solubility FESO4

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Thermodynamic model for acidic Fe(II) sulphate from solubility data

P.M. Kobylin a,n, H. Sippola a,b, P.A. Taskinen a

a Department of Materials Science and Engineering, Aalto University, FI-00076 Aalto, Finlandb FCG Finnish Consulting Group Oy, Osmontie 34, FI-00601 Helsinki, Finland

a r t i c l e i n f o

Article history:

Received 1 March 2012

Received in revised form

28 June 2012Accepted 28 June 2012Available online 31 July 2012

Keywords:

Ferrous sulphate

Solubility

Ferrous sulphate hydrates

Pitzer model

Sulphuric acid

CALPHAD method

a b s t r a c t

Acidic ferrous sulphate solutions are generated in a large scale in the hydro- and pyrometallurgical

industries. They are also produced in the steel industry and titanium dioxide production. Acid mine

drainage has long been a significant environmental problem in the coal and metal sulphide mining. The

demand of recycling and reuse of materials has increased significantly especially in EU. Dumping and

land filling a neutralised deposit is not an option anymore. Thus, efficient techniques of recycling and

reuse of sulphuric acid and/or metal sulphates from the side streams are needed.

When developing alternative solutions, a better understanding of the thermodynamic behaviour of

the FeSO4H2SO4H2O system is needed. In the present study a thermodynamic model of this system

has been developed, in order to yield a thermodynamically consistent set of values for the solubility of

iron sulphate in a wide temperature and concentration range. The current model presents the

experimental data available with a good accuracy and consistently up to 100 1C, and sulphuric acid

concentrations up to 10 mol/kg. The model also predicts well the solubility measurements available in

dilute sulphuric acid solutions at 160220 1C.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The waterferrous sulphatesulphuric acid system has been

studied due to its key importance in many hydrometallurgical

applications, which typically operate at temperatures between 50

and 300 1C. Hydrometallurgical processes such as stainless steel

pickling acid regeneration, lateritic nickel hydrometallurgy, titania

manufacturing and zinc leaching as well as acid mine drainage from

tailings ponds need internally consistent thermodynamic databases

to improve, develop and understand deeper the systems and

phenomena in the aqueous process solutions and environments.

In aqueous sulphuric acid solutions, ferrous sulphate forms

hydrates with 1, 4, 5, 6 and 7 molecules of crystalline water, with

the chemical names szomolnokite, rozenite, siderotil, ferrohex-

ahydrite and melanterite, respectively [1]. Thermodynamics ofthe H2OFeSO4H2SO4 system have been modelled earlier by

Reardon and Beckie [2], Sippola [3] and Kobylin [4], Kobylin

et al. [5] and Przepiera[6] using the Pitzer model. Those models

have also been reviewed critically in this work.

Reardon and Beckie [2] assessed the FeSO4-H2SO4H2O sys-

tem using Harvies modification of the Pitzer model for describing

activity coefficients over a temperature range from 10 to 60 1C in

the ternary system and from 10 to 90 1C for the binary FeSO4H2O. The solubility data in H2O were used to generate the

temperature dependent equations for the solubility products

(Ksp) for melanterite and szomolnokite, which were used with

the ternary solubility data to generate Pitzer parameters for the

FeSO4H2SO4H2O system. Reardon and Beckie did an iterative

regression analysis on the ternary system with the concentration

limit of the experimental data 6 mol/kg of H2SO4. They used the

sulphuric acid second dissociation constant K2 from Pitzer et al.

[7] and a different ternary Pitzer interaction parameter c(H

Fe2HSO4) than the other authors. This model is limited in

concentration and temperature range, and extrapolations using

the model fail.

Sippola [3] assessed the FeSO4H2SO4H2O system, using the

same Pitzer model version as Reardon and Beckie [2]. Instead ofusing the solubility products he used the DfH1298.15, S1298.15andCp(T)

data. Heat capacity data for melanterite were taken from Lyon and

Giauque[8], at 260.8307.67 K. Sippola estimated the heat capacity

data of the rozenite and szomolnokite from MgSO4 H2O(s) and

MgSO4 4H2O(s) using the relation Cp(FeSO4 nH2O)Cp(FeSO4)

Cp(MgSO4 nH2O)Cp(MgSO4), where n is 1 for monohydrate and

4 for tetrahydrate. He was able to reproduce the solubility of FeSO4 in

H2O and up to 6.1 mol/kg of sulphuric acid over a temperature range

of 01001C. Sippola usedc(Fe2HSO4SO4

2) ternary Pitzer para-

meter in his assessment. The parameters of Sippola have been listed

in Kobylin et al. [5]. Sippolas [3] model is extrapolating well also

outside that concentration and temperature range but his binary

Contents lists available at SciVerse ScienceDirect

journal homepage: www .elsevier.com/locate/calphad

CALPHAD: Computer Coupling of Phase Diagrams andThermochemistry

0364-5916/$- see front matter& 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.calphad.2012.06.011

n Corresponding author. Tel.: 358 50 3251489; fax: 358 94 7022798.

E-mail addresses: [email protected] (P.M. Kobylin),

[email protected] (H. Sippola),[email protected] (P.A. Taskinen).

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 185193
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FeSO4H2O system is not able to reproduce enthalpy and heat

capacity of solution data.

Kobylin [4] and Kobylin et al. [5] assessed the H2OFeSO4

H2SO4 and H2OFe2(SO4)3H2SO4 systems at 0100 1C and 25 1C,

respectively, using the original Pitzer model [1315], excluding

unsymmetrical mixing terms and following the same procedure

as in Sippola[3], and adopting the solubility data (up to 10 mol/kg

of sulphuric acid) only in the parameter optimisation. This model

presents well FeSO4 H2O(s) solubility data but is lacking accuracyfor FeSO4 7H2O at lower temperatures. As in Sippolas model,

Kobylin et al. set of Pitzer parameters in the binary FeSO4H2O

system is not able to reproduce enthalpy and heat capacity of

solution data.

Przepiera[6]assessed the H2OFeSO4H2SO4system at 0100 1C

and up to 30 mol/kg of sulphuric acid using the same Pitzer model

version as Reardon and Beckie [2] and Sippola [3]. Przerpiera

included both enthalpy of solution and solubility data in his

assessment, but the paper is lacking some thermodynamic data

and that is why Przepiera results are not recalculated in this work.

Przepiera[6] tabulated solubility data at 0, 25, 50, 80 and 100 1C

which are included inFigs. 15for comparison up to 10 mol/kg of

H2SO4. The concentration range of Przepiera[6] seems to be too

high for the Pitzer model, 30 mol/kg of sulphuric acid.

The new improved thermodynamic models of the binarysystems FeSO4H2O and H2SO4H2O have been published in

separate papers [9,10] by authors. In the FeSO4H2O study [9]

melanterite and szomolnokite were found to be stable phases with

the peritectic transition temperature at 56.5 1C. Adding sulphuric

acid to the system will decrease this temperature due to lowering

of the activity of water so that there is a peritectic point with

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Molality of H2SO4/ molkg-1

MolalityofFeSO

4

/molkg-1 FeSO47H2O

FeSO4H2O

Fig. 1. The assessed and experimental solubility data on the system H2OFeSO4H2SO4 at 0 1C.

this work; (- - -) Sippola [3]: extrapolated outside the H2SO4concentration range of the original work; (- - -) Reardon and Beckie[2]: extrapolated outside the temperature and H2SO4concentration range of the original work; (....)

Kobylin et al.[5]; ( ) Przepiera[6]; (&) Belopolskii and Urusov[23]; () Bullough et al.[24]; (J) Kobe and Fredrickson[25]; (D) Cameron[20]: data was not included in

the assessment. Transition compositions are shown as larger symbols; open and close symbols refer to FeSO4 7H2O(s) and FeSO4 H2O(s), respectively.

0.0

0.5

1.0

1.5

2.0

2.5

0 2 4 6 8 10

Molality of H2SO

4/ molkg-1

MolalityofFeSO4

/molkg-1

FeSO47H2O

FeSO4H2O

Fig. 2. The assessed and experimental solubility data on the system H2OFeSO4H2SO4 at 251C. this work; (- - -) Sippola [3]: extrapolated outside the H2SO4concentration range of the original work; (- - -) Reardon and Beckie[2]: extrapolated outside the H2SO4concentration range of the original work; (y) Kobylin et al.

[5];( )Przepiera[6]; (&) Belopolskii et al. [22]; (D) Cameron[20]: data was not included in the assesssmet; ( ) Bullough et al.[24].Transition compositions are shown

as larger symbols; open and close symbols refer to FeSO4 7H2O(s) and FeSO4 H2O(s), respectively.

P.M. Kobylin et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 185193186


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0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8 10


MolalityofFeSO4

/molkg-1

FeSO4H2O

Fig. 4. The assessed and experimental solubility data on the system H2OFeSO4H2SO4 at 801C. this work; (- - -) Sippola [3]: extrapolated outside the H2SO4concentration range of the original work; (- - -) Reardon and Beckie[2]: extrapolated outside the temperature and H2SO4concentration range of the original work; (y)

Kobylin et al.[5]; ( )Przepiera[6]; (~) Bullough et al. [24].

0.0

0.5

1.0

1.5

2.0

2.5

0 2 4 6 8 10


MolalityofFeSO4

/molk

g-1

FeSO4H2O

Fig. 5. The assessed and experimental solubility data on the system H2OFeSO4H2SO4 at 1001C.

this work; (- - -) Sippola [3]: extrapolated outside the H2SO4concentration range of the original work; (- - -) Reardon and Beckie[2]: extrapolated outside the temperature and H2SO4concentration range of the original work; (y)

Kobylin et al.[5]; ( )Przepiera[6]; (~) Bullough et al. [24]; (K) Kobe and Fredrickson [25]: data was not included in the assessment.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 2 4 6 8 10

Molality of H2SO

4/ molkg-1

MolalityofFe

SO4

/molkg-1

FeSO47H2O

FeSO4H2O

Fig. 3. The assessed and experimental solubility data on the system H2OFeSO4H2SO4at 501C. this work; (- - -) Sippola[3]: extrapolated outside the H2SO4concentration

range of the original work; (- - -) Reardon and Beckie[2]: extrapolated outside the H2SO4concentration range of the original work; (y) Kobylin et al.[5];( )Przepiera[6];

(&) Belopolskii and Shpunt[21]. Transition compositions are shown as larger symbols; open and close symbols refer to FeSO 4 7H2O(s) and FeSO4 H2O(s), respectively.

P.M. Kobylin et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 185193 187


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different compositions in each temperature from 0551C. The

FeSO4H2O system was successfully assessed from 2 to 220 1C

from pure water up to solubility limit of ferrous sulphate 3.58 mol/kg.

The H2SO4H2O system has been assessed by Sippola [10]with

the experimental EMF cell and osmotic coefficient data only, and

it is valid up to 6.1 mol/kg and over a temperature interval of

055 1C. Sippola [10] found out that four different K2 equations

for the dissociation of HSO4 are equally suitable for presenting

the H2SO4H2O system. The equation of Matsushima and Okuwaki[11]was chosen since it has been found out to be able to describe

the H2SO4FeSO4H2O system up to 100 1C[3].

The aim of this study is to compile and reassess critically the

experimental solubility observations of the FeSO4H2OH2SO4 sys-

tem at 01001C and H2SO4 concentration range up to 10 mol/kg

and test the thermodynamic description for the system up to 220 1C

to validate our previous FeSO4H2O and H2SO4H2O binary models

[9,10] with this ternary system. All experimental data used in the

modelling were taken from the literature. The resulting thermo-

dynamic model was obtained using the thermodynamic equilibrium

calculation program MTDATAs (www.mtdata-software.com), which

uses global Gibbs energy minimisation routine and includes the

Pitzer activity coefficient model for the excess Gibbs energy of the

aqueous solutions. The CALPHAD (CALculation of PHAse Diagrams)

method[12] was used in the modelling, to ensure internal consis-

tency of the thermodynamic database.

2. Modelling the aqueous solutions

The Pitzer model is one of the most used activity coefficient

models for aqueous solutions. The original approach assumes that

the aqueous solution consists only of ions, and no ion complexes

are formed. Details of the Pitzer model used are available in

[1315]. Later, Harvie and Weare [16] and Harvie et al. [17]

included unsymmetrical electrostatic mixing terms in their mod-

ification of the Pitzer model, which has been shown to improve

the fit in multicomponent systems. The values for the internalconstant parameters Harvies modification of the Pitzer equation

used in this work are shown in Table 1. All the necessary Pitzer

model equations, variables and parameters have been explained

in our previous paper[9].

2.1. Thermodynamic functions

The consistent concentration unit in aqueous solutions is

molality of FeSO4 and H2SO4 (mol/kg of water), which is used

throughout this paper. The temperature dependency equation in

MTDATAs for heat capacity of a species has the following form:

Cp A B T

K

C T

K 2

D T

K 2

, 1

and thus Gibbs energy has a temperature-dependent form

GT AG BGT

K

CG

T

K

ln

T

K

DG

T

K

2EG

T

K

3FG

T

K

1

2

The general temperature dependency available in MTDATAs

for the Pitzer equation parameter (p) is

p APitz BPitzT

K

CPitz

T

K

ln

T

K

DPitz

T

K

2

EPitzT

K

3FPitz

T

K

13

3. Experimental observations

3.1. Solubility data

Solubility measurements have been made at temperatures

ranging from 0 to 220 1C[1831]. The solubilities measured until

1958 have been reviewed by Linke and Seidell [32]. Hasegawa

et al. [31] have measured the solubilities at 1602201C. Accord-

ing to Hasegawa et al., FeSO4 H2O is the stable phase at those

temperatures.

The peritectic point, which means the condition at which the

phase transition from melanterite (FeSO4 7H2O(s)) to szomolno-

kite (FeSO4 H2O(s)) is in equilibrium with the aqueous sulphuric

acid phase, has been determined experimentally at 0, 25, 27, 40,

45 and 50 1C[20,21,24,25].

3.2. Enthalpy and heat capacity data

Przepiera et al.[33]measured enthalpies of solution at 25 1C as

a function of H2SO4 additions up to 2 mol/kg. Bhattacharyya and

Bhattacharyya [34]measured enthalpy and heat capacity of H2O

FeSO4H2SO4 solution at a temperature range of 060 1C. Agde

and Holtmann [35] determined the heat capacity of solution of

H2OFeSO4H2SO4from 2545 1C. No enthalpy and heat capacity

data were used for the ternary model in this work because the

enthalpy data have not been taken into account in the modelling

of the binary H2SO4H2O system[10].

3.3. Density of solution

Konigsberger et al.[36]measured densities of the H2OFeSO4

H2SO4 system using high-precision vibrating-tube densimetry

up to 10 mol/kg of H2SO4 at 25 1C. This data were connected to

thermodynamic functions through pressure dependency of the

Gibbs energy function and partial molal volume.

3.4. Raman spectroscopy measurements

Sobron et al. [37]measured H2OFeSO4H2SO4solutions with

Raman spectroscopy at 01.65 mol/kg of FeSO4. Concentrations of

sulphate, bisulphate and hydrogen ions have been determined in

that work.

4. Parameter optimisation

Evaluation of the thermodynamic properties of the aqueous

phase as well as the condensed ferrous sulphate hydrates was

carried out using the MTDATAs assessment module, version 4.81

and MTDATA Studio 5.03, using Harvies modification of the Pitzer

equation [16,17]. The assessment module minimises the weighted

sum of squares of errors between the measured and fitted values,

according to Eq. (4). Thus, the objective function (OF) to be

minimised in the parameter optimisation can be written as

OF Xn

i 1Wi

CiEi

Ui

2

4

Table 1

Internal parameters (b1.2) of the Pitzer model used in this work.

Parameter 1 1 , 1 2 , 1 3 and 1 4 elect rolyt e 2 2 electr olyt e

a1(kg/mol)1/2 2.0 1.4

a2(kg/mol)1/2 12



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wheren is the number of properties (data items) to be reproduced,

Ci and Ei are the calculated and experimental values of

property i ,

Ui is the uncertainty associated with value EiandWi is the weight assigned to property (data item) i.

4.1. Experimental phase equilibrium data used in the optimisation

The experimental solubility data used in the optimisation at a

temperature range of 0100 1C are shown in Table 2. The H2SO4

concentration upper limit was 10 mol/kg. Details of the experi-

mental data used have been added as supplemental material

including uncertainties of each experiment. In the earlier works

less data were used. Peritectic points and solubility measure-

ments at higher temperatures were used in the validation of the

Pitzer parameters used in this work.

All weights for experimental data were set to 1, with the

exception of rejected values, where 0 was used.

4.2. Thermodynamic data used in the optimisation

The simplified HelgesonKirkhamFlowers (HKF) model

[38,39] was used for the ions (except HSO4); see Appendix 1.

Thermodynamic data for HSO4 were calculated from SO4

2 data

and the sulphuric acid second dissociation (HSO4SO4

2H)

constant K2 value of Matsushima and Okuwaki [11], from the

equation

log10K2T,K 577:214246:01 log10T12717

T 0:283133T

1:37566 104 T2 5

Cp function of the H2O was fitted to experimental data from

the literature; see details in Kobylin et al. [9].

The thermodynamic values DfH1298.15, S1298.15 and Cp for ions

and Cp for FeSO4 7H2O(s), FeSO4 4H2O(s) and FeSO4 H2O(s)

were taken from Sippola[3]. DfH1298.15, S1298.15of FeSO4 7H2O(s),

FeSO4 4H2O(s) and FeSO4 H2O(s) at 25 1C were optimised with

the H2OFeSO4 binary system[9]. The gas phase was assumed to

be ideal.

5. Results and discussion

The temperature dependencies of the Pitzer parameters b(0),

b(1) andCf for the Fe2HSO4 binary interaction and c for Fe2

HSO4SO4

2 ternary interaction were optimised in this work

following Sippola [3]with a temperature dependency of APitz

FPitz/T. Reardon and Beckie[2] used a different set of parameters

in their model. The assessed Pitzer parameters (APitzandFPitz) are

shown inTable 3. The interaction parameters used for H2SO4H2O

Table 3

Assessed Pitzer parameters used in this work. FeSO4H2O binary parameters from

[9]were used.

APitz FPitz

b(0) 0.75865 96.8922 Fe2(aq)HSO4(aq) this work

b(1) 14.45279 5787.6144 Fe2(aq)HSO4(aq) this work

CF 0.00000 3 .2 09 7 F e2(aq)HSO4(aq) this work

b(0) 0.04083 20.4876 H(aq)SO42(aq) [10]a

CF 0.18522 42.794 H(aq)SO42(aq) [10]a

b(0) 0.02808 54.141 H(aq)HSO4(aq) [10]a

b(1) 0.00516 147.759 H(aq)HSO4(aq) [10]a

c 0.25247 71.407 Fe2(aq)HSO4(aq)SO4

2(aq) this work

a Okuwaki set A from reference [10]was used in this work.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fig. 6. The calculated solubility data on the system H2OFeSO4H2SO4at 1401C. The predictive feature of the model is demonstrated as no experimental data was used at

this temperature. this work: extrapolated outside the temperature range of the original work; (- - -) Sippola[3]: extrapolated outside the temperature range of the

original work; (- - -) Reardon and Beckie [2]: extrapolated outside the temperature range of the original work; (y) Kobylin et al. [5]: extrapolated outside the

temperature range of the original work; ( ) Bruhn et al. [40]and (~) Hasegawa et al. [31].

Table 2

The experimental data used in the assessment of the H2OFeSO4H2SO4 ternary

system. H2SO4 cut-off limit was 10 mol/kg.

Experiment Temperature 1C Dat a p oint s

Solubility of melanterite 055 109/120a [2126]

Solubility of sz omo lnokite 0100 110/153b [2125,28]

a Excluded values: Bullough et al. [24] metastable solubilities at 0451C

(7 points); Belopolskii et al. [22]values at 45 1C (4 points).b Excluded values: Bullough et al. [24] metastable solubilities at 0451C

(5 point), 7.88 and 9.45 mol/kg of H2SO4 at 251C (2 points); Kobe et al. [25]at1001C (4 points). In addition Bullough et al. [24] values were the only values

included at 601C (32 points were excluded from other authors[21,25,28]).



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binary from[10]are also shown inTable 3and FeSO4H2O binary

parameters are published in [9].

5.1. Solubility data

The solubility of FeSO4in aqueous sulphuric acid solutions was

calculated from 0 to 220 1C, using the optimised properties of this

work from 0 to 100 1C. Calculated solubilities, higher than 100 1C,are extrapolated. Figs. 18 show the solubility results together

with the experimental points (some of the experimental points

have not been included in assessment; see figure captions for

more details) at 0, 25, 50, 80, 100, 140, 160 and 220 1C, respec-

tively. Data from the earlier thermodynamic modelling studies

[2,3,5,6] have been superimposed in the figures. Model extrapola-

tions of Reardon and Beckie [2] (at 01C, above 601C and

concentrations higher than 6 mol/kg of H2SO4), Sippola[3](above

6.1 mol/kg and 100 1C) and Kobylin et al. [5] (above 100 1C) are

also shown.

FromFig. 1we can see that Reardon and Beckie[2]set of Pitzer

parameters cannot extrapolate solubilities at higher than 3.5 mol/kg

acid concentrations at 01C, and our set of Pitzer parameters is not

able to properly model the chosen data at low acid concentrations

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


MolalityofFeSO4

/molkg-1

FeSO4H2O

Fig. 7. The calculated and experimental solubility data on the system H2OFeSO4H2SO4at 1601C. this work: extrapolated outside the temperature range of the original

work; (- - -) Sippola[3]: extrapolated outside the temperature range of the original work; (- - -) Reardon and Beckie[2]: extrapolated outside the temperature range

of the original work; (y) Kobylin et al. [5]: extrapolated outside the temperature range of the original work and (~) Hasegawa et al. [31].

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


MolalityofFeSO4

/molkg-1

FeSO4H2O

Fig. 8. The calculated and experimental solubility data on the system H2OFeSO4H2SO4at 2201C. this work: extrapolated outside the temperature range of the original

work; (- - -) Sippola[3]: extrapolated outside the temperature range of the original work; (- - -) Reardon and Beckie[2]: extrapolated outside the temperature range

of the original work; (y) Kobylin et al. [5]: extrapolated outside the temperature range of the original work and (~) Hasegawa et al. [31].

Table 4

Values of the objective functions of the current set of experimental data. Columns

35 show the calculated objective functions (OF) using thermodynamic data of

other assessments and the experimental data used in this work.

This work [3] [2] [45]

Experiment OF OF OF OF

Solubility of melanterite 0501C 0.54 0.42 76.32a 4.73

Solubility of szomolnokite 01001C 0.71 1.12 8979.48b 6.66

Total fit 0.63 0.77 4548.23 5.70

a Value extrapolated outside the temperature range of the original work at 0

and 5 1C.b Value extrapolated outside the temperature and concentration range of the

original work.



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(0.13 mol/kg H2SO4). Kobylin et al. [5] set of Pitzer parameters

have problems in modelling the solubility of melanterite at 0

501C temperatures and low acid concentrations (see Figs. 13). As

can be seen inFigs. 4 and 5, the Reardon and Beckie model cannot

predict the solubilities at temperatures higher than 60 1C, while

Kobylin et al. [5], Sippola [3] and this work calculate well the

solubilities at 80 and 1001C. An interesting feature of slight

increase of solubility with increasing sulphuric acid concentration

from 0.5 to 2 mol/kg of H2SO4 can be seen inFig. 5. Przepiera[6]

set of Pitzer parameters do not really follow experimental mea-

surements and only give rough estimates of the solubility data at

temperatures other than 25 1C. This maybe due to the fact that the

data is optimised up to 30 mol/kg of H2SO4.The objective functions of the four models have been com-

pared (see Table 4). As can be seen from the table there is not

much difference between the OF value of Sippola[3] model and

that of this work (0.77 and 0.63, respectively). OF which is

calculated using Kobylin et al. [5] Pitzer parameters is also

reasonably good while the Reardon and Beckie [2] model, which

has been referred in many publications, cannot be used outside its

concentration (06 mol/kg) and temperature (10601C) range

which can be seen also from the large OF value.

The solubilities have also been calculated at 1401C where

ternary solubility data are not available (seeFig. 6). As can be seen

the binary solubility is best calculated using this work while the

values of Sippola[3], Reardon and Beckie[2]and Kobylin et al.[5]

deviate from that value. Solubility measurements by Hasegawa

Table 5

Comparison of the calculated and measured peritectic points (transition of FeSO4 7H2O(s) to FeSO4 H2O(s)) at 0,25 and 501C in the system FeSO4H2SO4 H2O.

t01C t25 1C t501C

m(H2SO4) m(FeSO4) m (H2SO4) m(FeSO4) m( H2SO4) m(FeSO4)

mo l/kg mol/kg mol/kg mo l/kg mol /kg mol /kg

7.78 0.38 5.28 1.13 1.31 2.93 This

work

7.20 0.08 5.18 1.09 1.31 2.78 [2]

8.06 0.30 5.26 1.13 0.96 2.97 [3]

8.21 0.31 5.19 1.17 0.97 3.10 [4,5]

6.79 0.38 4.60 1.14 [20]

1.38 2.85 [21]a

7.81 0.32 5.13 1.15 [24]

7.37 0.41 [25]

a According to Belopolskii and Shpunt [21] this phase transition point is

between FeSO4 4 H2O(s) and FeSO4 H2O(s).

0

50

100

150

200

250

300

0 50 100 150 200 250

Temperature / C

MassofFeSO4

dissolved/g

FeSO47H2O

FeSO4H2O

All FeSO4

0

50

100

150

200

250

300

0 50 100 150 200 250

Temperature / C

MassofFeSO4

dissol

ved/g

FeSO47H2O

FeSO4H2O

All FeSO4

Fig. 9. (a and b) Amount of FeSO4 dissolved when temperature is increased in FeSO4H2O (a) and FeSO4H2SO4H2O (b) systems. this work; (- - -) Sippola[3]; (- - -)

Reardon and Beckie[2]; (y) Kobylin et al.[5].Initial concentrations are 250 g of FeSO4per kg of H2O in both systems and H2SO4addition is 300 g in the ternary system.



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et al. [31] at 1602201C have been used for validation of the

models and this work, Sippola [3] and Kobylin et al. [5] and are

reproducing the measurements quite well up to the highest

sulphuric acid and ferrous sulphate concentrations of 0.5 and

0.58 mol/kg, respectively, while Reardon and Beckie fail in the

extrapolations (seeFigs. 7 and 8).

The peritectic point, FeSO4 7H2O(s)FeSO4 H2O(s) transition,

was calculated using the model and compared to literature

measurements to further validate different Pitzer models (seeTable 5). There is deviation in the molality of H2SO4at peritectic

points in the literature at 01C. According to Cameron [20],

molalities of H2SO4 and FeSO4 are 6.79 and 0.38 mol/kg, while

Bullough et al. [24]have 7.81 and 0.32 mol/kg, respectively. Our

calculated point 7.78 and 0.38 is between the measured values,

while Sippola [3]has molalities of 8.06 and 0.3 mol/kg that are

outside the measured values. The model of Reardon and Beckie

gives too low FeSO4 concentration of 0.08 mol/kg as also seen in

Fig. 1. All model results are rather close to Bullough et al.[24]5.13

and 1.15 mol/kg value at 25 1C while Cameron measured smaller

acid concentration 4.6 mol/kg. This work and Reardon and Beckie

values at 50 1C are close to the experimental value by Belopolskii

and Shpunt[21]while Kobylin et al. [5] and Sippola [3]models

calculate little lower acid concentrations and higher FeSO4

concentrations.

5.2. Example on how to use the model

Here it is demonstrated how this thermodynamic model can

be used in predicting the behaviour of process solution. For

example if there is process solution with 250 g FeSO4 and

1000 g of water and system is heated the dissolution of FeSO4in the solution is changed according toFig. 9a (binary system) and

b if 300 g of H2SO4is added to the solution (ternary system). Also

shown are results of other models. As can be seen the behaviour

of the solutions is different when acid is added. An interesting

feature is observed at temperatures higher than 100 1C where due

to domination of bisulphate ion addition of sulphuric acid will

increase solubility of FeSO4.

6. Conclusions

In this work, the earlier models were carefully compared for

the solubility data. The current model presents the experimental

data available with a good accuracy and consistently up to 100 1C,

and sulphuric acid concentrations up to 10 mol/kg. The model

also predicts the solubilities between 100 and 1601C, where

experimental data are not available. The solubility measurements

available in dilute solutions only by Hasegawa et al. [31]at 160

2201C, which were used for validation of this model, have beenreproduced well up to the highest sulphuric acid and ferrous

sulphate concentrations of 0.5 and 0.58 mol/kg, respectively. The

model has limitations at temperatures higher than 100 1C due to

lack of experimental data.

Due to the lack of experimental data, the heat capacity of

crystalline FeSO4 H2O(s) should be measured on a wide tem-

perature interval, preferably from 0 to 500 K. More solubility

measurements of FeSO4 in sulphuric acid solution at higher

temperatures, above 100 1C, are also needed to ensure the correct

saturation line. There is also a need to make water activity and

vapour pressure measurements at moderate to high temperatures

to improve the current model in the areas of industrial processes.

A new evaluation of the DfG1298.15, S1298.15, DfH1298.15 and Cp

values of Fe2

ion is also needed.

Acknowledgements

The authors would like to acknowledge the financial support

provided by Technology Industries of Finland Centennial Foundation.

Appendix A. Thermodynamic properties of ions

Enthalpy of formation and standard entropy of ions were taken

from the literature (seeTable A.1). The heat capacities of the ions

were estimated using a simplified HKF model. According to the

HKF model; seeTable A.2.[9,42]

Appendix B. Supplementary material

Supplementary data associated with this article can be found

in the online version at http://dx.doi.org/10.1016/j.calphad.2012.

06.011.

References

[1] B.S. Hemingway, R.R. Seal, I.-M. Chou, Thermodynamic Data for ModelingAcid Mine Drainage Problems: Compilation and Estimation of Data SelectedSoluble IronSulphate Minerals, United States Department of the Interior USGeological Survey, 2002. Open-File Report 02-161./http://pubs.usgs.gov/of/2002/of02-161/OF02-161.htmS (15.1.2011).

[2] E.J. Reardon, R.D. Beckie, Modelling chemical equilibria of acid mine-drai-nage: the FeSO4H2SO4H2O system, Geochim. Cosmochim. Acta 51 (1987)23552368.

[3] H. Sippola, Solubility of Ferrous Sulphate in Sulphuric AcidA Thermody-namic Model (in Finnish). Licentiate Thesis, Helsinki University of Technol-ogy, Department of Chemical Engineering, Espoo, Finland, 1992.

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Table A.1

The thermodynamic properties of ions at 25 1C.

Ion DfH1298.15/J mol1 S1298.15/J mol

1 K1

H(aq) 0.0 0.00 By definition

OH(aq) 230015.0 10.90 [41]

Fe2(aq) 92260.0 105.90 [42]

SO42(aq) 909340.0 18.50 [41]

HSO4(aq) 885200.0 137.50 Calculated from eq. (5)

and SO42

(aq) data

Table A.2

The temperature dependency ofCp(J/(mol K))A B(T/K) C(T/K)2 D(T/K)2 for

ions. Data of Sippola[3]; the minimum temperature of theCpfunction is 283.15 K.

Heat capacity of HSO4 ion was calculated from Eq. (5) and heat capacity of the

SO42 ion.

Ion Tmax, K A B C 103 D 105

OH(aq ) 343 .15 21 245.3 0 8 4.19 29 9 3.51 45 4083.14

448.15 5250.28 2 0.4 720 23.0421 985.66

Fe2(aq ) 328 .15 14 279.4 0 5 7.89 48 6 5.93 39 2588.70

413.15 1363.44 6.4203 8.5393 165.15

448 .15 3170.88 5.6005 0.0000 1585.87SO4

2(a q) 328 .15 462 00.60 186.8004 211.9290 8546.29

4 03 .15 1080.77 0.7188 3.9917 676.58

448 .15 58 57.7 8 10.7722 0.0000 2907.89

HSO4(aq) 3 28 .1 5 4 82 46 .0 5 197.6415 227.7310 8546.29

4 03 .15 31 26.2 2 1 1.55 99 1 1.81 03 676.58

448 .15 7903.23 2 1.61 33 1 5.80 20 2907.89

http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.calphad.2012.06.011http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.calphad.2012.06.011http://pubs.usgs.gov/of/2002/of02-161/OF02-161.htmhttp://pubs.usgs.gov/of/2002/of02-161/OF02-161.htmhttp://pubs.usgs.gov/of/2002/of02-161/OF02-161.htmhttp://pubs.usgs.gov/of/2002/of02-161/OF02-161.htmhttp://pubs.usgs.gov/of/2002/of02-161/OF02-161.htmhttp://pubs.usgs.gov/of/2002/of02-161/OF02-161.htmhttp://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.calphad.2012.06.011http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.calphad.2012.06.011


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