Thermodynamic Modeling of Sodium Aluminosilicate Formation in

Cp° of the SiO32- ion was found to be equal to −77.98 cal/(mol K) or −326.27 J/(mol ..... Wannenmacher, P. N.; Frederick, W. J.; Hendrickson, K. ...
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Ind. Eng. Chem. Res. 1999, 38, 4959-4965

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Thermodynamic Modeling of Sodium Aluminosilicate Formation in Aqueous Alkaline Solutions Hyeon Park and Peter Englezos* Department of Chemical & Bio-Resource Engineering and Pulp and Paper Centre, The University of British Columbia, 2216 Main Mall, Vancouver, British Columbia V6T 2C7, Canada

A thermodynamics-based model for sodium aluminosilicate formation in aqueous alkaline solutions was developed. Pitzer’s method was adopted to calculate the activity of water and the activity coefficients of the other species in solution. The system under consideration contained the ions of Na+, Al(OH)4-, SiO32-, OH-, CO32-, SO42-, Cl-, and HS- dissolved in water and in equilibrium with two possible solid phases (sodalite dihydrate, Na8(AlSiO4)6Cl2‚2H2O; hydroxysodalite dihydrate, Na8(AlSiO4)6(OH)2‚2H2O) at 368.15 K. The equilibrium constants of sodalite dihydrate and hydroxysodalite dihydrate formation reactions were determined using the thermodynamic properties of the species involved. Property values that were not available in the literature were estimated by group contribution methods. The model calculates the molality of all species at equilibrium including the amount of solid precipitates. The results were found to be sensitive to the value of the equilibrium constant for hydroxysodalite dihydrate formation and generally in good agreement with experimental values. Introduction Sodium aluminosilicate scale may form in the recovery cycle of kraft pulp mills and during the Bayer process for aluminum production.1-3 This scale is glossy and hard to remove. It may lower the efficiency of heat exchangers and the evaporation capacity of a kraft pulp mill.4 The scale formation becomes more severe in closed-cycle plant operation because the effluent is recycled and the aluminum and silicon ion concentrations increase rapidly. Closed-cycle plant operation is regarded as the ultimate method to avoid water pollution. Knowledge of the scale precipitation conditions is required to design closed-cycle pulp mills.1 Ulmgren4 studied the formation of this scale using synthetic solutions made to simulate kraft pulp mill black liquors. Streisel5 measured scale precipitation conditions in aqueous alkaline solutions at 95 and 150 °C. He also developed a relevant model. The model used Meissner’s method to calculate species activity coefficients. The parameters in Meissner’s equations were regressed from the precipitation data. Gasteiger et al.1 also presented a model that used Pitzer’s method6,7 for the activity coefficients. The model contained five adjustable parameters which were regressed by using Streisel’s scale precipitation data. Wannenmacher et al.8 reported the effect of CaO and MgSO4 addition on scale precipitation conditions in an unclarified kraft mill green liquor at 368.15 K. They also reported correlations to calculate the apparent solubility product, [Al][Si], in systems containing sodalite (Na8(AlSiO4)6Cl2) and/or hydroxysodalite (Na8(AlSiO4)6(OH)2), cancrinite, natrolite, and hydrotalcite. Park and Englezos9 measured scale precipitation conditions in two alkaline systems that simulated typical kraft pulp mill green and white liquor streams. System A was prepared by dissolving NaOH, Na2CO3, Na2SO4, and NaCl in distilled and deionized water. System B was prepared in a similar manner by using NaOH, Na2CO3, and Na2S. * To whom correspondence should be addressed. Phone: 604-822-6184.Fax: 604-822-603.E-mail: [email protected].

In this work we present a thermodynamics-based model for sodium aluminosilicate formation in aqueous alkaline solutions. Such a model that will not depend on parameters correlated from the precipitation data is needed in order to account for the effect of various ions on the aluminosilicate formation. Pitzer’s activity coefficient method was used to calculate the activity of water and the activity coefficients of ions in the solution because it performs well even at high molalities.6,7 All parameters needed by the model were obtained from independent experimental data or available property estimation methods. The effect of the anions of OH-, CO32-, SO42-, Cl-, and HS- is taken into account. The model predicts the precipitation conditions of sodalite dihydrate and/or hydroxysodalite dihydrate. Model Equations and Solution Method Only the two solid phases (sodalite dihydrate, Na8(AlSiO4)6Cl2‚2H2O; hydroxysodalite dihydrate, Na8(AlSiO4)6(OH)2‚2H2O) were assumed to be present in the system according to the experimental results in our lab.9 All other salts were assumed to be dissolved completely at 368.15 K and 1 atm. The model considers that 11 species are present at equilibrium at 368.15 K and 1 atm: two solid species (Na8(AlSiO4)6Cl2‚2H2O and Na8(AlSiO4)6(OH)2‚2H2O), one liquid (H2O), and eight ions (Na+, Al(OH)4-, SiO32-, OH-, CO32-, SO42-, HS-, and Cl-). Because the system is very alkaline (pH > 13), the predominant aluminum and silicon species in solution were assumed to be Al(OH)4- and SiO32-, respectively.2,10-13 The preparation of this system and the identification of the species have been presented elsewhere.9,11 The model equations consist of the reaction equilibrium equations for sodalite dihydrate and hydroxysodalite dihydrate, one charge balance equation, and the mass balance equations for the elements of Na, Al, Si, Cl, O, H, S, and C. Formulas for sodalite dihydrate and hydroxysodalite dihydrate formation in alkaline aqueous solutions can be written as follows:3,9

10.1021/ie990229r CCC: $18.00 © 1999 American Chemical Society Published on Web 10/19/1999

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8Na+(aq) + 6Al(OH)4-(aq) + 6SiO32-(aq) + 2Cl(aq) T Na8(AlSiO4)6Cl2‚2H2O(s) + 4H2O(l) +

Table 1. Pitzer’s Binary Parameters for the Modeling of Na-Al-Silicate Formation

12OH-(aq) (1) 8Na+(aq) + 6Al(OH)4-(aq) + 6SiO32-(aq) + 2OH(aq) T Na8(AlSiO4)6(OH)2‚2H2O(s) + 4H2O(l) + 12OH-(aq) (2) Assuming the solids to be pure, then their activity is unity and the thermodynamic equilibrium constant of sodalite dihydrate, Ksod, can be written as

Ksod ) 12 4 aH (mOH 2O

12 γOH -)

6 6 6 6 2 2 8 8 (mNa + γNa+)(mAl(OH)- γAl(OH)- )(m SiO 2-γ SiO 2-)(mCl- γCl-) 4 4 3 3 (3)

where a is the activity, m is the molality, and γ is the activity coefficient of the species. Similarly, the equilibrium constant of hydroxysodalite dihydrate, Khsod, can be written as follows: Khsod ) 12 12 4 (mOH aH - γOH-) 2O 8 8 6 6 6 6 2 2 (mNa + γNa+)(mAl(OH)- γAl(OH)- )(m SiO 2-γ SiO 2-)(mOH- γOH-) 4 4 3 3 (4)

The mass balance equations for the Na, Al, Si, Cl, O, H, S, and C elements are given by

ntotal Na ) ntotal Al

(

)

(

ntotal ) Si

nH2O

1000/18.015 nH2O

1000/18.015

(

)

1000/18.015

) ntotal Cl ntotal ) nH2O + O

(

(

)

(mNa+ + 8msod + 8mhsod)

(5)

)

(mSiC32- + 6msod + 6mhsod) (7)

n H 2O

1000/18.015

)

nH2O

)

(mCl- + 2msod)

(8)

(4mAl(OH)4- + 3mSiO32- + 1000/18.015 mOH- + 3mCO32- + 4mSO42- + 26msod + 28mhsod) (9)

ntotal ) 2nH2O + H

ntotal ) S

(

nH2O

)

(

nH2O

)

(4mAl(OH)4- + mOH- + 1000/18.015 mHS- + 4msod + 6mhsod) (10)

1000/18.015

ntotal C

)

(

Na+OH-

Na+ClNa+CO32Na+SO42Na+HSNa+SiO32Na+Al(OH)4a

β(0)

β(1)

Cφ

0.08476

0.38826

0.100815 0.0581116 0.0988a 0.13966 0.057711 -0.008312

0.320715 1.241916 1.4325a 0.06 2.896511 0.071012

0.000 216 -0.003 3715 0.005 216 -0.014 62a -0.012 76 0.009 7711 0.001 8412

This study.

Table 2. Pitzer’s Mixing Parameters for the Modeling of Na-Al-Silicate Formation ion pair

θaa′

ψaa′Na+

OH-ClOH-CO32OH-SO42OH-SiO32OH-Al(OH)4Cl-CO32Cl-SO42Cl-Al(OH)4CO32-SO42-

-0.056 0.16 -0.0136 -0.270311 -0.225512 -0.026 0.036 -0.243012 0.026

-0.0066 -0.0176 -0.0096 0.023311 -0.038812 0.00856 0.0006 0.237712 -0.0056

The eleven model equations were solved by the Newton-Raphson method to give the molalities of the species. The activity coefficients of species as well as the activity of water were also calculated. The product of the molalities of Al(OH)4- and SiO32- at equilibrium was taken as the solubility product. To perform the calculations, values for the activity coefficients are needed. These were computed by using Pitzer’s electrolyte thermodynamic model.6 A Priori Determination of Model Parameters

(mAl(OH)4- + 6msod + 6mhsod) (6)

nH2O

ion pair

(mSO42- + mHS-)

nH2O

1000/18.015

)

(mCO32-)

(11)

Pitzer’s Parameters. Pitzer’s binary and mixing parameters are shown in Tables 1 and 2. A value of 0.455 at 368.15 K was used for the Debye-Hu¨ckel parameter.6 Pitzer introduced the mixing parameters θ and Ψ to account for the differences of ion interactions between multicomponent and single salt electrolyte solutions. Thus, the mixing parameters have smaller effects than the binary parameters β(0), β(1), and Cφ have.14 The binary parameters for NaOH, NaCl, and Na2CO3 for 368.15 K were determined using available numerical expressions.6,15,16 Although numerical expressions for the binary parameters for Na2SO4 were available in the literature, they were not used because they were based on the value of 1.4 for the “R1 parameter” instead of the usual value of 2.0 for a 1-2 electrolyte.6,17 Osmotic coefficient data for Na2SO4 are available at 298.15, 323.15, 348.15, 373.15, and 398.15 K.17 These data were interpolated at 368.15 K and gave a set of values. The binary parameters of Na2SO4 at 368.15 K were then determined by using these interpolated osmotic coefficient data and minimizing the leastsquares objective function N

S(β(0),β(1),Cφ) ) (12)

The charge balance equation can be written as follows:

mNa+ ) mAl(OH)4- + 2mSiO32- + mOH- + 2mCO32- + 2mSO42- + mHS- + mCl- (13)

cal 2 (φint ∑ d -φd ) d)1

(14)

where φint is the interpolated osmotic coefficient and φcal is the calculated osmotic coefficient. On the basis of a study with NaCl, Pitzer noted that change in the parameter values from 298.15 to 573.15 K was very small. This justified the use of the values at 298.15 K whenever values at 368.15 K were not available. How-

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4961 Table 3. Thermodynamic Data at 298.15 K and 1 bar Published in the Literaturea Na+(aq)

∆Hf° (kJ/mol)

Cp° [J/(mol K)]

-262.0 ( -131.2 ( 0.119 -157.2 ( 0.119 -237.14 ( 0.0419 -1311.684 ( 1.25520 -939.7310 N/A N/A

-240.34 ( -167.1 ( 0.119 -230.01 ( 0.0419 -285.83 ( 0.0419 -1488.9221 N/A N/A N/A

+46.4310 -136.410 -148.519 +75.351 ( 0.0819 +241.4421 N/A N/A N/A

0.119

Cl-(aq) OH-(aq) H2O(l) Al(OH)4-(aq) SiO32-(aq) Na8(AlSiO4)6Cl2‚2H2O(s) Na8(AlSiO4)6(OH)2‚2H2O(s) a

∆Gf° (kJ/mol)

0.0619

N/A: not available in the literature.

Table 4. Estimated Thermodynamic Data at 298.15 K and 1 bar SiO32-(aq) Na8(AlSiO4)6Cl2‚2H2O(s) Na8(AlSiO4)6(OH)2‚2H2O(s)

∆Gf° (kJ/mol)

∆Hf° (kJ/mol)

Cp° [J/(mol K)]

-13191.59 ( 20.92 -13384.23 ( 25.10

-1075.38 ( 1.14 -14054.91 ( 22.04 -14283.02 ( 25.82

-326.27 ( 82.71 886.28 ( 4.69 895.01 ( 5.37

ever, the Debye-Hu¨ckel parameter, Aφ, changes significantly, and the value at 95 °C was used.7 Equilibrium Constants. Values of the equilibrium constants of sodalite dihydrate and hydroxysodalite dihydrate formation at 368.15 K were not available in the literature. Assuming that the heat capacity change of reaction, ∆Cp°, is not a function of temperature over a temperature interval from T0 to T, the equilibrium constants at specific temperatures can be calculated using eq 15 18 where K is the equilibrium constant at

(

ln K ) -

)

(

) (

∆G0° ∆H0° 1 1 + RT0 R T T0 T0 ∆CP° T - 1 (15) ln + R T0 T

)

temperature T, ∆G0° is the Gibbs free energy change of reaction, ∆H0° is the enthalpy change of reaction, ∆CP° is the heat capacity change of reaction, R is the gas constant, and T0 is the reference temperature. Values for ∆G0°, ∆H0°, and ∆CP° can be obtained by the equations

∑ν∆Gf°products - ∑ν∆Gf°reactants ∆H0° ) ∑ν∆Hf°products - ∑ν∆Hf°reactants ∆Cp° ) ∑νCp°products - ∑νCp°reactants ∆G0° )

(16) (17) (18)

where ν is the number of moles of reactants or products. Table 3 shows property values for the species required to calculate the above equilibrium constants. Property values that were not available were estimated in this work as follows. ∆Hf° and ∆Gf° of Sodalite Dihydrate and Hydroxysodalite Dihydrate. These values were estimated by the method of Mostafa et al.22 Because a value for ∆Hf° for the anhydrous sodalite (Na8(AlSiO4)6Cl2) is available, ∆Hf° of Na8(AlSiO4)6Cl2‚2H2O can be calculated by adding the contribution term due to the 2 mol of H2O to the published value, -13 457.04 kJ/mol,23 for the ∆Hf° for Na8(AlSiO4)6Cl2. Thus, ∆Hf° of Na8(AlSiO4)6Cl2‚2H2O is equal to -14 054.91 kJ/mol. ∆Gf° of Na8(AlSiO4)6Cl2‚2H2O can be calculated by the same logic, and its value is found to be equal to -13 191.59 kJ/mol. Similarly, the values for ∆Hf° and ∆Gf° of hydrated hydroxysodalite dihydrate (Na8(AlSiO4)6(OH)2‚ 2H2O) were calculated and found to be -14 283.02 and -13 384.23 kJ/mol, respectively. The uncertainties in

Table 5. Thermodynamic Data of Na2SiO3(s), Na+(aq), and SiO32-(aq) for the Calculation of ∆G°, ∆H°, and ∆S° of Reaction 19 ∆Gf° (kJ/mol)

∆Hf° (kJ/mol)

Na2SiO3(s) -1469.6710 -1556.710 Na+(aq) -262.0 ( 0.119 -240.34 ( 0.0619 SiO32-(aq) -939.7310 a

S° [J/(mol K)] 113.810 58.4519 -20.87a

Calculated by the method of Couture and Laidler.28

the calculations of ∆Hf° and ∆Gf° for Na8(AlSiO4)6Cl2‚ 2H2O and Na8(AlSiO4)6(OH)2‚2H2O were also calculated.24-26 Their values are shown in Table 4 together with the estimated property values. Cp° of Sodalite Dihydrate and Hydroxysodalite Dihydrate. Another group contribution technique proposed by Mostafa et al.27 was used to calculate Cp° of Na8(AlSiO4)6Cl2‚2H2O by adding the contribution term of 2 mol of H2O to the published value of 812.28 J/(mol K)23 for Na8(AlSiO4)6Cl2. Cp° of hydrated hydroxysodalite dihydrate, Na8(AlSiO4)6(OH)2‚2H2O, was calculated by the same method. The estimated Cp° values are shown in the Table 4 together with their uncertainties. ∆Hf° of SiO32-. The enthalpy of formation of SiO32was calculated by considering the equation ∆H° ) ∆G° + T∆S° for the dissociation of sodium metasilicate, Na2SiO3(s), at 298.15 K10 and values given in Table 5.

Na2SiO3(s) f 2Na+(aq) + SiO32-(aq)

(19)

The calculated value for ∆Hf° of SiO32- was found to be equal to -1075.38 kJ/mol. The uncertainty in the calculation was found to be (1.14 kJ/mol.24,25 Cp° of SiO32-. This value was computed by eq 2029

Cp° ) Cp°abs - 28.0z ) a + b(S° - 5.0z) - 28.0z (20) where parameters a and b are equal to -145 and 2.20, respectively, for oxyanions (XOn-m) at 298.15 K and z is the charge of the ion. Cp° of the SiO32- ion was found to be equal to -77.98 cal/(mol K) or -326.27 J/(mol K). Calculation of Ksod and Khsod at 368.15 K. The equilibrium constants were calculated by using eq 15 with the data from Tables 3 and 4. The equilibrium constant of sodalite dihydrate (Ksod) was found to be equal to 1.82 × 1017 (ln Ksod ) 39.74 ( 8.71). The value of Khsod was found to be equal to 3.38 × 1038 (ln Khsod ) 88.71 ( 10.41). The uncertainties were computed by using the method of Baird.24 The major contribution in the uncertainties was due to the uncertainty in the ∆Gf° values for Na8(AlSiO4)6Cl2‚2H2O and Na8(AlSiO4)6(OH)2‚

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Table 6. Comparison of the Calculation Results for the NH4+-NH4OH-H+-HCl-NH4Cl-Cl--Na+-NaCl-K+-KCl System at 573.15 Ka calculated molalities (mol/kg of H2O) species +

NH4 NH4OH H+ HCl NH4Cl ClNa+ NaCl K+ KCl

Anderson and Crerar18

this work

0.163 0 0.002 844 0.001 206 0.001 638 0.084 16 0.478 2 0.138 5 0.111 5 0.175 5 0.074 50

0.162 978 0.002 876 0.001 220 0.001 657 0.084 145 0.478 185 0.138 489 0.111 511 0.175 497 0.074 503

a The molalities of the species at equilibrium were calculated using the following input amounts of chemicals: NH4Cl of 0.25 mol, NaCl of 0.25 mol, KCl of 0.25 mol, and H2O of 1.0 kg.

2H2O. These uncertainties were found to be (8.71 for ln Ksod and (10.41 for ln Khsod, respectively.26 Results and Discussion To check the reliability of the modeling procedure, calculations for the NH4+-NH4OH-H+-HCl-NH4ClCl--Na+-NaCl-K+-KCl system were performed. The calculation results were compared with the published ones.18 For the exact comparison, the Davies revision of the Debye-Hu¨ckel equation was used for the activity coefficient calculation because the same equation was used in the literature. As seen from the Table 6, the values obtained agree well with the published ones. The reliability of Pitzer’s activity coefficient method was checked in previous work.11,12 Calculations were performed at 368.15 K for the Na+-Al(OH)4--SiO32--OH--CO32--SO42--Cl-- H2O system (system A) and the Na+-Al(OH)4--SiO32-OH--CO32--Cl--HS--H2O system (system B). Experimental data are available for these systems.9 The calculations showed that only hydroxysodalite dihydrate forms in both systems. During the experiments, most of the precipitates were found to have the structure of hydroxysodalite dihydrate. Only in solutions of low OHand high Cl- concentration of system A was a small amount of sodalite dihydrate precipitates found together with hydroxysodalite. A comparison of the calculated results with experimental data is presented next. Na+-Al(OH)4--SiO32--OH--CO32--SO42--Cl-H2O (System A). Figure 1 shows data and calculated values (solid line) for the concentration of the aluminum species versus that of the silicon at equilibrium. As seen, the predicted values define a boundary for the precipitation conditions. When the concentration of the Al and Si species in the solution correspond to a point on the right of the line, then precipitation occurs. Calculations were also performed to test the sensitivity of the model to the value of Khsod. These calculations using values equal to Khsod ( uncertainty are shown as dotted lines in Figure 1. As seen, the experimental data are located within the range of the precipitation conditions computed by taking into account the uncertainty in Khsod. The value of Khsod was subsequently adjusted to 4.39 × 1036 (ln Khsod ) 84.37) instead of the calculated 3.38 × 1038 (ln Khsod ) 88.71) and was used to give a solubility product calculation in perfect agreement with the data (dot-dashed line). Figure 2 shows the effect of varying the concentration of OH- on the precipitation conditions. As seen from the

Figure 1. Equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, the input amount of NaOH was 1.0 mol/kg of H2O, that of Na2CO3 was 1.0 mol/kg of H2O, that of Na2SO4 was 0.1 mol/kg of H2O, and that of NaCl was 0.25 mol/kg of H2O. Input amounts of AlCl3‚6H2O and Na2SiO3‚9H2O were varied from 0.04 to 0.01 and from 0.01 to 0.04 mol/kg of H2O, respectively.)

Figure 2. Effect of hydroxyl ion concentration changes on the equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, only the input amount of NaOH was varied from 0.25 to 2.0 mol/kg of H2O. Input amounts of other chemicals were the same as those of Figure 1.)

plot, the solubilities of Al and Si increase with increasing hydroxyl concentration, and the model is able to capture this behavior. The amount of hydroxysodalite formed was also calculated to be smaller. This result is also in agreement with the experiments.26 Figure 3 shows the effect of the carbonate ion on the precipitation conditions. The experimental data show that the solubilities of Al and Si decrease when the amount of carbonate ion increases. The calculations show only a small sensitivity to the concentration changes of the carbonate ion. Figure 4 shows that the model agrees well with the data, which indicate that the sulfate ion did not change the precipitation conditions. Calculations at different concentrations of Al, Si, and other species have shown similar agreement between the published data9 and the calculated results. For example, Figure 5

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Figure 3. Effect of carbonate ion concentration changes on the equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, only the input amount of Na2CO3 was varied from 0.5 to 1.5 mol/kg of H2O. Input amounts of other chemicals were the same as those of Figure 1.)

Figure 4. Effect of sulfate ion concentration changes on the equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, only the input amount of Na2SO4 was varied from 0.05 to 0.2 mol/kg of H2O. Input amounts of other chemicals were the same as those of Figure 1.)

Figure 5. Effect of hydroxyl ion concentration changes on the equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, the input amount of Na2CO3 was 0.3 mol/kg of H2O, that of Na2SO4 was 0.1 mol/kg of H2O, and that of NaCl was 0.1 mol/kg of H2O. The input amount of NaOH was varied from 2.0 to 3.0 mol/kg of H2O. Input amounts of AlCl3‚6H2O and Na2SiO3‚9H2O were varied from 0.08 to 0.02 and from 0.02 to 0.08 mol/kg of H2O, respectively.)

Figure 6. Effect of carbonate ion concentration changes on the equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, the input amount of Na2CO3 as varied from 0.1 to 0.5 mol/kg of H2O. That of NaOH was 2.5 mol/kg of H2O. Those of other chemicals were the same as those of Figure 5.)

shows the effect of the hydroxyl ion and Figure 6 that of the carbonate ion. Na+-Al(OH)4--SiO32--OH--CO32--Cl--HS-H2O (System B). In experiments with system B, Na2S was used. Na2S dissociates in water to Na+, OH-, and HS- according to the reaction Na2S + H2O f 2Na+ + HS- + OH-.30 The effect of different HS- concentrations is shown in Figure 7. As seen from the plot, the model and data indicate that increasing HS- concentration increases the solubility of Al and Si. The same agreement is also seen in Figure 8 which shows results at different total concentrations of chemicals.

dalite dihydrate) precipitation conditions in aqueous alkaline solutions was presented. Activity coefficients were calculated by Pitzer’s method. Comparison of the model-based calculated results with precipitation data showed good agreement. The effects of the OH-, CO32-, SO42-, HS- ions were predicted satisfactorily. The calculations were found to be sensitive to the value of the equilibrium constant for hydroxysodalite dihydrate formation.

Conclusions A thermodynamics-based model to calculate sodium aluminosilicate (hydroxysodalite dihydrate and/or so-

Acknowledgment The financial support provided by the Natural Sciences and Engineering Research Council of Canada

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Figure 7. Effect of sodium sulfide ion concentration changes on the equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, input chemicals consisted of AlCl3‚6H2O, Na2SiO3‚9H2O, NaOH, Na2CO3, and Na2S. The input amount of NaOH was 0.25 mol/kg of H2O, and that of Na2CO3 was 1.0 mol/kg of H2O. That of Na2S was varied from 0.0 to 1.0 mol/kg of H2O. Input amounts of AlCl3‚ 6H2O and Na2SiO3‚9H2O were varied from 0.1 to 0.05 and from 0.05 to 0.1 mol/kg of H2O, respectively.)

∆Cp° ) heat capacity change of reaction ∆Hf° ) standard enthalpy of formation, kJ/mol ∆Hr° )enthalpy change of reaction ∆Gf° ) standard Gibbs free energy of formation, kJ/mol ∆G0° ) Gibbs free energy change of reaction at the reference state, kJ/mol K ) equilibrium constant Khsod ) thermodynamic equilibrium constant of hydroxysodalite dihydrate formation reaction Ksod ) thermodynamic equilibrium constant of sodalite dihydrate formation reaction m ) molality, mol/kg of H2O n ) number of moles R ) gas constant, 8.314 J/(mol K) S ) objective function S° ) standard entropy ∆Sr° ) change of standard entropy T ) temperature, K T0 ) temperature of the standard state, K z ) charge of ion R1 ) numerical constant of Pitzer’s equation β(0), β(1), and Cφ ) Pitzer’s binary parameters θaa′ ) Pitzer’s mixing parameters for anion-anion Ψaa′Na+ ) Pitzer’s mixing parameters for anion-anion-Na+ γ ) activity coefficient ν ) number of moles of reactants or products Superscripts total ) total number of moles of an element in the system int ) interpolated cal ) calculated Subscripts (aq) ) aqueous (s) ) solid (l)) liquid hsod ) hydroxysodalite dihydrate, Na8(AlSiO4)6(OH)2‚2H2O sod ) sodalite dihydrate, Na8(AlSiO4)6Cl2‚2H2O d ) number of data

Literature Cited

Figure 8. Effect of sodium sulfide ion concentration changes on the equilibrium concentration of aluminum and silicon species. (For experiments and model calculations at 368.15 K and 1 atm, the input amount of NaOH was 2.0 mol/kg of H2O, and that of Na2CO3 was 0.25 mol/kg of H2O. That of Na2S was varied from 0.0 to 1.0 mol/kg of H2O. Input amounts of AlCl3‚6H2O and Na2SiO3‚9H2O were varied from 0.1 to 0.05 and from 0.05 to 0.1 mol/ kg of H2O, respectively.)

(NSERC) through the strategic grants program is greatly appreciated. The support received from the Pulp and Paper Research Institute of Canada (PAPRICAN) is also appreciated. Nomenclature a ) activity Aφ ) Debye-Huckel parameter Cp° ) standard heat capacity at standard state, J/(mol K) Cp°abs ) absolute heat capacity

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Received for review March 29, 1999 Revised manuscript received August 26, 1999 Accepted September 8, 1999 IE990229R