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Ind. Eng. Chem. Res. 2000, 39, 518-526
A Solubility Model for Aqueous Solutions Containing Sodium, Fluoride, and Phosphate Ions† Charles F. Weber,* Edward C. Beahm, Douglas D. Lee, and Jack S. Watson Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6370
A computational model is developed to calculate thermodynamic phase equilibria in aqueous solutions of fluoride, phosphate, and hydroxide up to 100 °C. A variety of data are used, including isopiestic and electromotive force measurements, freezing point data, vapor pressure data at 100 °C, heat capacities, heats of dilution, and solubility measurements. Pitzer’s ion-interaction treatment is used to model electrolyte solutions, and many unknown parameters are determined from existing data through nonlinear least-squares fitting. Phase equilibria are determined by minimization of the total Gibbs energy using a modification of the code SOLGASMIX. Results calculated using the model accurately predict phase equilibria from many quantitative experiments. Qualitative experiments are performed to evaluate calculated solubilities in regions of sparse or nonexistent data; the calculated results are reasonable and exhibit a general qualitative agreement with such data. Model predictions are useful in understanding problems that may arise in the treatment of waste streams containing fluoride and phosphate anions in highly caustic solutions. Introduction A significant problem in the processing of radioactive wastes is uncontrolled precipitation in solutions containing hydroxide, fluoride, and phosphate ions. For example, the treatment of radioactive sludge from underground storage tanks at the Hanford site near Richland, WA, will likely involve leaching in a sodium hydroxide solution. Failure to understand and control precipitation could result in the formation of crystalline solids and gels that are unacceptable because they will prevent mixing, impede pumping, retard separations, coat surfaces, and clog pipes, equipment, and filters. This issue is of great practical concern, because solids containing both phosphate and fluoride have been found in several caustic leaching tests on sludge from the Hanford tanks. It is generally understood that the presence of even small amounts of fluoride or phosphate will drastically affect the solubility of the other anion. However, quantification of mutual solubility effects has been hampered by the paucity of data, conflicting data, and failure to account for phosphate hydrolysis and excess hydroxide. The present effort is driven by the need to characterize aqueous mixed waste containing Na+, F-, PO43-, HPO42-, and OH- and to evaluate various processing strategies. This requires modeling such systems to 100 °C and at high caustic concentrations. Experimental Data Before the full system Na-PO4-HPO4-F-OH is evaluated, it is necessary to examine the simpler subsystems Na-F, Na-OH, Na-HPO4, and Na-HPO4PO4-OH. Those not involving fluoride have been evalu* To whom correspondence should be addressed. Phone: 423 576-4475. Fax: 423 576-3513. E-mail:
[email protected]. † Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy under Contract DE-AC05-96OR22464.
ated elsewhere, and the results will be appropriated for use here. In this section existing data from a variety of sources are examined and used to develop models of needed subsystems and the total phosphate-fluoridehydroxide system. Common Electrolyte Systems. An exhaustive evaluation of the binary system NaOH-H2O has been performed by Simonson et al.1 These authors utilized a variety of activity data, enthalpy data, and heat capacities to construct a rigorous and comprehensive model over the temperature range 0-250 °C and at pressures up to 20 kPa. Their results are used here, applied to more limited conditions (atmospheric pressure, 0-100 °C). Numerous studies of NaCl aqueous systems have been performed. While the present study does not involve Cl- directly, some additional mixed salt data are available if this anion is included. Because this system has been characterized thoroughly, it poses little additional effort to do so. The model results given by Pitzer2 are used, again applied within the temperature and pressure limits of this study. A recent evaluation of trisodium phosphate (TSP) solutions provides needed data for the current study.3,4 Thermodynamic parameters for the Na-PO4-HPO4OH-H2O system have been determined from activity and solubility data over the range 0-100 °C. The procedures were similar to those used in the present study. Subsystem NaF-H2O. Data for this system are listed in Table 1. While considerable data are available, there are many discrepancies. For example, Figure 1 shows solubilities of the binary solution in the temperature range 0-100 °C. The dashed line represents a fit by Linke5 of many early results, and he notes that there was considerable scatter in the data used. The more recent data shown in Figure 1 also show considerable scatter and seem to indicate systematic, rather than random, error. In particular, the results of Guiot6 seem
10.1021/ie990457l CCC: $19.00 © 2000 American Chemical Society Published on Web 12/30/1999
Ind. Eng. Chem. Res., Vol. 39, No. 2, 2000 519 Table 1. Data Used To Characterize NaF Aqueous Systems range of validity T (°C)
ref
data type
I (m)
7 8 9 10 12 12 5
isopiestic emf freezing pt. vapor pressure enthalpy of dilution heat capacity binary solubilities
0.1-1.0 0.05-0.9 0.04-0.5 0.24-1.07 0.004-1.0 0.08-0.72 ∼1
13 14 16 16 17
Na-Cl-F solubility Na-Cl-F solubility Na-OH-F Na-OH-F Na-Cl-F emf
1-6.2 1-6.2 1-1.4 1-5.7 1-6
Binary System 25 15-35 0 100 25 25 0-100
Data in Mixed Systems 25, 35 50 0, 40, 80, 94 20 25
fitted parametera
data variance
no. of points
φ γ φ φ ∆Hdil Cp mi
10-5 3 × 10-5 5 × 10-4 10-5 0.1 0.01 10-3
6 15 5 5 26 11 6
mi mi mi mi γ
10-3 10-3 10-3 10-3 3 × 10-5
7 10 16 8 25
a Data fitted include osmotic coefficient (φ), activity coefficient (γ), heat capacity (C ), enthalpy of dilution (∆H ), and molal solubility p dil (mi).
Table 2. Data for Fluoride-Phosphate Solubilities
Figure 1. NaF solution solubilities: 0, ref 16; O, ref 15; b, ref 14; ], ref 6; 3, ref 13; - - - , ref 5; s, this study.
artificially low, which is disappointing. This author also has a large quantity of data for the Na-PO4-F system, which is somewhat questionable in view of these NaF results. Activity coefficients at 25 °C have been measured by both isopiestic7 and electromotive force (emf)8 experiments, although these two data sets are somewhat inconsistent with each other. Additional binary system data are used to evaluate activity coefficients at other temperatures. Direct activity measurements arise from freezing point lowering,9 vapor pressure measurements10 at 100 °C, and the emf data8 at 15 and 35 °C. Freezing point data are translated into values of the osmotic coefficient using the correlation of Robinson and Stokes11
φ)
∆T (0.5377 + 0.0002684∆T) m
(1)
where ∆T ) temperature lowering of the freezing point (K) and m ) total ions in solution (assuming complete dissociation). Measurements of the dilution enthalpy and heat capacities12 help establish the temperature dependence, even though they occur only at 25 °C. In addition to the binary data, several researchers have considered systems involving Na+, F-, and a third ion. Such systems are particularly useful, because they involve ionic strengths well above the NaF solubility
ref
temperature (°C)
usable points
18 19 6 20 21
25-40 25-75 0-100 25 100+
6 17 0 0 5
limit and also allow estimation of ternary mixture parameters and Gibbs energies of formation. Solubility data are available for Na-Cl-F systems13-15 and NaOH-F systems.16 Because there appear to be serious inconsistencies in the data of Campbell,15 they were not actually included in this analysis and do not appear in Table 1. The data in hydroxide solutions are especially useful, because they span the temperature range 0-100 °C, although they extend above I ) 1.5 only at 20 °C. In addition, mixture emf data17 are available for NaCl-F systems at 25 °C; while they do not help determine temperature coefficients or Gibbs energies, these data contribute to the determination of binary parameters at high ionic strengths and ternary mixture parameters. Fluoride-Phosphate Systems. The thermodynamics of sodium-fluoride-phosphate mixtures is complicated somewhat by the usual presence of hydroxide, making this a four-component system (with components H2O, NaF, Na3PO4, and NaOH). Unfortunately, many researchers have not accounted for this additional quantity, which is often present through use of reagentgrade TSP (and may contain up to 2.5% excess hydroxide). Hence, an important part of this effort has been to estimate hydroxide inventories through heuristic means. Mason and Ashkroft18 have reviewed earlier studies dating back to the mid-19th century, in which the double salt NaF‚2Na3PO4‚19H2O (hereafter referred to as double salt or DS) was noticed as a dominant crystallization product. While the earlier studies were more qualitative, Mason and Ashkroft sought to determine invariant points of the solubility curve and actually performed a quantitative evaluation. Several more recent sources of data are also available and are listed in Table 2. The first three have performed some crystallographic analysis and have concluded that the precipitate is DS, TSP, or NaF. Reference 20 regards the precipitate as a solid solution of TSP and NaF, based on the changing ratio of F/P. Reference 21 makes no analysis but simply assumes the results from ref 20. It appears that the weight of evidence favors the formation of DS and that other factors (such as contamination of
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mixture solubilities are significantly different from those of any other researchers (cf. Figures 1 and 2). Part of the problem may be in the experimental procedure for measuring fluoride. In addition, the author mentions that he determined equilibrium by constancy of the solution density, which usually occurred within 12-72 h. Mason and Ashkroft18 mention a solution that initially crystallized to TSP but that over the course of 1 week converted to DS, evidently the more stable form. Likely the solution density remained fairly constant during this time. Thus, it is possible that much of the data from ref 6 do not represent a true equilibrium state. Description of Calculational Model
Figure 2. Solubility in the system Na-F-PO4-OH at 25 °C: 0, ref 18; 4, ref 6; O, ref 20; ] (pure water) and [ (in 1 M NaOH), ref 19.
samples, unaccounted effects of OH-, or faulty measurements) have given the appearance of a solid solution. Throughout the remainder of this work, the DS is assumed to be the product formed. With regard to equilibrium solution concentrations, the various references are not in good agreement, as can be seen from the plot of values at 25 °C, shown in Figure 2. While some of the discrepancies may arise from differences in OH- concentration (or temperature, in the case of ref 6), there are undoubtedly other difficulties as well. In some cases, the measurements were probably taken on systems not in equilibrium. Also, there are certain inconsistencies in some measurements with regard to the F/P ratio; most likely these are caused by faulty fluoride measurements. Most researchers do not measure OH- in their solutions; however, for some it is possible to ascertain reliable values from the descriptions of the experimental procedure. References 18-21 all mention (or imply) that they use reagent-grade TSP without regard to the excess hydroxide. This constitutes only 2.5% (by weight) impurity and is evidently regarded as negligible. To use such data, the anhydrous solid is assumed to be 20 mol % NaOH, consistent with the research of Wendrow and Kobe,22 who give the primary solid as Na3PO4‚12H2O‚ 1/ NaOH. In addition, it is necessary to know the exact 4 total inventories of all constituents initially or finally (including the amount of precipitate), because this describes how much OH- actually is in solution. All data from ref 18 were used, because the authors state complete initial inventories. Some data from ref 19 were also usablesnamely, those for which quantitative results were obtained. No data from ref 20 were used, because it was impossible to adequately determine OHconcentrations. Finally, the values from ref 21 were used for ionic strengths below 9. This was justified because the experimental procedure describes that sampling is done as soon as the first crystals appear. Hence, the OH- can be determined from the PO43- aqueous inventory, with the amount of precipitate being negligible. The data in ref 6 is quite extensive, spanning 0-100 °C and involving more than 150 solution measurements, in addition to examination of solid phases and determination of invariant points. Unfortunately, it is not usable, because there are evidently serious errors in many of the values. Both the pure-component and
The vehicle used for building a quantitative model is an adaptation of the chemical equilibrium code SOLGASMIX,23,24 modified to perform aqueous electrolyte calculations. This code calculates phase equilibrium by minimizing the total Gibbs energy. A special module has been developed to perform nonlinear optimization, for the purpose of fitting the various parameters to actual data. This procedure uses a combination of GaussNewton and the BFGS quasi-Newton algorithms to minimize squared error as parameter choices vary. The combined use of these algorithms and the step-size procedure are described by Fletcher.25 Gibbs Energies of Formation. Values for Gibbs energies were obtained at 25 °C from the CODATA26 database. These were established through international consensus and are particularly applicable to solutions containing uranium and other actinides. While this current study does not involve such elements, the motivation of this work is the evaluation of mixed waste solutions where actinides may be present. At temperatures different from 25 °C, values for Gibbs energy of formation were obtained from the HSC database,27 because it is well documented and up to date. Furthermore, it matches very well the CODATA values for water throughout the temperature range 0-100 °C. The reduced Gibbs energies µˆ i ≡ µi0/RT are considered to be functions of temperature of the form:
(
µˆ i ) µˆ i1 + µˆ i2(T - T0) + µˆ i3
)
1 1 T + µˆ i4 ln + T0 T T0 µˆ i5(T2 - T02) (2)
Here, the first subscript refers to the species in question; the second refers to the particular temperature coefficient in eq 2. From eq 2, it is seen that µˆ i(T0) ) µˆ i1, where T0 ) 298.15 K throughout. Activity Coefficients. To evaluate activity coefficients, the ion-interaction approach developed by Pitzer2 is used. Often described as semiempirical, this model uses three parameters, β(0), β(1), and C, to describe interactions of each cation-anion pair. In mixed salt systems, additional parameters Φ and ψ are also used. The latter describes interactions of three ions, not all having the same charge. The former describes interactions of like-charged ion pairs (e.g., OH- and F-) and is represented as Φ ) θ + Eθ(I). The last term is a known function of ionic strength; the parameter θ must be determined from data for each ion pair. Activity and osmotic coefficients are given as functions of these parameters and the concentrations of each ion. Tem-
Ind. Eng. Chem. Res., Vol. 39, No. 2, 2000 521 Table 3. Optimal Parameters coefficienta parameterb
species
1
2
3
4
5
µˆ µˆ β(0) β(1) C θ θ ψ ψ C0p µˆ θ
NaCl NaF Na-F Na-F Na-F Cl-F OH-F Na-Cl-F Na-OH-F NaF soln. DS F-PO4
-155.003 -219.391 0.0330 0.2456 0.00281 -0.0164 0.1193 -0.00045 -0.0350 -88.4014 -3512.445 0.5513
0.45193 2.02 0 0 0
0 0 246.83 2833.0 12.25
0 0 -0.6728 -9.451 -0.0436
0. -0.002 087 1 0 0 0
36.15256
0
0
-0.037 739 5
a Column headings indicate subscripts for coefficients in eq 2. b See sections “Gibbs Energies of Formation” and “Activity Coefficients” for parameter definitions.
perature dependence is modeled by fitting each of the Pitzer parameters to the form of eq 2. Enthalpies and heat capacities involve temperature derivatives of the parameters. The implementation of this system and details of the parameter estimation process can be found in refs 3 and 4. Modeling the Fluoride-Phosphate System The modeling tools mentioned above are now applied to the data. Following the analysis of subsystems NaF-H2O and Na-F-OH-H2O, modeling of the full system Na-OH-F-HPO4-H2O will be possible. In each case, it is necessary to determine ion-interaction coefficients and Gibbs energies of formation as functions of temperature through the range 0-100 °C and, hopefully, for ionic strengths of I < 6 m. Results for Na-F Systems. From Figure 1, despite the data scatter, it is clear that the solubility limit for binary NaF data is never far from 1 m. However, in mixed solutions, the ionic strength will easily exceed this value, and it is desired to model solutions up to I ) 6 m. Extrapolation of NaF activity coefficient data this far is highly unreliable, but it is still necessary to have reasonable binary parameters in this range. To accomplish this, values for activity coefficients are estimated to 6 m by comparison with NaCl and NaBr data through this range. The values so obtained are used in preliminary stages of parameter estimation but are not used to obtain final values. The relevant parameters have been determined and are listed in Table 3. Use of these parameters allows calculation of activities and phase equilibria in the Na-F subsystem, such as the solid solubility curve shown in Figure 1. Unlike the fit of Linke,5 the parameters used to produce this curve have been derived using solubilities of mixed systems as well as the binary system data. Figures 3 and 4 depict activity data and model calculations at 25 °C. Model predictions of both isopiestic results and emf results are low. This is due to inconsistency in these two sets of datasraising either calculated curve would force the other even lower. Also shown in Figure 4 are the added data points above the solubility limit, formed from comparison with NaCl and NaBr data. Model predictions of temperature dependence are compared with data in Figures 5-9. Figure 5 depicts freezing point depression data, consisting of osmotic coefficients derived using eq 1. Also shown are the
Figure 3. NaF isopiestic data at 25 °C: 0, ref 7; s, this study.
Figure 4. NaF emf data at 25 °C: 0, ref 8; ], estimated values (from comparison with NaCl and NaBr); s, this study.
estimated points (using NaCl and NaBr data) at higher concentrations. The model calculation is somewhat lower than actual data; however, the data appears artificially high and even goes above 1 at very dilute concentration. Thus, it is likely that the model is as good as the datasperhaps better. Vapor pressure data at 100 °C are shown in Figure 6, together with the model calculation. There is good agreement with the actual data, although some discrepancy exists at low molalities. However, in this region the measurements are much more uncertain. As is the
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Figure 5. NaF freezing point depression data: 0, ref 9; ], estimated values; s, this study.
Figure 6. NaF vapor pressure data at 100 °C: 0, ref 10; ], estimated values; s, this study.
Figure 7. NaF enthalpies of dilution: 0, ref 12; s, this study.
case with freezing point measurements, these data are quite old and may be suspect for that reason. Much more recent data are available for other thermodynamic quantities, shown in Figures 7 and 8. Model calculations closely match the dilution enthalpy measurements and give a reasonably good prediction of the
Figure 8. NaF heat capacity data: 0, ref 12; s, this study.
Figure 9. NaF emf data. Reference 8: 0, 15 °C; O, 25 °C; ], 35 °C. s: this study.
heat capacity. In the former case, the initial concentration was exactly twice the final value for each pair, making it possible to compare results as a function of concentration. The final set of binary system data is a comparison of emf data at 15, 25, and 35 °C (the values at 25 °C are also shown in Figure 4). As seen in Figure 9, there is very little change in activity coefficients because of temperature, in either the data or the model calculations. The model is, however, slightly low in each case. Solubilities in mixed systems are shown in Figures 10-13. For Na-Cl-F (Figures 10 and 11), agreement with the data is quite good, showing a decrease in NaF solubility as NaCl is added. In the vicinity of 6 m NaCl, an invariant point is reached which appears as a corner on the computed curve. Both the curve and data continue sharply downward, indicating a region of NaCl precipitation. In Figure 10, the data of Campbell13 match closely the calculated results for concentrations m < 2 but are quite inconsistent with all other data (and the calculated solubilities) at high molalities. For this reason, this data set was not included in the optimization process. Solubilities in Na-Cl-F solutions are very nearly identical at 35 and 50 °C, as seen in Figure 11. The model calculations are quite consistent with data in this regard. They are also consistent with the binary solubilities (Figure 1) and the activity data (Figure 8), which indicate only slight temperature effects.
Ind. Eng. Chem. Res., Vol. 39, No. 2, 2000 523
Figure 10. Solubility in the ternary system Na-Cl-F at 25 °C: 0, ref 13; ], ref 15; s, this study.
Figure 11. Solubility in the ternary system Na-Cl-F above 25 °C: ], ref 13 (35 °C); ∇, ref 14 (50 °C); - - -, this study at 35 °C; s, this study at 50 °C.
Figure 12. Solubility in the ternary system Na-OH-F. Reference 16: ], 0 °C; 0, 20 °C; O, 40 °C. s: this study.
For Na-OH-F systems, the results in Figure 12 also show small temperature effects. Only at 20 °C does the data extend to high concentrations, and the model predictions match the data fairly well. Data at 0, 20, 40, 80, and 94 °C are compared with the model calculations in Figure 13. A perfect match would lie on the
Figure 13. Comparison of calculated and measured solubility data for the Na-OH-F system (0-94 °C). Data from ref 16.
Figure 14. Comparison of calculated and measured phosphate in solution for the Na-F-PO4-OH system at 25 °C. Data from refs 18 and 19.
diagonal line. The model gives a reasonably good fit, at least within the uncertainty of the data. Fluoride-Phosphate Systems. The data at 25 °C from refs 18 and 19 were used to determine the mixture parameter θ for F-PO4 interactions and the nominal value of µˆ (DS). These two quantities are given in the last two lines of Table 3. Calculated and measured phosphate values in equilibrium with solids are compared in Figure 14, where the diagonal line denotes a perfect match. Despite scatter in the data, the plot indicates reasonable agreement between data and calculated values. A similar plot of fluoride data does not indicate such good agreement, indicating that fluoride measurements are more uncertain. Solubility data at temperatures other than 25 °C were used to fit temperature coefficients for DS, assuming the mixture parameter θ was constant. These values are also given in Table 3 and were used to recalculate solubilities at many temperatures, which are compared with data in Figures 15 and 16. It can be seen in the figures that there is good agreement between the two. Experimental Verification The parameters from Table 3 allow construction of a comprehensive model of sodium-fluoride-phosphate
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Figure 15. Solubility of the double salt between 35 and 75 °C. Reference 19: 9, pure H2O; 0, 1 M NaOH . s: this study.
Figure 17. Qualitative data of double salt solubilities at 25 °C. Model predictions: - - -, no added OH; - -, 1 m OH-; s, 3 m OH-. Data: •, ref 19 (1 M OH-); ], [, in 1 m OH-; 0, 9, in 3 m OH(this study). Table 4. Prediction of Precipitation Temperature initial concentration (m)
Figure 16. Comparison of calculated and measured values for the Na-F-PO4-OH system at 25-100 °C. Data from refs 18, 19, and 21.
behavior. The purpose of this section is to verify the predictive capability of this model. The data used in this section are from new experiments and are not as quantitative as data mentioned previously. However, they do lend themselves to qualitative comparison over a wide range of conditions, including extrapolations outside the range of data used in parameter estimation. The solubility curve of sodium fluoride-phosphate solutions at 25 °C is shown in Figure 17, for cases involving no excess OH-, 1 m NaOH, and 3 m NaOH. For each hydroxide level, the solubility of three different solids is depicted, with invariant points appearing as corners on the curves. The hydroxide dependence is obvious, because the solubility decreases drastically as OH- increases. This is true not only for the double salt but also for the simple salts TSP and NaF. It should be noted that the DS solubility in 3 m OH- is an extrapolation, because no data were available. However, data were used for the simple salts in 3 m (and higher) OH-, as well as the DS in 1 m OH-. The predicted curve is fully consistent with these data. To test these extrapolations, some qualitative experiments were run to ascertain general solubility behavior of solutions high in hydroxide (the region of primary interest for waste treatment). Stoichiometric amounts
temperature of precipitation (°C)
F-
PO43-
OH-
data
model
0.10 0.05 0.20
0.20 0.28 0.08
3 3 3
52-57 52-57 52-57
53 54 80 (NaF) 43 (DS)
{
of H3PO4 and NaOH were mixed to obtain initial solutions containing exactly the mole ratio Na/PO4 ) 3. These were mixed with solutions containing NaF and NaOH in known amounts. Reagent-grade chemicals and ultrapure water, purified through an ion-exchange membrane, were used throughout. All components were mixed at about 60 °C until total dissolution occurred. Subsequently, the solutions were cooled to 25 °C and mixed for at least 1 day so they would come to equilibrium at the lower temperature. Precipitation (or lack thereof) was determined by visual inspection, microscopic examination of crystals, and X-ray diffraction. For a given starting concentration, these tests merely confirm whether precipitation occurs. No attempt was made to measure aqueous concentrations of the solution at equilibrium. The individual data points in Figure 17 denote initial concentrations of various experiments. Solid points indicate that solids formed (in every case, the precipitate was the DS), whereas hollow data points indicate no precipitation. (For the point with F- ) 0.1 m and PO43) 0.05 m in 3 m OH-, the analysis was indefinite.) If the model prediction is accurate, then solid points should occur above the lines and open points below. The single point used in model formulation (in 1 M OHfrom Herting19) lies close to the predicted curve. The additional data indicate that the model generally overpredicts the ability of the DS to remain in solution. However, recall that these data are largely extrapolations. The predictions do match the qualitative behavior of the data through more than an order-of-magnitude change in solubility. Finally, the temperature dependence of predictions was evaluated by mixing fluoride-phosphate solutions in 3 m NaOH at 100 °C and cooling until solids formed. To minimize supersaturation effects, the solution temperature was lowered a short interval and held constant for 1-3 days. Although complete equilibration might
Ind. Eng. Chem. Res., Vol. 39, No. 2, 2000 525 Table 5. Gibbs Energies of Formation (µˆ ) µ0/RT) temperature coefficienta species
µˆ 1
µˆ 2
µˆ 3 × 10-7
µˆ 4 × 10-3
µˆ 5 × 103
H2O(l) Na+(aq) H+(aq) OH-(aq) Cl-(aq) F-(aq) PO43-(aq) HPO42-(aq) NaCl(s) NaF(s) TSPb(s) DSPc(s) DSd(s)
-95.665 -105.730 0 -63.534 -52.928 -112.590 -411.192 -439.592 -155.315 -219.391 -1926.923 -1803.470 -3512.445
-1.00 29 0.851 94 0 0.756 06 0.367 999 1.132 20 4.330 69 4.740 18 1.198 614 2.022 907 -1073.417 7.653 92 36.152 56
0 0 0 0 0 0 0 0 0 0 -3.275 115 2 0 0
0.324 0 4 0 0 0 0 0 0 0 0 0 328.256 1 0 0
0.508 48 -0.883 27 0 -0.746 88 -0.358 00 -1.143 10 -4.362 32 -4.997 70 -1.200 0 -2.087 12 584.460 9 0 -37.739 5
a Coefficients for the right-hand side of eq 2. b TSP ) Na PO ‚12H O‚1/ NaOH. These values are for solutions high in caustic. Alternate 3 4 2 4 values are given in ref 3. c DSP ) Na2HPO4‚12H2O. d DS ) NaF‚2Na3PO4‚19H2O.
Summary and Conclusions
Table 6. Activity Coefficient Parameters temperature coefficientb speciesa
parameter
1
3
4
NaOH NaOH NaOH Na-Cl Na-Cl Na-Cl Na-F Na-F Na-F Na-PO4 Na-PO4 Na-PO4 Na-HPO4 Na-HPO4 Na-HPO4 OH-Cl OH-F Cl-F OH-PO4 F-PO4 Na-OH-Cl Na-OH-F Na-OH-PO4 Na-Cl-F
β(0) β(1) C β(0) β(1) C β(0) β(1) C β(0) β(1) C β(0) β(1) C θ θ θ θ θ ψ ψ ψ ψ
0.0864 0.2530 0.0021 0.0759 0.2765 0.00065 0.0330 0.2456 0.00281 0.2534 3.7384 -0.02260 -0.03045 1.3504 0.00359 -0.05 0.1193 -0.01 0.1 0.55 -0.0063 -0.035 0.03 -0.00218
531.5 894.4 -40.69 280.3 -128.9 -14.7 246.8 2833.0 12.25 130.3 23420.0 0 1826.0 6023.0 -282.6
-1.625 -2.748 0.116 -0.7339 0.6430 0.03392 -0.6728 -9.451 -0.0436 0.1247 -70.37 -0.00016 -5.159 -18.77 0.8267
a All species are aqueous ions. b Terms from eq 2; only coefficients 3 and 4 are used to describe temperature dependence.
take longer, especially at lower temperatures, this approach was probably sufficient to measure the onset of precipitation. The three initial solutions shown in Table 4 all experienced the onset of precipitation in the temperature interval 52-57 °C. That is, no precipitation occurred in the equilibrium solution at 57 °C, but solids did form as equilibrium was reached at 52 °C. Predictions above 80 °C showed some questionable behaviors a slight decrease in solubility as the temperature increased. This effect was likely the result of incorrect assumptions in the use of the data from ref 21 or of uncertainties in the data itself. However, below 80 °C the model predictions are consistent with observations in the first two cases as shown in Table 4. The third case is off, in both the prediction of NaF precipitation and the prediction of DS formation at a lower temperature. Evidently, this case is near the invariant point and may reflect uncertainties in both NaF and DS. Recall also that for parameter estimation no fluoridephosphate data were available at this high caustic concentration; i.e., this is an extrapolation.
A thermodynamic model has been constructed which describes the phase-equilibrium behavior of solutions containing mixtures of NaF, Na3PO4, and NaOH over the temperature range 0-100 °C. The model utilizes Pitzer’s ion-interaction approach for electrolyte solutions, and a number of the necessary parameters have been determined in this study from data at various temperatures. Parameter estimation was accomplished by a nonlinear least-squares technique, applied to the subsystem Na-F-OH and to the whole system NaF-PO4-HPO4-OH. Phase equilibria were determined by minimizing the total Gibbs energy, utilizing modifications to the code SOLGASMIX. All parameters used in the model are listed in Tables 5 and 6. Model calculations were verified by reproducing the data used in parameter estimation. A variety of data were used for the Na-F system, including isopiestic and emf measurements, freezing point lowering and vapor pressure lowering data, heat capacities, heats of dilution, and solubilities. In addition, the model was validated by comparison with many data points, including some qualitative solubility measurements done as part of this study. The primary solid species are trisodium phosphate (Na3PO4‚12 H2O‚1/4NaOH), sodium fluoride (NaF), and the fluoride-phosphate double salt (NaF‚2Na3PO4‚ 19H2O). Within the range 25-80 °C, predictions of temperature effects on the solubility of the DS were within the uncertainty of the data (about 10%). With regard to NaF, the large scatter in solubility data creates more uncertainty in the model calculation. However, both are consistent in depicting only a slight increase in the solubility with increasing temperature. Qualitative solubility experiments were performed to evaluate the overall model performance. These indicated that model predictions were good in regions where good data had been available in the parameter estimation process. Both the model predictions and experimental data have shown that the solubility of each solid declines rapidly as hydroxide levels increase. In fact, for OH- > 3 m, solubilities are so low that the error in measurement is of the same magnitude as the aqueous concentrations. For any hydroxide level, the presence of small amounts of either phosphate or fluoride will drastically reduce the solubility of the other. This effect is especially pronounced for small amounts of phosphate in predominantly fluoride solutions.
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Received for review June 22, 1999 Revised manuscript received October 22, 1999 Accepted November 11, 1999 IE990457L
