Solubility of FeSO4·7H2O in the H2SO4–Ti(SO4)2–H2O, H2SO4

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Solubility of FeSO4·7H2O in the H2SO4−Ti(SO4)2−H2O, H2SO4−MgSO4−H2O, and HCl−H2O Systems from 278 to 313 K Yan Zhang,† Juan Zhou,‡ and Zhibao Li*,† †

Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China ABSTRACT: The solubilities of FeSO4·7H2O in the H2SO4−Ti(SO4)2−H2O and H2SO4−MgSO4−H2O systems were measured with a dynamic method from 278.15 to 308.15 K. Due to the hydrolysis property of Ti(IV), it was found that the common ion effect of Ti(SO4)2 was not so obvious as that of MgSO4 for the solubility of FeSO4·7H2O. The solubility of FeSO4·7H2O in the HCl−H2O system was also measured by same method. The solubility did not change much at first, yet substantially increased when more HCl was added into the solution. New interaction parameters of ions for the mixed-solvent electrolyte (MSE) model were regressed by the experimental solubility data, with the average relative deviations of less than 5.0%. The speciation and the activity coefficients of species in the FeSO4−HCl−H2O system with an FeSO4 concentration of 1.0 mol·kg−1 were predicted by the MSE model with the newly regressed parameters at 303.15 K.

process, the precipitation of FeSO4·7H2O is conducted for the purpose of preventing product contamination by iron. The typical thermodynamic properties exhibited in the H2SO4−FeSO4− Ti(SO4)2−H2O system, especially the solid−liquid phase equilibrium, are very important for the process control and engineering design for FeSO4·7H2O crystallization. There are many investigations conducted for the phase equilibrium of the H2SO4−FeSO4−H2O system.8−12 However,

1. INTRODUCTION Titanium is an abundant metal element on the earth.1 About 95% of the titanium ore is used for the production of TiO2, which is an important white pigment with good scattering properties and chemical stability.1−3 Generally, the minerals containing titanium include ilmenite, leucoxene, and rutile. Ilmenite provides more than 90% of the raw materials for the TiO2 production.1 Titanium dioxide is produced industrially through two major processes: the sulfate process was invented at the early twentieth century, and the chloride process was invented at the midtwentieth century.4 Greater than 90% of the TiO2 pigment is manufactured through the sulfuric acid process in China, and nearly half of the TiO2 pigment in the world is produced through this process. In the sulfuric acid process, step one is the leaching of ilmenite or titanium slag by concentrated H2SO4.5 The resulting liquid contains titanyl sulfate and iron sulfate. The next step is the addition of iron chips or iron powder to reduce the ferric ions, followed by the separation of iron as FeSO4·7H2O.6 The hydrated titanium dioxide is obtained through hydrothermal hydrolysis of the titanium sulfate solutions; it is then calcined to produce TiO2 pigment.7 As a critical step in the sulfuric acid Table 1. Description of the Chemicals in this Work chemical name

CAS No.

sources

mass fraction purity

iron(II) sulfate 7782-63-0 Xilong Chemical Co., Ltd. heptahydrate magnesium sulfate 10034-99-8 Xilong Chemical Co., Ltd. heptahydrate titanium(IV) sulfate 13693-11-3 Sinopharm Chemical Reagent Co., Ltd. sulfuric acid 7664-93-9 Beijing Chemical Plant hydrochloric acid 7647-01-0 Beijing Chemical Plant © XXXX American Chemical Society

Figure 1. Solubility of FeSO4·7H2O in the H2SO4−Ti(SO4)2−H2O system from 278.15 to 298.15 K. The points are the experimental data; the solid lines represent the values predicted by the MSE model with the new parameters.

≥99.0% ≥99.0% ≥96.0%

Received: September 5, 2016 Accepted: February 15, 2017

95−98% 36−38% A

DOI: 10.1021/acs.jced.6b00783 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Solubility of FeSO4·7H2O in the FeSO4−Ti(SO4)2−H2SO4−H2O System at the Temperature Range from 278.15 to 298.15 K and Pressure p = 0.1 MPaa

a

m(H2SO4) (mol·kg−1)

m(Ti(SO4)2) (mol·kg−1)

3.7345 3.7372 3.7382 3.7358 3.7363 3.7336 3.7474 3.7363 3.7494 3.7403 3.7418

0.1867 0.1969 0.3738 0.3934 0.5604 0.589 0.7495 0.7903 0.9373 0.9852 1.1867

3.6578 3.6642 3.6649 3.6653 3.6665 3.6673 3.669 3.6695 3.6725 3.6743 3.6768

0.1829 0.193 0.3859 0.3665 0.55 0.966 0.5788 0.7762 0.9181 0.7349 1.1661

3.5658 3.5688 3.5662 3.5727 3.5722 3.5748 3.5676 3.5748 3.5703 3.5644 3.5696

0.1783 0.188 0.3566 0.3762 0.5358 0.5639 0.7135 0.7562 0.8926 0.9389 1.1321

3.451 3.4559 3.4481 3.4473 3.4535 3.452 3.4398 3.4474 3.4471 3.4438 3.4358

0.1726 0.1821 0.3448 0.363 0.518 0.5446 0.688 0.7292 0.8618 0.9071 1.0896

3.3175 3.3068 3.2996 3.2969 3.2822 3.2638

0.1748 0.3482 0.5205 0.6974 0.8646 1.0351

m(FeSO4) (mol·kg−1) T = 278.15 K 0.5269 0.5214 0.5195 0.5241 0.5233 0.5285 0.5012 0.5232 0.4973 0.5152 0.5123 T = 283.15 K 0.679 0.6661 0.6649 0.6642 0.6616 0.66 0.6566 0.6557 0.6497 0.6463 0.6412 T = 288.15 K 0.8616 0.8554 0.8607 0.8478 0.8488 0.8436 0.8579 0.8435 0.8526 0.8643 0.8539 T = 293.15 K 1.0894 1.0796 1.095 1.0965 1.0843 1.0872 1.1115 1.0964 1.0969 1.1036 1.1194 T = 298.15 K 1.3542 1.3753 1.3896 1.3951 1.4241 1.4607

x(H2SO4)

x(Ti(SO4)2)

x(FeSO4)

0.0623 0.0623 0.0622 0.0621 0.0619 0.0619 0.0619 0.0617 0.0618 0.0616 0.0614

0.0031 0.0033 0.0062 0.0065 0.0093 0.0098 0.0124 0.0131 0.0154 0.0162 0.0195

0.0088 0.0087 0.0086 0.0087 0.0087 0.0088 0.0083 0.0086 0.0082 0.0085 0.0084

0.0609 0.061 0.0609 0.0609 0.0607 0.0603 0.0607 0.0605 0.0605 0.0607 0.0603

0.003 0.0032 0.0064 0.0061 0.0091 0.0159 0.0096 0.0128 0.0151 0.0121 0.0191

0.0113 0.0111 0.011 0.011 0.011 0.0109 0.0109 0.0108 0.0107 0.0107 0.0105

0.0593 0.0594 0.0591 0.0592 0.0591 0.0591 0.0588 0.0589 0.0587 0.0586 0.0585

0.003 0.0031 0.0059 0.0062 0.0089 0.0093 0.0118 0.0125 0.0147 0.0154 0.0185

0.0143 0.0142 0.0143 0.0141 0.014 0.0139 0.0141 0.0139 0.014 0.0142 0.014

0.0573 0.0574 0.0571 0.0571 0.057 0.057 0.0566 0.0567 0.0566 0.0565 0.0562

0.0029 0.003 0.0057 0.006 0.0086 0.009 0.0113 0.012 0.0141 0.0149 0.0178

0.0181 0.0179 0.0181 0.0181 0.0179 0.0179 0.0183 0.018 0.018 0.0181 0.0183

0.055 0.0546 0.0543 0.0541 0.0537 0.0533

0.0029 0.0058 0.0086 0.0115 0.0142 0.0169

0.0224 0.0227 0.0229 0.0229 0.0233 0.0238

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.

until recently, the solubility of FeSO4·7H2O in the H2SO4− Ti(SO4)2−H2O system has been reported by our group with initial H2SO4 concentrations of 2.0−3.5 mol·kg−1.13 Generally, magnesium is also included in the ilmenite, and FeSO4·7H2O

solubility in the system H2SO4−MgSO4−H2O is also important. However, to our knowledge, there is no solubility data for FeSO4·7H2O in the system H2SO4−MgSO4−H2O has been reported. B

DOI: 10.1021/acs.jced.6b00783 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 2. Solubility of FeSO4·7H2O in the H2SO4−MgSO4−H2O system from 298.15 to 308.15 K. The points are the experimental data; the solid lines are the values predicted by the MSE model with the new parameters.

Figure 3. Solubility of FeSO4·7H2O in the HCl−H2O system from 293.15 to 313.15 K. The points are the experimental data, the solid lines are the values predicted by the MSE model with the new parameters, and the dashed lines represent the results calculated by the MSE model with the default parameters.

FeSO4·7H2O, commonly known as copperas, constitutes the first coproduct of the sulfuric acid process for the manufacture of TiO2.2 Indeed, about 3−4 tons of copperas are formed in the sulfate process per ton of TiO2 pigment produced. Most of these wastes is disposed directly, which has been causing serious pollution.14 Recently, a patent has been authorized about our new green technology of preparing Fe2O3 from FeSO4·7H2O.15 The first step is the crystallization of FeCl2·4H2O by addition of FeSO4·7H2O into HCl solution. The solubility of FeSO4·7H2O in HCl solution is necessary for better understanding the new process. In this paper, the solubilities of FeSO4·7H2O in both H2SO4− Ti(SO4)2−MgSO4−H2O and HCl−H2O systems were determined through dynamic method at the temperature range from 278.15 to 313.15 K. The mixed solvent electrolyte (MSE) model was used for the regression of the middle-range interaction parameters of ions in the systems. The model with new

parameters was used for the prediction of specious and aqueous species’ activity coefficients in the FeSO4−HCl−H2O solution.

2. EXPERIMENTAL SECTION 2.1. Materials. Analytical grade FeSO4·7H2O and MgSO4· 7H2O were from Xilong Chemical Co., Ltd. with a minimum purity of 99.0 wt %. Ti(SO4)2 of chemical grade was produced by Sinopharm Chemical Reagent Co., Ltd. with purities of more than 96 wt %. Sulfuric acid and hydrochloric acid were provided by Beijing Chemical Plant with concentrations of 95−98 wt % and 36−38 wt %, respectively. The sources and purities of the materials are also listed in Table 1. All solutions used in the experiments were prepared by these reagents without any further treatment. H2O used for preparing the solutions were deionized

Table 3. Solubility of FeSO4·7H2O in the FeSO4−MgSO4−H2SO4−H2O System at the Temperature Range from 298.15 to 308.15 K and Pressure p = 0.1 MPaa m(H2SO4) (mol·kg−1)

a

m(MgSO4) (mol·kg−1)

3.3265 3.3631 3.4182 3.4580 3.5131 3.5798

0.2079 0.4204 0.6409 0.8645 1.0978 1.3424

3.1179 3.1563 3.2158 3.2614 3.3405 3.3932

0.1949 0.3945 0.6030 0.8154 1.0439 1.2725

2.9449 2.9813 3.0570 3.0787 3.1805 3.2367

0.1841 0.3727 0.5732 0.7697 0.9939 1.2138

m(FeSO4) (mol·kg−1) T = 298.15 K 1.3364 1.2638 1.1543 1.0755 0.9661 0.8338 T = 303.15 K 1.7503 1.6740 1.5560 1.4655 1.3086 1.2040 T = 308.15 K 2.0934 2.0213 1.8711 1.8279 1.6260 1.5145

x(H2SO4)

x(MgSO4)

x(FeSO4)

0.0551 0.0555 0.0563 0.0568 0.0575 0.0584

0.0034 0.0069 0.0106 0.0142 0.0180 0.0219

0.0221 0.0209 0.0190 0.0177 0.0158 0.0136

0.0515 0.0520 0.0528 0.0534 0.0546 0.0553

0.0032 0.0065 0.0099 0.0134 0.0171 0.0207

0.0289 0.0276 0.0256 0.0240 0.0214 0.0196

0.0485 0.0490 0.0501 0.0503 0.0519 0.0527

0.0030 0.0061 0.0094 0.0126 0.0162 0.0197

0.0345 0.0332 0.0307 0.0299 0.0265 0.0246

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. C

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Table 4. Solubility of FeSO4·7H2O in the HCl−H2O System at the Temperature Range from 293.15 to 313.15 K and Pressure p = 0.1 MPaa m(HCl) (mol·kg−1)

m(FeSO4) (mol·kg−1) T = 293.15 K 1.7682 1.7471 1.7428 1.7272 1.7496 1.707 1.7451 1.7895 1.8378 1.9063 1.9796 T = 298.15 K 1.9758 1.9538 1.9372 1.8936 1.9138 1.8884 1.9309 1.9915 2.0568 2.1184 2.1908 T = 303.15 K 2.1936 2.1608 2.1458 2.0998 2.1178 2.1081

0.1554 0.3119 0.4682 0.6259 0.7796 1.1774 1.5602 1.9363 2.3053 2.6593 3.0023 0.1502 0.3015 0.4535 0.6091 0.7589 1.1431 1.5134 1.8727 2.2225 2.5657 2.8959

a

x(HCl)

0.1447 0.2911 0.4378 0.5883 0.7332 1.1016

m(HCl) (mol·kg−1)

x(FeSO4)

0.0027 0.0054 0.0081 0.0108 0.0134 0.0202 0.0265 0.0327 0.0386 0.0443 0.0496

0.0308 0.0303 0.0302 0.0299 0.0301 0.0292 0.0297 0.0302 0.0308 0.0317 0.0327

0.0026 0.0052 0.0078 0.0105 0.0130 0.0195 0.0257 0.0315 0.0372 0.0426 0.0478

0.0343 0.0338 0.0335 0.0326 0.0329 0.0323 0.0328 0.0335 0.0344 0.0352 0.0362

0.0025 0.0050 0.0075 0.0101 0.0126 0.0188

0.0379 0.0373 0.0369 0.0361 0.0363 0.0359

m(FeSO4) (mol·kg−1) T = 303.15 K 2.1386 2.2141 2.2813 2.336 2.4275 T = 308.15 K 2.4128 2.3845 2.374 2.3178 2.3399 2.3191 2.35 2.4399 2.4897 2.5761 2.6577 T = 313.15 K 2.6596 2.6213 2.5967 2.5664 2.5603 2.5524 2.5926 2.6745 2.7383 2.8237 2.9039

1.4611 1.8025 2.1376 2.4697 2.7765 0.1392 0.2798 0.4205 0.5664 0.7052 1.0617 1.4078 1.7314 2.0588 2.3639 2.6605 0.1330 0.2679 0.4037 0.5413 0.6774 1.0176 1.3467 1.6575 1.9649 2.2547 2.5364

x(HCl)

x(FeSO4)

0.0247 0.0303 0.0357 0.0409 0.0457

0.0362 0.0372 0.0381 0.0387 0.0400

0.0024 0.0048 0.0072 0.0097 0.0120 0.0180 0.0238 0.0290 0.0343 0.0391 0.0437

0.0416 0.0410 0.0407 0.0397 0.0400 0.0394 0.0397 0.0409 0.0415 0.0426 0.0437

0.0023 0.0046 0.0069 0.0092 0.0115 0.0172 0.0227 0.0277 0.0326 0.0372 0.0416

0.0456 0.0449 0.0444 0.0438 0.0436 0.0432 0.0436 0.0447 0.0455 0.0466 0.0476

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.

Table 5. Default MSE Middle Range Interaction Parameters Mainly Used in the FeSO4−HCl−H2O System species i

species j

BMD0

BMD1

BMD2

SO42− HSO4− Cl−

Fe2+ Fe2+ FeCl+

5.720929 −33.56567 25.50017

−0.02804112

1179.33

−0.158621

0

CMD0 0 −32.63413

CMD1 0

CMD2 0

0.08153292

Table 6. Newly Regressed MSE Middle Range Interaction Parameters species i

species j

BMD0

BMD1

BMD2

SO42− SO42− Ti(OH)2·2H2O2+ Ti(OH)2·2H2O2+ Ti(OH)2·2H2O2+ HSO4− HSO4− Cl−

Mg2+ Fe2+ Fe2+ SO42− H3O+ Cl− Fe2+ FeCl+

1812.158 88.85705 −31.71357 −1019.826 177.7287 166.6729 −14.23924 392.0615

−7.526737 −0.1716762 1.760314 −1.846117 −0.4977020 0.5062946 0.1368698 −5.172780

22343.47 −10575.28 76260.94 260265.3 140454.3 −92032.72 −20612.67 388115.8

water with specific conductivity of 0.1 μS·cm−1. Stock solutions of about 50 wt % H2SO4 and 18 wt % HCl were prepared respectively as the sources of H2SO4 and HCl used in the experiments. The accurate concentrations of the stock solutions were measured through acid−base titration method. 2.2. Determination of Solubility. The dynamic method was used to do the solubility experiments. A schematic diagram of the apparatus can be found in our earlier publications.16,17 The H2SO4−Ti(SO4)2−H2O system of known composition was placed into the 250 mL glass vessel. An airtight lid was covered to prevent

CMD0

CMD1

CMD2

3876.357

15.20705

−2148451

108.6675 −50.53186 −115.4621

0.3595983 11.48928 2.027584

200760.5 −907129.8 −16688.24

the oxidation of Fe(II). The temperature of the solution was kept constant during each experiment within ±0.1 K by circulating water bath. Some FeSO4·7H2O was weighted and added into the vessel which was agitated with a magnetic stirrer. After a while, more FeSO4·7H2O of known weight was put into the vessel if the crystals in it were found to completely dissolve. The addition process was repeated until a small amount of crystals remained in the vessel. It takes about 12 h for the systems to arrive equilibrium at each temperature. The equilibrium concentration of FeSO4 was the number of moles of FeSO4·7H2O added in the D

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Table 7. Sensibility for the MSE Middle Range Interaction Parametersa interactions SO42−−Mg2+

SO42−−Fe2+

Ti(OH)2·2H2O2+−Fe2+

Ti(OH)2·2H2O2+−SO42−

Ti(OH)2·2H2O2+−H3O+

HSO4−−Cl−

HSO4−−Fe2+

Cl−−FeCl+

a

parameters

(change objective)/(1% change in parm)

parameters

BMD0 BMD1 BMD2 BMD0 BMD1 BMD2 BMD0 BMD1 BMD2 BMD0 BMD1 BMD2 BMD0 BMD1 BMD2 BMD0 BMD1 BMD2 BMD0 BMD1 BMD2 BMD0 BMD1 BMD2

0.7383329 −0.9258228 3.0148097 × 10−2 5.077885 −2.877509 −2.062184 −0.1445902 2.304636 1.214081 8.6943681 × 10−2 4.2068568 × 10−2 −8.2939027 × 10−2 −1.325814 1.064160 −3.657407 −0.1324381 −0.1237907 0.2377448 −3.5663604 × 10−2 0.1038836 −0.1704491 −0.1270305 0.5072275 −0.4157311

CMD0 CMD1 CMD2 CMD0 CMD1 CMD2 CMD0 CMD1 CMD2 CMD0 CMD1 CMD2 CMD0 CMD1 CMD2 CMD0 CMD1 CMD2 CMD0 CMD1 CMD2 CMD0 CMD1 CMD2

(change objective)/(1% change in parm) 0.4139586 0.4904212 −0.7603559

0.2888972 0.2740060 1.864634 1.1628914 × 10−2 −0.7476449 0.7365118 0.5431339 −2.731500 0.2743370

“parm” means the values of the parameters; objective = calculated value/experimental value − 1.

solutions divided by the total mass of water in the finally equilibrated systems. All of the reagents were weighed with an electronic balance (JA5003), which precision is 1 mg.

An empirical equation can be utilized for the calculation of the solubility product of the solid as follows: log K = A +

3. THERMODYNAMIC MODELING FRAMEWORK 3.1. Chemistry of the H2SO4−FeSO4−Ti(SO4)2−H2O, H2SO4−FeSO4−MgSO4−H2O, and FeSO4−HCl−H2O Systems. For all of the systems, the MSE model was used as the modeling tool with H2O as the only solvent. In the H2SO4− FeSO4−Ti(SO4)2−H2O system, weak interactions of Fe(II) and sulfate or Ti(IV) in acidic titanyl sulfate solution are of critical importance in the sulfate process for TiO2 production.5 In ferrous chloride solutions, Fe2+ has a tendency to form complexes with chloride ions such as FeCl+ (eq 5),18,19 which is stable, that exist in the FeSO4−HCl−H2O system. The major dissolution reactions of the H2SO4−FeSO4−Ti(SO4)2−H2O, H2SO4−FeSO4−MgSO4−H2O, and FeSO4−HCl−H2O systems can be seen as follows: −

HSO4 + H 2O = SO4

2−

+

+ H3O

K (HSO−4 ) =

FeSO4 ·7H 2O(s) = Fe

+ SO4

(4)

FeCl+ = Fe 2 + + Cl−

(5)

3

4

(9)

ex GMR = −(∑ ni) ∑ ∑ xixjBij (Ix) RT i i j

7

K (FeSO4 ·7H 2O) = a Fe2+aSO4 2−aW = (m Fe2+γFe2+) 4

4

(m HSO4−γHSO −)aW

ex where GLR is the long-range interactions developed from Debye−Hückel theory; Gex SR is the contribution of the shortrange interactions from the molecule/molecule, molecule/ion, and ion/ion calculated with the UNIQUAC model; Gex MR represents ionic interactions that are excluded from the longrange term. The middle-range interaction is very important for the electrolyte solutions, and it is represented by an ionic strength-dependent symmetrical second virial coefficient-type expression:

For solid species such as FeSO4·7H2O, the equilibrium constant (solubility product) is expressed as

× (mSO4 2−γSO 2−)aW

(mSO4 2−γSO 2−)(m H3O+γH O+)

G ex G ex G ex Gex = LR + MR + SR RT RT RT RT

(3)

MgSO4 ·7H 2O(s) = Mg 2 + + SO4 2 − + 7H 2O

a HSO4−aW

=

3.2. Activity Coefficient Model. In the MSE model, the excess Gibbs free energy consists of three items:20

(1)

+ 7H 2O

aSO4 2−a H3O+

(8)

(2) 2−

(7)

where A, B, C, and D are empirical parameters and T is the absolute temperature. For aqueous species such as HSO4−, the equilibrium constant is expressed as

Ti(OH)2 (H 2O)2 2 + + H3O+ = TiOH(H 2O)33 + + H 2O 2+

B + CT + DT 2 T

(10)

where Ix represents the mole fraction-based ionic strength; Bij(Ix) is the interaction parameter for species i and j (ion or molecule). It is ionic strength-dependent and symmetric (Bij = Bji, and

7

(6) E

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in the H2SO4−Ti(SO4)2−H2O, H2SO4−MgSO4−H2O, and HCl− H2O systems are all used to regress the middle-range interaction parameters. The newly regressed parameters are shown in Table 6. The comparisons between the predictions and the experimental FeSO4·7H2O solubilities are shown in Figures 1 to 3. It can be found that the predicted values are in good agreement with the experimental solubility data with the average relative deviations of 0.4%, 1.2%, and 5.0% for the FeSO4− Ti(SO4)2−H2SO4−H2O, FeSO4−MgSO4−H2SO4−H2O, and FeSO4−HCl−H2O systems, respectively. The sensitivities of the MSE parameters are provided in Table 7. 4.5. Speciation and Activity Coefficients. To better understand the solubility curves of FeSO4·7H2O, the iron speciation and the activity coefficients of ions in the FeSO4− HCl−H2O system was calculated by the MSE model with the newly regressed parameters. Figure 4 illustrates that the mole

Bii = Bjj = 0). It can be expressed by the empirical equation as listed below: Bij (Ix) = bij + cij exp( − Ix + 0.01 )

(11)

where Bij and cij are adjustable parameters which are functions of temperature: bij = BMD0 + BMD1 × T + BMD2/T

(12)

cij = CMD0 + CMD1 × T + CMD2/T

(13)

where BMD0 to BMD2 and CMD0 to CMD2 are the middlerange activity coefficient parameters in the MSE model.

4. RESULTS AND DISCUSSION 4.1. Solubility of FeSO4·7H2O in the H2SO4−Ti(SO4)2− MgSO4−H2O System. The performance of the apparatus used to measure the solubility and the solubility determining method have been verified in our previous work.13 The solubility of FeSO4·7H2O in the Ti(SO4)2−H2SO4−H2O system with an initial H2SO4 concentration of 4.0 mol·kg−1 and Ti(SO4)2 concentration of 0.2−1.0 mol·kg−1 has been measured from 278.15 to 298.15 K. The results are illustrated in Figure 1 and listed in Table 2. It can be observed from the figure that the solubility of ferrous sulfate increases with the temperature while the concentration of Ti(SO4)2 has no significant influence on FeSO4·7H2O solubility in this system over the whole temperature range investigated. The interactions of Ti(IV) and sulfate and the hydrolysis of Ti(IV) in the solution may relieve the common ion effect of sulfate. The solubility of FeSO4·7H2O in the H2SO4−MgSO4−H2O system at 298.15−308.15 K was also measured with an initial H2SO4 concentration of 4.0 mol·kg−1 and MgSO4 concentration of 0.25−1.5 mol·kg−1. As shown in Figure 2 and Table 3, the solubility of FeSO4·7H2O increases with temperature and decreases with the concentration of MgSO4 which can be attributed to the common ion effect of sulfate. 4.2. Solubility of FeSO4·7H2O in the HCl−H2O System. Figure 3 and Table 4 present the FeSO4·7H2O solubility in HCl solution with an initial HCl concentration of 0.2−4.0 mol·kg−1 at 293.15−313.15 K. It is shown that the solubility of ferrous sulfate almost keep constant when the concentration of HCl is below about 1.5 mol·kg−1, while above this value, the solubility of FeSO4· 7H2O increases with HCl concentration. In this system, there is a tendency to form complexes such as FeCl+ and HSO4−, which make the solubility of FeSO4·7H2O much more complicated. 4.3. Evaluation of the Model. The MSE model with default parameters was evaluated by comparing the calculated solubility of FeSO4·7H2O in HCl solution with the experimental values. As shown in Figure 3, the predicted solubilities are consistent with the experimental data in diluted HCl solutions at lower temperatures, while in the solutions with higher concentration of HCl at higher temperatures, there is a more significant deviation. Limited solubility data available for the databank may be responsible for this. The default MSE middle range interaction parameters mainly used are listed in Table 5. 4.4. Model Parameterization. In order to develop a rigorous chemical model for the FeSO4−Ti(SO4)2−MgSO4− H2SO4−H2O and FeSO4−HCl−H2O systems, new interaction parameters of MSE model were determined for SO42−−Mg2+, SO 4 2−−Fe 2+ , Ti(OH) 2 ·2H 2 O 2+ −Fe 2+ , Ti(OH) 2 ·2H 2 O 2+− SO42−, Ti(OH)2·2H2O2+−H3O+, HSO4−−Cl−, HSO4−−Fe2+, and Cl−−FeCl+. The experimental solubility data of FeSO4·7H2O

Figure 4. Relative concentrations of iron species as a function of HCl concentration in the FeSO4−HCl−H2O system with the FeSO4 concentration of 1.0 mol·kg−1 at 303.15 K.

fraction of complex FeCl+ increases with the concentration of HCl at 303.15 K, and the concentration of Fe2+ decreases. Furthermore, the relative concentration of SO42− also decreases with HCl in the same system as shown in Figure 5. The decrease

Figure 5. Relative concentrations of sulfate species as a function of HCl concentration in the FeSO4−HCl−H2O system with the FeSO4 concentration of 1.0 mol·kg−1 at 303.15 K.

of Fe2+ and SO42− is beneficial for the dissolution of FeSO4. Moreover, the solubility of FeSO4·7H2O can also be influenced F

DOI: 10.1021/acs.jced.6b00783 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

(2) Gázquez, M. J.; Bolívar, J. P.; Garcia Tenorio, R.; Vaca, F. A Review of the Production Cycle of Titanium Dioxide Pigment. Mater. Sci. Appl. 2014, 5, 441−458. (3) Buxbaum, G.; Pfaff, G. Industrial inorganic pigments, 3rd ed.; WileyVCH Verlag GmbH & Co. KGaA: Weinheim, 2005. (4) Filippou, D.; Hudon, G. Iron removal and recovery in the titanium dioxide feedstock and pigment industries. JOM 2009, 61, 36−42. (5) Szilágyi, I.; Königsberger, E.; May, P. M. Characterization of Chemical Speciation of Titanyl Sulfate Solutions for Production of Titanium Dioxide Precipitates. Inorg. Chem. 2009, 48, 2200−2204. (6) Zhang, Y.; Asselin, E.; Li, Z. Solubility Measurement and Chemical Modeling of MgSO4·7H2O in the Ti(SO4)2−H2SO4−H2O System. J. Chem. Eng. Data 2016, 61, 2363−2370. (7) Tolchev, A. V.; Pervushin, V. Y.; Kleshchev, D. G. Hydrolysis of Titanium(IV) Sulfate Solutions under Hydrothermal Conditions. Russ. J. Appl. Chem. 2001, 74, 1631−1635. (8) Bullough, W.; Canning, T. A.; Strawbridge, M. I. The solubility of ferrous sulphate in aqueous solutions of sulphuric acid. J. Appl. Chem. 1952, 2, 703−707. (9) Reardon, E. J.; Beckie, R. D. Modelling chemical equilibria of acid mine-drainage: The FeSO4−H2SO4−H2O system. Geochim. Cosmochim. Acta 1987, 51, 2355−2368. (10) Filippou, D.; Demopoulos, G. P.; Papangelakis, V. G. Hydrogen ion activities and species distribution in mixed metal sulfate aqueous systems. AIChE J. 1995, 41, 171−184. (11) Kobylin, P.; Kaskiala, T.; Salminen, J. Modeling of H2SO4− FeSO4−H2O and H2SO4−Fe2(SO4)3−H2O systems for metallurgical applications. Ind. Eng. Chem. Res. 2007, 46, 2601−2608. (12) Kobylin, P. M.; Sippola, H.; Taskinen, P. A. Thermodynamic model for acidic Fe(II) sulphate from solubility data. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2012, 38, 185−193. (13) Zhang, Y.; Li, Z.; Asselin, E. Determination and chemical modeling of the solubility of FeSO4·7H2O in the Ti(SO4)2−H2SO4− H2O system. J. Chem. Thermodyn. 2016, 102, 219−227. (14) Zhong, W.; Wei, S.; Zhang, Y.; Hu, G.; Zhang, H. Circular economy model for titanium white production by sulphuric acid process. Sulphuric Acid Ind. 2010, 4, 1−5. (15) Li, Z.; Li, G. Circulation method for preparing ferrous chloride tetrahydrate, iron oxide red and sulfuric acid by using ferrous sulfate heptahydrate. CN Patent 201410023284.6, 2010. (16) Zeng, Y.; Li, Z.; Demopoulos, G. P. Determination and Modeling of the Solubility of Na2SiO3·9H2O in the NaCl−KCl−H2O System. J. Chem. Eng. Data 2014, 59, 1264−1272. (17) Zeng, Y.; Zhang, Y.; Li, Z. Measurement and Chemical Modeling of the Solubility of Na2SiO3·9H2O and Na2SiO3 in Concentrated NaOH Solution from 288 to 353 K. Ind. Eng. Chem. Res. 2014, 53, 9949−9958. (18) Bach, R. D.; Shobe, D. S.; Schlegel, H. B.; Nagel, C. J. Thermochemistry of Iron Chlorides and Their Positive and Negative Ions. J. Phys. Chem. 1996, 100, 8770−8776. (19) Fein, J. B.; Hemley, J. J.; D’Angelo, W. M.; Komninou, A.; Sverjensky, D. A. Experimental study of iron−chloride complexing in hydrothermal fluids. Geochim. Cosmochim. Acta 1992, 56, 3179−3190. (20) Wang, P.; Anderko, A.; Young, R. D. A speciation-based model for mixed-solvent electrolyte systems. Fluid Phase Equilib. 2002, 203, 141− 176.

Figure 6. Activity coefficients of species in the FeSO4−HCl−H2O system with the FeSO4 concentration of 1.0 mol·kg−1 at 303.15 K.

by the activity coefficients of ions. Figure 6 shows that both water activity and the activity coefficient of SO42− have little changes with the concentration of HCl, while the activity coefficient of Fe2+ increases with HCl concentration. This is not beneficial for the dissolution of FeSO4. Due to the two opposite effects of the factors, the solubility curves appear a trend as can be seen in Figure 3.

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CONCLUSIONS The solubility of FeSO4·7H2O was measured in the H2SO4− Ti(SO4)2−H2O, H2SO4−MgSO4−H2O, and HCl−H2O systems at temperature ranges of 278.15−313.15 K. FeSO4·7H2O solubility increases with the temperature for all of the systems, and the common ion effect in the H2SO4−FeSO4−Ti(SO4)2−H2O system was not so obvious as that in the H2SO4−FeSO4− MgSO4−H2O system due to the hydrolysis of Ti(IV) in the solution. The newly regressed middle range interaction parameters in the MSE chemical model for SO42−−Mg2+, SO42−−Fe2+, Ti(OH)2·2H2O2+−Fe2+, Ti(OH)2·2H2O2+−SO42−, Ti(OH)2· 2H2O2+−H3O+, HSO4−−Cl−, HSO4−−Fe2+, and Cl−−FeCl+ were obtained. The average relative deviations between the regressed and the experimental solubility data were less than 5.0%. The distribution and activity coefficients of aqueous species of the FeSO4−HCl−H2O system were calculated by the MSE model with the newly regressed parameters.

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AUTHOR INFORMATION

Corresponding Author

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

Zhibao Li: 0000-0002-5737-1289 Funding

The authors acknowledge the National Natural Science Foundation of China (Grants 21506218, 21476235, and U1407112) and the Science and Technology Planning Project of Qinghai Province (2012-G-213A) for financial support in this work. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Zhang, W.; Zhu, Z.; Cheng, C. Y. A literature review of titanium metallurgical processes. Hydrometallurgy 2011, 108, 177−188. G

DOI: 10.1021/acs.jced.6b00783 J. Chem. Eng. Data XXXX, XXX, XXX−XXX