1598
Ind. Eng. Chem. Res. 2007, 46, 1598-1604
GENERAL RESEARCH Electrical Conductivity of Concentrated Al2(SO4)3-MgSO4-H2SO4 Aqueous 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
The extended mean spherical approximation (MSA) model was applied to previously published electrical conductivity data for H2SO4-H2O, Al2(SO4)3-H2SO4-H2O, and MgSO4-H2SO4-H2O solutions. It was found that the dominant ion pairs affecting solution conductivities are H3O+-HSO4-, Al3+-HSO4-, and Mg2+HSO4-. Coefficients determining the effective radii of the H3O+-HSO4-, Al3+-HSO4-, and Mg2+-HSO4ion pairs were obtained by regressing experimental data. With these coefficients, the conductivities of H2SO4-H2O and MgSO4-H2SO4-H2O solutions can be reproduced up to 250 °C with an average relative difference of less than 2%. For Al2(SO4)3-H2SO4-H2O solutions, this approach worked only between 225 and 250 °C because of insufficient speciation data at other temperatures. These coefficients were used to predict the electrical conductivities of mixed Al2(SO4)3-MgSO4-H2SO4-H2O solutions at temperatures between 225 and 250 °C. The difference between calculated values and experimental data was below 5%, which is good for engineering use. Finally, a previously suggested equal-change assumption was used to calculate the equivalent conductivity of H3O+ at 250 °C, producing a 4% difference compared to that obtained from the MSA model. Introduction The aqueous chemistry of concentrated electrolyte solutions is of great importance in industrial and technological applications such as the modern hydrometallurgical process for Ni and Co extraction at temperatures between 230 and 270 °C.1 In this process, the extraction of nickel and cobalt from laterite ores into aqueous solution is acid-driven process.2 A sufficient amount of acid is required to reduce the processing time and to maximize the fractions of Ni and Co dissolved. The study of electrical conductivity in this type of solution can offer valuable insight into the solution chemistry. The dominant electrolytes in this process are H2SO4, as well as Al2(SO4)3 and MgSO4 as impurities. The electrical conductivities of H2SO4-H2O, Al2(SO4)3-H2SO4-H2O, and MgSO4-H2SO4-H2O solutions were investigated in the past.3,4 It was found that the solution conductivity drops with the addition of Al2(SO4)3 or MgSO4 to sulfuric acid solutions. For Al2(SO4)3-H2SO4-H2O solutions, the drop was attributed to the decrease of the ionic conductivity of H+ ion resulting from the loss of free water to the hydration of free and complex Al ions.3 For MgSO4-H2SO4-H2O solutions, the drop was caused by the loss of H+ ion to bisulfate formation.4 In this article, the investigation has been furthered to include quaternary Al2(SO4)3-MgSO4-H2SO4-H2O solutions. The ultimate objective is to model process solutions, which contain a variety of electrolytes such as NiSO4, CoSO4, MnSO4, and Fe2(SO4)3, in addition to H2SO4, Al2(SO4)3, and MgSO4. However, the number of necessary experiments increases exponentially with increasing number of electrolytes. Because of the complexity of high-temperature experiments and the * To whom correspondence should be addressed. Tel.: 1-416-9781093. Fax: 1-416-978-8605. E-mail:
[email protected].
exponential increase of associated costs, the effectiveness of a simple additive approach is investigated here. It should be able to predict the conductivity of multicomponent solutions using data from binary or ternary systems, which are easier to measure or obtain from literature. The specific conductivity, σ (Ω-1‚m-1), is a function of the equivalent conductivities of the individual ions and the respective concentrations, i.e. n
σ)
|zi|ciλi ∑ i)1
(1)
where zi is the ionic valence, ci is the molar concentration, and λi is the equivalent conductivity of ion i. To describe the conductivity of a certain system, both a conductivity model and a chemical model are necessary, the latter to yield the ionic speciation. In this work, the conductivity model adopted is the mean spherical approximation (MSA) model. Because of its capability to model single or mixed solvent systems ranging from infinite dilution to the molten salt state, and from the solution freezing point up to 300 °C, the mixed-solvent electrolyte (MSE) model was adopted as the chemical model. Only details of the MSA model are discussed in this work. Speciation calculations using the MSE model can be found elsewhere.5 Both the MSA and MSE models are now incorporated into commercial software, by OLI Systems. To calculate solution conductivity in electrolyte solutions, many conductivity models based on perturbation theory6 and integral equation theory7 have been proposed. Among these models, the MSA has received extensive attention.8,9 As shown
10.1021/ie060878k CCC: $37.00 © 2007 American Chemical Society Published on Web 02/01/2007
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007 1599
in eq 2, it includes two corrections for electrophoretic and relaxation effects
λi )
λ0i
(
1+
)( )
δυiel υ0i
δX 1+ X
NS
∑k ckκk,i
∑k ckκi,k
κj,eff ) κi,j
(3)
∑k ckκk,j
∑k ckκj,k
(4)
where the sum over k covers all species in the solution (i.e., ions, ion-pairs, and solvent molecules) and ck is the concentration (in mol‚dm-3) of species k. The parameter κi,j (and similarly κi,k, κk,i, κj,k, and κk,j) can be interpreted as the effective radius of species i in the presence of species j, reflecting the short-range interactions between the two species. The binary parameter between ions i and j is defined as a function of the ionic strength, I 0 exp[I0.2(d1,ij + d2,ijI0.4 + d3,ijI)] κi,j ) κi,j
0 κi,j
(2)
In the above equation, λ0i is the ionic conductivity of ion i at infinite dilution, υ is the ion’s velocity with respect to the collective current mode of the ion atmosphere, X is the timedependent interaction of the moving ion with the surrounding ions in the solution, δυeli is the electrophoretic correction, and δX/X is the relaxation correction. The closed form of δυeli /υ0i and δX/X can be achieved only for systems with a single cation and a single anion.10 To extend the MSA model to multi-electrolyte aqueous solutions in wide concentration and temperature ranges, Anderko and Lencka10 introduced several equations for engineering use. They suggested that it is possible to use the parameters obtained from binary systems to predict the conductivities of ternary and quaternary systems, which is very useful for industrial applications. This model was extended further to describe the conductivity of mixed-solvent electrolyte solutions by Wang et al.13 This latest version of the MSA model is adopted in the present work. The modeling methodology consists of two parts: (1) computation of limiting conductivities of ions in pure and mixed solvents as a function of temperature and solvent composition and (2) computation of the dependence of electrical conductivity on electrolyte concentration. Part 2 is achieved using eq 2. For part 1, the limiting conductivity of an ion i in a mixed solvent consisting of two miscible solvents is a function of its limiting ion conductivities in both solvents and modified volume fractions of the two solvents.11 The equations that link effective radii and the electrical conductivity can be found elsewhere.10 For accurate modeling of electrical conductivity using the MSA model, the essential quantities are the ionic radii κi and κj. These values are needed to quantify the electrophoretic and relaxation corrections included in eq 2. After considering shortrange and middle-range interactions, i.e., ion-ion, ion-ionpair, and ion-solvent, Wang et al.13 defined the effective radii for each cation (i)-anion (j) pair as
κi,eff ) κi,j
0 , d1,ij, d2,ij, and d3,ij are linearly dependent The values of κi,j on solvent composition and are calculated as
(5)
)
(0) ∑L xLκL,ij
(6)
and NS
dM,ij )
(M) ∑L xLdL,ij
(M ) 1, 2, 3)
(7)
where xL is the mole fraction of solvent L on a solute-free basis and the sums are over all solvent components. In eqs 6 and 7, (0) (M) κL,ij and dL,ij are adjustable MSA parameters that can be determined from experimental conductivity data. The equations that link the effective radii and the electrical conductivity can be found elsewhere.10 In this work, the MSA parameters for H2SO4-H2O, Al2(SO4)3-H2SO4-H2O, and MgSO4-H2SO4-H2O subsystems are reported. Then, the experimental conductivities of Al2(SO4)3-MgSO4-H2SO4-H2O solutions at temperatures up to 250 °C are presented and compared with predictions based on the MSA parameters of the subsystems. Finally, a previously suggested equal-change assumption was used to calculate the equivalent conductivity of H3O+ at 250 °C and compared with that obtained from the MSA model. Experimental Section In 2000, Baghalha and Papangelakis3,12 introduced a new conductivity cell in an effort to understand the electrochemistry of laterite leach solutions at high temperature and high electrolyte concentrations. With a known cell constant (19.97 ( 0.06 cm-1), the cell was used to measure the conductivities of Al2(SO4)3-H2SO4-H2O solutions3 and MgSO4-H2SO4H2O solutions4 at temperatures from 15 to 250 °C inside a pressure vessel. The same cell was used to measure the conductivities of Al2(SO4)3-MgSO4-H2SO4-H2O solutions in the present work. The details of the experimental setup and procedures were published previously.12 Preparation of Solutions. The reagents used were Al2(SO4)3‚ 18H2O (99.4 wt %) and MgSO4 (98.5 wt %) from Fisher Scientific and reagent-grade H2SO4 (96.8 wt %) from J.T. Baker Chemicals. Deionized water was produced using a Millipore water system and had 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 to produce 1200 g of total water, including water from Al2(SO4)3‚18H2O (99.4 wt %), MgSO4 (98.5 wt %), and H2SO4 (96.8 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. NO3- is a strong oxidizing ion that can inhibit corrosion of titanium alloys in acids such as H2SO4.3 The conductivity contribution of Ni(NO3)2 to the experimental data was ignored based on blank tests. Theoretically, concentrations in molality are independent of temperature. However, because of water evaporation in a closed vessel, they increase above 100 °C. Thus, all concentrations above 100 °C reported in this work are nominal. The procedure to estimate the true electrolyte molalities has been published previously.12 According to that procedure, the real concentration of a solution is its nominal concentration times 1.007 at 250 °C.
1600
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007
Table 1. Coefficients Determining the Ionic Strength Dependence of the Average Effective Radius for the H3O+-HSO4- Ion Pair (Eqs 5-7) parameter
value
parameter
κH(00) + 2O,H3O /HSO4
-1.30607
κH(01) + 2O,H3O /HSO4
dH(10) + 2O,H3O /HSO4
-2.00191
dH(20) + 2O,H3O /HSO4 dH(30) + 2O,H3O /HSO4
parameter
value
10-2
κH(02) + 2O,H3O /HSO4
426.351
dH(11) + 2O,H3O /HSO4
-0.192620 × 10-1
dH(12) + 2O,H3O /HSO4
2854.71
-9.26779
dH(21) + 2O,H3O /HSO4
10-1
3.52463
dH(31) + 2O,H3O /HSO4
Results Because of a lack of thermodynamic data, the speciation of the Al2(SO4)3-H2SO4-H2O system was obtained between 225 and 250 °C only, based on known solubility data16 and the methodology described in the work of Liu and Papangelakis.5 The speciation is sufficient, as it can describe solubility within a wide range of temperatures and concentrations accurately. For the MgSO4-H2SO4-H2O system, solubility-calibrated speciation data were available for the whole temperature range of interest in the present work. All speciation reported in this work is based on the OLI-MSE-H3O+ framework,11 where the H3O+ ion is assumed to exist rather than the H+ ion. H2SO4-H2O Solutions. The specific conductivities of concentrated H2SO4-H2O solutions were reported previously by Papangelakis and his co-workers3,4 up to 250 °C and up to 0.45 m H2SO4. It was found that the electrical conductivity of aqueous sulfuric acid solutions increases with increasing concentration of sulfuric acid. The solution conductivity increases first with increasing temperature up to about 225 °C, and then it drops slightly as a result of thermal expansion, which means that fewer ions exist in a fixed volume. It is well known that the second dissociation constant of sulfuric acid decreases with increasing temperature. Thus,
value 0.603295 × 0.463615 ×
-0.166199 × 10-1 Table 2. Coefficients Determining the Ionic Strength Dependence of the Average Effective Radius for the Al3+-HSO4- Ion Pair (Eqs 5-7) parameter
value
κH(00) 3+ 2O,Al /HSO4
0.146912
dH(10) 3+ 2O,Al /HSO4
0.422601
dH(20) 3+ 2O,Al /HSO4
1.35702
dH(30) 3+ 2O,Al /HSO4
-0.77424
sulfuric acid can be considered as a monoprotic acid above 150 °C. The speciation of H2SO4-H2O solutions at 250 °C is shown in Figure 1. The dominant ion species are H3O+ and HSO4-. Therefore, in applying the MSA model to these solutions, the only ion-ion pair considered for H2SO4-H2O solutions was H3O+-HSO4-. The model-calculated values are plotted against experimental data in Figure 2. The average relative difference (ARD) between these two, as calculated by eq 8, was 1.56%. The respective MSA parameters are listed in Table 1. These same parameters were used for all solutions discussed subsequently.
ARD )
Figure 1. Speciation of H2SO4-H2O solutions at 250 °C.
Figure 2. Conductivity modeling of H2SO4-H2O solutions up to 250 °C.3,14
σexp. - σcal. | σexp. × 100 N
∑|
(8)
The MSA parameters listed in Table 1 were also tested against other independent measurements, yielding an average difference of 4.89%, as shown in Figure 3. It should be noted that some original data points for Figure 3 are in units of molarity instead of molality. The conversions from molarity to molality were done with the OLI software. Al2(SO4)3-H2SO4-H2O Solutions. It appears reasonable to use MSA parameters from H2SO4-H2O and Al2(SO4)3-H2O solutions to predict the conductivity of the Al2(SO4)3-H2SO4H2O system. However, the solubility of Al2(SO4)3 in water is less than 0.001 m at 250 °C under saturated vapor pressure.5 Although it is possible to measure the conductivity of Al2(SO4)3-H2O solutions, it is not practical to use these data to obtain MSA model parameters to predict acidic solutions with 100 times higher concentrations of aluminum. As shown in Figure 4, the dominant ion species in Al2(SO4)3-H2SO4-H2O solutions at 250 °C and 0.45 m H2SO4 are HSO4-, H3O+, and Al3+. Therefore, it was decided to obtain MSA model parameters directly from Al2(SO4)3-H2SO4-H2O solutions instead of Al2(SO4)3-H2O solutions. Because the MSA parameters for H3O+-HSO4- were already obtained from H2SO4-H2O solutions, only the Al3+-HSO4pair had to be considered. Because of the uncertainty in Al speciation between 100 and 200 °C,5 the MSA model was applied to Al2(SO4)3-H2SO4-H2O solutions at temperatures between only 225 and 250 °C. The model calculations are shown in Figures 5 and 6. The average relative difference between experimental data and calculations was 1.26%. The MSA parameters are listed in Table 2. Fewer parameters were required
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007 1601
Figure 3. Specific conductivities of H2SO4-H2O solutions up to 250 °C.14,15
Figure 4. Speciation of Al2(SO4)3-H2SO4-H2O solutions at 250 °C and 0.45 m H2SO4.
Figure 5. Conductivity modeling of Al2(SO4)3-H2SO4-H2O solutions at 225 °C.3
for Al2(SO4)3-H2SO4-H2O solutions because of a narrower target temperature range. MgSO4-H2SO4-H2O Solutions. Similarly to Al2(SO4)3, the solubility of MgSO4 in water under saturated vapor pressure is less than 0.02 m at 250 °C.5 In addition, the dominant ion-ion interaction in MgSO4-H2O solution is that between Mg2+ and SO42-. In MgSO4-H2SO4-H2O or more complex systems, the concentration of SO42- is usually not significant because of bisulfate formation. Therefore, the parameters obtained from MgSO4-H2SO4-H2O solutions were adopted instead of those from MgSO4-H2O solutions. The specific conductivities of MgSO4-H2SO4-H2O solutions were reported previously by Huang and Papangelakis up to
Figure 6. Conductivity modeling of Al2(SO4)3-H2SO4-H2O solutions at 250 °C.3
Figure 7. Speciation of MgSO4-H2SO4-H2O solutions at 250 °C and 0.45 m H2SO4.
Figure 8. Specific conductivity contributed by each ion species in MgSO4H2SO4-H2O solutions at 250 °C and 0.45 m H2SO4.
250 °C with maximum measured MgSO4 and H2SO4 concentrations of 0.30 and 0.45 m, respectively. It was previously concluded that the addition of MgSO4 decreases the conductivity in the whole temperature range as a result of the loss of H+ through HSO4- formation. The speciation of MgSO4-H2SO4H2O solutions at 250 °C were calculated using the MSE-H3O+ model and are shown in Figure 7. The dominant ion species are HSO4-, H3O+, and Mg2+. As shown in Figure 7, the concentration of H3O+ drops by 66.0% when 0.30 m MgSO4 is added. To quantify the decrease of solution conductivity after the addition of MgSO4, the conductivity contributions of each of the three ion species (H3O+, HSO4-, and Mg2+) were
1602
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007
Figure 9. Specific conductivities of MgSO4-H2SO4-H2O solutions at 0.35 m H2SO4 up to 250 °C.3,4
Figure 12. Specific conductivities of Al2(SO4)3-MgSO4-H2SO4-H2O solutions at 0.45 m H2SO4 for temperatures up to 250 °C.3
Figure 10. Specific conductivities of MgSO4-H2SO4-H2O solutions at 0.45 m H2SO4 up to 250 °C.3,4
Figure 13. Speciation of 0.05 m Al2(SO4)3-MgSO4-0.35 m H2SO4-H2O solutions at 250 °C.
Figure 11. Specific conductivities of Al2(SO4)3-MgSO4-H2SO4-H2O solutions at 0.35 m H2SO4 for temperatures up to 250 °C.3
calculated according to eq 1 using the MSE and MSA models and are shown in Figure 8 as stacked bands. It is clear that the relative conductivity contributions of Mg2+ and HSO4increase upon addition of MgSO4 whereas the contribution of H3O+ drops by 75.4%. Therefore, the previous conclusion is correct. Only the Mg2+-HSO4- pair was considered over the whole concentration range up to 0.45 m H2SO4 and for temperatures up to 250 °C. The results of applying the MSA model are shown in Figures 9 and 10. The average relative difference between the experimental data and the reproduced results calculated by eq 8 is 1.91%. The MSA parameters are listed in Table 3. It should be mentioned that the MSA parameters reported in a previous work4 were obtained from a H+-based Pitzer speciation with a higher average relative difference of 2.47%.
Figure 14. Speciation of Al2(SO4)3-0.15 m MgSO4-0.45 m H2SO4-H2O solutions at 250 °C.
Al2(SO4)3-MgSO4-H2SO4-H2O Solutions. The measured specific conductivities of quaternary Al2(SO4)3-MgSO4-H2SO4-H2O solutions are reported in Table 4 and plotted in Figures 11 and 12. All solutions are undersaturated at all temperatures.16 As shown in Figures 11 and 12, the conductivity decreases upon addition of Al2(SO4)3 and MgSO4 except for temperatures below 50 °C. As shown in Figures 13 and 14, the concentration of H3O+ decreases, whereas that of HSO4- increases, when the concentration of either MgSO4 or Al2(SO4)3 increases at fixed concentration of H2SO4 and the other electrolyte. We can conclude that the main reason for the decrease in conductivity is due to the loss of H3O+ to bisulfate formation. All coefficients obtained were subsequently used for Al2(SO4)3-MgSO4-H2SO4-H2O solutions at 225 and 250 °C.
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007 1603 Table 3. Coefficients Determining the Ionic Strength Dependence of the Average Effective Radius for the Mg2+-HSO4- Ion Pair (Eqs 5-7) value
parameter
parameter
value
κH(00) 2+ 2O,Mg /HSO4
parameter
0.281846
κH(01) 2+ 2O,Mg /HSO4
value 0.422144 ×
10-3
κH(02) 2+ 2O,Mg /HSO4
-74.254
dH(10) 2+ 2O,Mg /HSO4
-5.13242
dH(11) 2+ 2O,Mg /HSO4
0.106785 × 10-2
dH(12) 2+ 2O,Mg /HSO4
2376.4
dH(20) 2+ 2O,Mg /HSO4
1.10573
dH(21) 2+ 2O,Mg /HSO4
0.311742 ×
10-2
dH(30) 2+ 2O,Mg /HSO4
-1.47052
dH(31) 2+ 2O,Mg /HSO4
0.335988 × 10-2
Table 4. Specific Conductivities (mS/cm) of Al2(SO4)3-MgSO4-H2SO4-H2O Solutions 0.35 m H2SO4
0.45 m H2SO4
temp (°C)
0.05 m Al2(SO4)3 0.05 m MgSO4
0.05 m Al2(SO4)3 0.15 m MgSO4
0.05 m Al2(SO4)3 0.15 m MgSO4
0.10 m Al2(SO4)3 0.15 m MgSO4
15 25 50 75 100 125 150 175 200 225 250
118.0 130.8 151.9 164.4 174.7 184.7 194.7 197.6 203.6 205.3 200.6
109.2 116.8 128.6 133.7 140.6 146.7 161.0 179.2 187.6 192.2 189.0
168.8 193.5 208.3 223.7 229.0 241.0 253.2 264.0 273.3 276.9 270.6
156.0 163.5 188.8 197.8 205.6 215.2 228.1 242.0 254.9 263.0 256.5
Table 5. Comparison between Experimental Results and Prediction of Conductivities of Al2(SO4)3-MgSO4-H2SO4-H2O Solutions at 225 and 250 °C 225 °C
250 °C
solution
experiment
prediction
experiment
prediction
0.35 m H2SO4-0.05 m Al2(SO4)30.05 m MgSO4 0.35 m H2SO4-0.05 m Al2(SO4)30.15 m MgSO4 0.45 m H2SO4-0.05 m Al2(SO4)30.15 m MgSO4 0.45 m H2SO4-0.10 m Al2(SO4)30.15 m MgSO4
205.3
218.3
200.6
212.5
192.2
201.1
189.0
190.5
276.9
256.9
270.6
252.1
263.0
250.6
256.5
247.7
The modeling results are reported in Table 5. The average relative difference between the predictions and the experimental measurements is below 5%, which is sufficient for engineering applications. The following factors should be considered for reasonable and good predictions: (1) No extra significant species should be formed in the multicomponent system that is not in the subsystems. (2) No extra significant ion-ion interactions should occur in the multicomponent system that does not occur in the subsystems. (3) The multicomponent system to be predicted should be in a similar concentration range as the subsystems measured. Limiting Equivalent Conductivity of H3O+ at 250 °C. To calculate the equivalent conductivity of H+ in Al2(SO4)3-H2SO4 aqueous solutions, Baghalha and Papangelakis3 assumed that changes in the solution affect each species equally. The same assumption was adopted by Huang and Papangelakis4 to calculate the equivalent conductivity of H+ in MgSO4-H2SO4 aqueous solutions, as described by eq 9. It should be noted that both works employed the Pitzer model and H+ was assumed instead of H3O+.
λH + λH0 +
)
λHSO40 λHSO 4
)
λMg2+ 0 λMg 2+
)
λSO420 λSO 24
Al(SO4)+, HSO4-, and SO42- were reported previously.3,4 The limiting conductivity of H3O+ was assumed to be equal to that of H+. The limiting conductivity of Al(SO4)2- can be estimated using eq 13, which was suggested by Anderko and Lencka.10
[
λH3O+ ) σ/ mH3O+ + mHSO4-
[
Although this equal-change assumption is convenient for engineering use, it needs to be evaluated against other independent models, such as the MSA model discussed in the present work. Equations 10-12 were used to calculate the points shown in Figure 15. The limiting conductivities of Mg2+, Al3+,
0 λHSO 4
λH0 3O+
λH0 3O+
0 λSO 24
]
+ mSO42- 0 λH3O+
(10)
0 λSO 24
+ mSO42- 0 + λH3O+ 0 λMg 2+
]
(11) mMg2+ 0 λH3O+
λH3O+ ) σ/ mH3O+ + mHSO40 λAl 3+
(9)
[
λH3O+ ) σ/ mH3O+ + mHSO4-
0 λHSO 4
0 λHSO 4
λH0 3O+
0 λSO 24
+ mSO42- 0 + λH3O+
0 λAl(SO 4)2-
+ mAl(SO4)2- 0 + mAl(SO4)+ 0 mAl3+ 0 λH3O+ λH 3 O + λH3O+
λ0complex )
]
0 λAl(SO 4)+
(12)
|Zcomplex|
[∑( ) ] n
Zi
i)1
λ0i
3 1/3
(13)
1604
Ind. Eng. Chem. Res., Vol. 46, No. 5, 2007
Acknowledgment Dr. Haixia Liu is acknowledged for providing speciation calculations. 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
Figure 15. Molal ionic equivalent conductivity of H3O+ as a function of ionic strength at 250 °C (ECA ) equal-change assumption).
As shown in Figure 15, both models suggest that the equivalent conductivity of H3O+ decreases with increasing ionicstrength. With the exception of the H2SO4-MgSO4 system, the two models gave similar results. Overall, the average relative difference between these two calculations is 4%, which suggests that the equal-change assumption is good enough for engineering use, particularly for systems without MgSO4. Conclusions Because of the complexity of high-temperature experiments and the associated costs, it is desired to have a method that can be used to predict the conductivities of multicomponent solutions using data from binary or ternary systems, which are easier to obtain. The extended mean spherical approximation (MSA) model was adopted for use with previously published electrical conductivity data for H2SO4-H2O, Al2(SO4)3-H2SO4-H2O, and MgSO4-H2SO4-H2O solutions. It was found that the dominant ion pairs affecting the conductivities of these solutions are H3O+-HSO4-, Al3+-HSO4-, and Mg2+-HSO4-. With the MSA coefficients obtained by regressing the experimental data, the conductivities of H2SO4-H2O and MgSO4-H2SO4-H2O solutions were reproduced up to 250 °C with an average relative difference of less than 2%. Because of the lack of speciation data, this approach worked only between 225 and 250 °C for Al2(SO4)3-H2SO4-H2O solutions. Then, these coefficients were used to predict the electrical conductivities of Al2(SO4)3MgSO4-H2SO4-H2O solutions at temperatures between 225 and 250 °C. The difference between the model and the experimental data was below 5%, which is sufficient for engineering use. Finally, a previously suggested equal-change assumption was used to calculate the equivalent conductivity of H3O+ in H2SO4, MgSO4-H2SO4, and Al2(SO4)3-MgSO4H2SO4 aqueous solutions. The difference between the results obtained with this assumption and those obtained with the MSA model was 4%, which suggests that that the equal-change assumption is also adequate for engineering use.
(1) 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, 131-137. (2) 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. (3) Baghalha, M.; Papangelakis, V. G. High-Temperature Conductivity Measurements for Industrial Applications. 2. H2SO4-Al2(SO4)3 Solutions. Ind. Eng. Chem. Res. 2000, 39, 3646-3652. (4) Huang, M.; Papangelakis, V. G. Electrical Conductivity of Concentrated MgSO4-H2SO4 Solutions up to 250 °C. Ind. Eng. Chem. Res. 2006, 45, 4757-4763. (5) Liu, H.; Papangelakis, V. G. Chemical modeling of high temperature aqueous processes. Hydrometallurgy 2005, 79, 48-61. (6) Barker, J. A.; Henderso, D. Perturbation Theory and Equation of State for Fluids. 2. A Successful Theory of Liquids. J. Chem. Phys. 1967, 47, 4714-4721. (7) 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, 2187-2192. (8) Copeman, T. M.; Stein, F. P. An Explicit Non-equal Diameter MSA Model for Electrolytes. Fluid Phase Equilib. 1986, 30, 237-245. (9) 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, 111-139. (10) 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, 1932-1943. (11) Wang, P.; Springer, R. D.; Anderko, A.; Young, R. D. Modeling phase equilibria and speciation in mixed-solvent electrolyte systems. Fluid Phase Equilib. 2004, 222-223, 11-17. (12) Baghalha, M.; Papangelakis, V. G. High-Temperature Conductivity Measurements for Industrial Applications. 1. A New Cell. Ind. Eng. Chem. Res. 2000, 39, 3640-3645. (13) Wang, P.; Anderko, A.; Young, R. D. Modeling Electrical Conductivity in Concentrated and Mixed-Solvent Electrolyte Solutions. Ind. Eng. Chem. Res. 2004, 43, 8083-8092. (14) Hinatsu, J. T.; Tran, V. D.; Foulkes, F. R. Electrical conductivities of aqueous ZnSO4-H2SO4 solutions. J. Appl. Electrochem. 1992, 22, 215. (15) Noyes, A. A.; Coolidge, W. D. Publication No. 63; Carnegie Institution of Washington: Washington, DC, 1907. (16) Baghalha, M.; Papangelakis, V. G. The ion-association-interaction approach as applied to aqueous H2SO4-Al2(SO4)3-MgSO4 solutions at 250 degrees C. Metall. Mater. Trans. B: Proc. Metall. Mater. Proc. Sci. 1998, 29, 1021-1030.
ReceiVed for reView July 7, 2006 ReVised manuscript receiVed November 13, 2006 Accepted November 28, 2006 IE060878K
