High-Temperature Conductivity Measurements for Industrial

of high-temperature H2SO4-Al2(SO4)3 solutions. These electrolytes exist in the laterite leach slurry of the pressure acid leaching process. It was fou...
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Ind. Eng. Chem. Res. 2000, 39, 3646-3652

High-Temperature Conductivity Measurements for Industrial Applications. 2. H2SO4-Al2(SO4)3 Solutions Morteza Baghalha and Vladimiros G. Papangelakis* Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3E5

A new conductivity cell, developed previously, was employed from 15 to 250 °C, in an effort to investigate the inter-relation between the measured conductivities and the solution chemistry of high-temperature H2SO4-Al2(SO4)3 solutions. These electrolytes exist in the laterite leach slurry of the pressure acid leaching process. It was found that, at 250 °C, the effect of Al2(SO4)3 on conductivity decreases with increasing Al2(SO4)3. This is in agreement with our previous findings that aluminum mostly forms Al(SO4)+ at low molalities, whereas 85% of aluminum is associated as Al2(SO4)30 at near-saturation molalities. At 250 °C and constant H2SO4 molality, the solution conductivity drops with increasing Al2(SO4)3 molality. It is suggested that this drop is caused by a sharp decrease in ionic equivalent conductivities of H+, HSO4-, and Al(SO4)+. This drop was found to be similar in nature to the drop when H2SO4 is added at very low concentrations. A new unified correlation for ionic equivalent conductivity in terms of one-third power of individual ionic strength was found. Finally, a simple mixing rule was developed to calculate the ionic equivalent conductivities in H2SO4-Al2(SO4)3 solutions. Introduction The modern hydrometallurgical process for Ni and Co extraction from laterite (oxide) ores involves leaching by sulfuric acid inside a pressure vessel (autoclave) at temperatures of around 250 °C.1 The resulting leach solution from the autoclave contains three dominant electrolytes, namely, H2SO4, Al2(SO4)3, and MgSO4.2 To control the extent of dissolution reactions in an industrial plant, it is first necessary to monitor (or “measure”) the solution chemistry and particularly acidity. Based on solubility data at high temperatures, the chemistry of the above three electrolytes at temperatures of around 250 °C was recently identified.3,4 In the present work we deal, however, only with the binary H2SO4-Al2(SO4)3 solutions. For this system at 250 °C, the identified aqueous aluminum-bearing species were Al3+, Al(SO4)+, and Al2(SO4)30, with Al2(SO4)30 as the dominant aluminum species at moderate to high H2SO4 concentrations. It was felt that if the conductivities of binary electrolyte H2SO4-Al2(SO4)3 solutions at temperatures of up to 250 °C are measured, they could confirm the existence of these species. Appropriate correlations would then be potentially used for monitoring the solution chemistry through conductivity measurements. To measure the conductivities for this study, a high-temperature conductivity cell, which was discussed in the first part5 of this series, was employed. In general, the specific conductivity of a solution, σ [in 1/(Ω‚m)], is a function of the conductivity of the individual ions which are present in the solution, i.e.,

∑ i)1

|zi|ciλi

NA

λi )

n

σ)

mol of ion), concentration (in mol/m3), and ionic equivalent conductivity [in 1/(Ω‚m‚mol of charge)] of ion i, respectively. The total number of different ions that exist in the solution is given by n. The values of the ionic equivalent conductivities are rather established at infinite dilutions.6,7 However, λi values at finite concentrations are estimated from conductivity theories. For the concentration ranges of interest in this work, the mean spherical approximation (MSA) conductivity theory has been suggested to work.8,9 MSA, which assumes ions are charged hard spheres, is an integral equation approximation for the statistical mechanics theory of solutions.10 Based on the crystallographic radii of ions, MSA theory predicts the properties of 1-1 electrolyte solutions up to the limit of the primitive model, i.e., 1 M concentration. In the case of 1-2 and 1-3 electrolytes, the applicability of MSA theory drops to concentrations much lower than 1 M.8,10,11 The analytical MSA conductivity theory can be only applied to electrolytes with one cation and one anion. Hence, it cannot be applied to binary H2SO4-Al2(SO4)3 solutions. More recently, in 1997, Anderko and Lencka11 empirically extended the MSA conductivity model. To extend the MSA model for multielectrolyte solutions, they introduced a mixing rule to calculate an average value for ionic equivalent conductivities. For the ith cation, λi, for instance, the average equivalent conductivity is obtained by averaging over all anions that exist in the mixed solution, i.e.11

(1)

where zi, ci, and λi are the valence (in mol of charge/ * To whom correspondence should be addressed. Tel.: 1-416978-1093. Fax: 1-416-978-8605. E-mail: [email protected].

∑j fjλi(j)(I)

(2)

where NA is the total number of anions, fj is the equivalent fraction of the jth anion, and λi(j) is the conductivity of cation i in the presence of anion j. λi(j) is calculated at the ionic strength of the multicomponent mixture (I). Furthermore, to extend the concentration range of the original MSA model, Anderko and Lencka11

10.1021/ie000215h CCC: $19.00 © 2000 American Chemical Society Published on Web 08/16/2000

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3647 Table 1. Measured Specific Conductivities (mS/cm) of H2SO4-Al2(SO4)3 Solutions at 0.35 m H2SO4 Al2(SO4)3 molality

Figure 1. Solution composition of the performed experiments for the high-temperature conductivity measurements.

proposed the use of an effective ion radius (instead of the crystallographic radius in the original MSA theory) correlated as a function of the ionic strength. For this purpose, the conductivity data of a single aqueous electrolyte solution that only contains one set of ion pairs are fitted into a function with six adjustable parameters. In H2SO4-Al2(SO4)3 solutions, two pairs of ions are dominant, namely, H+-HSO4- and Al(SO4)+HSO4-. Hence, it results in 12 adjustable parameters for these two sets of ion pairs. Furthermore, producing experimental conductivity data for the Al(SO4)+-HSO4pair is not feasible, because if this pair of ions is placed in water, it undergoes the following equilibrium reaction:

2Al(SO4)+ + HSO4- a Al2(SO4)30(aq) + H+

(R1)

As a result, another ion, i.e., H+, is produced and makes the solution a ternary system. In conclusion, the extended MSA theory cannot be applied to this binary H2SO4-Al2(SO4)3 electrolyte system. To fill the gap for a conductivity theory applicable to our system, some engineering approximations are introduced. The individual ionic conductivities are then estimated and correlated as a function of the ionic strength. Experimental Section Depending on the ore composition, the laterite leach solution, exiting from the autoclave, contains about 0.25-0.50 m H2SO4. To resemble the sulfuric acid content of these solutions, two series of conductivity experiments at 0.35 and 0.45 m H2SO4 were performed. In Figure 1, the solid circles represent the solution compositions of the performed conductivity experiments. The solid line in this figure shows the solubility of Al2(SO4)3 in H2SO4 solutions at 250 °C, as reported by Baghalha and Papangelakis.3 As seen in this figure, the concentration of Al2(SO4)3 in each experiment was less than its saturation value at 250 °C. Furthermore, because Al2(SO4)3 has inverse solubility with temperature, no solids of aluminum compounds were expected to form in the solution when the temperature was raised from 25 to 250 °C.

temp (°C)

0.00

0.05

0.10

15 25 50 75 100 125 150 175 200 225 250

131 ( 0.5 147 177 199 216 230 240 248 250 247 240 ( 1

121 134 157 173 186 198 210 219 227 230 226

114 126 145 156 165 176 189 203 215 222 223

For each experiment, the required amounts of Baker Analyzed reagent grade H2SO4 (96.8 wt %) and Al2(SO4)3‚18H2O (99.4 wt %) were weighed. These were then dissolved into enough deionized water to produce 1100.0 g of total water, including water from H2SO4 (96.8 wt %) and Al2(SO4)3‚18H2O. Using the conductivity cell and the experimental procedure presented in part 15 of this series, the specific conductivities of each solution shown in Figure 1 at 15 °C and from 25 to 250 °C in 25 °C intervals were measured. After every three experiments, the value of the cell constant was checked with the 100 000 µS/cm conductivity standard at 25 °C. The reproducibility of the measured conductivity of the standard solution remained always within (0.5%. As a result, the conductivity cell was neither replatinized nor recalibrated during these experiments. To prevent corrosion of the bare titanium parts inside the autoclave, about 40 ppm nickel (in the form of Ni(NO3)2) was maintained in all solutions.12 Both Ni2+ and NO3- are among the oxidizing cations and anions, respectively, that have very high inhibitor potency to inhibit corrosion of the titanium alloys in reducing acids such as H2SO4.12 In our previous solubility experiments,3,4 hydrogen peroxide was used to prevent corrosion. However, it was not suitable for the conductivity experiments, because the measurements showed heavy fluctuations. Once heated, it produces considerable amounts of oxygen gas bubbles, which interfere with the conductance of ions in the solution. Nevertheless, the solution after each experiment was inspected for corrosion. If titanium is corroded by H2SO4, H2S (detectable by its distinct odor) is produced. In this study, no incident of corrosion was ever detected. Results The measured specific conductivities for the first set of experiments at 0.35 ((0.0005) m H2SO4 are reported in Table 1 and plotted in Figure 2. Each curve represents the conductivities as a function of temperature at 0.35 m H2SO4 and at a constant molality of Al2(SO4)3, i.e., at 0, 0.05, and 0.10 m, from the top to the bottom curve, respectively. The specific conductivities for the second set of experiments at 0.45 ((0.0005) m H2SO4 solutions are reported in Table 2 and also plotted in Figure 3. For each curve, the Al2(SO4)3 molality is constant at 0, 0.05, 0.10, 0.15, and 0.20 m, from the top to the bottom curve, respectively. The reproducibility of the measured conductivities was within (0.5%. Furthermore, as seen from Figure 4, the conductivities of H2SO4-Al2(SO4)3 solutions at 25 °C measured in this study are also in agreement with those reported in the literature.13 Also, the conductivities of H2SO4-Al2(SO4)3 solutions at 250 °C are further shown in Figure 5.

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Figure 2. Specific conductivities (mS/cm) of H2SO4-Al2(SO4)3 solutions at 0.35 m H2SO4 and different Al2(SO4)3 molalities at temperatures of up to 250 °C. Table 2. Measured Specific Conductivities (mS/cm) of H2SO4-Al2(SO4)3 Solutions at 0.45 m H2SO4

Figure 4. Specific conductivities of H2SO4-Al2(SO4)3 solutions at 25 °C, as compared to the literature values.13 **: The conductivities at 0.377 M H2SO4 and 0 M Al2(SO4)3 were estimated here based on the H2SO4 conductivities at concentrations between 0.079 and 1.97 M (six data point), as reported by Arifin.13 For this purpose, an interpolation method, based on a cubic spline function, was employed.

Al2(SO4)3 molality temp (°C)

0.00

0.05

0.10

0.15

0.20

15 25 50 75 100 125 150 175 200 225 250

166 ( 0.5 184 219 244 266 282 295 304 309 310 304

153 168 197 216 231 247 259 271 281 285 284

143 156 181 196 208 221 235 249 261 270 273

135 148 170 183 192 204 217 233 251 263 269

127 141 163 173 181 191 206 225 242 257 266

Figure 5. Specific conductivities of H2SO4-Al2(SO4)3 solutions at 250 °C, at 0.35 and 0.45 m H2SO4.

conductivities for all ions, this overestimation was roughly calculated as 0.3%. However, because the reproducibility of the measurements is within (0.5%, the correction of 0.3% due to the presence of Ni(NO3)2 may be neglected. Figure 3. Specific conductivities (mS/cm) of H2SO4-Al2(SO4)3 solutions at 0.45 m H2SO4 and different Al2(SO4)3 molalities at temperatures of up to 250 °C.

Because of a small water evaporation into the vapor phase,5 the molalities mentioned here are nominal. To convert these to the true molalities, a correction factor (reported in Table 2 of part 15 of this series) for the respective temperature must be used. Furthermore, because of the presence of Ni(NO3)2 as the corrosion inhibitor, an overestimation in the measured conductivities is expected. Assuming equal ionic equivalent

Chemistry of H2SO4-Al2(SO4)3 Solutions at 250 °C A hybrid ion-association-interaction approach was previously implemented to identify the species in the ternary H2SO4-Al2(SO4)3-MgSO4 solutions at 250 °C.3,4 The complexes in the solution and the ion-interaction parameters (in the Pitzer model) were identified through processing solubility data in the binary, H2SO4-Al2(SO4)3 and H2SO4-MgSO4, as well as the ternary, H2SO4-Al2(SO4)3-MgSO4, electrolyte solutions at or near 250 °C. In the H2SO4-Al2(SO4)3 system (a Fortran

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3649

Figure 6. Speciation diagram of H2SO4-Al2(SO4)3 solutions at 250 °C, at 0.45 m H2SO4, as calculated by the solution chemical model.3,4 In these solutions, no solid phase forms.

computer code for optimization of the parameters in this chemical system was given elsewhere4), the identified aqueous aluminum-bearing species were Al3+, Al(SO4)+, and Al2(SO4)30, with Al2(SO4)30 as the dominant species at H2SO4 concentrations higher than 0.1 m. It should be noted that, in our previous work,3,4 other aluminum species were also tested but could not fit the hightemperature solubility data in binary and ternary electrolyte systems. Hence, in the following calculations and discussions, the existing aluminum species in solution are assumed to be those we identified in our previous work.3,4 The experiments performed in the present work were designed so that no solid phase (hydronium alunite) forms in the solutions, as shown in Figure 1. Hence, the equilibrium reactions among the aluminum species are3,4

2Al(SO4)+ + HSO4- a Al2(SO4)30(aq) + H+ Al3+ + SO42- a Al(SO4)+

(R1) (R2)

The Pitzer ion-interaction parameters for the species and the equilibrium constants for the reactions were known from our previous study. Hence, the resulting chemical model was solved for 0.45 m H2SO4 and various molalities of Al2(SO4)3 at 250 °C, and the distribution of species was obtained. The species concentrations and the distribution of aluminum species at 0.45 m H2SO4 are plotted in Figures 6 and 7, respectively. As seen from these figures, the Al3+ concentration is small at all molalities of Al2(SO4)3. This is mainly due to the fact that the equilibrium constant of reaction R2 is large. Furthermore, it should be noted that, because of the presence of 0.45 mol/kg of H2SO4 in all solutions, the concentration of SO42- is relatively constant, changing from 3.0 × 10-4 to 3.6 × 10-4 m where Al2(SO4)3 changes from 0.0 to 0.20 m, respectively. As a result, the ratio of Al(SO4)+/Al3+ is large at all concentrations of Al2(SO4)3, as shown in Figures 6 and 7. An important observation in Figure 5 is the variable slope of the conductivity curve at different Al2(SO4)3 molalities. The slope of the curve is the steepest at 0 m

Figure 7. Distribution diagram of aluminum species in H2SO4Al2(SO4)3 solutions at 250 °C, at 0.45 m H2SO4. In these solutions, no solid phase forms. Table 3. Estimation of λ0 Values at 250 °C

ion H+ HSO4Al3+ SO42Al(SO4)+ a

∆S0str at λ0 at 25 °Ca λ0 at 250 °Ca 25 °C16 (mS/cm/ (mS/cm/ 11 11 (J/K‚mol) A (eq 3) B (eq 3) equiv/L) equiv/L) -32 -44 -332 -69

-3.9726 837.79 -3.5038 119.58 0.0391a -877.0a -2.9457 90.983

347.4 49.9 61.017 79.2

872.6 353.4 1818.0 584.6 282.1

Calculated in this study.

Al2(SO4)3 and becomes rather small at a molality of 0.20. On the other hand, the solution chemistry (Figure 7) predicts that the neutral Al2(SO4)30 changes from 0% to 85% of the total aluminum when Al2(SO4)3 molality changes from 0 to 0.20 m. As shown in Figure 7, at around 0 m Al2(SO4)3, because of the dissociation of Al2(SO4)3, the largest change in the ionic environment occurs; hence, the solution conductivity is affected the most. On the other hand, the observation that the conductivity does not change appreciably around 0.20 m Al2(SO4)3 is probably due to the high percentage of neutral Al2(SO4)30. Interpretation of the Conductivities in H2SO4-Al2(SO4)3 Solutions at 250 °C At temperatures up to 250 °C, the values of λ0 can be calculated based on the equation of Smolyakov14

ln λ0(T) η(T) ) A + B/T

(3)

where η is the viscosity of pure water (900 × 10-6 and 107 × 10-6 Ns/m2 at 25 and 250 °C, respectively15) and A and B are adjustable constants. The values of these constants for H+ and HSO4- are given by Anderko and Lencka.11 Hence, the values of λ0 at 250 °C for H+ and HSO4- were calculated and reported in Table 3. These values are in agreement with the values calculated6 from high-temperature limiting equivalent conductivities of various electrolytes. The amount of complex ion Al(SO4)+ in solution is also significant. Anderko and Lencka11 have suggested the following relation for the estimation of limiting equivalent conductivity for com-

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plex ions.

λ0complex )

|Zcomplex|

[∑( ) ] n

Zi

i)1

λ0i

(4)

3 1/3

where λ0i ’s are the limiting equivalent conductivities of the constituent ions of the complex. Hence, to calculate 0 0 0 at 250 °C, the values of λAl λAl(SO 3+ and λSO 2- at 250 4)+ 4 °C are required. For SO42-, the values of A and B in eq 0 3 are given in the literature,11 hence λSO42- at 250 °C was readily calculated and reported in Table 3. For Al3+, the values of A and B in eq 3 are not given in the literature. These were estimated through a procedure suggested by Anderko and Lencka.11 B was estimated based on a correlation in terms of ∆S0str, the structural entropy at 25 °C. ∆S0str of Al3+ at 25 °C, as reported by Marcus,16 and the calculated value of B are reported in Table 3. As reported in Table 3, the value of A for Al3+ 0 was estimated from eq 3 using the known value of λAl 3+ 17 at 25 °C, i.e., 61 mS/cm/equiv/L. Finally, using the 0 calculated values of A and B in eq 3, the value of λAl 3+ at 250 °C was calculated and is also reported in Table 0 0 3. Using the calculated values of λAl 3+ and λSO 2- at 250 4 0 °C, eq 4 was then used to estimate λAl(SO4)+ at 250 °C, i.e., 282.1 mS/cm/equiv/L. In addition to the calculated values of limiting equivalent conductivities at 250 °C, the calculated values at 25 °C (based on eq 3) are reported for reference in Table 3. Based on eq 1, the specific conductivity of the solution at 250 °C can now be related to the equivalent conductivities of major ions in the solution, i.e., H+, HSO4-, and Al(SO4)+, as shown in Figure 6.

σ ) mH+λH+ + mHSO4-λHSO4- + mAl(SO4)+λAl(SO4)+ Rearranging eq 5, we obtain

[

]

λHSO4λAl(SO4)+ + mAl(SO4)+ σ ) λH+ mH+ + mHSO4λH+ λH+

(5)

(6)

If the chemistry of the solution is known, all of the molalities in eq 6 are known. Hence, to estimate λH+ at 250 °C and at high concentrations, λHSO4-/λH+ and λAl(SO4)+/λH+ are approximated as follows, using the calculated limiting equivalent conductivities at 250 °C, as reported in Table 3.

λHSO4λH+ λAl(SO4)+ λH+

)

)

0 λHSO 4 0 λH +

)

0 λAl(SO 4)+ 0 λH +

353.4 ) 0.405 872.6

)

282.1 ) 0.323 872.6

(7)

(8)

As a result, eq 6 can be simplified to

λH+ ) σ/[mH+ + 0.405mHSO4- + 0.323mAl(SO4)+]

(9)

Hence, using the experimental data of specific conductivity at 250 °C and the known solution chemistry, λH+ at high concentrations can be calculated from eq 9. The results are shown in Figure 8 as a function of the ionic

Figure 8. Molal ionic equivalent conductivity of H+ as a function of ionic strength in H2SO4-Al2(SO4)3 solutions at 250 °C.

strength. It should be noted that λH+ values in Figure 8 0 are based on molality. The molarity-based value of λH + at 250 °C (872.6 mS/cm/equiv/L reported in Table 3) was multiplied by the density of pure water at 250 °C (0.80 kg/L)15 to convert it to the molal unit, i.e., 698.1 mS/ cm/equiv/kg. As shown in Figure 8, up to 0.45 m ionic strength, the calculated values of λH+ correspond to the pure aqueous H2SO4 solutions. The data at ionic strengths higher than 0.45 m correspond to the binary H2SO4-Al2(SO4)3 aqueous solutions. As seen in this figure, when aluminum species are introduced into the H2SO4 solution at 0.45 m, the equivalent conductivity of H+ (as well as those of HSO4- and Al(SO4)+, according to eqs 7 and 8) drops dramatically. The observed sharp drop in Figure 8 can be attributed to very strong structure-making characteristics of Al3+ and other aluminum species in water.16 ∆S0str, the structural entropy, is a measure of the structure-making capability of ions. For Al3+ in water,16 as reported in Table 3, this value is about 10 times that for H+ and HSO4-. Hence, the introduction of Al3+ into the solution enhances the structure of water, and so the viscosity of the solution increases.18 Furthermore, the solution viscosity may also increase because of the presence of Al2(SO4)30 (5.5 wt % of the solution at 0.2 m Al2(SO4)3) which has a much higher inertia (weight) than H2O. As a result, increased solution viscosity causes increased drag force on the moving ions, which, in turn, reduces the mobility of ions and their equivalent conductivity. In the case of the H+ ion (and OH-), the enhanced water structure reduces the rate of proton jump apparently because of positioning of the water molecules in an unfavorable direction. This, in turn, slows the rate of water reorientation, which is the rate-determining (slow) step19 for H+ conduction in solution. In Figure 8, the sharp drop in λH+ when Al2(SO4)3 is added is similar to the sharp drop in λH+ when H2SO4 is added. Apparently, the addition of H2SO4 to water has the same relative effect of adding Al2(SO4)3 to a H2SO4 solution. To test this hypothesis quantitatively, the data in Figure 8 were replotted as in Figure 9. The horizontal axis in this figure represents the individual electrolyte ionic strength. For Al2(SO4)3, it can be calculated from eq 10, where IH2SO4 is the true ionic

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3651

λH+,at IAl2(SO4)3)0 ) λH+,at IH2SO4

(15)

λH+,at IH2SO4 can be calculated using eq 11:

F(IH2SO4) ) λH+,at IH2SO4/λH+,at IH2SO4)0

(16)

λH+,at IH2SO4 ) 0 is, in fact, the infinite-dilution equiva0 lent conductivity of H+, i.e., λH +. Hence, when eqs 1416 are combined, the following mixing rule can be concluded: 0 λ H+ ) λH +F(IH SO )F(IAl (SO ) ) 2 4 2 4 3

Figure 9. Relative conductivity of individual ions as a function of the individual solute ionic strength at 250 °C.

strength of H2SO4 before addition of Al2(SO4)3.

IAl2(SO4)3 + IH2SO4 ) ITotal

(10)

where I is the true ionic strength accounting for the solution speciation. The vertical axis shows the relative conductivity defined as follows:

relative conductivity of H+ ) λH+,at Ielectrolyte/λH+,at Ielectrolyte ) 0 (11) where λH+,at IH2SO4 ) 0 ) 698.1 mS/cm/equiv/kg and corresponds to point A in Figure 8. Also, λH+,at IAl2(SO4)3 ) 0 ) mS/cm/equiv/kg and corresponds to point B in Figure 8. By using eqs 10 and 11, the data in Figure 8 were converted to the data shown in Figure 9. The points in this figure represent a single function. Hence, the relative conductivity data were then fitted against the individual solute ionic strengths. The best fit (solid line in Figure 9) with a correlation coefficient of r2 ) 0.986 was found to be

relative conductivity ≡ F(Ielectrolyte) ) 1 - 0.4056 (Ielectrolyte)1/3 (12) The one-third power in eq 12 is well-known in the literature17 for concentrated solutions such as the one involved in this study. Now, to calculate the equivalent conductivity of H+ in H2SO4-Al2(SO4)3 solutions, eq 11 can be used to relate it to the equivalent conductivity of H+ in a H2SO4 solution, as follows:

relative conductivity of H+ ) F(IAl2(SO4)3) ) λH+,at IAl2(SO4)3/λH+,at IAl2(SO4)3)0 (13) where λH+,at IAl2(SO4)3 is the equivalent conductivity in H2SO4-Al2(SO4)3 solutions and is simply shown as λH+. Hence, eq 13 can be written as

λH+ ) F(IAl2(SO4)3) λH+,at IAl2(SO4)3)0

(14)

where λH+,at IAl2(SO4)3 ) 0 is in fact the equivalent conductivity of H+ in H2SO4. Hence

(17)

In conclusion, the ionic strength function in eq 12 and the mixing rule in eq 17 can now be employed to calculate λH+. Furthermore, eqs 7 and 8 can be used to calculate the equivalent conductivities of the other ionic species in our system. These calculated ionic equivalent conductivities along with the measured solution conductivities can now be used through eq 9 to obtain the solution chemistry. Conclusions A new conductivity cell was used 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 and at temperatures from 15 to 250 °C. The observed behavior of the measured conductivities of H2SO4-Al2(SO4)3 solutions at 250 °C was in agreement with the chemistry of these solutions at 250 °C, as determined previously from solubility data. The measured conductivities at 250 °C and at constant molality of H2SO4 have the steepest slope at low concentrations of Al2(SO4)3, but the slope approaches zero as the solution approaches aluminum saturation. This was explained by the different extents of dissociation of Al2(SO4)3 at different molalities. The specific conductivity of H2SO4-Al2(SO4)3 solutions at 250 °C drops as Al2(SO4)3 molality increases. This drop was attributed to a sharp drop in the ionic equivalent conductivities. A function with one-third power in individual solute ionic strength was found to fit single ion equivalent conductivities in both H2SO4 and Al2(SO4)3 solutions. Furthermore, a simple mixing rule was proposed for calculation of the equivalent conductivity of ions in the mixed H2SO4-Al2(SO4)3 solutions. Acknowledgment Funding was provided by the Center for Chemical Process Metallurgy of the University of Toronto and the Natural Sciences and Engineering Research Council of Canada (NSERC). Professors F. R. Foulkes and D. W. Kirk of the Department of Chemical Engineering and Applied Chemistry, University of Toronto, are also acknowledged for their insights and suggestions. Literature Cited (1) Krause, E.; Singhal, A.; Blakey, B. C.; Papangelakis, V. G.; Georgiou, D. Sulfuric acid leaching of nickeliferous laterites. In Proceedings of the Nickel-Cobalt 97 International Symposium; Cooper, W. C., Mihaylov, I., Eds.; Canadian Institute of Mining, Metallurgy and Petroleum: Montreal, Canada, 1997; Vol. I, 441. (2) Baghalha, M.; Papangelakis, V. G. Pressure acid leaching of laterites at 250 °C: A solution chemical model and its applications. Metall. Mater. Trans. B 1998, 29B, 945.

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Received for review February 9, 2000 Revised manuscript received June 22, 2000 Accepted July 4, 2000 IE000215H