Geochimica et Cosmochimica Acta, Vol. 62, No. 1, pp. 15–23, 1998 Copyright © 1998 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/98 $19.00 1 .00
Pergamon PII S0016(97)00320-7
Solution equilibria for uranium ore processing: The BaSO4-H2SO4-H2O system and the RaSO4-H2SO4-H2O system C. R. PAIGE,1 W. A. KORNICKER,1 O. E. HILEMAN JR.,1 and W. J. SNODGRASS2 1
Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada Department of Civil Engineering, McMaster University, Hamilton, Ontario L8S 4M1, Canada
2
(Received May 6, 1996; accepted September 2, 1997)
Abstract—A radio-tracer determination of the solubility of BaSO4 in H2SO4-H2O mixtures was undertaken at temperatures of 25°C and 60°C. These were subsequently modelled using the Pitzer model for the activity coefficients, and estimates were made for Ba21-SO422 and Ba21-HSO42 interaction parameters. The final model yields an excellent description of the solubility of BaSO4 in H2SO4-H2O mixtures up to 6 mol/kg and at both 25°C and 60°C. The logarithm of the thermodynamic solubility product constant (logKsp) for barite obtained by regression analysis was 210.02 6 0.02 at 25°C and 29.68 6 0.01 at 60°C. The values of the ion association constant derived from these data are 2.49 6 0.03 at 25°C and 2.55 6 0.1 at 60°C. The enthalpy of dissolution for BaSO4 was estimated to be 17.6 6 0.2 kJ mol21. Literature solubility data for the RaSO4-H2SO4-H2O system have also been interpreted, using the Pitzer model for the necessary activity coefficients. The logarithm of the thermodynamic solubility product constant (logKsp) for radium sulfate obtained was 210.21 6 0.06 at 25°C, while the value of the ion association constant derived is 2.76 6 0.05 at 25°C. The high negative value of the Pitzer parameter b2 obtained by regression analysis of these data suggests that the explicit recognition of a RaSO4(aq) ion association species is to be preferred in this case. Copyright © 1998 Elsevier Science Ltd and kaolinite and its coprecipitation have been investigated experimentally and theoretically by Reise (1983) and Langmuir and Reise (1985). Their results suggest an hypothesis that Ra behaviour can be explained by coprecipitation at low pH (,4) and by reversible adsorption behaviour in the neutral pH range. This would imply that a coprecipitate would be plausible for explaining Ra-226 behaviour in the leaching tank. In a nuclear emulsion study on leaching tank solids, locations of high alpha activity were examined using SEM; small microcrystalline barium sulfate crystals which had precipitated on the surface of a silicate mineral were identified (Snodgrass, 1986). The barite crystals were the likely source of the Ra radiation and contained small quantities of Pb. For the National Uranium Tailings Program (NUTP) source term model, it is suggested that Ra-226 dissolution be modelled as controlled by barium sulfate and by lead sulfate host crystals. The Snodgrass and Hileman (1985) models for leach tank processes and for the evolution of U mill waste tailings as a function of time have been reviewed in a previous paper (Paige et al., 1993). A major obstacle to the evaluation of these models is the existence of significant data gaps in the current literature. These missing data include the solubility of potential host solids such as BaSO4 in H2SO4 solutions from 0 to 6 M in concentration and at 60°C, required in order to trace the fate of each of the solids and soluble species in the mill processing streams from the leaching tanks until placement in the tailings ponds and subsequent evolution has occurred. Appropriate thermodynamic parameters for the modelling of such data in sulfuric acid according to one of the modern activity coefficient models will also be required. Consideration of these gaps in the data required to evaluate the Snodgrass and Hileman (1985) models led to the goals for this study. These are (1) to obtain equilibrium solubility data
1. INTRODUCTION
Uranium milling is the starting point of the nuclear fuel cycle. For every ton of U ore that is milled, not more than 2 kg of U is usually extracted, leaving the remainder to be discharged as finely ground, sand-like tailings. From the mill the tailings go as a slurry into a tailings pond. Through drying, they form a large sprawling delta around the tailings pond, and consequently huge tailings piles have been created. About 185 million tons of tailings have been produced from Canada’s U mines and are stored at seventeen inactive and five active mines. The tailings contain other naturally radioactive elements, such as Th-230, Ra-226, Pb-210, and Po-210. The radionuclide responsible for more than 75% of the radioactivity that was originally in the ore is Ra-226. Leaching of the Ra-226 from U mill tailings contributes the major component of the radiological dose to human beings resulting from uranium mill tailings (Snodgrass et al., 1982). The rate of leaching will depend on the hydrogeochemistry of the tailings and surrounding rock or unconsolidated sediments, on the integrity of any retaining structure, and on the permeability of any capping material. The results of previous work (Snodgrass and Robertson, 1983; Snodgrass and Hileman, 1985; Snodgrass, 1986; Constable and Snodgrass, 1987) has suggested that Ra-226 coprecipitation with barium sulfate is the controlling mechanism. Previous work (Paige et al. 1988, 1989) has demonstrated the growth of hetero-epitaxial deposits of Pb, Ba, and (barium/ lead) sulfates on mica and quartz, as well as differences in the behaviour of Ba21, Ra21, and Pb21 ions undergoing desorption from quartz and mica surfaces (Paige et al., 1994). A literature review (Benes, 1984) suggests that dissolution of a (radium/barium) sulfate coprecipitate may control much of the Ra-226 found in tailings. The adsorption of Ra-226 onto quartz 15
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C. R. Paige et al.
for BaSO4 in H2SO4 solutions at both 25°C and 60°C, (2) to model these data using the Pitzer formalism for the required activity coefficients, by deriving the required interaction parameters, and (3) to model the available data for the solubility of RaSO4 in H2SO4. 2. PARAMETERIZATION FOR THE PITZER FORMULATION 2.1. Barium Sulfate Solubility as a Function of Temperature
A substantial number of measurements of barium sulfate solubility in water have been made. The earlier data of Melcher (1910), LeMarchands (1928), Herovsky and Berezicky (1929) and Neuman (1933) have been collected and reviewed by Seidell (1940). The more recent data include the measurements of Templeton (1960), Uchameyshvili et al. (1966), Strubel (1967), and Puchelt (1967). These latter have been reviewed by Blount (1977) who also presents the determination of the solubility of coarse-grained barites in water at temperatures from 22°C to 280°C. The solubility of barite in pure water was also determined at 25°C and 60°C by Kornicker et al. (1991) as part of an investigation of the dissolution kinetics of the barium/lead sulfate solid solution series. We used the Pitzer model with the parameters for PbSO4 as surrogates for BaSO4 to compute the activity coefficients for Ba21 and SO422 ions in pure water. Using these values we have calculated the thermodynamic solubility product constant for BaSO4 in pure water at 25°C and 60°C. At the very low ionic strength of barite in pure water, there will be virtually no dependence of the thermodynamic solubility product constant on the actual values of the parameters determined later in this work. These values are compared with those derived from our sulfate anlayses later in this work. There are two sets of solubility measurements for BaSO4 in Na2SO4 solutions reported in the literature (Lieser, 1965; Felmy et al., 1990). The reliability of the data of Lieser (1965) was brought into question by Monnin and Galinier (1988). There are a small number of solubility data available in the literature for BaSO4-H2SO4-H2O (Seidell, 1940). However, the concentration of sulfuric acid used in all of these studies far exceeds 6 m. There appears to be no data available for the solubility of BaSO4 in H2SO4 at elevated temperatures. There appear to be no data for the solubility of BaSO4 in any bariumrich solutions. It became evident from a consideration of literature values for the solubility of other sparingly soluble sulfates in sulfuric acid that the only methods likely to succeed in providing reliable data for the solubility of barium sulfate in sulfuric acid solutions to 6 m in concentration would be either the radiotracer method or the use of inductively coupled plasma-mass spectrometry (ICP/MS). After careful consideration of the properties of readily available radio-isotopes we decided to use barium-133 as a radio-tracer for the determination of the solubility of BaSO4 in H2SO4. The properties and production of this isotope are described in Brown and Firestone (1986). 2.2 Determination of the Solubility of BaSO4 in H2SO4 Solutions at 25°C and 60°C In this study BaSO4 was labelled with 133-Ba radiotracer by adding 18.537 MBq of 133-Ba (DuPont) in the form of barium chloride, to
Fig. 1. The approach to constant concentration for BaSO4 in pure water at 25°C and 60°C. These data (taken from Kornicker et al., 1991) confirm that a constant concentration was obtained from undersaturation in about 60 min at both temperatures.
220.5 mg of barium nitrate (Baker Analyzed Reagent) dissolved in 100 mL of distilled, demineralized water (MILLI-Q water) filtered through 0.45 mm membrane filters. The BaSO4 was then prepared by the method of homogeneous precipitation using the slow hydrolysis of purified sulfamic acid as the source of sulfate ions (Gordon et al., 1959). The precipitate was allowed to ripen for 18 h in the mother liquor and then washed by decantation. Nonradioactive specimens of the fresh and aged precipitate prepared at the same time using this technique were submitted for scanning electron microscopic examination. Aliquots of the labelled BaSO4 in the form of a slurry were pipetted into polypropylene snap-top tubes. The tubes and contents were centrifuged, the excess supernatant solution decanted, and pairs of the tubes were then placed in the clips of a Labquake™ shaker. Finally 3 mL of the selected solvent was pipetted into each tube. The distilled, demineralized water used for the solubility determination in the absence of sulfuric acid was deaerated by passing dry nitrogen from a cylinder through it. The solutions were allowed to shake gently for 5 months at 25°C 6 1°C before separation and counting was performed. Research carried out concurrently into the dissolution of Ba/PbSO4 solid solutions and endmembers demonstrated that BaSO4 achieved equilibrium in pure water in less than 30 min at 25°C and in about 5 min at 60°C. This is shown in Fig. 1 (Kornicker et al. 1991). The solution was separated from the precipitate before counting by filtration through 0.2 mm Teflon filter media prewashed with methanol. Counting was carried out using a well-type NaI scintillation counter with a Baird-Atomic amplifier-analyzer and a Baird-Atomic Scaler type 955150. The system was tuned to the 133-Ba photo-peak at 355.9 keV using an Advance Instruments OS250 dual-trace oscilloscope to monitor both the photo-peak and the instrument window. As the half-life of 133-Ba is 10.543a (Brown and Firestone, 1986), a careful counting programme could be designed and followed, with counting periods of 2 h for each of the samples. Blank counts were performed on 2 mL samples of the solvent solutions, these blanks being counted between samples. The total counts collected in all cases was greater than 100,000 counts. The long-term stability of the system was monitored by the counting of a sealed tube containing a 2 mL sample of 133-Ba of fixed concentration. No significant drift in the performance of the system was detected. Once the 25°C solutions had been filtered the solvent was replenished and the tubes placed in a thermostat at 70°C 6 0.2 C. The temperature was then reduced to 60°C 6 0.2 C and the solutions were allowed to reach equilibrium from above. The same procedure as before was followed for separation of the solutions from the solid, with the exception being that the syringe and filter used for the filtration step was a jacketed syringe pre-heated to the temperature of the thermostat. The specific activity of the labelled solid was determined by filtering off a sample of the BaSO4 using a pre-weighed Teflon filter pre-washed with methanol, then dissolving the sample in alkaline E. D. T. A. using an ultrasonic cleaner. Quantitative dilutions
Solubilities of BaSO4 and RaSO4 in sulfuric acid
17
Table 1. Measured solubilities of barium sulfate in water and sulfuric acid solutions at 25°C.
Fig. 2. Comparison of the Ksp obtained from the regression analyses of solubility data for BaSO4 in sulfate media (1) and the solubility data for BaSO4 found in the literature. The solid line was fitted to the Ksp values found from the data in pure water.
were then made using alkaline E. D. T. A. until the count rate of a 2 mL aliquot was measurable with acceptable precision. 2.3 Parameter Estimation for the Pitzer Equations for Ion Activity Coefficients in Aqueous Sulfate Systems
For full details of the formulation of the Pitzer model, reference should be made to Harvie et al (1984). The use of the Pitzer equations to describe solution equilibria in mixed-salt systems of high ionic strength requires data for the interaction parameters of pairs and triplets of ions. While an extensive database of ion interaction parameters currently is in existence (see for example, Zemaitis et al., 1986), in many cases, such as the BaSO4-H2SO4-H2O system, the required ion interaction parameters of interest are unavailable. These data must be obtained through the regression analysis of published data based on mineral solubility, isopiestic, activity, osmotic, and E.M.F. measurements in single and mixed salt systems. The binary interaction parameters b0MSO4, b1MSO4, b2MSO4, and Cf can in principle be determined from one of the colligative properties of a binary solution of MSO4 measured as a function of the concentration of the MSO4. For extremely insoluble compounds, few such measurements may be possible. In the case of BaSO4 the method of choice was to use solubility data either found in the literature or determined in our laboratory. The regression model for the solubility data had the following form: lnK sp-lnm Ba-lnmSO4 5 ln gBa 1 ln gSO4
[H2SO4] mol/kg
[Ba] mol/kg
0 (water) 3.00 3 1024 1.00 3 1023 3.00 3 1023 7.92 3 1022 4.50 3 1021 8.90 3 1021 1.84 2.89 3.95 6.19
9.88 4.80 2.14 1.32 9.20 8.86 9.57 1.13 1.14 1.11 1.28
3 3 3 3 3 3 3 3 3 3 3
1026 1027 1027 1027 1028 1028 1028 1027 1027 1027 1027
69 3 1027
69 3 10210 62 3 1029 62 3 1029 66 3 1029 65 3 1029 62 3 1029 67 3 1029
Note: The values at 7.92 3 1022 m and 8.90 3 1021 m were checked in a separate experiment using ICP/MS and nonradioactive BaSO4. The values obtained for these data were 7.65 3 1028 m and 1.29 3 1027 m, respectively.
Pitzer (1981). In addition, we accepted the parameterization of the sulfuric acid system as presented by Reardon and Beckie (1987), including their expressions for the values of the log KH-SO4, and the parameters b0H-SO4, b0H-HSO4, b1H-HSO4, C0H1 0 1 HSO , C H-HSO C H-SO and C H-SO as a function of tempera4 4 4 4 ture. While aware of the more recent parameterization of the sulfuric acid system by Clegg et al., 1994, the use of the Reardon and Beckie (1987) model retains consistency with our earlier work on the analogous PbSO4 system (Paige et al., 1992). Species distribution was calculated by an iterative solution of the law of mass action for the simultaneous equilibria: under the assumption that the first dissociation of sulfuric acid is complete. Further details of the procedure for the fitting of the parameters may be found in the paper by Paige et al. (1992). 3. RESULTS AND DISCUSSION
The results of our determination of the solubility of BaSO4 in H2SO4-H2O solutions at 298K and 333K are presented in Tables 1 and 2 while the results of our modelling of these data are shown in Fig. 3. During our researches we only approached saturation from above for the 60°C solutions or from below for
Table 2. Solubility of barium sulfate in water and sulfuric acid solutions at 60°C.
(1)
The Pitzer expressions, as formulated by Harvie et al. (1984), were substituted for the individual ion activity terms in Eqn. 1. The Ksp was treated as a parameter of the model and derived by regression analysis. The solubility of BaSO4 in pure water was included in each data set analyzed. Regression analysis of the BaSO4-Na2SO4 solubility data of Felmy et al. (1990) was used in order to obtain an initial estimate of the Ba21-SO422 interaction parameters. We used the temperature functional expression for the Pitzer parameters b(0), b(1), C(f) for the Na2SO4 system given by De Lima and Pitzer (1983) and Rogers and
95% confidence interval (3 replicates)
[H2SO4] mol/kg
[Ba] mol/kg
0 (water) 1.00 3 1023 3.00 3 1023 7.92 3 1022 4.50 3 1021 8.90 3 1021 1.84 2.89 3.95 6.19
1.56 3 1025 5.64 3 1027 3.84 3 1027 3.33 3 1027 3.55 3 1027 4.87 3 1027 5.21 3 1027 7.25 3 1027 8.25 3 1027 7.67 3 1027
95% confidence interval (based on # of replicates shown in parentheses) 61 3 1026 (6) 62 3 1029 (3)
62 3 1028 (4) 65 3 1028 (3)
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Fig. 3. (a) Plot of experimental data from this study for the solubility of BaSO4 in solutions of sulfuric acid; 1 5 298K; F 5 333K. The solid line shows the result of fitting the solubility data using the Pitzer model for the activity coefficients. (b) Plot of the experimental data shown in (a) showing the lower concentration region in greater detail.
the 25°C solutions. In each case, however, our sample tubes contained BaSO4 in pure water in order to allow a comparison with the data shown in Fig. 1 obtained by Kornicker et al. (1991) and with data presented in Blount (1977). As a result of the agreement between our results for the solubility of barium sulfate in pure water at 25°C and 60°C and results obtained from separate experiments at the same temperatures, we feel confident that we approached saturation closely in our experiments. The procedure followed for determining the solubility of BaSO4 in water and sulfuric acid solutions gave rise to an number of questions: the effect of labelling on the solubility of the barium sulfate; the effect of particle size on the solubility of substances and the potential adsorptive losses to the filters used for the separation of the radio-labelled solid from the solutions. A discussion of these considerations follows. The work of Bovington (1965) on 35S labelled BaSO4 suggested that for BaSO4 a 10% increase of solubility over the accepted values for inactive material occurred and that this increase was independent of the specific activity. The enhanced solubility of radioactive BaSO4 was attributed to the production of minute surface crystallites, which probably arise as a result of self-irradiation damage in the crystals. This damage is produced by the b-particles of 35S, a proportion of which have energy in excess of the 0.1 MeV required to directly transfer sufficient energy to an atomic nucleus to result in an atomic displacement (Durup and Platzmann, 1961). However, in a careful investigation, Berdonosov (1973) found that for the case of cerium oxalate, if allowance for adsorption and colloid formation was made, the radiochemical method of determining solubility gave results which agreed with those obtained using other methods. He found that the specific activity of the samples used did not have an effect on the solubility values determined. The situation with respect to enhancement of solubility due to radio-labelling would thus appear to be open to debate. If such an effect occurs it appears to be (1) mainly exhibited by very sparingly soluble substances and (2) is due to radiation damage which is probably caused by of the samples used did not have an effect on the solubility values determined. The situation with respect to enhancement of solubility due to
radio-labelling would thus appear to be open to debate. If such an effect occurs it appears to be (1) mainly exhibited by very sparingly soluble substances and (2) is due to radiation damage which is probably caused by displacement of atoms. The most effective particles in bringing about such displacements are heavy particles (e.g., protons, a-particles, or fast neutrons). Direct displacement is much less likely in the case of irradiation by X-rays (Durup and Platzmann, 1961). The study carried out in the present research with radiotracer labelling utilized a relatively low level of specific activity (approximately 2.39 mCi/g BaSO4 as compared to the 30 mCi/g used by Bovington (1965), with a much higher level of efficiency for the detector system. And an X-ray emitter (133Ba) which appears unlikely to cause atomic displacements was used. The inclusion of pure water as a solvent was intended to act as a quality control on the determination of the solubility. The mean value of the solubility of BaSO4 in pure water at 25°C determined in this study, 9.9 3 1026 6 0.9 3 1026 mol/kg, compares favourably with the value of 1.06 3 1025 mol/kg given in Blount (1977) based on the data of Melcher (1910) and Templeton (1960). The value at 60°C, 1.56 3 1025 6 0.1 3 1025 mol/kg also compares well with 1.52 3 1025 mol/kg taken from Blount (1977). Many reported data for the solubility of sparingly soluble substances exhibit a wide variability in results at any particular temperature. For example the solubility of celestite in both water and solutions of NaCl-H2O (Reardon and Armstrong, 1987) exhibits such variation. The variability has been attributed to two major factors. The first is the well documented effect of particle size on solubility. This has been extensively studied by Enustun and Turkevich (1960) for the case of celestite. These researchers found, in a series of experiments using material of varying particle size distributions, that the smallest-sized particles present appeared to control the solubility. Typical particle sizes likely to give rise to significant enhancement of solubility would be approximately 0.4 mm or less in diameter. Scanning electron microphotography gave no indication of the presence of a population of particles of this magnitude for the barium sulfate grown using the technique of precipitation from homogeneous solution (Gordon et al., 1959)
Solubilities of BaSO4 and RaSO4 in sulfuric acid Table 3. Ion interaction parameters for Ba21-SO422. 95% confidence interval on T°K
b0
b1
b2
b1
b2
298 333
0.000 0.000
5.25 5.99
2156 2177
60.3 61.5
611 648
The parameter b0 was found to be not significantly different from zero after the first cycle of regression. It was consequently removed from the regression analysis. The parameter values for b1 at 25°C and 60°C are statistically indistinguishable. Consequently, this parameter may be set at the average value, 5.62.
used in this work. In addition, the mixing process for BaSO4 with the sulfuric acid solutions was deliberately carried out in such a manner as to avoid crushing or breaking the crystals, processes which appear likely to produce fragments of a very small size. The possibility of the presence of extremely small particles was investigated further. Four samples of unlabelled BaSO4 prepared using the method of precipitation from homogeneous solution (Gordon et al., 1959) were gently shaken for 2 weeks in 0.1 M and 1.0 M H2SO4 solutions at 25°C. The resulting solutions were then filtered through 0.1 mm polycarbonate and 0.2 mm Teflon membrane filter media and submitted to analysis by ICP/MS. No significant difference in the concentrations of the solutions filtered through these different media was found. It was concluded that no very small particles were present in the filtered solutions that could lead to artificially high values for the solubility. The second factor which has been suggested to account for the variability in the published data for the solubility of sparingly soluble compounds relates to the susceptibility of these materials to surface poisoning. A detailed study of this phenomenon was carried out by Campbell and Nancollas (1969). They identified the source of this surface poisoning effect as the deionized water used in the experiments. When double-distilled water was used, all inhibitory effects on dissolution and precipitation were removed. For this reason, all water used in the experiments carried out in this research, including that used to prepare the solutions of H2SO4 was distilled, demineralized, filtered water of the highest obtainable quality with a measured conductance of less than 1.8 mS/cm. In the case of the solubility measurements in pure water, the water was deaerated by use of dry nitrogen from a cylinder in order to avoid the presence of any carbonate formation due to dissolved CO2. The polypropylene tubes used for the solubility determinations were all washed with H.P.L.C. grade methanol before use in order to remove any manufacturing residues likely to be present. The effect of adsorption and colloid formation on the measured values of the solubility of sparingly soluble substances has been discussed in the literature (Bagnall, 1960). In the case of the determination of the solubility of RaSO4, for example, ignoring the adsorptive losses to the filter led to very low results (Lind et al., 1918; Nikitin and Tolmatscheff, 1933). It was found during the research described in the present study that losses of activity of radio-labelled solutions to filters could be substantial. For example, adsorption on cellulose acetate filters caused the loss of virtually all the activity of even highly
19
active solutions of 133-Ba in water. Teflon filter media were found to cause no loss of activity due to adsorption under the same conditions. Consequently, during the course of the present study all filtration was carried out using 0.2 mm Teflon filter media prewetted with H.P.L.C. grade methanol. Adsorption losses to the filters were allowed for by rejecting the first ten drops of the filtrate for each solution. Such losses are likely to be insignificant for cations at the low pHs of the acidic solutions used in our research. 4. RESULTS OF MODELLING THE DATA FOR THE SOLUBILITY OF BaSO4 IN H2SO4 AT 298K AND AT 333K
We found the b0 and b1 parameters for Ba21-SO422 to be highly negatively correlated, as indicated by the values of the correlation coefficients in the output from our fitting program. An analysis of our results from the modelling shows that b0 could be set equal to zero. A similar situation for the b parameters has been noted by Monin and Galinier (1988) in the cases of BaSO4 and SrSO4 and by Paige et al. (1991) in the case of PbSO4. The final parameter sets for Ba21-SO422 and Ba21HSO2 4 are shown in Table 3 and Table 4. The pKsp at each temperature, derived from the modeling is also shown in Table 4. Further, the ion products obtained from the modelling of the sulfate data may be compared with those obtained in pure water and with literature data. This comparison has been made in Fig. 2. It has been shown (Pitzer, 1986) that for the 2:2 sulfates Kassociation 5 22b2 at low ionic strength. This yields log Kassociation of 2.49 6 0.03 using the 25°C value for b2 and log Kassociation of 2.55 6 0.1 using the 60°C value. The uncertainties quoted are the 95% confidence intervals about the estimates. The values for the logarithm of the BaSO4(aq) association constant given in the literature appear to range between 2.16 and 2.7 (Smith and Martell, 1976) while Felmy et al. (1990) give a value of 2.72 6 0.09 based upon their redetermination of the solubility of BaSO4 in Na2SO4 solutions up to 0.01 M in concentration. The agreement between our results and the value of Felmy et al. (1990) appears quite reasonable, given the large differences in ionic strengths. The parameter b2 is often considered to be indicative of the tendency of ions to form an ion pair. When it is negative and larger in absolute value than 200, then it is more convenient to explicitly include an ion pair. This is discussed by Weare (1987). Thus, in the case of barite it is not clear whether it is necessary to introduce an ion association species, as suggested by Felmy et al. (1990). The variation in the Ksp with temperature between 25°C and
Table 4. Ion interaction parameters for Ba21-HSO42 and pKsp values. 95% confidence interval on T°K
b0
b1
pKsp
b1
pKsp
298 333
0.000 0.000
3.20 3.60
10.02 9.68
60.1 60.2
60.02 60.01
The electrostatic coefficient for the barium-hydrogen interaction was found to be 0.03 at 25°C and 0.08 at 60°C, when estimated by regression.
20
C. R. Paige et al.
60°C allows an estimate to be made of the enthalpy of dissolution for BaSO4 by using the isochore equation. The Ksp data in Table 4 were used to calculate DHdissolution and a value of 18.5 6 1.7 kJ mol21 was obtained. The error was calculated from the 95% confidence interval about the estimates of the Ksp. For the similar PbSO4 system the authors estimated a value of 13.3 6 1 kJ mol21 for the enthalpy of dissolution. Literature data for DHdissolution for the barite system are reviewed by Blount (1977) and vary from 19.4 kJ mol21 (Latimer, 1952) to 26.6 kJ mol21 (Blount, 1977). The data quoted from Blount (1977) have been converted from kcal mol21. Use of existing thermodynamic data (Weast, 1974) for the BaSO4, Ba21aq and SO422aq system and an appropriate thermochemical cycle lead to a calculated value of 19.37 kJ mol21. 5. MODELLING THE AVAILABLE LITERATURE DATA FOR THE SOLUBILITY OF RaSO4 IN H2SO4 AT 298K AND THE PREDICTION OF THE SOLUBILITY AT 333K
There is a single set of data available on the solubility of RaSO4 in sulfuric acid at 25°C (Lind et al., 1918). The studies of Nikitin and Tolmatscheff (1933) provided data on the solubility of RaSO4 in aqueous solutions at 20°C. They measured the solubility at 20°C in water (five determinations) and in Na2SO4 solutions (three determinations). In their paper, Lind et al. (1918) state that the filters used in their investigations were 1 inch of closely packed cotton or asbestos fibre for the solutions containing more than 45% sulfuric acid. As noted in Seidell (1940), the solubility data for water given by Lind et al. (1918) are 1870 times too low compared to that given by Nikitin and Tolmatscheff (1933). It would appear likely that the data obtained by Lind et al. (1918) from the studies in water— and perhaps in low concentrations of sulfuric acid as solvent— are too low, probably due to adsorption losses to the filters. It should also be noted here that the solubility data for RaSO4 in H2SO4 given in Seidell (1940) are quoted as g/25 cc but in our original paper of Lind et al. (1918) the data are in g/cc. It would appear that there is an error in the data as reported by Seidell (1940). Consequently we selected the data from Nikitin and Tolmatscheff (1933) for the solubility of RaSO4 in pure water and those data for the solubility of RaSO4 in sulfuric acid solutions below a concentration of 45% sulfuric acid, quoted in the original paper by Lind et al. (1918). The conversion from % sulfuric acid to the molality scale of concentrations was effected with the use of formulae and tables of concentration found in Weast (1974). The data selected from those reported by Nikitin and Tolmatscheff (1933) and Lind et al. (1918) were analyzed, using four treatments. In all treatments examined it was assumed that the parameters b0Ra-SO4 and b0Ra-HSO4 were zero, by analogy with the values derived for PbSO4 (Paige et al., 1992) and BaSO4 in this work. The four treatments examined were: (1) Regression of the selected data at 25°C for the parameters b1Ra-SO4, b2Ra-SO4, b1Ra-HSO4, and the solubility product constant, Ksp; (2) Regression of the selected data at 25°C for the parameters b1Ra-SO4, b2Ra-SO4, b1Ra-HSO4, Ksp, and the electrostatic coefficient QRa212H1; (3) Use of the parameter set for BaSO4 as surrogates for those for RaSO4 and regression for the Ksp and the electrostatic coefficient QRa212H1; (4) Setting all parameters and the electrostatic coefficient QRa212H1 to zero and regression for the Ksp.
Table 5. A comparison of treatments for the modeling of literature solubility data for RaSO4 in H2SO4-H2O solutions at 25°C. Treatment considered Regression of the data for 25°C to estimate Ksp, b1, b2, b1; QRa21-H1 5 0
Residual sum of squares Regression of the data for 25°C to estimate Ksp, b1, b2, b1, QRa21-H1
Residual sum of squares Use the b parameters for BaSO4; regress for Ksp, QRa21-H1
Residual sum of squares Set all parameters to zero; regress for Ksp Residual sum of squares
Value of constants of the model 695% confidence interval
b1 5 7.085 6 1 .8 b2 5 2288 6 29 1 b 5 2.595 6 0 .93 pKsp 5 10.41 6 0 .04 5 1.0 3 1022
b1 5 6.80 6 1 .1 b2 5 2277 6 19 1 b 5 2.357 6 0 .59 pKsp 5 10.41 6 0 .03 QRa21-H1 5 0.060 6 0 .014 5 2.8 3 1023
pKsp 5 QRa21-H1 5
10.21 6 0 .06 0.049 6 0 .026
5 0.113
pKsp 5
10.72 6 0 .29
5 9.71
Note 1: In all treatments considered, the b0 parameters for both the Ra21-SO422 and the Ra21-HSO42 interactions were set equal to zero. In each treatment presented above, the first stated value for b1 is for the Ra21-SO422 interaction while the second stated value is for the Ra21HSO42 interaction.
The parameters derived using these treatments and the associated residual sums of squares are presented in Table 5. The fits obtained using these treatments are presented in Fig. 4a– d. From a consideration of the data in Table 5, it appears that the first two treatments yield parameter estimates which are statistically identical, within their individual 95% confidence intervals. The better fit provided by the second treatment, as judged by the smaller residual sum of squares, is merely due to an extra parameter included in the fitting. However, the agreement between the value of the pKsp derived using these two treatments, 10.41, and the value of 10.26 calculated using the equation log K sp (RaSO4) 5 137.98 2 8346.87/T 2 48.595 log T
(2)
given by Langmuir and Reise (1985) can only be regarded as fair. The value of the pKsp provided by the final treatment, and
Solubilities of BaSO4 and RaSO4 in sulfuric acid
21
Fig. 4. Plots of selected data for the solubility of RaSO4 in sulfuric acid solutions (Linde et al., 1918) at 25°C and the solubility in pure water (Nikitin and Tolmatscheff, 1933). The solid lines represent the results of using the treatments described in Table 5: (a) Regression of the data for 25°C to estimate Ksp, b1, b2, b1; set QRa21-H1 5 0; (b) Regression of the data for 25°C to estimate Ksp, b1, b2, b1, QRa21-H1; (c) Use of the parameter set for BaSO4 and use regression to estimate Ksp, QRa21-H1; (d) Set all parameters to zero and use regression to estimate Ksp.
the quality of the fit as shown in Fig. 4d, must be regarded as unacceptable. Using the parameter set derived for BaSO4 and obtaining the Ksp and electrostatic coefficient for RaSO4 by regression analysis of the data for solubility of RaSO4 in water and sulfuric acid solutions at 25°C appears to give a good fit and yields a value for the Ksp which is in good agreement with that of Langmuir and Reise (1985). Accordingly, we have selected this option in order to model the solutbility of RaSO4 in water and sulfuric acid solutions. Based on the selected parameters at 25°C and using a linear interpolation, we estimated values for the parameters for RaSO4 at 35°C, 45°C, and 60°C. The Ksp was calculated using Eqn. 2 taken from Langmuir and Reise (1985). Given the agreement between the value obtained by regression at 25°C
and the value predicted using Eqn. 2 this seemed to be a reasonable approach. The values of these estimates of the parameters are presented in Tables 6 and 7, while Table 8 shows the predicted solubility of RaSO4 in H2SO4 at 35°C, 45°C, and 60°C. The paper of Lind et al. (1918) contains two measurements of the solubility of RaSO4 in sulfuric acid at 35°C and one measurement of the solubility at 45°C. These data permit a very limited comparison to be made of the predicted solubility at 35°C and 45°C with experimental data. As shown in Table 8 the agreement between observed and predicted solubility appears quite reasonable at 35°C, but poor at 45°C. This suggests that the predicted solubility at 60°C, also shown in Table 8, is at best only of the correct order of magnitude. Attempts to vary the value of b2 and the electro-
22
C. R. Paige et al.
static coefficient QRa212H1 by hand did not markedly improve the agreement at 45°C. For example, reducing the value of QRa212H1 to 0 and setting b2 arbitrarily to 238 only reduced the predicted solubility of RaSO4 by a factor of ;2. Any further discussion of this system must await further investigation of the data of Lind et al. (1918), which involve very low levels of Ra, using modern filtration media and counting techniques. Meanwhile setting the bRaSO4 parameters equal to those of BaSO4 is a very useful approximation. 6. SUMMARY
Systems of potential interest in the development of an overall predictive model for the purpose of describing solution and mineral equilibria in uranium mill leaching tanks and mill waste drainage waters include BaSO4-H2SO4-H2O. Available literature data does not include data at either 25°C or 60°C necessary for such modelling. Consequently, the solubility of BaSO4 in H2SO4 solutions has been measured at 25°C and 60°C. The solubility of BaSO4 in H2SO4 solutions has been modelled using the Pitzer equations for the activity coefficients for the individual ions. Literature compilations of Pitzer interaction did not include values for Ba21-SO422 and Ba21-HSO42. We estimated these parameters using nonlinear least-squares techniques. The values for the Ksp derived from the Pitzer modeling of the solubility of BaSO4 in sulfuric acid are in good agreement with those derived from literature solubility data in pure water and our experimental data in pure water. The available solubility data for RaSO4 in H2SO4 solutions at 25°C may be modeled using the Pitzer ion activity model and regressing the data, but the large negative value of b2 obtained suggests that the ion association model may be preferable. The parameters obtained from the regression analysis of our data for the solubility of barite in sulfuric acid solutions at 25°C may be used to model the literature solubility data for RaSO4 in sulfuric acid solutions at 25°C. The value for the pKsp derived is in excellent agreement with that derived by Langmuir and Reise (1985). Predictions for the solubility of RaSO4 in sulfuric acid solutions at temperatures higher than 35°C do not correlate well with the very limited data available at present.
Table 6. Selected ion interaction parameters for Ra21-SO422. T°K
b0
b1
b2
298 308 318 333
0.000 0.000 0.000 0.000
5.260 5.452 5.643 5.931
2153.0 2160.7 2168.4 2179.9
The parameters were not obtained by regression but were approximated using the parameters obtained at 25°C for BaSO4 in place of those for RaSO4. At 35°C, 45°C, and 60°C the parameters were estimated using a linear interpolation of the parameters of BaSO4 estimated in this study, assuming the same slope with temperature, as surrogates for those of RaSO4.
Table 7. Selected ion interaction parameters for Ra21-HSO42 T°K
b0
b1
Value of pKsp
298 308 318 333
0.0000 0.0000 0.0000 0.0000
3.128 3.278 3.427 3.652
10.21 6 0.06 (regressed) 10.05 (Langmuir & Reise) 9.87 (Langmuir & Reise) 9.66 (Langmuir & Reise)
The electrostatic coefficient for radium-hydrogen was found to be 0.049 6 0.038 at 25°C. At 35°C, 45°C, and 60°C the parameters were estimated using a linear interpolation of the parameters for BaSO4 estimated in this study, assuming the same slope with temperature, as surrogates for those of RaSO4. Table 8. Comparison of observed and predicted solubility of RaSO4 in H2SO4-H2O solutions at 308, 318, and 333K. [H2SO4] mol kg21 0.005 3.02 3.02 3.02
Temperature K
Observed (Lind et al., 1918) Solubility mol kg21
Predicted
308 308 318 333
9.32 3 1028 1.02 3 1027 1.55 3 1027 No data known
1.0 3 1027 1.1 3 1027 4.6 3 1027 6.2 3 1027
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