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Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Solubility of NaHCO3 and NH4HCO3 in the Relevant Media and Prediction of High-Pressure Phase Equilibria for the NH3−CO2−NaCl−H2O System Juan Zhou,† Yan Zeng,‡ George P. Demopoulos,‡ Chunxi Li,† and Zhibao Li*,§ †

College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China Materials Engineering, McGill University, 3610 University Street, Montreal, QC H3A 0C5, Canada § Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡

ABSTRACT: The solubility of NaHCO3 was determined in the NH4+−Na+− CO32−−HCO3−−Cl−−H2O system with the concentration up to 6 mol·kg−1 by a dynamic method from 283.15 to 333.15 K. It was found that the solubility of NaHCO3 decreases with increasing concentration of Na2CO3, NH4HCO3, or NaCl. A speciation-based model was developed with mixed-solvent electrolyte interaction parameters newly obtained by regressing both the experimental and literature solubility data. The average relative deviations are less than 5.0%. The new model is able to predict the solubility of NaHCO3 at high pressures up to 6.0 MPa for the NH3−CO2−NaCl−H2O system at 313.15 and 323.15 K. This work can provide a theoretical basis for producing Na2CO3 with a better crystal form and higher productivity in the carbonation process.

1. INTRODUCTION Sodium carbonate (Na2CO3), also called soda ash, is majorly produced by the Solvay process after thermal decomposition of sodium bicarbonate (NaHCO3).1−4 In the Solvay process, CO2 passes through a NH3-saturated aqueous solution of NaCl to form NH4Cl and solid NaHCO3 in a carbonating tower. The reaction is described as eq 1:

2NH4Cl(aq) + Ca(OH)2 (aq) = 2NH3(g) + H 2O(l) + CaCl 2(aq)

(3)

(1)

The suspension is filtered to separate NaHCO3 solid from NH4Cl solution. By calcination, NaHCO3 is converted to Na2CO3, generating CO2 and H2O as byproducts (eq 2). CO2 is recovered and reused in the carbonating tower. In the mother liquor, the free ammonia such as ammonium carbonate and ammonium hydroxide can be directly removed by heating. However, the ammonium chloride in the mother liquor is subjected to react with lime milk and distill to obtain free ammonia. The ammonia generated from ammonia distillation process is recycled back to the carbonating tower, and the reaction of this process is written as eq 3. The lime milk used in the ammonia distillation process is prepared by the reaction of hot water and lime which is produced from the calcination of limestone with the reaction equation depicted as eqs 4 and 5. Carbon dioxide produced by the calcination of limestone is used in the carbonation process. The Solvay flowsheet of the manufacture process of sodium carbonate is shown in Figure 1. 2NaHCO3(s) = Na 2CO3(s) + CO2 (g) + H 2O(g) © XXXX American Chemical Society

(4)

CaO(s) + H 2O(l) = Ca(OH)2 (aq)

(5)

In the Solvay process, the carbonation process is a key step of producing sodium bicarbonate. Sodium bicarbonate crystal precipitates from the solution containing NH3−CO2−NaCl. For the purpose of obtaining sodium bicarbonate with a better crystal form and higher productivity, the solubility of NaHCO3 in the NH4+−Na+−CO32−−HCO3−−Cl−−H2O system is necessary. Many investigations have been done on the solubility of NaHCO3 in the Na2CO3−H2O system.5−7 Fedoteeff8 determined the solubility of NaHCO3 in the NH4HCO3−NH4Cl−NaCl−H2O system at a temperature range from 273.15 to 303.15 K. Neumann and Domke9 also measured the solubility of NaHCO3 in the NH4HCO3−NH4Cl−NaCl−H2O system under pressure of 0.12 and 0.25 MPa from 293.15 to 313.15 K. Trypuć and Kiełkowska10 determined the solubility of NaHCO3 in the NH4HCO3−H2O system. The solubility of NaHCO3 in the NH3−CO2−NaCl−H2O system at high pressure of CO2 up to 6.0 MPa was reported in the literature.11 In this paper, the solubility of NaHCO3 in the NaHCO3−H2O, NH4HCO3−H2O, and NaCl−H2O systems was determined in

NaCl(aq) + NH3(aq) + CO2 (g) + H 2O(l) = NaHCO3(s) + NH4Cl(aq)

CaCO3(s) = CaO(s) + CO2 (g)

Received: September 3, 2017 Accepted: November 16, 2017

(2) A

DOI: 10.1021/acs.jced.7b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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was constantly stirred by using a magnetic stirrer. The mass of chemicals used in this experiment was weighed by the digital balance (model JA5003) with a sensitivity of 0.001 g.

3. THERMODYNAMIC MODELING 3.1. Chemistry of the NaHCO 3 −Na 2 CO 3 −H 2 O, NH4HCO3−NaHCO3−H2O, and NaHCO3−NaCl−H2O Systems. There are many chemical equilibria in the NaHCO3− Na2CO3−H2O, NH4HCO3−NaHCO3−H2O, and NaHCO3− NaCl−H2O systems, such as the dissolution equilibrium of NaHCO3, Na2CO3, NH4Cl, NH4HCO3, and NaCl. The main dissolution reactions can be described by the following equations:

Figure 1. Solvay flowsheet of the manufacture process of sodium carbonate.

the temperature range from 283.15 to 333.15 K. A chemical model with new parameters was developed via the regression of both the experimental and literature solubility data. The species distributions were calculated by the new model in the NaHCO3− Na2CO3−H2O, NH4HCO3−NaHCO3−H2O, and NaHCO3− NaCl−H2O systems, respectively. The solubility of NaHCO3 in the NH3−CO2−NaCl−H2O system at high pressure and the solubility of NH4HCO3 in the NH4Cl−NaHCO3−NaCl−H2O system were successfully predicted by the new model.

NaHCO3(s) = Na + + HCO3−

(6)

HCO3− + H 2O = H3O+ + CO32 −

(7)

Na 2CO3(s) = 2Na + + CO32 −

(8)

Na 2CO3 · 10H 2O(s) = 2Na + + CO32 − + 10H 2O

(9)

Na 2CO3 ·H 2O(s) = 2Na + + CO32 − + H 2O

(10)

Na 2CO3 ·7H 2O(s) = 2Na + + CO32 − + 7H 2O

(11)

NH4HCO3(s) = NH4 + + HCO3−

(12)

NaCl(s) = Na + + Cl−

(13)

For instance, the equilibrium constant (also called solubility product) of NaHCO3 can be expressed as KSP(NaHCO3) = a Na+ × a HCO−3 = (m Na+ × γNa+) × (m HCO−3 × γHCO−)

2. EXPERIMENTAL SECTION 2.1. Experimental Materials. Analytical grade NaHCO3, Na2CO3, NaCl, and NH4HCO3 with purities of 99.5 wt %, 99.8 wt %, 99.5 wt %, and 21.0−22.0 wt % (the purity of NH3), respectively, were provided by Xilong Chemical Co., Ltd. All reagents used in this work were used directly without further purification and are listed in Table 1. Deionized water with specific conductivity of 0.1 μS·cm−1 was used in the experiment.

3

(14)

where KSP is the solubility equilibrium constant; a is the activity of species; m is the molality of species; and γ is the activity coefficient of species. The equilibrium constant of the dissolution

Table 1. CAS Numbers, Sources, and Mass Fraction Purities of the Chemicals Used in this Work chemical name sodium bicarbonate sodium carbonate ammonium bicarbonate sodium chloride

CASRN

sources

mass fraction purity

144-55-8 Xilong Chemical Co., Ltd. ≥99.5% 497-19-8 Xilong Chemical Co., Ltd. ≥99.8% 1066-33-7 Xilong Chemical Co., Ltd. 21.0−22.0% (NH3) 7647-14-5 Xilong Chemical Co., Ltd. ≥99.5%

2.2. Experimental Procedure. The solubility was determined by a dynamic method. The experimental apparatus was also used in our earlier works.12−14 In the experiment, the solutions of Na2CO3, NaCl, and NH4HCO3 with a known concentration were first added into the glass vessel with a volume of 250 mL. Sodium bicarbonate of certain quality was placed into the solution. The addition was repeated until it was not dissolved. The temperature of this procedure was controlled by a circulating water bath and was kept constant within ±0.1 K. The solution

Figure 2. Solubility of NaHCO3 in the Na2CO3−H2O system at the temperature range from 293.15 to 333.15 K. The points represent the experimental solubility data, the dash lines represent the results predicted by MSE model with default parameters, and the solid lines represent the results calculated by the chemical model with new parameters. B



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reactions can be calculated by the standard state Gibbs free energy which is expressed by the following equation: ΔR G° = −RT ln K

(15)

where ΔRG° is the partial molal standard state Gibbs free energy of reaction, R is the gas constant, and T is the temperature in Kelvin. The standard partial molal Gibbs free energy of reaction can be calculated by the Helgeson−Kirkham−Flowers (HKF)15 equation which is described by the following equation ⎤ ⎡ ⎛T ⎞ ΔGP0, T = ΔGf0 − S P0r, , Tr(T − Tr) − c1⎢T ln⎜ ⎟ − T + Tr ⎥ ⎥⎦ ⎢⎣ ⎝ Tr ⎠ ⎛ Ψ + P ⎞⎛ Ψ + P ⎞ + a1(P − Pr) + a 2 ln⎜ ⎟ ⎟⎜ ⎝ Ψ + Pr ⎠⎝ Ψ + Pr ⎠ ⎡ ⎛ Ψ + P ⎞⎤⎛ 1 ⎞ ⎟ + ⎢a3(P − Pr) + a4 ln⎜ ⎟ ⎥⎜ ⎢⎣ ⎝ Ψ + Pr ⎠⎥⎦⎝ T − Θ ⎠

Figure 3. Solubility of NaHCO3 in the NH4HCO3−H2O system at the temperature range from 283.15 to 303.15 K. The points represent the experimental solubility data, the dash lines represent the results predicted by the MSE model with default parameters, and the solid lines represent the results calculated by the chemical model with new parameters.

⎡⎛ ⎤ ⎛ ⎞⎞ ⎢ ⎜⎜⎜⎛ 1 ⎟⎞ − ⎜ 1 ⎟⎟⎟⎜⎛ Θ − T ⎟⎞ ⎥ ⎢ ⎝⎝ T − Θ ⎠ ⎝ Tr − Θ ⎠⎠⎝ Θ ⎠ ⎥ ⎥ − c 2⎢ ⎢ T ⎛ T (T − Θ) ⎞ ⎥ ⎢− 2 ln⎜ r ⎥ ⎟ ⎥⎦ ⎝ T (Tr − Θ) ⎠ ⎣⎢ Θ ⎛ 1 ⎞ ⎛1 ⎞ + ω⎜ − 1⎟ − ω Pr , Tr⎜⎜ − 1⎟⎟ ⎝ε ⎠ ⎝ εPr , Tr ⎠ + ω Pr , TrYPr , Tr(T − Tr)

(16)

where T and P are the temperature and pressure; Tr and Pr are the reference temperature and pressure of 298.15 K and 1 bar; a1, a2, a3, and a4 are pressure dependent parameters; c1 and c2 are temperature dependent parameters; Y is the born function; ω is temperature and pressure dependent term for the electrostatic nature of the electrolytes; Ψ and Θ are solvent-dependent parameters equal to 2600 bar and 228 K for water; and ε is the dielectric constant of water. The equilibrium constant can also be calculated by an empirical equation, which is defined by the following equation:16 log K = A +

B + CT + DT 2 T

Figure 4. Solubility of NaHCO3 in the NaCl−H2O system at the temperature range from 288.15 to 318.15 K. The points represent the experimental solubility data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid lines represent the results calculated by the chemical model with new parameters.

(17)

where A, B, C, and D are empirical parameters, and T is the Kelvin temperature. 3.2. Activity Coefficient. Compared with the aqueous model, the mixed-solvent electrolyte (MSE) model embedded in the OLI platform is very flexible and has no component limitations. For this reason, the MSE model was selected as modeling tool in this work. In the MSE model, the activity coefficient of species in the nonideal solution can be expressed by the excess Gibbs free energy.17−20 The excess Gibbs free energy is described as follows: G ex G ex G ex Gex = LR + MR + SR RT RT RT RT

interactions can be calculated by an ionic strength-dependent symmetrical second-virial-coefficient-type expression. The equation of middle-range interactions is expressed as follows: ex ⎛ ⎞ GMR = −⎜⎜∑ ni⎟⎟ ∑ ∑ xixjBij (Ix) RT ⎝ i ⎠ i j

(18)

(19)

where x is the mole fraction of species, Ix is ionic strength, and Bij(Ix) represents a binary interaction parameter between species i and j. The Bij(Ix) is calculated by

ex GLR

where is the contribution of long-range electrostatic interactions which are calculated by the Pitzer-Debye−Hückel equation; Gex SR represents the short-range contribution resulting from molecule−molecule, molecule−ion, ion−ion which are described by the UNIQUAC model; and Gex MR is ionic interactions which are not included in long-range term. The middle-range

Bij (Ix) = bij + cij exp( − Ix + 0.01 )

(20)

where the bij and cij are parameters relevant to temperature, which can be expressed as follows: C



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Table 2. Solubility of NaHCO3 in Aqueous Solution of Na2CO3 from 293.15 to 333.15 K at Pressure of 0.1 MPaa m(Na2CO3) (mol·kg−1)

m(NaHCO3) (mol·kg−1)

x(Na2CO3)

x(NaHCO3)

0.0035 0.0070 0.0105 0.0140 0.0174 0.0209 0.0243 0.0277 0.0310 0.0344

0.0186 0.0172 0.0158 0.0143 0.0132 0.0133 0.0127 0.0115 0.0111 0.0102

0.0035 0.0070 0.0105 0.0140 0.0174 0.0208 0.0242 0.0276 0.0310 0.0343

0.0222 0.0197 0.0183 0.0169 0.0154 0.0149 0.0142 0.0137 0.0128 0.0124

0.0035 0.0070 0.0105 0.0139 0.0174 0.0208 0.0242 0.0275 0.0309 0.0342

0.0249 0.0231 0.0211 0.0198 0.0179 0.0176 0.0164 0.0159 0.0150 0.0144

0.0035 0.0070 0.0104 0.0139 0.0173 0.0207 0.0241 0.0275 0.0308 0.0342

0.0285 0.0262 0.0248 0.0226 0.0222 0.0210 0.0200 0.0188 0.0176 0.0169

0.0035 0.0069 0.0104 0.0138 0.0172 0.0206 0.0240 0.0274 0.0307 0.0340

0.0309 0.0298 0.0281 0.0259 0.0254 0.0244 0.0230 0.0224 0.0214 0.0203

T = 293.15 K 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.0555 0.9804 0.8993 0.8149 0.7586 0.7659 0.7344 0.6621 0.6418 0.5933

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.2638 1.1228 1.0449 0.9665 0.8869 0.8612 0.8232 0.7952 0.7460 0.7219

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.4237 1.3241 1.2083 1.1400 1.0307 1.0185 0.9506 0.9222 0.8734 0.8427

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.6333 1.5043 1.4265 1.3013 1.2829 1.2165 1.1607 1.0942 1.0301 0.9914

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.7807 1.7174 1.6256 1.4966 1.4729 1.4185 1.3418 1.3076 1.2571 1.1952

T = 303.15 K

T = 313.15 K

T = 323.15 K

T = 333.15 K

a

Water is used as the solvent for molality calculation. Standard uncertainties u are u(T) = 0.15 K, u(p) = 0.6 kPa, and u(m) = 0.02 mol·kg−1.

bij = BMD0 + BMD1 × T + BMD2/T + BMD3 × T 2 + BMD4 × ln T

cij = CMD0 + CMD1 × T + CMD2/T + CMD3 × T 2

(21)

+ CMD4 × ln T D

(22) DOI: 10.1021/acs.jced.7b00790 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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Table 3. Solubility of NaHCO3 in the Aqueous Solution of NH4HCO3 from 283.15 to 303.15 K at Pressure of 0.1 MPaa m(NH4HCO3) (mol·kg−1)

m(NaHCO3) (mol·kg−1)

x(NH4HCO3)

x(NaHCO3)

0.0035 0.0070 0.0105 0.0140 0.0174 0.0209 0.0243 0.0276

0.0168 0.0161 0.0155 0.0147 0.0142 0.0138 0.0133 0.0130

0.0035 0.0070 0.0105 0.0140 0.0174 0.0208 0.0242 0.0276 0.0309 0.0343

0.0186 0.0180 0.0172 0.0167 0.0159 0.0152 0.0148 0.0145 0.0139 0.0137

0.0035 0.0070 0.0105 0.0139 0.0174 0.0208 0.0242 0.0275 0.0309 0.0342

0.0202 0.0196 0.0188 0.0183 0.0176 0.0169 0.0165 0.0160 0.0157 0.0155

0.0035 0.0070 0.0105 0.0139 0.0173 0.0208 0.0241 0.0275 0.0308 0.0342

0.0215 0.0209 0.0202 0.0197 0.0191 0.0186 0.0181 0.0176 0.0171 0.0168

0.0035 0.0070 0.0105 0.0139 0.0173 0.0207 0.0241 0.0275 0.0308 0.0341

0.0229 0.0223 0.0219 0.0214 0.0208 0.0204 0.0198 0.0193 0.0189 0.0186

T = 283.15 K 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000

0.9508 0.9163 0.8843 0.8426 0.8136 0.7917 0.7669 0.7504

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.0577 1.0243 0.9827 0.9567 0.9165 0.8782 0.8561 0.8396 0.8060 0.8007

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.1473 1.1161 1.0761 1.0502 1.0135 0.9746 0.9533 0.9321 0.9123 0.9036

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.2249 1.1970 1.1585 1.1333 1.1017 1.0740 1.0474 1.0218 0.9981 0.9858

0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000

1.3074 1.2775 1.2595 1.2344 1.2020 1.1838 1.1511 1.1268 1.1060 1.0901

T = 288.15 K

T = 293.15 K

T = 298.15 K

T = 303.15 K

a

Water is used as the solvent for molality calculation. Standard uncertainties u are u(T) = 0.15K, u(p) = 0.6 kPa, and u(m) = 0.02 mol·kg−1.

4. RESULTS AND DISCUSSION

where the BMD0, BMD1, BMD2, BMD3, BMD4, CMD0, CMD1, CMD2, CMD3, and CMD4 are adjustable middle-range interaction parameters.

4.1. Solubility of NaHCO 3 in the Na 2 CO 3−H 2 O, NH4HCO3−H2O, and NaCl−H2O Systems. The solubility of E



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NaHCO3 in aqueous solutions of Na2CO3, NH4HCO3, and NaCl, respectively, was determined by the dynamic method described in the Experimental Section. The results are shown as solid symbols in Figures 2 to 4 and listed in Tables 2 to 4. In the aqueous solution of Na2CO3 (Figure 2), the solubility of NaHCO3 decreases with the increase concentration of Na2CO3 from 0.2 to 2.0 mol·kg−1 and increases with the increasing temperature from 293.15 to 333.15 K. The decreases of the solubility of NaHCO3 with the addition of Na2CO3 is caused by the common ion effect. The solubility of NaHCO3 in the NH4HCO3−H2O system was also investigated with 0.2 to 2.0 mol·kg−1 of NH4HCO3 from 283.15 to 303.15 K, as shown in Figure 3 and Table 3. From Figure 3, it is indicated that the solubility of NaHCO3 decreases with the addition of NH4HCO3 concentration and the decrease of temperature. The common ion effect can explain the decrease in solubility of NaHCO3 with increasing concentration of NH4HCO3. The experimental solubility of NaHCO3 in the NaCl−H2O system was determined with the concentration of NaCl from 0 to 6.0 mol·kg−1 at 308.15 to 318.15 K. Both the experimental results and the literature21 solubility data of NaHCO3 in the NaCl−H2O system at 288.15 and 298.15 K were shown in Figure 4 and Table 4. Figure 4 illustrates that the solubility of NaHCO3 increases with the rise of temperature and significantly decreases with the increase of NaCl concentration resulting from the common ion effect. It is also observed from Figures 2 and 4 that the solubility of NaHCO3 decreases faster with increasing concentration of NaCl than that with the addition of Na2CO3. The reason for this difference is that the pH of mixed electrolyte aqueous solution increases with the increasing concentration of Na2CO3, which is beneficial to the dissolution of NaHCO3. However, the addition of NaCl concentration has no effect on pH. 4.2. Solubility of NH4HCO3 in the NaHCO3−H2O, NH4Cl−H2O, and NaCl−H2O Systems. The solubility of NH4HCO3 in the NaHCO3−H2O, NH4Cl−H2O, and NaCl−H2O systems was obtained from the literature.10,21 From Figure 5, it can be seen that the solubility of NH4HCO3 increases insignificantly with the addition of NaHCO3 concentration at the temperature range from 293.15 to 323.15 K. This slight change of NH4HCO3 solubility is correlated with the existence of HCO3−. It can be observed from Figure 6 that the solubility of NH4HCO3 decreases with increasing concentration of NH4Cl from 288.15 to 303.15 K. The common ion effect can be responsible for the decreases of NH4HCO3 solubility. As can be seen from Figure 7, the solubility of NH4HCO3 increases with the increases of NaCl concentration at the temperature range from 273.15 to 293.15 K, which is opposite to that of NH4Cl. This occurs because there is no common ion effect in the NH4HCO3−NaCl−H2O system. The increases of NH4HCO3 solubility can be associated with the changes of activity coefficients of species in the NH4HCO3− NaCl−H2O system with the addition of NaCl concentration. The solubility of NH4HCO3 increases with the temperature in all the systems mentioned above. 4.3. Evaluation of the Model. The MSE model with the default interaction parameters in the OLI system22 was evaluated by comparing the calculated solubility (dashed lines) with the experimental results (solid symbols) as shown in Figures 2 to 7. In the Na2CO3 solution, it can be found that the solubility of NaHCO3 was predicted well by the default model at low temperatures. However, a significant deviation can be found when the temperature is above 323.15 K. In the NH4HCO3 solution, the predicted solubility of NaHCO3 agrees well with

Table 4. Solubility of NaHCO3 in the Aqueous Solution of NaCl from 288.15 to 318.15 K at Pressure of 0.1 MPaa m(NaCl) (mol·kg−1) 0.0000 0.5205 1.0302 1.6782 2.1098 3.1994 3.4356 4.3877 6.1117 0.0000 0.2967 0.6685 0.9884 1.3158 1.7630 2.2186 2.5814 2.8620 4.1516 4.2898 4.7470 5.7427 6.0376 6.1050 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 5.5000 6.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 5.5000 6.0000

m(NaHCO3) (mol·kg−1) T = 288.15 K 1.0493 0.8192 0.6392 0.5164 0.4094 0.2796 0.2918 0.1894 0.1468 T = 298.15 K 1.2207 1.0503 0.9311 0.7995 0.6947 0.5858 0.5458 0.4530 0.4210 0.2943 0.2730 0.2160 0.1964 0.1627 0.1962 T = 308.15 K 1.2268 1.0054 0.8463 0.6838 0.6010 0.5167 0.4327 0.3808 0.3472 0.2888 0.2665 0.2464 T = 318.15 K 1.4357 1.1851 1.0171 0.8716 0.7254 0.6324 0.5360 0.4763 0.3777 0.3335 0.2996 0.2893

x(NaCl)

x(NaHCO3)

0.0000 0.0091 0.0180 0.0291 0.0363 0.0542 0.0580 0.0730 0.0989

0.0185 0.0144 0.0112 0.0089 0.0070 0.0047 0.0049 0.0031 0.0024

0.0000 0.0052 0.0117 0.0172 0.0229 0.0304 0.0380 0.0441 0.0486 0.0692 0.0714 0.0784 0.0934 0.0978 0.0987

0.0215 0.0185 0.0163 0.0139 0.0121 0.0101 0.0094 0.0077 0.0072 0.0049 0.0045 0.0036 0.0032 0.0026 0.0032

0.0087 0.0174 0.0259 0.0343 0.0426 0.0508 0.0588 0.0667 0.0745 0.0822 0.0897 0.0971

0.0214 0.0175 0.0146 0.0117 0.0102 0.0087 0.0073 0.0064 0.0057 0.0047 0.0043 0.0040

0.0087 0.0173 0.0258 0.0342 0.0425 0.0507 0.0587 0.0666 0.0745 0.0821 0.0896 0.0970

0.0250 0.0205 0.0175 0.0149 0.0123 0.0107 0.0090 0.0079 0.0062 0.0055 0.0049 0.0047

a

Water is used as the solvent for molality calculation. Standard uncertainties u are u(T) = 0.15K, u(p) = 0.6 kPa, and u(m) = 0.02 mol·kg−1.

experimental data when NH4HCO3 concentration is below 0.6 mol·kg−1. While above this value, there is an obvious discrepancy F



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Figure 5. Solubility of NH4HCO3 in the NaHCO3−H2O system at the temperature range from 293.15 to 323.15 K. The points represent the literature solubility data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid lines represent the results calculated by the chemical model with new parameters.

Figure 7. Solubility of NH4HCO3 in the NaCl−H2O system at the temperature range from 273.15 to 293.15 K. The points represent the experimental solubility data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid lines represent the results calculated by the chemical model with new parameters.

Figure 6. Solubility of NH4HCO3 in the NH4Cl−H2O system at the temperature range from 288.15 to 303.15 K. The points represent the literature solubility data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid lines represent the results calculated by the chemical model with new parameters.

the MSE model for Na+−HCO3−, HCO3−−CO32− and NH4+− HCO3− were obtained by regression as summarized in Table 5. The experimental solubility of NaHCO3 in the NH4HCO3− Na2CO3−NaHCO3−NaCl−H2O system, the literature solubility of the NH4Cl in the NaCl−H2O system, and the literature solubility of the NH4HCO3 in the NH4Cl−NaHCO3−NaCl− H2O system were all used for the regression. The comparisons between experimental and calculated solubility by chemical model with new middle-range interaction parameters are shown in Figures 2 to 7(solid lines). It can be seen from Figures 2 to 4 that the calculated solubilities of NaHCO3 agree well with the experimental solubility values in the Na2CO3−H2O, NH4HCO3− H2O, and NaCl−H2O systems. Figures 5 to 7 show that the calculated solubilities of NH4HCO3 are consistent with experimental values in the NaCl−H2O, NaHCO3−H2O and NH4Cl− H2O systems. The average relative deviations between the experimental and regressed results are less than 5% for all the systems investigated above. 4.5. Model Application. The species distributions were predicted by the chemical model with new parameters in the NaHCO3−Na2CO3−H2O, NH4HCO3−NaHCO3−H2O, and NaHCO3−NaCl−H2O systems with NaHCO3 concentration of 1 mol·kg−1 at 303.15 K. Figure 8 reveals the effect of Na2CO3 concentration on the relative concentration of HCO3− and CO32−. It can be seen that the relative concentration of HCO3− decreases with the addition of Na2CO3 concentration, while the relative concentration of CO32− increases with increasing concentration of Na2CO3. The species distribution in the NH4HCO3−NaHCO3−H2O system as a function of NH4HCO3 concentration is shown in Figure 9. It can be observed that the relative concentration of HCO3− decreases insignificantly with the increment of NH4HCO3 concentration, while the relative concentration of CO32− has the opposite trend. The NaCl concentration effect on the species distribution in the NaHCO3−NaCl−H2O system is shown in Figure 10. It can be found that the relative concentration of HCO3− reduces with increasing concentration of NaCl, yet the relative concentration of Na+ increases with the increment of NaCl concentration.

between the predicted and experimental solubility of NaHCO3. There is limited solubility data in the NH4HCO3−NaHCO3− H2O system, which may be the source of the difference between predicted and experimental values. In the NaCl solution, the solubility of NaHCO3 predicted by the default model has a small difference with the experimental solubility. For the NaHCO3− H2O system, the solubility of NH4HCO3 predicted by the MSE model with existing parameters is in good agreement with literature solubility data at 293.15 K. However, the predicted solubility of NH4HCO3 is much higher than literature solubility when the temperature is above 293.15 K. For the NaCl−H2O and NH4Cl−H2O systems, it can be seen that there is a noticeable difference between predicted values and literature solubility data. 4.4. Model Parametrization. To improve the accuracy of OLI’s prediction, new middle-range interaction parameters of G



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Table 5. MSE Middle Range Interaction Parameters species i

species j

BMD0

BMD1

BMD2

CMD0

CMD1

CMD2

Na+ HCO3− NH4+

HCO3− CO32− HCO3−

192.0272 −402.8618 259.3183

−0.4422725 1.193196 0.2115024

−17865.27 9089.862 −113825.3

−112.8770 −533.1128 556.6473

0.3717335 9.2869626 × 10−02 −1.896808

2719.748 157697.6 29977.03

Figure 8. Relative concentration of HCO3− and CO32− as the function of Na2CO3 concentration in the Na2CO3−NaHCO3−H2O system with NaHCO3 concentration of 1 mol·kg−1 at 303.15 K.

Figure 10. Relative concentration of HCO3− and Na+ as the function of NaCl concentration in the NaCl−NaHCO3−H2O system with NaHCO3 concentration of 1 mol·kg−1 at 303.15 K.

Figure 9. Relative concentration of HCO3− and CO32− as the function of NH4HCO3 concentration in the NH4HCO3−NaHCO3−H2O system with NaHCO3 concentration of 1 mol·kg−1 at 303.15 K.

Figure 11. Solubility of NaHCO3 in the NH4HCO3−H2O system at 313.15 K and 1.0 MPa. The points represent the literature data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid line represents the calculated results by the chemical model with new parameters.

4.6. Prediction of Phase Equilibria for the NH3−CO2− NaCl−H2O System at High Pressure. In the carbonation process, carbon dioxide is passed through an ammonia-saturated salt water to prepare sodium bicarbonate. Sodium bicarbonate crystal precipitates from the solution containing NH3−CO2− NaCl at elevated pressure. For better understanding of the carbonation process, the phase equilibria data for the NH3− CO2−NaCl−H2O system are necessary. Luckily, the solubility data of NaHCO3 for the NH3−CO2−NaCl−H2O system at high CO2 pressure up to 6.0 MPa at 313.15 and 323.15 K was reported in the literature,11 which was applied in this work for new model evaluation. The phase equilibria data in this literature was predicted by the MSE model with existing parameters and the new chemical model. The comparisons of literature data with

predicted values are displayed in Figures 11 to 15. It can be found that there is a significant deviation between the solubility of NaHCO3 predicted by the MSE model with default parameters and literature solubility data. It is also exhibited that the results calculated by the new model are in good agreement with the literature solubility data of NaHCO3 in the NH4HCO3−H2O, NaCl−H2O, NH4HCO3−NH4Cl−H2O, and NH4Cl−NaCl− H2O systems, respectively. It is indicated that the solubility of NaHCO3 in the NH3−CO2−NaCl−H2O system at high pressure can be predicted well by the newly developed chemical model. H



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Figure 12. Solubility of NaHCO3 of the NaCl−H2O system at 313.15 K and 1.0 MPa. The points represent the literature data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid line represents the calculated results by the chemical model with new parameters.

Figure 14. Solubility of NaHCO3 in the NH4Cl−NaHCO3−NaCl−H2O system at 313.15 K and 1.0 MPa. The points represent the literature data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid line represents the calculated results by the chemical model with new parameters.

Figure 13. Solubility of NaHCO3 in the NH4Cl−NH4HCO3−H2O system at 313.15 K, 1.0 MPa, and 323.15 K, 4.0 MPa. The points represent the literature data, the dash lines represent the results calculated by the MSE model with default parameters, and the solid line represents the calculated results by the MSE model with default parameters.

Figure 15. Comparisons of literature and predicted solubility of NaHCO3 in the NH3−CO2−NaCl−H2O system with the pressure range from 1.0 to 6.0 MPa at 313.15 and 323.15 K.

using the chemical model with new parameters. The solubility of NaHCO3 in the NH3−CO2−NaCl−H2O system under high pressure at 313.15 and 323.15 K was also predicted by this model.

5. CONCLUSIONS In this work, the solubility of NaHCO3 in the Na2CO3−H2O, NH4HCO3−H2O, and NaCl−H2O systems was determined by a dynamic method at the temperature range from 283.15 to 333.15 K. The chemical model with new interaction parameters was developed by the regression of the experimental and literature solubility data. New middle-range interaction parameters of Na+−HCO3−, HCO3−−CO32−, and NH4+−HCO3− were obtained. The regressed solubility results are in good agreement with experimental and literature solubility data with the average relative deviations less than 5.0%. The species distributions and the solubility of NH4HCO3 in the NH4Cl− NaHCO3−NaCl−H2O system were successfully predicted

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel./Fax: +86-10-62551557. ORCID

George P. Demopoulos: 0000-0001-8112-5339 Zhibao Li: 0000-0002-5737-1289 Funding

The authors are grateful for financial support provided by the National Natural Science Foundation of China (Grants 21476235, 21776279, and U1407112) in this work. I



Article

Notes

The authors declare no competing financial interest.

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REFERENCES

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