Ind. Eng. Chem. Res. 2006, 45, 4757-4763
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GENERAL RESEARCH Electrical Conductivity of Concentrated MgSO4-H2SO4 Solutions up to 250 °C Ming Huang and Vladimiros G. Papangelakis* Department of Chemical Engineering and Applied Chemistry, UniVersity of Toronto, 200 College Street, Toronto, Ontario, Canada M5S 3E5
A conductivity cell, developed previously, was employed to investigate the speciation of MgSO4-H2SO4 solutions particularly at high temperatures. These solutions were measured from 15 to 250 °C at the equilibrium vapor pressures. The maximum measured concentrations of MgSO4 and H2SO4 were 0.30 m and 0.45 m, respectively. At 250 °C and constant H2SO4 concentration, the solution conductivity drops with the increase of MgSO4 concentration. It is postulated that this drop is caused by a decrease in the concentration of H+ due to bisulfate formation. However, the limiting equivalent conductivity of H+ was not significantly affected by MgSO4. Application of the extended mean spherical approximation (MSA) theory to the experimental data allowed the coefficients that determine the ionic strength dependence of the average effective radius to be obtained. With these coefficients, the conductivity of the MgSO4-H2SO4 aqueous system can be reproduced up to 250 °C with an average absolute difference of 2.47%. Introduction Much progress has been achieved in measuring and modeling the electrical conductivity of dilute aqueous solutions at high temperatures.1-4 However, less work has been done on the theory and the modeling of conductivity in concentrated solutions. Many industrial installations are processing concentrated electrolyte solutions at high temperatures. The study of electrical conductivity in this type of solutions can offer valuable insights on the solution chemistry. A typical industrial example is from the hydrometallurgy of nickel and cobalt mineral industries where the sulfuric acid pressure leaching process employs temperatures above 150 °C and in a certain process between 230 and 270 °C.5 In this process, the extraction of nickel and cobalt from laterite ores to the aqueous solution is an acid-driven process.6 A sufficient amount of acid is required to reduce the processing time and to maximize the fraction of Ni and Co dissolved. In this type of solution, the dominant electrolyte is H2SO4 with Al2(SO4)3 and MgSO4 as impurities. It is known that the amount of required free acid concentration at the end of the leach increases with increasing Mg concentration in solution.6 This has been explained previously by a solubility-based speciation study that postulated bisulfate ion formation was the main cause for the decrease of hydrogen ion concentration.7 Previous measurements of the electrical conductivity of H2SO4-Al2(SO4)3 solutions up to 250 °C investigated how conductivity relates to the solution speciation and concluded that aluminum sulfate does not effect the bisulfate ion formation because it does not dissociate much.8 However, the effect of MgSO4 and its speciation on the electrical conductivity of leach solutions remains unclear. Because of the Grotthus conduction,9 H+ has a more significant contribution to the bulk conductivity than other ions in aqueous solutions. If there is a drop in [H+], there should also be a drop in the * To whom correspondence should be addressed. Tel.: 1-416-9781093. Fax: 1-416-978-8605. E-mail:
[email protected].
electrical conductivity. This hypothesis is tested in the present work, and the phenomenon is quantified. The specific conductivity, σ [given in 1/(Ω m)], is a property that can be directly obtained from electrical conductivity measurements.
σ)
(R1)(Al )
(1)
where R (in Ω) is the solution resistance between the electrodes, l (in m) is their distance, and A (in m2) is their surface area. The cell constant (l/A) is obtained experimentally through calibration of the cell using solutions with known conductivities. For a single electrolyte solution, the specific conductivity can be normalized for the equivalent concentration to be a value known as the equivalent conductivity of the electrolyte, Λ (in 1/[Ω m mol of charge])
Λ)
σ zc
(2)
where zc is the ionic charge z (in mol of charge/mol of ion) times the molar concentration c (in mol/m3) of either the cation or the anion. For a single electrolyte, the product zc is the same for either cation or anion. If there is more than one electrolyte in solution, eq 3 can be applied to obtain the specific conductivity in terms of the equivalent conductivities of the individual ions n
σ)
|zi|ciλi ∑ i)1
(3)
where zi is the ionic valence, ci is the molar concentration, and λi is the equivalent conductivity of ion i. This equation is used to calculate the equivalent conductivity of H+ in this work. To describe solution conductivity in electrolyte solutions, many models have been proposed based on perturbation theory10
10.1021/ie0507631 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/18/2006
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Figure 1. Conductivity cell.15
theory.11
and integral equation Among those models, the mean spherical approximation (MSA) model has received extensive attention.12,13 To extend the MSA model to multielectrolyte aqueous solutions in wide concentration and temperature ranges, Anderko and Lencka14 introduced several equations for engineering use. According to their work, it is possible to use the parameters obtained from binary systems to predict the conductivity of ternary and quaternary systems, which is very useful for industrial applications. Such parameters of the MgSO4-H2SO4-H2O system were obtained and reported in this paper. These parameters are needed to model the electrical conductivity of high-temperature hydrometallurgical solutions in an effort to gain useful chemistry insights and possible correlations between conductivity and major process variables such as free acidity. Experimental Section In 2000, Baghalha and Papangelakis8,15 introduced a conductivity cell to measure sulfuric acid solutions in an effort to understand the electrochemistry of laterite leach solutions at high temperature and high electrolyte concentrations. With its high cell constant (19.97 ( 0.06 cm-1), the cell was able to measure the conductivity of H2SO4-Al2(SO4)3 solutions at 0.35 and 0.45 m H2SO4 and various molalities of Al2(SO4)3 up to 0.20 m and at temperatures from 15 to 250 °C inside a pressure vessel. The same cell was used to measure the MgSO4-H2SO4-H2O system in this work. It is shown in Figure 1. A titanium Parr autoclave is used to house the conductivity cell which is shown in Figure 2. Platinization of Electrodes. To obtain stable and accurate data, the electrodes were platinized to reduce polarization. The cell was immersed in a platinizing solution (Yellow Springs Instrument Inc.) at room temperature. The amount of solution was carefully controlled so that only the bottom faces of the electrodes were immersed to avoid platinizing the top surfaces of the electrodes. The leads of the cell were then connected to an AR50 pH/conductivity meter from Fisher Scientific Inc. for automatic platinization. To stabilize the newly platinized electrodes, the cell was immersed first in tap water and then in deionized water at room temperature for 12 h each before calibration. Calibration of the Cell. The cell was calibrated at room temperature by using three different conductivity standards from Fisher Scientific Inc. with nominal conductivities of 1000,
Figure 2. 2 L Parr titanium autoclave used to house conductivity cell.15
10 000, and 100 000 µS/cm. The signal generated by the AR50 pH/conductivity meter was an alternating square-wave voltage with an amplitude of 0.6 V. The frequency of this signal was fixed at 225 Hz. The meter output was the specific conductivity (in mS/cm) which was calculated based on eq 1. In a typical calibration, the cell was rinsed three times with fresh standard solutions. The cell was then immersed in the fresh conductivity standard at room temperature until a stable value was obtained. The cell constant was automatically calculated by the conductivity meter. Preparation of Solutions. The reagents used in this work were MgSO4 (98.5 wt %) from Fisher Scientific and Baker Analyzed reagent grade H2SO4 (96.8 wt %). Deionized water was obtained from a Millipore water system with a conductivity of 4 × 10-4 mS/cm after exposure to the atmosphere. For each experiment, the required amounts of reagents were weighed and dissolved in enough deionized water produce 1200 g of total water, including the water from H2SO4 (96.8 wt %) and MgSO4 (98.5 wt %). About 40 ppm nickel (in the form of Ni(NO3)2) was added to all solutions to prevent corrosion of the titanium parts inside the autoclave. The NO3- is a strong oxidizing ion that can inhibit corrosion of the titanium alloys in acids such as H2SO4.8 The conductivity contribution of Ni(NO3)2 to the experimental data was ignored on the basis of blank tests. Measurement of Conductivity. A total of 1100 mL solution was placed in a Pyrex glass liner inside the autoclave bomb. The autoclave head was then closed, and the bomb was heated by an electrical heating mantel to 25 °C. The specific conductivity of the solution at 25 °C was recorded. The autoclave bomb was then heated to 250 °C in about 50 min. The specific conductivity of the solution at 250 °C was recorded. Afterward, the autoclave was cooled by passing tap water through the cooling coil, so that the specific conductivity could be recorded on cooling at 25 °C intervals down to 25 °C. The conductivity at 25 °C was then compared with the previously recorded data at 25 °C. The conductivity at 15 °C was also recorded. During the experiment, the pressure in the autoclave was always the equilibrium vapor pressure of the solution, which was slightly below that of pure water at the given temperatures. Results Theoretically, concentrations in molality are independent of temperature. However, because of water evaporation, they will
Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4759
Figure 3. Solubility of MgSO4 in water.16
Figure 5. Equivalent conductivity of 0.01 m MgSO4.3
Figure 4. Solubility of MgSO4 in water.7,16 Table 1. Specific Conductivities (mS/cm) of the MgSO4-H2O Solutions
Figure 6. Specific conductivities of the MgSO4-H2O solutions. Table 2. Specific Conductivities (mS/cm) of H2SO4-H2O Solutions
MgSO4
H2SO4
temp (°C)
0.01 m
0.10 m
0.20 m
0.40 m
temp (°C)
0.05 m
0.25 m
15 25 50 75 100 125 150 175 200 225 250
1.395 1.716 2.534 3.355 3.925 4.156 4.047 3.510 2.817 2.110 1.464
8.861 10.87 16.01 19.80 22.60 23.24 21.81 18.65 14.64
15.14 18.82 27.68 34.26 38.97 40.03 37.71 32.90
24.53 29.78 43.31 54.92 62.26 64.49 62.08 55.04
15 25 50 75 100 125 150 175 200 225 250
22.16 24.36 28.32 30.92 33.26 35.56 37.42 38.83 39.51 39.02 38.16
100.1 108.3 131.4 148.8 161.3 170.9 178.8 182.9 183.9 180.8 174.6
increase above 100 °C. Thus, all concentrations above 100 °C reported in this paper are nominal. The procedure to estimate the true electrolyte molalities has been published previously.15 According to that procedure, the real concentration of a solution is its nominal concentration times 1.007 (correction factor at 250 °C) at 250 °C. MgSO4-H2O Solutions. The solubility of MgSO4 in water from 25 to 250 °C is shown in Figure 3. Details of the solubility curve from 180 to 250 °C are shown in Figure 4.7,16 Because the solubility of MgSO4 in water at 250 °C is 0.02 m (a calculated value based on the work of Baghalha and Papangelakis7), only the solution with 0.01 m ((0.0005) MgSO4 could be heated to 250 °C without precipitation. Higher concentrations of MgSO4 were measured up to their respective maximum temperature limits that would not trigger precipitation.16 Specific conductivities are reported in Table 1 and plotted in Figures 5 and 6. The reproducibility of the measured values was always within (0.5%.
As can be seen from Figure 5, excellent agreement exists between measured and processed literature values reported by Ritzert and Franck3 in the form of equivalent conductivity. The latter values were obtained under different densities at fixed pressures. Because density and conductivity are commonly reported together as smooth curves,3,17 the original data were extrapolated to the density of solutions tested in this study. The density was calculated on the basis of the work of Casas et al.18 Figure 6 depicts a characteristic maximum in the conductivity curve resulting from the association of Mg2+ with SO42with increasing temperature.7 This maximum does not depend on concentration and is always around 125 °C. H2SO4-H2O Solutions. The specific conductivity of H2SO4-H2O solutions was also measured up to 250 °C and 0.25 m. Values are reported in Table 2 and plotted in Figure 7. Previously published data at 0.35 and 0.45 m H2SO4 ((0.0005) are also included in Figure 7.8
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Figure 7. Specific conductivities of the H2SO4-H2O solutions up to 250 °C.8,19
Figure 9. Specific conductivities of the MgSO4-H2SO4-H2O solutions at 0.35 m H2SO4 up to 250 °C.8
Figure 8. Solution composition of the tested MgSO4-H2SO4 system.7
Figure 10. Specific conductivities of the MgSO4-H2SO4-H2O solutions at 0.45 m H2SO4 up to 250 °C.8
Table 3. Measured Specific Conductivities (mS/cm) of MgSO4-H2SO4-H2O Solutions at 0.35 m H2SO4
Table 4. Measured Specific Conductivities (mS/cm) of MgSO4-H2SO4-H2O Solutions at 0.45 m H2SO4 MgSO4
MgSO4 temp (°C)
0.10 m
0.20 m
temp (°C)
0.10 m
0.20 m
0.30 m
15 25 50 75 100 125 150 175 200 225 250
126.0 140.1 166.5 177.2 184.8 194.1 202.3 209.8 213.9 213.8 202.2
119.3 130.2 150.5 160.2 167.1 175.5 183.0 189.8 193.5 193.3 186.9
15 25 50 75 100 125 150 175 200 225 250
158.0 173.8 208.1 233.3 252.1 263.3 276.2 285.4 288.3 288.1 282.1
147.7 162.2 189.7 202.7 215.5 226.0 236.9 246.3 251.5 251.2 242.0
138.5 151.8 173.2 184.0 192.2 199.1 207.6 224.2 225.7 223.2 216.8
MgSO4-H2SO4-H2O Solution. The compositions of the MgSO4-H2SO4-H2O solutions are shown in Figure 8 with a previously established solubility.7 This ensured there was no solid precipitate within the temperature range tested. The specific conductivities of the three MgSO4-H2SO4-H2O solutions at 0.10 and 0.20 m MgSO4 with a constant 0.35 m H2SO4 are reported in Table 3 and plotted in Figure 9. The specific conductivities for the MgSO4-H2SO4-H2O system at 0.45 m H2SO4 are reported in Table 4 and plotted in Figure 10. The values at 0 m MgSO4 in Figures 9 and 10 are from Baghalha and Papangelakis.8 As shown in Figures 9 and 10, the addition of MgSO4 dramatically decreases the conductivity. Figure 11 shows a speciation diagram for Mg species in MgSO4-H2SO4-H2O solutions at 250 °C and at 0.45 m H2SO4, as calculated using an ion-association-interaction approach.7 All related equilibrium constants employed in this paper were obtained from the
independent work of Baghalha and Papangelakis.7 For all ions except H+, the concentration is increasing. The drop in the solution conductivity can only be attributed to the drop in the concentration of H+ caused by the formation of HSO4- (reaction R2). The reactions are
MgSO4 f Mg2+ + SO42-
(R1)
H+ + SO42- f HSO4-
(R2)
Mg2+ + SO42- f MgSO04(aq)
(R3)
Recent data have confirmed that the HSO4- anion in aqueous solutions is a non-complexing anion.20 However, it just proves that HSO4- does not form contact ion pairs with transition metals. The possibility of inner-sphere ion-pairing which would affect conductivity still exists. Rather than introducing a new
Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4761
Figure 11. Speciation of the MgSO4-H2SO4-H2O solutions at 250 °C and 0.45 m H2SO4.
Mg2+-HSO4-,
reaction which generates a cation-anion binary interaction in the activity coefficient model was adopted in this paper. Limiting Equivalent Conductivity of H+ at 250 °C. Baghalha and Papangelakis8,15 used eq 4 to obtain λH+ in H2SO4Al2(SO4)3 solutions.
λH+ λHo +
)
λHSO4o λHSO 4
)
λAl(SO4)+
(4)
o λAl(SO 4)+
σ ) mH+λH+ + mHSO4-λHSO4- + mMg2+λMg2+ + mSO42-λSO42(5) Rearranging eq 5, we obtain
[
λHSO4λH+
+ mMg2+
]
λSO42λMg2+ + mSO42λH + λH+ (6)
Using the same assumption
λ H+ λHo +
)
λHSO4o λHSO 4
)
λMg2+ o λMg 2+
)
λSO42-
(7)
o λSO 24
We obtain
[
σ ) λH+ mH+ + mHSO4-
o λHSO 4
λHo +
+ mMg2+
o λMg 2+
λHo +
]
o λSO 24 + mSO42+ o λH+ (8)
Rearranging eq 8, we obtain
[
o λHSO 4
λH+ ) σ/ mH+ + mHSO4-
λHo +
+ mMg2+
o λMg 2+
λHo +
]
o λSO 24
+ mSO42+
λHo + (9)
o o The limiting conductivities, λoH+, λHSO -, and λMg2+ can be 4 21 calculated by using the Smolyakov equation.
ln λo(T)η(T) ) A + B/T
Table 5. Estimation of λ° Values at 250 °C
ion H+
HSO4Mg2+ SO42-
A (Anderko and Lencka)14
B (Anderko and Lencka)14
λ° at 250 °C (mS/cm/equiv/L) (this work)
-3.9726 -3.5038 -3.0347 -2.9457
837.79 119.58 -3.505 90.983
872.6 353.3 446.4 584.6
Table 6. Structural Entropy at 25 °C
They assumed that changes in the solution will affect each species equally. The same assumption is used in this work. The specific conductivity of the MgSO4-H2SO4-H2O solution at 250 °C can be related to the equivalent conductivities of major ions in the solution (i.e., H+, HSO4-, Mg2+, and SO42-).
σ ) λH+ mH+ + mHSO4-
Figure 12. Molal ionic equivalent conductivity of H+ as a function of ionic strength at 250 °C.8
(10)
ion
∆S°str at 25 °C (J/K mol)22
H+ HSO4SO42Mg2+ Al3+
-32 -44 -69 -82 -332
where λ° is the limiting conductivity, η is the viscosity of pure water, and A and B are adjustable constants. Table 5 shows regressed A and B values (by Anderko and Lencka14) with an average deviation of less than 1% from the experimental data points. The limiting equivalent conductivities of ions shown in Table 5 are calculated using eq 10. The viscosity of water at 250 °C used is 107 × 10-6 N s/m2.8 Using the experimental data of specific conductivity at 250 °C and the known solution chemistry shown in Figure 11, we calculated λH+ at high concentrations from eq 9. The results are shown in Figure 12 as a function of the ionic strength which was calculated on the basis of previous work.7 In Figure 12, the solutions measured include 0.05-0.45 m H2SO4, 0.35 m H2SO4-up to 0.20 m MgSO4, 0.45 m H2SO4-up to 0.30 m MgSO4, and the previously published 0.45 m H2SO4-up to 0.20 m Al2(SO4)3.8 The λH+ values in Figure 12 are based on molality. The molarity-based value of λH0 + at 250 °C (872.6 mS/cm/ equiv/L in Table 5) was multiplied by the density of pure water at 250 °C (0.80 kg/L)8 to convert it to molality units. As can be seen in Figure 12, the equivalent conductivity of H+ is less sensitive to ionic strength change in MgSO4 solutions than in Al2(SO4)3 solutions. The ionic strength for all solutions reported in Figure 12 are obtained using an ion-associationinteraction approach.7 As pointed out by Baghalha and Papangelakis,7,8 the majority of Al tends to exist as Al2(SO4)30 at 250 °C. According to Table 6, this is attributed to the much higher tendency of Al3+ to form stable structures with water molecules (hydration) and other ions, which reduce the amount of free water H+ can use in its Grotthus conduction. The structural entropy of Mg2+ is only -82 J/K mol22 which has a
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Table 7. Coefficients that Determine the Ionic Strength Dependence of the Average Effective Radius (for eqs 11 and 12) cation-anion pair
c1,0
H+-HSO4Mg2+-HSO4-
c2,0
0.3623 -3.2461
0.6649 5.0504
c3,0 0.7121 1.9112
c1,1
c2,1 10-1
0.3057 × 0.2381 × 10-1
c3,1 10-1
-0.2837 × -0.2667 × 10-1
0.1731 × 10-2 -0.3064 × 10-2
much less impact on the amount of free water. It can be concluded that MgSO4 affects the solution conductivity mainly through the formation of bisulfates which caused a drop in [H+]. MSA Parameters of MgSO4-H2SO4-H2O System. To model the electrical conductivity of concentrated electrolyte solutions, Anderko and Lencka14 suggested the use of an effective ion size to reflect the altered solvation structure around ions which affects interactions between ions. Equations 11 and 12 were proposed by them to calculate the ionic-strength dependence of an effective ion radius.
κjeff )
I1/2 + c3 (c1 + c2I1/2)10
(11)
where c1, c2, and c3 are adjustable parameters and I is the ionic strength. To account for the temperature dependence of ci (i ) 1, 2, 3), eq 12 was proposed for regressing the experimental data in wide temperature ranges.14
ci ) ci,0 + ci,1(T - 298.15)
i )1, 2, 3
(12)
When only overall conductivity data are available, it is not possible to distinguish the conductivity contribution from cations and anions without transference data. It’s more reasonable to calculate the average effective radii of the cation-anion pair.14 Applying the extended mean spherical approximation theory to the obtained experimental data, coefficients that determine the ionic strength dependence of the average effective radius of binary cation-anion pairs were obtained from regression using commercial software from OLI Systems Inc. and are shown in Table 7. The temperature-dependent coefficients, c1,1, c2,1 and c3,1, are in the magnitude of 10-2 or higher. As a comparison, the coefficients of the Na+-Cl- pair are in the magnitude of 10-3.14 Thus, the temperature has a greater impact on the effective radius of H+-HSO4- and Mg2+-HSO4-. With the coefficients obtained from regression, the conductivity of the MgSO4-H2SO4-H2O system can be reproduced at temperatures up to 250 °C with an average absolute difference (AAD) of 2.47%, calculated by eq 13. Figures 13 and 14 show the calculation result for MgSO4-H2SO4-H2O solutions.
AAD )
∑|
|
σexptl - σcald σexptl × 100 N
Figure 13. Specific conductivity of the MgSO4-H2SO4-H2O solutions.
(13)
Conclusions A conductivity cell, developed previously, was employed in an effort to investigate the conductivity of MgSO4-H2SO4H2O solutions at high temperatures (up to 250 °C). There was a very good agreement for the conductivity measurements of 0.01 m MgSO4 between this study and the literature. The addition of MgSO4 to H2SO4 solutions caused a significant drop of the conductivity. This was explained by the decrease of H+ caused by the reaction between H+ and SO42- forming bisulfate ions that act as a proton sink. However, the limiting equivalent conductivity of H+ was not significantly affected by the addition of MgSO4. This was attributed to the low tendency of Mg2+ to form stable solvated structures. By applying the extended mean spherical approxima-
Figure 14. Specific conductivity of the MgSO4-H2SO4-H2O solutions.
tion model to the experiment data, we obtained the coefficients needed to describe the ionic strength dependence of the average effective radius. With these coefficients, the conductivity of the MgSO4-H2SO4-H2O system can be reproduced at temperatures up to 250 °C with an average absolute difference at 2.47%. These coefficients are very useful in modeling the electrical conductivity of hydrometallurgical process solutions, particularly in high-temperature process solutions from 150 to 250 °C where highly acidic multicomponent solutions prevail. Accurate measurement of the conductivity provides useful insights into the chemistry of highly concentrated industrial solutions and the identification of useful correlations between the electrical conductivity and major process variables such as free acidity. Acknowledgment Financial support for this work was provided by the Centre for Chemical Process Metallurgy of the University of Toronto and the Natural Sciences and Engineering Research Council of Canada (NSERC). Literature Cited (1) Hnedkovsky, L.; Wood, R. H.; Balashov, V. N. Electrical Conductances of Aqueous Na2SO4, H2SO4, and Their Mixtures: Limiting Equivalent Ion Conductances, Dissociation Constants, and Speciation to 673 K and 28 MPa. J. Phys. Chem. B 2005, 109, 9034. (2) Quist, A. S.; Marshall, W. L. Electrical conductances of aqueous potassium nitrate and tetramethylammonium bromide solutions to 800 °C and 4000 bar. J. Chem. Eng. Data 1970, 15, 375.
Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4763 (3) Ritzert, G.; Franck, E. U. Electrical conductivity of aqueous solutions at high temperatures and pressures 0.1. KCl, BaCl2, Ba(OH)2 and MgSO4 up to 750 °C and 6 kbar. Ber. Bunsen-Ges. Phys. Chem. 1968, 72, 798. (4) Corti, H. R.; Trevani, L. N.; Anderko, A. In Aqueous systems at eleVated temperatures and pressures: Physical chemistry in water, steam and hydrothermal solutions, 1st ed.; Palmer, D. A., Fernaandez-Prini, R. J., Harvey, A. H., Eds.; Elsevier Academic Press: Boston, 2004; pp 321375. (5) Rubisov, D. H.; Papangelakis, V. G. The effect of acidity “at temperature” on the morphology of precipitates and scale during sulphuric acid pressure leaching of laterites. CIM Bull. 2000, 93, 131. (6) Papangelakis, V. G.; Liu, H.; Rubisov, D. H. In International Laterite Nickel Symposium; Proceedings of [a] Symposium held during the TMS Annual Meeting; Imrie, W. P., Lane, D. M., Eds.; Minerals, Metals & Materials Society: Charlotte, NC, 2004; pp 289-305. (7) Baghalha, M.; Papangelakis, V. G. The ion-association-interaction approach as applied to aqueous H2SO4-Al2(SO4)3-MgSO4 solutions at 250 °C. Metall. Mater. Trans. BsProc. Metall. Mater. Proc. Sci. 1998, 29, 1021. (8) Baghalha, M.; Papangelakis, V. G. High-temperature conductivity measurements for industrial applications. 2. H2SO4-Al2(SO4)3 solutions. Ind. Eng. Chem. Res. 2000, 39, 3646. (9) Agmon, N. The Grotthus mechanism. Chem. Phys. Lett. 1995, 224, 456. (10) Barker, J. A.; Henderson, D. Perturbation theory and equation of state for fluids. 2. A successful theory of liquids. J. Chem. Phys. 1967, 47, 4714. (11) Talbot, J.; Lebowitz, J. L.; Waisman, E. M.; Levesque, D.; Weis, J. J. A comparison of perturbative schemes and integral-equation theories with computer-simulations for fluids at high-pressures. J. Chem. Phys. 1986, 85, 2187. (12) Copeman, T. M.; Stein, F. P. An explicit nonequal diameter MSA model for electrolytes. Fluid Phase Equilib. 1986, 30, 237. (13) Gering, K. L.; Lee, L. L.; Landis, L. H.; Savidge, J. L. A molecular approach to electrolyte solutions: Phase behavior and activity coefficients
for mixed-salt and multisolvent systems. Fluid Phase Equilib. 1989, 48, 111. (14) Anderko, A.; Lencka, M. M. Computation of electrical conductivity of multicomponent aqueous systems in wide concentration and temperature ranges. Ind. Eng. Chem. Res. 1997, 36, 1932. (15) Baghalha, M.; Papangelakis, V. G. High-temperature conductivity measurements for industrial applications. 1. A new cell. Ind. Eng. Chem. Res. 2000, 39, 3640. (16) Seidell, A.; Solubilities of inorganic and metal organic compounds: A compilation of quantitatiVe solubility data from the periodical literature, 3d ed.; Linke, W. F., Ed.; D. Van Nostrand: New York, 1940; pp 985. (17) Quist, A. S.; Marshall, W. L.; Jolley, H. R. Electrical conductances of aqueous solutions at high temperature and pressure. II. The conductances and ionization constants of sulfuric acid-water solutions from 0 to 800 °C and at pressures up to 4000 bar. J. Phys. Chem. 1965, 69, 2726. (18) Casas, J. M.; Papangelakis, V. G.; Liu, H. Performance of three chemical models on the high-temperature aqueous Al2(SO4)3-MgSO4H2SO4-H2O system. Ind. Eng. Chem. Res. 2005, 44, 2931. (19) Hinatsu, J. T.; Tran, V. D.; Foulkes, F. R. Electrical conductivities of aqueous zinc sulfate-sulfuric acid solutions. J. Appl. Electrochem. 1992, 22, 215. (20) Tremaine, P. R.; Trevani, L. N. In 34th Annual Hydrometallurgy Meeting of CIM; Papangelakis, V. G., Ed.; Canadian Institute of Mining, Metallurgy and Petroleum: Banff, Alberta, Canada, 2004; pp 545-560. (21) Smolyakov, B. S. Limiting equivalent ionic conductance up to 200 °C. Int. Corros. Conf. Ser. 1976, NACE-4, 177-181. (22) Marcus, Y. Ion SolVation; John Wiley & Sons: New York, 1985; pp 125-127.
ReceiVed for reView June 27, 2005 ReVised manuscript receiVed March 28, 2006 Accepted April 19, 2006 IE0507631
