A Pitzer Interaction Model for the NaNO3âNaNO2

Article pubs.acs.org/IECR

A Pitzer Interaction Model for the NaNO3−NaNO2−NaOH−H2O System from 0 to 100 °C Jacob G. Reynolds* Washington River Protection Solutions, LLC, P.O. Box 850 MSIN H6-04, Richland, Washington 99352, United States

Robert Carter EnergySolutions, 423 West 300 South, Suite 200, Salt Lake City, Utah 84101, United States

Andrew R. Felmy Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, United States S Supporting Information *

ABSTRACT: The solubility relations and water activities in NaNO3, NaNO2, and NaOH solutions are used in many applications, including the management of alkaline high-level nuclear waste. Only limited water activity data is available at temperatures above ambient for NaNO3 and NaNO2 aqueous solutions, so water activity was measured by isopiestic methods at 50 and 100 °C in this study. The results are consistent with the limited experimental data previously available. These data are used to parameterize the Pitzer electrolyte solution model for these electrolytes and NaOH in water between 0 and 100 °C. Neutral ion pairs between Na+ and NO3− as well as Na+ and NO2− were required in order to fit the data adequately. Ternary Pitzer ion interaction parameters for the interactions between the electrolytes were also required and developed to model solubility in mixtures of the electrolytes. These results provide a strong foundation for modeling the effect of NaNO2, NaNO3, and NaOH on the solubility of other key electrolytes of interest to the management of high-level nuclear waste.

1.0. INTRODUCTION Sodium nitrate, sodium nitrite, and sodium hydroxide are the three most prevalent electrolytes in liquid high-level nuclear waste in the United States. The solubility of NaNO3 and NaNO2 are thus important for managing the waste, NaOH being much too soluble to crystallize under normal conditions. Historically, nuclear waste was evaporated sufficiently to crystallize NaNO2 and NaNO3 and stored in tanks.1 These wastes must now be retrieved and treated. They will be retrieved by dissolving the salts in water.2 The solubility of NaNO2 and NaNO3 mixtures under various processing conditions defines the volume of dissolution water required and the tank space required to store the retrieved waste. Therefore, understanding the solubility of these species is crucial for managing the waste. The solubility of NaNO3 and NaNO2 may also be important to the fractional crystallization or dilution of waste to remove selected radionuclides.2−4 A solubility model is being developed for employment at the Hanford site, near Richland, WA, to develop waste treatment flowsheets. This solubility model will employ the Pitzer equations for aqueous phase activity coefficients and water activities.5 This model will eventually include all major electrolytes and salts in the waste.1,6,7 This first study, focused on the ubiquitous waste electrolytes NaNO3, NaNO2, and NaOH, will provide a foundation for modeling other major waste electrolytes (Na2CO3, Na2C2O4, Na2SO4, Na3PO4, etc.). Many of the solid salts in Hanford waste have waters of hydration in their crystal structure,1,6,7 so even ions that are not © 2015 American Chemical Society

in these salts have a direct impact on their solubility by affecting the water activity. The Pitzer model has been widely applied to modeling concentrated electrolyte solutions. The earliest version of the Pitzer model used for Hanford waste was published by Reynolds8 but was strictly a compilation of binary interaction factors from the literature available at that time. Reynolds abandoned this model because of its inability to model NaOH− NaNO3−NaNO2−H2O mixtures at high concentrations using the coefficients available (Daniel A. Reynolds, personal communication). Later, others validated his frustration that the standard Pitzer binary parameters do not model even simple NaNO3−H2O and NaNO2−H2O systems well at high concentrations,9 though Hasan and Louhi-Kultanen10 successfully modeled the system at low temperatures. Archer11 modeled the NaNO3−H2O system using an extended version of the Pitzer equation. Using the extended version of the equation makes it awkward to employ with standard versions of the Pitzer model for electrolyte mixtures. None of these modelers included contact ion pairs for NaNO2 or NaNO3. The solubility of NaNO2 is very high (22 m at high temperature), which drastically limits the number of water molecules in the Received: Revised: Accepted: Published: 3062

January 7, 2015 February 26, 2015 March 2, 2015 March 2, 2015 DOI: 10.1021/acs.iecr.5b00016 Ind. Eng. Chem. Res. 2015, 54, 3062−3070

Article

Industrial & Engineering Chemistry Research solution to solvate the ions. In addition, there is experimental evidence for contact ion pairs in NaNO3 solutions.12 The original Pitzer interaction model does not formally include ion pairs. The inclusion of complex species or ion pairs within the Pitzer ion interaction model is now well-established, beginning in 1984 with the work of Harvie et al. in which they included simple species such as HSO4−, HCO3−, and MgOH+ within their thermodynamic model.13 Since then, numerous publications have included complex species including borate species, calcium species, lead speciation, silica speciation, cadmium, technetium, chromium, nickel, and actinide complex species, to name just a few.14−24 The CaCl2−H2O system is another system in which ion pairs are a useful formalism for modeling concentrated electrolyte systems. Pitzer et al.25 determined that the osmotic coefficients of CaCl2 in water could not be modeled adequately at high concentrations using just the standard Pitzer interaction model. Consequently, Pitzer et al. successfully amended the Pitzer model by adding additional binary Pitzer model parameters, even though they recognize that there is a shift of Cl− into the inner hydration shell that occurs at about 5 m.25,26 Sterner et al.15 showed that the CaCl2−H2O system could be modeled adequately with essentially equivalent accuracy using either ion pairs or by adding additional binary Pitzer model parameters. However, modeling the CaCl2−H2O system using ion pairs did not require changing the standard Pitzer formulation and allows a more stringent test of the model when additional spectroscopic data become available in these highly concentrated solutions. Sodium hydroxide is the third most prevalent electrolyte present in Hanford waste, and Pitzer interaction coefficients for this electrolyte are also required. Pabalan and Pitzer developed a comprehensive Pitzer-based model for the NaOH−H2O system.27 Those Pitzer coefficients are updated here to employ the model temperature coefficient convention employed for the rest of the electrolytes (see below) and to develop ternary interaction coefficients with nitrite and nitrate species. This Pitzer model will become part of the Hanford Tank Waste Operations Simulator (HTWOS), a flowsheet software code used for mission planning. HTWOS currently uses simple split-factors for solid−liquid equilibria. Incorporating thermodynamic-based solubility models into HTWOS will enhance the accuracy of mission plans. The development of the new NaNO3 and NaNO2 binary interaction coefficients are aided by new data reported here. Water activity data are available for these electrolyte solutions near ambient temperatures (see tables below) over wide concentration ranges.28,29 Less data is available between 50 and 100 °C, which are temperatures relevant to leaching of Hanford waste. Additional data was thus collected at 50 and 100 °C.

Table 1. Data Sources for Properties of NaNO3 ref (figure legend entry)

temperature range (°C)

concentration range (mol kg‑1)

number of points

34 (28ICT) 42 (37PEA/ HOP) 43 (62KAN/ GRO) 32 (67SHP/ MIS) 44 (35ROB) 33 (90VOI/ DIT) this study (this study) 45 (04DEC) 46 (58SEI)

0−100 25

0.6−21 0.1−10.83

66 18

Ps Ps

20−25

1−10

19

Ps

1−75

0.3−17

101

Ps

25 100

0.1−6.0 0.9−16

49 18

ϕ ϕ

50−100

0.2−19

39

ϕ

Tfus 0−100

1.4−8.2 8.5−20.7

7 10

ΔTf msat

data type

using the data of Ananthaswamy and Atkinson.31 A complete description of the isopiestic apparatus, which was originally built by W. Voigt, is given in Grjotheim et al.30

3.0. EXPERIMENTAL RESULTS The water activities of the NaNO3 and NaNO2 solutions at 50 and 100 °C measured here are reported in Table 1. Figure 1

Figure 1. Comparison of current and Shpigel and Mishchenko32 water activity data for NaNO3−H2O system at 50 °C.

compares the 50 °C NaNO3 data against data available at this same temperature reported by Shpigel and Mishchenko,32 showing excellent agreement for comparable data points. Similarly, Figure 2 compares the 100.3 °C temperature data from Voight et al.33 against the present data, also showing excellent agreement. The present study provides many more data points in the more concentrated regions. There is minimal data for the NaNO2−H2O system at 50 °C for comparison, but several reference books provide data at 100 °C from unknown original origin.34,35 Figure 3 compares these reference book values to the present data, showing excellent agreement. These results indicate that the data in those reference books34,35 appear to be reliable.

2.0. MATERIALS AND METHODS Water activity for NaNO3−H2O and NaNO2−H2O solutions were determined at 50 and 100 °C using isopiestic methods over a range of electrolyte concentrations described in Table 1. Isopiestic measurements were performed using the method described by Grjotheim et al.30 using CaCl2 as a reference electrolyte. NaNO2 and NaNO3 were determined in vitreous carbon cups inside a stainless steel container. Equilibrium periods generally ranged from 4 days to 1 week, depending on the salt concentration and temperature. After equilibrium, the cups were sealed inside the vessel and removed for weighing. Isopiestic molalities were calculated from the CaCl2 reference

4.0. MODEL DESCRIPTION Central to any thermodynamic model are the standard state Gibbs free energies. The standard state Gibbs free energies were either taken from the literature consistent with the large amount of Pitzer parameters developed by Oak Ridge National Laboratory36−38 or determined here by fitting the model to 3063

DOI: 10.1021/acs.iecr.5b00016 Ind. Eng. Chem. Res. 2015, 54, 3062−3070

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Industrial & Engineering Chemistry Research

NaNO3−NaNO2−H2O system. The temperature dependence of these parameters is typically determined by regressing water activity data and/or salt solubility data as a function of temperature. Modelers have employed a number of different equations to represent the temperature dependence of these parameters. The present study uses the convention of Weber et al.,38 shown in eq 1, because the model is then consistent with all of the parameters that they have published. When eq 1 is used for Pitzer parameters, the Pitzer parameter is the P in eq 1. In the present study, the binary Pitzer parameters are determined by regressing water activity as a function of solution molality, whereas θ and ψ are determined by regressing solubility data in mixed salts. For practical application, not all of the coefficients in eq 1 are required to adequately model the parameter variations within the chosen temperature range of 0 to 100 °C.39 For all of the binary Pitzer parameters, it was found that the E coefficient was not required and was therefore set to zero, making the model equivalent to the temperaturedependent expression proposed by Königsberger.39 Similarly, only A and B parameters were required for the θ and ψ parameters. Gibbs energy minimization is used to solve for the chemical equilibrium composition at constant temperature and pressure following the method of Karpov et al.:40

Figure 2. Comparison of water activity data for NaNO3−H2O system between current data (100 °C) and ref 33 (100.3 °C).

nt

minimize: G =

∑ μj nj (2)

j=1 nt

subject to: ∑ Aji nj = bi , Figure 3. Comparison of current data and reference book water activity data for NaNO2−H2O system at 100 °C.

(3)

n

t

∑ zjnj = 0, data (see below). The Gibbs free energies are included in the model as “reduced chemical potentials” (the chemical potential divided by RT). Weber et al.’s38 temperature (T) dependence of reduced chemical potential (μ) used for the present study (eq 1) is

for each phase s in e

j=1

(4)

nj ≥ 0 for all j

(5)

where G = the Gibbs energy of the system μj = the reduced chemical potential of species j nj = the number of moles of species j nt = the total number of species in the system mc = the number of independent components (IC) Aji = the number of moles of IC i in one mole of species j zj = the charge of species j in electrolyte solution phase s e = the number of electrolyte solution phases bi = the number of moles of each independent component i Equation 2 simply describes the minimization of Gibbs energy, whereas eqs 3 and 4 are mass balance constraints on the species. Equation 5 is a species constraint. The equation can be solved by use of Lagrange multipliers to form the Lagrangian

⎛T ⎞ ⎛1 1⎞ PT = A + B(T − Tr) + C ⎜ − ⎟ + D ln⎜ ⎟ Tr ⎠ ⎝ Tr ⎠ ⎝T + E(T 2 − Tr 2)

i = 1, mc

j=1

(1)

The P in eq 1 is either a μ or a Pitzer parameter (see below). This expression has a reference temperature, Tr, set to 298.15 K. The A through E parameters are empirically determined by fitting the model to data. Aqueous activity coefficients are represented here by the Pitzer model.5 The review by Pitzer provides a comprehensive overview of the model,5 and a detailed description of how the present model is built is included in the Supporting Information. The Pitzer interaction model is amended with neutral ion-pair species for NaNO3 and NaNO3 using the methodology described by Felmy and Weare14 and reviewed by Sterner et al.15 The Pitzer model uses interaction parameters to correct for nonstandard state conditions. The binary cation−anion interaction, given the symbols B0, B1, and C, are the most important interaction parameters. The anion−anion interaction parameters (θ) and ternary cation−anion−anion parameters (ψ) are sometimes also important for electrolyte mixtures. The present study develops these parameters for the NaOH−

mc

L=G−

nt

e

∑ λi ∑ (Ajinj − bi) − ∑ ηi ∑ zjnj i=1

j=1

i=1

j in i

(6)

Here, λi is a Lagrange multiplier for a mass balance constraint and ηi is a Lagrange multiplier for a charge balance constraint. There is one λi and one ηi for each electrolyte phase. The optimal binary Pitzer model parameters were determined using this method, minimizing the difference between measured and predicted water activities. The need for ternary Pitzer 3064


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Industrial & Engineering Chemistry Research Table 2. Coefficients for Temperature Dependence of Reduced Chemical Potentials (Equation 1) species

A

B

C

D

E

H2O Na+ NO3− OH− NO2− NaNO3(aq) NaNO3(s) NaNO2(aq) NaNO2(s)

−95.665 −105.73 −43.984 −63.534 −12.931 −148.5809 −147.1552 −116.4318 −114.7734

−1.0029 0.85194 0.68002 0.75606 0 1.546306 −0.32363 0.622791 −0.633181

0 0 0 0 7624.179 421.4583 −43090.9 0 −22669.2

324.04 0 0 0 16.5833 −4.69261 515.8652 91.20799 410.5574

0.000548 −0.000883 −0.000675 −0.000747 0 −0.001558 −0.000487 −0.000756 0

ref 38 38 this 38 36 this this this this

study

study study study study

Table 3. Binary Pitzer Parameters cation

anion

parameter

A

B

C

D

temp.

Na+ Na+ Na+ Na+ Na+ Na+ Na+ Na+ Na+

NO3− NO3− NO3− OH− OH− OH− NO2− NO2− NO2−

β0 β1 C β0 β1 C β0 β1 C

0.028327 0.330682 0 0.091763 0.212694 0.001748 0.072382 0.16036 −0.001711

−0.01831 0.004124 0 −0.07308 0.414149 0.002725 0.073633 −0.25287 −0.00465

−1406.73 0 0 −7118.75 46598 267.9999 8977.806 −34241.4 −560.099

10.51503 0 0 45.78472 −279.171 −1.7259 −51.5162 187.8694 3.246429

0−100

0−100

0−100

are shown in Tables 2 and 3. The standard deviation1 of fit to the solubility data is 0.041. Figure 4 shows the excellent fit of the model to the solubility of NaNO3 in water as a function of temperature. Figure 5

parameters was determined graphically by plotting the model results without them in the model. Once the need for the ternary Pitzer parameters was identified, they were determined by minimizing the squared difference between measured and predicted solubilities in mixed salt systems. The exact data sets that were fit are described in section 5.0. This minimization routine, using the numerical method described by Harvie et al.,41 was built with Visual Basic inside a Microsoft Excel 2010 spreadsheet. In the next subsections, the temperature-dependent Pitzer parameters and reduced chemical potentials are derived for the NaNO3−NaNO2−NaOH−H2O subsystems. The binary systems NaNO3−H2O, NaNO2−H2O, and NaOH−H2O, as well as each of the associated aqueous ternary systems, are investigated. The sodium ion is the lone cation in this mixture. The temperature-dependent reduced chemical potential for Na+ reported by Weber et al.38 was used throughout the present study.

Figure 4. Solubility of sodium nitrate in water as a function of temperature.

5.0. DEVELOPMENT OF PITZER MODEL PARAMETERS 5.1. NaNO3−H2O. Sources of data used to evaluate the Pitzer parameters for NaNO3 solutions are given in Table 1. The data types available include osmotic coefficients (ϕ) from isopiestic measurements, solution vapor pressure (Ps) measurements, freezing point temperature depression (ΔTf) measurements, and solubility data (msat). A preliminary fit of the data using the reduced chemical potentials from Weber et al.38 and Weber36 for Na+ and NO3−, respectively, resulted in a poor fit to the data in Table 2 when a dissolved neutral NaNO3 was not included in the model. This is consistent with the results of Marshall et al.9 Given that the NaNO3 ion pair has been observed experimentally in aqueous solutions, the ion pair was included in the model and the regression of the data in Table 2. The standard deviation of fit to the solubility data is just 0.041 molal over the entire temperature range. The temperature-dependent reduced chemical potentials and Pitzer parameters thus determined

Figure 5. Water activity as a function of NaNO3 molality at 25 °C. 3065


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molecules in solution to reside between each Na+ and NO2− ion in such solutions. Thus, there must be ion pairs in solutions with such high solubility.55,56 Consequently, a neutral NaNO2 ion pair was included in the fit of the data in Table 4. The temperature-dependent reduced chemical potentials for NO2− were taken from Weber.36 The reduced chemical potentials and the temperature-dependent Pitzer parameters determined are provided in Tables 2 and 3. The standard deviation of fit to the solubility data is 0.039 molal over the entire temperature range. Figure 6 shows the excellent fit of the model to the solubility of NaNO2 as a function of temperature in water. Figure 7

shows the excellent prediction of the water activity as a function of NaNO3 molality at 25 °C. The model fit is represented by the line labeled “HTWOS” (for HTWOS model) in Figures 4 and 5. The Supporting Information provides additional graphical evaluation of the data and likewise shows a comparable fit of the water activity data over the entire temperature range. These results show an excellent fit to both types of data over the entire temperature range, from low concentrations to saturation. 5.2. NaNO2−H2O. The data in Table 4 was used to develop the model for NaNO2. Table 4. Data Sources for Properties of NaNO2 ref (figure legend entry) 47 (67CH/PR) 48 (56RAY/OGG) 34 (28ICT) 35 (92ZAY/ASE) this study (this study) Bureau (1937) as reported in ref 46 (37BUR) 49 (72PRO/SAV) Bureau (1937) as reported in ref 46 (37BUR) 50 (57ERD/SIM) 51 (85SOH/NOV) 52 (98APE/KOR)


concentration range (mol kg−1)

number of points

data type

25 25 100 25, 100 50, 100 Tfus

0.1−12.25 0.3−12.34 1−16 0.76−14.49 0.58−17.74 0.9−5.7

16 7 8 19 32 6

Ps Ps Ps Ps ϕ ΔTf

Tfus 0−103

1.6−9.3 10.3−24.3

12 8

ΔTf msat

11.9−52 0−100 5−50

11−15.3 10.4−23.4 10.7−15

7 10 10

msat msat msat

Figure 7. Water activity as a function of NaNO2 molality at 25 °C.

shows the excellent prediction of the water activity as a function of NaNO2 molality at 25 °C. As with the NaNO3−H2O system, the model results are represented by the HTWOS line in Figures 6 and 7. The Supporting Information provides additional graphical evaluation of the data and likewise shows a comparable fit of the water activity data over the entire temperature range. These results show an excellent fit to both types of data over the entire temperature range, from low concentrations to saturation. 5.3. NaOH−H2O. The data in Table 5 was used to develop the model for NaOH.

Consistent with the results for NaNO3 and Marshall et al.,9 preliminary modeling of the data over the entire concentration and temperature range of interest resulted in a poor fit unless a neutral NaNO2 ion pair was included. No spectroscopic data in the literature could be found to confirm or refute the existence of a NaNO2 ion pair in aqueous solution. Work by Kameda et al.,53,54 however, indicates that NO2−(aq) is less hydrated than NO3− in Na+ solutions. Thus, if Na+ and NO3− form an ion pair in aqueous solutions,12 then it is reasonable to assume that the less hydrated NO2− ion also forms an ion pair with Na+. An argument for the existence of a NaNO2 ion pair can also be made based on the extremely high solubility of NaNO2 in water. At high temperatures, the solubility of NaNO2 in water exceeds 22 molal (Figure 6). There are not enough water

Table 5. Data Sources for Properties of NaOH ref (legend entry)


concentration range (mol kg−1)

number of points

57 (18PAR) 58 (31HAY/ PER) 34 (28ICT) 43 (62KAN/ GRO) 59 (64DIB) 60 (40AKE/ KEG) 61 (45STO) 62 (03ZHO) 34 (28ICT)

0−40 30−80

3.75−22.5 2.4−39.0

82 51

Ps Ps

20−100 20, 25

1.25−75 1−27

73 19

Ps Ps

25−97 0−70

1.7−20.6 0.25−16.9

50 192

Ps ϕ

25 25, 40 Tfus

1.98−28.8 0.09−3.0 0.01−6.11

33 6 10

data type

ϕ ϕ ΔTf

The temperature-dependent reduced chemical potential coefficients of Weber et al.38 for the ions (Na+ and OH−) were used in the regression of the data in Table 5, with results shown in Table 3. The water activity data was regressed only up to 10 molal NaOH because it is believed that the NaOH concentration will never exceed this value for any practical application of the model at Hanford. This means that no solid-

Figure 6. Solubility of sodium nitrite in water as a function of temperature. 3066


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Figure 10 shows the model predictions at the four separate temperatures together with the experimental data. The

phase NaOH salts are included in the model. Figure 8 show the excellent fit of the data up to at least 10 molal NaOH with the

Figure 8. Water activity as a function of NaOH molality at 25 °C.

new model coefficients at 25 °C. As with the NaNO3−H2O system, the model results are represented by the HTWOS line in Figure 8. The Supporting Information provides additional graphical evaluation of the data and likewise shows an excellent fit of the water activity data over the entire temperature range. Of note is that the model actually fits the data up to 22 molal at 100 °C, despite being fit to only 10 molal NaOH (see Supporting Information). 5.4. NaNO2−NaNO3−H2O System. The predicted solubilities of NaNO2 and NaNO3 in water from 0 to 103 °C are shown in Figure 9 using solely the binary system Pitzer

Figure 10. Solubility of NaNO3 in the NaOH−NaNO3−H2O System from 25 to 100 °C.

additional mixing parameters, θ OH−NO3, ψ Na−OH−NO3, λ OH−NaNO3, and ζ Na−OH−NaNO3 were adjusted so that the predictions better matched the experimental data (Table 6). Table 6. Ternary and Anion−Anion Pitzer Parameters i

j

NO3− Na+ OH− OH− NO2− Na+ Na+

OH− NO3− NaNO2 NaNO3 NaNO2 NO2− OH−

k OH−

NaNO2 NaNO3

parameter

A

B

θ ψ λ λ λ ζ ζ

−0.092138 0.003629 0.02 0.114519 0.012787 0.00151 −0.00818

0 0 0 −0.0011 −0.00162 0.000168 8.53 × 10−5

This was achieved by minimizing the squared errors between the predicted and the experimental NaNO3 concentration at the same NaOH concentration. The final optimized values for the mixing parameters were −0.0921 for θ OH−NO3 and 0.0036 for ψ Na−OH−NO3 respectively. The neutral species mixing terms, λ OH−NaNO3 and ζ Na−OH−NaNO3, were found to linearly depend on the temperature (requiring only A and B coefficients in eq 1). The lines in Figure 10 represent the model prediction with these revised parameters. Figure 10 shows that the model can make accurate solubility predictions in this system at very high NaOH concentrations, 12 molal and above, even though the original fitting of the NaOH−H2O system was limited to 10 molal NaOH. 5.6. NaNO2−NaOH−H2O. The experimental data for the NaNO2−NaOH−H2O system is available only at 20 and 25 °C and came from Plekhotkin and Bobrovskaya. 64 Their experimental data is displayed graphically in Figure 11 along with model predictions at both temperatures. The only ternary mixing parameter required to fit this data was λ OH−NaNO2, with a value of 0.02 (Table 6), determined by fitting the data in Figure 11. Given that there was data at only two temperatures, the λ OH−NaNO2 parameter is currently assumed to be temperature-independent (only an A value for eq 1). The experimental data indicates that solid NaOH precipitates between 14 and 15 molal NaNO2 at both temperatures, but

Figure 9. Solubilities of NaNO2 and NaNO3 in the NaNO2−NaNO3− H2O System from 0 to 103 °C.

parameters. The experimental data was taken from the extensive compilation of Seidell.46 As can be seen in Figure 9, the model predicts the experimental data well. The largest deviations are in the predictions for the solid NaNO2 at the highest temperature of 103 °C, which is just above the maximum temperature limit of the binary system parameter fitting. Given this excellent fit of the data, no ternary or anion− anion Pitzer parameters were developed for this system. 5.5. NaNO3−NaOH−H2O. The experimental data for to this system was taken from the compilation of Seidell,46 as well as data from refs 63−66. 3067


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narrow temperature range (20−25 °C), but the ternary Pitzer interaction coefficients in this system is unlikely to have a large temperature impact, given that the ternary interaction is weak to begin with. Therefore, the model coefficients developed here can be used by modelers interested in these systems. Table 7 shows all of the Pitzer parameters determined in this study calculated at several key temperatures. Comparing the OH−− NaNO2 λ parameter to the λ parameter for OH−−NaNO3 shows that the OH−NaNO2 mixing interaction is weaker than that of the OH−−NaNO3. NaNO3, NaNO2, and NaOH represent the three most prevalent dissolved electrolytes in Hanford high-level waste. Consequently, the model developed here represents the backbone for developing Pitzer-based solubility models for the rest of the electrolytes of interest to Hanford waste. Solid phases of interest to Hanford waste include Al(OH)3, Na2C2O4, NaF, NaFSO4, Na2SO4, Na7F(PO4)2·19H2O, Na3PO4·12H2O, Na2CO3·H2O, and NaAl(OH)2CO3.1,6,7,67−69 Complications caused by the precipitation of these phases have been observed.69 The present model provides the starting point for identifying blending strategies that minimize precipitation.

Figure 11. Solubility of NaNO2 in the NaNO2−NaOH−H2O System at 20 and 25 °C.

because this solid is not part of the model, the model continues to predict NaNO2 as the solid phase. Hence, a deviation away from the experimental data can be seen when solid NaOH precipitates, a solid that is not included in the model because it is not a credible species in Hanford waste. Thus, the model provides an excellent fit of this system for all ranges of data relevant to processing Hanford waste.

7.0. CONCLUSION This study has reported new water activity as a function of concentration at 50 and 100 °C for NaNO3(aq) and NaNO2(aq) solutions. This data was consistent with other available data in the literature when they were comparable and also filled in data gaps in the literature. This study has also developed temperature-dependent reduced chemical potentials and Pitzer interaction coefficients for the subsystems within the NaNO3−NaNO2−NaOH−H2O system. The model was found to predict solubility and water activity of the NaNO2−H2O and NaNO3−H2O systems from dilute concentrations to saturation between 0 and 100 °C. The NaNO2 and NaNO3 ion pairs were included in the model to obtain this excellent fit of the data. The NaOH−H2O system was predicted well up to at least 10 molal concentrations over the same temperature range. The

6.0. DISCUSSION This study shows that the developed Pitzer-based solubility model accurately represents data from dilute solutions to saturation between 0 and 100 °C for the NaNO2−H2O, NaNO3−H2O, and NaNO3−NaNO2−H2O systems. The model also represents NaOH−H2O system up to at least 10 molal in concentration and the NaNO3−NaOH−H2O system up to saturation with NaNO3 over the entire temperature range. The NaNO2−NaOH−H2O system was evaluated over a

Table 7. Pitzer Parameters Calculated at Several Key Temperatures Pitzer Binary Parameters between 0 and 100 °C T (°C)

75

100

Na+−OH−

β0 β1 C

0.094447 0.003064 0.002498

0

0.091763 0.212694 0.001748

0.104156 0.178792 0.000446

0.106983 0.084286 −0.00048

0.085076 0.045553 −0.00047

Na+−NO2−

β0 β1 C

−0.01284 0.540695 0.002253

0.072382 0.16036 −0.00171

0.094668 0.080849 −0.00198

0.09165 0.149558 −0.00086

0.087641 0.266579 0.000151

Na+−NO3−

β0 β1 C

−0.00296 0.028327 0.227585 0.330682 0 0 Pitzer Mixing Parameters between 0 and

0.065455 0.536875 0

0.066195 0.639972 0

T (°C) θ ψ λ

ζ



−

NO3 −OH Na+−NO3−OH− OH−−NaNO2 OH−−NaNO3 NO2−−NaNO2 Na+−NO2−−NaNO2 Na+−OH−−NaNO3

25

50

0.052241 0.433778 0 100 °C

0

25

50

75

100

−0.09214 0.003629 0.02 0.142032 0.053224 −0.00268 −0.01031

−0.09214 0.003629 0.02 0.114519 0.012787 0.00151 −0.00818

−0.09214 0.003629 0.02 0.087006 −0.02765 0.005701 −0.00605

−0.09214 0.003629 0.02 0.059493 −0.06809 0.009891 −0.00391

−0.09214 0.003629 0.02 0.03198 −0.10852 0.014081 −0.00178

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Industrial & Engineering Chemistry Research ternary systems NaNO3−NaOH−H2O and NaNO2−NaOH− H2O could be fit well using weak Pitzer ternary interaction coefficients in the model. The NaNO3−NaNO2−H2O system could be predicted by the model without requiring any ternary interaction coefficients. This set of model coefficients can be used to predict the solubility of NaNO3 and NaNO2 in aqueous electrolyte solutions, such as the high-level nuclear waste at Hanford.

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ASSOCIATED CONTENT

S Supporting Information *

The tabulated experimentally determined water activities as a function of NaNO3 and NaNO2 concentration determined in this study, a more detailed description of the Pitzer model as built in this study, and additional graphical evaluation of the Pitzer model at temperatures other than 25 °C. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (509)-373-5999. Fax: (509)-373-3883. Notes

The authors declare no competing financial interest.

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A Pitzer Interaction Model for the NaNO3âNaNO2

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