The effect of seawater on the thermodynamics and

Universidad de Antofagasta

Departamento de Ingeniería Química y Procesos de Minerales

Doctorado en Ingeniería de Procesos de Minerales

The effect of seawater on the thermodynamics and

crystallization of copper sulfate pentahydrate

”THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR

THE DEGREE OF DOCTOR OF MINERALS PROCESSING ENGINEERING”

Author: Francisca J. Justel Retamal

Director of thesis: Dra. María E. Taboada

Co-Director: Dr. Yecid Jiménez Bellott

October 2017

Antofagasta , Chile

ii

A mi Familia, mis padres Digna y Arturo y a mis hermanos

Pablo y Sebastián por el apoyo incondicional que me brindan…

iii

Agradecimientos

A Dios por bendecirme con perseverancia y sabiduría para alcanzar mis metas.

A mis padres Arturo Justel y Digna Retamal, y a mis hermanos por brindarme su apoyo

incondicional siempre, sobre todo durante el proceso de desarrollo de la tesis doctoral.

A mis supervisores de tesis Dra. María Elisa Taboada y Dr. Yecid Jiménez Bellott, por el

excelente trabajo de dirección, enseñanza y guía realizado en estos años.

Al Dr. Kevin Roberts, por colaborar con nosotros y recibirme 8 meses en el CDT CP3

(Centre for Doctoral Training in Complex Particulate Products and

Processes),Universidad de Leeds, para realizar la estadía de investigación.

A Diana Camacho, por su apoyo incondicional durante mi estadía de Investigación en la

Universidad de Leeds.

Al Gobierno de Chile por la beca doctoral CONICYT doctorado Nacional, Año académico

2013. Nro. 21130894 que ayudó a financiar mis estudios doctorales y al Proyecto Fondecyt

1140169 por el financiamiento de la presente investigación.

A mi querida Elsita por ayudarme en la parte experimental de mi tesis y cada vez que lo

necesité.

A mis amigos, por la compañía y apoyo durante estos años de tesis doctoral.

A todos mis compañeros y profesores del Programa de Doctorado en Ingeniería de

Procesos de Minerales de la Universidad de Antofagasta por los buenos momentos

compartidos y las enseñanzas entregadas.

iv

RESUMEN

En la presente tesis doctoral, se determinó la influencia del agua de mar en el equilibrio

sólido-líquido de soluciones ácidas de sulfato de cobre a diferentes temperaturas (293.15 a

333.15 K) y su efecto sobre las propiedades físicas (densidad, viscosidad y actividad

termodinámica del agua).

La representación termodinámica del equilibrio sólido-líquido del sistema de sulfato de

cobre - ácido sulfúrico - agua de mar se llevó a cabo utilizando una metodología simple

reportada en la literatura a la que se le realizaron algunas modificaciones. Fue utilizado el

modelo de Pitzer y una ecuación tipo Born para modelar el sulfato de cobre y ácido

sulfúrico, respectivamente, además, el agua de mar fue considerada como solvente. Esta

metodología permitió determinar las cantidades de sulfato de cobre precipitadas y el

rendimiento óptimo en función de la concentración de ácido sulfúrico.

A su vez, se realizó un estudio termodinámico del sistema Cu-Na-H-SO4-Cl-HSO4-H2O

utilizando el modelo de Pitzer en el intervalo de temperatura de 293.15 a 333.15 K para

representar el equilibrio sólido-líquido del sistema sulfato de cobre-ácido sulfúrico- agua de

mar y se determinaron nuevos parámetros binarios y ternarios de Pitzer en un amplio rango

de temperaturas, los que pueden ser utilizados para predecir las solubilidades de otros

sistemas sólido-líquido en los que estén implicados los iones Cu2+

, Na+, H

+, SO4

2-, Cl

-,

HSO4- y H2O.

Además, con el fin de determinar el efecto de los principales iones presentes en el agua de

mar (Na+ y Cl

-) en el proceso de cristalización, se evaluó el efecto del cloruro de sodio en la

forma, tamaño, composición y cinética de crecimiento de los cristales de sulfato de cobre

pentahidratado, y se realizaron comparaciones con resultados en agua fresca, donde se

concluye que los cristales obtenidos en los medios con cloruro de sodio, son más grandes y

prismáticos con respecto a los obtenidos en agua fresca. Este comportamiento se atribuye

principalmente a la cinética de crecimiento; debido a que las tasas de crecimiento de las

caras (1-10) y (1-1-1) se ven afectadas cuando el cloruro de sodio está presente en la

solución, especialmente en el caso de la cara (1-10), donde se observa un cambio en el

mecanismo de crecimiento.

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ABSTRACT

In this doctoral thesis, the influence of seawater on the solid–liquid equilibrium in acidic

solutions of copper sulfate at different temperatures (293.15 to 333.15 K), and its effect on

physical properties (density, viscosity, and thermodynamic water activity) was determined.

The thermodynamic representation of the solid–liquid equilibrium of the copper sulfate–

sulfuric acid–seawater system was carried out using a simple methodology reported in the

literature with some modifications, where the Pitzer model and a Born-type equation were

used for modeling the copper sulfate and sulfuric acid effects, respectively, and the

seawater was considered as a solvent. The amounts of copper sulfate precipitated and the

optimum yield as a function of the sulfuric acid concentration were estimated.

Additionally, a thermodynamic study of the Cu-Na-H-SO4-Cl-HSO4-H2O system using the

Pitzer model in the temperature range of 293.15 to 333.15 K was performed to represent the

solid–liquid equilibrium of the copper sulfate–sulfuric acid–seawater system, where new

binary and ternary Pitzer parameters in a wide temperature range were determined; these

can be used to predict solubilities of other solid-liquid systems where the Cu2+

, Na+, H

+,

SO42-

, Cl-, HSO4

-, and H2O ions are involved.

Furthermore, in order to understand the effect of the principal ions present in seawater (Na+

and Cl-) in the crystallization process, the effect of sodium chloride on the shape, size,

composition, and growth kinetics of copper sulfate pentahydrate crystals was evaluated and

compared with results in freshwater; and it is concluded that crystals grown in sodium

chloride media are larger and more prismatic than those grown in H2O. This behavior is

mainly attributed to the growth kinetics because growth rates of both the (1-10) and (1-1-1)

faces are affected when sodium chloride is present in the solution, especially in the case of

the (1-10) face, where a change in the growth mechanism is observed.

vi

THESIS ORGANIZATION

This thesis consists of six chapters with their respective references; moreover, an

Appendices section is included at the end, where additional information along with a

summary of the publications and different works presented at several national and

international conferences is presented.

Chapter I presents the introduction and background to the study, highlighting the research

problematic, hypotheses, and the objectives.

Chapter II describes the influence of seawater on the solid–liquid equilibrium for acid

solutions of copper sulfate in the temperature range of 293.15 to 318.15 K, and its effect on

the physical properties of density and viscosity. This work was performed in order to gain a

better knowledge of the design of copper sulfate pentahydrate crystallization plants using

seawater by means of the addition of sulfuric acid. This work, entitled ‘Solubilities and

physical properties of saturated solutions in the copper sulfate + sulfuric acid + seawater

system at different temperatures’ was published in the Brazilian Journal of Chemical

Engineering, Vol. 32 (2015) 629-635.

Chapter III presents the experimental determination of the solubilities and water activities

for aqueous solutions of copper sulfate in seawater at different temperatures (from 293.15

to 333.15 K), to represent the solid–liquid equilibrium of a copper sulfate–sulfuric acid–

seawater system. The thermodynamic representation of the phase equilibrium was based on

a simple methodology reported in the literature, which also allowed the estimation of the

amounts of copper sulfate precipitated and the optimum yield as a function of the sulfuric

acid concentration. This work, entitled ‘Solid–liquid equilibrium and copper sulfate

crystallization process design from a sulfuric acid–seawater system in the temperature

range from 293.15 to 333.15 K has been published in the Industrial and Engineering

Chemistry Research Journal, Vol. 56 (2017) 4477-4487.

Chapter IV presents the determination of water activities for aqueous solutions of copper

sulfate, where these values, along with the Pitzer ion-interaction model, were used to

represent the solid–liquid equilibrium of the copper sulfate-sulfuric acid-seawater system

vii

over a wide temperature range. This representation was performed through the

thermodynamic study of the Cu-Na-H-SO4-Cl-HSO4-H2O system. This work, entitled

‘Thermodynamic study of the Cu-Na-H-SO4-Cl-HSO4-H2O system for the solubility of

copper sulfate in acid seawater at different temperatures’ has been accepted for publication

in the Journal of Molecular Liquids.

Chapter V describes the effect of sodium chloride on the shape, size, composition, and

growth kinetics of copper sulfate pentahydrate crystals, in order to understand the effect on

the crystallization process of the principal ions present in seawater (Na+ and Cl

-). This

work, entitled ‘Sodium chloride effect in the copper sulfate pentahydrate crystallization’

has been submitted for publication in the Journal of Crystal Growth.

Chapter VI presents the main conclusions of this work, and makes some recommendations

for future works.

viii

CONTENTS

CHAPTER I 1

GENERALITIES 1

1. INTRODUCTION 1

2. PROBLEMATIC, HYPOTHESES, AND OBJECTIVES 2

2.1 Problematic 2

2.2 Hypotheses 3

2.3 Objectives 4

2.3.1 General objective 4

2.3.2 Specific objectives 4

CHAPTER II 5

STATE OF THE ART 5

1. THE USE OF SEAWATER IN MINING 5

1.1 Introduction 5

1.2 Characteristics of seawater 6

1.3 Consumption of seawater in Chile 8

1.4 Physicochemical properties of seawater 9

2. COPPER SULFATE PENTAHYDRATE 15

2.1 Characteristics and properties 15

2.2 Industrial process of copper sulfate pentahydrate crystallization 16

2.3 Solubilities and physical properties of the copper sulfate-sulfuric acid-water system.

20

2.4 Copper sulfate pentahydrate crystallization. 21

3. CRYSTALLIZATION PROCESS AND CRYSTALLIZATION KINETICS 26

3.1 Sodium chloride effect in crystallization 26

3.2 Growth kinetics of single crystals and Crystal growth mechanisms 27

4. SOLID-LIQUID EQUILIBRIUM MODELING. 29

4.1 Models for electrolyte solutions 29

4.2 Pitzer model applied to the thermodynamics of natural water and copper sulfate. 33

4.2.1 Thermodynamics of natural water systems using the Pitzer model. 33

4.2.2 Thermodynamic properties of copper sulfate solutions 35

4.2.3 Pitzer ion-interaction model applied to the CuSO4-H2SO4-H2O system 36

4.2.4 Thermodynamics of multicomponent solutions involving sodium and copper

chlorides and sulfates. 38

5. REFERENCES 41

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CHAPTER III 49

SOLUBILITIES AND PHYSICAL PROPERTIES OF SATURATED SOLUTIONS IN

THE COPPER SULFATE + SULFURIC ACID + SEAWATER SYSTEM AT

DIFFERENT TEMPERATURES 49

ABSTRACT 49

INTRODUCTION 50

MATERIALS AND METHODS 51

2.1 Reagents 51

2.2 Apparatus 51

2.3 Procedures 52

2.3.1 Equilibrium time determination 52

2.3.2 Measurement of physical properties in different conditions 52

3. RESULTS AND DISCUSSION 53

3.1 Experimental results 53

3.1.1 Solubilities 55

3.1.2 Physical properties 55

4. CONCLUSIONS 64

5. REFERENCES 65

CHAPTER IV 67

SOLID–LIQUID EQUILIBRIUM AND COPPER SULFATE CRYSTALLIZATION

PROCESS DESIGN FROM A SULFURIC-ACID–SEAWATER SYSTEM IN THE

TEMPERATURE RANGE FROM 293.15 TO 333.15 K. 67

ABSTRACT 67

1. INTRODUCTION 68

2. EXPERIMENTAL SECTION 70

2.1 Materials 70

2.2 Apparatus and Procedures 71

2.2.1 Solubility measurements for the CuSO4–H2SO4–seawater system at 323.15 and

333.15 K 71

2.2.2 X-ray diffraction and thermogravimetric analysis of copper sulfate crystals 72

2.2.3 Water activity measurements of CuSO4 in seawater at different temperatures 72

3. THERMODYNAMIC FRAMEWORK 73


4.1 Solubilities of copper sulfate in acidic seawater at different temperatures 76

4.2 Solids analysis: X-ray diffraction and thermogravimetric analysis 78

4.3 Water activities of the copper-sulfate–seawater system at different temperatures 81

4.4 Determination of the Pitzer parameters βMX(0)

, βMX(1)

, βMX(2)

, and CMX(ϕ)

for copper

sulfate in seawater at different temperatures 84

x

4.5 Solubility products of copper sulfate pentahydrate in seawater at different

temperatures 85

4.6 Representation of the solid–liquid equilibrium 86

4.6.1 Experimental and calculated solubility isotherms of the CuSO4–H2SO4–

seawater system at different temperatures 86

4.7 Predictions of precipitated amounts and yield of copper sulfate 87

4.8 Conceptual design of the copper sulfate crystallization process by means of the

addition of sulfuric acid using the phase diagram 90

5. CONCLUSIONS 94

6. REFERENCES 95

CHAPTER V 98

THERMODYNAMIC STUDY OF THE Cu-Na-H-SO4-Cl-HSO4-H2O SYSTEM FOR

THE SOLUBILITY OF COPPER SULFATE IN ACID SEAWATER AT DIFFERENT

TEMPERATURES 98

ABSTRACT 98

1. INTRODUCTION 99

2. EXPERIMENTAL SECTION 101

2.1 MATERIALS 101

2.2 APPARATUS AND PROCEDURES 101

2.2.1 Water activity measurements of CuSO4 in H2O at different temperatures 101

3. THERMODYNAMIC FRAMEWORK. 102

3.1 The ion-interaction model 102

3.2 Ion-interaction parameters in binary aqueous solutions 106

3.3 Ion-mixing interaction parameters in ternary solutions 108


4.1 Water activities of aqueous CuSO4 solutions at different temperatures. 112

4.2 Determination of the Pitzer parameters 𝛽MX(0)

, 𝛽𝑀𝑋(1)

, 𝛽𝑀𝑋(2)

, and 𝐶𝑀𝑋(𝜙)

for CuSO4, CuCl2,

and Cu(HSO4)2 at different temperatures. 114

4.3 Ternary mixing parameters at different temperatures. 118

4.4 Solubility products of copper sulfate pentahydrate at different temperatures 119

4.5 Representation of the solid-liquid equilibrium of the CuSO4 - H2SO4 - seawater

system at six different temperatures. 120

5. CONCLUSIONS 123

6. REFERENCES 124

CHAPTER VI 128

CRYSTALLIZATION OF COPPER SULFATE PENTAHYDRATE IN ABSENCE AND

PRESENCE OF SODIUM CHLORIDE 128

ABSTRACT 128

1. INTRODUCTION 129

xi

2. MATERIALS AND METHODS 132

2.1 Materials 132

2.2 Equipment and experimental procedure 132

2.2.1 Solubilities measurements of copper sulfate in aqueous solutions and in 2.4 wt

% sodium chloride media. 132

2.2.2 Crystallization experiments. 132

2.2.3 Thermal Analysis (TGA/DSC) and Chemical Analysis 134

2.2.4 Crystal Growth measurements by In-situ Microscopy 134

2.2.5 Determination of activity coefficients for the assessment of ion interactions of

copper sulfate in aqueous solutions and sodium chloride media 136

2.2.6 Assessment of crystals single faces growth kinetics 138

2.2.7 Crystal faces indexation 138

3 RESULTS AND DISCUSSION 139

3.1 Solubilities of copper sulfate in aqueous solutions and in 2.4 wt % sodium chloride

media. 139

3.2 Crystallization and dissolution temperatures of the CuSO4 + H2O and CuSO4 +

NaCl + H2O systems at different cooling rates. 144

3.3 On-line Visualization and Particle size analysis of copper sulfate crystals at

different cooling rates. 146

3.4 Solid-state characterization 150

3.5 Copper sulfate pentahydrate crystals faces indexation 151

3.6 Mean Growth rates and growth rates mechanism of the (1-10) and (1-1-1) faces of

copper sulfate pentahydrate crystals as a function of the growth environment 152

4. CONCLUSIONS 161

5. REFERENCES 163

CHAPTER VII 168

GENERAL CONCLUSIONS AND RECOMMENDATIONS 168

1. GENERAL CONCLUSIONS FOR THIS STUDY 168

2. RECOMMENDATIONS FOR FUTURE WORK 173

APPENDICES SECTION 175

Abstract 175

1. Sequence of images of copper sulfate pentahydrate crystals growing in H2O and 2.4 wt

% NaCl media at different supersaturations. 176

2. Fits of the Power law, B&S and BCF growth models for both the (1-10) and (1-1-1)

faces for copper sulfate pentahydrate grown in H2O and NaCl media. 178

3. Summary of the different works presented at the national and international

conferences

180

4. Published works from the present doctoral thesis 189

xii

LIST OF TABLES

CHAPTER II

Table 1. Examples of seawater use in mining [6]................................................................... 6

Table 2. Reference composition of seawater [8]. ................................................................... 7

Table 3. Mining operations that use seawater in Chile [9]. .................................................... 8

CHAPTER III

Table 1. Individual ions in seawater from Bahia San Jorge, Chile (mg·L−1

) [4]. ................ 51

Table 2. Solubility (wCuSO4), density (ρ), and viscosity (η) for saturated solutions of

copper sulfate in seawater at various acid concentrations and temperatures. ...................... 54

Table 3. Parameters values for density, viscosity and solubility for saturated copper sulfate

in acidic seawater system. .................................................................................................... 56

Table 4. Parameter values for density and solubility for saturated copper sulfate in acidic

seawater system. ................................................................................................................... 61

CHAPTER IV

Table 1. Chemical composition of synthetic seawater obtained from the literature [15]. .... 70

Table 2. Synthetic seawater densities (g/cm3) at different temperatures. ............................. 71

Table 3. Solubilities for saturated solutions of copper sulfate in acidic seawater from 293.15

to 318.15 K at different acid concentrations obtained in a previous work [12]. .................. 76

Table 4. Solubilities and densities for saturated solutions of copper sulfate in acidic

seawater at 323.15 and 333.15 K at different acid concentrations obtained in the present

work. ..................................................................................................................................... 77

Table 5. Experimental and calculated water activities (aw) at different molalities of CuSO4

in seawater and at five different temperatures. ..................................................................... 82

Table 6. Pitzer parameters of copper sulfate in seawater within the temperature range of

293.15 to 323.15 K. .............................................................................................................. 84

Table 7. Solubility products and activity coefficient values at different temperatures and

copper sulfate concentrations. .............................................................................................. 85

Table 8. 𝐴∅ values for copper sulfate in seawater media at different temperatures. ............ 86

Table 9. Parameter values of the Born-type empirical equation. ......................................... 86

Table 10. Optimum values of 𝑤 and 𝑌 for the CuSO4–H2SO4–seawater system at the six

different temperatures. .......................................................................................................... 90

Table 11. Compositions of the input and output currents at 298.15 and 323.15 K. ............. 92

CHAPTER V

Table 1. Parameters for Equation (22) [20]. ....................................................................... 106

xiii

Table 2. Pitzer binary parameters (𝛽𝑀𝑋(0)

, 𝛽𝑀𝑋(1)

, 𝛽𝑀𝑋(2)


) for CuSO4 and CuCl2 at

298.15 K. ............................................................................................................................ 107

Table 3. Pitzer binary parameters (𝛽𝑀𝑋(0)

, 𝛽𝑀𝑋(1)

, 𝛽𝑀𝑋(2)


) for Na2SO4, NaCl, NaHSO4,

HSO4-, HCl, and H2SO4 at six different temperatures. ....................................................... 108

Table 4. 𝜃𝑖𝑗 parameter values used in the present work. .................................................... 109

Table 5. Calculated 𝜓𝑖𝑗𝑘 values using the temperature dependence model from Christov

and Moller. ......................................................................................................................... 111

Table 6. Experimental water activities (aw) at different molalities of CuSO4 and

temperatures........................................................................................................................ 112

Table 7. Pitzer parameters within the temperature range of 293.15 to 323.15 K for CuSO4,

and from 293.15 to 333.15 K for CuCl2, and Cu(HSO4)2. ................................................. 116

Table 8. Values of activity coefficients, water activities, and solubility products at different

copper sulfate concentrations and temperatures. ................................................................ 119

CHAPTER VI

Table 1. Binary Pitzer parameters for copper sulfate solutions in H2O and NaCl media. . 137

Table 2. Experimental solubility and density data of copper sulfate in sodium chloride

media at different temperatures. ......................................................................................... 140

Table 3. Crystallization and dissolution temperatures of the CuSO4 + H2O and CuSO4 +

NaCl + H2O systems at different cooling rates. ................................................................. 144

Table 4. Percentage copper sulfate crystals in three different size ranges at different cooling

rates. .................................................................................................................................... 149

Table 5. Chemical Analysis of CuSO4·5H2O crystals obtained at 1°C/min in NaCl media.

............................................................................................................................................ 151

Table 6. Experimental mean growth rates of (1-10) and (1-1-1) faces of copper sulfate

pentahydrate crystals growing from H2O and 2.4 wt % NaCl media. ................................ 154

Table 7. Crystal growth kinetics parameters obtained from the best fit of the models given

by the Equations (6) and (8) to the experimental 𝐺𝜎 data. ................................................. 158

APPENDICES

Table 4. Crystal growth kinetics parameters obtained from the fit of the Power Law, B&S

and BCF models to the experimental 𝐺𝜎 data. ................................................................... 179

xiv

LIST OF FIGURES

CHAPTER II

Figure 1. Percentage of seawater use of each operation [9]. .................................................. 9

Figure 2. Scheme of the copper sulfate pentahydrate crystallization process. ..................... 16

Figure 3. Industrial copper sulfate pentahydrate crystallization process [33]. .................... 18

Figure 4. Copper sulfate pentahydrate dissolution and re-crystallization processes [33]. ... 19

CHAPTER III

Figure 1. Solubility for the saturated solutions (CuSO4 + acid seawater): ■, 293.15; ♦,

298.15 K; ▲, 308.15 K; ●, 318.15 K; ─, correlations with Eq. (1). .................................... 57

Figure 2. Density for the saturated solutions (CuSO4 + acid seawater): ■, 293.15 K; ♦,


Figure 3. Viscosity for the saturated solutions (CuSO4 + acid seawater): ■, 293.15 K; ♦,







298.15 K; ▲, 308.15 K; ●, 318.15 K. Black lines show freshwater data at different

temperatures from the work of Milligan and Moyer [5]. ..................................................... 63

CHAPTER IV

Figure 1. Solubility of saturated solutions of CuSO4–H2SO4–seawater. ■ = 293.15 K; ♦ =

298.15 K; ▲ = 308.15 K; ● = 318.15 K; × = 323.15 K; * = 333.15 K; Solid line: correlated

data; Dashed line: data predicted by the methodology proposed in this work. .................... 78

Figure 2. XRD patterns of copper sulfate samples obtained at three different temperatures:

a) 293.15 K, b) 308.15 K, and c) 323.15 K. Black and red lines correspond to the standard

patterns and samples, respectively. ...................................................................................... 80

Figure 3. Thermal decomposition curve of copper sulfate pentahydrate crystals obtained

from a CuSO4–H2SO4–seawater solution at 308.15 K. ........................................................ 81

Figure 4. Comparison between the experimental and literature data of water activities of

CuSO4 in seawater and freshwater at 298.15 and 323.15 K: ● and ♦ correspond to the water

activities at 323.15 and 298.15 K, respectively; Solid line: CuSO4–freshwater [10, 11];

Dashed line: CuSO4–seawater [present work]...................................................................... 83

Figure 5. Predicted amounts of copper sulfate pentahydrate precipitated versus sulfuric acid

weight percent at two different temperatures. ♦ and × correspond to the predicted data at

298.15 and 323.15 K, respectively. ...................................................................................... 88

xv

Figure 6. Solubility diagram of CuSO4–H2SO4–seawater system at 298.15 K (♦) and 323.15

K (×). .................................................................................................................................... 91

Figure 7. Process flow sheet of the copper sulfate crystallization process using sulfuric acid.

.............................................................................................................................................. 92

Figure 8. Amount of CuSO4·5H2O precipitated versus sulfuric acid weight percent. Solid

and dashed lines represent the analytical method while the symbols ♦ and × represent the

graph method at 298.15 and 323.15 K, respectively. ........................................................... 93

CHAPTER V

Figure 1. Comparison between the experimental and literature data of the water activities of

CuSO4 in H2O at 298.15 and 323.15 K. ●, CuSO4 - H2O at 323.15 K [this work]; ▲,

CuSO4 - H2O at 298.15 K [this work]; , CuSO4 - H2O at 323.15 K [26]; ---, CuSO4 - H2O

at 298.15 K [19]. ................................................................................................................. 113

Figure 2. a) CuSO4, b) CuCl2, and c) Cu(HSO4)2 activity coefficients at different salt

concentrations: ■, 293.15 K; ♦, 298.15 K; ▲, 308.15 K; ●, 318.15 K; ×, 323.15 K; ,

333.15 K; ---, predicted data; , values from Christov [13] at 298.15 K. .......................... 117

Figure 3. Solubility of saturated solutions of CuSO4 - H2SO4 – seawater system. ■, 293.15

K; ♦, 298.15 K; ▲, 308.15 K; ●, 318.15 K; ×, 323.15 K; *, 333.15 K; − correlated data; ---,

correlated data using predicted Pitzer parameters for CuSO4 at 333.15 K......................... 121

CHAPTER VI

Figure1. Habit of CuSO4·5H2O crystal [6]. ........................................................................ 129

Figure 2. Experimental set up for crystal growth rates measurements. (a) Olympus BX51

optical DIC microscope integrated with QImaging/QICAM camera. (b) Picture of the

crystal growth cell. ............................................................................................................. 135

Figure 3. Example of measurement from the centre of the copper sulfate crystal to the

faces. The distances are obtained by drawing a perpendicular line to each face from the

centre of the crystal using QCapture Pro software. ............................................................ 136

Figure 4. Activity coefficients of CuSO4 in H2O solutions at different salt concentrations:

■, 293.15 K; ▲, 303.15 K; ●, 313.15 K; ×, 323.15 K; , 333.15 K. ................................ 141

Figure 5. Activity coefficients of CuSO4 in 2.4 wt % NaCl solutions at different salt

concentrations: ■, 293.15 K; ▲, 303.15 K; ●, 313.15 K; ×, 323.15 K; , 333.15 K. ...... 141

Figure 6. Activity coefficients comparison between CuSO4 solutions in (■) H2O and (♦) 2.4

wt % NaCl as a function of the concentration at five different temperatures (293.15, 303.15,

313.15, 323.15, and 333.15 K). .......................................................................................... 143

Figure 7. Plot of the crystallization (-) and dissolution (---) temperatures for 29.52 wt %

CuSO4 solutions in different media: (●) H2O and (■) 2.4 wt % NaCl, as a function of

solution cooling rate. .......................................................................................................... 145

xvi

Figure 8. Sequence of pictures of copper sulfate crystals in H2O at different cooling rates.

............................................................................................................................................ 147

Figure 9. Sequence of pictures of copper sulfate crystals in 2.4 wt % NaCl media at

different cooling rates. ........................................................................................................ 148

Figure 10. a) TGA and b) DSC curves for copper sulfate pentahydrate crystals obtained at

1°C/min in H2O and NaCl media. ...................................................................................... 150

Figure 11. a) Prediction of the BFDH morphology of copper sulfate pentahydrate crystals

using the Miller indices in the obtained unique solutions and comparison with the crystal

micrograph obtained experimentally. b) and c) Enlarged pictures of copper sulfate

pentahydrate crystals obtained in aqueous solutions and sodium chloride media,

respectively, from Avantium Crystalline® system. ............................................................ 152

Figure 12. Series of optical micrographs of copper sulfate crystals grown in: a) H2O at σ =

0.682 and σ = 0.787, and b) 2.4 wt % NaCl at σ = 0.348 and σ = 0.458 at the 0.5 ml scale

size showing the growth of the crystals and their morphology as a function of media,

elapsed time, and supersaturation. Black line in the picture represents the scale bar of 100

µm. ...................................................................................................................................... 153

Figure 13. Copper sulfate crystals growing from H2O media. For each set of four plots, a)

𝐺𝜎 experimental data fitted to the Power law and BCF models; b) trend of the total

resistance to mass transfer as a function of ∆𝐶 using the parameters obtained from the data

fitting to these models. The dotted red line shows the trend of the ratio of the resistance to

mass transfer in the bulk to the total mass transfer resistance. Left (♦) refers to the (1-10)

and right (■) to the (1-1-1) faces respectively. ................................................................... 155

Figure 14. Copper sulfate crystals growing from 2.4 wt % NaCl media. For each set of four

plots, a) 𝐺𝜎 experimental data fitted to the BCF model; b) trend of the total resistance to

mass transfer as a function of ∆𝐶 using the parameters obtained from the data fitting to

these models. The dotted red line shows the trend of the ratio of the resistance to mass

transfer in the bulk to the total mass transfer resistance. Left (♦) refers to the (1-10) and

right (■) to the (1-1-1) faces, respectively. ......................................................................... 156

Figure 15. Sodium chloride effect in the a) (1-10) and b) (1-1-1) crystal faces of copper

sulfate pentahydrate. Extrapolated data are given by the black and dotted lines representing

the best fit of the data through the Power law and BCF models, respectively. .................. 160

APPENDICES

Figure 1. Series of optical micrographs of copper sulfate crystals grown in H2O in the

supersaturation range from σ = 0.682 to σ = 0.787 at the 0.5 ml scale size showing the

growth of the crystals and their morphology as a function of elapsed time and

supersaturation. Black line in the picture represents the scale bar of 100 µm. .................. 176

Figure 2. Series of optical micrographs of copper sulfate crystals grown in NaCl media in

the supersaturation range from σ = 0.348 to σ = 0.458 at the 0.5 ml scale size showing the

xvii


supersaturation. Black line in the picture represents the scale bar of 100 µm. .................. 177

Figure 3. 𝐺𝜎 experimental data of copper sulfate pentahydrate grown in a) H2O and b)

NaCl media fitted to the Power law, B&S and BCF models. Left (♦) refers to the (1-10) and

right (■) to the (1-1-1) faces respectively. .......................................................................... 178

xviii

LIST OF SYMBOLS

𝐴∅ Debye-Hückel term

𝑏 Constant used in the Pitzer model

𝐴, 𝐵, 𝐶, and 𝐷 Fitting parameters for density, viscosity and solubility

𝑎, 𝑏, 𝑎𝑛𝑑 𝑐 Unit cell parameters

𝑎𝑤 Water activities

𝑎, 𝑏, 𝑐 and 𝑑 Parameter values of the Born-type empirical equation

𝐴1 Growth parameter in B&S model

𝐴2 Growth parameter in the BCF model

𝑏 Constant of the Pitzer model

𝐶∅ Solute-specific interaction parameter of the Pitzer model

𝑏 Dimensionless thermodynamic parameter

𝐶𝑒 Equilibrium concentration (𝑚−3)

∆𝐶 Driving force

𝑒 Electron charge (1.6022∙10-19

)

E𝜃𝑀𝑋 and E𝜃′𝑀𝑋

Higher-order electrostatic terms

𝑓𝛾, 𝐵𝛾, 𝐶𝛾 Ion-interaction parameters of the Pitzer model

𝐹1, 𝐹2, 𝐹3 and 𝐹4 Input and output currents in the crystallizer

𝐺 Single face growth rate (𝑚 · 𝑠−1)

𝐺𝑒𝑥 𝑅𝑇⁄ Excess free energy

𝐼 Ionic strength

𝑘 Boltzmann constant (1.38066∙10-23

),

𝐾𝑠𝑝 Solubility product

xix

𝑘𝐺 Growth rate constant (m(1

𝑚)𝑠−1)

𝑘𝑀𝑇 Mass transfer coefficient (𝑚 · 𝑠−1)

1

𝐾𝑀𝑇𝑂𝑇 Trend of the total resistance to transfer of growth units

𝑚 Molality

𝑚0 Molality in the initial saturated solution

𝑁0 Avogadro number (6.022045∙1023

)

𝑛𝑤 Number of kilograms of solvent

𝑅 Gas constant (8.314 J·mol-1

·K-1

).

𝑟 Growth exponent

𝑇 Solution temperature (𝐾)

𝑇𝑐𝑟𝑦𝑠𝑡 Crystallization temperature (𝐾)

𝑇𝑑𝑖𝑠𝑠 Equilibrium dissolution temperature (𝐾)

𝑢 Standard uncertainties

𝑣 Stoichiometric coefficient

𝑤 Mass fraction

𝑋 Precipitated amount (in mol/Kg)

X Mass percentage of H2SO4 in solution

𝑌 Yield

Y Mass percentage of CuSO4·5H2O in saturated solution

𝑌0 Mass percentage of CuSO4·5H2O in saturated solution with no acid content

𝑧 Charge of ion

xx

Greek Letters

𝛼1 , 𝛼2 Constants used in the Pitzer model

𝛽(0), 𝛽(1), 𝛽(2) Solute-specific interaction parameters of the Pitzer model

𝛼, 𝛽, and 𝛾 Unit cell parameters

Ɛ Dielectric constant of seawater

𝜀0 Vacuum permittivity (C2·J

-1·m

-1)

𝜀𝑟 Relative permittivity of the solution

𝛾± Mean activity coefficient of ions in the solution

𝜌 Density in g·cm-3

𝜂 Viscosity in mPa·s

𝜓𝑖𝑗𝑘 Ion-mixing interaction parameters

𝜇𝑖𝑗𝑘 Third virial coefficients

𝜙 Osmotic coefficient

𝜆𝑖𝑗 , 𝛷𝑖𝑗 Second virial coefficients

𝜃𝑀𝑋 Single parameter for each pair of cations or anions

𝜎 Relative supersaturation

𝜎𝑐𝑟𝑖𝑡 Critical relative supersaturation

Subscripts

𝑖, 𝑗, and 𝑘 Solute species

𝐵 Binary system

𝑇 Ternary system

𝑒𝑥𝑝 Experimental value

xxi

𝑐𝑎𝑙𝑐 Calculated value

𝑀, 𝑐 and 𝑐’ Cations

𝑋, 𝑎 and 𝑎’ Anions

𝑤 Water

LIST OF ABBREVIATIONS

AAD Average absolute deviation

BCF Burton-Cabrera-Frank model

BFDH Bravais-Friedel-Donnay-Harker model

B&S Birth and Spread model

Cif Crystallographic information file

𝑀𝑆𝑍𝑊 Metastable zone width

𝑀𝑊 Molecular weight

𝑁𝑅𝑇𝐿 Non-Random Two-Liquid model

𝑃𝐿𝑆 Pregnant Leach Solution

RIG Rough Interface Growth model

𝑆𝑋 Solvent extraction process

𝑆𝐷 Standard deviation

1

CHAPTER I

GENERALITIES

1. INTRODUCTION

Freshwater is a unique and scarce natural resource, essential for life and productive

activities, and therefore directly related to economic growth. Besides the limited

availability of freshwater in the world, there is an unequal distribution of this resource in

the different continents, creating zones of abundance and scarcity. An example of the latter

is the north of Chile, which is one of the driest areas on the planet, with scarce superficial

water resources and where there is an increasing demand for water by the different

production activities as well as for human consumption [1].

The most important economic activity in Chile is mining, which is concentrated in the arid

northern part of the country; therefore, the mining sector requires the identification of

alternative sources of water; it has been found that seawater can substitute for the limited

freshwater resources in the region [2].

Copper sulfate pentahydrate is the most common commercial product of copper, and is

produced industrially in the form of blue triclinic crystals [3]. The usual method to obtain

these crystals from the solution is through the addition of sulfuric acid, which generates a

supersaturated aqueous solution of the salt [4]. This compound has an extensive range of

agricultural, environmental, industrial, and hydrometallurgical uses.

In Chile, some mining companies crystallize this salt in hydrometallurgical processes using

freshwater, where copper is obtained from ores containing oxidized copper minerals [5].

Nevertheless, in order to minimize the use of freshwater in the crystallization process, the

effect of seawater on crystallization and on the thermodynamic behavior of copper sulfate

pentahydrate needs to be evaluated. The determination and interpretation of the

thermodynamic data related to the interactions of CuSO4 is necessary for a better

understanding of the seawater effect in the industrial production of copper sulfate

pentahydrate. Additionally, the information obtained in this work will be useful in the

2

design of processes to produce copper sulfate pentahydrate crystals using seawater by

means of the addition of sulfuric acid.

2. PROBLEMATIC, HYPOTHESES, AND OBJECTIVES

2.1 Problematic

For mining, which is one of the most important productive activities in Chile, the

availability and adequate management of water is key to its sustainability. As is known, the

national mining activity is developed under particular conditions; most of the deposits are

located in the north of the country, an area that faces a limited availability of freshwater

resources, so that water has become a critical, strategic and high-cost input. Therefore, this

situation of limited availability of the resource, which also presents an increasing demand

that competes with other sectors of the economy, has motivated the mining sector to

continue increasing efficiency levels, using technological solutions.

An alternative is the use of seawater, which is increasingly being used by the mining

industry, giving satisfactory results in several mining processes.

Some small and medium mining companies, to give an added value to the raw materials

that they exploit, obtain copper sulfate pentahydrate crystals (CuSO4·5H2O). However, one

of the problems presented in these crystallization plants is the cooling recrystallization

process required, since the crystals obtained after the addition of sulfuric acid in the

crystallization process are ‘snow’-like, and not of a suitable size, so it is necessary to

dissolve these crystals in water and recrystallize, obtaining crystals of a size and purity

suitable for commercialization; however, this process involves high energy and water

consumption.

In addition, there is information in the literature regarding the effect of sodium chloride on

the crystallization process, where it has been determined that Na+ and Cl

- ions (the principal

ions present in seawater), when present in a medium of crystallization, can cause changes in

the structure, size and growth rate of some crystals. Accordingly, in the present work, the

3

effect of seawater on the thermodynamic behaviour and crystallization of CuSO4·5H2O

needs to be assessed to analyze the feasibility of the use of seawater in this

hydrometallurgical process.

2.2 Hypotheses

Hypothesis 1:

There are differences in the solubilities, and physical properties such as density, viscosity,

and water activities, between the CuSO4-H2SO4-seawater and the CuSO4-H2SO4-H2O

systems, which are attributed to the presence of salts in the seawater.

Hypothesis 2:

The ion interaction model of Pitzer can be successfully applied to mining processes using

seawater, where it can be used to determine the solubilities of complex systems, such as

CuSO4-H2SO4-seawater, at different temperatures.

Hypothesis 3:

If copper sulfate pentahydrate is crystallized in saline solutions, the growth kinetics of the

crystals can be affected, where an increase in the growth rates can lead to obtaining larger

crystals than those obtained in freshwater.

4

2.3 Objectives

2.3.1 General objective

To study the effect of seawater on the thermodynamic behaviour and crystallization of

copper sulfate pentahydrate in order to analyze the feasibility of the use of seawater in this

hydrometallurgical process.

2.3.2 Specific objectives

- To study the effect of the seawater on the solid–liquid equilibrium and physical

properties (density, viscosity, and water activities) of acid solutions of copper

sulfate from 293.15 to 333.15 K. Correlate the obtained results using empirical

equations.

- To represent the solid–liquid equilibrium of a copper sulfate-sulfuric acid-seawater

system using the Pitzer model and a Born-type equation for modeling the effects of

copper sulfate and sulfuric acid, respectively, considering the seawater as a solvent.

- To estimate the amounts of copper sulfate precipitated, and the optimum yield, as a

function of the sulfuric acid concentration.

- To perform a thermodynamic study of the Cu-Na-H-SO4-Cl-HSO4-H2O system

using the Pitzer ion-interaction model in the temperature range of 293.15 to 333.15

K.

- To study the effect of sodium chloride (2.4 wt % NaCl) on the crystal shape, particle

size, composition, and growth kinetics of copper sulfate pentahydrate crystals.

5

CHAPTER II

STATE OF THE ART

1. THE USE OF SEAWATER IN MINING

1.1 Introduction

The largest resource of water in the planet is the water of the oceans, which represent 97%

of available water. The other 3% includes: the 2% of water available in polar ice caps and

glaciers and therefore difficult to use as a water resource; and traditional freshwater

resources (groundwater, lakes, wetlands, rivers, among others) representing 1% of the total

water of the planet [6]. The overexploitation of these traditional resources in arid and semi-

arid areas, such as northern Chile, southern Peru, and some regions of Africa, Asia, and

Australia, has created a situation of scarcity of the resource, which forces a search for new

water sources and for improvements in the efficiency of their use.

The use of seawater in mining has been addressed in numerous studies and publications [7].

There are several examples of its successful application in the processing of copper, zinc,

uranium and iodine minerals, as shown in Table 1, where of mineral concentration

technologies such as flotation and leaching are included [8].

6

Table 1. Examples of seawater use in mining (*saline water) [6].

Plant Country Metal Status Technology

El Boleo Project Mexico Copper, Cobalt,

Zinc, Manganese Operating Leaching

Mount Keith (*) Australia Nickel Operating Flotation

Sierra Gorda SCM Chile Copper,

Molybdenum Operating

Flotation

Leaching

Black Angel Greenland Lead, Zinc Closed Flotation

Batu Hijau Indonesia Copper, gold Operating Flotation

Beverley Uranium

Mine (*) Australia Uranium Operating In-situ Leaching

Michilla Mine Chile Copper Closed Leaching

Antucoya Project Chile Copper Project Leaching

Las Luces Mine Chile Copper Operating Flotation

Algorta Norte S.A

Mine Chile Iodine Operating Leaching

1.2 Characteristics of seawater

The water in the oceans contains chemical compounds, most of them in the form of

dissolved ions, which constitute about 3.5%, with water being the remaining 96.5%. The

cations present in the highest amounts are sodium, magnesium, potassium, and calcium,

whereas the anions in highest amounts are chloride, carbonate, sulfate, and bicarbonate [8]

(Table 2). The dissolved quantity of these ions changes from one place to another, but their

relative composition is considered constant. Seawater also contains dissolved gases, due to

the sea is being in contact with atmospheric gases. The most abundant gases are nitrogen,

oxygen, and carbon dioxide; the last reacts with seawater forming carbonate and

bicarbonate. There are also other gases, such as argon, krypton, xenon, neon and helium

dissolved in small amounts [6].

7

Table 2. Reference composition of seawater [8].

Solute g/kg solution

Na+ 10.78145

Mg2+

1.28372

Ca2+

0.41208

K+ 0.39910

Sr2+

0.00795

Cl- 19.35271

SO42-

2.71235

HCO3- 0.10481

CO32-

0.01434

Br- 0.06728

B(OH)4- 0.00795

F- 0.00130

OH- 0.00014

B(OH)3 0.01944

CO2 0.00042

Total 35.16504

The presence of these species in seawater generates changes that can affect its use in

mining processes. First, salinity has an effect on the physicochemical properties of water.

For example, density and viscosity increase with salinity and may have an effect on the

movement of fluids, such as transport or agitation of seawater. Other properties that change

with salinity in mining processes are vapor pressure and surface tension; important since

they are related to water evaporation and interaction with solid particles, respectively.

Secondly, the species present in seawater are found in different forms. For example,

magnesium is not found 100% as Mg2+

, but only 88%; the remaining 12% is found to form

complexes with sulfate, bicarbonate, carbonate, among other anions. Thus, sodium,

calcium, potassium and strontium are found in 98, 89, 99 and 86% as Na+, Ca

2+, K

+, and

Sr2+

, respectively. Similarly, the Cl-, SO4

2-, HCO3

-, CO3

2- and OH

- anions are found as free

ions at 100, 45, 72, 9, and 15%, respectively. The remaining percentage corresponds to

complexes formed with the different cations present in the seawater.

These percentages of the ions are a function of the pH, and will change according to the pH

used in a mining process. Thus, the physicochemical properties of seawater are different

8

from those of water normally used in mining processes, and these differences can have

positive and negative effects on mineral processing and extraction.

1.3 Consumption of seawater in Chile

This section reviews the consumption of seawater based on studies performed by Cochilco

[9], which concentrate on the copper industry. The total consumption of water in 2015 was

55.8 m3/s; the region of Antofagasta was the one with the highest consumption at national

level, with 51%. The mining companies make efforts to recycle as much water as possible,

and 73% of the water used in the process is made up of recirculated water.

Table 3 shows the mining operations in Chile that use seawater, either with or without

desalination [9]. The operations of Centinela Mine (Antofagasta Minerals) and Sierra

Gorda (Quadra Chile Mine) stand out due to the volume of raw seawater used in their

operations.

Table 3. Mining operations that use seawater in Chile [9].

Company Name Capacity Desalination

Plant (l/s)

Capacity direct

Seawater (l/s)

BHP Billiton Planta Coloso 525

Antofagasta

Minerals

Planta Desaladora

Michilla 75 23

Antofagasta

Minerals Distrito Centinela 50–150 780–1500

SLM Las Cenizas Las Cenizas Taltal 9 55

Tocopilla Mine Mantos de la Luna 20 5

Lundin Mining Candelaria 300–500

AngloAmerican Manto Verde 120

Quadra Chile Mine Sierra Gorda 63 1315

Antofagasta

Minerals

Planta Desaladora

Antucoya 50 280

Camarones Pampa Camarones 5 25

9

In the copper industry, the operation that consumes most water is concentration, with 71%

of the total [9] (Figure 1). Its function is to generate a pulp of particles of the mineral,

which is then treated with bubbles to achieve the separation of the valuable species from

the gangue. Considering that the particles are of small size (from 20 to 80 µm), the

separation of the solids from the liquid is difficult, limiting the amount of water recycled

and consequently increasing the consumption of freshwater [10]. On the other hand,

hydrometallurgy consumes 15% of the water, where the water acts as a solvent, and comes

into contact with the mineral through the heap leach, where the particles are also

considerably larger in size, resulting in lower consumption.

.

Figure 1. Percentage of seawater use of each operation [9].

1.4 Physicochemical properties of seawater

In the literature, some authors have studied the characteristics and physical properties of

seawater. All this information is important for this research and is detailed below:

Fabuss et al. [11] determined experimentally the densities of binary and ternary aqueous

solutions of NaCl, Na2SO4, and MgSO4 in the temperature range of 298.15 to 448.15 K.

These solutions contained these compounds at concentrations similar to those in seawater,

and up to fivefold concentration. In this work, the data were fitted to the temperature and

composition of the solutions with a method based on the apparent molal volumes of the

seawater salt components, and a single interaction constant. Additionally, the authors used

Concentration

71%

Hydrometallurgy

15%

Others

14%

10

this method to estimate densities of solutions at concentrations similar to seawater and of

the concentrated solutions.

Korosi and Fabuss [12] were interested in the seawater desalination process, so they

determined experimental viscosity and density values of binary salt solutions related to the

principal salts present in seawater: NaCl, KCl, Na2SO4, and MgSO4. In this work, the

solvent was pure water and the measurements were performed in the temperature range of

298.15 to 423.15 K, and at molality ranges of 0.1 to 3.5 mol/kg for chlorides, of 0.03 to

1.18 mol/kg for sodium sulfate, and of 0.025 to 0.885 mol/kg for magnesium sulfate; all

these concentrations are similar to those in seawater. These data were correlated using

Othmer’s rule, and the correlation was compared with literature data.

Fabuss et al. [13] measured experimental viscosity and density of ternary solutions of

several electrolytes present in the seawater, where NaCl is present in each one. These

systems were the following: NaCl-KCl-H2O, NaCl-Na2SO4-H2O and NaCl-MgSO4-H2O.

Here, the studied temperature and ionic strength ranges were from 298.15 to 423.15 K, and

from 0.7 to 3.5 mol/kg, respectively. The experimental viscosity values were correlated

using Othmer’s rule, obtaining a deviation of 0.2 to 0.3% between the experimental and

correlated data, which was considered acceptable.

Bromley et al. [14, 15] measured the heat capacities of solutions of natural seawater in a

salinity range of 1 to 12%, in a temperature range of 275.15 to 353.15 K, and at a pressure

of 1 atm. These data were correlated using the extended Debye-Hückel equation. Later,

Bromley [16] reported experimental measurements of the heats of dilution and

concentration of seawater at 298.15 K; these data were also correlated using the extended

Debye-Hückel equation. Also, values of the relative, apparent, and partial enthalpies of sea-

salt solutions were calculated. These values differed considerably from those for NaCl

solutions. Additionally, Bromley et al. [17] measured the heat capacities and enthalpies of

seawater in a temperature range of 353.15 to 473.15 K, with salinities up to 12%. These

experimental data were correlated using the extended Debye-Hückel model.

Gibbard and Scatchard [18] measured the vapor pressures of synthetic seawater solutions

(prepared in the laboratory) at ionic strengths of 1.0, 2.8, and 5.8 mol/kg, and in the

11

temperature range of 298.15 to 373.15 K. From this experimental information, the osmotic

coefficients were determined, which were fitted to the thermodynamic model of Scatchard,

showing a very good agreement over the whole temperature range, and up to ionic strengths

of 2.8 mol/kg.

Singh and Bromley [19] evaluated the relative enthalpy of seawater, the apparent enthalpy

of sea salts, and the relative partial enthalpies of sea salts and water in the temperature

range of 273.15 to 348.15 K and in the salinity range of 0 to 12%. These data were

evaluated from accurate calorimetric measurements of the heats of mixing of sea-salt

solutions. Additionally, these data were correlated using the extended Debye-Hückel

equation, where the results were consistent with those reported in the literature regarding

heat capacity and the heat of mixing. These data are useful for calculating the change of

free energy of seawater with temperature, the temperature variation of activity and osmotic

coefficients, and the variation of the boiling point with temperature.

Millero [20] performed a detailed review of the physics and chemistry of seawater,

addressing such issues as water structure, ion-water interactions, seawater composition, ion

speciation, and the effects of temperature and pressure.

Feistel [21] determined the specific Gibbs energy of seawater using experimental data of

heat capacities, freezing points, vapor pressures and heats of mixing at atmospheric

pressure in the temperature range of 267.15 to 353.15 K, and in the absolute salinity range

of 0 to 120 g/kg .

Sun et al. [22] established a set of fitted polynomial equations for calculating the physical

variables such as density, entropy, heat capacity, and potential temperature of a thermal

saline fluid. These authors used previously reported experimental information, and the

equations were valid in the temperature range of 273.15 to 647.15 K, a pressure range of

0.1 to 100 MPa, and an absolute salinity range of 0 to 40 g/kg.

Philippe et al. [23] discussed the effects of the use of desalinated seawater compared to raw

seawater in mining projects, and included the economic aspects of both alternatives. In this

work it was shown that the desalination process removes over 99.4% of the dissolved salts

contained in the seawater. As seawater contains only 3.5% of dissolved salts, in desalinated

12

seawater this amount is negligible; this difference in the water quality may have significant

effects on the overall process. Some of the parameters that are directly influenced are:

specific gravity, viscosity, chemical buffering effects, product and by-product

contamination, corrosion, scaling, evaporation, and capillary forces. Additionally, in this

work it was shown that there are differences in the viscosity and density properties between

seawater and desalinated seawater, which have a direct consequence on the operational

costs of pumping. Accordingly, it was concluded that the investment costs associated with a

desalination plant for the supply of seawater to mining projects are generally lower than the

investment associated with the conveyance system, especially under corrosive conditions.

Moreno et al. [24] have given a brief introduction of the unit operations employed in the

‘Las Luces’ beneficiation plant. Even more important, the flow rates and chemical analyses

of the water samples collected from main unit operations at the plant were presented, and

the variations in the chemistry of the recycled seawater as a result of grinding and flotation

were discussed. In this work, the operational measurements showed that metallurgic results

were not affected by the salinity of the seawater. Analytical data showed that the dissolved

salt content of the process increased 0.7 g/L/year, which is essentially due to solar

evaporation. The authors suggested that there is most likely a limit of total dissolved salts

above which flotation operations would not be viable. Based on this finding Las Cenizas is

now investigating options to minimize the loss of water to evaporation.

Torres et al. [2] studied the use of seawater to recover potassium and nitrate from the waste

tails of mining operations. In this study, the performance of four leaching agents was

evaluated for recovering potassium and nitrate from discarded salts: 1) freshwater; 2)

seawater; 3) seawater saturated with chloride ions; and 4) seawater saturated with chloride,

sulfate and magnesium ions. These tests showed that leaching with seawater provides

nearly the same potassium and nitrate leaching efficiency as when freshwater is used.

However, leaching with seawater saturated with chloride, sulfate and magnesium ions

yielded approximately 10% lower potassium and nitrate recoveries compared to the tests

where seawater was used alone. In contrast, the use of saturated seawater is expected to

yield a geomechanically more stable heap because most of the chloride-, sulfate- and

magnesium-containing salts will remain unleached. The main conclusion of this work is

13

that it is possible to leach certain types of salts with seawater, obtaining recovery rates of

nitrates and potassium above 80%, which is attractive from an economic point of view.

With a view to industrial applications, Taboada et al. [25] determined the solubilities and

physical properties (densities, viscosities, refractive indices, and ionic conductivities) of

saturated solutions of sodium nitrate in seawater, caliche mineral in freshwater and caliche

mineral in seawater (3.5% salinity), in the temperature range of 298.15 to 323.15 K.

Additionally, the physical properties of sodium nitrate in seawater were measured for

unsaturated solutions in the concentration range of 1 to 11 mol/kg and at different

temperatures (from 298.15 to 323.15 K). These properties were compared to the sodium

nitrate-freshwater system obtained experimentally in this work; however the solubility was

compared to data from the literature [26]. Results showed that the solubility, density,

refraction index and ionic conductivity of saturated solutions of sodium nitrates in seawater

and in freshwater increased as temperature increased. On the other hand, viscosity showed

an inverse behavior. The solubility and density values of the sodium nitrate-freshwater

system were higher than those of the sodium nitrate-seawater system due to the higher

nitrate concentration in freshwater. The solubility of sodium nitrate in the freshwater

system was higher than that in the seawater system; consequently, leaching with seawater

dissolves less nitrate. The values of refractive index, ionic conductivity and viscosity of

saturated solutions of sodium nitrate in seawater were higher than those obtained in

freshwater. This increase in the viscosity implies a higher cost of pumping the solution;

however, viscosity values for both systems decrease with increasing temperature.

Additionally, the measured properties of caliche in the seawater system were greater than

those of the freshwater system, with the viscosity values showing the most significant

differences. Consequently, using seawater in nitrate treatment systems of mining operations

is a technically viable alternative that does not present major differences with using

freshwater. Its economic viability should be studied case-by-case, considering the costs of

pumping seawater and the cost of accessing freshwater.

In the book of Cisternas and Moreno [7] ‘El Agua de Mar en la Mineria: Fundamentos y

Aplicaciones’ (‘Seawater in Mining: Fundamentals and Applications’) it is stated that due

to the scarce availability of freshwater in the northern regions of Chile, and the constant

14

increase in the required water flow due to the growing and sustained interest in the

development of more new projects, the mining industry has been betting on innovative

solutions, among which is the use of raw or desalinated seawater in production processes.

In addition, it is explained that the sustainable development of mining lies in the search for

new water resources; up to now the main initiative that has been considered to address the

lack of water resources in the activity has been the use of seawater, which appears to be an

attractive alternative supply. The chapters of the book include the following: 1)

Management of water resources in mining; 2) Unprocessed seawater as process water; 3)

Physicochemical properties of seawater for industrial processes; 4) Flotation with seawater;

5) The use of seawater in the leaching of copper; 6) The nitrate industry and water

resources; 7) Measurement and prevention of corrosion; and 8) Thermodynamics of

leaching of copper with seawater.

In the book by Cisternas et al. [6] ‘Agua de Mar Atacama: Oportunidades y Avances para

el uso sostenible de agua de mar en mineria’ (‘Atacama Seawater: Opportunities and

advances for the sustainable use of seawater in mining’), it is discussed that the scarcity of

water sources in northern Chile has generated concern in the mining industry, which

requires large volumes of water for its production processes. Due to this, desalinated

seawater has taken on enough importance to meet this need; however, its use faces different

problems, such as high energy costs, organic and inorganic particles that cause obstructions

in the systems, as well as the accumulation of brines from the treated seawater which

generate ecological problems. The use of raw seawater also faces other challenges, such as

the suitability of the production processes to the characteristics of seawater. Accordingly,

the chapters of the book include the following: 1) Use of seawater in mining; 2) Use of

reverse osmosis brines for the processing of non-metallic minerals; 3) Design of

desalination plants and water distribution networks: A holistic look; 4) Partial removal of

calcium and magnesium from seawater by the addition of carbon dioxide and alkaline

compounds; 5) Application of bio-mineralization processes to the pre-treatment of seawater

for the selective removal of calcium and magnesium ions; 6) Removal of impurities using

flotation for the pre-treatment of seawater and mining effluents; 7) Marine bacteria and

their importance as controllers in the formation of biofouling in water treatment systems; 8)

15

Physicochemical, thermodynamic and transport properties of saline solutions for process

design; 9) Technological evaluation: Support for decision-making in the use of seawater.

2. COPPER SULFATE PENTAHYDRATE

2.1 Characteristics and properties

Copper sulfate pentahydrate (CuSO4·5H2O), also called bluestone, or blue vitriol, is found

in nature as the mineral chalcanthite [4]. It belongs to the triclinic system (sp.gr. P1), and its

unit-cell parameters are: a = 6.1224 (4) Å; b = 10.7223 (4) Å; c = 5.9681 Å; α = 82.35 (2)°;

β = 107.33 (2)°; γ = 102.60 (4)°; V = 364.02 (3) Å3; Z = 2; D = 2.278 g/cm

3 [27].

Copper sulfate pentahydrate is an important industrial compound of copper due to the wide

range of commercial uses and applications:

According to Richardson [4], among the major uses of copper sulfate pentahydrate are the

following: in agriculture it is used to produce active foliar fungicides such as Bordeaux

mixture, tribasic copper(II) sulfate, or copper(II) hydroxide; it is also used in combination

with sodium dichromate and arsenic acid for the preservation of wood; it is an effective and

economical algicide for lakes and ponds; in mining it is used as a flotation activator for

lead, zinc, and cobalt ores. Moreover, this compound is also used as a mordant in textile

dyeing, in the preparation of azo and formazan dyes, as a pigment in paints and varnishes,

for preserving hides and tanning leather, in pyrotechnic compositions, and in synthetic fire

logs.

It is also used in copper electrolysis, the control of fungal diseases, and in the correction of

copper deficiency in soils and in animals [29, 30]. On the other hand, there are some

chemical tests that use copper sulfate; for example, in Fehling's and Benedict's solutions to

test for reducing sugars, which reduce the soluble blue copper(II) sulfate to insoluble red

copper(I) oxide. Moreover, copper sulfate is used in the Biuret reagent to test for proteins

and in the blood test for anemia [31, 32].

16

2.2 Industrial process of copper sulfate pentahydrate crystallization

Direct hydrometallurgical extraction is used to obtain copper from ores containing oxidized

copper minerals such as carbonates, hydroxysilicates, sulfates, and hydroxychlorides [5].

In Chile, there are some mining companies that crystallize copper sulfate pentahydrate from

hydrometallurgical processes using freshwater, where copper is obtained from ores

containing oxidized copper minerals by means of the production process shown in Figure 2

and detailed below.

Figure 2. Scheme of the copper sulfate pentahydrate crystallization process.

a) Grinding stage

The mineral from the mine presents a varied granulometry, from particles of less than 1 mm

to fragments larger than 50 cm in diameter. The objective of crushing is to reduce the size

of the larger fragments to a maximum uniform size of 0.6 cm. This operation is performed

dry [33].

17

b) Acid agglomeration and ‘curing’

In order for the process to proceed, the bed of particles that will make up the leach heap

needs to be permeable to ensure good percolation and dispersion of the leach solution

without preferential runoff. This is achieved by subjecting the material to a moisture

agglomeration process, consisting of moistening the crushed mineral with liquid to a water

content that gives sufficient surface tension; by colliding the particles together, the fines

adhere to the coarse sizes. Then, curing consists of spraying the previously crushed mineral

with the solvent (sulfuric acid), followed by a period of ‘cure’ or rest [33].

c) Copper leaching process

The leaching is mostly performed by dripping dilute sulfuric acid onto of heaps of broken

or crushed ore and allowing the acid to trickle through to collection ponds. In this stage, a

solution called PLS (pregnant leach solution) is obtained, which has a concentration of

copper in the range of 5–7 g/L and 6–15 g/L of sulfuric acid. This rich solution is generally

impure, and has to be purified and concentrated before the metal recovery. In the copper

hydrometallurgy this is realized by the ‘solvent extraction process’ [33].

d) Solvent extraction process (SX)

The solvent extraction (SX) plant, receives the rich solution generated in the heap leaching

process (the PLS). This solution is characterized by its low dissolved copper concentration,

along with impurities such as iron, chloride, aluminum, manganese, magnesium, sodium,

among others. The main objective of the solvent extraction process is to extract selectively

the copper contained in the impure rich solution by an ionic exchange in the aqueous phase

(rich solution) and the organic reagent. This reagent is able to discharge the copper in a

later process step into a high purity solution, forming an electrolyte suitable for the

crystallization [33].

18

e) Copper sulfate pentahydrate crystallization

According to Tabilo [33], in this stage the organic extractant loaded with copper in the

solvent extraction stage is discharged to obtain the crystals of copper sulfate pentahydrate

present in this solution, it is possible by adding concentrated acidic solutions that allow the

organic to release the copper to the solution, obtaining copper sulfate crystals. The loaded

organic is mixed with saturated electrolyte in a ratio of 2:1 and sulfuric acid, in order to

increase the acidity and to increase the efficiency of the system for discharging the loaded

organic. The saturated electrolyte (S-E) is composed of Cu (53–58 g/L) and H+ (200–205

g/L).

This mixture continues its course through the phase separators and decanters, hereinafter

termed ‘crystallizers’, where the extraction of sulfate is performed by saturation of the

solution, where the organic is discharged, releasing the excess of copper as solid crystals.

These solids called ‘sulfate of mining degree’ are separated from the solution by

decantation, and by means of pumps are brought to ponds called ‘crystal scrubbers’ (Figure

3). In the crystallizers occurs the separation of the discharged organic, which is returned to

the solvent extraction stage, and the saturated electrolyte is recirculated in this

crystallization stage.

Figure 3. Industrial copper sulfate pentahydrate crystallization process [33].

19

f) Dissolution and re-crystallization processes

Copper sulfate crystals obtained in the crystallization stage are dissolved by using hot

water, forming a pulp of copper sulfate; the solution obtained from hot water, sulfuric acid

and impurities is evacuated from the equipment by overflow to be recycled to the hot water

circuit [33]. Then, the copper sulfate pulp obtained in the dissolution crystallizers is sent to

the re-crystallizers in which this pulp is brought into contact with cooling water to begin the

nucleation process and crystal growth for the production of copper sulfate pentahydrate

crystals in feed grade. In addition, the design of this equipment allows recirculation of the

water solution obtained to the crystallizers. Then, the copper sulfate crystals obtained in the

re-crystallizers are passed to the drying step [33] (Figure 4).

Figure 4. Copper sulfate pentahydrate dissolution and re-crystallization processes [33].

g) Drying and packaging stages

The drying of the copper sulfate crystals is carried out in a batch operation in a rotary dryer,

resulting in a material containing 3 to 10% moisture. This range of humidity depends on the

residence time of the crystals inside the dryer, obtaining finally the copper sulfate

pentahydrate feed grade, which is sent to the packaging stage.

20

2.3 Solubilities and physical properties of the copper sulfate-sulfuric acid-water

system.

One of the first studies carried out into the CuSO4-H2SO4-H2O system was performed by

Holler and Peffer [34] who proposed an empirical model for the determination of density of

this system. Additionally, these authors proposed that density is a function of the

concentration summation (CuSO4·5H2O-H2SO4) rather than of the concentrations of the

individual components. Milligan and Moyer [35], presented two empirical models to

estimate the density and solubility of the CuSO4-H2SO4-H2O system at different

temperatures. In the work of Price and Davenport [36], the densities, electrical

conductivities, and viscosities of CuSO4-H2SO4 solutions in the electrorefining and

electrowinning ranges of composition and temperature were measured. These properties

were studied because density, electrical conductivity, and viscosity all have considerable

economic importance; in the case of conductivity because of its impact on electrical energy

consumption, and density and viscosity because of their influences on mass and heat

transfer. Additionally, density and viscosity also influence the carryover of impure

particulates into the final copper cathode product. In this work empirical and semi empirical

equations describing the measured properties were also presented, where density and

conductivity results showed a good agreement with previously measured values. However,

the viscosity results agreed with previous work at 25 °C, but tended to be somewhat higher

at 50 °C. Hotlos and Jaskula [37] determined densities and kinematic viscosities for the

ternary system CuSO4-H2SO4-H2O in the temperature range of 25 to 60 °C, and over a wide

range of concentrations: for CuSO4 from 0.2 to 1.15 M, and for H2SO4 from 0.25 to 2.5 M.

These results were described using empirical equations, where the results obtained showed

that the density depends on CuSO4 concentration much more than on H2SO4 concentration;

additionally, the temperature dependence is relatively small. On the other hand, the

influence of the concentrations of components on the viscosity is analogous to that on the

density, where an increase in the CuSO4 concentration causes a 3–4 times larger change

than a corresponding increase in the H2SO4 concentration, however, in this case the

influence of temperature is considerable. In the work of De Juan et al. [38] the

crystallization conditions of copper sulfate solutions were determined as a function of the

temperature and sulfuric acid concentration. In this work, an empirical model was proposed

21

to represent the solubility of copper sulfate as a function of the temperature and sulfuric

acid concentration, where it was demonstrated that Cu2+

concentration in the solution is

mainly a direct function of the logarithm of temperature and sulfuric acid concentration. In

addition, in this work the effect of Zn2+

on the copper sulfate solubility was also studied,

where the results obtained led to a multiple linear regression between Cu2+

concentration in

the solution and sulfuric acid and Zn2+

concentrations in the medium. Hernández et al. [39]

studied the effects of seawater on the solid–liquid equilibrium of copper sulfate in acid

solutions in the temperature range of 298.15 to 323.15 K, for possible industrial

applications. In this work, experimental data of solubilities and physical properties such as

density, refractive index, ionic conductivity, and viscosity were provided for CuSO4 in

seawater at pH 2. This pH was used because it is similar to those in copper mining

operations. Moreover, physical properties (density, refractive index, ionic conductivity and

viscosity) were measured for unsaturated solutions of CuSO4 in an acidic seawater system.

These experimental data were fitted using Othmer’s rule, and the Casteel–Amis equation

was used for conductivity. Results showed that the solubility of CuSO4 in an acidic

seawater system is similar to that of CuSO4 in a freshwater system, but the differences

increase at higher temperatures. The physical property values for the saturated system of

copper sulfate in seawater are greater than those of the saturated system of copper sulfate in

freshwater, and both systems (seawater and freshwater) maintain the same trend for the

measured physical property values as a function of temperature. In addition, using

Othmer’s rule, the experimental values for the physical properties in the unsaturated

concentrations of CuSO4 in seawater correlated satisfactorily.

2.4 Copper sulfate pentahydrate crystallization.

Copper sulfate pentahydrate crystallization studies using freshwater have been carried out

by several authors:

Ishii and Fujita [40] measured the crystallization rate of copper sulfate solutions at the first

supersaturation concentration. Here, the stability of aqueous copper sulfate solutions at the

first supersaturation concentration was examined, in a batch-wise stirred reactor, using

22

different temperatures and stirring rates. It was concluded that below the impeller Reynolds

number of 4233 such a solution would be reasonably metastable if the liquid surface were

not cooled. Above the impeller Reynolds number of 4520 such a solution is metastable for

a short latent period only, then a shower of many fine crystals occurs suddenly and the

solute concentration decreases rapidly.

Zumstein and Rosseau [41] examined the formation of agglomerates during the continuous,

semi-batch and batch crystallization of copper sulfate pentahydrate. Additionally, the

feasibility of determining crystallization kinetics from an analysis of measured crystal size

distribution was evaluated. The results from this work showed that the agglomeration was

significant in copper sulfate pentahydrate MSMPR (mixed-suspension, mixed-product-

removal) crystallization, where the agglomeration was increased as supersaturation

increased, agitation decreased, and solids concentration increased. On the other hand,

greater agglomeration was observed among small crystals, and a reduced agglomeration

was observed, in batch crystallization. This is thought to be due to the much shorter periods

of exposure to high supersaturations in batch operations, even though the supersaturation at

nucleation is much higher than that of the MSMPR experiments. Finally, this work

concluded that simple models of the crystal size distribution are ineffective in predicting

the percentage agglomerates because of difficulties in separating anomalous crystal growth

– which may be caused by size dependency, growth rate dispersion, or reductions in active

growth area – from the phenomenon of agglomeration.

Macpherson et al. [42] have developed a novel technique employing the scanning

electrochemical microscope (SECM), in order to study the dissolution kinetics of copper

sulfate pentahydrate single crystals in aqueous sulfuric acid solutions over a wide

concentration range. Here, the general concept was to employ the ultramicroelectrode

(UME) probe of the SECM to induce and monitor the dissolution process of interest by

depleting the concentration of one (or more) of the solution components of a target crystal

surface via electrolysis. For this application, the dissolution reaction was induced and

monitored at a platinum UME through the reduction of Cu2+

ions to Cu. Copper sulfate was

selected as an appropriate material for study because single crystals of the pentahydrate,

exhibiting a variety of well-defined faces, can readily be grown from aqueous solutions.

23

Additionally, it is characterized by high solubility and rapid dissolution kinetics, making

rate measurements difficult when conventional approaches are used. Results have

demonstrated that SECM-induced dissolution is a powerful approach in the study of rapid

dissolution kinetics when one (or more) of the constituent components of the target material

can be detected amperometrically.

Giulietti et al. [43-45] have developed several studies regarding the crystallization of

copper sulfate pentahydrate, where interesting findings have been reported. First, Giulietti

et al. [43], studied the CuSO4·5H2O resulting from batch cooling experiments, in the

temperature range of 70 to 30 °C, where free sulfuric acid was added in some experiments.

In this work, the metastable zone width, nucleation and growth kinetic parameters, as well

as the system kinetic constant, were determined and compared with the data published in

the literature. Later, in the work of Giulietti et al. [44], the morphology of copper sulfate

pentahydrate crystals produced from batch cooling experiments in the temperature range of

70 to 30 °C was described and correlated with the process conditions. Results showed that

slow linear cooling rates (90 min) predominantly caused the appearance of well-formed

crystals. Exponential cooling (120 min) resulted in the additional formation of

agglomerates and twins. However, the presence of seeds in both cooling modes led to round

crystals, agglomerates and twins. A fast linear cooling (15 min) gave rise to a mixture of

the former types, where broken crystals and adhering fragments were often found. The

intense twinning observed in seeded experiments was possibly associated with stresses in

the seed particles, whereas twinning under exponential cooling was consistent with the

additional supersaturation required for twin formation. Growth zoning was pronounced in

seeded and linear cooling experiments. Fluid inclusions were always found and were more

pronounced for larger particles; however, their formation could be avoided to some extent

by choosing conditions that inhibited zoning. Additionally, Giulietti et al. [45], studied the

effects of several additives on copper sulfate pentahydrate crystallization. For this, different

batch cooling modes of copper sulfate aqueous solutions were studied (quick and slow

cooling with constant cooling rate, programmed cooling with nearly constant

supersaturation) in order to find the optimum conditions for the investigation of the effect

of additives on crystallization. Three types of additives (solvents, ionic substances and

surfactants) were used, and their effects on crystal size, habit and yield were studied.

24

Results from this work showed that crystals produced in the absence of additives were

predominantly flat with |1-10| and |110| faces dominant; sometimes |100| and |001|. Ethanol

slightly reduced the |1-10| face and the |100| face was slightly prolonged, but the shape

unchanged. Other solvents (such as n-butyl alcohol and acetone) as well as H+ and Zn

2+ did

not affect the crystal habit significantly. A small amount of Fe3+

induced the formation of

nearly prismatic crystals, where the growth rate of the |001| and |110| faces seemed to be

significantly reduced. Detergents changed significantly the crystal shape of copper sulfate,

resulting in thin plate-like crystals with strongly emphasized |1-10| face. Organic solvents

led to a moderate yield increase due to reduced solubility of copper sulfate in mixed

solvents. The overall growth rate of copper sulfate was significantly reduced by Fe3+

and

detergents; whereas the nucleation rate was increased by these additives.

Lyall et al. [46] applied in situ ultrasonic attenuation spectroscopy for monitoring the

nucleation and growth of copper sulfate pentahydrate crystallized from supersaturated

aqueous solutions. This technique was used because the copper sulfate system is not readily

amenable to analysis via optical methods due to the intense blue colour of the saturated

crystallizing solution. In this work, procedures were developed to retrieve the nucleation

parameters, metastable zone width and apparent order of nucleation, and subsequently the

crystallization parameters, overall mass and linear growth rates, from the dynamically

recorded attenuation spectra, concluding that growth of copper sulfate pentahydrate crystals

was successfully monitored throughout the process and characterized in terms of acoustic

attenuation spectra.

In the work of Aktas [47], the objective was to precipitate copper sulfate selectively, thus

allowing impurities to remain in the solution, and to purify this precipitated compound

thoroughly with repeated precipitations to yield an analytical-grade product. From this

work, it has been suggested that if a higher degree of supersaturation is desired, the copper

sulfate concentration should be near saturation. On the other hand, ethanol was

demonstrated to disrupt the ligand bonds of a metal sulfate in solution and thus promote

selective precipitation. The presence of ethanol lowers the thermodynamic water activity

and makes it less available as a ligand for Cu2+

and SO42−

, so with fewer water ligands,

these two ions can form direct bonds more easily. They consequently precipitate as copper

25

sulfate pentahydrate when a substantial amount of ethanol is added to the solution.

Additionally, in this work it was demonstrated that the copper sulfate precipitation becomes

weaker at lower pH values due to the gradual appearance of HSO4−, which interferes with

the formation of the Cu–SO4 bond, preventing the precipitation to a certain degree and

resulting in poorer efficiencies. Finally, the effect of acid type on copper sulfate

precipitation was investigated, where nitric acid, hydrochloric acid and hydrobromic acid

were employed and it was concluded that almost no precipitate was observed after these

acids were added to the copper sulfate solution along with a substantial amount of ethanol.

In the work of Singh et al. [48], batch cooling and antisolvent crystallization of copper

sulfate pentahydrate using surfactant additives was investigated in order to understand the

effect of various factors on the crystal morphology. It was found that non-ionic surfactants

have a marginal effect on this ionic compound, whereas ionic surfactants are able to modify

the morphology substantially. Additionally, this effect is also specific to the surfactant

used; for example, SDS (sodium dodecylsulfate) produces flake-like crystals, whereas AOT

(dioctyl sodium sulphosuccinate) produces prismatic crystals of different morphology, and

CTAB (cetyltrimethyl ammonium bromide) produces crystals of irregular shape.

Antisolvent crystallization using ethanol produces elongated crystals; moreover, it has been

shown that surfactants and antisolvents can achieve a combined effect. Also, in this work it

was determined that the effect of the surfactant was observed over a certain threshold

concentration.

Manomenova et al. [28] have developed a technique for growing large single CuSO4·5H2O

crystals to apply them as broadband UV optical filters. In this work, samples of crystals

were grown and their transmission spectra, associated impurities, thermal stability, and

crystal structure were investigated. The dehydration onset temperature was determined to

be 46 °С, and the effective distribution coefficients keff of individual impurities in crystal

were evaluated. It was shown that keff >1 for most metals, indicating that the solution must

be additionally purified. Additionally, the internal crystal homogeneity was estimated by X-

ray topography.

26

3. CRYSTALLIZATION PROCESS AND CRYSTALLIZATION KINETICS

Crystallization is a solubility-related process and it represents one of the basic processes in

the process engineering. That is, a solid crystal is formed when a solute exceeds its

solubility in the solution. The crystallization refers also to the separation of solid,

crystalline phases from melts or gases. Some thermal processes, which involve

crystallization, are separation of mixtures of substances, purification of materials, recovery

of solvents or concentration of solutions. The diversity of the crystallization processes is

due to the variety of material systems, operating conditions and product specifications, such

as crystal purity, crystal size distribution, and crystal shape [49].

This section is a brief overview of the crystallization process where topics such as sodium

chloride effect in the crystallization, growth kinetics of single crystals, and crystal growth

mechanisms have been addressed.

3.1 Sodium chloride effect in crystallization

There is limited information in the literature regarding to the effect of seawater in

crystallization processes; however, some authors have studied the effect of sodium chloride

(which is the main salt in seawater) in the crystallization of some salts as follows:

Brandse et al. [50] studied the growth kinetics of gypsum in supersaturated solutions both

in pure water and in the presence of NaCl using a seeded growth technique, where

radioactive tracer techniques were employed to follow the growth process. In this work, the

mean linear growth rate 𝐺 was plotted against the relative supersaturation σ, and the results

showed that for low values of σ, the relation between 𝐺 and σ is given by a linear law; for

higher σ values it was given by a parabolic law; and for the highest σ values it was given by

a growth order higher than two. From this research it was concluded that the addition of

sodium chloride increased the crystallization rate remarkably; that is to say, the higher the

NaCl concentration the higher the growth rate.

In the work of Sheikholeslami and Ong [51] the effect was examined of the salinity on the

kinetics and thermodynamics of precipitation of CaCO3 and CaSO4 when they exist in

27

isolation and together. Batch tests under isothermal conditions (30 °C) were carried out for

salinity values ranging between 0.5 and 1.5 M of NaCl, calcium sulfate in the range of 0.06

to 0.15 M, calcium carbonate in the range of 0.007 to 0.02 M; for the mixed calcium sulfate

carbonate system, the SO4/CO3 molar ratio was changed. In this work, the thermodynamic

solubility constants were determined using the Pitzer model for determination of the

activity coefficients of ionic species, where, as expected, the thermodynamic solubility

constants (Ksp) of the pure salts were not affected by different salinity levels; however, the

salinity level affected Ksp in mixed salt systems. Additionally, images of the pure and

mixed system were produced using scanning electron microscopy (SEM), demonstrating

that the co-precipitation in the mixed system changed the scale morphology of the crystals.

Also, it was shown that as the NaCl concentration was increased from 0.5 to 1.5 M, the size

of calcium sulfate and calcium carbonate crystals increased from approximately 300 to

1000 μm and 30 to 60 μm, respectively. Finally, results showed that the kinetics of pure

CaSO4 precipitation were found to be strongly affected by the level of salinity; however,

the salinity level had no significant effect on the kinetics of pure CaCO3 precipitation.

3.2 Growth kinetics of single crystals and Crystal growth mechanisms

In the book of Garside et al. [52] has been mentioned that the growth rate of each unique

crystal face is different depending on the growth environment such as supersaturation,

temperature, solvents, and impurities. It was pointed out that the most common methods for

the measurement of the growth rate of crystals are the measurement of the linear growth

rate on specific faces of a single crystal or by estimating an overall linear growth rate from

the mass deposition rates on the bulk mass of a large number of crystals.

In the literature, there are some studies regarding to the growth rates measurements of

single crystals that have been carried out in ionic compounds as follows:

In the work of Mullin and Amatavivadhana [53] were measured the growth rates of

ammonium and potassium dihydrogen phosphate crystal faces under controlled conditions

of temperature, supersaturation and solution velocity, and it was found that the growth rates

of the ammonium salt (ADP) were much higher than those of the potassium salt (KDP)

under equivalent conditions. It is suggested that this is due to the occurrence of hydrogen

28

bonding between ADP molecules, which give larger integrating units (thicker growth

layers) than occur with KDP.

Later, Davey and Mullin [54], reported that the (100) faces of ammonium dihydrogen

phosphate (ADP) crystals grow extremely slowly compared with the (101) faces, so it was

not possible to measure their growth rates by direct microscopic measurement by the flow

cell technique used for the (101) faces. However, distinct growth layers could be seen

moving across growing (100) faces so it was characterized the growth kinetics of these

faces by measuring the layer velocities under well-defined conditions of supersaturation

and temperature. According to this, the present work was concerned with the kinetics of

movement of growth layers on the (100) faces of ADP crystals, and was also investigated

the extent to which these impurities are incorporated into the crystal faces during growth.

In the work of Sweegers et al. [55] in-situ optical microscopy to measure the growth rates

of gibbsite single crystals growing from aqueous sodium aluminate solutions was used.

The growth rate was measured to the (001), (110), and (100) crystal faces as a function of

the driving force, and the results were fitted with growth rate equations for various growth

mechanisms.

Later, in the work of Suharso [56] was studied the growth rate mechanism of sodium borate

tetrahydrate (borax) single crystals along the (111) direction at various relative

supersaturations using in situ optical microscopy technique to elucidate the mechanism of

growth and the crystal growth rate equation. The results showed that the growth mechanism

of the (111) face of borax crystal at temperature of 20 °C was spiral growth mechanism

below the relative supersaturation of 0.49 and a Birth and spread mechanism above the

relative supersaturation of 0.49.

Additionally, some studies have been carried out to measure the growth rates of individual

faces in organic materials. Nguyen [57] reported the measurement of the solution

solubilities and crystal growth rates of single (RS)-Ibuprofen crystals as a function of

solvent and supersaturation, where the interfacial growth mechanisms within this range of

supersaturation were characterized. Then, Camacho et al. [58, 59], studied the crystal

29

morphology and the measurement of the growth rates of the individual faces of N-docosane

and methyl stearate crystals as a function of solution environment.

4. SOLID-LIQUID EQUILIBRIUM MODELING.

4.1 Models for electrolyte solutions

Electrolyte solutions are encountered in many natural and industrial processes. Phase

equilibrium calculations for solutions containing electrolytes are gaining increasing

importance and it is important to choose the most suitable thermodynamic model for such

systems [60]. In electrolyte solutions, the ions interact strongly with each other and with the

solvent through their electric charges, so deviations from ideality are important even at low

concentrations. Also, the ions are not volatile at atmospheric pressure and ambient

temperature, so a different approach is needed in order to formulate a limiting law for the

thermodynamic behavior of electrolyte solutions.

A number of activity coefficient models for electrolyte solutions have been developed for

calculating the thermodynamic properties of electrolyte solutions for engineering

applications. A brief description of these models is detailed below:

a) Debye-Hückel Model

Based on the assumption of each ion being surrounded by an ionic atmosphere consisting

of ions of the opposite charge, the Debye-Hückel limiting law for electrolyte solutions was

formulated by Peter Debye and Erich Hückel [61, 62]. The Debye-Hückel limiting law

describes the non-ideal behavior caused by electrostatic forces in extremely dilute

electrolyte solutions. The limiting law expressed for a salt with the stoichiometric

coefficients 𝑣𝑖 and the sum of stoichiometric coefficients 𝑣 is:

ln 𝛾± = −1

𝑣∑ 𝑣𝑖𝑧𝑖

2𝐴𝐼1

2⁄ + ln 𝑥𝑤𝑖 (1)

30

where 𝛾±is the mean molal activity coefficient of ions in the solution and 𝑧𝑖 is the charge of

ion 𝑖,

𝐴 =𝐹3

4𝜋𝑁0[

𝑑

2(𝜀0𝜀𝑟𝑅𝑇)3]1

2⁄

(2)

where 𝐹 corresponds to the Faraday constant (C·mol-1

), 𝑁0 to the Avogadro’s number

(6.022045∙1023

), 𝜀0 to the permittivity of vacuum (8.85418∙10-12

), R is the gas constant

(8.314 J·mol-1

·K-1

), T is the temperature (K), d is the density (kg/m3), 𝜀𝑟 is the relative

permittivity (dielectric constant, dimensionless) of the solution. 𝑑 and 𝜀𝑟 are both functions

of temperature,

𝐼 =1

2∑ 𝑚𝑖𝑧𝑖

2𝑖 (3)

where 𝐼 is the ionic strength and 𝑚𝑖 is the molality of ion 𝑖.

The Debye-Hückel limiting law provides an accurate representation of the limiting

behavior of the activity coefficients in dilute ionic solutions. It is however not valid at ionic

strengths higher than 0.01 mol/kg H2O.

The Debye-Hückel limiting law (Eq. (1)) is derived from the Debye-Hückel theory by

neglecting terms that play a role only at concentrations higher than 0.01 mol/kg H2O. An

extended form of the Debye-Hückel limiting law includes some of these terms. It can be

expressed as:

ln 𝛾± = −1

𝑣∑ 𝑣𝑖𝑧𝑖

2 𝐴𝐼1

2⁄

1+𝑏𝐼1

2⁄+ ln 𝑥𝑤𝑖 (4)

where b is dependent on the size of the ions involved, but is usually considered constant.

The extended Debye-Hückel law is applicable at ionic strengths up to 0.1 mol/kg H2O.

31

b) Guggenheim model

The Guggenheim model [63] makes a distinction between short-range and long-range

interactions to calculate the excess Gibbs energy. The expression of the excess Gibbs

energy becomes:

𝐺𝐸

𝑛𝑠𝑅𝑇= −

4

3𝐴𝛾𝐼

32⁄ 𝜏√𝐼 + 2 ∑ ∑ 𝜆𝑖𝑗𝑚𝑖𝑚𝑗𝑗𝑖 (5)

with

𝜏√𝐼 = (3

𝐼3 2⁄ ) [ln(1 + √𝐼) − √𝐼 +𝐼

2] (6)

where 𝜆𝑖𝑗 are constant parameters, analogous to the second virial coefficient, representing

the net effect of the various short-range interaction forces between cations and anions.

c) Pitzer model

Pitzer model [64] was based on the Guggenheim model to develop his ion interaction

equation for electrolytes. He extended the formulation of the Debye-Hückel equation to

make it consistent with the McMillan-Mayer approach [65] to the theory of osmotic virial

expansion. The excess Gibbs energy of solutions containing 𝑚𝑠 kg of solvent and 𝑚𝑖, 𝑚𝑗,

etc. moles of the solute species i, j, etc. is equal to:

𝐺𝐸

𝑅𝑇= −

1

3𝑛𝑠𝐴𝛾 [

𝐼1 2⁄

1+𝑏𝐼1 2⁄ ] +1

𝑛𝑠∑ ∑ 𝜆𝑖𝑗(𝐼)𝑚𝑖𝑚𝑗 +

1

𝑛𝑠2 ∑ ∑ ∑ 𝜇𝑖𝑗𝑘𝑚𝑖𝑚𝑗𝑚𝑘𝑘𝑗𝑖𝑗𝑖 (7)

Pitzer's model adds to the expression of excess Gibbs energy the second and third terms of

virial expansion. Specifically, the third parameter 𝜇𝑖𝑗𝑘 is constant and represents the net

effect of various short-range interaction forces between three species.

32

Also, Pitzer and Mayorga [66] obtained other relationships that differ from the first, the

dependence of the second virial coefficient (𝜆𝑖𝑗) with respect to ionic strength being the

most important. This is also evident in the tabulated values [66-71].

In 1980 Pitzer [72] published other extensions of the Debye-Hückel equation, using molar

fractions of the components and with differences in the expression of excess Gibbs energy

of long-range interactions:

𝐺𝐸,𝐼,𝑅

𝑅𝑇= −(∑ 𝑛𝑘) (

1000

𝑀𝑠)

1 2⁄

(4𝐴𝛾𝐼

𝑏𝑠) ln(1 + 𝑏𝑠𝐼1 2⁄ ) (8)

The summation of this equation includes all species, whether neutral or ionic. From this

extension new terms are added and with the second virial coefficient written in terms of

ionic strength, one has:

𝐺𝐸

𝑛𝑠𝑅𝑇=

−4𝐼

𝑏𝑠(

𝑀𝑠

1000) 𝐴𝛾 ln(1 + 𝑏𝑠𝐼1 2⁄ ) + (

𝑀𝑠

1000) (∑ ∑ 𝜆𝑖𝑗(𝐼)𝑚𝑖𝑚𝑗 + ∑ ∑ ∑ 𝜇𝑖𝑗𝑘𝑚𝑖𝑚𝑗𝑚𝑘𝑘𝑗𝑖𝑗𝑖 ) (9)

where 𝑏𝑠 is a constant depending on the solvent.

Although the method proposed by Pitzer to calculate the activity coefficient has been

applied successfully to the description of many solutions, other proposals can be found in

the literature, such as the model of Chen and Evans [73] that uses the NRTL (Non-Random

Two-Liquid) model of Renon and Prausnitz [74].

d) NRTL (Non-Random Two-Liquid) model

While the Pitzer model specifically considers the ion–ion interactions, Chen's model takes

into account interactions such as ion–molecule and molecule–molecule, which may

eventually be important. In 1979, Chen et al. [75] proposed an extension of the Pitzer

33

model that allows interactions between all kinds of solutes, ionic or molecular. These

interactions are reduced rapidly with increasing distance, unlike electrostatic interactions.

Therefore, long-range forces have a dominant effect in dilute solutions, but as the

concentration increases the importance of short-range forces increases. The authors used

the extension of the Debye-Hückel model proposed by Pitzer to represent the contribution

of long-range (ion–ion) interactions. The short-range interaction is calculated as a

symmetric model, based on the hypothetical reference state of pure solvent, and

homogeneously mixed with completely dissociated electrolytes. The model is normalized

by the activity coefficient at infinite dilution to obtain an asymmetrical model. The NRTL

model belongs to the group of so-called local-composition models.

Among all the previously detailed models, the present work has focused on the Pitzer ion-

interaction model, due to this model has been successfully used by different authors for the

prediction of solubilities in binary, ternary, and multicomponent systems over a wide range

of concentrations and temperatures [76].

Because of this, the following section outlines the work performed by several authors

related to this topic.

4.2 Pitzer model applied to the thermodynamics of natural waters and copper sulfate.

4.2.1 Thermodynamics of natural waters systems using the Pitzer model.

In the work of Harvie and Weare [76], the accuracy of the Pitzer equations was tested in the

modeling of the mineral solubilities for the Na-K-Mg-Ca-Cl-SO4-H2O system. It has been

developed for predicting mineral solubilities in brines from zero to high ionic strengths.

This model utilizes activity coefficient expressions developed by Pitzer and co-workers and

an algorithm for rapidly identifying the coexisting phases and their composition at

equilibrium. The activity coefficient expressions were parameterized using binary and

ternary system solubility and osmotic data. In this work, it was found that the third virial

coefficients are essential for predicting thermodynamic properties at high concentrations;

however, the addition of a fourth virial coefficient term is not necessary for accurate

34

solubility predictions. The authors also outlined an algorithmic procedure for rapidly

finding the equilibrium configuration of a system; this algorithm has been found to be quite

reliable and efficient.

Moller [77] described a chemical equilibrium model for the Na-Ca-Cl-SO4-H2O system in

the temperature range of 298.15 to 523.15 K and from zero to high concentrations (up to 18

m). The concentration and temperature dependence of the model was established by fitting

available activity, solubility, osmotic and electromotive force (emf) data, where a single ion

complex, CaSO4, which increases in strength with temperature, was included in the model.

The validation of model accuracy by comparison with laboratory and field solubility data

was included. In this work, phase diagrams constructed for the Na-Ca-Cl-SO4-H2O system,

and the predicted solubilities of anhydrite and hemihydrate in concentrated seawater at high

temperature showed very good agreement with the reported data. Calculations of the

temperature of gypsum-anhydrite coexistence as a function of water activity were

compared to reported values, and were used to estimate the composition-temperature

relation for the gypsum–anhydrite transition in natural brine evaporation. A preliminary

model for barite solubility in sodium chloride solutions at high temperatures (from 373.15

to 523.15 K), based on this parameterization of the CaSO4-NaCl-H2O system, showed good

agreement with the reported data. Later, Greenberg and Moller [78] developed an

expansion of the variable temperature model of the Na-Ca-Cl-SO4-H2O system reported

previously by Moller [77]. In this work, a chemical equilibrium model used to calculate

solubilities within the Na-K-Ca-Cl-SO4-H2O system from zero to high ionic strengths and

in the temperature range of 273.15 to 523.15 K was described. It was parameterized by

fitting available osmotic and solubility data in all common ion systems involving the

potassium ion: Na-K-Cl-H2O, Na-K-SO4-H2O, K-Cl-SO4-H2O, K-Ca-Cl-H2O and K-Ca-

SO4-H2O. Limitations of the model due to data insufficiencies were discussed because at

high temperatures there is a lack of data in some ternary systems, and the model was non-

convex at very high ionic strengths (𝐼 > 20 m); therefore, the model must be used cautiously

in the temperature range of 423.15 to 523.15 K. Additionally, model predictions for

solubility in the complex reciprocal systems, Na-K-Cl-SO4-H2O and K-Ca-Cl-SO4-H2O,

were compared with experimental data; however, data for the two systems were available

only in the temperature ranges 273.15–373.15 K and 273.15–328.15 K, respectively. The

35

phase diagram predicted for the halite-saturated Na-K-Ca-Cl-SO4-H2O quinary system at

373.15 K was also presented.

In the work of Christov and Moller [79], a model was described that calculated the solute

and solvent activities and solid-liquid equilibria in the H-Na-K-OH-Cl-HSO4-SO4-H2O

system from dilute to high solution concentration within the temperature range of 0 to

523.15 K. All binary and ternary subsystems were included in the model parameterization.

This model expanded the variable temperature Na-K-Cl-SO4-H2O model reported by

Greenberg and Moller [78] by including acid (H2SO4, HCl) and base (NaOH, KOH)

species, where the behavior of bisulfate formation in multicomponent acidic solutions, the

solid/solution equilibria involving very soluble acid sulfate, and solid-liquid equilibria in

NaOH and KOH solutions were described at high temperatures and concentrations.

Accordingly, in this work temperature functions for the chemical potentials of 11 acidic and

basic sodium and potassium salts were established from solubility data in corresponding

binary and ternary solutions.

4.2.2 Thermodynamic properties of copper sulfate solutions

In the literature, there are several authors who have determined the thermodynamic

properties of copper sulfate, as water activities, osmotic coefficients and activity

coefficients.

Robinson and Jones [80] determined values of osmotic and activity coefficients for aqueous

solutions of CuSO4, MgSO4, ZnSO4, CdSO4, MnSO4, and NiSO4 at 298.15 K over a wide

concentration range. In the case of copper sulfate, the concentration range used was from

0.1 to 1.4 m. The work of Wetmore and Gordon [81] reported the activity coefficients of

copper sulfate at different molalities (up to 1 m) in the temperature range of 288.15 to

318.15 K. Miller et al. [82] presented thermodynamic and transport data for aqueous CuSO4

solutions at 298.15 K from low concentrations to near saturation (from 0.00458 to 0.10355

m). Among the determined values were diffusion coefficients, electrical conductances and

osmotic coefficients. These data were critically compared with those found in the literature.

36

Apelbat [83] presented values for vapor pressures, water activities, and osmotic coefficients

of saturated solutions of KBr, (NH4)2SO4, CuSO4, FeSO4, and MnCl2 in the temperature

range of 283.15 to 308.15 K. The temperature dependence of the vapor pressures at

saturation has permitted the evaluation of enthalpy changes associated with the

simultaneously occurring evaporation and crystallization processes.

In the work of Guendouzi et al. [84], the hygrometric method described in a previous work

[85] was used for the determination of the water activities of aqueous solutions of Li2SO4,

Na2SO4, K2SO4, (NH4)2SO4, MgSO4, MnSO4, NiSO4, CuSO4, and ZnSO4 at 298.15 K, and

in the concentration range of 0.1 mol/kg up to saturation. Using these data, it was possible

to determine thermodynamic properties such as osmotic and activity coefficients for each

salt solution using the Pitzer model. Yang et al. [86] mentioned in their work that the

hydrometallurgical processes based on heavy metal sulfate solutions are important for the

extraction and purification of many important metals, including Mn, Co, Ni, Cu, and Zn.

Accordingly, the water activities of the binary heavy metal sulfate aqueous systems MSO4-

H2O (M = Mn, Co, Ni, Cu, Zn) were measured at 323.15 K using an isopiestic apparatus. In

the case of copper sulfate, the values reported were in the concentration range of 0.1289 to

2.0560 m. The reliability of the apparatus was verified by comparing the present data with

established literature results at 298.15 K for the test systems, and for the two reference

systems; CaCl2-H2O and H2SO4-H2O at both the 298.15 and 323.15 K. From this work it

was concluded that the measured water activities reported can be useful tools to

parameterize thermodynamic models of heavy-metal hydrometallurgical processes.

4.2.3 Pitzer ion-interaction model applied to the CuSO4-H2SO4-H2O system

The modelling of aqueous mixtures of a bivalent metal sulfate (such as copper sulfate) and

sulfuric acid, according to the treatment of Pitzer, is complicated by the formation of

bisulfate ion (HSO4-) and by the need to include the effects of unsymmetrical mixing of

ions of like but unequal charge. Because of the economic importance of the recovery of

copper by the leaching of its ores with sulfuric acid, it is especially important to improve

estimates of the Pitzer parameters for the CuSO4-H2SO4-H2O system.

37

In the literature, there are only a few works where the ion-interaction model of Pitzer have

been applied to systems containing copper sulfate; however, all these works have been

developed at 298.15 K and are detailed below:

Pitzer and Mayorga [66] discussed the behavior of 2-2 and higher valence type electrolytes,

where the model parameters of the binary systems MSO4-H2O (M = Ca, Cu, Zn, Ni, Mn) at

298.15 K, have been reported. In the work of Tanaka [87], the equilibrium distribution

ratios of Cu(II) between sulfuric acid solutions and xylene solutions have been measured

over a wide copper concentration range. In this work, a model was described with special

attention to the aqueous phase formulation, where Pitzer equations for free activity

coefficients of the ions in the aqueous phase were employed. Estimated values of the ratios

of the activity of Cu(II) to the square of the activity of hydrogen ion in the CuSO4-H2SO4-

H2O system have been compared with literature data. These results have supported the

effectiveness of Pitzer’s equations as a tool for the prediction of equilibrium distribution

ratios. Baes et al. [88] applied the Pitzer ion-interaction model to available osmotic,

solubility and emf data for the CuSO4-H2SO4-H2O system at 298.15 K, with inclusion of

unsymmetrical mixing effects, where published parameters for the H2SO4-H2O system and

evaluated literature data were employed to obtain parameters for the CuSO4-H2O system.

This work included numerical results of isopiestic and emf measurements of Majima and

Awakura [89], data on the solubility of CuSO4·5H2O in H2SO4 solutions [26], and emf

results of Holland and Bonner [90]. Wang et al. [91] selected a thermodynamic model to

simulate the properties of binary and ternary systems, and to predict the solubility phase

diagrams of the quaternary systems over a wide concentration range. This work simulated

the solubility of gypsum in the binary and ternary systems MSO4-H2O (M = Ca, Cu, Zn, Ni,

Mn), MSO4-H2SO4-H2O (M = Ca, Cu, Zn, Ni, Mn), and CaSO4- MSO4-H2O (M = Cu, Zn,

Ni, Mn) at 298.15 K with a Pitzer model in its simple form, and also predicted the

solubility of gypsum in the quaternary systems CaSO4-MSO4-H2SO4-H2O (M = Cu, Zn, Ni,

Mn) at 298.15 K. Necessary experiments were carried out to check the reliability of the

model predictions, which showed that the Pitzer thermodynamic model can predict

perfectly the solubilities of gypsum in quaternary systems. These predicted results provided

a profound understanding of how the solubility of gypsum is comprehensively affected by

H2SO4 and MSO4 (M = Cu, Zn, Ni, Mn) concentrations.

38

4.2.4 Thermodynamics of multicomponent solutions involving sodium and copper

chlorides and sulfates.

Studies on the solubility diagrams of ternary and multicomponent solutions involving

sodium and copper chlorides and sulfates are of importance especially for the production of

copper chloride and copper sulfate. This is why these solutions have been the subject of

many experimental and thermodynamic investigations by several authors. However, all

these studies have been carried out at 298.15 K.

Druzhinin and Kosyakina [92] studied the quaternary Na-Cu-Cl-SO4-H2O system at 298.15

K, finding the crystallization zone of the double salt CuSO4·Na2SO4·2H2O in the ternary

CuSO4-Na2SO4-H2O system at 298.15 K. The double salt CuCl2·NaCl·2H2O was present in

the CuCl2-NaCl-H2O ternary system. Nine crystallization fields were determined, including

a Na2SO4·CuSO4·2H2O·nNa2SO4 solid solution, in the reciprocal aqueous system that was

studied.

Filippov et al. [93] and Filippov and Nohrin [94] determined the compositions of the

saturated ternary solutions and the solid phases crystallizing from them in the NaCl-CuCl2-

H2O and Na2SO4-CuSO4-H2O systems at 298.15 K.

Downes and Pitzer [95], have used the isopiestic method to determine the dependence of

the osmotic coefficients on the concentration of the binary CuCl2 (aq) and CuSO4 (aq) and

the ternary NaCl-CuCl2-H2O, Na2SO4-CuSO4-H2O, and CuCl2-CuSO4-H2O solutions. In

addition, the authors also determined the binary and ternary Pitzer ion-interaction

parameters. These mixtures, which also involve a salt of the 2-2 type, seemed likely to be

more complicated because CuCl2 is known to be associated [96]. It was therefore of interest

to compare the experimental osmotic coefficients for the binary mixtures with those

predicted by the equations using only the parameters characteristic of the single-salt

solutions. In addition, the experimental osmotic coefficients for the four-ion mixtures were

compared with the values calculated using the different parameters deduced from the

common-ion mixtures.

In the work of Palaban and Pitzer [97], the solubilities in binary and ternary electrolyte

mixtures in the system Na-K-Mg-Cl-SO4-OH-H2O were calculated at high temperatures

39

using available thermodynamic data for solids and for aqueous electrolyte solutions.

Activity and osmotic coefficients were derived from the ion-interaction model of Pitzer, the

parameters of which were evaluated from experimentally determined solution properties or

from solubility data in binary and ternary mixtures. In this work, a good agreement with

experimental solubilities for binary and ternary mixtures indicated that the model can be

successfully used to predict mineral-solution equilibria at high temperatures. Then, Palaban

and Pitzer [98] developed a model for the thermodynamic properties of Na2SO4 (aq) in

hydrothermal solutions based on the ion-interaction or virial coefficient approach of Pitzer

[64, 99]. In this model, the experimental heat capacities of aqueous Na2SO4 solutions were

used, together with other experimental data on heat capacities, enthalpies and osmotic

coefficients available in the literature. In addition, NaCl (aq) was used as a model substance

to approximate the pressure dependencies of the thermodynamic properties of Na2SO4 (aq).

Standard state properties and activity and osmotic coefficients derived from this model

permitted the calculation of sodium sulfate solubilities up to 573.15 K. In this work, a good

agreement between experimental and predicted solubilities of mirabilite and thenardite in

water indicated that the ion-interaction approach can be used successfully to predict

mineral-solution equilibria up to 573.15 K. In the work of Christov [100] the molalities of

the CuCl2-CuSO4-H2O system were investigated in saturated solutions at 298.15 K by the

physico-chemical analysis method, where the crystallizations of only the simple salts

CuCl2·2H2O, and CuSO4·5H2O were established. The ternary solutions NaCl-CuCl2-H2O,

Na2SO4-CuSO4-H2O and CuCl2-CuSO4-H2O, were simulated thermodynamically at 298.15

K using the Pitzer model. The ternary parameters of ionic interaction were chosen on the

basis of the compositions of saturated ternary solutions, taking into account the

unsymmetrical mixing terms. The calculated thermodynamic properties were used for a

thermodynamic study of the quaternary reciprocal system Na-Cu-Cl-SO4-H2O, where very

good agreement was found between calculated and experimental solubility isotherms.

In addition, some authors have used a simple methodology for the determination of

solubilities in multicomponent systems where the Pitzer model was used to quantify the

effect of a salt, while a similar equation from the Born model was used to quantify a

cosolvent effect. These works are detailed below:

40

Kan et al. [101] presented a model to calculate the effect of methanol on barite, gypsum,

celestite and halite solubility in methanol/water/salt and ethylene glycol/water/salt

solutions. Here, the Pitzer theory was used to model the effect of the salt, while a Born-type

equation approach was used to model the effect of the cosolvent. Results showed that the

barite solubility was significantly reduced with 50% methanol, and other mineral

solubilities were also reduced significantly. On the other hand, ethylene glycol had much

less impact on the mineral solubility than did methanol. In this work, good agreements

between the model predictions and both experimental and literature results were observed,

concluding that these equations provide a predictive algorithm to assess the potentially

adverse effects of methanol and ethylene glycol on mineral scale formation during oil and

gas production.

A similar work was performed by Jiménez et al. [102], where a representation of the solid–

liquid equilibrium of potassium sulfate in diverse water/organic solvent mixtures (water/1-

propanol, water/methanol, water/ethanol, and water/acetone) in the temperature range of

288.15 to 318.15 K was carried out. In this work, the experimental solubility data of

potassium sulfate in diverse mixed solvents were obtained from the literature, while the

thermodynamic representation of the phase equilibrium was based on a simple

methodology reported in the literature [101]. Results of this work showed a good agreement

between the calculated and the experimental solubility data of K2SO4 in the different

solvent mixtures.

It is important to mention that the simple methodology used in these works [101, 102] also

allowed the calculation of amounts of precipitated salt, and the optimum yield, as a function

of the cosolvent concentration.

41

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49

CHAPTER III

SOLUBILITIES AND PHYSICAL PROPERTIES OF SATURATED SOLUTIONS

IN THE COPPER SULFATE + SULFURIC ACID + SEAWATER SYSTEM AT

DIFFERENT TEMPERATURES

Francisca J. Justel, Martha Claros, María E. Taboada*

Department of Chemical Engineering, University of Antofagasta, Angamos 601,

Antofagasta, Chile

ABSTRACT

In Chile, the most important economic activity is mining, concentrated in the north of the

country. This is a desert region with limited water resources; therefore, the mining sector

requires research and identification of alternative sources of water. One alternative is

seawater, which can be a substitute of the limited freshwater resources in the region. This

work determines the influence of seawater on the solid−liquid equilibrium for acid

solutions of copper sulfate at different temperatures (293.15 to 318.15 K), and its effect on

physical properties (density, viscosity, and solubility). Knowledge of these properties and

solubility data are useful in the leaching process and in the design of copper sulfate

pentahydrate crystallization plants from the leaching process using seawater by means of

the addition of sulfuric acid.

Keywords: Seawater, Copper sulfate, Sulfuric acid.

“This is an extended version of the manuscript presented at the VII Brazilian Congress of

Applied Thermodynamics – CBTermo 2013, Uberlândia, Brazil”

50

INTRODUCTION

The most important economic activity in Chile is mining. Currently, there is a worldwide

shortage of available freshwater. Therefore, mining industries are developing new methods

to optimize water use [1]. In northern Chile, for example, certain mining companies are

using raw seawater in their production processes [2] and purified seawater by reverse

osmosis [3]. In a mining process, the solid−liquid equilibrium and physical properties of

solutions change upon seawater incorporation, especially the density and viscosity; which

are used in pipe-sizing and pumping calculations. These properties are related to the cost of

energy required to bring seawater to mining operations, usually farther than 120 km [4].

Copper sulfate pentahydrate (Blue vitriol) is a copper salt with a wide range of commercial

applications: in agriculture as a pesticide, fungicide, feed, and soil additive [5]; in mining, it

is used as a floatation reagent in recovery of zinc and lead [6]; as a blue and green pigment

in dyes, as a print toner in photography, in the production of other copper compounds, and

in leather tanning [7].

Actually, the production process of copper sulfate pentahydrate includes the following

steps: 1) Heap leaching, where copper is obtained from oxidized ores using a mixture of

sulfuric acid and water; 2) Solvent extraction, where copper is extracted from the leaching

solution by mixing with a product called organic; 3) Crystallization, where the copper-

loaded organic is discharged using a concentrated acid solution; 4) Re-crystallization,

where copper sulfate is dissolved in freshwater at a temperature of 80-90 °C, and then

crystallized by cooling to 25-30 °C, in order to remove the impurities [8].

Copper sulfate in distilled water solutions has been investigated for crystallization,

supersaturation, solid-liquid equilibrium, and properties [5, 6, 9]. In these studies,

crystallization conditions of copper sulfate solutions were determined as a function of both

temperature and sulfuric acid concentration. In order to optimize the water use, it is

interesting to investigate the influence of seawater on the copper sulfate crystallization

process. In the literature, there is a publication available of the behavior of copper sulfate in

a seawater system [4], which provides solubilities and physical properties data of CuSO4 in

seawater at pH 2. The present work studies the effect of seawater (3.5% salinity) on the

solid-liquid equilibrium of copper sulfate in acid solutions at different temperatures (from

293.15 K to 318.15 K). This temperature range was chosen because is within the range in

51

which the crystallization process operates. In addition, the physical properties, density, and

viscosity of the saturated solution are experimentally measured and correlated with

empirical equations, finding a good agreement.

From the results obtained in this investigation, and in order to minimize the use of

freshwater, the next step of this work is to perform the copper sulfate crystallization process

from leaching solutions using seawater to study the effect of the ions present in seawater on

the habit and size of copper sulfate pentahydrate crystals.

2. MATERIALS AND METHODS

2.1 Reagents

Analytical grade reagents were used (copper (II) sulfate pentahydrate, Merck, 99 %;

absolute sulfuric acid, Merck, 95 to 97 %, absolute). The experiments were performed

using filtered natural seawater obtained from San Jorge Bay, Antofagasta, Chile. Table 1

shows the composition of the seawater, obtained by chemical analysis, used in this work

[4].

Table 1. Individual ions in seawater from Bahia San Jorge, Chile (mg·L−1

) [4].

Na+

Mg+2

Ca+2

K+

B+3

Cu2+

Cl-

SO4-2

HCO3-

NO3-

9480 1190 386 374 4.6 0.072 18765 2771 142 2.05

2.2 Apparatus

The solutions were prepared using an analytical balance (Mettler Toledo Co. model

AX204, with 0.07 mg precision). To obtain the phase equilibrium data at different

temperatures, a rotary thermostatic bath (to ± 0.1 K, 50 rpm) with a capacity of ten 90 mL

glass flasks was used. The densities were measured using a Mettler Toledo DE-50 vibrating

tube densimeter with ± 5·10−2

kg·m−3

precision.

The kinematic viscosities were obtained using a calibrated micro-Ostwald viscometer with

a Schott-Gerate automatic measuring unit (model AVS 310), equipped with a thermostat

52

(Schott-Gerate, model CT 52) for temperature regulation. The absolute viscosities were

calculated by multiplying the kinematic viscosity and the respective density.

2.3 Procedures

2.3.1 Equilibrium time determination

The equilibrium time was determined at 298.15 K. Acidic seawater was prepared by adding

sulfuric acid to seawater and stirring the solution until it reached pH 2; this pH was used

because it is similar to the pH levels in copper mining operations. The masses of copper (II)

sulfate pentahydrate in the solution (seawater at pH 2) were measured. An excess of copper

(II) sulfate pentahydrate was added to ensure saturation of the solution. Several saturated

solutions (CuSO4 + acid seawater) were placed in closed glass flasks and immersed in a

rotary water bath at 298.15 K, these solutions were mechanically shaken. Every hour, the

rotation was stopped, one flask was removed from the bath and, maintaining the work

temperature (298.15 K) and using a syringe filter (to ensure that no copper sulfate

pentahydrate solid was present in the solution), the solution density was measured. The

equilibrium time was determined when the solutions that were taken at different times

(every one hour), reached constant densities.

2.3.2 Measurement of physical properties in different conditions

After the equilibrium time was determined, ten solutions (CuSO4 + acid seawater) at

different acid concentrations were prepared.

These solutions were stirred in a rotatory water bath for 8 hours (equilibrium time). The

rotation was then stopped and the solutions were decanted, maintaining the work

temperature. Then, in the thermostatic bath, and using a syringe filter at a slightly elevated

temperature (to prevent salt precipitation at lower temperatures), the solutions (without

solid) were obtained for each equilibrium point.

53

Physical properties (density and viscosity) were measured in triplicate for each solution. On

the other hand, copper (II) concentration was measured in duplicate by atomic absorption

and the CuSO4 solubility was obtained by stoichiometry. All measurements of the physical

properties and solubilities were performed at four different temperatures: 293.15, 298.15,

308.15, and 318.15 K.

3. RESULTS AND DISCUSSION

3.1 Experimental results

The solubilities, densities, and viscosities are shown in Table 2, for the system studied at

different temperatures and acid concentrations.

54

Table 2. Solubility (wCuSO4), density (ρ), and viscosity (η) for saturated solutions of

copper sulfate in seawater at various acid concentrations and temperatures.

wH2SO4 wCuSO4 ρ/g·cm−3

η/mPa·s

293.15 K

0.0036 0.1684 1.21779 2.549

0.0075 0.1669 1.21679 2.514

0.0152 0.1620 1.21807 2.485

0.0235 0.1570 1.21861 2.448

0.0396 0.1506 1.21897 2.379

0.0608 0.1369 1.22326 2.370

0.0828 0.1260 1.22722 2.353

0.1056 0.1179 1.22998 2.342

0.1298 0.1043 1.23603 2.361

0.1810 0.0813 1.25036 2.432

298.15 K

0.0035 0.1763 1.22742 2.368

0.0071 0.1745 1.22705 2.345

0.0143 0.1705 1.22707 2.293

0.0221 0.1661 1.22731 2.261

0.0375 0.1572 1.22838 2.213

0.0571 0.1477 1.23131 2.175

0.0775 0.1388 1.23369 2.164

0.0994 0.1284 1.23776 2.160

0.1214 0.1182 1.24130 2.165

0.1691 0.0956 1.25438 2.204

308.15 K

0.0034 0.2020 1.25381 2.113

0.0070 0.1995 1.25379 2.114

0.0142 0.1952 1.25285 2.069

0.0219 0.1898 1.25355 2.032

0.0369 0.1832 1.25575 1.982

0.0561 0.1754 1.25452 1.949

0.0761 0.1659 1.25710 1.927

0.0981 0.1558 1.25794 1.910

0.1183 0.1498 1.26527 1.910

0.1640 0.1330 1.27592 1.937

318.15 K

0.0032 0.2335 1.28672 2.014

0.0065 0.2316 1.28680 2.004

0.0132 0.2252 1.28478 1.966

0.0203 0.2228 1.28468 1.934

0.0350 0.2076 1.28364 1.866

0.0527 0.2039 1.28466 1.840

0.0711 0.1973 1.28634 1.801

0.0940 0.1758 1.28865 1.777

0.1134 0.1703 1.29342 1.797

0.1579 0.1526 1.30287 1.811

55

3.1.1 Solubilities

Table 2 shows the solubility results, expressed as mass fraction of copper sulfate (wCuSO4)

for different acid mass fractions (wH2SO4). A significant decrease in solubility was clearly

observed with the increase of sulfuric acid in solution; this behavior was observed for all

the temperatures. This behavior of the solubility is due to the common ion effect, because

copper sulfate and sulfuric acid share the same SO42-

ion [10].

Solubility, expressed as a mass fraction, decreases from approximately 0.1684 to 0.0813 at

293.15 K; 0.1763 to 0.0956 at 298.15 K; 0.2020 to 0.1330 at 308.15 K; and 0.2335 to

0.1526 at 318.15 K. These results show that sulfuric acid might be used as an advantageous

co-solvent in the crystallization processes design of copper sulfate pentahydrate.

The solubility results of the saturated solution may be correlated with the sulfuric acid

composition by the following equation:

𝑠 = 𝐴 + 𝐵 × 𝑤20.5 (1)

where 𝑠 is the solubility in mass fraction, 𝑤2 represents H2SO4 mass fraction, and 𝐴 and

𝐵 are fitting parameters.

3.1.2 Physical properties

Table 2 presents the densities and viscosities of the saturated solutions for the copper

sulfate + seawater + sulfuric acid system.

The values for density and viscosity were correlated as a function of copper sulfate and

sulfuric acid composition following Equations (2) and (3), respectively:

𝜌 = 𝑒𝑥𝑝(𝐴 + 𝐵 × 𝑤10.5 𝑙𝑛 𝑤1 + 𝐶 × 𝑤2

2.5) (2)

𝜂 = 𝑒𝑥𝑝(𝐴 + 𝐵 × 𝑤1 + 𝐶 × 𝑤22.5 + 𝐷 × 𝑤2

2.5 × 𝑤13.5) (3)

56

where, 𝑤1 represents the CuSO4 mass fraction, 𝑤2 represents sulfuric acid mass fraction,

and 𝐴, 𝐵, 𝐶, and 𝐷 are fitting parameters. The units for density and viscosity used in these

equations are g·cm−3

and mPa·s, respectively.

The parameter values were obtained by means of the least squares method, for all

experimental data, and are shown in Table 3.The absolute average deviations (AAD) for the

fitted parameters are also presented.

Table 3. Parameters values for density, viscosity and solubility for saturated copper sulfate

in acidic seawater system.

Property 𝐴 𝐵 𝐶 𝐷 𝐴𝐴𝐷a

293.15 K

ρ/g·cm-3

-0.2322 -0.5861 2.6112 0.0005

η/mPa·s 0.8566 0.5137 1.6012 -1198.5 0.0056

w 0.1905 -0.2353 0.0043

298.15 K

ρ/g·cm−3

-0.0399 -0.3351 1.9916 0.0004

η/mPa·s 0.9453 -0.4092 -4.2035 -1455.1 0.0029

w 0.1966 -0.2238 0.0038

308.15 K

ρ/g·cm−3

0.2287 0.0037 1.6397 0.0007

η/mPa·s 0.6205 0.6883 3.2718 -607.6 0.0048

w 0.2181 -0.1980 0.0023

318.15 K

ρ/g·cm−3

0.3255 0.1054 1.7079 0.0007

η/mPa·s 0.3784 1.4117 7.1461 -311.5 0.0055

w 0.2530 -0.2401 0.0037 aAAD= ∑|𝑠𝑒𝑥𝑝 − 𝑠𝑐𝑎𝑙| /n, where n is the number of experimental points.

The results show that these equations fit satisfactorily the density, viscosity, and solubility

experimental data.

The solubility of copper sulfate in acidic seawater with different concentrations of sulfuric

acid and physical properties of the saturated solutions, at four different temperatures

(293.15, 298.15, 308.15, and 318.15 K) are shown in Figures 1 to 3, along with correlated

data.

57


298.15 K; ▲, 308.15 K; ●, 318.15 K; ─, correlations with Eq. (1).

It is possible to note that, for all the temperatures, the solubility decreases with increasing

acid concentration. Also, the figure shows that solubility levels increased with temperature;

this is because, as the solution temperature increases, the average kinetic energy of the

molecules that make up the solution also increases. This increase allows the solvent

molecules to break apart the solute molecules more effectively that are held together by

intermolecular attractions.

Figure 2 compares the density of saturated solutions of copper sulfate in acid seawater at

four different temperatures (293.15, 298.15, 308.15, and 318.15 K).

0.07

0.09

0.11

0.13

0.15

0.17

0.19

0.21

0.23

0.25

0 0.05 0.1 0.15 0.2

s (g

/g s

olu

tio

n)

wH2SO4

58



As can be seen, there is a slight decrease in the density of the solutions at low acid

concentrations. However, at a certain point, it begins to increase. This behavior is better

observed at higher temperatures (at low temperatures this decrease is not clear). This

phenomenon could be attributed, at low acid concentrations, to the copper sulfate solubility

decrease, and therefore, the density; however, as the acid concentration increases, the

solution density begins to increase, due to the high density of the sulfuric acid. Figure 2

also shows that the density values increased slightly with temperature.

Figure 3 compares the viscosity of saturated solutions of copper sulfate in acid seawater at

four different temperatures (293.15, 298.15, 308.15, and 318.15 K).

1.21

1.22

1.23

1.24

1.25

1.26

1.27

1.28

1.29

1.3

1.31

0 0.05 0.1 0.15 0.2

𝜌 (

g∙c

m-3

)

wH2SO4

59

Figure 3. Viscosity for the saturated solutions (CuSO4 + acid seawater): ■, 293.15 K; ♦,


It is possible to note that, for all the temperatures, viscosity values decrease with increasing

acid concentration. Also, the figure shows that viscosity levels decrease slightly with

increasing temperature. This behavior is expected, as observed in the work of Hernández,

Hotlos and Price [4, 11, 12].

These results confirmed the good fit between experimental values for concentrations of the

salt and the physical properties of the saturated solutions at four temperature levels, in a

broad range of acid concentrations.

On the other hand, looking for a single equation that includes the effect of different

temperatures, we used the empirical models proposed in the work of Milligan and Moyer

[5]; to estimate the density and solubility of the system CuSO4-H2SO4-H2O at different

temperatures (Equations (4) and (5)). The parameters of these equations were adjusted in

acid seawater; for 𝑌0, solubility values of CuSO4∙5H2O in freshwater from the literature

[13] were utilized.

1.7

1.9

2.1

2.3

2.5

2.7

0 0.05 0.1 0.15 0.2

η (

mP

a·s)

wH2SO4

60

The proposed equations are shown below:

𝜌 = 1

𝐶2ln [𝑒𝐶2𝐴2 + 𝑒𝐶2((𝑎2)𝑋+𝐵2)] (4)

𝑌 = 1

𝐶1𝑙𝑛 [𝑒𝐶1(𝐴1𝑋+𝑌0) − 𝑒𝐶1(𝐴1𝑋+𝐵1) + 𝑒𝐶1𝐵1] (5)

Where:

Y = mass percentage of CuSO4∙5H2O in saturated solution

ρ = density of saturated solution in g∙cm-3

X = mass percentage of H2SO4 in solution

T = temperature in °C

Y0 = 20.37e0.01316T = mass percentage of CuSO4∙5H2O in saturated solution with no acid

content

A1= -𝑎1e(𝑏1)T (6)

B1= 𝐶1[1+ e-(𝑑1)(T-𝑒1)]-1

(7)

C1=𝑓1 [1+𝑔1(T- ℎ1)2]

-1

(8)

A2= 𝑏2e(𝑐2)T(𝑑2)

(9)

B2= 𝑒2+𝑓2T (10)

C2=𝑔2 [1+ℎ2(T- 𝑖2)2]

-1

(11)

The parameter values are shown in Table 4.The absolute average deviations (AAD) for the

fitted parameters are also presented.

61

Table 4. Parameter values for density and solubility for saturated copper sulfate in acidic

seawater system.

Property Parameters Temperature AADa

Solubility

𝑎1 0.1165 293.15 K 0.2222

𝑏1 0.0943

𝑐1 21.7293 298.15 K 0.3287

𝑑1 0.0931

𝑒1 30.6388 308.15 K 0.2861

𝑓1 16.7409

𝑔1 2.0939 318.15 K 0.4501

ℎ1 15.0081

Density

𝑎2 0.0094 293.15 K 0.0008

𝑏2 1.187

𝑐2 0.00017 298.15 K 0.0005

𝑑2 1.5986

𝑒2 0.9897 308.15 K 0.0011

𝑓2 0.00162

𝑔2 15.51

318.15 K 0.0014 ℎ2 0.00038

𝑖2 34.16

𝐴𝐴𝐷𝑎=|(sexp-scal)/n|, where 𝑛 is the number of experimental points.

In Figures 4 and 5, the density and solubility values of saturated solutions of copper sulfate

in acid seawater at four different temperatures (293.15, 298.15, 308.15, and 318.15 K), and

the correlations with the Equations (4) and (5) can be seen.

The experimental values for density, and solubility in the saturated solutions were

correlated adequately using Equations (4) and (5) shown previously.

62





1.21

1.22

1.23

1.24

1.25

1.26

1.27

1.28

1.29

1.30

1.31

0 5 10 15 20

𝜌 (

g∙c

m-3

)

Weight percent H₂SO₄

10

15

20

25

30

35

40

0 5 10 15 20

Wei

gh

t per

cent C

uS

O₄∙

5H

₂O

Weight percent H₂SO₄

63

Also, the comparison between experimental values of solubility for saturated solutions of

copper sulfate in seawater, with data of copper sulfate in fresh water presented by Milligan

and Moyer [5] as a function of acid concentration at four different temperatures 293.15 K,

298.15 K, 308.15 K, and 318.15 K is performed and the results are shown in Figure 6.


298.15 K; ▲, 308.15 K; ●, 318.15 K. Black lines show freshwater data at different

temperatures from the work of Milligan and Moyer [5].

It is possible to note that the solubility of copper sulfate pentahydrate in seawater is lower

than the solubility of this salt in freshwater. This phenomenon is due to the presence of salts

in seawater, which contribute to decrease the solubility of copper sulfate. This is because

the water activity of seawater is lower than the water activity of freshwater and therefore

the solubility is lower. Furthermore, as mentioned in Table 1, seawater composition

presents 2771 mg∙L-1

of SO42-

ion, which could be responsible of the decrease in the copper

sulfate solubility in this medium, due to the common ion effect. This can be the reason

why the average deviation is higher with this equation with respect to the equation

proposed in this work.

10

15

20

25

30

35

40

0 5 10 15 20

Wei

ght

per

cent C

uS

O₄∙

5H

₂O

Weight percent H2SO4

64

4. CONCLUSIONS

With increasing temperature and acid concentration, an increase is observed in the density

of the solutions, and there is a slight decrease in the density of the solutions at low acid

concentrations.

With increasing acid concentration and temperature, there is a decrease in the solution

viscosity.

With increasing acid concentration, there is a decrease in the solubility; on the other hand,

when the temperature increases, the solubility increases.

The experimental values for density, viscosity, and solubility in the saturated solutions,

were adequately correlated using Equations (1) to (3) proposed in this work, with absolute

average deviations for density, viscosity, and solubility of 0.0005, 0.0056, and, 0.0043,

respectively, at 293.15 K; 0.0004, 0.0029 and, 0.0038, respectively, at 298.15 K; 0.0007,

0.0048, and 0.0023, respectively, at 308.15 K; and 0.0007, 0.0055, and 0.0037,

respectively, at 318.15 K.

The experimental values for density, and solubility in the saturated solutions were

correlated adequately using Equations (4) and (5), with absolute average deviations for

density, and solubility of 0.0008, and 0.2222, respectively, at 293.15 K; 0.0005, and

0.3287, respectively, at 298.15 K; 0.0011, and 0.2861, respectively, at 308.15 K; and

0.0014, and 0.4501, respectively, at 318.15 K.

The solubility of copper sulfate pentahydrate in seawater is lower than the solubility in

freshwater due to the presence of salts in seawater, which contribute to decrease the

solubility of copper sulfate.

ACKNOWLEDEGMENTS: This work was supported by Fondecyt Project 1140169.

Francisca Justel gratefully acknowledges the CONICYT grant.

65

5. REFERENCES

[1] M.A. Torres, G.E. Meruane, T.A. Graber, P.C. Gutiérrez, M.E. Taboada, Recovery of

nitrates from leaching solutions using seawater, Hydrometallurgy, 133 (2013) 100-105.

[2] O.A. Rocha, M. Claros, T.A. Graber, E.K. Flores, M.E. Taboada, Solid–Liquid

Equilibrium and Process Design of CuSO4+ NaCl+(H2O or H2SO4/H2O) Systems at 298.15


[3] R. Philippe, R. Dixon, S. Dal Pozzo, Seawater supply options for the mining industry,

2nd International Seminar on Geology for the Mining Industry, 2011.

[4] P.a.C. Hernandez, H.c.R. Galleguillos, T.f.A. Graber, E.K. Flores, M.E. Taboada, Effect

of Seawater on the Solubility and Physicochemical Properties of Acidic Copper Sulfate

Solutions, Journal of Chemical & Engineering Data, 57 (2012) 2430-2436.

[5] D. Milligan, H. Moyer, Crystallization in the Copper sulphate - Sulfuric acid - Water

System, ENG MIN J, 176 (1975) 85-89.




[8] F.I. Tabilo Christoforou, Proyecto Anico, (2012).

[9] E. Domic, Hidrometalurgia: Fundamentos, procesos y aplicaciones, Chile. Andros

Impresos, (2001).

[10] L.A. Cisternas, Diagramas de fases y su aplicación, Reverte 2009.

[11] J. Hotlos, M. Jaskuła, Densities and viscosities of CuSO4-H2SO4-H2O solutions,


[12] D.C. Price, W.G. Davenport, Densities, electrical conductivities and viscosities of

CuSO4/H2SO4 solutions in the range of modern electrorefining and electrowinning

electrolytes, Metallurgical Transactions B, 11 (1980) 159-163.

66


ACS, Washington DC.

67

CHAPTER IV

SOLID–LIQUID EQUILIBRIUM AND COPPER SULFATE CRYSTALLIZATION

PROCESS DESIGN FROM A SULFURIC-ACID–SEAWATER SYSTEM IN THE

TEMPERATURE RANGE FROM 293.15 TO 333.15 K.

Francisca J. Justel, María E. Taboada, Yecid P. Jiménez*

Department of Chemical and Mineral Process Engineering, University of Antofagasta, Av.

Angamos 601, Antofagasta, Chile

ABSTRACT

The objective of this work is to determine experimentally the solubilities and the water

activities for aqueous solutions of copper sulfate in seawater at different temperatures and

to use this information to represent the solid–liquid equilibrium of a copper-sulfate–

sulfuric-acid–seawater system. In a previous work, the experimental solubility data of

copper sulfate in acidic seawater from 293.15 to 318.15 K were obtained experimentally; in

this study, these data were complemented by measuring solubilities at 323.15 and 333.15

K.

The thermodynamic representation of the phase equilibrium is based on a simple

methodology reported in the literature with some modifications, where the Pitzer model and

a Born-type equation were used for modeling the copper sulfate and sulfuric acid effects,

respectively, and the seawater was considered as a solvent.

The amounts of copper sulfate precipitated and the optimum yield as a function of the

sulfuric acid concentration were estimated, giving relevant information for the drowning-

out crystallization process design of copper sulfate using seawater.

Keywords: Solid–liquid equilibrium, Copper sulfate, Sulfuric acid, Seawater.

68

1. INTRODUCTION

Copper mining is the most significant economic activity in the north of Chile. However,

due to the arid conditions in this zone along with water scarcity, mining industries have

required innovative solutions for the optimization of water consumption and have started to

use seawater in their productive processes [1].

Copper sulfate pentahydrate is the most important industrial compound of copper, with a

wide variety of commercial uses [2-4]; it can be crystallized from an acidic solution from

copper leaching by the addition of greater amounts of sulfuric acid, which generates

supersaturation in the aqueous dissolution of the salt [5]. In Chile, some small and medium-

sized mining companies crystallize copper sulfate from hydrometallurgical processes using

freshwater. However, it would be interesting to know the effect of seawater on the

crystallization and on the thermodynamic behavior of copper sulfate pentahydrate. This

information will be useful in the process design to produce copper sulfate pentahydrate

crystals obtained from leaching solutions using seawater by means of the addition of

sulfuric acid.

Thermodynamic properties of copper sulfate (water activities, activity, and osmotic

coefficients) have been reported in the literature by several authors: Wetmore and Gordon

[6] reported the activity coefficients of copper sulfate at different molalities (up to 1 m) and

different temperatures (288.15, 298.15, 308.15, and 318.15 K). Downes and Pitzer [7]

reported the activity and osmotic coefficients of copper sulfate in freshwater at molalities

from 0.1 to 2.0 and at 298.15 K. In this article, the Pitzer equations for 2-2 electrolytes for

the representation of the osmotic and activity coefficients for a salt and the Pitzer

parameters for copper sulfate solutions at 298.15 K were presented. Miller et al. [8]

presented thermodynamic and transport data (diffusion coefficients, electrical

conductances, and osmotic coefficients) for aqueous CuSO4 solutions at 298.15 K from low

concentrations to near saturation, where the osmotic coefficients for CuSO4 at

concentrations from 0.00458 to 0.10355 m were reported. Apelbat [9] reported the water

activities and osmotic coefficients of saturated solutions of copper sulfate in freshwater at

six different temperatures (from 283.15 to 308.15 K). Later, Gendouzi et al. [10] reported

the water activities, osmotic coefficients, and activity coefficients values of copper sulfate

69

in freshwater at 298.15 K at different molalities (from 0.2 to 1.4 m). Furthermore, the Pitzer

parameters for copper sulfate at 298.15 K were also reported. Yang et al. [11] reported the

water activities and osmotic coefficients of the binary systems MSO4 + H2O (M = Mn, Co,

Ni, Cu, and Zn) at 323.15 K from isopiestic measurements. For copper sulfate, the values

reported are in the range of concentrations of 0.1289 to 2.0560 m.

In a previous work, [12] solubility, density, and viscosity values for saturated solutions of a

copper-sulfate–sulfuric-acid–seawater system at four different temperatures (from 293.15

to 318.15 K) were reported.

The objective of the present work is to determine the saturation concentrations and water

activities of copper sulfate in seawater at different concentrations and temperatures (from

293.15 to 323.15 K). All this information was used to represent the solid–liquid equilibrium

of the copper-sulfate–sulfuric-acid–seawater system by the model proposed in this work,

which is based on a variation of the methodology of Kan et al. [13, 14].

Kan’s methodology uses the Pitzer model to quantify the effect of a salt, whereas a similar

equation to the Born model is used to quantify the cosolvent effect. The present work

proposes a variation of this method where the Pitzer model is used to represent the copper

sulfate effect and the Born model is used to represent the sulfuric acid effect, instead of a

cosolvent. Moreover, it is important to mention that in the Pitzer model, seawater is the

solvent and the seawater ions are not considered separately.

Additionally, the amounts of precipitated salt and the maximum yield from the CuSO4–

H2SO4–seawater system at different temperatures in function of the sulfuric acid

concentration were predicted. This information will be useful in the process design to

obtain copper sulfate pentahydrate crystals using seawater by applying a simple

methodology.

70

2. EXPERIMENTAL SECTION

2.1 Materials

All reagents employed in this research were of analytical grade and supplied by Merck:

copper sulfate pentahydrate, 99%; absolute sulfuric acid, 95 to 97%, and distilled deionized

water (0.054 μS/cm).

Solutions were prepared using synthetic seawater, which was prepared according to ASTM

International [15]: NaCl, 99%; MgCl2, 99–101%; Na2SO4, 99–100.5%; CaCl2∙2H2O, 99–

102%; KCl, 99.5%; NaHCO3, 99.7%; KBr, 99.5%; H3BO3, 99.5–100.5%; SrCl2∙6H2O, 99–

103%; and NaF, 99.5%. The chemical composition of the synthetic seawater is shown in

Table 1.

Table 1. Chemical composition of synthetic seawater obtained from the literature [15].

Compound Concentration (g/cm

3)

(·10-2

)

NaCl 2.4530

MgCl2 0.5200

Na2SO4 0.4090

CaCl2 0.1160

KCl 0.0695

NaHCO3 0.0201

KBr 0.0101

H3BO3 0.0027

SrCl2 0.0025

NaF 0.0003

Table 2 shows the density of synthetic seawater at six different temperatures measured in

triplicate using a Mettler Toledo DE-50 vibrating tube densimeter with a precision of ±

5·10−5

g/cm3.

71

Table 2. Synthetic seawater densities (g/cm3) at different temperatures.

Temperature (K) 293.15 298.15 308.15 318.15 323.15 333.15

Density (g/cm3) 1.02464 1.02338 1.01982 1.01586 1.01362 1.01180

Standard uncertainty u for seawater densities is 𝑢(𝜌) = 0.00005 𝑔/𝑐𝑚3

2.2 Apparatus and Procedures

2.2.1 Solubility measurements for the CuSO4–H2SO4–seawater system at 323.15 and

333.15 K

Justel et al. [12] reported density, viscosity, and solubility data for saturated solutions of

copper-sulfate–sulfuric-acid–seawater at four different temperatures (from 293.15 to 318.15

K). Here, solubilities and densities at 323.15 and 333.15 K were measured in triplicate.

Density was measured using a Mettler Toledo DE-50 vibrating tube densimeter with

precision of ± 5·10−5

g/cm3. The methodology utilized for the determination of the

solubility is described below.

The methodology for the equilibrium time determination has been reported previously [12,

16]. For the CuSO4–H2SO4–seawater system, the equilibrium time for different

temperatures was determined by Justel et al. [12], where acidic seawater was prepared by

adding sulfuric acid to seawater until it reached pH 2. The pH was measured using an

Accumet pH meter model 50 with a measurement range from –2 to 20 between 268.15 and

378.15 K and a precision of ± 0.002. The masses of the copper sulfate pentahydrate in the

solution (acidic seawater) were measured using an analytical balance (Mettler Toledo Co.,

model AX204, with a precision of 0.07 mg), and an excess of copper sulfate pentahydrate

was added to ensure that the solution was saturated. Several saturated solutions in closed

glass flasks were immersed in a rotary water bath and mechanically shaken. Every hour, the

rotation was stopped, and the solution density was measured. The equilibrium time was

determined when the solutions obtained at different times reached constant densities.

Then, ten solutions (CuSO4–acid seawater) at different acid concentrations were prepared

and stirred at 323.15 and 333.15 K in a rotary water bath during the equilibrium time. The

72

rotation was then stopped, and the solutions were decanted. In the thermostatic bath, using

a syringe filter, solutions (without solid) were obtained for each equilibrium point. The

copper (II) concentration was measured in triplicate by atomic absorption, and the CuSO4

solubility was obtained by stoichiometry; density was measured in triplicate for each

solution. Solids were kept for further analysis.

2.2.2 X-ray diffraction and thermogravimetric analysis of copper sulfate crystals

To analyze the composition of the crystals obtained in seawater medium at different

temperatures, the same procedure as described above was used, and crystals obtained at

working temperatures of 293.15, 308.15, and 323.15 K were recovered. The crystals

remaining after decantation were dried and analyzed by powder X-ray diffraction (XRD)

using an automatic, computerized X-ray diffractometer (Siemens Co., model D5000), Cu

Kα radiation with a wavelength of 1.5406 Å, and a voltage of 40 kV.

To confirm the XRD results, crystals obtained at 308.15 K (intermediate temperature) were

subjected to thermogravimetric analysis (TGA). Thermal assays were conducted with a

Mettler Toledo Thermogravimetric Analyzer TGA/DSC1, STARe system. The crucibles

used in the TGA instrument were made of platinum and were hermetically sealed. The test

was conducted in a flowing inert nitrogen atmosphere (50 ml/min) at a heating rate of

283.15 K/min. The equipment was calibrated with indium, and the sample mass was 10 mg.

The temperature range used in the experiment was from 298.15 to 573.15 K.

2.2.3 Water activity measurements of CuSO4 in seawater at different temperatures

Water activities were measured using a Novasina Corp. model AW-Center 500 electronic

hydrometer. The hydrometer was calibrated before making each set of measurements by

using standard salt solutions supplied by the manufacturer. This instrument works in the

temperature range from 273.15 to 323.15 K, so the measurements of the activities of

copper-sulfate–seawater solutions were performed in duplicate from 293.15 to 323.15 K. At

each temperature, solutions at six different concentrations of copper sulfate were measured.

73

With the objective of improving the accuracy, calibration curves using sodium sulfate

aqueous solutions were developed at each working temperature (293.15, 298.15, 308.15,

318.15, and 323.15 K). For each temperature, at least five sodium sulfate solutions were

prepared at different molalities, and the obtained data were compared and fitted to the

values reported by Holmes and Mesmer [17] obtaining calibration curves at each

temperature. Using these calibration curves for the water activities, the Pitzer parameters

𝛽(0), 𝛽(1), 𝛽(2), and 𝐶∅ for copper sulfate in synthetic seawater from 293.15 to 323.15 K

were determined.

It is important to mention that in the present work, the solutions were prepared using

synthetic seawater (Table 1) elaborated under ASTM International standards [15], which

makes reproducible all the parameters determined in the present work.

3. THERMODYNAMIC FRAMEWORK

According to Gendouzi et al. [10], using the experimental data of the water activities as a

function of molality, it is possible to determine the osmotic coefficients (∅) for each

solution using Equation (1):

∅ = −(1000 𝑣𝑚𝑀⁄ ) ln 𝑎𝑤 (1)

where 𝑣 is the number of ions released by dissociation, 𝑚 the molality, 𝑀 the molar mass,

and 𝑎𝑤 the water activity.

On the other hand, a simple method based on a variation of Kan’s methodology [13, 14] to

correlate copper sulfate solubilities in acidic seawater is proposed.

Accordingly, the activity coefficients due to the copper sulfate effect 𝛾 ±𝑆 𝐶𝑢𝑆𝑂4 were

determined by the Pitzer model [18], where for 2-2 electrolytes, the mean activity ionic

coefficients are given by the following expression:

ln 𝛾± = 4𝑓𝛾 + 𝑚𝐵𝛾 + 𝑚2𝐶𝛾 (2)

74

where:

𝑓𝛾 = −𝐴∅[𝐼1 2⁄ (1 + 𝑏𝐼1 2⁄ )⁄ + 2 𝑏⁄ ln(1 + 𝑏𝐼1 2⁄ )] (3)

𝐵𝛾 = 2𝛽(0) + (2𝛽(1) 𝛼12𝐼⁄ ) [1 − (1 + 𝛼1𝐼1 2⁄ − 1 2⁄ 𝛼1

2𝐼)𝑒𝑥𝑝−𝛼1𝐼1 2⁄] + (2𝛽(2) 𝛼2

2𝐼⁄ ) [1 −

(1 + 𝛼2𝐼1 2⁄ − 1 2⁄ 𝛼22𝐼)𝑒𝑥𝑝−𝛼2𝐼1 2⁄

] (4)

𝐶𝛾 = 3 2⁄ 𝐶∅ (5)

In these equations, m and I correspond to the molality and ionic strength, respectively. The

symbols 𝛽(0), 𝛽(1), 𝛽(2), and 𝐶∅ are solute specific parameters, and the parameters 𝛼1 , 𝛼2,

and b are constant, with values of 1.4, 12, and 1.2 Kg1/2

·mol-1/2

, respectively. Pitzer and

Mayorga [18], have reported that the values of 𝛽(2) and 𝛼2 reproduce the anomalous

behavior of 2-2 electrolytes, where have been demonstrated that these values fitted all cases

very well and were adopted for all 2-2 electrolytes.

In Equation (3), the function 𝑓𝛾 includes the Debye-Hückel term (𝐴∅) represented by the

following expression [19]:

𝐴∅ = 1 3⁄ √2 ∙ 𝜋 ∙ 𝜌 ∙ 𝑁0[𝑒2 4 ∙ 𝜋 ∙ 𝐸𝑜 ∙ 𝜀 ∙ 𝑘 ∙ 𝑇⁄ ]3 2⁄ (6)

where ρ corresponds to the density of seawater (Kg/m3), N0 to the Avogadro number

(6.022045∙1023

), 𝑘 to the Boltzmann constant (1.38066∙10-23

), e to the electron charge

(1.6022∙10-19

), E0 to the permittivity of vacuum (8.85418∙10-12

), Ɛ to the dielectric constant

of seawater, and T to the temperature in K. The values of the dielectric constant (Ɛ) of

seawater at different temperatures were obtained by the method of Hernández-Walls using

the equations reported by Stogryn [20]. Here 𝐴∅ is calculated considering the seawater as

solvent.

75

The solubility product (𝐾𝑠𝑝) of a hydrated salt is a value obtained from the solubility

(concentration), the water activity, and activity coefficient values of copper sulfate in

seawater (without acid). These last two were calculated using the Pitzer model through the

Equations (1) and (2), respectively. The 𝐾𝑠𝑝values at different temperatures were

determined by the following expression [21]:

𝐾𝑠𝑝𝐶𝑢𝑆𝑂4∙5𝐻2𝑂 = (𝑚𝐶𝑢𝑆𝑂4

)2

(𝛾 ±𝑆 𝐶𝑢𝑆𝑂4 )

2(𝑎𝑤)5 (7)

On the other hand, the sulfuric acid effect 𝛾 ±𝑁 𝐶𝑢𝑆𝑂4 is represented by an empirical equation

similar to the Born expression of the type:

𝛾 ±𝑁 𝐶𝑢𝑆𝑂4 = 10(𝑎+𝑏 𝑇(𝐾)⁄ +𝑐𝐼) 𝑥𝐻2𝑆𝑂4+𝑑𝑥2

𝐻2𝑆𝑂4 (8)

where a, b, c, and d are fitting parameters and 𝑥𝐻2𝑆𝑂4 and 𝐼 represent the mole fraction of

sulfuric acid in the H2O–H2SO4 mixture and the ionic strength, respectively.

From Equation (7), the copper sulfate saturation molality in the ternary CuSO4–H2SO4–

seawater system (𝑚𝑇) is obtained by:

𝑚𝑇 = [(𝐾𝑠𝑝𝐶𝑢𝑆𝑂4∙ 5𝐻2𝑂)

𝐵((𝛾

±𝑆 𝐶𝑢𝑆𝑂4)2 × (𝛾

±𝑁 𝐶𝑢𝑆𝑂4)2 × 𝑎𝑤

5 )𝑇

⁄ ]1 2⁄

(9)

where the subscripts B and T represent the binary (CuSO4–H2O) and ternary (CuSO4–

H2SO4–H2O) systems, respectively.

Experimental data of the solubilities of the copper-sulfate–sulfuric-acid–seawater system at

five different temperatures were correlated, minimizing the following objective function:

76

𝑂𝐹 = ∑(𝑚𝑇𝑒𝑥𝑝 − 𝑚𝑇𝑐𝑎𝑙𝑐 𝑚𝑇𝑒𝑥𝑝⁄ )2

(10)

where the subscripts exp and calc are the experimental and calculated saturation

concentrations, respectively.


4.1 Solubilities of copper sulfate in acidic seawater at different temperatures

The experimental solubility data of copper sulfate in seawater at six different temperatures

(from 293.15 to 333.15 K) and experimental density values at 323.15 and 333.15 K are

shown in Tables 3 and 4.

The experimental solubility data (in mol/Kg H2O) of copper sulfate in seawater at four

different temperatures (from 293.15 to 318.15 K) obtained in a previous work [12] are

shown in Table 3. Solubility and density values at 323.15 and 333.15 K obtained in the

present work are presented in Table 4.

Table 3. Solubilities for saturated solutions of copper sulfate in acidic seawater from

293.15 to 318.15 K at different acid concentrations obtained in a previous work [12].

T = 293.15 K T = 298.15 K T = 308.15 K T = 318.15 K

mH2SO4 mCuSO4 mH2SO4 mCuSO4 mH2SO4 mCuSO4 mH2SO4 mCuSO4

0.0000 1.3252 0.0000 1.3946 0.0000 1.6401 0.0000 1.9517

0.0460 1.3119 0.0454 1.3869 0.0461 1.6391 0.0445 1.9404

0.0958 1.3040 0.0913 1.3756 0.0933 1.6204 0.0899 1.9288

0.1943 1.2699 0.1851 1.3495 0.1885 1.5907 0.1819 1.9054

0.3013 1.2350 0.2868 1.3200 0.2918 1.5514 0.2815 1.8800

0.5136 1.1848 0.4902 1.2603 0.4960 1.5116 0.4843 1.8283

0.7940 1.0980 0.7547 1.1987 0.7651 1.4682 0.7416 1.7628

1.0948 1.0238 1.0385 1.1432 1.0508 1.4061 1.0251 1.6906

1.4221 0.9563 1.3531 1.0732 1.3731 1.3406 1.3445 1.6092

1.7690 0.8738 1.6776 1.0043 1.6873 1.3126 1.6506 1.5313

2.5546 0.7051 2.4184 0.8401 2.4278 1.2099 2.3824 1.3449

77

Table 4. Solubilities and densities for saturated solutions of copper sulfate in acidic

seawater at 323.15 and 333.15 K at different acid concentrations obtained in the present

work.

T = 323.15 K T = 333.15 K

mH2SO4 mCuSO4 ρ(g/cm3) mH2SO4 mCuSO4 ρ(g/cm

3)

0.0000 2.0746 1.30330 0.0000 2.4675 1.34400

0.0439 2.0657 1.30419 0.0419 2.4585 1.34420

0.0883 2.0568 1.30286 0.0847 2.4492 1.34378

0.1794 2.0384 1.30092 0.1717 2.4304 1.33843

0.2780 2.0185 1.29873 0.2658 2.4101 1.33682

0.4741 1.9789 1.29731 0.4541 2.3694 1.33508

0.7307 1.9271 1.29634 0.6992 2.3164 1.33350

1.0096 1.8709 1.29816 0.9649 2.2590 1.33097

1.3058 1.8111 1.30040 1.2558 2.1961 1.33481

1.6192 1.7478 1.30622 1.5536 2.1318 1.33684

2.3129 1.6079 1.31380 2.2288 1.9859 1.34757

Standard uncertainties 𝑢 for molalities of H2SO4 and CuSO4 and densities of the saturated solutions

are 𝑢(𝑚𝐻2𝑆𝑂4) = 0.0002 mol Kg H2O⁄ and 𝑢(𝑚𝐶𝑢𝑆𝑂4

) = 0.0003 mol Kg H2O⁄ , and 𝑢(𝜌) =

0.00005 g cm3⁄ , respectively.

The experimental and calculated solubility data (expressed as the molality of CuSO4 for

different molalities of H2SO4) from 293.15 to 333.15 K are shown in Figure 1, where a big

effect of sulfuric acid on the reduction of the copper sulfate solubility is observed.

According to Cisternas [22], this behavior is attributed to the common ion effect, which

causes the reduction in solubility. For the studied system, copper sulfate and sulfuric acid

share the SO42-

ion.

78

Figure 1. Solubility of saturated solutions of CuSO4–H2SO4–seawater. ■ = 293.15 K; ♦ =

298.15 K; ▲ = 308.15 K; ● = 318.15 K; × = 323.15 K; * = 333.15 K; Solid line: correlated

data; Dashed line: data predicted by the methodology proposed in this work.

4.2 Solids analysis: X-ray diffraction and thermogravimetric analysis

XRD and TGA were used to analyze the composition of the crystals obtained at different

temperatures using sulfuric acid and seawater.

Figure 2 shows the XRD patterns of samples obtained at three different temperatures

(293.15, 308.15, and 323.15 K).

0.5

1

1.5

2

2.5

3

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75

CuS

O4

(m

ol/

Kg H

2O

)

H2SO4 (mol/Kg H2O)

79

a)

b)

80

c)

Figure 2. XRD patterns of copper sulfate samples obtained at three different temperatures:

a) 293.15 K, b) 308.15 K, and c) 323.15 K. Black and red lines correspond to the standard

patterns and samples, respectively.

At the three different temperatures (293.15, 308.15, and 323.15 K), the results showed that

the obtained salt is 99.9% copper sulfate pentahydrate.

To validate the XRD results, the crystals obtained at 308.15 K were analyzed using TGA.

The results of mass loss as a function of time are shown in Figure 3.

81

Figure 3. Thermal decomposition curve of copper sulfate pentahydrate crystals obtained

from a CuSO4–H2SO4–seawater solution at 308.15 K.

From Figure 3, it is evident that when copper sulfate pentahydrate is heated (from 298.15 to

573.15 K), it loses its water of crystallization in two steps at different temperatures.

Additionally, Figure 3 shows that the total dehydration is 35.98%, where the water loss is

28.62% in the first step, corresponding to the loss of four water molecules, and 7.36% in

the second step, corresponding to the loss of one water molecule. These results allowed us

to validate the sample composition, confirming that it corresponds to copper sulfate

pentahydrate.

4.3 Water activities of the copper sulfate – seawater system at different

temperatures

The water activities of copper sulfate in seawater in the temperature range from 293.15 to

323.15 K were measured in order to validate the Pitzer model used to represent the solid–

liquid equilibrium of the copper-sulfate–sulfuric-acid–seawater system later. These water

activity values with their respective absolute average deviations (𝐴𝐴𝐷) are presented in

Table 5.

82

Table 5. Experimental and calculated water activities (aw) at different molalities of CuSO4

in seawater and at five different temperatures.

m

(mol/Kg H2O) aw

exp aw

calc AAD (∙10

-3)a

T = 293.15 K

0.8615 0.9842 0.9848

0.222

0.9598 0.9822 0.9824

1.0422 0.9806 0.9804

1.1260 0.9787 0.9782

1.2114 0.9764 0.9758

1.3017 0.9738 0.9733

T = 298.15 K

0.8617 0.9845 0.9849

0.218

0.9604 0.9826 0.9826

1.0426 0.9809 0.9806

1.1244 0.9790 0.9784

1.2124 0.9768 0.9761

1.4046 0.9711 0.9705

T = 308.15 K

0.8613 0.9848 0.9853

0.249

1.0413 0.9815 0.9811

1.2123 0.9773 0.9767

1.3085 0.9748 0.9741

1.4049 0.9720 0.9713

1.6072 0.9652 0.9653

T = 318.15 K

1.0418 0.9816 0.9815

0.341

1.2127 0.9777 0.9771

1.4050 0.9727 0.9718

1.6075 0.9665 0.9658

1.8043 0.9596 0.9597

2.0002 0.9516 0.9534

T = 323.15 K

1.0509 0.9818 0.9814

0.374

1.2126 0.9782 0.9774

1.4044 0.9732 0.9722

1.6079 0.9672 0.9664

1.8041 0.9607 0.9605

1.9998 0.9531 0.9545

𝐴𝐴𝐷𝑎 = ∑|𝑎𝑤𝑒𝑥𝑝 − 𝑎𝑤

𝑐𝑎𝑙𝑐| /𝑛, where 𝑛 is the number of experimental points. The standard

uncertainties 𝑢 for the adjusted water activities and molalities of copper sulfate are 𝑢(𝑎𝑤) =

0.0006 and 𝑢(𝑚𝐶𝑢𝑆𝑂4) = 0.0001 mol Kg H2O⁄ , respectively.

83

On the other hand, the effect of seawater on the water activities of copper sulfate solutions

is represented in Figure 4, where the experimental results of the CuSO4–seawater system

from this work (Table 5) were compared with water activity values in freshwater reported

by Guendouzi et al. [10] and Yang et al. [11] at 298.15 and 323.15 K, respectively. The

comparison between the copper sulfate water activities in both media at two different

temperatures is shown in Figure 4.

Figure 4. Comparison between the experimental and literature data of water activities of

CuSO4 in seawater and freshwater at 298.15 and 323.15 K: ● and ♦ correspond to the water

activities at 323.15 and 298.15 K, respectively; Solid line: CuSO4–freshwater [10, 11];

Dashed line: CuSO4–seawater [present work].

From Figure 4, it is possible to observe that in both systems (freshwater and seawater) at

298.15 and 323.15 K, the water activity values decrease with increases in the solution

concentration. Moreover, the activity values in seawater are lower than in freshwater; this

behavior is due to the increment in the number of water molecules associated with the

different ions in the solution [23]. On the other hand, with regard to the temperature effect

0.945

0.955

0.965

0.975

0.985

0.995

1.005

1.015

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

aw

CuSO4 (mol/Kg H2O)

84

in both systems (Table 5 and Figure 4), the activity values are slightly higher at 323.15 K;

these results agree with those of Guendouzi and Dinane [23], who reported that the water

activities are highly affected by the solute concentration but slightly influenced by the

temperature.

4.4 Determination of the Pitzer parameters 𝜷(𝟎), 𝜷(𝟏), 𝜷(𝟐), and 𝑪𝝓 for copper

sulfate in seawater at different temperatures

Regarding the Pitzer ion-interaction parameters, Ning et al. [24] reported that ion

interaction parameters for a single salt at different temperatures could be expressed using

the following equation based on the works of Marliacy et al. [25] and Hovey et al. [26]:

𝑃(𝑇) = 𝑃0 + 𝑃1(1 𝑇⁄ − 1 298.15⁄ ) + 𝑃2 ln 𝑇 298.15⁄ (11)

where 𝑃 represents 𝛽(0), 𝛽(1), 𝛽(2), and 𝐶∅; T is the temperature in Kelvin; and 𝑃0, 𝑃1, and

𝑃2 are fitting parameters.

Using the experimental water activity data of copper sulfate in seawater (cf. Table 5) and

Equation (11), it was possible to establish the values of 𝑃0, 𝑃1, and 𝑃2 for the determination

of the CuSO4 Pitzer parameters in seawater in the temperature range from 293.15 to 323.15

K. These values are presented in Table 6.

Table 6. Pitzer parameters of copper sulfate in seawater within the temperature range of

293.15 to 323.15 K.

Parameters 𝛽(0) 𝛽(1) 𝛽(2) 𝐶∅

𝑃0 0.5750 2.9831 0 –0.0721

𝑃1 –0.0008 –0.0010 0 0.0004

𝑃2 0.2463 0.3079 0 –0.1326

Here, the seawater with all its constituent salts was considered as a solvent. On the other

hand, the low AAD values of the water activities (Table 5) demonstrated the reliability of

85

Equation (11) [24] for the determination of the Pitzer parameters of the copper sulfate–

seawater system in the temperature range from 293.15 to 323.15 K.

4.5 Solubility products of copper sulfate pentahydrate in seawater at different

temperatures

Table 7 shows the solubility product and activity coefficient values of copper sulfate

pentahydrate in seawater from 293.15 to 333.15 K. These values were calculated by

Equation (7), where the solubility values and water activities of copper sulfate in seawater

in the absence of acid were utilized for the calculations.

It is important to mention that due to the measurement range of the hydrometer used to

determine water activities, it was not possible to realize measurements over 323.15 K.

Thus, the values for 𝛾 ±𝑆 𝐶𝑢𝑆𝑂4 and 𝑘𝑠𝑝

𝐶𝑢𝑆𝑂45𝐻2𝑂 at 333.15 K correspond to predicted values,

where the Pitzer parameters used for these calculations were determined using the values

from Table 6.

Table 7. Solubility products and activity coefficient values at different temperatures and

copper sulfate concentrations.

T (K) m (mol/Kg H2O) 𝛾 ±𝑆 𝐶𝑢𝑆𝑂4 𝐾𝑠𝑝

𝐶𝑢𝑆𝑂4∙5𝐻2𝑂

293.15 1.3252 0.0317 0.00153

298.15 1.3946 0.0304 0.00155

308.15 1.6401 0.0276 0.00171

318.15 1.9517 0.0255 0.00196

323.15 2.0746 0.0245 0.00203

333.15 2.4675 0.0226* 0.00230*

* Predicted values for 𝛾 ±𝑆 𝐶𝑢𝑆𝑂4 and 𝐾𝑠𝑝

𝐶𝑢𝑆𝑂45𝐻2𝑂 at 333.15 K.

Christov [27] reported the solubility product of copper sulfate pentahydrate in freshwater at

298.15 K, obtaining a value of 0.00245. Accordingly, there is a difference of 0.00090

between the solubility product obtained in the present work (Table 7) and that reported in

86

the literature [27]; this small difference between 𝐾𝑠𝑝 values is mainly due to the presence of

salts in the seawater, which have a direct effect on the solubilities and water activities used

for the calculations.

4.6 Representation of the solid–liquid equilibrium

4.6.1 Experimental and calculated solubility isotherms of the CuSO4–H2SO4–

seawater system at different temperatures

Considering the seawater as a solvent, the values of 𝐴∅ for copper sulfate in seawater at

temperatures from 293.15 to 333.15 K were calculated using Equation (6) and are shown in

Table 8.

Table 8. 𝑨∅ values for copper sulfate in seawater media at different temperatures.

T (K) 293.15 298.15 308.15 318.15 323.15 333.15

𝐴∅ 0.49377 0.49726 0.50464 0.51191 0.51354 0.5195

On the other hand, regarding the sulfuric acid effect, the parameter values of the Born-type

empirical equation (Equation 8) for the CuSO4–H2SO4–seawater system were obtained.

These are valid in the temperature range from 293.15 to 323.15 K and are presented in

Table 9.

Table 9. Parameter values of the Born-type empirical equation.

Parameter values of Eq.(8)

a 5.1564

b 0.0191

c –0.4248

d 0.1947

87

Figure 1 shows the correlation of the solubility data of the copper-sulfate–sulfuric-acid–

seawater system from 293.15 to 323.15 K and also includes the predicted solubilities of

copper sulfate in acid seawater at 333.15 K using the parameter values from Tables 6 and 9.

A good agreement between the experimental and correlated values for the CuSO4–H2SO4–

seawater system at the five temperatures (from 293.15 to 323.15 K) was obtained, with an

AAD of 0.0062 mol/Kg H2O. On the other hand, predicted data at 333.15 K have a

deviation with respect to the experimental data of 0.0053 mol/Kg H2O, allowing the

reproducibility of the model proposed in the present work to be verified.

The approach that has been given here considers the studied system as a ternary one, where

seawater was taken as a solvent, instead of considering the seawater ions individually;

moreover, the sulfuric acid effect was considered separately by means of the Born-type

equation. Despite this consideration, the average deviation obtained in the present work

indicates that the proposed method is a successful tool to represent the solubility of copper

sulfate in a complex medium such as seawater and could be used by the mining industry.

4.7 Predictions of precipitated amounts and yield of copper sulfate

As shown above, sulfuric acid has a significant effect on the reduction of copper sulfate

solubility, being a good agent for its crystallization. For this reason, the quantification of

the copper sulfate precipitated at different percentages of sulfuric acid can provide relevant

information for the isothermal crystallization process design.

According to Jiménez et al. [14], this prediction can be performed starting from an initial

equilibrium condition where the copper sulfate is saturated in seawater and no copper

sulfate precipitates. Then, if any amount of sulfuric acid is added to the system, the

precipitation is produced and a new equilibrium condition is established, where the copper

sulfate is present in lower quantity and is saturated again but is now in a new seawater–

sulfuric-acid medium. If this new concentration is substituted into Equation (7), the

following expression is obtained and can be used to predict these precipitated amounts:

𝑋 = 2 ∙ 𝑚0 − [4 ∙ 𝑚02 − 4 (𝑚0

2 − 𝐾𝑠𝑝𝐶𝑢𝑆𝑂4∙ 5𝐻2𝑂 (𝛾

±𝑆 𝐶𝑢𝑆𝑂4)2 · (𝛾

±𝑁 𝐶𝑢𝑆𝑂4)2 ∙ 𝑎𝑤

5⁄ )] 2⁄ (12)

88

where 𝑚0 is the copper sulfate molality in the initial saturated solution (without acid) and 𝑋

is the precipitated amount (in mol/Kg) obtained when the sulfuric acid is added to the

system. This amount can also be expressed in grams per liter, considering the molar mass

of copper sulfate and the density of seawater (Table 2).

This method was applied to different sulfuric acid concentrations (wt %) and temperatures.

The results of the predictions (in grams of CuSO4·5H2O per liter of saturated solution) at

298.15 and 323.15 K for the CuSO4–H2SO4–seawater system are presented in Figure 5.

Figure 5. Predicted amounts of copper sulfate pentahydrate precipitated versus sulfuric

acid weight percent at two different temperatures. ♦ and × correspond to the predicted data

at 298.15 and 323.15 K, respectively.

From Figure 5, it is readily apparent that in both cases the precipitation is highly affected

by the acid concentration, where, as the sulfuric acid concentration is increased, a greater

amount of copper sulfate is precipitated. Similar results were obtained at the other

temperatures.

0

25

50

75

100

125

150

175

0 2 4 6 8 10 12 14 16 18 20

ppt

(g/L

CuS

O4 5

H2O

)

H2SO4 (wt %)

89

Also, it is possible to observe that the precipitated amounts are not highly affected by the

temperature, with similar amounts of copper sulfate pentahydrate being obtained in both

cases when sulfuric acid is added to the system. This is because, in the temperature range

from 293.15 to 333.15 K, the solubility curves of the CuSO4–H2SO4–seawater system (cf.

Figure 1) have similar slopes, which causes the precipitated amounts to be similar at the

different temperatures.

On the other hand, based on the work of Jiménez et al. [14], once the values of 𝑋 have been

determined, it is possible to calculate the percentage of sulfuric acid that produces the

maximum precipitate. This amount is defined as the yield 𝑌.

The prediction of the amount of acid that produces the maximum yield (𝑌) can be

calculated by the following expression [14]:

𝑌 = 𝑋𝑀(100 − 𝑠)(1 − 𝑤)10−5 (13)

where 𝑠 is the CuSO4 solubility expressed as weight percent, and 𝑀 and 𝑤 represent the

molecular weight of copper sulfate and the mass fraction of sulfuric acid (free of salt),

respectively.

This estimation has been performed for the CuSO4–H2SO4–seawater system using the

copper sulfate and sulfuric acid concentrations from Tables 3 and 4 (as a weight percent

and mass fraction, respectively) in the temperature range from 293.15 to 333.15 K. Table

10 shows the results of the optimum values 𝑌, with their respective sulfuric acid

concentrations, obtained at each temperature.

90

Table 10. Optimum values of 𝒘 and 𝒀 for the CuSO4–H2SO4–seawater system at the six

different temperatures.

T (K) H2SO4 (wt %) Yield (%)

293.15 18.1037 11.419

298.15 16.9197 10.523

308.15 16.4071 9.181

318.15 15.7963 10.402

323.15 14.9704 8.858

333.15 14.0057 8.102

From Table 10, it can be noted that independently of the temperature, the yield reaches a

maximum value at the highest concentration of sulfuric acid used at each temperature.

Also, it is important to mention that the higher value of 𝑌 obtained at 293.15 K is attributed

to the higher acid concentration used for the calculations.

As can be seen in Figure 5 and Table 10, with the range of sulfuric acid concentrations used

for the calculations, it was not possible to achieve a maximum precipitated amount (𝑋) and

yield (𝑌), so it is possible that the optimum acid concentration necessary to reach maximum

values of 𝑋 and 𝑌 is higher. However, our calculations of 𝑌 are based on the sulfuric acid

values normally used by the mining industry (over 100 g/L H2SO4) [5].

On the other hand, despite the high copper concentrations present in the initial solutions

(Table 3 and 4), high yields were not obtained (Table 10). So it is proposed that a

continuous crystallization process with recirculation would help to obtain higher values of

𝑌.

4.8 Conceptual design of the copper sulfate crystallization process by means of the

addition of sulfuric acid using the phase diagram

The conventional methodology used to make the graph of yield versus the sulfuric acid

weight percent is through a solubility diagram (graph form). In the present work, this

91

calculation has been carried out at 298.15 and 323.15 K (Figure 6), and these results were

compared to those obtained analytically using Equation (12).

The solution compositions used for the calculations were obtained from Figure 6, which

shows the solubility diagram (expressed as the mass fraction) of the studied system at

298.15 and 323.15 K, where the conceptual process design was realized. 𝐹1 and 𝐹2

correspond to the input currents of pure sulfuric acid and saturated aqueous solution of

copper sulfate, respectively. These flows (𝐹1 and 𝐹2) are subsequently mixed and separated

into copper sulfate pentahydrate crystals (𝐹3) and saturated solution (𝐹4) at the outlet of the

crystallizer.

Calculations were realized considering the crystallization process as isothermal and F2 as

100 g/s, while the mass flows 𝐹1, 𝐹3, and 𝐹4were obtained from a material balance (Figure

7). The compositions were also read directly from the solubility diagram (Figure 6).

Figure 6. Solubility diagram of CuSO4–H2SO4–seawater system at 298.15 K (♦) and

323.15 K (×).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225

wC

uS

O4

wH2SO4

F3

F2 F1

F4

F4

F2

F1

92

Figure 7 shows the flow sheet of the isothermal copper sulfate crystallization process,

where the input and output currents were also represented in Figure 6. Flows compositions

are given in Table 11.

Figure 7. Process flow sheet of the copper sulfate crystallization process using sulfuric

acid.

Table 11. Compositions of the input and output currents at 298.15 and 323.15 K.

Currents 𝐹1 𝐹2 𝐹3 𝐹4

Compositions (w) X1 X2 X1 X2 X1 X2 X1 X2

T = 298.15 K 0 1 0.1770 0 0.639 0 0.0956 0.1691

T = 323.15 K 0 1 0.2428 0 0.639 0 0.1735 0.1497

X1 and X2 correspond to the mass fractions of copper sulfate and sulfuric acid, respectively.

Figure 8 shows the precipitated amounts of copper sulfate pentahydrate at 298.15 and

323.15 K using the analytic and graph forms. In both cases, the same acid concentrations

values from Tables 3 and 4 were used and the results are expressed in grams of

CuSO4·5H2O per liter of saturated solution versus sulfuric acid weight percent.

Crystallizer

Calculation of precipitate

F2

F4

F3

F1

93

Figure 8. Amount of CuSO4·5H2O precipitated versus sulfuric acid weight percent. Solid

and dashed lines represent the analytical method while the symbols ♦ and × represent the

graph method at 298.15 and 323.15 K, respectively.

It is observed that at both temperatures, the amounts of copper sulfate precipitated increase

as the acid concentration increases. On the other hand, it is possible to note that the results

obtained using the analytical and graph methods are similar, with mean deviations of 2.67

and 3.54% at 298.15 and 323.15 K, respectively. This indicates that the analytical

methodology proposed in the present work is suitable for the design of the isothermal

copper sulfate crystallization process using seawater by means of the addition of sulfuric

acid. Similar results were obtained at other temperatures (293.15, 308.15, 318.15, and

333.15 K).

The main contribution of the present work is that a simple methodology has been proposed

to correlate the CuSO4–H2SO4–seawater system, which also allows the prediction of the

sulfuric acid concentration that maximizes the copper sulfate precipitation. This approach

could be very useful in the crystallization process design and for the mining industry,

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14 16 18 20

ppt

CuS

O4·5

H2O

(g/L

)

H2SO4 (%)

94

because only a few solubility data are needed to know the optimal amount of sulfuric acid

to obtain the maximum yield. In the future, the next step is to realize crystallization

experiments with seawater by adding sulfuric acid to validate the model proposed in the

present work.

5. CONCLUSIONS

A simple methodology, based on a variation of Kan’s method, has been applied to represent

the solid–liquid equilibrium of the copper-sulfate–sulfuric-acid–seawater system at

different temperatures and considering the seawater as a solvent, obtaining an AAD of

0.0062 mol/Kg H2O. Also, a simple analytical procedure has been applied to construct

yield-versus-concentration diagrams, which can be used to estimate the sulfuric acid

concentration that maximizes the copper sulfate precipitation.

From the methodology proposed in the present work, it has been possible to obtain valuable

information that could be useful in the design of the copper sulfate crystallization process

by means of the addition of sulfuric acid. So in the future, it would be interesting to prove

the reproducibility of the model through experimental tests, to validate the model, and to

apply it in the mining industry.

ACKNOWLEDGEMENTS: Funding for this research was provided by CONICYT

(Fondecyt Project 1140169 and grant 21130894).

95

6. REFERENCES



[2] D. Milligan, H. Moyer, Crystallization in the Copper sulphate - Sulphuric acid - Water

system, ENG MIN J, 176 (1975) 85-89.






[6] F.E.W. Wetmore, A. Gordon, The Activity Coefficient of Copper Sulphate in Aqueous

Solution, The Journal of chemical physics, 5 (1937) 60-63.


from aqueous NaCl, Na2SO4, CuCl2, and CuSO4, at 25 °C, Journal of Solution Chemistry, 5

(1976) 389-398.

[8] D.G. Miller, J.A. Rard, L.B. Eppstein, R. Robinson, Mutual diffusion coefficients,

electrical conductances, osmotic coefficients, and ionic transport coefficients ij for aqueous

CuSO4 at 25 °C, Journal of Solution Chemistry, 9 (1980) 467-496.

[9] A. Apelblat, The vapour pressures of saturated aqueous solutions of potassium bromide,

ammonium sulfate, copper (II) sulfate, iron (II) sulfate, and manganese (II) dichloride, at

temperatures from 283 K to 308 K, The Journal of Chemical Thermodynamics, 25 (1993)

1513-1520.

[10] M.E. Guendouzi, A. Mounir, A. Dinane, Water activity, osmotic and activity

coefficients of aqueous solutions of Li2SO4, Na2SO4, K2SO4,(NH4)2SO4, MgSO4, MnSO4,

NiSO4, CuSO4, and ZnSO4 at T= 298.15 K, The Journal of Chemical Thermodynamics, 35

(2003) 209-220.

96




[12] F. Justel, M. Claros, M. Taboada, Solubilities and physical properties of saturated

solutions in the copper sulfate + sulfuric acid + seawater system at different temperatures,

Brazilian Journal of Chemical Engineering, 32 (2015) 629-635.

[13] A.T. Kan, G. Fu, M.B. Tomson, Effect of methanol and ethylene glycol on sulfates

and halite scale formation, Industrial & Engineering Chemistry Research, 42 (2003) 2399-

2408.

[14] Y.P. Jimenez, M.E. Taboada, H.R. Galleguillos, Solid–liquid equilibrium of K2SO4 in

solvent mixtures at different temperatures, Fluid Phase Equilibria, 284 (2009) 114-117.

[15] A. D-98, Standard Practice for the Preparation of Substitute Ocean Water, ASTM

International West Conshohocken, PA, 2008.

[16] W. Alavia, J.A. Lovera, B.A. Cortez, T.f.A. Graber, Solubility, density, refractive

index, viscosity, and electrical conductivity of boric acid+ lithium sulfate+ water system at

(293.15, 298.15, 303.15, 308.15 and 313.15) K, Journal of Chemical & Engineering Data,

58 (2013) 1668-1674.

[17] H. Holmes, R. Mesmer, Thermodynamics of aqueous solutions of the alkali metal

sulfates, Journal of Solution Chemistry, 15 (1986) 495-517.



[19] D. Fernandez, A. Goodwin, E.W. Lemmon, J.L. Sengers, R. Williams, A formulation

for the static permittivity of water and steam at temperatures from 238 K to 873 K at

pressures up to 1200 MPa, including derivatives and Debye–Hückel coefficients, Journal of

Physical and Chemical Reference Data, 26 (1997) 1125-1166.

97

[20] A. Stogryn, Equations for calculating the dielectric constant of saline water

(correspondence), IEEE transactions on microwave theory and Techniques, (1971) 733-

736.

[21] J.A. Lovera, A.P. Padilla, H.R. Galleguillos, Correlation of the solubilities of alkali

chlorides in mixed solvents: Polyethylene glycol + H2O and Ethanol + H2O, Calphad, 38

(2012) 35-42.





[24] P. Ning, W. Xu, H. Cao, X. Lin, H. Xu, Determination and modeling for the solubility

of Na2MoO4·2H2O in the (Na++

MoO42−

+ SO42−

) system, The Journal of Chemical


[25] P. Marliacy, R. Solimando, M. Bouroukba, L. Schuffenecker, Thermodynamics of

crystallization of sodium sulfate decahydrate in H2O–NaCl–Na2SO4: application to

Na2SO4·10H2O-based latent heat storage materials, Thermochimica Acta, 344 (2000) 85-

94.

[26] J.K. Hovey, K.S. Pitzer, J.A. Rard, Thermodynamics of Na2SO4 (aq) at temperatures T

from 273 K to 373 K and of ((1-y)H2SO4+ yNa2SO4) (aq) at T= 298.15 K, The Journal of

Chemical Thermodynamics, 25 (1993) 173-192.



98

CHAPTER V

THERMODYNAMIC STUDY OF THE Cu-Na-H-SO4-Cl-HSO4-H2O SYSTEM FOR

THE SOLUBILITY OF COPPER SULFATE IN ACID SEAWATER AT


Francisca J. Justel, María E. Taboada, Yecid P. Jiménez*

Department of Chemical and Mineral Process Engineering, University of Antofagasta, Av.

Angamos 601, Antofagasta, Chile

([email protected], [email protected], [email protected]*)

ABSTRACT

The objective of the present work is the thermodynamic study of the Cu-Na-H-SO4-Cl-

HSO4-H2O system using the Pitzer model in the temperature range from 293.15 to 333.15

K. Also, the water activities for aqueous solutions of copper sulfate were experimentally

determined. This information and the Pitzer ion-interaction model were used to represent

the solid-liquid equilibrium of the copper sulfate – sulfuric acid – seawater system.

A simplification of the seawater system has been carried out, where the main ions from

seawater (Na+ and Cl

-) have been considered in the modelling. A good agreement between

the correlated and the experimental solubility data of the CuSO4 - H2SO4 - seawater system

was obtained, with an absolute average deviation of 0.0157 mol/kg.

The ion-interaction model of Pitzer has been successfully used to predict the solubilities of

an electrolyte in a system as complex as natural seawater, which makes it a suitable model

to be applied to mining processes using seawater.

Keywords: Copper sulfate; Seawater; Solubility; Water activity; Pitzer model.

99

1. INTRODUCTION

Copper sulfate pentahydrate is the most important industrial compound of copper and has

many commercial uses, including as soil additives, fungicides, bulk preparations of other

copper compounds, and an important component in the electronic industry [1, 2]. The most

common method of crystallizing copper sulfate pentahydrate is through the addition of

sulfuric acid, which generates a supersaturated aqueous solution of the salt [3].

In Chile, there are some mining companies that use seawater in the hydrometallurgical and

flotation concentration processes [4]. Due to this and to understand the effect of the

principal ions present in seawater (Na+

and Cl-), the experimental determination of

thermodynamic properties of salts, especially at moderate or high concentrations is of

interest because it provides information needed to determine the interaction parameters in

thermodynamic models. These models are valuable tools in the study of the optimization

and simulation of industrial processes for the recovery of salts [5].

Accordingly, some authors studied the applicability of the ion interaction or virial-

coefficient model of Pitzer [6, 7] to correlate the solubility data at different temperatures of

multicomponent systems. Harvie and Weare [8], used this model to predict the mineral

solubilities at 298.15 K in the seawater Na-K-Ca-Mg-Cl-SO4-H2O system at high ionic

strengths. The authors used activity coefficient expressions that were parameterized using

the solubility and osmotic data of binary and ternary systems, obtaining a good agreement

between the experimental and calculated solubility data. The authors concluded that the

methodology applied can be accurately used to predict solubilities in more complex

systems. Palaban and Pitzer [9], calculated the mineral solubilities in binary and ternary

electrolyte mixtures of the Na-K-Mg-Cl-SO4-OH-H2O system at high temperatures using

the available thermodynamic data for solid and aqueous electrolyte solutions, and some

parameters were fitted to represent ternary systems. Good agreement with the experimental

solubility data indicates that the model can be successfully used to predict mineral

solubilities at high temperatures. Moller [10] presented a variable temperature model for

the Na-Ca-Cl-SO4-H2O system that calculates the solubilities from dilute to high

concentrations in the temperature range from 298.15 to 523.15 K. Later, Greenberg and

100

Moller [11] extended the model of Moller [10] by including potassium interactions and

increasing the temperature range from 273.15 to 523.15 K. In that work, the Na-K-Ca-Cl-

SO4-H2O system from zero to high ionic strengths was studied. The application of the

variable temperature models for Na-Ca-Cl-SO4-H2O and Na-K-Ca-Cl-SO4-H2O discussed

by Moller [10] and Greenberg and Moller [11], respectively, suggests the utility of a full

seawater variable temperature model in geochemical and industrial studies. Baes et al. [12]

applied the Pitzer ion interaction model to the CuSO4 - H2SO4 - H2O system at 298.15 K,

using available data of osmotic, solubility, and emf data for this system, including

unsymmetrical mixing effects. In that work, an extensive evaluation of available data on the

system CuSO4-H2SO4-H2O has been made. Christov [13] reported a thermodynamic study

of the quaternary system Na-Cu-Cl-SO4-H2O at 298.15 K using the Pitzer model, where the

crystallization of the simple salts CuCl2∙2H2O and CuSO4∙5H2O was evaluated.

Additionally, simulation of the NaCl-CuCl2 (aq), Na2SO4-CuSO4 (aq), and CuCl2-CuSO4

(aq) systems was performed, demonstrating a good agreement between the experimental

and calculated solubility isotherms. Later, Christov and Moller [14] studied the H-Na-K-

OH-Cl-HSO4-SO4-H2O system under high solution concentrations over a wide temperature

range (from 273.15 to 523 K), where the temperature functions for potentials of sodium and

potassium salts from the solubility data of binary and ternary solutions were reported, and a

comparison with the experimental data validated the model. Wang et al. [15] predicted the

solubility of gypsum at 298.15 K in the quaternary systems CaSO4-HMSO4-H2SO4-H2O

(HM=Cu, Zn, Ni, Mn) up to saturated concentrations of heavy metal sulfates and to a

H2SO4 concentration of 2 m by the Pitzer thermodynamic model, where experimental

solubilities and water activities of the sub binary and sub ternary systems were used for the

model parameterization, concluding that the Pitzer model in its simple form can sufficiently

predict the solubility behavior of gypsum in the quaternary system. Justel et al. [16]

determined solubilities and water activity values of copper sulfate in seawater at different

temperatures, and used this information to represent the solid-liquid equilibrium of copper

sulfate-sulfuric acid-seawater system by means of a methodology that uses the Pitzer and

the Born model to quantify the copper sulfate and sulfuric acid effect, respectively.

Additionally, the precipitated amounts of copper sulfate as a function of the sulfuric acid

concentration were predicted.

101

The prediction or correlation of salt solubility data in mixed solvents is an important tool to

design and simulate the drowning-out crystallization process [17]. Thus, the present work is

focused on the representation of the solid-liquid equilibrium of the CuSO4 - H2SO4 -

seawater system in a wide temperature range (from 293.15 to 333.15 K). Here, the

thermodynamic study of the Cu-Na-H-SO4-Cl-HSO4-H2O system using the Pitzer model,

and considering sodium and chloride as seawater components is realized. The necessary

parameters for the binary and ternary systems have been compiled from the literature to

correlate the experimental solubility data of the CuSO4-H2SO4-seawater system. This

information will be useful in the process design to produce copper sulfate pentahydrate

crystals using seawater by means of the addition of sulfuric acid, contributing to the use of

seawater in the hydrometallurgy of copper.

2. EXPERIMENTAL SECTION

2.1 MATERIALS

The reagents used in this work were of analytical grade. Copper (II) sulfate pentahydrate,

Merck, 99-100.5%, and distilled deionized water (0.054 𝜇𝑆 ∙ 𝑐𝑚−1).

2.2 APPARATUS AND PROCEDURES

2.2.1 Water activity measurements of CuSO4 in H2O at different temperatures

The water activities (𝑎𝑤) were measured using a Novasina Corp. model AW-Center 500

electronic hydrometer with the temperature controlled at ± 0.2 K and an accuracy of ±

0.003 𝑎𝑤, this instrument works in the temperature range from 273.15 to 323.15 K, and was

calibrated prior to making each set of measurements by using standard saturated salt

solutions of NaCl and LiCl supplied by the manufacturer. With the objective of improving

the accuracy, calibration curves were developed at each working temperature (293.15,

298.15, 308.15, 318.15, and 323.15 K) using the methodology proposed by Justel et al.

102

[16]. Activities measurements of aqueous solutions of copper sulfate were performed in

duplicate from 293.15 to 323.15 K. At each temperature, solutions at six different

concentrations of copper sulfate were measured, and the results were adjusted with the

calibration curves to maximize the equipment precision.

3. THERMODYNAMIC FRAMEWORK

3.1 The ion-interaction model

The ion interaction model has been discussed in several publications [6-10]. These authors

have shown that this approach could be expanded to accurately calculate solubilities in

complex brines and to predict the behavior of natural fluids.

The ion-interaction model begins with a virial expansion of the excess free energy: 𝐺𝑒𝑥 𝑅𝑇⁄

[8], as shown in Equation (1).

𝐺𝑒𝑥

𝑅𝑇= 𝑛𝑤[𝑓(𝐼) + ∑ ∑ 𝜆𝑖𝑗(𝐼)𝑚𝑖𝑚𝑗 + ∑ ∑ ∑ 𝜇𝑖𝑗𝑘𝑚𝑖𝑚𝑗𝑚𝑘𝑘𝑗𝑖𝑗𝑖 ] (1)

where 𝑛𝑤 is the number of kilograms of solvent and 𝑚𝑖𝑗𝑘 is the molality of species 𝑖, 𝑗, and

𝑘. 𝑓(𝐼) is the Debye-Hückel term and is a function of the ionic strength. 𝜆𝑖𝑗 and 𝜇𝑖𝑗𝑘 are the

second and third virial coefficients, respectively, and represent the effects of short-range

forces between ions [7].

The expressions for the osmotic and activity coefficients follow directly from the equation

𝐺𝑒𝑥 𝑅𝑇⁄ through the appropriate derivatives with respect to 𝑛𝑤 and 𝑚, respectively [9].

Equation (2) shows the expression for modeling the osmotic coefficient (𝜙), and equations

(3) and (4) are used to model the activity coefficients of the cation (M) and anion (X),

respectively.

103

(𝜙 − 1) = 2

(∑ 𝑚𝑖𝑖 )[−

𝐴𝜙𝐼3 2⁄

1+𝑏𝐼1 2⁄ + ∑ ∑ 𝑚𝑐𝑚𝑎(𝐵𝑐𝑎𝜙

+ 𝑍𝐶𝑐𝑎) + ∑ ∑ 𝑚𝑐𝑚𝑐′(𝛷𝑐𝑐′𝜙

+𝑐′𝑐𝑎𝑐

∑ 𝑚𝑎𝜓𝑐𝑐′𝑎𝑎 ) + ∑ ∑ 𝑚𝑎𝑚𝑎′(𝛷𝑎𝑎′𝜙

+ ∑ 𝑚𝑐𝜓𝑎𝑎′𝑐𝑐 )𝑎′𝑎 ] (2)

ln 𝛾𝑀 =

𝑧𝑀2 𝐹 + ∑ 𝑚𝑎(2𝐵𝑀𝑎 + 𝑍𝐶𝑀𝑎)𝑎 + ∑ 𝑚𝑐(2𝛷𝑀𝑐 + ∑ 𝑚𝑎𝜓𝑀𝑐𝑎𝑎 )𝑐 + ∑ ∑ 𝑚𝑎𝑚𝑎𝜓𝑎𝑎′𝑀𝑎′𝑎 +

|𝑧𝑀| ∑ ∑ 𝑚𝑐𝑚𝑎𝐶𝑐𝑎𝑎𝑐 (3)

ln 𝛾𝑋 =

𝑧𝑋2𝐹 + ∑ 𝑚𝑐(2𝐵𝑐𝑋 + 𝑍𝐶𝑐𝑋)𝑐 + ∑ 𝑚𝑎(2𝛷𝑋𝑎 + ∑ 𝑚𝑐𝜓𝑋𝑎𝑐𝑐 )𝑎 + ∑ ∑ 𝑚𝑐𝑚𝑐𝜓𝑐𝑐′𝑋𝑐′𝑐 +

|𝑧𝑋| ∑ ∑ 𝑚𝑐𝑚𝑎𝐶𝑐𝑎𝑎𝑐 (4)

where the subscripts M, c and c’ represent the cations and X, a and a’ are the anions; 𝑧𝑀

and 𝑧𝑥 are the ion charges and 𝑚𝑐 and 𝑚𝑎 are the molalities (mol/kg solvent) of the cations

and anions, respectively; I corresponds to the ionic strength; and b is 1.2 and remains the

same for all solutes.

The double summation indices c<c’ and a<a’ denote the sum over all of the distinguishable

pairs of dissimilar cations and anions, respectively. Additionally, the parameters 𝜓𝑖𝑗𝑘 are

the ion-mixing interaction parameters and are used when 𝑖 and 𝑗 are different anions and 𝑘

is a cation, or vice versa. In all cases, 𝜓𝑖𝑗𝑘 is assumed to be independent of the

concentration.

The function F includes the Debye-Hückel and other terms, as shown in Equation (5).

𝐹 = −𝐴𝜙 [𝐼1 2⁄

1+𝑏𝐼1 2⁄ +2

𝑏ln(1 + 𝑏𝐼1 2⁄ )] + ∑ ∑ 𝑚𝑐𝑚𝑎𝐵′𝑐𝑎𝑎𝑐 + ∑ ∑ 𝑚𝑐𝑚𝑐𝛷′𝑐𝑐′𝑐′𝑐 +

∑ ∑ 𝑚𝑎𝑚𝑎𝛷′𝑎𝑎′𝑎′𝑎 (5)

where 𝐴𝜙 corresponds to the Debye-Hückel term and is given by equation (6) [18].

𝐴𝜙 = 0.13422(4.1725332 − 0.1481291𝑇0.5 + 1.5188505𝐸 − 5 𝑇2 − 1.8016317𝐸 −

8𝑇3 + 9.3816144𝐸 − 10𝑇3.5) (6)

104

The coefficients 𝐵𝑀𝑋 are functions of the ionic strength and for electrolytes 1-1 and 1-2 are

represented by the Equations (7), (8), and (9).

𝐵𝑀𝑋𝜙

= 𝛽𝑀𝑋(0)

+ 𝛽𝑀𝑋(1)

𝑒−𝛼𝐼12 (7)

𝐵𝑀𝑋 = 𝛽𝑀𝑋(0)

+ 𝛽𝑀𝑋(1)

𝑔 (𝛼𝐼1

2) (8)

𝐵′𝑀𝑋 = 𝛽𝑀𝑋(1)

𝑔′(𝛼𝐼

12)

𝐼 (9)

For electrolytes 2-2 (as copper sulfate), an additional term is added, and the above

equations become:

𝐵𝑀𝑋𝜙

= 𝛽𝑀𝑋(0)

+ 𝛽𝑀𝑋(1)

𝑒−𝛼1𝐼12 + 𝛽𝑀𝑋

(2)𝑒−𝛼2𝐼

12 (10)

𝐵𝑀𝑋 = 𝛽𝑀𝑋(0)

+ 𝛽𝑀𝑋(1)

𝑔 (𝛼1𝐼1

2) + 𝛽𝑀𝑋(2)

𝑔 (𝛼2𝐼1

2) (11)

𝐵′𝑀𝑋 = 𝛽𝑀𝑋(1)

𝑔′(𝛼1𝐼

12)

𝐼+ 𝛽𝑀𝑋

(2)

𝑔′(𝛼2𝐼12)

𝐼 (12)

where the symbols 𝛽𝑀𝑋(0)

, 𝛽𝑀𝑋(1)

, 𝛽𝑀𝑋(2)

, and 𝐶𝑀𝑋𝜙

are solute specific parameters and the values

of the parameters 𝛼1, 𝛼2, and b, are constants. For copper sulfate 𝛼1 = 1.4 and 𝛼2 = 12;

for copper chloride, 𝛼1 = 2.0 and 𝛼2 = 1.0; for an electrolyte with one or two univalent

ions, 𝛼1 = 2, and 𝛽𝑀𝑋(2)

, is not required [19].

The functions 𝑔 and 𝑔′ are given by Equations (13) and (14), respectively.

𝑔(𝑥) =2[1−(1+𝑥)𝑒−𝑥]

𝑥2 (13)

𝑔′(𝑥) =−2[1−(1+𝑥+

1

2𝑥2)𝑒−𝑥]

𝑥2 (14)

where 𝑥 = 𝛼𝐼1

2.

105

The 𝐶𝑀𝑋 parameter is related to the parameter 𝐶𝑀𝑋𝜙

as shown in Equation (15).

𝐶𝑀𝑋 = 𝐶𝑀𝑋

𝜙

2(𝑧𝑀𝑧𝑋)12

(15)

Moreover, some terms containing 𝐶𝑀𝑋 parameters have a concentration dependence given

by the function 𝑍 represented in the Equation (16).

𝑍 = ∑ 𝑚𝑖|𝑧𝑖|𝑖 (16)

For 𝛷 terms, there is a large ionic strength dependence and the equations for the second

virial coefficients, 𝛷𝑖𝑗, are the following:

𝛷𝑀𝑋 = 𝜃𝑀𝑋 + E𝜃𝑀𝑋(𝐼) (17)

𝛷′𝑀𝑋 = E𝜃′𝑀𝑋(𝐼) (18)

𝛷𝑀𝑋𝜙

= 𝜃𝑀𝑋 + E𝜃𝑀𝑋(𝐼) + 𝐼 E𝜃′𝑀𝑋

(𝐼) (19)

where 𝜃𝑀𝑋 is a single parameter for each pair of cations or anions, and E𝜃𝑀𝑋 accounts for

the electrostatic unsymmetrical mixing effects, which are dependent on the charge of the

ions and total ionic strength. E𝜃𝑀𝑋 and E𝜃′𝑀𝑋

are zero when the ions 𝑖 and 𝑗 are of the same

charge [8].

The higher-order electrostatic terms E𝜃𝑀𝑋 and E𝜃′𝑀𝑋

are calculated by the Equations (20)

and (21) given by Pitzer [20].

E𝜃𝑀𝑋(𝐼) =

𝑧𝑀𝑧𝑋

4𝐼(𝐽(𝑥𝑀𝑁) −

1

2𝐽(𝑥𝑀𝑀) −

1

2𝐽(𝑥𝑁𝑁)) (20)

E𝜃′𝑀𝑋(𝐼) = − (

E𝜃𝑀𝑋

𝐼) + (

𝑧𝑀𝑧𝑋

8𝐼2 ) (𝑥𝑀𝑁 𝐽′(𝑥𝑀𝑁) −1

2𝑥𝑀𝑀 𝐽′(𝑥𝑀𝑀) −

1

2𝑥𝑁𝑁 𝐽′(𝑥𝑁𝑁)) (21)

where 𝑥𝑀𝑋 = 6𝑧𝑀𝑧𝑋𝐴𝜙𝐼1

2

106

The expression for 𝐽 is a function of the concentration and contributes to the electrostatic

unsymmetric mixing effects, it has been given by Pitzer [20] as follows:

𝐽 = 𝑥(4 + 𝐶1𝑥−𝐶2𝑒(𝐶3𝑥−𝐶4))−1

(22)

where the corresponding values of the parameters for the Equation (22) are presented in

Table 1.

Table 1. Parameters for Equation (22) [20].

Parameters 𝐶1 𝐶2 𝐶3 𝐶4

Equation (22) 4.5810 0.7237 0.0120 0.5280

On the other hand, 𝐽′ values correspond to the derivative of 𝐽 functions and were calculated

from Pitzer [20].

3.2 Ion-interaction parameters in binary aqueous solutions

For pure electrolytes, the ion interaction parameters 𝛽𝑀𝑋(0)

and 𝛽𝑀𝑋(1)

define the second virial

coefficients, which describe the interaction of pairs of oppositely charged ions. In the case

of electrolytes 2-2, one additional term, 𝛽𝑀𝑋(2)

, is added, which reproduces the irregular

behavior in the range below 0.1 m [21]. However, Christov [13] have reported the

additional 𝛽𝑀𝑋(2)

term for copper chloride solutions at 298.15 K.

Some authors have determined the ion interaction parameters of the binary subsystems of

this work (CuSO4-H2O, CuCl2-H2O, Cu(HSO4)2-H2O, Na2SO4-H2O, NaCl-H2O, NaHSO4-

H2O, HSO4-H2O, HCl-H2O, and H2SO4-H2O); some of them proposed models for their

determination over a wide temperature range.

For Na2SO4, the parameters were calculated using the model proposed by Moller [10],

which can be used in the temperature range from 298.15 to 523.15 K. Parameters for NaCl

were determined using the model proposed by Palaban and Pitzer [9], which is valid from

273.15 to 573 K. For HCl, the parameters were taken from Holmes et al. [22], where the

equations were valid over the temperature range from 273 to 523 K. For NaHSO4, HSO4-,

107

and H2SO4 values, the model proposed by Christov and Moller [14] was used, which is

valid from 273.15 to 473.15 K.

Parameters values for CuSO4 and CuCl2 have been reported at 298.15 K by Christov [13].

In the case of Cu(HSO4)2, Pitzer parameters at 298.15 K have been reported by Tanaka

[23], where these values were determined using the parameters for Cu2+

-ClO4- as an

alternate of those for Cu2+

-HSO4-, which was based on the works of Pitzer et al. [24] and

Hughes and Sungshou [25]. Due to that, in the present work, these reported Cu(HSO4)2

values in the modelling were not considered.

In this work, binary Pitzer parameters for copper sulfate at different temperatures have been

determined from experimental water activities values. Moreover, the ion interaction

parameters for CuCl2 and Cu(HSO4)2 were considered as fitting parameters.

Tables 2 and 3 show the reported parameter values used in this work for CuSO4 and CuCl2

at 298.15 K, and for Na2SO4, NaCl, NaHSO4, HSO4-, HCl, and H2SO4 at six different

temperatures.

Table 2. Pitzer binary parameters (𝜷𝑴𝑿(𝟎)

, 𝜷𝑴𝑿(𝟏)

, 𝜷𝑴𝑿(𝟐)

, and 𝑪𝑴𝑿𝝓

) for CuSO4 and CuCl2 at

298.15 K.

CuSO4 (aq) [13] CuCl2 (aq) [13]

T(K) 𝛽𝑀𝑋(0)

𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

𝛽𝑀𝑋(0)

𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

298.15 0.23400 2.52700 -48.3300 0.00440 0.17661 0.57402 0.63405 -0.01089

where b=1.2. α1= 1.4, α2= 12.0 for CuSO4, and α1= 2.0, α2= 1 for CuCl2.

108

Table 3. Pitzer binary parameters (𝜷𝑴𝑿(𝟎)

, 𝜷𝑴𝑿(𝟏)

, 𝜷𝑴𝑿(𝟐)


) for Na2SO4, NaCl,

NaHSO4, HSO4-, HCl, and H2SO4 at six different temperatures.

Na2SO4 (aq)a NaCl (aq)

b


𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

𝛽𝑀𝑋(0)

𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

293.15 0.0061 1.0679 - 0.0092 0.0715 0.2723 - 0.0020

298.15 0.0187 1.0993 - 0.0063 0.0754 0.2770 - 0.0014

308.15 0.0394 1.1532 - 0.0014 0.0820 0.2854 - 0.0004

318.15 0.0557 1.1973 - -0.0023 0.0871 0.2931 - -0.0005

323.15 0.0627 1.2164 - -0.0039 0.0893 0.2967 - -0.0008

333.15 0.0747 1.2495 - -0.0064 0.0928 0.3038 - -0.0015

NaHSO4 (aq)c HSO4

- (aq)

c


𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

𝛽𝑀𝑋(0)

𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

293.15 0.1099 -0.0249 - -0.0064 0.0959 0.0000 - 0.0536

298.15 0.1057 0.0208 - -0.0058 0.0910 0.0000 - 0.0552

308.15 0.0980 0.1067 - -0.0048 0.0813 0.0000 - 0.0564

318.15 0.0910 0.1854 - -0.0040 0.0720 0.0000 - 0.0551

323.15 0.0878 0.2221 - -0.0036 0.0677 0.0000 - 0.0536

333.15 0.0598 0.0000 - 0.0491

HCl (aq)d H2SO4 (aq)

c


𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

𝛽𝑀𝑋(0)

𝛽𝑀𝑋(1)

𝛽𝑀𝑋(2)

𝐶𝑀𝑋𝜙

293.15 0.1786 0.2929 - 0.0010 0.2136 0.4411 - 0.0000

298.15 0.1766 0.2929 - 0.0007 0.2104 0.4411 - 0.0000

308.15 0.1726 0.2929 - 0.0001 0.2046 0.4409 - 0.0000

318.15 0.1686 0.2929 - -0.0005 0.1993 0.4401 - 0.0000

323.15 0.1665 0.2929 - -0.0008 0.1968 0.4395 - 0.0000

333.15 0.1625 0.2929 - -0.0014 0.1920 0.4378 - 0.0000

where b=1.2, and α1= 2.0. a, b, c, and

d correspond to the calculated values using the temperature dependence model from Moller

[10], Palaban and Pitzer [9], Christov and Moller [14], and Holmes et al. [22], respectively.

3.3 Ion-mixing interaction parameters in ternary solutions

For the Cu-Na-H-SO4-Cl-HSO4-H2O system, a large number of ternary systems have been

studied, where the parameters 𝜓𝑖𝑗𝑘 and 𝜃𝑖𝑗 are necessary to determine the thermodynamic

properties of electrolyte solutions [9], which have been reported at different temperatures

by some authors.

109

𝜃𝑖𝑗 parameters at 298.15 K have been reported previously: Values for 𝜃𝐶𝑙,𝑆𝑂4 , 𝜃𝐶𝑢,𝑁𝑎, and

𝜃𝐶𝑢,𝐻 were reported by Palaban and Pitzer [9], Downes and Pitzer [19], and Wang et al.

[15], respectively. In the present work, these parameters have been considered constant in

the temperature range from 293.15 to 333.15 K.

Additionally, a model for the temperature dependence of the 𝜃𝑆𝑂4,𝐻𝑆𝑂4 , 𝜃𝑁𝑎,𝐻 , and

𝜃𝐶𝑙,𝐻𝑆𝑂4 parameters was reported by Christov and Moller [14], which is valid in the

temperature range from 273.15 to 473.15 K, 273.15 to 370.15, and 273.15 to 523.15 K,

respectively. All these information is summarized in Table 4.

Table 4. 𝜽𝒊𝒋 parameter values used in the present work.

T(K) 𝜃𝐶𝑙,𝑆𝑂4 a 𝜃𝐶𝑢,𝑁𝑎

b 𝜃𝐶𝑢,𝐻

c 𝜃𝑆𝑂4,𝐻𝑆𝑂4

d 𝜃𝑁𝑎,𝐻

d 𝜃𝐶𝑙,𝐻𝑆𝑂4

d

293.15 0.0700 0.0770 -0.0230 -0.1251 0.0343 0.0000

298.15 0.0700 0.0770 -0.0230 -0.1190 0.0345 0.0000

308.15 0.0700 0.0770 -0.0230 -0.1086 0.0350 0.0000

318.15 0.0700 0.0770 -0.0230 -0.0995 0.0354 0.0000

323.15 0.0700 0.0770 -0.0230 -0.0953 0.0356 0.0000

333.15 0.0700 0.0770 -0.0230 -0.0872 0.0360 0.0000 a,

b, and

c, correspond to the data at 298.15 K reported by Palaban and Pitzer [9], Downes and Pitzer

[19], and Wang [15], respectively. d, Calculated values using the temperature dependence model

from Christov and Moller [14].

Other authors have reported 𝜓𝑖𝑗𝑘 parameters at 298.15 K: Values for 𝜓𝐶𝑢,𝐶𝑙,𝑆𝑂4, 𝜓𝐶𝑢,𝑁𝑎,𝑆𝑂4

,

and 𝜓𝐶𝑢,𝑁𝑎,𝐶𝑙 were determined by Christov [13], 𝜓𝐶𝑢,𝐻,𝑆𝑂4 was reported by Wang et al.

[15], and the values for 𝜓𝐶𝑢,𝐻,𝐻𝑆𝑂4 and 𝜓𝐶𝑢,𝑆𝑂4,𝐻𝑆𝑂4

were determined by Baes [12]. In the

present work, these parameters were considered to be constant in the temperature range

from 293.15 to 333.15 K, and the reported values are the following: 𝜓𝐶𝑢,𝐶𝑙,𝑆𝑂4= 0.0100,

𝜓𝐶𝑢,𝑁𝑎,𝑆𝑂4= 0.0530, 𝜓𝐶𝑢,𝑁𝑎,𝐶𝑙= -0.0036, 𝜓𝐶𝑢,𝐻,𝑆𝑂4

= 0, 𝜓𝐶𝑢,𝐻,𝐻𝑆𝑂4 = -0.0250, and

𝜓𝐶𝑢,𝑆𝑂4,𝐻𝑆𝑂4= 0.0440.

Additionally, in the literature, equations for the 𝜓𝑖𝑗𝑘 determination as a function of the

temperature were reported. In this work, the temperature dependence of 𝜓𝑁𝑎,𝐶𝑙,𝑆𝑂4 was

110

determined using the model proposed by Moller [10], which is valid in the temperature

range from 273.15 to 423.15 K. In the case of 𝜓𝐻,𝐶𝑙,𝑆𝑂4, 𝜓𝑁𝑎,𝐻,𝑆𝑂4

, 𝜓𝑁𝑎,𝐻,𝐶𝑙 𝜓𝑁𝑎,𝐻,𝐻𝑆𝑂4,

𝜓𝑁𝑎,𝑆𝑂4,𝐻𝑆𝑂4, 𝜓𝑁𝑎,𝐶𝑙,𝐻𝑆𝑂4

, 𝜓𝐻,𝑆𝑂4,𝐻𝑆𝑂4, and 𝜓𝐻,𝐶𝑙,𝐻𝑆𝑂4

, the temperature dependence was

determined using the model proposed by Christov and Moller [14], which is valid in a wide

temperature range: (273.15 to 523.15 K in the case of 𝜓𝐻,𝐶𝑙,𝑆𝑂4, 𝜓𝑁𝑎,𝐶𝑙,𝐻𝑆𝑂4

, and

𝜓𝐻,𝐶𝑙,𝐻𝑆𝑂4); (273.15 to 370.15 K for 𝜓𝑁𝑎,𝐻,𝑆𝑂4

, 𝜓𝑁𝑎,𝐻,𝐻𝑆𝑂4, 𝜓𝑁𝑎,𝑆𝑂4,𝐻𝑆𝑂4

, and 𝜓𝐻,𝑆𝑂4,𝐻𝑆𝑂4);

and (273.15 to 358.85 K for 𝜓𝑁𝑎,𝐻,𝐶𝑙).

Table 5 shows the calculated 𝜓𝑖𝑗𝑘 values using the temperature dependence model from

Christov and Moller [14] used in the present work.

There is no information in the literature regarding to the 𝜓𝐶𝑢,𝐻,𝐶𝑙 𝜓𝐶𝑢,𝑁𝑎,𝐻𝑆𝑂4 𝜓𝐶𝑢,𝐶𝑙,𝐻𝑆𝑂4

parameters; these values have been considered as fitting parameters constant with the

temperature, and were determined in the present work (cf. section 4.3).

111

Table 5. Calculated 𝝍𝒊𝒋𝒌 values using the temperature dependence model from Christov and Moller [14].

T(K) 𝜓𝑁𝑎,𝐶𝑙,𝑆𝑂4

𝜓𝐻,𝐶𝑙,𝑆𝑂4

𝜓𝑁𝑎,𝐻,𝑆𝑂4

𝜓𝑁𝑎,𝐻,𝐶𝑙 𝜓𝐻,𝐶𝑙,𝑆𝑂4

𝜓𝑁𝑎,𝐻,𝐻𝑆𝑂4 𝜓𝑁𝑎,𝑆𝑂4,𝐻𝑆𝑂4

𝜓𝑁𝑎,𝐶𝑙,𝐻𝑆𝑂4 𝜓𝐻,𝑆𝑂4,𝐻𝑆𝑂4

𝜓𝐻,𝐶𝑙,𝐻𝑆𝑂4

293.15 -0.0090 0.0000 0.0132 -0.0023 0.0000 -0.0146 0.0057 0.0000 0.0000 0.0000

298.15 -0.0090 0.0000 0.0131 -0.0025 0.0000 -0.0146 0.0052 0.0000 0.0000 0.0000

308.15 -0.0090 0.0000 0.0128 -0.0029 0.0000 -0.0146 0.0045 0.0000 0.0000 0.0000

318.15 -0.0090 0.0000 0.0126 -0.0033 0.0000 -0.0146 0.0039 0.0000 0.0000 0.0000

323.15 -0.0090 0.0000 0.0124 -0.0034 0.0000 -0.0146 0.0036 0.0000 0.0000 0.0000

333.15 -0.0090 0.0000 0.0122 -0.0038 0.0000 -0.0146 0.0031 0.0000 0.0000 0.0000

112


4.1 Water activities of aqueous CuSO4 solutions at different temperatures.

Table 6 shows the experimental and calculated values for the activity of water (𝑎𝑤) in the

CuSO4–H2O system at five different temperatures (from 293.15 to 323.15 K) and

concentrations with their respective average mean absolute deviations (𝐴𝐴𝐷).

Table 6. Experimental water activities (aw) at different molalities of CuSO4 and

temperatures.

m

(mol/kg H2O) 𝑎𝑤

𝑒𝑥𝑝 𝑎𝑤

𝑐𝑎𝑙𝑐 𝐴𝐴𝐷𝑎

(∙10-3

)

293.15 K

0.8360 0.9858 0.9859

0.04

0.9193 0.9844 0.9844

1.0096 0.9828 0.9827

1.1014 0.9809 0.9809

1.2452 0.9780 0.9780

1.3020 0.9768 0.9768

298.15 K

0.8364 0.9859 0.9859

0.03

0.9205 0.9845 0.9844

1.0114 0.9828 0.9827

1.1025 0.9810 0.9810

1.2467 0.9781 0.9781

1.4036 0.9747 0.9747

308.15 K

0.8330 0.9860 0.9860

0.09

1.0108 0.9829 0.9828

1.2468 0.9782 0.9783

1.3079 0.9770 0.9770

1.4003 0.9748 0.9750

1.6052 0.9704 0.9703

318.15 K

1.0065 0.9833 0.9829

0.22 1.2103 0.9792 0.9791

1.4011 0.9748 0.9752

1.6032 0.9708 0.9707

113

1.8041 0.9656 0.9657

1.9944 0.9608 0.9606

323.15 K

1.1023 0.9820 0.9808

1.44

1.2461 0.9793 0.9780

1.4032 0.9761 0.9748

1.6042 0.9717 0.9702

1.8039 0.9668 0.9653

1.9993 0.9618 0.9600

𝐴𝐴𝐷𝑎 = ∑|𝑎𝑤𝑒𝑥𝑝 − 𝑎𝑤

𝑐𝑎𝑙|/𝑛; where 𝑛 is the number of experimental points. The standard

uncertainties 𝑢 for the water activities and molalities of copper sulfate are 𝑢(𝑎𝑤) = 0.0005 and

𝑢(𝑚𝐶𝑢𝑆𝑂4) = 0.0002, respectively.

To validate our results, Figure 1 shows a comparison between the experimental results

obtained in this work and the activity data of copper sulfate solutions reported by Downes

and Pitzer [19] and Yang et al. [26] at 298.15 K and 323.15 K, respectively.

Figure 1. Comparison between the experimental and literature data of the water activities

of CuSO4 in H2O at 298.15 and 323.15 K. ●, CuSO4-H2O at 323.15 K (this work); ▲,

CuSO4-H2O at 298.15 K (this work); , CuSO4-H2O at 323.15 K (Yang et al. [26]); ---,

CuSO4-H2O at 298.15 K (Downes and Pitzer [19]).

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

aw

CuSO4 (mol/kg H2O)

114

In both cases (298.15 and 323.15 K), the water activity values decrease as the solution

concentration increases. This is attributed to the increment in the number of water

molecules associated with the different ions in the solution [27].

Figure 1 also shows that the temperature has a small effect on the copper sulfate water

activities, where at 323.15 K, the activities are slightly higher than at 298.15 K. These

results agree with those of Guendouzi and Dinane [27], who reported the water activities,

osmotic and activity coefficients of aqueous electrolyte solutions of KCl (aq), Na2SO4 (aq),

and NaNO3 (aq) at different concentrations over a wide temperature range, and concluded

that the water activities are highly affected by the solute concentration; but slightly

influenced by the temperature.

Moreover, the water activities of aqueous solutions of copper sulfate at different

temperatures, have been compared with activities of copper sulfate in seawater [16], where

has been noted that values in freshwater are higher than in seawater, with a mean difference

of 0.0108 due to the seawater salts which lead to an increment in the number of water

molecules associated with the different ions in the solution [27].

4.2 Determination of the Pitzer parameters 𝜷𝑴𝑿(𝟎)

, 𝜷𝑴𝑿(𝟏)

, 𝜷𝑴𝑿(𝟐)


for CuSO4,

CuCl2, and Cu(HSO4)2 at different temperatures.

As mentioned in section 3.2, some authors have determined the Pitzer parameters for CuCl2

[19], CuSO4 [19, 28], and Cu(HSO4)2 [23] at 298.15 K.

Pitzer parameters of CuSO4 from 293.15 to 323.15 K were determined from experimental

data of water activities. According to Palaban and Pitzer [9] the activity of water (𝑎𝑤) is

related to the osmotic coefficient (𝜙) by the Equation (23).

∅ = − (1000

𝑣𝑚𝑀𝑤) ln 𝑎𝑤 (23)

115

where 𝑣 is the number of ions released by dissociation, 𝑚 is the molality, and 𝑀𝑤 is the

molecular mass of water.

Additionally, according to Downes and Pitzer [19], the Equation (24) represents the

osmotic coefficient for a salt.

(𝜙 − 1) = |𝑧𝑀𝑧𝑋|𝑓𝜙 + 𝑚2𝑣𝑀𝑣𝑋

𝑣𝐵𝑀𝑋

𝜙+ 𝑚2 2(𝑣𝑀𝑣𝑋)

32

𝑣𝐶𝑀𝑋

𝜙 (24)

where 𝑧𝑀 and 𝑧𝑋 are the charges on the ions 𝑀 and 𝑋, respectively; 𝑚 is the molality;

𝑣 = 𝑣𝑀 + 𝑣𝑋; and 𝐶𝑀𝑋𝜙

is the binary solute specific parameter. 𝑓𝜙 and 𝐵𝑀𝑋𝜙

are defined by:

𝑓𝜙 = −𝐴𝜙 [𝐼

12

(1+𝑏𝐼12)

] (25)

𝐵𝑀𝑋𝜙

= 𝛽𝑀𝑋(0)

+ 𝛽𝑀𝑋(1)

𝑒−𝛼1𝐼12 + 𝛽𝑀𝑋

(2) 𝑒−𝛼2𝐼

12 (26)

In the work of Ning et al. [29] was reported that ion interaction parameters for a single salt

at different temperatures could be expressed using the Equation (27), which is based on the

works of Marliacy et al. [30] and Hovey et al. [31].

𝑃(𝑇) = 𝑃0 + 𝑃1 (1

𝑇−

1

298.15) + 𝑃2 ln (

𝑇

298.15) (27)

where 𝑃 represents 𝛽𝑀𝑋(0)

, 𝛽𝑀𝑋(1)

, 𝛽𝑀𝑋(2)

, and 𝐶𝑀𝑋∅ ; 𝑇 is the temperature in Kelvin; and 𝑃0, 𝑃1,

and 𝑃2 are fitting parameters.

Using the experimental water activity values of copper sulfate in H2O and Equation (27), it

was possible to establish the values of 𝑃0, 𝑃1, and 𝑃2 for the determination of the CuSO4

Pitzer parameters in the temperature range from 293.15 to 323.15 K. In the case of CuCl2

116

and Cu(HSO4)2, these values from 293.15 to 333.15 K have been considered as fitting

parameters, and the determined values are presented in Table 7.

Table 7. Pitzer parameters within the temperature range of 293.15 to 323.15 K for CuSO4,

and from 293.15 to 333.15 K for CuCl2, and Cu(HSO4)2.

CuSO4 CuCl2 Cu(HSO4)2

𝑃0 𝑃1 𝑃2 𝑃0 𝑃1 𝑃2 𝑃0 𝑃1 𝑃2

𝛽𝑀𝑋(0)

0.2340 1.0027 0.1815 0.1766 0.0007 -0.1925 0.3212 0.0058 -1.6611

𝛽𝑀𝑋(1)

2.5270 1.0001 0.9715 0.5740 0.0000 -0.0115 0.3627 0.0003 -0.0863

𝛽𝑀𝑋(2)

-48.3300 1.0000 1.0000 0.6341 0.0002 -0.0498 - - -

𝐶𝑀𝑋∅ 0.0044 1.0000 -0.2399 -0.0109 -0.0038 -0.5163 0.0988 0.0109 -0.3183

It is important to mention that due to the limited temperature range of the hydrometer (cf.

section 2.2.1), it was not possible to realize activity measurements over 323.15 K.

Therefore, Pitzer parameters of CuSO4 at 333.15 K were predicted using the values from

Table 7.

Additionally, in order to contribute with new thermodynamic data, activity coefficients for

CuSO4, CuCl2, and Cu(HSO4)2 solutions have been calculated in the temperature range

from 293.15 to 323.15 K using the Pitzer parameters values from Table 7. For CuSO4 and

CuCl2 solutions at 298.15 K, these data were compared with those reported by Christov

[13]. All these data are shown in Figure 2.

117

Figure 2. a) CuSO4, b) CuCl2, and c) Cu(HSO4)2 activity coefficients at different salt

concentrations: ■, 293.15 K; ♦, 298.15 K; ▲, 308.15 K; ●, 318.15 K; ×, 323.15 K; ,

333.15 K; ---, predicted data; , values from Christov [13] at 298.15 K.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Act

ivit

y c

oef

fici

ent

(γ)

CuSO4 (mol/Kg H2O)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Act

ivit

y c

oef

fici

ent

(γ)

CuCl2 (mol/Kg H2O)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Act

ivit

y c

oef

fici

ents

(γ)

Cu(HSO4)2 (mol/kg H2O)

a)

b)

c)

118

Figure 2 a, b, and c, show the activity coefficients (𝛾) vs molalities at different temperatures

and concentrations of CuSO4, CuCl2, and Cu(HSO4)2, respectively. All the curves show a

typical profile of the variation of 𝛾 with the concentration that, as is well known, is

governed by two types of interactions including those of ion-ion and ion-solvent [32].

Additionally, for the three electrolytes being compared, it is observed that the activity

coefficients decrease as the temperature increases. On the other hand, the concentration

effect is different for each of the electrolytes in the concentration range from 0 to 1.5 m: for

CuSO4 solutions, 𝛾 values decrease with the concentration increasing (ion-ion interactions

prevailed); in the case of CuCl2 at low temperatures (293.15 and 298.15 K), there is an

increasing in the 𝛾 values with the concentration, however at higher temperatures (from

308.15 to 333.15 K), 𝛾 values decrease with the concentration (ion-solvent and ion-ion

interactions prevailed, respectively); for Cu(HSO4)2, there is an increasing in the 𝛾 values

as the concentration increases (ion-solvent interactions prevailed).

Moreover, it is important to mention that the calculation of activity coefficients for CuCl2

solutions at several temperatures is a great contribution given its difficulty to be measured

due to its highly corrosive features [33].

4.3 Ternary mixing parameters at different temperatures.

As mentioned in section 3.3, models for the temperature dependence of the ternary mixing

parameters 𝜓𝑁𝑎,𝐶𝑙,𝑆𝑂4 𝜓𝐻,𝐶𝑙,𝑆𝑂4

, 𝜓𝑁𝑎,𝐻,𝑆𝑂4 , 𝜓𝑁𝑎,𝐻,𝐶𝑙 𝜓𝑁𝑎,𝐻,𝐻𝑆𝑂4

, 𝜓𝑁𝑎,𝑆𝑂4,𝐻𝑆𝑂4,

𝜓𝑁𝑎,𝐶𝑙,𝐻𝑆𝑂4, 𝜓𝐻,𝑆𝑂4,𝐻𝑆𝑂4

, and 𝜓𝐻,𝐶𝑙,𝐻𝑆𝑂4 have been determined in previous works [10, 14],

while the parameters 𝜓𝐶𝑢,𝐶𝑙,𝑆𝑂4, 𝜓𝐶𝑢,𝑁𝑎,𝑆𝑂4

, 𝜓𝐶𝑢,𝑁𝑎,𝐶𝑙, 𝜓𝐶𝑢,𝐻,𝑆𝑂4 𝜓𝐶𝑢,𝐻,𝐻𝑆𝑂4

, and

𝜓𝐶𝑢,𝑆𝑂4,𝐻𝑆𝑂4 were reported at 298.15 K [12, 13, 15] and considered in this work constant in

the temperature range from 293.15 to 333.15 K.

Additionally, there are no values reported for 𝜓𝐶𝑢,𝐻,𝐶𝑙, 𝜓𝐶𝑢,𝑁𝑎,𝐻𝑆𝑂4 and 𝜓𝐶𝑢,𝐶𝑙,𝐻𝑆𝑂4

, due to

this, and to the high complexity of the studied system and high ionic strengths used, these

values were considered as fitting parameters, which are constant in the temperature range

from 293.15 to 333.15 K. The fitted values of the ion-mixing interaction parameters

119

determined in the present work are: 𝜓𝐶𝑢,𝐻,𝐶𝑙= 0.0036, 𝜓𝐶𝑢,𝑁𝑎,𝐻𝑆𝑂4= 0.0957, and

𝜓𝐶𝑢,𝐶𝑙,𝐻𝑆𝑂4= -0.0990.

4.4 Solubility products of copper sulfate pentahydrate at different temperatures

The solubility product (𝐾𝑠𝑝) is a value that can be obtained from the solubility, activity

coefficient and water activity of copper sulfate in H2O (without acid). These 𝐾𝑠𝑝 values at

different temperatures (from 293.15 to 333.15 K) were determined by the following

expression reported by Lovera et al. [17].

𝐾𝑠𝑝𝐶𝑢𝑆𝑂4∙5𝐻2𝑂 = (𝑚𝐶𝑢𝑆𝑂4

)2

( 𝛾±𝐶𝑢𝑆𝑂4

)2

(𝑎𝑤)5 (28)

From Equation (28), the copper sulfate saturation molality in the ternary system is obtained

by:

𝑚𝐶𝑢𝑆𝑂4= [

(𝐾𝑠𝑝𝐶𝑢𝑆𝑂4∙5𝐻2𝑂)

(( 𝛾±𝐶𝑢𝑆𝑂4

)2

(𝑎𝑤)5)]

1

2

(29)

Table 8 shows the solubility product, activity coefficient, and water activity values of

copper sulfate in the temperature range from 293.15 to 333.15 K. At 333.15 K these values

were calculated using predicted Pitzer parameters of CuSO4 (Table 7). Moreover, solubility

values of copper sulfate (in mol/kg H2O) in the absence of acid [34] were used for the

calculations.

Table 8. Values of activity coefficients, water activities, and solubility products at different

copper sulfate concentrations and temperatures.

𝑇(K) 𝑚 (mol/kg H2O) 𝛾±𝐶𝑢𝑆𝑂4

𝑎𝑤 𝐾𝑠𝑝𝐶𝑢𝑆𝑂4∙5𝐻2𝑂

293.15 1.26023 0.03961 0.97767 0.00223

298.15 1.39404 0.03679 0.97523 0.00232

308.15 1.63900 0.03197 0.97104 0.00237

318.15 1.97317 0.02714 0.96535 0.00240

323.15 2.12206 0.02496 0.96332 0.00233

333.15* 2.46750 0.02060 0.95951 0.00211

* calculated values using predicted Pitzer parameters of CuSO4 at 333.15 K.

120

At 298.15 K, there is a mean deviation of 0.00013 between the solubility product of copper

sulfate in seawater obtained in the present work and the one reported by Christov [13] for

aqueous copper sulfate solutions. As expected, the copper sulfate solubility product

obtained in this work is very similar to that reported in the literature, allowing us to validate

the model used in the present work.

4.5 Representation of the solid-liquid equilibrium of the CuSO4 - H2SO4 - seawater

system at six different temperatures.

Experimental data of the solubilities of the copper sulfate - sulfuric acid - seawater system

at six different temperatures were correlated using the Pitzer model and minimizing the

following objective function:

𝑂𝐹 = ∑ (𝑚𝑒𝑥𝑝− 𝑚𝑐𝑎𝑙𝑐

𝑚𝑒𝑥𝑝)

2

(30)

where the subscripts 𝑒𝑥𝑝 and 𝑐𝑎𝑙𝑐 correspond to the experimental and calculated saturation

molalities, respectively.

Experimental solubility data of copper sulfate in seawater in the temperature range from

293.15 to 333.15 K reported by Justel et al. [16, 35] were correlated.

Figure 3 shows the experimental and calculated solubility data using the Pitzer ion-

interaction model, expressed as a molality (mol/kg H2O) of copper sulfate for different

molalities of sulfuric acid.

121

Figure 3. Solubility of saturated solutions of CuSO4-H2SO4-seawater system. ■, 293.15 K;

♦, 298.15 K; ▲, 308.15 K; ●, 318.15 K; ×, 323.15 K; *, 333.15 K; − correlated data; ---,

correlated data using predicted Pitzer parameters for CuSO4 at 333.15 K.

A good agreement between the experimental and correlated values for the CuSO4-H2SO4-

seawater system at the six different temperatures was obtained. In addition, a significant

effect of the sulfuric acid in the reduction of copper sulfate solubility, due to the common

ion effect [36], is observed. Therefore, sulfuric acid is considered a good agent for copper

sulfate crystallization.

A simplification of the seawater multicomponent system was carried out and the principal

ions from seawater (Na+ and Cl

-) were considered in the model, due to their presence at

high concentrations [16, 35]. Despite this consideration, and without regard to the other

ions from seawater, an average mean absolute deviation of 0.0157 mol/Kg was obtained.

Thus, it is possible to get a good fitting between the experimental and calculated values if

only the main ions from seawater are considered.

The results from the present work, were compared with those of Justel et al. [16], where a

representation of the solid-liquid equilibrium of the copper sulfate-sulfuric acid-seawater

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

CuS

O4 (

mo

l/kg H

2O

)

H2SO4 (mol/Kg H2O)

122

system at different temperatures was performed considering seawater as a solvent,

obtaining an AAD of 0.0062 mol/kg. This comparison allows concluding that the

correlation of solubilities in seawater systems could be performed only considering sodium

and chloride as part of the seawater, without regard to the effect of the other ions, which do

not have a significant influence in the modelling.

Among the greatest contributions of the present work are that the ion-interaction model of

Pitzer has been successfully used to predict the solubilities of an electrolyte in a system as

complex as natural seawater, which makes it a suitable model to be applied to mining

processes using seawater. Additionally, in this work new binary and ternary Pitzer

parameters in a wide temperature range have been determined; these values can be used to

predict solubilities of other solid-liquid systems (ternary, quaternary, quinary, etc.) where

the Cu2+

, Na+, H

+, SO4

2-, Cl

-, HSO4

-, ions are involved.

In a future work, it would be interesting to consider other ions as part of the seawater, in

order to determine their influence in the modelling.

123

5. CONCLUSIONS

This is the first work that applies Pitzer’s ion interaction model to mining processes using

seawater, where binary and ternary Pitzer parameters of the Cu-Na-H-SO4-Cl-HSO4-H2O

system at different temperatures were determined. Additionally, experimental water

activities of copper sulfate solutions at different temperatures were obtained, where it was

concluded that the water activities are highly affected by the solute concentration, but

slightly influenced by the temperature.

The ion interaction model of Pitzer was successfully used to determine the solubilities of

the CuSO4-H2SO4-seawater system at six different temperatures by modelling the Cu-Na-

H-SO4-Cl-HSO4-H2O system. Although only sodium and chloride ions were considered as

seawater components, a good agreement between the experimental and correlated values

was obtained, with an 𝐴𝐴𝐷 of 0.0157 mol/kg.

ACKNOWLEDGEMENTS: Funding for this research was provided by CONICYT

(Fondecyt Project 1140169 and grant 21130894).

124

6. REFERENCES

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[5] H.R. Galleguillos, T.A. Graber, M.E. Taboada, F.F. Hernandez-Luis, Activity of Water

in the KI+ KNO3+ H2O Ternary System at 298.15 K, Journal of Chemical & Engineering

Data, 48 (2003) 851-855.

[6] K.S. Pitzer, Thermodynamics of electrolytes. I. Theoretical basis and general equations,

The Journal of Physical Chemistry, 77 (1973) 268-277.

[7] K.S. Pitzer, J.J. Kim, Thermodynamics of electrolytes. IV. Activity and osmotic

coefficients for mixed electrolytes, Journal of the American Chemical Society, 96 (1974)

5701-5707.

[8] C.E. Harvie, J.H. Weare, The prediction of mineral solubilities in natural waters: the

Na-K-Mg-Ca-Cl-SO4-H2O system from zero to high concentration at 25 °C, Geochimica et

Cosmochimica Acta, 44 (1980) 981-997.

[9] R.T. Pabalan, K.S. Pitzer, Thermodynamics of concentrated electrolyte mixtures and the

prediction of mineral solubilities to high temperatures for mixtures in the system Na-K-Mg-

Cl-SO4-OH-H2O, Geochimica et Cosmochimica Acta, 51 (1987) 2429-2443.

[10] N. Møller, The prediction of mineral solubilities in natural waters: A chemical

equilibrium model for the Na-Ca-Cl-SO4-H2O system, to high temperature and

concentration, Geochimica et Cosmochimica Acta, 52 (1988) 821-837.

125

[11] J.P. Greenberg, N. Møller, The prediction of mineral solubilities in natural waters: A

chemical equilibrium model for the Na-K-Ca-Cl-SO4-H2O system to high concentration

from 0 to 250 C, Geochimica et Cosmochimica Acta, 53 (1989) 2503-2518.

[12] C. Baes Jr, E. Reardon, B.A. Moyer, Ion interaction model applied to the cupric

sulfate-sulfuric acid-water system at 25°C, The Journal of Physical Chemistry, 97 (1993)

12343-12348.



[14] C. Christov, N. Moller, Chemical equilibrium model of solution behavior and

solubility in the H-Na-K-OH-Cl-HSO4-SO4-H2O system to high concentration and

temperature, Geochimica et Cosmochimica Acta, 68 (2004) 1309-1331.

[15] W. Wang, D. Zeng, X. Yin, Q. Chen, Prediction and measurement of gypsum

solubility in the systems CaSO4+ HMSO4+ H2SO4+ H2O (HM= Cu, Zn, Ni, Mn) at 298.15


[16] F.J. Justel, M.E. Taboada, Y.P. Jimenez, Solid–liquid equilibrium and copper sulfate

crystallization process design from a sulfuric-acid–seawater system in the temperature

range from 293.15 to 333.15 K, (2017).

[17] J.A. Lovera, A.P. Padilla, H.R. Galleguillos, Correlation of the solubilities of alkali

chlorides in mixed solvents: Polyethylene glycol + H2O and Ethanol + H2O, Calphad, 38

(2012) 35-42.

[18] S. Clegg, M. Whitfield, Activity coefficients in natural waters, Activity coefficients in

electrolyte solutions, 2 (1991).


from aqueous NaCl, Na2SO4, CuCl2, and CuSO4, at 25°C, Journal of Solution Chemistry, 5

(1976) 389-398.

126

[20] K.S. Pitzer, Thermodynamics of electrolytes. V. Effects of higher-order electrostatic

terms, Journal of Solution Chemistry, 4 (1975) 249-265.

[21] H.T. Kim, W.J. Frederick Jr, Evaluation of Pitzer ion interaction parameters of

aqueous electrolytes at 25°C. 1. Single salt parameters, Journal of Chemical and

Engineering Data, 33 (1988) 177-184.

[22] H. Holmes, R. Busey, J.M. Simonson, R.E. Mesmer, D. Archer, R. Wood, The

enthalpy of dilution of HCl (aq) to 648 K and 40 MPa thermodynamic properties, The

Journal of Chemical Thermodynamics, 19 (1987) 863-890.

[23] M. Tanaka, Modelling of solvent extraction equilibria of Cu (II) from nitric and

hydrochloric acid solutions with (β-hydroxyoxime), Hydrometallurgy, 24 (1990) 317-331.

[24] K.S. Pitzer, R.N. Roy, L.F. Silvester, Thermodynamics of electrolytes. 7. Sulfuric


[25] M.A. Hughes, S. Hou, Equilibria in the system cobalt di-2-ethylhexylphosphoric

acid/water, Journal of Chemical and Engineering Data, 31 (1986) 4-11.









[29] P. Ning, W. Xu, H. Cao, X. Lin, H. Xu, Determination and modeling for the solubility

of Na2MoO4·2H2O in the (Na++

MoO42−

+ SO42−

) system, The Journal of Chemical


127

[30] P. Marliacy, R. Solimando, M. Bouroukba, L. Schuffenecker, Thermodynamics of

crystallization of sodium sulfate decahydrate in H2O–NaCl–Na2SO4: application to

Na2SO4·10H2O-based latent heat storage materials, Thermochimica Acta, 344 (2000) 85-

94.

[31] J.K. Hovey, K.S. Pitzer, J.A. Rard, Thermodynamics of Na2SO4 (aq) at temperatures T

from 273 K to 373 K and of ((1-y)H2SO4+ yNa2SO4)(aq) at T= 298.15 K, The Journal of

Chemical Thermodynamics, 25 (1993) 173-192.

[32] J.O.M. Bockris, A.K.N. Reddy, Modern Electrochemistry, in: N.Y. Reverté (Ed.),

1979.

[33] J. Rard, Isopiestic investigation of water activities of aqueous NiCl2 and CuCl2

solutions and the thermodynamic solubility product of NiCl2·6H2O at 298.15 K, Journal of

Chemical and Engineering Data, 37 (1992) 433-442.


ACS, Washington DC.





128

CHAPTER VI

CRYSTALLIZATION OF COPPER SULFATE PENTAHYDRATE IN ABSENCE

AND PRESENCE OF SODIUM CHLORIDE

F.J. Justel1, D.M. Camacho

2, M.E. Taboada

1, and K. J. Roberts

2*

1Department of Chemical Engineering and Mineral Processing,

University of Antofagasta,

Antofagasta, Chile

2School of Chemical and Process Engineering, University of Leeds, Leeds, United Kingdom

ABSTRACT

The recrystallization of copper sulfate represents an important unit operation in copper

mining and recovery. The effect of sodium chloride on the shape, size, composition and

growth kinetics of copper sulfate pentahydrate crystals is assessed and compared with

results in freshwater, in order to understand the effect of the principal ions present in

seawater (Na+ and Cl

-) in the crystallization process. The solubility of copper sulfate in

sodium chloride media is found to be slightly lower than in pure aqueous solutions. The

cooling rate and sodium chloride concentration are observed to have an effect in the crystal

shape and size of the copper sulfate crystals albeit the purity of crystals is not significantly

affected by the sodium chloride concentration used.

Analysis of the crystal growth kinetics reveals a significant dependence on the growth

environment, in which the growth of the (1-10) and (1-1-1) faces of crystals grown in

aqueous solutions is consistent with the power law and BCF mechanisms respectively. In

contrast for crystals grown in sodium chloride media the results suggest that both the (1-10)

and (1-1-1) faces grow via the BCF mechanism. This difference in the face-specific growth

mechanisms, in the different crystallization media, is evidenced in the crystal shape

revealing slightly more elongated crystals in aqueous solutions.

Keywords: Copper sulfate, Sodium Chloride, Solubility, Activity Coefficients, Crystal

Growth Kinetics and Morphology.

129

1. INTRODUCTION

Copper mining is the most significant economic activity on the north side of Chile,

however, in the dominant mining region close to the Atacama Desert, mining industries

have required innovative solutions for the optimization of water consumption and have

started to use seawater in their productive processes [1].

Copper sulfate pentahydrate is an important industrial compound of copper due to the wide

range of commercial uses [2-4]. In Chile, some mining companies crystallize this salt from

hydrometallurgical processes using freshwater, where copper is obtained from ores

containing oxidized copper minerals [5]. However, in order to be able to minimize the use

of freshwater in the crystallization process, seawater is now being used for the

crystallization of copper sulfate pentahydrate and the impact of this needs to be assessed.

Copper sulfate pentahydrate (CuSO4·5H2O), also called, bluestone, and blue vitriol, is

found in nature as the mineral chalcanthite [4]. It belongs to the triclinic system

crystallizing in space group P1 with unit-cell parameters: a = 6.1224 (4) Å; b = 10.7223 (4)

Å; c = 5.9681 Å; α = 82.35 (2)°; β = 107.33 (2)°; γ = 102.60 (4)°; V = 364.02 (3) Å3; Z = 2;

D = 2.278 g/cm3. Figure 1 shows the crystal habit of copper sulfate pentahydrate crystals

which is a combination of pinacoids [6].

Figure 1. Habit of CuSO4·5H2O crystal [6].

Copper sulfate pentahydrate crystallization studies using freshwater have been carried out

by several authors: Ishii and Fujita [7], examined the stability of copper sulfate aqueous

solutions at the first supersaturation concentration, in a batchwise stirred reactor, using

different temperatures and stirring rates. Zumstein and Rosseau [8] have focused their work

130

on the agglomerates formation during the batch and continuous copper sulfate

crystallization. Giulietti et al. [2, 9, 10], characterized the copper sulfate pentahydrate

crystallization from batch cooling experiments, and studied the effect of additives on the

crystallization. Manomenova et al. [6] developed a technique for growing large single

crystals for application as optical filters, analyzing the transmission spectra, associated

impurities, thermal stability, and crystal structure.

However, little information is available in the literature regarding the effect of seawater as a

recrystallization solvent. Hernández et al. [11] provided experimental data of solubilities

and physical properties (density, refractive index, ionic conductivity, and viscosity) of

CuSO4 in seawater at various temperatures and at pH 2. Justel et al. [12], studied the

influence of seawater on the solid-liquid equilibrium, and physical properties (density and

viscosity) in copper sulfate solutions at four different temperatures and ten different sulfuric

acid concentrations. Then, Justel et al. [13] determined solubilities and water activities

values of copper sulfate in seawater at different temperatures, and used this information to

represent the solid-liquid equilibrium of copper sulfate-sulfuric acid-seawater system by

means of a methodology that uses the Pitzer and the Born model to quantify the relative

impact of copper sulfate and sulfuric acid effect, respectively on the phase diagram.

Additionally, the precipitated amounts of copper sulfate as a function of the sulfuric acid

concentration were predicted [11-13]. In these studies the sodium chloride concentration

present in seawater was 2.4 wt %, and the experimental data were correlated obtaining

relevant information for the design of copper sulfate pentahydrate plants, using seawater as

a solvent and the addition of sulfuric acid as the crystallization initiator.

The impact of sodium chloride on crystallization processes have been studied previously:

Brandse et al. [14], studied the NaCl effect in the growth kinetics of calcium sulfate

dehydrate and Sheikholeslami and Ong [15] examined the salinity effect on the CaCO3 and

CaSO4 crystallization, where different NaCl concentrations were used to study the crystal

structure and size, among others.

131

The growth rate of each crystallographically unique crystal face is different depending on

the growth environment such as supersaturation, temperature, solvents, and impurities. The

most common methods for the measurement of the growth rate of crystals [16] are the

measurement of the linear growth rate on specific faces of a single crystal or by estimating

an overall linear growth rate from the mass deposition rates on the bulk mass of a large

number of crystals. The single crystal measurement method avoids the impact of other

physical phenomena such as the collision of crystals with other objects, e.g. the wall of the

vessel or other crystals that may have an effect on the growth kinetics [17]. Previous studies

have been carried out on a number of ionic compounds including the measurement of the

growth rates of ammonium and potassium dihydrogen phosphate crystal faces under

controlled conditions of temperature, supersaturation, and solution velocity [18]; Davey and

Mullin [19] studied the effect of ionic species on the growth kinetics and impurity

incorporation for the (101) and (100) faces of ammonium dihydrogen phosphate single

crystals; Sweegers et al. [20] used in-situ optical microscopy to measure the growth rates of

individual (001), (110), and (100) faces for different types of gibbsite crystals as a function

of the driving force; Suharso [21] reported the growth mechanism for sodium borate

tetrahydrate (borax) single crystals for the (111) habit planes at various relative

supersaturations using in situ optical microscopy.

Given the lack of studies on the growth kinetics of copper sulfate pentahydrate, it is the aim

of this study to deliver fundamental information on the morphology and crystal growth

kinetics of copper sulfate pentahydrate as a function of the solution environment. These

experimental data were collected using a methodology developed for the analysis of

Ibuprofen single crystal crystallization [22], while the analysis of crystal growth kinetics

was carried out using models which consider the effect in series of mass transfer and

integration of growth units to the crystal surface derived elsewhere [23, 24].

In general, the aim of the present work is to assess the effect of sodium chloride on the

crystal shape, particle size, composition, and growth rates of copper sulfate pentahydrate

crystals in order to understand the effect of the principal ions from seawater in the overall

crystallization process. This knowledge will allow us to obtain valuable information that

132

could be useful in the design of the copper sulfate crystallization process using seawater. In

all the experiments, a sodium chloride concentration of 2.4 wt % was used in order to

simulate the natural seawater system reported by Hernández et al. [11] and Justel et al. [12].

2. MATERIALS AND METHODS

2.1 Materials

The reagents used in this work were of analytical grade: Copper sulfate pentahydrate,

Merck, 99%; Sodium Chloride, Merck, 99.5%, and Distilled deionized water (0.054 𝜇𝑆 ∙

𝑐𝑚−1). No further purification was carried out.

2.2 Equipment and experimental procedure

2.2.1 Solubilities measurements of copper sulfate in aqueous solutions and in 2.4 wt

% sodium chloride media.

Linke and Seidell [25] reported solubility data of copper sulfate in freshwater at different

temperatures. In the present work, experimental solubility data of copper sulfate with 2.4 wt

% of sodium chloride at different temperatures (from 293.15 to 333.15 K) were determined.

The methodology used for the determination of the solubility have been previously reported

[12, 13].

2.2.2 Crystallization experiments.

Crystallization experiments were carried out using the Avantium Crystalline® system (see:

https://www.crystallizationsystems.com/Crystalline). This facilitates 8 parallel reactors and

can hold up to 8 standard disposable glass vials (O 16.6 mm, flat bottomed, 8 mL). Each

reactor can be independently loaded, programmed, and operated. The temperature range

can be varied from -15 to 150 °C and stirring rates between 0 to 1250 rpm are available

using magnetic and/or overhead agitators. Crystalline provides an inlet for a dry purge gas

133

(typically nitrogen) to prevent condensation on the reactor blocks and electronics. The high

quality digital visualization probes are independent of each other, and can be synchronized

with the turbidity measurements and temperature profile of each independent rector. This

equipment consist of two blocks equipped with a 2.0 x magnification lens and 1 block

equipped with a 1.0 x magnification lens. Data was collected using particle viewer mode

through which temperature and on-line particle image data was recorded.

In this study, in situ batch cooling crystallization experiments were performed for copper

sulfate solutions at the concentration of 29.52 wt %, in absence and in presence of 2.4 wt %

of sodium chloride, to visualize the crystallization at an early stage. The solutions were

subject to heating and cooling cycles, with each cycle initiated by heating the solutions up

to 70 °C where they were held for an hour to ensure complete homogenization and then

cooled to 0 °C where they were also held for an hour to allow equilibration. This

temperature profile was applied using four different rates 2.0, 1.0, 0.5, and 0.3 °C/min for

both the CuSO4 + H2O and CuSO4 + NaCl + H2O systems.

Images were obtained every five seconds and analyzed using Process Avantium Crystalline

software in order to assess the crystallization and dissolution temperatures, crystals shapes,

and particle size distributions. At each rate the temperature cycle was repeated three times

to obtain average values for the crystallization and dissolution temperatures 𝑇𝑐𝑟𝑦𝑠𝑡 and

𝑇𝑑𝑖𝑠𝑠.

As the copper sulfate system is not readily amenable to analysis via turbidometric optical

methods due to the intense blue colour of the saturated crystallizing solution [26]

turbidometric data was not examined. Because of this, the determination of the Metastable

zone width (MSZW) was performed using the particle viewer mode in the individual

reactors, where the crystallization and dissolution temperatures were visually estimated

based upon the points where the crystals appear and disappear, respectively. Finally, the

crystals obtained at the different cooling rates (2.0, 1.0, 0.5, and 0.3 °C/min), were filtered

and dried for further solid analysis.

134

2.2.3 Thermal Analysis (TGA/DSC) and Chemical Analysis

Copper sulfate crystals as obtained from aqueous and NaCl media at a cooling rate of

1°C/min were filtered, dried, and analyzed by thermogravimetric analysis (TGA) and

Differential Scanning Calorimetry (DSC) to determine their composition, melting points,

and to validate if the crystals grown in different media correspond to copper sulfate

pentahydrate.

Thermal assays were conducted with a Mettler Toledo Thermogravimeter TGA/DSC1,

STARe System. The crucibles used in the TGA/DSC instrument are made of platinum and

were hermetically sealed. The test was conducted in a flowing inert nitrogen atmosphere

(50 ml/min) and at a heating rate of 10 °C/min. The equipment was calibrated with indium

with a sample mass of 10 mg. The temperature used in the experiment ranged from 25 to

300 °C.

In addition to this, chemical analysis of copper sulfate crystals obtained in NaCl media at

1°C/min was performed to determine the chemical composition of the sample and the

concentration range of variation corresponding to the main impurities. Cu2+

and SO42-

concentrations were determined by oxidation-reduction volumetry and gravimetric method

with drying of residue, respectively, and Na+ and Cl

- were determined by Atomic and

Molecular absorption spectrophotometry, respectively.

2.2.4 Crystal Growth measurements by In-situ Microscopy

In-situ crystal growth studies were carried out using an experimental set-up comprising an

optical microscope (Olympus BX51) operated in Differential Interference Contrast (DIC)

mode, which was integrated with a QImaging/QICAM camera which captured crystal

images as a function of time. The images were then analyzed using the QCapture Pro

software (see: http://www.qimaging.com/products/software/qcappro7.php). The associated

growth cell comprised a simple temperature-controlled rectangular tank (10 x 12 cm, depth

135

1.5 cm) sealed with two removable rectangular glass plates. The solution was secured

within a 0.5 ml sealed UV glass cuvette with a path length of 1 mm which was placed

within the cell as close to the objective lens of the microscope as feasible. The temperature

within the cell controlled using a Huber Ministat 125 circulating water bath that circulates

water through the growth cell. The crystal growth system is shown in Figure 2.

Figure 2. Experimental set up for crystal growth rates measurements. (a) Olympus BX51

optical DIC microscope integrated with QImaging/QICAM camera. (b) Picture of the

crystal growth cell.

Crystal growth experiments were performed for copper sulfate solutions (29.52 wt %) in

two different media: H2O and 2.4 wt % NaCl, where copper sulfate solutions were heated

up to 70 °C to completely dissolve all crystals, after which the solutions were cooled down

to a constant temperature of 23, 22, 21, 20 and 19 °C for the CuSO4 + H2O system, and 39,

37, 36, 35, 33 °C for CuSO4 + NaCl + H2O system, respectively, in order to achieve a

specific supersaturation level. For each system, five different supersaturations were used.

The supersaturation for crystallization was generated by decreasing the solution

temperature from the equilibrium temperature (𝑇𝑒) by circulating water through the cell

until the targeted temperature had been established. The relative solution supersaturation

(σ) at each temperature is calculated using equation (1).

𝜎 =𝑥

𝑥𝑒− 1 (1)

Where 𝑥 is the molar fraction of the solute, and 𝑥𝑒 is the molar fraction of the solute in the

solution at equilibrium.

136

The crystal morphology and growth of the observed crystals were assessed recording

images every five seconds. The growth rates of the individual faces (𝐺) were estimated by

following the increase with time of the perpendicular distance from the centre of the

projected two dimensional crystal to the faces (Figure 3). The central point of the crystals

were determined by drawing lines connecting the crystal’s corners as defined by the two

most important habit faces. For each face, eleven measurements of the normal distance

increase were recorded, and each experiment was performed in duplicate.

Figure 3. Example of measurement from the centre of the copper sulfate crystal to the

faces. The distances are obtained by drawing a perpendicular line to each face from the

centre of the crystal using QCapture Pro software.

2.2.5 Determination of activity coefficients for the assessment of ion interactions of

copper sulfate in aqueous solutions and sodium chloride media

In order to assess the importance of the chemical interactions, the activity coefficients of

the copper sulfate solutions have been evaluated. An activity coefficient is a factor used in

thermodynamics to account for deviations from ideal behaviour in a mixture of chemical

substances [27].

In the present work, the activity coefficients of copper sulfate 𝛾± were determined by the

Pitzer model [28] where for 2-2 electrolytes (as copper sulfate), the mean activity ionic

coefficients are given by the following expressions:

ln 𝛾± = 4𝑓𝛾 + 𝑚𝐵𝛾 + 𝑚2𝐶𝛾 (2)

137

where:

𝑓𝛾 = −𝐴∅[𝐼1 2⁄ (1 + 𝑏𝐼1 2⁄ )⁄ + 2 𝑏⁄ ln(1 + 𝑏𝐼1 2⁄ )] (3)

𝐵𝛾 = 2𝛽(0) + (2𝛽(1) 𝛼12𝐼⁄ ) [1 − (1 + 𝛼1𝐼1 2⁄ − 1 2⁄ 𝛼1

2𝐼)𝑒𝑥𝑝−𝛼1𝐼1 2⁄] + (2𝛽(2) 𝛼2

2𝐼⁄ ) [1 −

(1 + 𝛼2𝐼1 2⁄ − 1 2⁄ 𝛼22𝐼)𝑒𝑥𝑝−𝛼2𝐼1 2⁄

] (4)

𝐶𝛾 = 3 2⁄ 𝐶∅ (5)

In these equations, 𝐴𝜙 corresponds to the Debye-Hückel term [29], and m and I correspond

to the molality and ionic strength, respectively. The symbols 𝛽(0), 𝛽(1), 𝛽(2), and 𝐶∅ are

copper sulfate specific parameters, and the parameters 𝛼1 , 𝛼2, and b are constant, with

values of 1.4, 12, and 1.2 Kg1/2

·mol-1/2

, respectively, for copper sulfate [28].

The values of the 𝛽(0), 𝛽(1), 𝛽(2), and 𝐶∅ for CuSO4 solutions in H2O and NaCl media from

293.15 to 333.15 K have been taken from the works of Justel et al. [13, 30]; in the case of

the solutions with sodium chloride, parameter values for copper sulfate in seawater were

considered [13]. All the values are shown in Table 1.

Table 1. Binary Pitzer parameters for copper sulfate solutions in H2O and NaCl media.

CuSO4 + H2O system [30] CuSO4 + Seawater system [13]

T(K) 𝛽(0) 𝛽(1) 𝛽(2) 𝐶∅ 𝛽(0) 𝛽(1) 𝛽(2) 𝐶∅

293.15 0.231 2.511 -48.347 0.009 0.571 2.978 0 -0.070

303.15 0.237 2.543 -48.313 0.000 0.579 2.988 0 -0.074

313.15 0.243 2.575 -48.281 -0.008 0.587 2.998 0 -0.079

323.15 0.248 2.605 -48.250 -0.015 0.595 3.008 0 -0.083

333.15 0.254 2.634 -48.219 -0.023 0.602 3.017 0 -0.087

138

2.2.6 Assessment of crystals single faces growth kinetics

The crystal growth mechanism was investigated by fitting 𝐺(𝜎) dependence to models

representing different interfacial crystal growth mechanisms [24], these models correspond

to the Power law [31], the Birth & Spread (B&S) and Burton-Cabrera-Frank (BCF) models

[32], and are given by the Equations (6), (7) and (8) respectively. A value of 𝑟 = 1 in

expression (6) corresponds to the case of Rough Interface Growth (RIG) [33].

𝐺 (𝑚

𝑠) =

11

𝑘𝑀𝑇′ +

1

𝑘𝐺(𝜎)𝑟−1

𝜎 (6)

𝐺 (𝑚

𝑠) =

11

𝑘𝑀𝑇′ +

1

𝑘𝐺 (𝜎)−1/6exp (𝐴1𝜎

)

(𝜎) (7)

𝐺 (𝑚

𝑠) =

11

𝑘𝑀𝑇′ +

1

𝑘𝐺(𝜎)𝑡𝑎𝑛ℎ(𝐴2𝜎

)

(𝜎) (8)

Where 𝑘𝐺 is the growth rate constant, 𝑟 is the growth exponent in the RIG interface growth

kinetic model, and 𝐴1 and 𝐴2 are thermodynamic parameters in the B&S and BCF interface

growth kinetic models, respectively. 𝑘𝑀𝑇′ is related to the coefficient of mass transfer within

the bulk of the solution, 𝑘𝑀𝑇 through expression (9).

𝑘𝑀𝑇′ (

𝑚

𝑠) =

𝑘𝑀𝑇𝐶𝑒 𝑀𝑊𝑠

𝜌𝑠 (9)

In this expression 𝜌𝑠 is the solute density, 𝑀𝑊𝑠 the solute molecular weight and 𝐶𝑒 the

solubility.

2.2.7 Indexation of the crystal morphology

In order to confirm the Miller indices corresponding to the copper sulfate pentahydrate

faces, an assessment was carried out making use of a methodology presented by Camacho

et al. [23], which uses modelling routines available in Mercury 3.1.

(http://www.ccdc.cam.ac.uk/Solutions/CSDSystem/Pages/Mercury.aspx) and HABIT [34].

http://www.ccdc.cam.ac.uk/Solutions/CSDSystem/Pages/Mercury.aspx

139

This methodology relies on the prediction of the Bravais-Friedel-Donnay-Harker (BFDH)

morphology using the known triclinic unit cell parameters for copper sulfate pentahydrate

as given by the cif file reported by Beevers [35]. See for example the work of Cunningham

et al. [36].

The BFDH approach relates the external shape of a crystal to the internal crystallographic

lattice dimensions and symmetry and states that: “After allowing for the reduction of the

growth slide thickness from space group symmetry considerations, the most

morphologically important forms (hkl), and hence those with the lowest growth rates, are

those having the greatest inter-planar distance dhkl” [37].

Using the BFDH approach, dhkl spacings can be taken as being inversely proportional to the

perpendicular distance from the centre of the crystals to the corresponding face, which in

turn can be considered as a measure of the relative growth rate for the simulation of the

crystal morphology [23].

3 RESULTS AND DISCUSSION

3.1 Solubilities of copper sulfate in aqueous solutions and in 2.4 wt % sodium

chloride media.

Table 2 shows the solubility data of copper sulfate in freshwater at different temperatures

reported by Linke and Seidell [25], and the experimental solubility and density data of

copper sulfate in sodium chloride media at five different temperatures (from 293.15 to

333.15 K) determined in the present work.

140

Table 2. Experimental solubility and density data of copper sulfate in sodium chloride

media at different temperatures.

T (K) ρ (g/cm3) SD (%)

CuSO4

(mol/Kg H2O) SD (%)

* CuSO4

(mol/kg H2O) [25]

293.15 1.21183 0.00004 1.2826 0.0042 1.2833

303.15 1.23393 0.00001 1.5139 0.0072 1.5196

313.15 1.26730 0.00001 1.7728 0.0081 1.7909

323.15 1.30610 0.00004 2.0988 0.0104 2.1074

333.15 1.34663 0.00005 2.4690 0.0107 2.4729

*Refers to the solubility values of copper sulfate in freshwater from literature.

The data clearly show that for both systems there is and increment in the solubility values

as the temperature increases. Also, the solubility values of copper sulfate in sodium

chloride media are slightly lower than the values in pure aqueous solutions. This behaviour

is attributed to the presence of sodium chloride in the solution, which contributes to

decrease the solubility of copper sulfate. These results agree with those of Hernández et al.

[11] and Justel et al. [12] who have reported that solubility values of copper sulfate in

seawater are slightly lower than those in freshwater, due to the presence of salts in the

seawater.

Additionally, Figures 4 and 5 show the activity coefficients (γ) for CuSO4 solutions in H2O

and NaCl media, respectively, in the temperature range from 293.15 to 333.15 K at copper

sulfate concentrations up to the saturation (values from Table 2). These values were

determined using the Pitzer binary parameters in aqueous and NaCl media, respectively,

obtained from the works of Justel et al. [13, 30].

141

Figure 4. Activity coefficients of CuSO4 in H2O solutions at different salt concentrations:

■, 293.15 K; ▲, 303.15 K; ●, 313.15 K; ×, 323.15 K; , 333.15 K.

Figure 5. Activity coefficients of CuSO4 in 2.4 wt % NaCl solutions at different salt

concentrations: ■, 293.15 K; ▲, 303.15 K; ●, 313.15 K; ×, 323.15 K; , 333.15 K.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5 2 2.5 3

Act

ivit

y c

oef

fici

ent

(γ)

CuSO4 (mol/Kg H2O)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.5 1 1.5 2 2.5 3

Act

ivit

y c

oef

fici

ent

(γ)

CuSO4 (mol/Kg H2O)

142

All the curves (from 293.15 to 333.15 K) for both systems, show a similar profile of

variation of the activity coefficient (γ) with both the concentration and temperature, where

it was found that γ decreased with increasing concentration, and decreased with increasing

temperature.

Bockris and Reddy [38], and Morales [39] have both pointed out that ion-ion interactions in

ionic solutions, give rise to a decrease in the activity coefficients with increasing ionic

concentration. On the other hand, an increase in the activity coefficients, shows a

prevalence of ion-solvent interactions, since at high concentrations the short-range

interactions increase in the system. This means that as the concentration of the electrolyte

increases, the amount of the effective solvent decreases, and the amount of water molecules

capable of dissolving the added ions decreases [39].

According to this, from Figures 4 and 5 it is noted that in both systems the tendency of

CuSO4 at low molalities shows a predominance of ion-solvent interactions over ion-ion

interactions, however, as the concentration increases, an increase of the ion-ion interactions

was observed.

In addition to this, for all temperatures (from 293.15 to 333.15 K), the activity coefficients

in pure aqueous media were found to be higher than those for NaCl media. This indicates

that the ion-solvent interactions within the aqueous solutions are stronger than those within

the NaCl media (Figure 6). These results agree with those from Table 2, where it was

shown that the solubility of copper sulfate in aqueous media was higher than in NaCl

media, which is due to the stronger interactions with the solvent.

143

Figure 6. Activity coefficients comparison between CuSO4 solutions in (■) H2O and (♦)

2.4 wt % NaCl as a function of the concentration at five different temperatures (293.15,

303.15, 313.15, 323.15, and 333.15 K).

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5

γ

CuSO4 (mol/kg H2O)

293.15 K NaCl

293.15 K H2O

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5 2

γ

CuSO4 (mol/kg H2O)

303.15 K NaCl

303.15 K H2O

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5 2

γ

CuSO4 (mol/kg H2O)

313.15 K NaCl

313.15 K H2O

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5 2 2.5

γ

CuSO4 (mol/kg H2O)

323.15 K Nacl

323.15 K H2O

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5 2 2.5 3

γ

CuSO4 (mol/kg H2O)

333.15 K NaCl

333.15 K H2O

144

3.2 Crystallization and dissolution temperatures of the CuSO4 + H2O and

CuSO4 + NaCl + H2O systems at different cooling rates.

Table 3 and Figure 7, show the results of Tcryst and Tdiss as a function of cooling rate for

29.52 wt % copper sulfate solutions in two different media: H2O and 2.4 wt % NaCl.

Table 3. Crystallization and dissolution temperatures of the CuSO4 + H2O and CuSO4 +

NaCl + H2O systems at different cooling rates.

System Cooling rate

(°C/min) Tcryst (°C) SD Tdiss (°C) SD

MSZW

(°C)

CuSO4 + H2O

2.0 20.90 0.14 70.93 0.29 50.03

1.0 26.87 0.29 68.13 0.19 41.27

0.5 30.60 0.28 66.07 0.25 35.47

0.3 34.47 0.29 66.03 0.31 31.57

0.0* 35.28 - 64.85 - 29.57

CuSO4 + NaCl

+ H2O

2.0 33.37 0.37 71.83 0.40 38.47

1.0 37.03 0.19 69.43 0.09 32.40

0.5 39.47 0.17 68.17 0.24 28.70

0.3 41.80 0.08 66.60 0.14 24.80

0.0* 42.33 - 66.30 - 23.97

*represents extrapolated data at 0 °C/min

145

Figure 7. Plot of the crystallization (-) and dissolution (---) temperatures for 29.52 wt %

CuSO4 solutions in different media: (●) H2O and (■) 2.4 wt % NaCl, as a function of

solution cooling rate.

The MSZW is a characteristic property of the crystallizations systems which describes the

amount of necessary undercooling to achieve the initiation of nucleation. In this study, the

equilibrium metastable value was determined by plotting the cooling rate versus the

temperature, and extrapolating back the dissolution and crystallization temperature trend

line to 0 °C/min cooling rate.

Table 3 and Figure 7 show that as is usually known [40-42], in both systems the metastable

zone width is wider as the cooling rate increases, while for CuSO4 solutions with 2.4 wt %

NaCl, the metastable zone width is narrower than in H2O media, which is attributed to the

influence of the higher salt concentration of the solutions, in terms of promoting the on-set

of nucleation. These results suggest that the limit of the metastability is influenced by both

the copper sulfate solubility and the NaCl content.

0

10

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5

Tem

per

ature

(°C

)

Cooling rate (°C/min)

146

Similar results were observed by Hernández et al. [11] and Justel et al. [12], where the

solubility of copper sulfate pentahydrate in acidic seawater is slightly lower than its

solubility in freshwater, due to the presence of different salts in the seawater, mainly

sodium chloride.

3.3 On-line Visualization and Particle size analysis of copper sulfate crystals at

different cooling rates.

Figures 8 and 9, show the sequence of images obtained by the Particle viewer at four

different cooling rates (from 2 to 0.3 °C/min) in two different media H2O and 2.4 wt %

NaCl.

147

System: CuSO4 + H2O

Cooling rate: 2 °C/min


Cooling rate: 0.5 °C/min


Figure 8. Sequence of pictures of copper sulfate crystals in H2O at different cooling rates.

148

System: CuSO4 + NaCl + H2O





Figure 9. Sequence of pictures of copper sulfate crystals in 2.4 wt % NaCl media at

different cooling rates.

149

The data reveal that cooling rate and sodium chloride content had a significant effect in the

crystal shape, where at high cooling rates (2 and 1 °C/min) in absence of sodium chloride,

copper sulfate crystals were observed to have a needle-like shape. However, at the slower

cooling rates (0.5 and 0.3 °C/min), the crystals were observed to become prismatic. On the

other hand, when 2.4 wt % NaCl is present in the solution, crystals were found to be

prismatic at the higher cooling rates, maintaining their shape as the cooling rate decreased.

The size range of copper sulfate crystals obtained in H2O and 2.4 wt % NaCl media by the

Process Avantium Crystalline software is shown in Table 4. The measurements were

carried out at four different cooling rates and the results were obtained in three different

size ranges: <100 µm, <200 µm, and <300 µm:

Table 4. Percentage copper sulfate crystals in three different size ranges at different cooling

rates.

System Size range 2 °C/min

(%)

1 °C/min

(%)

0.5 °C/min

(%)

0.3 °C/min

(%)

CuSO4 + H2O

<100 µm 97.79 96.40 95.96 95.07

<200 µm 2.06 3.34 3.40 4.22

<300 µm 0.21 0.26 0.64 0.71

CuSO4 + NaCl

+ H2O

<100 µm 96.03 94.56 95.08 93.15

<200 µm 3.53 4.67 4.14 6.09

<300 µm 0.44 0.77 0.78 0.76

Table 4 shows that there is no an obvious effect in the particle size when sodium chloride is

present in the solution. However, in both systems, most of the particles are in the size range

of <100 µm, and as the cooling rate decreases (from 2 to 0.3 °C/min), the presence of

crystals in the ranges of < 200 and < 300 µm increases. Likewise, when copper sulfate is

crystallized in sodium chloride media, the percentage of particles in the higher ranges is

slightly higher, i.e., in absence of sodium chloride, the particles in the size range of <100

µm are on average 1.63% smaller than the particles in the sodium chloride media.

Similar results have been obtained by Sheikholeslami and Ong [15] where the crystal

structure and size of CaSO4 and CaCO3 crystals at different NaCl concentrations were

150

studied, and was noted that as the NaCl is increased, the size of calcium sulfate and calcium

carbonate increased. The results of the present study suggest that copper sulfate crystals

grown in NaCl media (Table 4) are bigger likely due to the effect of crystal growth kinetics

as discussed in section (3.6).

3.4 Solid-state characterization

TGA/DSC shown in Figure 10 was performed to validate if the crystals obtained from

sodium chloride solutions corresponded to copper sulfate pentahydrate, as well as to

compare the temperatures at which the most loss of water of crystallization occurs for

crystals obtained in different media.

Figure 10. a) TGA and b) DSC curves for copper sulfate pentahydrate crystals obtained at

1 °C/min in H2O and NaCl media.

Figure 10a shows that when copper sulfate pentahydrate is heated (from 25 to 300 °C), it

loses its water of crystallization in two steps at different temperatures, obtaining a total

dehydration of 36.07 and 35.79% for crystals obtained in H2O and NaCl media,

respectively, where the water loss is 28.61 and 28.68%, respectively, in the first step,

corresponding to the loss of four water molecules, and 7.46 and 7.11%, respectively, in the

second step, corresponding to the loss of one water molecule. These results allowed us to

validate the composition of crystals obtained in both media, confirming that they

correspond to copper sulfate pentahydrate.

5

6

7

8

9

10

11

12

0 50 100 150 200 250 300 350

Weig

ht

(mg

)

Temperature (°C)

TGA - CuSO4 + NaCl

TGA - CuSO4 + H2O

H2O_Step 1: 28.61 %

NaCl_Step 1: 28.68 %

H2O_Step 2: 7.46%

NaCl_Step 2: 7.11%

-50

-40

-30

-20

-10

0

10

0 50 100 150 200 250 300 350

Hea

t F

low

(m

W)

Temperature (°C)

DSC-CuSO4 + NaCl

DSC-CuSO4 + H2O

H2O_Melting point = 96.83°C

NaCl_Melting point = 95.89°C

a) b)

151

Differential Scanning calorimetry (DSC) analysis from Figure 10b shows that the

temperature at which the most loss of water of crystallization occurs is at 96.83 and 95.89

°C, for the crystals grown in H2O and NaCl media, respectively; these are within the

temperature range found in the literature [43, 44]. This similarity allows us to corroborate

that crystals of copper sulfate pentahydrate obtained in H2O at high cooling rates (c.f.

Figure 8) with a needle-like shape, do not correspond to a different polymorph or hydrated

state of copper sulfate.

In order to evaluate the purity of copper sulfate pentahydrate crystallized from NaCl

solutions, chemical analysis was performed to the crystals obtained at 1 °C/min in NaCl

media, and the results are presented in Table 5.

Table 5. Chemical Analysis of CuSO4·5H2O crystals obtained at 1 °C/min in NaCl media.

Sample % Cu2+

% SO42-

% Na+ % Cl

-

CuSO4·5H2O 25.41 39.50 0.0819 0.1228

It was demonstrated that 2.4 wt % of sodium chloride is not influencing the crystal structure

of copper sulfate pentahydrate, where a purity of 99.8 wt % of CuSO4·5H2O, and a NaCl

percentage of 0.2 wt % were obtained. Allowing us to conclude that the change in the shape

of crystals at high cooling rates (Figures 8 and 9) , and the size increment when sodium

chloride is present in the solution (Table 4), is not due to the incorporation of NaCl in the

crystal structure.

3.5 Indexation of the crystal morphology of copper sulfate pentahydrate

Results from crystallization experiments, thermal assays (TGA/DSC), and chemical

analyses showed that coper sulfate crystals obtained in both H2O and NaCl media were

found to have the same morphology and structure. The only difference between these

crystals grown in different media is the aspect ratio, which was found to be higher for the

crystals grown in pure aqueous solutions.

152

Due to this, the validation of the crystals faces indexation for copper sulfate pentahydrate

grown in both media was carried out, based on the analysis from Beevers [35], as shown in

Figure 11. This information was complemented with enlarged pictures of crystals obtained

from the crystallization data from both aqueous and NaCl media from the in process image

data.

a) b) c)

Figure 11. a) Prediction of the BFDH morphology of copper sulfate pentahydrate crystals

using the Miller indices in the obtained unique solutions and comparison with the crystal

micrograph obtained experimentally. b) and c) Enlarged pictures of copper sulfate

pentahydrate crystals obtained in aqueous solutions and sodium chloride media,

respectively, from Avantium Crystalline® system.

Using the methodology described in section (2.2.7), the morphological analysis revealed

that the dominant faces of the copper sulfate crystal studied in this work are (1-10) and (1-

1-1), this indexation will be used along the paper to identify the faces in the growth kinetic

analysis. The analysis was performed making use of the Visual Habit Tool Kit currently

under development [45].

3.6 Mean Growth rates and growth rates mechanism of the (1-10) and (1-1-1) faces

of copper sulfate pentahydrate crystals as a function of the growth

environment

The growth kinetics of the (1-10) and (1-1-1) faces of single copper sulfate pentahydrate

crystals was investigated under limited conditions, as a function of media (H2O and 2.4 wt

153

% NaCl), and relative supersaturations, from 0.682 to 0.787 for CuSO4 + H2O and from

0.348 to 0.458 for CuSO4 + NaCl + H2O systems.

A sequence of images of copper sulfate pentahydrate crystals grown in a 0.5 mL cuvette

crystallization cell in H2O and 2.4 wt % NaCl is shown in Figure 12. The mean growth

rates of the (1-10) and (1-1-1) faces of single crystals growing from H2O and NaCl media

are presented in Table 6. The complete set of images of the crystal growth experiments is

given in the section (1) of the Appendices.

System σ Time = 0 sec. Time = 25 sec. Time = 60 sec.

a) CuSO4 +

H2O

0.682

0.787

b) CuSO4

+ NaCl +

H2O

0.348

0.458

Figure 12. Series of optical micrographs of copper sulfate crystals grown in: a) H2O at σ =

0.682 and σ = 0.787, and b) 2.4 wt % NaCl at σ = 0.348 and σ = 0.458 at the 0.5 ml scale

size showing the growth of the crystals and their morphology as a function of media,

elapsed time, and supersaturation. Black line in the picture represents the scale bar of 100

µm.

154

Table 6. Experimental mean growth rates of (1-10) and (1-1-1) faces of copper sulfate

pentahydrate crystals growing from H2O and 2.4 wt % NaCl media.

Solvent 𝜎 N° crystals Mean growth rate 𝐺 (𝜇𝑚/𝑠𝑒𝑐)

(1-10) (1-1-1)

H2O

0.682 2 0.5389 0.5202

0.708 2 0.5596 0.6124

0.733 2 0.5855 0.6607

0.759 2 0.5805 0.7409

0.787 2 0.6028 0.8040

NaCl +H2O

0.348 2 0.3115 0.7246

0.383 2 0.4389 0.8555

0.402 2 0.5026 0.9012

0.420 2 0.5443 1.0702

0.458 2 0.6621 1.3029

To evaluate the crystal growth mechanisms, the models described by Equations (6) to (8)

were fitted to the data collected for the (1-10) and (1-1-1) faces (Table 6). Given that the

experimental 𝐺(𝜎) observations showed that there is a critical supersaturation (𝜎𝑐𝑟𝑖𝑡)

below which growth does not occur (Figures 13 and 14), this parameter was introduced

within the models by subtracting it from the term 𝜎. In the present work, the quality of

regression was measured by the coefficient of determination 𝑅2, where the fitting is

considered reliable if the value of adjusted 𝑅2 is found to be close to 100%.

Figures 13 and 14 show the best fits of these growth models for both the (1-10) and (1-1-1)

faces for copper sulfate pentahydrate in H2O and NaCl media, respectively. Additionally,

they also presented the trend of the total resistance to transfer of growth units (1

𝐾𝑀𝑇𝑂𝑇) as a

function of driving force (∆𝐶 = 𝐶 − 𝐶𝑒), using the bulk and interface transfer coefficients

obtained from the experimental data fitting. 1

𝐾𝑀𝑇𝑂𝑇 is defined by the denominator of the

𝐺(𝜎) expressions given by the corresponding mechanistic model assessed.

Table 7 shows the obtained parameters for the best fits of the growth models, and the

corresponding 𝑅2 values for both (1-10) and (1-1-1) faces. Here, when more than one

model fitted well to the experimental data the corresponding modelled parameters were also

155

given. Also, an estimation of both the resistance to transfer within the bulk and that at the

interface are given in Table 7 using average values of 𝜎 and 𝐶𝑒within the range of study.

More detailed analysis about the fit of the Power Law, B&S and BCF models to the

experimental 𝐺(𝜎) data is given in the section (2) of the Appendices.

a)

b)

Figure 13. Copper sulfate crystals growing from H2O media. For each set of four plots, a)

𝑮(𝝈) experimental data fitted to the Power law and BCF models; b) trend of the total

resistance to mass transfer as a function of ∆𝑪 using the parameters obtained from the data

fitting to these models. The dotted red line shows the trend of the ratio of the resistance to

mass transfer in the bulk to the total mass transfer resistance. Left (♦) refers to the (1-10)

and right (■) to the (1-1-1) faces respectively.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

G (

µm

/s)

σ

Power Law

0

0.2

0.4

0.6

0.8

1

1.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

G (

µm

/s)

σ

BCF

51.3% 50.8%

50.3% 49.8%

49.3%

40%

43%

45%

48%

50%

53%

55%

58%

60%

1.2E+12

1.2E+12

1.2E+12

1.3E+12

1.3E+12

1.3E+12

1.3E+12

1.3E+12

1.4E+12

725 745 765 785 805 825 845

1/K

MT

OT

(s/

m)

𝞓C=C-C* (mol/m3)

Power Law 1/KMTOT

Power law % res transfer

bulk

98.3% 98.5% 98.7% 98.8% 98.9%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

3.8E+11

3.8E+11

3.8E+11

3.8E+11

3.8E+11

3.9E+11

3.9E+11

3.9E+11

725 745 765 785 805 825 845

1/K

MT

OT

(s/

m)

𝞓C=C-C* (mol/m3)

BCF 1/KMTOT

BCF % res transfer

bulk

𝜎𝑐𝑟𝑖𝑡

156

a)

b)

Figure 14. Copper sulfate crystals growing from 2.4 wt % NaCl media. For each set of four

plots, a) 𝑮(𝝈) experimental data fitted to the BCF model; b) trend of the total resistance to

mass transfer as a function of ∆𝑪 using the parameters obtained from the data fitting to

these models. The dotted red line shows the trend of the ratio of the resistance to mass

transfer in the bulk to the total mass transfer resistance. Left (♦) refers to the (1-10) and

right (■) to the (1-1-1) faces, respectively.

Figures 13 and 14 show that the mean growth rates (G) of the (1-10) and (1-1-1) faces of

copper sulfate pentahydrate crystals increase significantly with increasing relative

supersaturation, in addition to this, in the supersaturation range studied, regardless the

media in where the crystal were grown, the growth rate of the (1-1-1) face is always higher

than the (1-10) (Table 6), resulting in elongated crystals on the direction of the (1-1-1) face.

For crystals grown in pure aqueous solutions, in the supersaturation range between 0.682 to

0.787, the results suggest that for the (1-10) face of copper sulfate crystals, the best fitting

to the experimental data was obtained by the Power law model obtaining a 𝑅2 value of

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8

G (

µm

/s)

σ

BCF

0

0.5

1

1.5

2

2.5

3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

G (

µm

/s)

σ

BCF

57.7% 58.1% 58.2% 58.3% 58.4%

30%

35%

40%

45%

50%

55%

60%

65%

70%

75%

80%

3.1E+11

3.1E+11

3.1E+11

3.2E+11

3.2E+11

3.2E+11

3.2E+11

3.2E+11

3.3E+11

3.3E+11

450 500 550 600 650

1/K

MT

OT

(s/

m)

𝞓C=C-C* (mol/m3)

BCF 1/KMTOT

BCF % res transfer

bulk

98.5% 98.8% 98.9% 99.0% 99.2%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1.9E+11

1.9E+11

1.9E+11

1.9E+11

1.9E+11

1.9E+11

1.9E+11

450 500 550 600 650

1/K

MT

OT

(s/

m)

𝞓C=C-C* (mol/m3)

BCF 1/KMTOT

BCF % res transfer

bulk



157

90%, with a 𝜎𝑐𝑟𝑖𝑡 value of 0.003. This means that the growth practically occurs at any

supersaturation level. For the (1-1-1) face, the best fitting to the experimental data was

obtained for the model given by the BCF mechanism, which is confirmed by the 𝑟 value of

1.09 in the case of the Power law model for high supersaturations.

For crystals grown in NaCl media, in the supersaturation range from 0.348 to 0.458, the

best fitting to the experimental data was obtained for the BCF mechanism model for both

(1-10) and (1-1-1) faces, which is confirmed by the 𝑟 value of 0.99 and 1.03, respectively,

in the case of the Power law model for high supersaturations.

158

Table 7. Crystal growth kinetics parameters obtained from the best fit of the models given

by the Equations (6) and (8) to the experimental 𝑮(𝝈) data.

CuSO4 + H2O CuSO4 + NaCl + H2O

Range 𝜎 studied 0.682 to 0.787 0.348 to 0.458

Fitting

model

Range of

∆𝐶 = (𝐶 − 𝐶𝑒) studied 760.8 to 819.1 500.1 to 600.9

Power

law

Equation

(6)

Faces (1-10) (1-1-1) (1-10) (1-1-1)

1

𝑘′𝑀𝑇 6.40E+11 3.31E+11 4.74E+10 4.75E+10

𝑘𝑀𝑇 (𝑚

𝑠) 1.75E-11 3.38E-11 1.83E-10 1.82E-10

𝑘𝐺 (𝑚

𝑠) 1.33E+00 2.29E+01 3.66E-12 7.48E-12

1

𝑘𝐺(𝜎 − 𝜎𝑐𝑟𝑖𝑡)𝑟−1 6.34E-01 4.92E-02 2.72E+11 1.41E+11

𝜎𝑐𝑟𝑖𝑡 0.003 0.480 0.245 0.219

𝑟 0.45 1.09 0.9983 1.0331

𝑅2 90% 99% 99% 96%

BCF

Equation

(8)

1

𝑘′𝑀𝑇 3.75E+11 1.86E+11 1.87E+11

𝑘𝑀𝑇 (𝑚

𝑠) 2.98E-11 4.65E-11 4.63E-11

𝑘𝐺 (𝑚

𝑠) 7.68E+02 2.27E-10 2.70E-09

1

𝑘𝐺(𝜎 − 𝜎𝑐𝑟𝑖𝑡)𝑡𝑎𝑛ℎ (𝐴2

(𝜎 − 𝜎𝑐𝑟𝑖𝑡))

5.13E-03 1.32E+11 7.19E+08

𝜎𝑐𝑟𝑖𝑡 0.480 0.245 0.219

𝐴2 9.507 0.034 47.660

𝑅2 99% 99.5% 96%

Rate

limiting

step

Diffusion of growth units

within the bulk of the

solution

Diffusion of growth

units within the bulk of

the solution

Whilst the amount of experimental data collected is probably not enough to accurately

determine the values of 𝑘𝑀𝑇 and 𝑘𝐺 the fitting of the models presented to these data, can

deliver relevant mechanistic information.

159

From Table 7, which shows the comparison between the resistance to mass transfer within

the bulk of the solution (1

𝑘𝑀𝑇′ ) and the resistance to incorporation of growth units at the

crystal/solution interface (1

𝑘𝐺(𝜎−𝜎𝑐𝑟𝑖𝑡)𝑟−1). It was found that for both the (1-10) and (1-1-1)

faces in pure aqueous solutions media, the resistance to mass transfer is twelve and fourteen

orders of magnitude higher, respectively, than the resistance to incorporation of growth

units at the interface, which supports the diffusion of growth units within the bulk of the

solution as the rate limiting step. Likewise, a comparison of the 𝑘𝐺 (𝑚

𝑠) values showed that

𝑘𝐺 (𝑚

𝑠) is two orders of magnitude higher in the (1-1-1) face, which suggests that the

molecular integration in this face is higher, resulting in a more elongated habit of the

crystals at the studied supersaturations.

According to the Figure 13b, the trend of the total resistance to transfer of growth units

(1

𝐾𝑀𝑇𝑂𝑇) as a function of driving force (∆𝐶 = 𝐶 − 𝐶𝑒), where it is shown that in H2O

media, the resistance to mass transfer is 49.3% to 51.3% of the total resistance for the (1-

10) face, and 98.3 to 98.9% for the (1-1-1) face. In this figure, it is also shown that in the

(1-10) face, as the driving force increases, the total resistance increases, but an opposite

behaviour is observed for the (1-1-1) face where a decrease in the total resistance is

observed.

From Table 7, it is observed that for crystals grown in NaCl media, the resistance to mass

transfer is of the same order of magnitude to the resistance to transfer at the interface for

the (1-10) face. In the case of the (1-1-1) face, the resistance to mass transfer is three orders

of magnitude higher than the resistance to incorporation at the interface. Likewise, if the

𝑘𝐺 (𝑚

𝑠) values are analyzed, it is observed that these values are lower for crystals grown in

NaCl, additionally, it is noted that 𝑘𝐺 (𝑚

𝑠) is one order of magnitude higher in the (1-1-1)

face, which suggests that the molecules integration in this face is higher, resulting in a

slightly more elongated habit of the crystals at the studied supersaturations.

160

Regarding to the trend of the total resistance to transfer of growth units (1

𝐾𝑀𝑇𝑂𝑇) as a

function of driving force (∆𝐶 = 𝐶 − 𝐶𝑒) shown in Figure 14b, it is observed that in NaCl

media, the resistance to mass transfer is 57.7% to 58.4% of the total resistance for the (1-10)

face, and 98.5 to 99.2% for the (1-1-1) face. Additionally, it is shown that as the driving

force increases, the total resistance decreases for both faces.

The results obtained from the growth kinetic analysis are in agreement with those results

shown in Figure 12, where it is observed that at high and low supersaturations, crystals

grown in H2O media are slightly more elongated than those in NaCl, which could be

mainly attributed to the different mechanisms that regulate the growth of each face in the

case of H2O media. Likewise, these results are related with those presented in Figures 8 and

9, where more elongated crystals are observed at cooling rates of 2 and 1 °C/min in H2O

media.

With the aim of comparing the influence of the sodium chloride on the growth rates of (1-

10) and (1-1-1) faces, an extrapolation of the growth rate data was performed using

Equations (6) and (8), and the results are shown in Figure 15.

a) b)

Figure 15. Sodium chloride effect in the a) (1-10) and b) (1-1-1) crystal faces of copper

sulfate pentahydrate. Extrapolated data are given by the black and dotted lines representing

the best fit of the data through the Power law and BCF models, respectively.

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

G (

µm

/s)

σ

(1-10) NaCl

(1-10) H2O

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

G (

µm

/s)

σ

(1-1-1) NaCl

(1-1-1) H2O

161

Based on the comparison, it has been possible to conclude that for both the (1-10) and (1-1-

1) faces, the growth rates in NaCl are higher than in H2O media, the only exception is for

the (1-10) growth rates in NaCl at supersaturations below 0.348, which are lower than those

in H2O. These results are related with those of Brandse et al. [14] where the growth kinetics

of gypsum in H2O and NaCl media was studied, and was evidenced that the addition of

sodium chloride accelerates the growth rate of gypsum remarkably.

Summarizing, the increment in size of copper sulfate crystals when sodium chloride is

present in the solution (Table 4), is mainly attributed to the higher growth rate of the crystal

faces when crystals are grown in NaCl. Figure 15 also shows that the sodium chloride

effect is more relevant for the (1-10) face, where a change in its growth mechanism is

observed.

4. CONCLUSIONS

The present work studied the cooling rate and sodium chloride effect in the crystal

morphology, size, composition, and growth rates of copper sulfate pentahydrate crystals, in

order to evaluate the effect of using seawater as an alternative to pure water, for the

industrial process associated with copper sulfate pentahydrate crystallization. In general,

this research suggest that crystals grown in sodium chloride media are larger and more

prismatic compared to those grown in pure aqueous solutions. This behaviour can be

mainly attributed to changes on the growth kinetics reflecting the fact that the growth rates

of both the (1-10) and (1-1-1) faces are affected when sodium chloride is present in the

solution, especially in the case of the (1-10) face, where a change in the growth mechanism

is observed.

Higher cooling rates and/or the addition of sodium chloride were found to have a relevant

effect in the shape of copper sulfate pentahydrate crystals, where the habit was found to

change from an acicular shape, when crystals are in pure aqueous media, to prismatic

crystals in the presence of NaCl. The percentage of particles in higher size ranges was

slightly increased in the presence of NaCl.

162

For crystals grown from pure aqueous solutions, the kinetic data were found to be

consistent with the Power law and BCF interfacial growth mechanism for (1-10) and (1-1-

1) faces, respectively. On the other hand, for the crystals grown in NaCl media, the kinetic

data were found to be consistent with the BCF interfacial growth mechanism for both the

(1-10) and (1-1-1) faces.

In order to obtain a better understanding of the crystallization of copper sulfate

pentahydrate as a function of the solvation environment, it would be interesting to use

molecular and synthonic modelling techniques to carry out a chemical interaction analysis

between the solution species and the specific habit faces of the crystals.

ACKNOLEDGEMENTS: Francisca Justel acknowledge Kevin Roberts from University

of Leeds for the support in this Research which forms part of her doctoral studies, and

CONICYT, Chile for providing the Ph.D. scholarship. The authors also gratefully

acknowledge the UK's EPSRC for the support of nucleation and crystal growth research at

Leeds and Manchester through funding the Critical Mass Project: Molecules, Clusters and

Crystals (Grant references EP/IO14446/1 and EP/IO13563/1).

163

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electrolyte solutions, 2 (1991).

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Cl-HSO4-H2O system for the solubility of copper sulfate in acid seawater at different

temperatures, Journal of Molecular Liquids, (not published work).

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[31] J. Garside, Industrial crystallization from solution, Chemical engineering science, 40

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157-227.

[34] G. Clydesdale, R. Docherty, K. Roberts, HABIT-a program for predicting the

morphology of molecular crystals, Computer Physics Communications, 64 (1991) 311-328.

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CuSO4·5H2O, Proceedings of the Royal Society of London. Series A, 146 (1934) 570-582.

[36] D. Cunningham, D. Armstrong, G. Clydesdale, K. Roberts, Investigation into the

structural chemistry of Cu2+

ions in doped nearly perfect single crystals of ammonium

sulfate with reference to their role in habit modification, Faraday Discussions, 95 (1993)

347-365.

[37] J.D.H. Donnay, D. Harker, A new law of crystal morphology extending the law of

Bravais, Am. Mineral, 22 (1937) 446-467.

[38] J.O.M. Bockris, A.K.N. Reddy, Modern Electrochemistry, in: N.Y. Reverté (Ed.),

1979.

[39] J.W. Morales Saavedra, Tesis de Doctorado: Estudio Termodinámico de sistemas

ternarios Sal + PEG 4000 + Agua a las temperaturas de (288.15, 298.15 y 308.15) K, in,

2011.

[40] J. Ulrich, C. Strege, Some aspects of the importance of metastable zone width and

nucleation in industrial crystallizers, Journal of crystal growth, 237 (2002) 2130-2135.

[41] N. Kubota, A new interpretation of metastable zone widths measured for unseeded

solutions, Journal of crystal growth, 310 (2008) 629-634.

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[42] D. Kashchiev, A. Borissova, R.B. Hammond, K.J. Roberts, Effect of cooling rate on

the critical undercooling for crystallization, Journal of crystal growth, 312 (2010) 698-704.

[43] H. Tanaka, Thermal stabilities and enthalpy changes in the thermal dehydration stages

of CuSO4·5H2O and CuSO4·5D2O, Thermochimica Acta, 43 (1981) 289-295.

[44] P. Nandi, D. Deshpande, V. Kher, Dehydration steps in CuSO4·5H2O crystals, Journal

of Chemical Sciences, 88 (1979) 113-124.

[45] J. Pickering, R.B. Hammond, V. Ramachandran, M. Soufian, K.J. Roberts, Synthonic

Engineering Modelling Tools for Product and Process Design, Chapter 10 In: Engineering

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Docherty R and R Tamura), 2017, in press, Springer Advanced Study Institute (ASI)

Series.

168

CHAPTER VII

GENERAL CONCLUSIONS AND RECOMMENDATIONS

1. GENERAL CONCLUSIONS FOR THIS STUDY

In the thesis entitled "Seawater effect in the thermodynamics and crystallization of copper

sulfate pentahydrate" has been studied the seawater effect in the thermodynamic behaviour

and crystallization of copper sulfate pentahydrate in order to analyze the feasibility of the

seawater use in this hydrometallurgical process.

For this, the seawater effect on the solid−liquid equilibrium and physical properties of acid

solutions of copper sulfate in a wide temperature range was studied. Moreover, the

thermodynamic representation of the solid–liquid equilibrium of the copper sulfate-sulfuric

acid-seawater system over a wide temperature range has been carried out by two different

modeling routines:

- First, the Pitzer model and a Born-type equation were used for modeling the copper

sulfate and sulfuric acid effects, respectively, using the seawater as a solvent.

- Secondly, by means of the thermodynamic study of the Cu-Na-H-SO4-Cl-HSO4-

H2O system using the Pitzer ion-interaction model.

Finally, and in order to evaluate the seawater effect in the copper sulfate pentahydrate

crystallization, sodium chloride effect in the crystal shape, particle size, composition, and

growth kinetics of copper sulfate pentahydrate crystals was studied.

Accordingly, and regarding to the seawater effect on the solid-liquid equilibrium and

physical properties of acid solutions of copper sulfate, the following conclusions are

obtained:

- The experimental values for density, viscosity, and solubility in the saturated

solutions, were correlated using the empirical equations proposed in the present

work, obtaining absolute average deviations of 0.0005, 0.0056, and, 0.0043,

respectively, at 293.15 K; 0.0004, 0.0029 and, 0.0038, respectively, at 298.15 K;

169

0.0007, 0.0048, and 0.0023, respectively, at 308.15 K; and 0.0007, 0.0055, and

0.0037, respectively, at 318.15 K.

- In the saturated solutions, with increasing temperature and acid concentration, the

solutions densities increased. Moreover, with increasing acid concentration and

temperature, there is a decrease in the solution viscosity.

- Sulfuric acid has a big effect on the reduction of the copper sulfate solubility;

however, the temperature has an inverse behavior. In addition to this, the presence

of salts in the seawater contributes to the solubility decreasing of copper sulfate

pentahydrate in seawater media.

- X-ray diffraction and thermogravimetric analyses demonstrated that the

composition of crystals obtained at different temperatures using sulfuric acid and

seawater, correspond to copper sulfate pentahydrate.

Regarding to the thermodynamic representation of the solid-liquid equilibrium of the

copper sulfate - sulfuric acid - seawater system, the following conclusions are obtained:

- From the experimental water activities of copper sulfate solutions in seawater and

freshwater was concluded that in both systems, water activities decrease as the

solution concentration increase. Additionally, values in seawater are lower than

those in freshwater; both behaviors are due to the increment in the number of water

molecules associated with the different ions in the solution. Also, the water

activities are highly affected by the solute concentration; but slightly influenced by

the temperature.

- Binary Pitzer parameters for solutions of copper sulfate in seawater were

determined and used for the determination of the solubility products of copper

sulfate pentahydrate at different temperatures, where a difference of 0.0010 between

the solubility product obtained in the present work and the one in freshwater from

the literature at 298.15 K was mainly attributed to the respective experimental

uncertainties. The similarity of these values allowed us to validate the model used in

the present work.

- Pitzer parameters for CuSO4, CuCl2, and Cu(HSO4)2 solutions in freshwater from

293.15 to 333.15 K were determined and used for the determination of their activity

170

coefficients as a function of the concentration at several temperatures, where it was

observed in all cases a decrease in the activity coefficients as the temperature

increases. Also, the concentration effect was different for each of the electrolytes.

- Values for the ternary parameters 𝜓𝐶𝑢,𝐻,𝐶𝑙, 𝜓𝐶𝑢,𝑁𝑎,𝐻𝑆𝑂4 and 𝜓𝐶𝑢,𝐶𝑙,𝐻𝑆𝑂4

were

reported, and considered as constant fitting parameters in the temperature range

from 293.15 to 333.15 K.

- Solubility product values for aqueous solutions of copper sulfate at different

temperatures were determined and the similarity of the 𝐾𝑠𝑝 values at 298.15 K

between the data reported here with the literature data allowed the validation of the

model used in the present work.

- All the information reported in this work (water activities, binary and ternary Pitzer

parameters, activity and osmotic coefficients) are a great contribution for the

thermodynamics of electrolytes, especially for those systems where the Cu2+

, Na+,

H+, SO4

2-, Cl

-, and HSO4

- ions are involved.

- A simple methodology, based on a variation of the Kan’s method, has been applied

to represent the solid–liquid equilibrium of the CuSO4-H2SO4-seawater system at

different temperatures considering the seawater as a solvent, obtaining a good

agreement between the experimental and correlated values. In addition, using this

method was possible to estimate the sulfuric acid concentration necessary to

maximize the copper sulfate precipitation.

- The ion interaction model of Pitzer was successfully used to determine the

solubilities of the CuSO4-H2SO4-seawater system at six different temperatures by

modelling the Cu-Na-H-SO4-Cl-HSO4-H2O system. Despite only sodium and

chloride ions were considered as seawater components, a good agreement between

the experimental and correlated values was obtained. By means of this finding, was

concluded that thermodynamic studies for systems containing seawater could be

performed only considering these main ions, because the others from seawater do

not have a notorious influence in the modelling.

Regarding to the sodium chloride effect in copper sulfate pentahydrate crystallization, the

following conclusions have been established:

171

- Solubility values of copper sulfate in a media with 2.4 wt % NaCl are slightly lower

than the values in H2O, with a mean deviation of 0.0037; additionally, in solutions

with NaCl, the metastable zone width is narrower than in H2O media, both

behaviors are attributed to the higher salt concentration of the solutions.

- Activity coefficients of copper sulfate solutions in H2O and NaCl media showed a

predominance of ion-solvent interactions over ion-ion interactions at low

concentrations. However, as the concentration increases, an increase of the ion-ion

interactions was observed. In addition, higher values of the activity coefficients in

H2O than in NaCl media, indicated that the ion-solvent interactions of the CuSO4 +

H2O solutions are stronger than those of CuSO4 + NaCl + H2O solutions.

- Cooling rate and sodium chloride presence have a significant effect on the crystal

shape, where at high cooling rates with no sodium chloride, copper sulfate crystals

have a needle-like shape. However, at slow cooling rates the crystals became

prismatic. On the other hand, when NaCl is present in the solution, crystals are

prismatic at high and slow cooling rates.

- DSC analysis corroborated that crystals obtained in H2O at high cooling rates with a

needle-like shape, did not correspond to a different polymorph of copper sulfate

pentahydrate.

- There is a slight increase in the particle size when sodium chloride is present in the

solution, where in absence of sodium chloride, the particles in the size range of

<100 µm are on average 1.63% smaller than the particles in the sodium chloride

media. Also, this sodium chloride concentration did not influence notoriously in the

structure of copper sulfate pentahydrate, where a purity of 99.8 wt % of

CuSO4·5H2O was obtained.

- The mean growth rates (𝐺) of the (1-10) and (1-1-1) faces of copper sulfate

pentahydrate crystals increase significantly with increasing relative supersaturation.

Additionally, in both media (H2O and NaCl), the growth rate of the (1-1-1) face is

higher than the (1-10), resulting in more elongated crystals on the direction of the

(1-1-1) face.

- For crystals grown in H2O, in the case of the (1-10) face of copper sulfate crystals,

the best fitting to the experimental data was obtained by the Power law model

172

meaning that the growth practically occurs at any supersaturation level. For the (1-

1-1) face, the best fitting was obtained for the model given by the BCF mechanism;

which suggests that growth proceeds via screw dislocations.

- For crystals grown in NaCl media, the best fittings to the experimental data were

obtained for the model given by the BCF mechanism for both (1-10) and (1-1-1)

faces; which suggest that growth in this case proceeds via screw dislocations.

- The growth rate in NaCl is higher than in H2O media for the (1-10) and (1-1-1)

faces, confirming that the increment in size of copper sulfate crystals when sodium

chloride is present in the solution was attributed to the higher growth rate of the

crystal faces in NaCl media, and not to the incorporation of NaCl in the crystal

structure.

173

2. RECOMMENDATIONS FOR FUTURE WORK

Regarding to the thermodynamic representation of the solid-liquid equilibrium of the

copper sulfate - sulfuric acid - seawater system, the following recommendations for the

future work are proposed:

- Perform crystallization tests with seawater by the addition of sulfuric acid, to

validate the analytical model proposed in the present work, which predicts the

precipitated amounts of copper sulfate as a function of the acid concentration.

- Determine the economic feasibility of the copper sulfate crystallization process

using seawater.

- Find a methodology that allows to measure the thermodynamic properties such as

water activities and osmotic coefficients, in highly corrosive solutions such as

copper chloride, and highly acidic solutions as those containing sulfuric acid.

- Regarding to the Pitzer ion-interaction model applied to the Cu-Na-H-SO4-Cl-

HSO4-H2O system, would be interesting to include additional ions from the

seawater system, in order to evaluate their effect in the modelling. However, it

should be borne in mind that the number of parameters would be greatly increased

due to a higher number of combinations between ions, which would probably lead

to the number of parameters exceed the amount of experimental data.

- Based on the thermodynamic modelling works previously reported in the literature,

it would be a great contribution to develop models for the determination of the

binary and ternary Pitzer parameters as a function of the temperature, especially for

solutions containing the Cu2+

, Na+, H

+, SO4

2-, Cl

-, and HSO4

- ions which are the

most found in the copper mining solutions.

Regarding to the sodium chloride effect in copper sulfate pentahydrate crystallization, the

following recommendations are proposed:

- It would interesting to study the sodium chloride effect on the growth rates of other

individual faces of copper sulfate pentahydrate, in addition to the already analyzed

(1-10) and (1-1-1) faces.

174

- It could be worth to expand the supersaturation range used in the growth kinetics

experiments in order to evaluate if there is any additional change in the shape or

growth mechanisms of the crystals.

- Due to the crystallization experiments were performed only at the CuSO4

concentration of 29.52 wt %, it would be interesting to expand this range to

determine the metastable zone width at various concentrations, which could be

complemented by increasing the cooling rates range. This latter would also allow to

observe if there are any further changes in the copper sulfate crystals shape.

- Due to the sodium chloride effect on the shape, size, composition, and growth

kinetics of copper sulfate pentahydrate crystals is already known; it would be an

interesting contribution to use artificial seawater on these experiments in order to

determine the effect of the other ions; additionally, could be interesting to evaluate

the sulfuric acid effect on the growth kinetics. These experiments could lead to

additional changes in the crystals shape and size, and in the growth rates and

mechanisms of the individual faces of copper sulfate pentahydrate.

175

APPENDICES SECTION

THE EFFECT OF SEAWATER ON THE THERMODYNAMICS AND

CRYSTALLIZATION OF COPPER SULFATE PENTAHYDRATE

Abstract

Additional and more detailed materials are provided as a supplement to the thesis with the

above title. It includes:

1. Sequence of images of copper sulfate pentahydrate crystals growing in H2O and 2.4

wt % NaCl media at different supersaturations.

2. Fits of the Power law, B&S and BCF growth models for both the (1-10) and (1-1-1)

faces for copper sulfate pentahydrate grown in H2O and NaCl media.

3. Works presented at several national and international conferences during the

doctoral period.

4. Published works from the present Doctoral thesis.

176

1. Sequence of images of copper sulfate pentahydrate crystals growing in H2O

and 2.4 wt % NaCl media at different supersaturations.

a) Copper sulfate pentahydrate crystals grown in H2O.

Figure 1. Series of optical micrographs of copper sulfate crystals grown in H2O in the

supersaturation range from σ = 0.682 to σ = 0.787 at the 0.5 ml scale size showing the


supersaturation. Black line in the picture represents the scale bar of 100 µm.

20 sec

20 sec

20 sec

20 sec

20 sec

40 sec 60 sec 80 sec

40 sec 60 sec 80 sec

80 sec

40 sec

60 sec

60 sec

60 sec 40 sec

80 sec

80 sec 40 sec

T= 23°C σ = 0.682

T= 22°C σ = 0.708

T= 20°C σ = 0.760

T= 21°C σ = 0.733

T= 19°C σ = 0.787

177

b) Copper sulfate pentahydrate crystals grown in 2.4 wt % NaCl media.

Figure 2. Series of optical micrographs of copper sulfate crystals grown in NaCl media in

the supersaturation range from σ = 0.348 to σ = 0.458 at the 0.5 ml scale size showing the


supersaturation. Black line in the picture represents the scale bar of 100 µm.

20 sec

20 sec

20 sec

20 sec

40 sec 60 sec 80 sec 20 sec

40 sec

40 sec

40 sec

40 sec

60 sec

60 sec

60 sec

60 sec

80 sec

80 sec

80 sec

80 sec

T= 39°C σ = 0.348

T= 37°C σ = 0.383

T= 36°C σ = 0.402

T= 35°C σ = 0.420

T= 33°C σ = 0.458

178

2. Fits of the Power law, B&S and BCF growth models for both the (1-10) and (1-

1-1) faces for copper sulfate pentahydrate grown in H2O and NaCl media.

Figures 3a and 3b show the best fits of the growth models for both the (1-10) and (1-1-1)

faces for copper sulfate pentahydrate in H2O and NaCl media, respectively. Additionally,

all relevant parameters obtained through this analysis are presented in Table 1. For

comparative assessment, all fitting lines were drawn and the corresponding modelled

parameters were also given.

a)

b)

Figure 3. 𝑮(𝝈) experimental data of copper sulfate pentahydrate grown in a) H2O and b)

NaCl media fitted to the Power law, B&S and BCF models. Left (♦) refers to the (1-10) and

right (■) to the (1-1-1) faces respectively.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1

G (

µm

/s)

σ

B&S

Power Law

BCF

0

0.2

0.4

0.6

0.8

1

1.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

G (

µm

/s)

σ

B&S

Power Law

BCF

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8

G (

µm

/s)

σ

exp

B&S

Power Law

BCF

0

0.5

1

1.5

2

2.5

3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

G (

µm

/s)

σ

exp

B&S

Power Law

BCF




179

Table 4. Crystal growth kinetics parameters obtained from the fit of the Power Law, B&S

and BCF models to the experimental 𝑮(𝝈) data.

CuSO4 + H2O CuSO4 + NaCl + H2O

Range σ studied 0.682 to 0.787 0.348 to 0.458

Fitting

model

Range of

∆𝐶 = (𝐶 − 𝐶𝑒) studied 760.8 to 819.1 500.1 to 600.9

Power

law

Equation

(6)

Faces (1-10) (1-1-1) (1-10) (1-1-1) 1

𝑘′𝑀𝑇 6.40E+11 3.31E+11 4.74E+10 4.75E+10

𝑘𝑀𝑇 (𝑚

𝑠) 1.75E-11 3.38E-11 1.83E-10 1.82E-10

𝑘𝐺 (𝑚

𝑠) 1.33E+00 2.29E+01 3.66E-12 7.48E-12

1

𝑘𝐺(𝜎 − 𝜎𝑐𝑟𝑖𝑡)𝑟−1 6.34E-01 4.92E-02 2.72E+11 1.41E+11

𝜎𝑐𝑟𝑖𝑡 0.003 0.480 0.245 0.219

𝑟 0.45 1.09 0.9983 1.0331

𝑅2 90% 99% 99% 96%

B&S

Equation

(7)

1

𝑘′𝑀𝑇 3.81E+11 3.80E+11 1.88E+11 1.89E+11

𝑘𝑀𝑇 (𝑚

𝑠) 2.93E-11 2.94E-11 4.60E-11 4.59E-11

𝑘𝐺 (𝑚

𝑠) 8.47E-01 1.39E+00 5.60E-12 6.24E-12

1

𝑘𝐺(𝜎 − 𝜎𝑐𝑟𝑖𝑡)−1/6exp (𝐴1

𝜎 − 𝜎𝑐𝑟𝑖𝑡) 8.91E-01 1.10E-04 1.58E+11 3.78E+06

𝜎𝑐𝑟𝑖𝑡 0.004 0.480 0.245 0.219

𝐴1 0.1671 2.1737 0.0002 5.4302

𝑅2 90% 99% 99% 96%

BCF

Equation

(8)

1

𝑘′𝑀𝑇 3.70E+11 3.75E+11 1.86E+11 1.87E+11

𝑘𝑀𝑇 (𝑚

𝑠) 3.03E-11 2.98E-11 4.65E-11 4.63E-11

𝑘𝐺 (𝑚

𝑠) 6.21E+01 7.68E+02 2.27E-10

2.70E-09

1

𝑘𝐺(𝜎 − 𝜎𝑐𝑟𝑖𝑡)𝑡𝑎𝑛ℎ (𝐴2

(𝜎 − 𝜎𝑐𝑟𝑖𝑡))

9.11E-01 5.13E-03 1.32E+11 7.19E+08

𝜎𝑐𝑟𝑖𝑡 0.000 0.480 0.245 0.219

𝐴2 0.020 9.507 0.034 47.660

𝑅2 77% 99% 99.5% 96%

Rate

limiting

step

Diffusion of growth


the solution

Diffusion of growth


the solution

180

3. Summary of the different works presented at the national and international

conferences

SOLUBILITIES AND PHYSICAL PROPERTIES OF SATURATED SOLUTIONS

IN THE COPPER SULFATE + SULFURIC ACID + SEAWATER SYSTEM AT


Francisca Justel, Martha Claros, María E. Taboada

Department of Chemical Engineering, University of Antofagasta, Angamos 601,

Antofagasta, Chile

In Chile, the most important economic activity is mining, which is concentrated in the north

side of the country. The region is a desert with limited freshwater resources; therefore, the

mining sector requires research and the identification of alternative sources of water. One

alternative is Seawater, which can be substitute for the limited freshwater resources in the

region. This work determines the influence of Seawater on the solid−liquid equilibrium for

acid solutions of CuSO4 at different temperatures (298.15 to 318.15 K), and its effect on

physical properties (density, viscosity, and Solubility). Knowledge of properties and

Solubility data are useful in the design of Copper sulfate pentahydrate crystallization plants

from leaching process using Seawater by means of the addition of sulfuric acid.

Keywords: Seawater, Copper sulfate, Solubility.

181

CRYSTALLIZATION OF COPPER SULFATE FROM AQUEOUS SOLUTION

CONTAINING SEAWATER AND SULFURIC ACID

Francisca Justel, Teófilo Graber and María E. Taboada*

Chemical Engineering Department, Universidad de Antofagasta, Antofagasta,

Chile, [email protected]

ABSTRACT

In Chile, the most important economic activity is mining which is concentrated in the

northern region of the country across the Atacama Desert that is known as the driest place

in the world with limited freshwater resources. Therefore, the mining industry requires

research and identification of alternative water sources. One alternative is the use of

seawater, which can be a substitute for the limited freshwater resources. Currently, certain

mining companies are using raw seawater in their processes (Mineras Michilla, Esperanza

in copper/gold projects; and Las Luces in their beneficiation plant).

In copper hydrometallurgy, seawater is mainly used and studied in the leaching process;

however, there is no mining company that performs copper sulfate crystallization process

using seawater. Consequently, the study of copper sulfate pentahydrate crystallization with

seawater is of great importance, since this compound is the most important at industrial

level, due to the wide range of commercial applications such as agriculture as a pesticide,

germicide, and soil additive; in medicine it is used as a fungicide, and bactericide; and in

mining as a floatation reagent in recovery of zinc and lead. However, for carrying out this

process on an industrial scale, it is necessary to know the seawater effect in the

crystallization kinetics and in the morphology and size of the copper sulfate crystals.

In the present work the effect of seawater on the solid-liquid equilibrium of copper sulfate

in acidic solutions at different temperatures (from 293.15 to 333.15 K) is presented. In

182

addition physical properties, conductivity, density, and viscosity of the saturated solution

are measured and correlated with empirical equations finding a good agreement.

Knowledge of properties and solubility data are useful in the leaching process and in the

process design to obtain copper sulfate pentahydrate crystals from leaching solutions with

seawater by means of sulfuric acid addition.

Keywords: Copper sulfate, Sulfuric acid, Seawater, Crystallization.

183

SOLUBILIDADES Y PROPIEDADES FÍSICAS DEL SISTEMA CuSO4 - H2SO4 -

AGUA DE MAR

Francisca J. Justel, María E. Taboada*

Departamento de Ingeniería Química y Procesos de Minerales, Universidad de

Antofagasta, Avenida Angamos 601,1270300, Antofagasta, Chile

Resumen

La minería, es la actividad económica más importante de Chile, y se encuentra concentrada

en la zona norte del país. Ésta es una región desértica con limitadas fuentes de agua, por lo

que el sector minero requiere de la investigación e identificación de fuentes alternativas de

agua. Una alternativa es el agua de mar, la cual puede ser un substituto de las limitadas

fuentes de agua fresca en la región. Este trabajo determina la influencia del agua de mar

acidificada en el equilibrio sólido-líquido de soluciones saturadas de sulfato de cobre a

diferentes temperaturas (293.15 a 318.15 K), y su efecto en las propiedades físicas

(densidad y viscosidad) y solubilidad. Este conocimiento, es útil en el diseño de plantas de

cristalización de sulfato de cobre pentahidratado desde el proceso de lixiviación con

soluciones de ácido sulfúrico, en el que se sustituya el agua fresca por agua de mar, con el

fin de dar sustentabilidad a la actividad minera.

Palabras clave: Sulfato de cobre pentahidratado, Agua de mar, Equilibrio sólido-líquido,

Cristalización.

184

Universidad de Concepción | 15, 16, 17 de octubre de 2014

http://www.cchiq2014.cl/

EQUILIBRIO SÓLIDO-LÍQUIDO DEL SISTEMA CuSO4 – H2SO4 – AGUA DE

MAR A DIFERENTES TEMPERATURAS

Francisca J. Justel, Yecid P. Jiménez, Martha Claros, María E. Taboada*

Departamento de Ingeniería Química y Procesos de Minerales. Universidad de

Antofagasta.

Resumen

La minería es la actividad económica más importante de Chile, en donde la mayor parte de

los yacimientos están emplazados en la zona norte del país, zona que enfrenta una limitada

disponibilidad del recurso hídrico, por lo que el agua se ha convertido en un insumo crítico

y de alto costo. Esta situación ha motivado al sector minero al uso de nuevas fuentes de

agua, como lo es el agua de mar. Además, existen algunas empresas que para dar un valor

agregado a sus productos, cristalizan sulfato de cobre pentahidratado. El estudio de la

cristalización de sulfato de cobre con agua de mar sería de gran importancia, debido a que

este compuesto es muy importante a nivel industrial por la gran cantidad de aplicaciones

que posee: ya sea en agricultura, medicina, minería, industria textil, etc.

El objetivo del presente trabajo es representar el efecto del agua de mar en el equilibrio

sólido-líquido del sulfato de cobre pentahidratado en soluciones ácidas a diferentes

temperaturas (desde 293.15 a 333.15 K), y subsecuentemente utilizar esta información para

predecir la concentración de H2SO4 que proporcione un máximo rendimiento del proceso,

además se incluye el cálculo de las cantidades precipitadas de la sal desde el sistema

CuSO4-H2SO4-Agua de mar a seis diferentes temperaturas. Los datos de solubilidad del

sistema estudiado, fueron obtenidos experimentalmente mediante análisis del ion cobre por

absorción atómica. El modelo de Pitzer y una modificación del modelo de Born fueron

utilizados para correlacionar los datos de solubilidad, posteriormente esta información fue

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utilizada para predecir los valores antes mencionados. Este conocimiento sobre los datos de

solubilidad y la correlación de los mismos son útiles en el diseño de procesos para obtener

cristales de sulfato de cobre pentahidratado desde soluciones de lixiviación con agua de

mar por medio de la adición de ácido sulfúrico.

Palabras clave: Agua de mar, Sulfato de cobre pentahidratado, Solubilidad.

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SOLID - LIQUID EQUILIBRIUM OF CuSO4 – H2SO4 – SEAWATER SYSTEM

Francisca J. Justel , Yecid P. Jiménez and María Elisa Taboada*

Department of Chemical and Mineral Process Engineering, University of Antofagasta,

Chile

Introduction

Mining, is the most important economic activity in Chile, where there is a worldwide

shortage of available freshwater. Mining industries are developing new methods to

optimize water use, where certain mining companies are using raw seawater in their

production processes. The study of the copper sulfate crystallization using seawater would

be of great importance due to the large number of industrial applications of this salt. In this

research, we are focused in the CuSO4 - H2SO4 - seawater system, with the objective of

representing the physical properties (density and viscosity), and the solid-liquid equilibrium

of this system in a wide temperature range (from 293.15 to 333.15 K), and subsequently

use this information to estimate the composition of sulfuric acid to provide the highest yield

of the process.

Keywords: Seawater, Copper sulfate, Solid-liquid equilibrium, Crystallization.

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PROCESS DESIGN TO OBTAIN COPPER SULFATE CRYSTALS USING SOLID–

LIQUID EQUILIBRIUM OF COPPER SULFATE – SULFURIC ACID –

SEAWATER

María E. Taboada*, Francisca J. Justel, Yecid P. Jiménez, Teófilo A. Graber

Departamento de Ingeniería Química y de Procesos de Minerales. Universidad de

Antofagasta. Av. Angamos 601. Antofagasta. Chile

Abstract

In Chile, the most important economic activity is mining, which is concentrated in the north

side of the country. This region is a desert with limited freshwater resources; therefore, the

mining sector requires research and the identification of alternative sources of water. One

alternative is seawater, which can be an alternative to the limited freshwater resources in

the region.

In this work, using solid-liquid phase equilibrium, has been designed a copper sulfate

crystallization process, from a copper leaching solution, followed by a re-crystallization

stage which allows to obtain high purity crystals. The sulfuric acid acts as a co-solvent,

because as the acid concentration increases the copper sulfate solubility decreases. Thus,

this process could be considered as a drowning-out crystallization process.

The conceptual process includes the following four stages: mixer, crystallizer, centrifuge

and dryer.

Keywords: Seawater, Copper sulfate, Crystallization.

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SODIUM CHLORIDE EFFECT IN COPPER SULFATE PENTAHYDRATE

CRYSTALLIZATION

F. Justel1, D.M. Camacho

2, and K. J. Roberts

2

1Department of Chemical Engineering and Mineral Processing,

University of Antofagasta,

Antofagasta, Chile

2School of Chemical and Process Engineering, University of Leeds, Leeds, United Kingdom

Abstract

Copper mining is the most significant economic activity on the north side of Chile,

however, due to the arid conditions in this zone (located in the Atacama Desert) along with

water scarcity, mining industries have required innovative solutions for the optimization of

water consumption and have started to use seawater in their productive processes. Copper

sulfate (blue vitriol) is the most important industrial compound of copper, with a wide

variety of commercial uses as: soil additives, fungicides, and bulk preparation of other

copper compounds. In Chile, there are some small mining companies that crystallize copper

sulfate from hydrometallurgical processes using freshwater, thus in order to be able to

minimize the use of freshwater in the crystallization process, the effect of the seawater in

the copper sulfate pentahydrate crystals needs to be assessed.

To understand the effect of the principal ions present in seawater (Na+

and Cl-), the

objective of the present work is to study the sodium chloride effect in the crystal shape,

composition, and growth rate of copper sulfate pentahydrate crystals, and compare with

results in freshwater. This knowledge will allow us to obtain valuable information that

could be useful in the design of the copper sulfate crystallization process using seawater.

Keywords: Copper sulfate, Growth kinetics.

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5. Published works from the present doctoral thesis

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Documents

The effect of seawater on the thermodynamics and