Formation Quotients of Aluminum Sulfate Complexes in NaCF3SO3

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Environ. Sci. Technol. 2002, 36, 166-173

Formation Quotients of Aluminum Sulfate Complexes in NaCF3SO3 Media at 10, 25, and 50 °C from Potentiometric Titrations Using a Mercury/Mercurous Sulfate Electrode Concentration Cell CAIBIN XIAO, DAVID J. WESOLOWSKI,* AND DONALD A. PALMER Chemical Sciences Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6110

Mercury/mercurous sulfate electrode concentration cells (with liquid junction) are employed in this study to determine the formation constants of aluminum sulfate complexes, with the principal advantage that the change in the free sulfate concentration is measured directly without the need to know the standard potential of the electrode. Potentiometric titrations were conducted at temperatures of 10, 25, and 50 °C and ionic strengths of approximately 0.3, 0.5, and 1.0 molal in aqueous solutions of the inert 1:1 electrolyte sodium trifluoromethanesulfonate (NaTr). Stoichiometric molal formation quotients Q1 and Q2, respectively, for the reactions Al3+(aq) + SO42-(aq) h AlSO4+(aq) and Al3+(aq) + 2SO42-(aq) h Al(SO4)2-(aq) were determined. The values of log Q1 obtained from this work in NaTr media at ionic strengths of 0.3 and 1.0 mol‚kg-1 and 50 °C (1.72 ( 0.08 and 1.35 ( 0.06, respectively) are in excellent agreement with the values (1.71 ( 0.2 and 1.32 ( 0.1) determined in NaCl media from the recent potentiometric study conducted in the same laboratory using a hydrogen electrode concentration cell by Ridley et al. (Ridley, M. K.; Wesolowski, D. J.; Palmer, D. A.; Kettler, R. M. Geochim. Cosmochim. Acta 1999, 62, 459-472). The value of log Q2 (2.05 ( 0.05) in 1.0 mol‚kg-1 from this work is smaller than the value reported by Ridley et al. (2.6 ( 0.5) but within the combined experimental error. Empirical isothermal equations are presented to permit calculation of the equilibrium quotients as a function of ionic strength (0-1 mol‚kg-1), giving log K1 and log K2 values at 25 °C and infinite dilution of 3.84 ( 0.12 and 5.58 ( 0.09, respectively. The value for log K1 obtained in this study at 25 °C is bracketed within experimental uncertainty by values reported by Kryzhanovskii et al. (Kryzhanovskii, M. M.; Volokhov, Y. A.; Pavlov, L. N.; Eremin, N. I.; Mironov, V. E Zh. Prikl. Khim. 1971, 44, 476-479) and Nishide and Tsuchiya (Nishide, T.; Tsuchiya, R. Bull. Chem. Soc. Jpn. 1965, 38, 1398-1400), namely, 3.89 and 3.73, respectively. All other literature values for the first aluminum sulfate association constant are considerably lower than these results, which is also true for the second association constant, although there are few experimental data available for the latter. * Corresponding author phone: (865) 574-6903; fax: (865) 5744961; e-mail: [email protected]. 166

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Empirical equations are also presented for calculating values of log Q1 and log Q2 from 0 to 1 molal ionic strength and from 10 to 125 °C, spanning the range of most environmental conditions at which these reactions are important.

Introduction The presence of sulfate in areas affected by acid rain and acid mine drainage has significant effects on aluminum release to natural surface water and its biological availability and toxicity to terrestrial and aquatic organisms (4-11). Extremely high concentrations of sulfate and heavy metals, and extremely low pH, have been reported from abandoned coal and metal ore mines (10, 11). Thermodynamic data for the association of metal ions with sulfate are important for understanding the enhancement of mobility and bioavailability of metals (7-9). Sulfate forms strong complexes with the trivalent metal ions, including Al and Fe, and many bivalent metals (11). Consequently, sulfate enhances the solubility of many minerals in water. Furthermore, Ridley et al. (12) have demonstrated that in 5 °C solutions at constant ionic strength and pH, sulfate greatly enhances the dissolution rate of gibbsite, Al(OH)3, a commonly occurring soil mineral. Accurate thermodynamic data needed for modeling these environmental problems are incomplete. The available data were generally scattered and even controversial. For example, the reported formation constants for the Al3+-SO42- complex equilibria

Al3+(aq) + SO42-(aq) h AlSO4+(aq)

(I)

Al3+(aq) + 2SO42-(aq) h Al(SO4)2-(aq)

(II)

vary from 101.90 to 103.89 for K1 and from 102.70 to 104.92 for K2 at 25 °C (1-3, 12-19). The large discrepancy among these formation quotients is due in part to uncertainty in the standard potential of the Hg/Hg2SO4 electrode in cases where this electrode was used to measure the sulfate ion activity (20, 21). This source of error is eliminated in the present study, because only the difference in potential between two identical Hg/Hg2SO4 electrodes is measured. Another contributor to the discrepancy among the published formation constants is undoubtedly associated with differing activity coefficient models used to interpret results from experimental studies of the relatively weak aluminum-sulfate complexation at low temperature and the competing protonation of sulfate, as well as the high and variable ionic strengths dictated by the reaction stoichiometries. In the present study, this source of error is mitigated by using bisulfate formation constants measured in the same laboratory and interpreted using the same type of stoichiometric molal activity coefficient model (22). Recently, Ridley et al. (1) reported formation quotients for these complexation equilibria at temperatures from 50 to 125 °C, obtained by means of potentiometric pH titrations using a hydrogen electrode concentration cell (22-24) together with gibbsite solubility measurements at 50 °C. Solubility measurements at temperatures below 50 °C were found to be impractical for the study of Al3+-SO42- complexation due to the slow dissolution rate (12). In pH titrations at temperatures of 10 GΩ. The cell potential arises from the half-cell reaction 2Hg(l) + SO42-(aq) T Hg2SO4(s) + 2e-, which is the relevant reaction at each electrode. Any difference in the sulfate ion activity in the test compartment, relative to that in the reference compartment, gives rise to a measurable EMF, which thus enables monitoring of the sulfate activity in the test compartment during a titration. Materials. Electric grade mercury (99.9998%) and mercury(I) sulfate (99%) used for the preparation of the electrodes were purchased from Alfa Chemicals, Inc. Solid sodium trifluoromethanesulfonate (NaTr) was prepared by neutralizing trifluoromethanesulfonic acid (Alfa, 99%) with a NaOH solution in ethanol. The salt was recrystallized twice from ethanol and dried at 120 °C under a 30 mmHg vacuum to constant weight. Aluminum nitrate solution was prepared from Al(NO3)3‚xH2O (Alfa, 99.999% metal content). The nitrate concentration of this solution was 0.6594 mol‚kg-1, which was determined by titrating the effluent obtained by passing the aluminum nitrate solution through a Dowex-100 ion exchange column against a standard sodium hydroxide solution. The aluminum concentration of this solution, analyzed by EDTA titration, was 0.2188 mol‚kg-1. A slight excess of nitrate was probably due to the presence of free nitric acid in the commercial aluminum nitrate. The pH of

cell potential/mV measd calcd

Ej/mV

[SO42-] ) 0.09037 [H+] ) 0.02009 [Tr-] ) 0.08038 [Na+] ) 0.24103

0.07854

-2.75

-2.500 0.332

[SO42-] ) 0.07030 [H+] ) 0.02008 [Tr-] ) 0.1406 [Na+] ) 0.2611

0.05984

-5.96

-5.650 0.735

[SO42-] ) 0.04018 [H+] ) 0.02010 [Tr-] ) 0.2310 [Na+] ) 0.2913

0.03272

-12.94 -12.712 1.556

[SO42-] ) 0.02193 [H+] ) 0.01926 [Tr-] ) 0.1362 [Na+] ) 0.1589

0.01655

-12.37 -12.249 2.117

a The reference solution composition for the first three entries in this table is [SO42-] ) 0.11043 molal, [H+] ) 0.020078 molal, [Tr-] ) 0.020125 molal, and [Na+] ) 0.2209 molal. For the last entry, the reference solution composition is [SO42-] ) 0.06004 molal, [H+] ) 0.02008 molal, [Tr-] ) 0.02008 molal, and [Na+] ) 0.1200 molal. b The concentrations listed for the test and reference solutions do not include bisulfate. The stoichiometric molality of bisulfate and free sulfate in both the test and reference solutions is computed iteratively from the starting solution compositions listed above, with charge and mass balance equations, using the bisulfate dissociation constants given by ref 22 at the equivalent stoichiometric molal ionic strength. c Free SO42- concentration, after iterative calculation of bisulfate concentration.

this solution was 2.585, measured with a glass electrode. All other solutions were prepared from reagents with purity of >99% and standardized according to the standard methods. Procedure. The test and reference solutions had the same initial composition and consisted of 0.005 molal H2SO4(aq), ∼0.05 molal Na2SO4(aq), and enough NaTr(aq) to adjust the ionic strength (I) to 0.3, 0.5, and 1.0 mol‚kg-1. NaTr was used as the “inert” 1:1 supporting electrolyte, rather than NaCl, to avoid formation of mercury chloride compounds, both in solution and at the electrode surfaces. Prior to each titration, two mercury/mercurous sulfate electrodes were prepared using an Hg2SO4 slurry made by mixing the working solution with mercurous sulfate powder. A stable initial cell potential (0.02 ( 0.01 mV) was usually observed after 6, 3, and 2 h at 10, 25, and 50 °C, respectively, whereupon titrant, aqueous aluminum nitrate, was added stepwise to the test compartment until ∼50% of the sulfate in the test solution was complexed by Al3+(aq). After each addition of titrant, a stable EMF reading was recorded after the same amount of time as required for the initial equilibrium. Usually, the cell potential did not drift by >0.02 mV in 18 h at any of the conditions studied.

Results Separate runs were conducted to test the Nernstian behavior of the electrodes. Test and reference solution compositions and measured cell potentials are listed in Table 1. The calculated theoretical EMF of the cell is obtained from

∆E ) -RT/(2F) ln{m(SO42-)t/m(SO42-)r} RT/(2F) ln{γ(SO42-)t/γ(SO42-)r} + Ej (1) where T is temperature (Kelvin), R is the ideal gas constant, F is the Faraday constant, m(SO42-)t and m(SO42-)r represent the molalities of sulfate ions in the test and reference compartments, respectively, and γ(SO42-)t and γ(SO42-)r are VOL. 36, NO. 2, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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167

TABLE 2. Test/Reference Solution Compositions and Measured Cell Potentials at Different Temperatures and Ionic Strengths T ) 10.0 °C mtest ) 41.84 ga I ) 0.2930 mol‚kg-1 b

T ) 25.0 °C mtest ) 38.84 g I ) 0.2911 mol‚kg-1 b

T ) 50.0 °C mtest ) 38.82 g I ) 0.2877 mol‚kg-1 b

mtitrant/gc

EMF/mV

mtitrant/gc

EMF/mV

mtitrant/gc

EMF/mV

1.8392 2.0989 2.5248 3.6591 5.8080 6.2046

-3.740 -4.225 -5.070 -7.190 -10.531 -11.431

1.1052 1.6980 2.1545 2.8236 4.8054 5.1859

-2.665 -4.125 -5.144 -6.604 -10.798 -11.518

0.8972 1.6159 2.2067 3.4621

-2.565 -4.555 -6.157 -9.412

T ) 10.0 °C mtest ) 37.99 g I ) 0.4883 mol‚kg-1 d

T ) 25.0 °C mtest ) 34.51 g I ) 0.2864 mol‚kg-1 d

T ) 50.0 °C mtest ) 78.62 g I ) 0.4830 mol‚kg-1 d

mtitrant/gc

EMF/mV

mtitrant/gc

EMF/mV

mtitrant/gc

EMF/mV

1.6485 2.1374 2.5731 2.8629 3.7989 5.0668

-2.952 -3.784 -4.512 -4.987 -6.436 -8.295

2.5779 4.3865 4.7348 5.0026 5.3527 5.9516

-5.180 -8.472 -9.067 -9.514 -10.087 -11.040

1.0948 2.4655 4.1366 5.8098 7.3612 8.7912 10.2236 11.6323

-1.165 -2.627 -4.320 -5.975 -7.451 -8.753 -10.015 -11.120

T ) 10.0 °C mtest ) 37.27 g I ) 0.8240 mol‚kg-1 e

T ) 25.0 °C mtest ) 34.37 g I ) 1.002 mol‚kg-1 f

T ) 50.0 °C mtest ) 37.54 g I ) 0.9991 mol‚kg-1 f

mtitrant/g

EMF/mV

mtitrant/g

EMF/mV

mtitrant/g

EMF/mV

0.9915 2.2181 3.8014 5.7628 6.5307 7.2629 9.5628 10.7227

-1.125 -2.575 -4.360 -6.365 -7.110 -7.855 -9.930 -10.880

1.8096 2.2064 3.2436 4.4500 5.3692 6.6140 8.1943 8.8022

-2.605 -3.545 -4.920 -6.420 -7.505 -8.925 -10.605 -11.195

0.6964 1.8050 4.0649 5.7850 6.4023 7.3540 8.5692

-1.175 -2.995 -6.395 -8.785 -9.665 -10.805 -12.195

a Mass of the test solution used. b The ionic strength of the reference at the given temperatures; the composition of the test/reference solution was [SO42-]total ) 0.05000, [Na+]total ) 0.24044, [Tr-] ) 0.15036, and [H+]total ) 0.009909. c Mass of the titrant added; the composition of the titrant solution is given in the text. d [SO42-]total ) 0.05546, [Na+]total ) 0.4297, [Tr-] ) 0.3289, [H+]total ) 0.01009. e [SO42-]total ) 0.07833, [Na+]total ) 0.7302, [Tr-] ) 0.6215, [H+]total ) 0.04796. f [SO42-]total ) 0.06438, [Na+]total ) 0.9469, [Tr-] ) 0.8282, [H+]total ) 0.01015. The concentration unit is molality, mol‚kg-1. Note that these compositions do not include the bisulfate and free sulfate concentrations in the solutions, which are internally calculated in the data reduction program, using an iterative calculation involving charge and mass balance constraints and the bisulfate dissociation constants at the equivalent ionic strength given by ref 22.

the stoichiometric molal activity coefficients of sulfate ions in the test and reference solutions, respectively. At a given solution composition, the molalities of sulfate, bisulfate, and hydrogen ions were calculated using the value of the molal formation quotient (QB) of the reaction

SO42-(aq) + H+(aq) h HSO4-(aq)

(III)

obtained in the same laboratory by Dickson et al. (22). Note that the stoichiometric activity coefficient model used in this laboratory incorporates “ion pairing” of such species as NaTr0, HTr0, NaSO4-, NaHSO40, etc., implicitly (22). The small differences between the activity coefficients of sulfate in the reference and test solutions, which arise due to small changes in ionic strength of the test solution during a titration, are corrected using the simple extended Debye-Hu ¨ckel equation

γ(SO42-) ) -4AγI1/2/{1 + BaI1/2} 168

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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 36, NO. 2, 2002

TABLE 3. Equilibrium Constants and Parameters Calculated from Equation 3 log K1 log K2 a1/(mol‚kg-1) a2/(mol‚kg-1)

10.0 °C

25.0 °C

50.0 °C

3.69 ( 0.27 5.40 ( 0.28 0.912 ( 0.456 1.158 ( 0.576

3.84 ( 0.12 5.58 ( 0.12 0.863 ( 0.180 1.255 ( 0.208

3.84 ( 0.09 6.01 ( 0.10 1.291 ( 0.048 1.078 ( 0.096

¨ ckel slope, I is the stoichiometric where Aγ is the Debye-Hu molal ionic strength, and B ) 2NAe2/(0kBT), where NA is Avogadro’s number, e is the electronic charge, 0 is the vacuum permittivity, and  is the dielectric constant of water. The distance of the closest approach, a, is chosen to be 4 Å. The form of eq 2 was chosen to facilitate the nonlinear data reduction procedure, and additional calculations demonstrated that a more complex activity coefficient model was not needed simply to calculate the sulfate ion activity coefficient ratio in eq 1, which did not deviate significantly from unity during an individual titration. Ej in eq 1 is the liquid junction potential and is computed according to the Henderson equation (25) from the molalities, charges, and limiting equivalent conductances of the individual ions, which were taken from Robinson and Stokes (26) and Quist and Marshall (27) except for Al3+(aq), AlSO4+, and Al(SO4)2-(aq). The limiting equivalent conductance of Al3+(aq) is approximated by that of La3+(aq) (26), and the limiting equivalent conductances of complex ions AlSO4+(aq) and Al(SO4)2-(aq) are estimated according to a method suggested by Anderko and Lencka (28). As shown in Table 1, the cell potentials measured agree with those calculated within 0.3 mV. Because of the nature of the relative measurements in these concentration cells, this error invariably results in an uncertainty of ∼0.01 log unit in the sulfate molality at 25.0 °C, regardless of the magnitude of the absolute EMF value. The cell potentials measured at temperatures of 10, 25, and 50 °C, along with the test/reference solution compositions, are listed in Table 2. The data reduction method used to determine Q1 and Q2 for reactions I and II is similar to that employed to treat potentiometric results obtained from ORNL hydrogen electrode concentration cells (1, 23). Because there are three equilibria (I-III) to consider, the test solution contains nine ionic species: Na+, H+, Al3+, AlSO4+, SO42-, HSO4-, Al(SO4)2-, NO3-, and Tr-. The molalities of Na+, NO3-, and Tr- are not affected by equilibria I-III but contribute to the liquid junction potential. The molalities of other species can be computed by simultaneously solving three chemical equilibrium equations along with mass and charge balance equations, if the values of Q1 and Q2 are known. In other words, the potential of the concentration cell is an implicit function of the amount of titrant added, with two parameters to be determined. Thus, Q1 and Q2 can be obtained by leastsquares fitting of the experimental data. In this work, the sulfate molality was kept above 0.02 mol‚kg-1 to avoid the possible complication caused by the dissolution of the solid Hg2SO4. This high concentration of sulfate dictates that the ionic strength of the test solution cannot be entirely controlled by the addition of excess supporting electrolyte. For the starting test/reference solution with I ) 0.3 mol‚kg-1, the ionic strength of the test solution decreases to 0.26 mol‚kg-1 during the course of the titration because sulfate ion contributes up to 30% of the total ionic strength at this condition before addition of Al(NO3)3. Therefore, a more accurate activity coefficient model than eq 2 is needed to describe the ionic strength dependence of reactions I and II. After testing various forms, we chose the

TABLE 4. Al(SO4)n3-2n Formation Quotients in NaTr Media at Temperatures of 10, 25, and 50 °C 10.0 °C

25.0 °C

50.0 °C

I/(mol‚kg-1)

log Q1

log Q2

log Q1

log Q2

log Q1

log Q2

0.1 0.3 0.5 0.8 1.0

2.26 ( 0.25 1.63 ( 0.20 1.35 ( 0.15 1.14 ( 0.14 1.08 ( 0.13

3.48 ( 0.24 2.63 ( 0.19 2.24 ( 0.13 1.95 ( 0.11 1.86 ( 0.11

2.36 ( 0.11 1.71 ( 0.10 1.40 ( 0.09 1.17 ( 0.09 1.09 ( 0.08

3.62 ( 0.11 2.77 ( 0.10 2.38 ( 0.09 2.10 ( 0.08 2.02 ( 0.08

2.33 ( 0.08 1.72 ( 0.08 1.48 ( 0.07 1.35 ( 0.07 1.35 ( 0.06

3.94 ( 0.09 2.99 ( 0.08 2.54 ( 0.06 2.18 ( 0.06 2.05 ( 0.05

Discussion

FIGURE 2. Comparison of the calculated and measured cell potentials at T ) 50.0 °C: line, calculated; O, I ) 0.30 mol‚kg-1; 0, I ) 0.49 mol‚kg-1; ], I ) 1.0 mol‚kg-1; 9, data obtained using a cell configuration different from the present one (not listed in Table 2). simplest empirical function that adequately described the data

log Qn ) log Kn + 2

{

}

xI 2 ln(1 + 1.2xI) + anI (3) + ln(10) 1 + 1.2xI 1.2

∆zn Aφ

where Kn is the formation constant for equilibrium I or II, An is the Debye-Hu ¨ ckel slope for the osmotic coefficient, and ∆zn2 ) -12 and -16 for equilibria I and II, respectively. The extended Debye-Hu ¨ ckel formulation in eq 3 has been employed in other studies in this laboratory (22-24) and is taken from the Pitzer ion interaction model. Instead of computing Q1 and Q2 at each ionic strength, which varies within an individual titration, we fitted all of the experimental data at a given temperature to the model outlined above to determine K1, K2, and the activity coefficient parameters a1 and a2. These results are listed in Table 3. It must be stressed that the anI term in eq 3 is purely an empirical term which proved to minimize adequately the deviation of the observed cell potentials from the calculated potentials, and the application of this equation is limited to the ionic strength range studied (i.e., 0-1 molal). Furthermore, there is no expectation that the an values (Table 3) should follow a systematic trend with temperature. Additional ionic strength and temperature cross-terms could have been introduced to permit a polythermal fit of all data, but several attempts to do this did not significantly improve the fit to the experimental data or significantly alter the calculated infinite dilution values of log Kn. The formation quotients for reactions I and II calculated using eq 3 at various ionic strengths and temperatures are listed in Table 4. Figure 2 shows the comparison of the measured cell potentials with those calculated at 50.0 °C. Clearly, the model represents the experimentally measured cell potentials very well, and the average relative error of the fit is 1. Excellent agreement between the experimental data of the present study and the calculated potentials (Figure 2) demonstrates that one term, which is linear in ionic strength, is sufficient for the ionic strength range studied in this work (0.3 < I < 1.0 mol‚kg-1). The values for log K1 and log K2 are expected to be model dependent, because the Debye-Hu ¨ckel slopes for equilibria I and II with ∆z2 ) -12 and -16, respectively, are very large. Comparison with the Literature. Values of log Q1 and log Q2 at 25.0 and 50.0 °C are plotted as a function of ionic strength in Figures 3-6. Figures 5 and 6 also show the values for log Q1 and log Q2 calculated from the model of Ridley et al. (1) and their experimental values at individual ionic strengths obtained from the solubility measurements of gibbsite and potentiometric titrations using the hydrogen electrode concentration cell (1). Literature values for log K1 and log K2, obtained from a variety of methods, are also shown in Figures 3 and 4. At 25.0 °C, the log Q1 and log Q2 values at I ) 1.0 mol‚kg-1 from this work are >1 log unit higher than those obtained by Lo et al. (18) by means of calorimetry. Previous values for log K1 and log K2 are very scattered, and our values are among the highest of all the previous data. However, log K1 ) 3.84 ( 0.12 from this work at 25 °C agrees well with the value 3.73 obtained from the electric conductance measurements by Nishide and Tsuchiya (3), as well as the value 3.89 obtained from a spectrophotometric study of the competition of Al3+ and Cu2+ for sulfate reported by Kryzhanovskii et al. (2). The results of Kryzhanovskii et al. constitute the recommended equilibrium constants for reaction I selected by 170

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FIGURE 4. Plot of log Q2 at 25.0 °C calculated from eq 3 as a function of square root ionic strength: solid line, this work; 0, Lo et al. (18); 3, Izatt et al. (15); 4, Sharma and Prasad (17). Error bar at infinite dilution shows uncertainty range of smooth curve. Smith et al. (33) for the NIST critical stability constant database. However, it should be noted that our experimental value for the logarithm of the equilibrium quotient of reaction I in 1.0 molal NaTr (1.09 ( 0.08) differs significantly from the value of 1.48 reported by Kryzhanovskii et al. (2) in 1 M sodium perchlorate. As we have pointed out, the value of log K1 obtained by extrapolation of the formation quotients at I > 0.1 mol‚kg-1 to infinite dilution depends on the activity coefficient model used. Therefore, the value of log K1 from electric conductance measurements of very dilute solutions (3) is probably the least biased by the chosen activity coefficient model among those reported in the literature. Values for log K1 and log K2 obtained here are ∼2 log units higher than those obtained by Sharma and Prasad (17) from the EMF measurements with the cell Pt|QH; H2SO4||H2SO4||H2SO4; Hg2SO4|Hg, where QH stands for quinhydrone. Simple analysis reveals that this large disagreement is due to the fact that the potential of the cell used by Sharma and Prasad is not sufficiently sensitive to the presence of Al3+/SO42- complexes. The Nernst equation for this cell is given as

E ) E0 -

RT ln{(mH+γH+)(mSO42-γSO42-)} 2F

(4)

The activity product in the above equation is largely controlled by the bisulfate dissociation equilibrium III, so that the cell potential is not sensitive to the extent of equilibria I and II. Using our model and values for log K1 and log K2 listed in Table 3, we find that a decrease of 2 log units in K1 and K2 results in only a 2.8 mV change in the cell potential (eq 4), with the stoichiometric concentrations of H2SO4(aq) and Al2(SO4)3(aq) equal to 0.00108 and 0.00144 molar, respectively, at 25.0 °C, which is only 1.3% of the value of E - E0 (17). A very accurate value for the standard potential of the mercury/ mercurous sulfate electrode is required to determine accurate values for log K1 and log K2 using the Sharma and Prasad cell. Unfortunately, uncertainty still exists in the standard potential of this electrode. For example, E0 values of 0.6125 V (34), 0.6124 V (35), 0.61257 V (36, 37), 0.61535 V (38), and 0.61544 V (21) have been reported. The value used by Sharma and Prasad (17) was 0.6135 V. In contrast, a 2 log unit change in K1 and K2 causes a 50% change in the potential of our concentration cell. As shown in Figure 5, the values of log Q1 at I ) 0.3 and 1.0 mol/kg at 50.0 °C are in excellent agreement with those obtained with the hydrogen electrode concentration cell by Ridley et al. (1). The value of log Q2 at 50.0 °C, I ) 0.1 mol‚kg-1, extrapolated from values at higher ionic strengths using eq

FIGURE 5. Plot of log Q1 at 50.0 °C calculated from eq 3 as a function of square root ionic strength: solid line, this work; dashed line, Ridley et al. (1), model; O, Ridley et al. (1), hydrogen electrode concentration cell data; b, Ridley et al. (1), solubility data; 0, Lo et al. (18); 4, Matsushima et al. (19). The thin and thick error bars indicate the uncertainty in log K1 obtained in ref 1 and this work, respectively.

FIGURE 7. Plot of log Q1 at ionic strengths of 0.0, 0.1, and 1.0 mol‚kg-1 as a function of temperature: 0, this work, calculated values and uncertainties in Tables 3 and 4; dashed curves with uncertainty ranges represent the model fit reported by Ridley et al. (1) at 50-125 °C; b, Nishide and Tsuchiya (3); 1, Kryzhanovskii et al. (2); ], gibbsite solubility data (1); solid curves represent eqs 5-7.

FIGURE 6. Plot of log Q2 at 50.0 °C calculated from eq 3 as a function of square root ionic strength: solid line, this work; dashed line, Ridley et al. (1), model; O, Ridley et al. (1), hydrogen electrode concentration cell data; b, Ridley et al. (1), solubility data; 0, Lo et al. (18). The thin and thick error bars indicate the uncertainty in log K1 obtained in ref 1 and this work, respectively. 3, agrees with that from Ridley et al.(1) within the experimental error (Figure 6). The error limit in Q2 at this temperature from Ridley et al. (1) is 0.4 log unit, and this makes it difficult to compare their results at I ) 1.0 mol‚kg-1 with our data. The large discrepancy in log Q2 calculated by their model from the current values at ionic strengths between 0.1 and 1.0 mol‚kg-1 (Figure 6) is probably due to the absence of any constraints placed on the fitting of the former because no measurements in this ionic strength range were made. Temperature Dependence of Q1 and Q2. As discussed above, there is generally good agreement between this study and that of Ridley et al. (1) for the values of the formation quotients of reactions I and II at 50 °C, the only temperature at which the two studies overlap. The latter study covered the range 50-125 °C at 0.1-1.0 molal ionic strength in NaCl media. However, Palmer and Wesolowski (39-41) demonstrated that the aqueous speciation of aluminum is not significantly different in chloride, perchlorate, nitrate, or triflate media. Therefore, it is sensible to develop a combined model for the temperature dependencies of Q1 and Q2 that includes the results of this study and our previous work. The values of log Q1 and log Q2 at ionic strengths of 0.0, 0.10, and 1.0 molal from Tables 3 and 4 are plotted in Figures 7 and 8 along with the fitted functions describing these quantities

FIGURE 8. Plot of log Q2 at ionic strengths of 0.0, 0.1, and 1.0 mol‚kg-1 as a function of temperature: 0, this work, calculated values and uncertainties in Tables 3 and 4; dashed curves with uncertainty ranges represent the model fit reported by Ridley et al. (1) at 50-125 °C; ], gibbsite solubility data of Ridley et al. (1); [, hydrogen electrode cell data of Ridley et al. (1); solid curves represent eqs 5-7. (dashed curves) reported by Ridley et al. (1). The uncertainty ranges in both sets of values are also shown. Because of the nonlinear nature of the data reduction methodology required in this study, it was deemed acceptable to combine the smoothed quantities for these formation quotients listed in Tables 3 and 4 at ionic strengths of 0.3-1.0 molal with the experimental values for log Q1 and log Q2 listed in Table 4 of Ridley et al. (1), in order to derive empirical functions of temperature and ionic strength. For these fits, the following model was chosen:

log Qn ) log Kn +

{

∆zn2∆φ

}

xI 2 ln(1 + 1.2xI) + fn(I,T) (5) + ln(10) 1 + 1.2xI 1.2

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TABLE 5. Parameters for Equations 5-7 p1 p2 p3 p4 p5 p6

log Q1

log Q2

4546.525 -124194.5 -789.964 1.256856 3.51385 -741.9489

4939.103 -132438.8 -862.1794 1.418846 0.0 377.6896

Equation 5 is essentially the same form as eq 3, where again An is the Debye-Hu ¨ ckel slope for the osmotic coefficient [the temperature dependence of which is given by Dickson et al. (22)], and ∆zn2 ) -12 and -16 for reactions I and II, respectively. The same extended Debye-Hu ¨ckel formulation was used by Ridley et al. (1) and Dickson et al. (22), and so internal consistency is maintained. The equilibrium constants at infinite dilution for reactions I and II can be adequately described by a function of the absolute temperature (T) in Kelvin

log Kn ) p1 + p2/T + p3 ln(T) + p4T

(6)

whereas additional ionic strength terms found to be sufficient to fit the combined data sets are expressed as

fn(I,T) ) I(p5 + p6/T)

(7)

The best fit parameters obtained from the combined data sets for use in eqs 5-7 are listed in Table 5, and the resulting functions are plotted as the solid curves in Figures 7 and 8. The infinite dilution values of log K1 reported in refs 2 and 3 are also shown in Figure 7, as well as the values for log Q1 at 50 °C in 0.1 and 1.0 m NaCl extracted from gibbsite solubility studies (1). All of these results are shown to be adequately represented by eqs 5-7. In Figure 8, it can be seen that eqs 5-7 do not reproduce the infinite dilution values of log K2 for reaction II reported by Ridley et al. (1) within their experimental error estimates nor their model values for log Q2 at 1.0 molal ionic strength in the 50-75 °C range. However, it can be seen the new function does fit the actual experimental data points reported by Ridley et al. (1) acceptably. Because there are no reliable literature values for log Q2 with which to compare these results, eqs 5-7, as parametrized in Table 5, are considered to adequately represent the temperature and ionic strength dependencies of reaction II. As can be seen in Figures 7 and 8, both studies indicate a very weak temperature dependence of the equilibrium quotients at low temperature, whereas the constants are strongly temperature dependent in the 75-125 °C range. A plausible explanation for this observation is that at low temperatures, the hydrated aluminum ion Al(H2O)63+ forms outer sphere complexes with the sulfate anion, whereas at higher temperatures, the sulfate ion is able to displace water molecules to form inner sphere complexes. The detailed Raman spectroscopic study of aluminum sulfate solutions from room temperature to 184 °C recently published by Rudolph and Mason (42) provides clear documentation of this phenomenon, and this has long been suggested as being a common feature of polyvalent metal sulfate complexes (43, 44 and references cited therein). The constants for reactions I and II evaluated in this study and by Ridley et al. (1) represent overall constants incorporating both inner and outer sphere species, ion pairs, etc. It is extremely difficult to describe quantitatively the individual contributions of such species to the total ion association of Al3+ with SO42-, and no attempt has been made to do so here, although several authors have proposed equilibrium constants describing the 172

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transition from outer to inner sphere complexation for the monosulfate species (42, 43). The sigmoidal nature of the fit functions (solid curves) plotted in Figures 7 and 8 can be considered an artifact of this phenomenon. Nevertheless, the 25 °C enthalpies of reactions I and II obtained by differentiation of eq 6, using the parameters in Table 5, are 8 ( 12 and 29 ( 13 kJ‚mol-1 (uncertainties are 3σ), respectively, in reasonable agreement with the calorimetrically determined values of 9.6 ( 0.3 and 12.9 ( 1.2 kJ‚mol-1, respectively, reported at infinite dilution and 25 °C by Izatt et al. (15). Equations 5-7 may prove to be useful in developing models for the effect of sulfate on the mobility and toxicity of aluminum in acidic natural environments ranging from hot springs and geothermal systems, to weathering of sulfide ore bodies, to acidic soil, stream and lake waters at high latitudes and altitudes. The agreement of the present results with those obtained from conductance and spectrophotometric measurements at 25.0 °C (2, 3) and those at 50.0 °C obtained from potentiometric titrations using a hydrogen electrode concentration cell and gibbsite solubility studies (1) is reassuring because the remaining literature results for this system are very scattered. The results obtained here have important implications for aluminum geochemistry. The values for K1 and K2 at 25.0 °C from this work are the among the highest of all values reported previously. Using the 25 °C values currently incorporated in the PHREEQE computer code (log K1 ) 3.5 and log K2 ) 4.92), Serrano et al. (7) found that aluminum sulfate species constitute >40% of total aqueous aluminum in freshwaters affected by acid sulfate. The larger values for log K1 (3.84 ( 0.12) and log K2 (5.58 ( 0.12) from this study imply even more significant effects of sulfate on the release of aluminum to the aquatic environment.

Acknowledgments This research was sponsored by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DEAC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC. This work was supported in part by an appointment of C.X. to the Oak Ridge National Laboratory Postdoctoral Research Associates Program administered jointly by Oak Ridge National Laboratory and the Oak Ridge Institute for Science and Education. We thank Dr. Moira K. Ridley and Dr. Miroslaw Gruszkiewicz for helpful discussions.

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Received for review June 27, 2000. Revised manuscript received October 4, 2001. Accepted October 17, 2001. ES001424W

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