard deviation/mean concentration ofmeasured Al) of better than 3.0%; whereas samples 7 and 8 hada higher covariance (6.8%) showing greater relative error onaccount of their high Al concentrations. It must be noted that allexperiments were equilibrated from complete undersaturation(SAl 5 zero) and that the study was performed to verify thepotentiometric data for the formation of Al-malonate com-plexes and not to examine the kinetics of gibbsite dissolution.

In the absence of complexing species, the dissolution ofgibbsite is controlled by

Al(OH)3 1 3Hº Al31 1 3H2O (7)

and the hydrolysis of Al31

Al31 1 yH2Oº Al(OH)y32y 1 yH1 (8)

The concentration of total dissolved Al would, therefore, equal{[Al 31] 1 S[Al(OH)y

32y]} (Fig. 4). In this study only theAlOH21 and Al(OH)2

1 hydrolysis species were significant, asall other species are negligible at pH values less than five(Wesolowski and Palmer, 1994; Fig. 4). It is apparent fromFigs. 3 and 4, however, that the concentration of total dissolvedAl is not only a function of pH (Eqn. 7), but also a function ofthe stoichiometric concentration of malonate. Clearly, the sol-ubility of gibbsite is significantly enhanced by the presence ofmalonate (Fig. 4). The addition of malonate and acetate re-quires consideration of Al-malonate and Al-acetate species.The total dissolved Al in the experimental solutions is, there-fore, described by the mass balance equation:

Fig. 2. An example of the agreement between the n# values deter-mined by Eqn. 2 (n#obs) and calculated n# values (n#calc) from the least-squares fitting routine (Eqn. 4), when considering the AlMa1 andAl(Ma)2

2 complexes, are shown for a selection of titrations at 1.0 molalionic strength. The n#obsvalues are shown as symbols at temperatures of(● ) 5, (C ) 25, (n ) 50, and (▫) 75°C, whereas the solid lines representthe n#calc values (Eqn. 4).

SAl 5 [Al 31] 1 [Al(OH)21] 1 [Al(OH)21] 1 [AlMa1]

1 [Al(Ma)22] 1 [AlAc 21] 1 [Al(Ac) 2

1] (9)

Model calculations ofSAl in terms of these species at theknown solution composition and pH conditions of each exper-imental solution in the solubility study, will be presented be-low.

4. DISCUSSION

To provide empirical equations that described the tempera-ture and ionic strength dependence of the formation quotientsfor each complex obtained from the potentiometric titrations,the association quotients for AlMa1 and Al(Ma)2

2 (Table 4)

Fig. 3. Plot of the total dissolved aluminum, representing the disso-lution of gibbsite as a function of time, in malonic acid—NaCl mediaat 50°C. The symbols represent total malonic acid concentrations of (●)0.004 m; (n) 0.008 m; (Œ) 0.02 m; and (� ) 0.04 m. (The open andfilled symbols distinguish between duplicate samples). The connectinglines have been drawn for reference only.

were regressed, using the nonlinear least-squares fitting routineof Busing and Levy (1962). Criterion used to determine theempirical equations that best fitted the data are outlined byGiordano and Drummond (1991) and Palmer and Bell (1994).The empirical equations that best described the AlMa1 andAl(Ma)2

2 association quotients and required the fewest numberof adjustable parameters are defined by

log Qy 52Dz2Aw

ln (10) H ÎI

(11bÎI)1 Sa

bD ln ~1 1 bÎI!J1 p1 1

T1 p3T 1 p4I z T 1 p5F(I) 1 p6F(I) z T (10)

where F(I) is:

F(I) 5 1.02 exp (22.0 ÎI) (1.0 1 2.0 ÎI) (11)

The first term of Eqn. 10 comprises the extended Debye-Hu¨ckelexpression from Pitzer (1973) and includesa, b and Aw takenfrom Bradley and Pitzer (1979) and the limiting slope coeffi-cient (Dz2). The Dz2 value expresses the difference in thesquare of the charge of the complexed species(Al(CH2C2O4)y

322y) and the sum of the squares of eachcomponent ion’s charge multiplied by its stoichiometric coef-ficient (Al31 and y(CH2C2O4)

22) Eqn. 6). Thus,Dz2 5 212for the formation of AlMa1, and216 for Al(Ma)2

2 in Eqn. 10.Values for the variable parameters (p126) shown in Eqn. 10 aregiven in Table 6. Terms p12p3 define the equilibrium constant(log Ky) at infinite dilution. The additional three terms (p426),are functions of ionic strength and are required to fit thedeviation from the Debye-Hu¨ckel expression at finite ionicstrengths.

The goodness of fit between Eqn. 10 and the formationquotients given in Table 4 are shown for both associatedspecies in Figs. 5 and 6. The agreement between the asso-ciation quotients and modelled curves and between duplicatetitrations is excellent. The slightly poorer agreement at 0.1molal ionic strength arises from the increased difficulty inaccurately measuring complexation reactions at low ionicstrength: any small change in ionic strength caused bycomplexation is significant. The association quotients increasein stability with increasing temperature and decreasing ionicstrength, as is expected for electrostatic interactions in adielectric medium (Giordano and Drummond, 1991; Palmerand Bell, 1994).

Differentiation of Eqn. 10 with respect to temperature yieldsthe thermodynamic quantitiesDH, DS and DCp; values forthese parameters, at select temperatures and ionic strengths aregiven in Tables 7 and 8. The enthalpy, entropy, and heatcapacity values, at all conditions, are large and positive andincrease with increasing temperature. The increase in stabilityof the association quotients with increasing temperature(Figs. 5 and 6), results from the change inDS to morepositive values, which outweighs the positive change inDHvalues, and clearly drives the complexation reaction. TheDCp

values are larger for the formation of Al(Ma)22 (Table 8) than

AlMa1 (Table 7), which results from the greater charge neu-tralization for the formation of Al(Ma)2

2 (Dz25 216) com-pared with AlMa1 (Dz25 212), causing a greater restructuringof the solvating water. The thermodynamic trends mentionedabove are consistent with those observed in previous complex-ation studies (Giordano and Drummond, 1991; Palmer andBell, 1994; Palmer and Drummond, 1988) and are characteris-tic of association reactions in which electrostricted water isreleased.

Fig. 4. The logarithm of total dissolved Al concentrations measuredin the gibbsite solubility study (M) after 111 days are compared tocalculated Al concentrations (f) (Eqn. 9). The procedure followed tocalculate the Al concentrations is outlined in the text. In addition, theplot shows the distribution of the total Al-acetate species (SAl(Ac)q

32q)(�) for the experimental solutions; and the distribution of Al31 andAl-hydrolysis species as a function of pH (light curves), which werecomputed from the model of Wesolowski and Palmer (1994). In theabsence of any complexing species the concentration of dissolvedaluminum in a solution at equilibrium with gibbsite is shown by theheavy curve {[Al31] 1 S[Al(OH)p

32p]}.

The concentration of total dissolved Al in equilibriumwith gibbsite was calculated for each solution in the 50°solubility experiment using an iterative process and a step-wise refinement of each solution’s ionic strength. This rou-tine included the aluminum-malonate association quotientsdetermined from the potentiometric study (Eqn. 10), thestoichiometric concentration of malonate and acetate (Table3), the pH values measured after 111 days (Table 5), and thereactions and the equilibrium quotients listed in Table 9involving aluminum-hydrolysis species and acetate com-plexes. The calculated Al speciation and ionic strength ofeach solution, after 111 days are given in Table 10. It isapparent from Table 10 and Fig. 4 that the formation ofAl-acetate species contributes more than the Al(OH)p

species to the concentration of total dissolved Al (note thatthe formation quotients of Palmer and Bell (1994; Table 9)for the Al(Ac)21 and Al(Ac)2

1 species are generally higherthan those reported by Benezeth et al. (1994) and, therefore

this probably represents the maximum concentration of thetwo Al-acetate complexes); however, the presence of mal-onate and the formation of Al-malonate complexes signifi-cantly enhances the concentration of total dissolved Al: byas much as 5 orders of magnitude at the highest level of totalmalonate used in this study. Moreover, the pH and ionicstrength of the experimental solutions corresponds system-atically with the stoichiometric concentration of malonate(Table 10).

The agreement between the calculated total dissolved Alvalues (Eqn. 9) and the measured Al concentrations is excel-lent, as apparent from Fig. 4. The variation between the calcu-lated Al concentrations and the measured Al concentrations(log SAlmeas— log SAlcalc) is less than60.1 log units for theexperimental solutions; which is well within the error range forthe calculated Al values. Clearly, the results of the gibbsitesolubility experiments are quantitatively consistent with thepotentiometric data at the same conditions and thus support thevalues determined for the formation quotients of AlMa1 andAl(Ma)2

2 at 50°C.

Fig. 5. The relationship between log Qy values taken from Table 4and ionic strength, where the symbols define the measured log Qy

values at temperatures of (●) 5, (n) 25, (Œ) 50, and (�) 75°C. Thecurves were computed from Eqn. 10, and the dashed lines represent theDebye-Huckel expression at 5°C.

Fig. 6. The relationship between log Qy values taken from Table 4and temperature (°C), where the symbols define the measured log Qy

values at ionic strengths of (v) 0.1, (f) 0.3, (Œ) 0.5, and (�) 1.0 molal.The curves were computed from Eqn. 10, and the dashed lines repre-sent association constants at infinite dilution, also computed from Eqn.10.

4.3. Comparison with Literature Data

Equilibrium data previously available for the complexationof Al31 with malonate were typically limited to ambient con-ditions (Table 1). An exception is the solubility study per-formed by Fein et al. (1995), at 35 and 80°C. Fein et al. (1995)explain their experimental solubility data by the formation ofeither an Al(Ma)2

2 or Al(OH)2(HMa)22 complex, however, they

could not distinguish between the two species. At the pHconditions employed in this study, it was not possible to assessthe validity of the mixed Al(OH)2(HMa)2

2 species reported by

Fein et al. (1995). Their log K2 (Al(Ma)22) values of 11.3 and

14.5 at 35 and 80°C, respectively, are substantially differentfrom the equivalent infinite dilution values of this study: ap-proximately 1.5 log unit at 35°C, and half a log unit at 80°C.Uncertainty in the pH at the time of sampling in the experi-ments of Fein et al. (1995) may in part explain this discrepancy,as Table 5 indicates the pH changed significantly in our “buff-ered” solubility experiments with time, perhaps due to surfacesorption and reconstitution processes involving malonate spe-cies.

Equilibrium data for the formation of Al(Ma)y322y complexes

are presented in the thermodynamic compilations of Chris-tensen and Izatt (1983) and Harrison and Thyne (1992). In bothcases, Tedesco and Gonza´lez Quintana (1974) were eitherdirectly or indirectly referenced as the original data source.Tedesco and Gonza´lez Quintana (1974), however, reportedassociation quotients for the formation of Al-bimalonate spe-cies (Al(HMa)y

32y), not for Al(Ma)y322y species, and this was

not recognized by the later authors. Moreover, this studyshowed no evidence of Al(HMa)y

32y species having formed. Acomparison of the experimental data obtained in this study withthe predictions of Harrison and Thyne (1992) are significantlydifferent. For example, at infinite dilution and 25°C, Harrisonand Thyne (1992) predicted an association constant of logK1 5 3.56 for AlMa1, compared with 7.496 0.18 from thisstudy, a difference of nearly 4 orders of magnitude.

4.4. Comparison with Al-Acetate Data

The chelate effect, which is a manifestation of the enhancedstability of complexes with polydentate ligands compared to

complexes with monodentate ligands containing the same do-nor groups, could be examined by comparing the thermody-namic data for Al-malonate (AlMa1) with equivalent data forAl-acetate complexes, measured by Palmer and Bell (1994;Table 11). The chelate effect (Chel), as defined by Schwarzen-bach (1952), is equal to the difference in the logarithms of theformation constant of a polydentate complex and the formationconstant of the equivalent monodentate complex (Anderegg,1971), for example:

Chel5 logQAICH2C2O41 2 log QAl(CH3CO2)2

1 (12)

Expressed in this way, the chelate effect is large and positivefor the formation of AlMa1 with respect to the formation of theequivalent Al(Ac)2

1 complex (Table 11); from which it may beinferred that AlMa1 is a chelate complex, and is more stablethat the equivalent Al(Ac)2

1 complex. The greater stability ofthe chelated Al-malonate complex is accounted for by theformation of a 6-member ring structure (Anderegg, 1971;Jones, 1965; Schwarzenbach, 1961). Surprisingly, the thermo-

dynamic data (Table 11) suggest that the chelate effect for theAl(Ma)1 complex is controlled by enthalpy changes, asDHvalues are lower for the formation of the Al(Ma)1 complexthan for the Al(Ac)2

1 complex; whereasDS values for the twocomplexes are approximately equal.

4.5. Aluminum Speciation in Aqueous Fluids

The speciation of aluminum as a function of temperature andionic strength can be computed from the equilibrium quotientsdetermined in this study and association quotients for compet-ing ligands (Table 12). For example, the speciation of alumi-num in solutions at 25°C and 0.6 molal ionic strength (NaClmedia), comprising 0.0075m total Al and a combination ofmalonic, acetic, and oxalic acids, are shown in Fig. 7a–c.Initially, only the effect of malonic acid, in a pH 4, solution wasconsidered (Fig. 7a). The contribution of AlOH21 to the totalAl concentration was negligible (Fig. 7a), therefore, Al-hydro-lysis species are not shown in Fig. 7b and 7c. The addition of

0.03m acetate to the malonic acid solution has little affect onthe distribution of Al-species, except when acetate exceeds theconcentration of malonate by 4 orders of magnitude. The effecton the speciation of Al when 1024m oxalate was added isshown in Fig. 7c. It is apparent from this series of speciationplots (and the 50°C gibbsite solubility experiments performedin this study), that the greater thermodynamic stability of themetal-dicarboxylate complexes dominate the Al-speciation, de-spite a greater abundance of acetate. It must be noted, however,that changing any variable, such as pH, temperature, ionicstrength, and total Al, used to compute the plots in Fig. 7a–cwould change the Al-speciation.

6. CONCLUSIONS

A potentiometric study was performed to determine forma-tion quotients for the complexation of Al with malonate from 5to 75°C. Two complexes, Al(Ma)1 and Al(Ma)2

2, were iden-tified. The magnitude of the Al-malonate formation quotients at50°C were verified by the excellent agreement between theresults of the potentiometric study and the gibbsite solubilitystudy. The temperature and ionic strength dependencies of theformation quotients for each complex are described by empir-ical equations that comprise an extended Debye-Hu¨ckel expres-sion and variable temperature and ionic strength parameters.The thermodynamic quantities ofDH, DS andDCp were ob-tained by differentiating the empirical equations with respect totemperature. The resulting thermodynamic trends were consis-tent with the results of previous complexation studies (Gior-dano and Drummond, 1991; Palmer and Bell, 1994; Palmer andDrummond, 1988). Furthermore, the bidentate AlMa1complexis more stable than the monodentate Al(Ac)2

1 complex, whichis consistent with the chelate effect.

The experimental results presented in this study providemuch needed thermodynamic data at geochemically relevantconditions to evaluate the behavior of malonic acid (and byanalogy other difunctional carboxylic acids) in geochemicalprocesses, e.g., Al31 transportation, dissolution of aluminosili-cate minerals, and biogeochemical cycling of Al31. In addition,the equations provide an accurate model for comprehensivespeciation calculations, and when combined with complexation

data for other Al-ligands they can be used to assess Al31

speciation in diverse aqueous environments. Despite the greaterabundance and thermal stability of acetic acid, the greaterstabilities of the Al-malonate complexes suggest malonate (andother dicarboxylic acids) may dominate Al-carboxylate specia-tion in some natural aqueous systems.

Acknowledgments—This research was sponsored by the Office of BasicEnergy Sciences, U.S. Department of Energy, contract DE-AC05-960R22464 with Oak Ridge National Laboratory, managed by Lock-heed Martin Energy Research Corp. and NSF grant EAR-9317075 toR. M. Kettler. The helpful suggestions of R. E. Mesmer were gratefullyappreciated.

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Potentiometric and solubility studies of association quotients of aluminum malonate complexation in...

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