Outi Post

CALCULATION OF ACTIVITY COEFFICIENT AND SOLUBILITY FOR AQUEOUS METAL SOLUTIONS

Master´s Programme in Chemical, Biochemical and Materials Engineering Major in Chemical Engineering

Master’s thesis for the degree of Master of Science in Technology submitted for inspection, Espoo, 30 September, 2019.

Supervisor Professor Marjatta Louhi-Kultanen

Instructor Postdoctoral Researcher Bing Han

Aalto University, P.O. BOX 11000, 00076 AALTO www.aalto.fi Abstract of Master's Thesis

Author Outi Post Title of thesis Calculation of Activity Coefficient and Solubility for Aqueous Metal Solutions Degree Programme Chemical, Biochemical and Materials Engineering Major Chemical and Process Engineering Thesis supervisor Professor Marjatta Louhi-Kultanen Thesis advisor(s) / Thesis examiner(s) Postdoctoral Researcher Bing Han Date 30.09.2019 Number of pages 64+6 Language English

Abstract

The metal recovery has been a big topic in the media lately. The demand for the metals has increased drastically for due to major increase of the electrical cars. The recycling system of metals is close to nonexistent, and due to increased demand, it is important to gain the metals back to the production. The recycling is important not only to enhance the electrical car battery industry, but also in order to prevent metal electrolytes leaking to the environment, since most of them are hazardous. In the industry the metals become a problem in membrane processes, since the metal containing substances are fouling on the membrane and decrease the effectivity of the membrane.

The purpose of this work was to study if the Pitzer model could be used in order to study the pure electrolytes and predict the behaviour in multicomponent systems. The work was done with mathematical tools including calculations and literature data.

The results indicate that the Pitzer model works, therefore, it is possible to predict the behaviour of the metal electrolytes in the system. It was noticed that for the mixed electrolytes the model works between 0 to 6 mol/kg (water), and outside of this range the results were not reliable.

Tin order to receive reliable results it is important to use low molalities between 0 to 6 mol/kg (water). It was noticed the original Pitzer parameters were accurate, however, in some cases more precise optimizations can be done. With these optimizations it can be possible to gain more precise results, which can be used in appliances, which need specifically accurate modelling results. The model is an easy and inexpensive way to study if the conditions can be optimised by choosing more suitable substances in order to minimize the fouling on the membranes, increasing the coagulation of toxic substances from the wastewater and maximizing the yield of the needed metals.

Keywords activity coefficient, Pitzer model, solubility, aqueous solutions, metals

Aalto-yliopisto, PL 11000, 00076 AALTO www.aalto.fi Diplomityön tiivistelmä

Tekijä Outi Post Työn nimi Aktiivisuuskerroinlaskelmat ja liukoisuus metalli-vesiseoksissa Koulutusohjelma Kemian-, bio- ja materiaalitekniikan koulutusohjelma Pääaine Kemian- ja prosessitekniikka Työn valvoja Professori Marjatta Louhi-Kultanen Työn ohjaaja(t)/Työn tarkastaja(t) Tutkijatohtori Bing Han Päivämäärä 30.09.2019 Sivumäärä 64+6 Kieli englanti

Tiivistelmä

Metallit ja niiden liuokset ovat olleet suuresti esillä mediassa. Metallien tarve on kasvanut tasaisesti viime vuosien aikana muun muassa lisääntyneen sähköautoteollisuuden myötä. Autojen akuissa tarvittavat metallit uhkaavat loppua nykyisellä käytöllä ja alhaisella kierrätysasteella, joten niiden takaisin saaminen käyttöön on todella tärkeää. Metallien kierrättäminen on tärkeää myös siksi, että monet niistä ovat ympäristölle haitallisia, mikäli ne pääsevät vuotamaan esimerkiksi kaivoksista lähtevien vesien mukana. Teollisuudessa on tärkeää löytää apukeinoja, joilla voidaan vähentää mineraalien saostumista esimerkiksi elektrodialyysissä puoliläpäisevien kalvojen pinnalle.

Työn tarkoituksena oli tutkia Pitzer-teoriaa ja sen soveltuvuutta puhtaiden elektrolyyttien tutkimiseksi ja liuosten käyttäytymisen ennustamisessa monikomponenttiliuoksissa. Työ tehtiin matemaattisiin malleihin perustuen ja työssä käytettiin apuna kokeellista dataa.

Tuloksista huomataan, että Pitzer-malli soveltuu aineiden liukoisuuksien ennustamiseksi mallin vaatimien rajojen sisällä. Tulokset ovat kannustavia, koska virheprosentti laskujen ja kokeellisen datan välillä on pieni. Pitzer-malli toimii työkaluna myös monikomponenttisysteemeille molaliteettirajojen sisällä. Ongelmaksi muodostui se, että monet kokeelliset tulokset ovat rajojen ulkopuolella, jolloin Pitzer-malli ei toimi luotettavasti.

Tuloksista voidaan päätellä, että Pitzer-teoriaa voidaan parhaiten käyttää, mikäli käytettyjen komponenttien konsentraatiot ovat suhteellisen pieniä. Parametrien optimointi toimii parhaiten, kun tarkastellaan erittäin pieniä määriä, jolloin jokaisen komponentin epäpuhtaudet ovat kriittisiä. Pitzer-teoria on suhteellisen halpa ja helppo työkalu selvittää liukoisuuksia ja aineiden käyttäytymistä muiden aineiden kanssa. Mallia voidaan käyttää saannon maksimoimiseksi, saostumisen vähentämiseksi ja arvokomponenttien tai haitta-aineiden erottamiseksi vesiliuoksista.

Avainsanat aktiivisuuskerroin, Pitzer-malli, liukoisuus, vesiliuokset, metallit

Preface

First, I would like to thank my thesis supervisor Professor Marjatta Louhi-Kultanen for giving me this opportunity to study the given subject. I cannot express my gratitude enough not only for the valuable perspectives and guidance through the work, but also encouraging me through this whole process.

I would like to thank my thesis advisor, Postdoctoral researcher Bing Han, who has provided me support and great advices through the work. With her guidance I was able to get valuable tools in order to complete this Master’s Thesis.

I would like to thank my family, friends and colleagues not only for giving me the inspiration and support, but also always having faith in me. Your support has been tremendous, and you have always been able to encourage me to do better, and I am ever grateful for that.

Last but not least I would like to thank my boyfriend for your infinite patience. It has been life changing to have someone, who has been there for all of the ups and downs. You have always been there for me and given me inspiration and lifted my spirit up. You have the ability of finding the right words and acts, when I have needed them the most.

I am sincerely thankful for everyone, who has been part of this journey.

Outi Post

30.09.2019

The List of Abbreviations and Symbols

AMD acidic mine drainage

A" Debye-Hückel parameter for osmotic coefficient b a universal interaction parameter C$ a specific parameter for the electrolyte dw density of water e electronic charge ϵ dielectric constant or the relative permittivity of water I ionic strength (mol/kg)

Ksp solubility product k Boltzmann’s constant m molality (mol/kg (water)) MX electrolyte in aqueous solution

N0 Avogadro’s number T temperature (K) v+ stoichiometric coefficient of a cation v- stoichiometric coefficient of an anion z charge of ions

α', α) a specific parameter dependent on electrolyte type, such as 1-1 and 2-2 - ' ) β+, , β+, , β+, specific parameters for electrolytes γ activity coefficient θ, Ψ mixing parameters for mixed electrolytes

Table of Contents

1 INTRODUCTION ...... 1 2 PITZER THEORY ...... 7 2.1 PURE ELECTROLYTES ...... 9 2.2 MIXED ELECTROLYTES ...... 12 2.3 SOLUBILITY ...... 14 2.4 ACTIVITY COEFFICIENT ...... 16 2.5 ELECTROLYTES ...... 17 3 MODELLING OF THE AQUEOUS SOLUTIONS ...... 19 3.1 MODELLING OF THE PURE ELECTROLYTES ...... 19 3.2 MODELLING OF THE MIXED ELECTROLYTES ...... 20 4 RESULTS ...... 22 4.1 PURE ELECTROLYTES ...... 22 4.1.1 1-1 Electrolytes ...... 24 4.1.2 1-2 Electrolytes ...... 30 4.1.3 2-1 Electrolytes ...... 33 4.1.4 2-2 Electrolytes ...... 36 4.2 MIXED ELECTROLYTES ...... 39 5 DISCUSSION AND CONCLUSIONS ...... 53

REFERENCES ...... 58

List of appendices

Appendix A. Parameters used in the calculations for pure electrolytes and mixed electrolytes Appendix B. Pure NaCl 1-1 electrolyte calculations

Appendix C. Pure Li2SO4 1-2 electrolyte calculations

Appendix D. Pure CoCl2 2-1 electrolyte calculations

Appendix E. Pure NiSO4 2-2 electrolyte calculations Appendix F. Determination of the molality of NaCl by changing the molality of HCl

1 Introduction

The popularity of the electric cars has increased quickly during the past years, and the demand for the metals used in the electric car batteries (figure 1) has increased at the same time. Some of the metals used in electric car batteries, such as cobalt, are classified as a critical resource in the EU and it is becoming a critical problem due to the quick increase in the demand. Currently the recycling of the car battery metals is close to non-existing and it is important to find solutions to recycle the old batteries and gather the usable metals back to production. The recycling of the metals becomes important not only for the production, but also from the environmental point of view. For example, nickel has been connected with cancer issues. Therefore, it is a win-win situation, when old car batteries are recycled and not treated only as hazardous waste, or in the worst-case scenario, dumped into the environment. (Törmänen, 2018; Meister & Falck, 2018; Group, 2015)

Figure 1. Battery of the electric car in Chevrolet Bolt EV (Voelcker, 2016).

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The lack of car battery metals needs to be solved, but at the same time the shortage might be a good thing for Finland. The lack of cobalt is going to be a huge problem, since it is produced 100 000 tons annually and most of it is needed for the car batteries. However, in Finland it is possible to produce all of the metals needed for the car batteries, therefore, for example Terrafame has announced to invest in car battery metal factory. The vision of Terrafame is to produce nickel and cobalt sulfate (figure 2), which are needed in the electric car batteries, as they are producing already. However, currently the refining process is done elsewhere, therefore, the purpose of the new factory is going to be concentrating on the whole process to be done at the same place instead of transferring the resources between the factories. The process is going to be done in three phases, from where the crystallizing of nickel, cobalt and ammonium sulfate is going to be the last step. (Mäki-Petäjä, 2017; Terrafame, 2018a; Terrafame, 2018b)

Figure 2. Various nickel and cobalt products including both nickel (blue/green) and cobalt (orange) sulfate (Nornickel, not dated).

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The metal need for the car batteries and the lacking recycling system of the used metals are not the only problematic issue regarding metals and aqueous metal solutions. The mining industry in Finland has gained a lot of media publicity due to problems related to water, such in Talvivaara. In November 2012 there was a huge leak in the waste pool releasing more than 1 000 000 cubic meters water and sediment containing metals to the environment. In theory the mining is done in small area, however, in practice the impacts appear in a larger scale in the environment. (Parviainen, 2012; Salomons, 1994; Muhonen, 2016)

Naturally one of the biggest leaks of the metals to the environment happen via acid mine drainages. AMDs (figure 3) are formed in a reaction between air, water and pyrite FeS2, which is a common sulfide mineral also known as fool’s gold. In this reaction dissolved iron and sulfuric acid are formed. Since the mining process includes the contamination of water by metal impurities, it is important to find solutions how to purify the water and prevent that the metal impurities are not leaked to the environment. For example, mining can increase the concentration of mercury, arsenic and sulfuric acid to hazardous levels both to environment and human health. By modeling the metallic aqueous solutions, it is possible to study, how to gain the impurities from the mining waters and recycle those metals into better use than polluting the environment. (Chepekmoi, 2017; Rickard, 2015; Salomons, 1994; Williams, D. & Diehl, S., 2014; Jacobs, Lehr & Testa, 2014)

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Figure 3. Acid mine drainage (Kanawha Forest Coalition, 2016).

Today, electrochemical processes are used widely in the industry in both organic and inorganic processes. Electromembranes have become an important application of electrochemistry, because utilization of electromembranes is relatively cheap due to low energy demand while the production purity stays high and efficient. Electromembranes are easy to use in an automatized process and they do not take too much space. Compared to some other processes, electromembranes are more environmentally friendly due to low environmental impact. (Handojo et al, 2019; Paidar, Fateev & Bouzek, 2016)

Membranes are used as a barrier between substances, which are usually fluids. Membranes are usually used to block certain size particles from going through the membrane in order to for example purify the liquid flow. However, in electromembrane processes the driving force of the transport is the electric potential, and typically the applications have either ion-exchangers or bipolar

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membranes (figure 4) as a basic element of the process. (Paidar, Fateev & Bouzek, 2016; Koter & Warszawski, 2000)

Figure 4. Bipolar membrane electrodialysis system (Pourcelly, 2002).

One important application of bipolar membranes is using them in electrodialysis. The bipolar membrane electrodialysis must be designed to be fit in the specific process, however, the principle is the same. There is a cell system containing an anion membrane, a cation membrane and a bipolar membrane, which form a unit. This repeating system is placed in between of two electrodes. The bipolar membrane is placed in the middle of the anion and cation exchange membranes, and the flow is set between these membranes. The dissociation happens in the bipolar electromembrane, and dissociated anions as to the anion exchange side and dissociated cations go through the cation exchange side. (Pourcelly, 2002)

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Even though the membranes have many advantages compared to the other processes, they have also some problems. One of the biggest problems is the fouling of the membrane, which means that the efficiency of the pores in the membrane is decreased by blocking of the other particles. When fouling occurs, the membrane loses its ability and efficiency of separation. In the process there are some substances, which do not dissolve as well as some other substances, such as CaCO3, MgCO3 and

Mg(OH)2. (Handojo et al., 2019)

The purpose of this work was to study the solubility of pure substances and to compare the gained data to literature values. When the chosen pure substances were modelled and compared, the goal was to study the aqueous metallic solutions and their behavior. By modelling these issues, it is possible to study the changes in the solubility of certain substance in varying conditions, such as changing the base or acid in the mixture.

In the theory section the theory behind Pitzer model and aqueous solutions are studied. The second part consists of modelling of aqueous metal solutions, which was done in two parts. First, the pure substances, such as NiCl2 and NH4Cl, were studied and compared. After studying the pure components, mixtures of various aqueous solutions containing certain metals were studied. The purpose was to find out if it is possible to predict the behavior of aqueous mixtures, when the molality of the substance is changed.

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2 Pitzer Theory and Determination of Activity Coefficient

Pitzer theory is a modification of the Debye-Hückel theory, which is a model for aqueous electrolyte solutions behaving ideally. In practice, aqueous electrolyte solutions are not ideal, therefore, a more precise model is needed. Pitzer theory is a semi-empirical model, which uses specific parameters in order to make the equations more reliable and more suitable for non-ideal aqueous solutions. Using Pitzer theory it is possible not only to understand the behavior of the ions in the aqueous solutions, but also calculate activity coefficients and predict the solubility of pure substances, such as sodium, nickel, cobalt, mixtures and more complex systems. (Gupta, 1978; Pitzer, 1991; Simoes et al, 2016)

In the Pitzer model molality, which refers to how many moles of the substance there are per kilogram of the solvent, is in an important role by being the base of the calculations. Even though the Pitzer model can be used for very non-ideal solutions, the recommended degree of molality should usually be maximum 6.0 mol/kg (water) in order to the model to work properly. (Gupta, 1978; Pitzer, 1991; Simoes et al, 2016)

Pitzer model can be used to predict the behavior of the chosen substance rather accurate without proceeding expensive modellings. These predictions can be used in the industry in order to study how increasing the molality of the substance changes the behavior of the whole system. For example, this kind of modelling can be used when optimizing the right mixture in membrane selection. (Pitzer, 1991; van der Stegen et al, 1999)

The biggest problem with Pitzer theory is that it is based on empiric data, since the model works for low molalities and for the most cases the molalities were too big for the model. The parameters are specific to substances, because they are gathered from different experiences in varying temperatures. Mostly this problem is considered minor, since for wide variety of substances it is possible to gather

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empirical data. However, determination of the parameters for each of the substances in specific temperature is slow and expensive process and cannot be performed for example for radioactive substances. (Simoes et al, 2016)

The idea of the model is to predict the behavior and properties of the system, especially mixed electrolytes, without losing the accuracy. This idea is based on the theoretical knowledge of pure substances added with some knowledge of the mixed solutions. (Pitzer, 1991)

Pitzer model and its parameters have been studied widely, and it has been stated as one of the most important thermodynamic models for predicting the behavior of electrolyte solutions. However, the main question has been how can this model be applied into various applications in industry? Would it be possible to improve the model so that it would not need the empirical data in order to work? (Simoes et al, 2016; Kim & Frederick Jr., 1988 a; Kim & Frederick Jr., 1988b).

In 1988 Kim and Frederick Jr. were studying the ion interaction of various substances based on the Pitzer model. They were trying to optimize the parameters that Pitzer had presented earlier, and they obtained successful results. In their study Kim and Frederick Jr. noticed that the maximum molality 6 mol/kg (water) presented by Pitzer was not applicable for all of the substances, and it was noticed that some of the substances have a lower maximum molality than 6 mol/kg (water). (Kim & Frederick Jr., 1988a)

Kim and Frederick Jr. studied not only the pure electrolytes but also the ternary mixing parameters. They were able to optimize mixing parameters for certain mixtures having a minor deviation, and these parameters are presented in their study. (Kim & Frederick Jr., 1988b)

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In 2016 published study Simoes et al. were working on the pure electrolytes of 1-1, 2-1, 3-1, 4-1 and 2-2 at 25 °C in order to determinate new parameters, which would not be depending on the empirical data. They were able to simplify the model and decrease the number of used parameters without the losing accuracy. (Simoes et al, 2016)

These publications are shortly presented in this section, and they are discussed more in the chapter 3. These studies are used in order to evaluate the gained results. For example, as mentioned the study of Simoes et al., the simplifications of the Pitzer parameters are studied for mixed electrolytes in order to find out, if the simpler model is accurate enough to use in the larger scale.

2.1 Pure electrolytes

The Pitzer equation can be modified to be exact for each type of electrolytes. For - ' example, for 1-1 electrolytes the needed parameters are β+, and β+, , but in 2-2 ) aqueous electrolyte solutions one more parameter β+, is needed in order to gain 2 more accurate predictions of the behavior. The β+, parameters are adjustable and are specific to each of the salts, and it has to be remembered that they are temperature dependent. These equations are further explained in this chapter. (Gupta, 1978; Pitzer, 1991)

One of the basic equations for these calculations is presented in equation 1, which is the calculation of the molality for an aqueous solution. Since the Pitzer parameter calculations are done using molalities instead of concentrations, this equation is very important in order to gain correct results. The Ksp is the solubility product constant and γ is the activity coefficient for certain substance.

9 6 : m∗ = 78 (1) ;±

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The Pitzer theory uses a lot of parameters in the calculations, and typically these $ parameters are specific to each of the salts, such as C+, presented in equation 2 and 3, which can be simplified to 4, but some of them have a defined value that is specific depending on the electrolyte types. In the calculations β and α are universal

9 9 9 9 E E parameters with constant values of 1,2 kgA ∙ mol A and 2,0 kgA ∙ mol A . These parameters are used in equations 5 and 6. It must be remembered that these values are valid for most of the electrolyte types, but not for 2-2 electrolytes due to more complex electrostatic ion paring. To solve the problem with 2-2 electrolytes, one extra term and new parameter α) must be added, as presented in the equation 7.

For 2-2 electrolytes the values for parameters α' and α) vary from other electrolyte 9 9 9 9 E E types. Their values in the calculations are 1,4 kgA ∙ mol A for α' and 12 kgA ∙ mol A for α). The values for these universal parameters are valid at 25 ° C. (Gupta, 1978; Pitzer, 1991)

W )O O )(O O A ln γ = |z z |f ; + m N P QR B ; + m)[ P Q) ]C $ (2) ± + , O +, O +,

$ Y C+, = [ 9](v+µ++, + v,µ++,) (3) (OPOQ)A

Y\] C ; = (4) +, )

√` ) f ; = −A [ + lnc1 + b√If] (5) " ('ab√`) b

9 $ - ' B+, = β+, + β+, exp(−αIA) (6)

9 9 $ - ' ) B+, = β+, + β+, exp N−α'IAR + β+, exp N−α)IAR (7)

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As seen in the equations above, the equations are also dependent on ionic strength. When calculating ionic strength in Pitzer model, the calculations are made by using molalities as the measure of concentration. In addition, the ionic strength depends on not only the molality of the solution, but also on all of the anions and cations present in the solution. Therefore, it can be said that the ionic strength describes the concentration of the ions present in the solution, and the equation is presented in equation 8. This equation can be made in a simpler version, which can be easily used in the modelling calculations, and this equation is presented in equation 9. (Pitzer, 1991)

' I = ∑ m z ) (8) ) k k

' I = (v z )m + v z )m ) (9) ) + + + , , ,

In the calculations the Debye-Hückel constant A$ is the same with all of the electrolytes having the valency type. The constant can be calculated using equation 10. (Pitzer, 1991)

9 A W ' )lmnop q A = ( )( )A( )A (10) $ Y '--- rst

Some of the equations can be manipulated into a simpler form. For 2-2 electrolytes the equations are presented in equations 11 and 12, and in equation 13 for the rest of the electrolyte types. For activity coefficients the equations have been presented in equations 4, 5 and 14 to 17 (Pitzer, 1991):

9 9 - ' ) B+, = β+, + β+, g Nα'IAR + β+, g Nα)IAR (11)

)['E('au)q(vw)] g(x) = (12) uA

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9 - ' B+, = β+, + β+, g(αIA) (13)

; $ B+, = B+, + B+, (14)

- ' B+, = β + β f) (15)

) f = [1 − c1 + α√IfeEx√`] (16) ) (x√`)A

9 $ - ' Ex`A B+, = β + β e (17)

2.2 Mixed Electrolytes

The Pitzer model can be used also for solutions containing more than one electrolyte to predict the behavior of the components if the molalities are changed. With this model it can be mathematically modelled, if the solubilities of other substances are affected when the molality of one component is changed.

The modeling is based on the same equations as presented in the pure electrolytes part, and some new equations specific to mixed electrolytes are added. Since Pitzer theory is based on specific parameter, for mixed electrolytes there are specific mixing parameters θ and Ψ. θ represents the interaction between the independent ions, which are not common with the substances, and Ψ represents the interaction between the common ions. Similar to pure electrolytes, the mixing parameters are specific to certain mixtures, such as NaCl-KCl or KCl-KOH. (Kim & Frederick Jr., 1988; Pitzer, 1991)

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The calculation of parameter Z is presented in equation 18, and it must not be mixed up with z, which is the value for charge of the ion. The equations needed to calculate the activity coefficient for mixtures are presented in equations 18 to 23. (Pitzer, 1991)

Z = ∑k mk|zk| (18)

' f = z−1 + (1 + 2√I + 2I)eE)√`{ (19) Y )`A

| ' f (B) = ∑+, m+m,β+,fY (20)

)' f = [1 − c1 + 2√IfeE)√`] (21) ) )`

Ionic strength for the mixture can be calculated with equation 22. (Pitzer, 1991)

' I = ∑ })~ + ∑ })~ (22) )   Ä Ä

Equation 23 takes into account both cations and anions, and for example depending on the valence type of the mixture and the quantity of cations and anions, the equation can be simplified better into the matrix the calculations are needed for. The mean activity coefficient for an anion and a cation can be calculated by using equation 24. In equation 23 a < a’ refers to the sum of all of the dissimilar anions in the solution, as well as the c < c’ refers to the sum of all of the dissimilar cations in the solution. (Pitzer, 1991; Lassin et al, 2015)

OP OQ OQ ln γ+, = |z+z,|F + N R ∑Ç mÇ z2B+Ç + ZC+Ç + 2 N R ϕ,Ç{ + N R ∑Ñ mÑ z2BÑ, + O OP O

OP E' ZCÑ, + 2 N R ϕ+Ñ{ + ∑Ñ ∑Ç mÑmÇv [2v+z+CÑÇ + v+ψÑÇ,] + OQ

OQ OP ∑ ∑ m m N R ψ Ü + ∑ ∑ m m N R ψ + 2 ∑ m (v λ + v λ )/v (23) ÑáÑ| Ñ Ñ O ÑÑ , ÇáÇ| Ç Ç O +ÇÇ| 2 2 + 2+ , 2,

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) ; ln γ+ = z+f + ∑Ç mÇ(2B+Ç + ZC+Ç) + ∑Ñ mÑ(2θ+Ñ + ∑Ç mÇΨ+ÑÇ) + ) |z+| ∑Ñ ∑Ç mÑmÇCÑÇ + z+f′(B) (24)

In equation 23 can be noticed term F, which is the combination of the Debye-Hückel term and other terms. The calculation of the F is presented in equation 25. The constant B shown in the equation is an unitless constant and it has a value of 1.2. (Lassin et al, 2015)

√` ) F = −A" z + ln (1 + B√1){ (25) ('aã√` ã

2.3 Solubility

Solubility is a chemical property of a substance, and it is defined as the maximum quantity of specific substance that can be dissolved into the solvent in certain temperature. For example, if at 25 °C saturated NaCl-water solution is heated, it becomes unsaturated and more of NaCl can be dissolved into the water. However, if the water is saturated with NaCl, another substance with different solubility value can be dissolved into the solvent. Solubility of certain substances are presented in figure 5. (Helmenstine, 2018)

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Figure 5. Solubility curves for specific substances (Suresh & Blosse, 2015).

Ksp is temperature dependent parameter that describes the equilibrium of the solution in saturated state. Ksp value is gained from the equation that describes the dissolving process. When the equilibrium constant takes into account the whole process, Ksp parameter value takes into account only the ions in the dissolution process. Below is presented the dissolution of substance B2A in equation 26 and the calculation of Ksp in equation 27. (Aghaie & Shahamat, 2013)

+ 2- B2A à 2 B + A (26)

) Kçé = [B] ∙ [A] (27)

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2.4 Activity Coefficient

One of the key elements in thermodynamics is the activity coefficient, which represents the correction needed between concentration of a solution and the ideal value. For a pure, ideal liquid solution the activity coefficient is one, therefore, there are no interactions between substances. When the activity coefficient is more than 1.0, has a positive deviation from the Raoult’s law. On contrarily, when the activity coefficient is less than 1.0, the solution has a negative deviation. Activity coefficient is a dimensionless value that can be used for liquids, but not for gases. (Harvey, 2016; Struchtrup, 2014; Suresh & Blosse, 2017)

For an ideal solution the activity can be compared directly with the mole fraction of the component X, because the activity coefficient is 1.0 for an ideal solution. However, when calculating the activity of a non-ideal solution, the activity coefficient must be taken into account, because the deviation can change the activity in a large scale. (Struchtrup, 2014)

For an electrolyte the mean activity coefficient, which is dimensionless, can be calculated using the equation 28 (Louhi-Kultanen, not dated):

9 OP OQ (è êè ) γ+, = (γ+ γ, ) P Q (28)

If γ is less than 1, molecules have a strong force keeping them together, and more energy is needed in order to separate the particles from each other. On the contrary, if γ is more than 1, molecules have a strong rejecting force, therefore, the particles are easier to separate from each other. (Struchtrup, 2014)

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2.5 Electrolytes

An aqueous solution is a mixture, where the substance has been dissolved in the water. An electrolyte is a substance that provides electricity when mixing with a solvent, such as water. Electrolytes contain ions, which produces the electricity when moving in the solution. One common application for electrolytes is in the car batteries. (Helmenstine, 2019)

A traditional car battery is a lead-acid battery, where the positive plate contains PbO2 and the negative plate contains pure Pb. The electrolyte solution is a mixture of distilled water and H2SO4, and the electrode plates are separated from each other with a separator bag. H2SO4 works as a catalyst and helps the reaction to happen via pure lead and lead oxide. This chemical reaction produces movement of electrons, which produces electricity in the battery to be used. The reaction is reversible and the reaction for discharging is presented in equation 29 and the reaction for charging is presented in equation 30. The discharge reaction is presented in figure 6. (Varta, not dated; Firestone Complete Auto Care, 2016)

Pb + PbO2 + 2 H2SO4 à 2 PbSO4 + 2 H2O (29)

2 PbSO4 + 2 H2O à Pb + PbO2 + 2 H2SO4 (30)

Figure 6. The discharging reaction of the car battery (Varta, not dated).

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Electrolytes can be divided in different groups based on how many cations or anions either donate or receive. In this thesis the main focus is in groups 1-1, such as NaCl or KCl, 1-2, such as CaCl2 and Na2SO4, 2-1, such as Li2CO3, and 2-2, such as NiSO4 and

CoSO4. (Mishutin, 2010; Vitz et al, 2017)

Aqueous electrolyte solutions can be divided into two sub-categories, which are ideal and non-ideal solutions. The division has been done based on Raoult’s law and how they follow it. It is rare to find naturally ideal solutions, however, some solutions have some ideal solution behavior. In practice all of the electrolyte solutions are non-ideal. Therefore, they have either a positive or a negative deviation from the ideal solution. (Clark, 2005)

If the deviation from Raoult’s law is positive, it means that the vapour pressure of the mixture is greater than what the Raoult’s law presents. When the vapour pressure is greater than what could be expected, the molecules are breaking away more eager than in an ideal solution. This means that the intermolecular forces are weaker than in an ideal solution. If the deviation is negative comparing to Raoult’s law, it means that the vapour pressure of the mixture is smaller than in an ideal solution. (Clark, 2005)

18

3 Modelling of Aqueous Solutions

The modelling was done in several parts. First the different pure electrolytes were modelled using Excel. The theoretical calculations were based on Pitzer equations presented in the theory section. These calculated values were compared to experimentally gained values, which were from the CRC Handbook of Chemistry and Physics. The calculated values were compared to data found in the studies of Kim & Fredercik Jr. (1988a, 1988b) and Simoes et al. (2016).

The modelling environment was chosen to be at 25 °C and pressure of 1.0 bar. The solutions were assumed to be evenly mixed. The parameters used for the calculations are presented in appendix A.

3.1 Modelling of Pure Electrolytes

The modelling of the pure electrolytes was sarted with 1-1 electrolytes, such as NaOH and KOH, in order to find out if these solutions followed the Pitzer theory. Parameters for pure electrolytes were obtained from Kenneth Pitzer’s book Activity Coefficients in Electrolyte Solutions and are presented in the appendix A. Experimentally gained values were gained from CRC Handbook of Chemistry and Physics, 97th edition.

After getting the results for several 1-1 electrolytes, the other electrolyte types chosen for this work were modelled. The modelling of 1-2 and 2-1 electrolytes were otherwise similar to 1-1 electrolytes, but the parameter values had to be changed.

í ë ë )A For these electrolytes the parameter values were given as β-, β' and C$, which Y Y Y means the values (Pitzer, 1991) had to be converted in the modelling part in order to gain the correct activity coefficient values.

19

The 1-1, 1-2 and 2-1 electrolytes were rather simple to model, however, the 2-2 electrolytes took more modification of the base model. The 1-1, 1-2 and 2-1 electrolytes had simpler terms in the calculations, since the α) and β) equals 0 and α' can be simplified to α. For the 2-2 electrolytes these terms must be taken into

9 E account. Therefore, for the 2-2 electrolytes α' equals 1,4 (mol ∙ kgE') A, α) equals

9 E 12,0 (mol ∙ kgE') A and β)is specific for the electrolyte. The appendices B to F present the calculation models used for pure 1-1, 1-2, 2-1 and 2-2 electrolytes.

3.2 Modelling of the Mixed Electrolytes

The modelling of γ of the pure electrolytes was done first in order to find out if the Pitzer model was suitable for evaluating these chosen electrolytes in constant temperature and solvent. Since the results were good, the modelling was continued with mixed electrolytes having water as the solvent. The temperature was thought to be constant 25 °C with pressure of 1 bar. Parameters for mixed electrolytes were obtained from Kenneth Pitzer’s book Activity Coefficients in Electrolyte Solutions (1991) in table 16 “Binary Symmetrical Mixtures with Common Ion at 25 °C”.

The modelling was carried out with calculations having the common ion in the compound. If the compounds have same ion, the calculations are simpler, since there are no other cations or anions that must be taken into account. For example, calculations for KCl-NaCl mixture are simpler than for KCl-NaOH, since the common substance is Cl-, which is found both in KCl and NaCl. The calculations were done the same for all of the mixtures. An example for the calculations is presented in appendix F. The parameters used for mixed electrolytes are presented in appendix A.

In the modelling of the mixtures the calculations were made simpler by excluding compounds that have crystallized water in the mixture. These kinds of compounds

20

make the calculations more complex, since the molality of crystallized water must also be taken into account when doing the modelling.

The modelling of the mixtures require data from the modelling of the pure electrolytes; therefore, the modelling of the mixtures must be done after the data from the pure electrolytes is received. The results of the calculations of the mixtures were compared to data from the books by Stephen H. and Stephen T. The data used in the comparison was taken from Ternary Systems Part 1 and Ternary and Multicomponent Systems of Inorganic Substances Part 1, 2 and 3.

The modelling sheet has calculations for both a simpler and more complex Pitzer model. When calculating the activity coefficient, the more complex calculations are calculated with equation 24. The simplified model, Pitzer 1, excludes the term

|z+| ∑Ñ ∑Ç mÑmÇCÑÇ from the equation 24.

21

4 Results

In this section, the results for different type of pure and mixed electrolytes are presented. First, the results for pure electrolytes are presented for each type of electrolytes. After the results of pure electrolytes, the results for mixed electrolytes are presented.

The results are slightly discussed in this section in order to make preliminary conclusions about the results. The results are compared to each other in order to get a better view about the variety of the results and difference between both in one electrolyte type and different electrolyte types. However, a deeper study of the results is presented in chapter 5.

The results present both the original Pitzer model-based calculations and the experimental data from CRC handbook or by Stephen & Stephen. For a comparison, the values gained from an optimized model by Kim & Frederick Jr. and Simoes et al., and a simplified model with fewer terms, are presented.

4.1 Pure Electrolytes

The results for pure electrolytes consist of figures, which have three different curves combined in one figure. The first values indicate the activity coefficient values, which are calculated using the Pitzer model equations. The equations used for each of the type of the electrolytes are presented in the earlier sections. The used parameters are presented in appendix A.

The second values indicate the values for mean activity coefficients, which were found in the CRC Handbook of Chemistry and Physics from page 5-100 to 5-106 “Mean Activity Coefficients of Electrolytes as a Function of Concentration”. The third values indicate values for activity coefficients found in the CRC Handbook of

22

Chemistry and Physics pages 5-98 and 5-99 “Activity Coefficients of Acids, Bases and Salts”.

The fourth values indicate the values gained from the study of Kim & Frederick Jr. (1988a) from pages 178-179 “Ion Interaction parameters for 1-1 Electrolytes at 25 °C”, from page 179 “Ion Interaction Parameters for 1-2Electrolytes at 25 °C”, from pages 180-181 “Ion Interaction Parameters for 2-1 Electrolytes at 25 °C” and from page 182 “Ion Interaction Parameters for 2-2 Electrolytes at 25 °C”.

The fifth values indicate the values found in study done by Simoes et al. (2016) from pages 12-15. The values were gained from the table 1 presenting both the simplified model values and the original Pitzer model values.

23

4.1.1 1-1 Electrolytes

The first calculated and modelled results were obtained for pure 1-1 electrolytes. The results for these electrolytes are presented in figures 7-14. The electrolytes were chosen to the electrolytes based on the common ion, the possibility to use it in industrial applications and if it was relevant for example in comparison to other electrolytes. The parameter values were gained from Pitzer (1991), Kim & Frederick Jr. (1988a) and Simoes et al (2016), and these values lead to activity coefficient values, which were compared in the figures.

NaCl

1.1

1.0 -

0.9

0.8 Activity coefficient,

0.7

0.6 0 1 2 3 4 5 6 7 Molality, mol/kg

Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp 178-179 Simoes et al. pp. 12-13

Figure 7. Activity coefficient per molality for NaCl at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

24

NaOH

1.1

1.0 -

0.9

0.8 Activity coefficient,

0.7

0.6 0 1 2 3 4 5 6 Molality, mol/kg

Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp. 178-179 Simoes et al. pp. 12-13

Figure 8. Activity coefficient per molality for NaOH at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

As seen in figures 7 and 8, NaCl and NaOH have rather similar behavior in the solution. When the molality of the substance increases, the activity coefficient has a drastic decrease between molality 0…1 mol/kg (water). After reaching molality 1.0 mol/kg (water), the activity coefficient increases drastically, and NaOH is having slightly larger increase compared to NaCl.

It can be also noted that the behavior of NaCl and NaOH vary by the data gained from the studies by Kim & Frederick Jr. and Simoes et. al. When in the NaCl case all of the data points followed each other well, the deviation in the NaOH case is much bigger between the different data points.

25

KCl

1.0

- 0.9

0.8

0.7 Activity coefficient, 0.6

0.5 0 1 2 3 4 5 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp. 178-179 Simoes et al. pp. 12-13

Figure 9. Activity coefficient per molality for KCl at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

KOH 1.0

- 0.9

0.8

Activity coefficient, 0.7

0.6 0 1 2 3 4 5 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp. 178-179 Simoes et al. pp. 12-13

Figure 10. Activity coefficient per molality for KOH at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

26

Comparing KCl and KOH to each other (figures 9 and 10), it can be seen that the behavior is not similar to the behavior of NaCl and NaOH. KCl has a large decrease in the activity coefficient compared to KOH, since the activity coefficient for KCl decreases until it stabilizes towards the end. For KOH the behavior is more like it is for NaCl and NaOH, since it has a major drop between 0.0 and 0.5 mol/kg (water) and after reaching 0.5 mol/kg (water) it begins to increase.

It can be noted that the behavior of the KCl and KOH are rather similar to the behavior of NaCl and NaOH. The data points follow each other within acceptable error range in the KCl case, however, the deviation is much bigger within the data points in the KOH case.

LiCl

1.0 -

0.9

0.8 Activity coefficient,

0.7 0 1 2 3 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp. 178-179 Simoes et al. pp. 12-13

Figure 11. Activity coefficient per molality for LiCl at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

27

NH4Cl 1.0

0.8 -

0.6

0.4 Activity coefficient, 0.2

0.0 0 1 2 3 4 5 6 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederik Jr. pp. 178-179 Simoes et al. pp. 12-13

Figure 12. Activity coefficient per molality for NH4Cl at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

HNO3 1.0 - 0.9

0.8

0.7 Activity coefficient,

0.6 0 1 2 3 Molality, mol/kg

Pitzer model Kim & Frederick Jr. pp. 178-179 Simoes et al. pp. 12-13

Figure 13. Pitzer model calculations (Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

28

HCl 1.0 - 0.9

0.8

0.7 Activity coefficient,

0.6 0 1 2 Molality, mol/kg

Pitzer model Kim & Frederick Jr. pp. 178-179 Simoes et al. pp. 12-13

Figure 14. Pitzer model calculations (Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

In figures 13 and 14 is presented the comparison between Pitzer model and the optimized parameters of Kim & Frederick Jr. As seen in the figure, it can be noted that both of the models follow the same trend in small molalities, however, the deviation become bigger when the molality is increased.

Comparing all of the figures to each other (figures from 7 to 14), it can be concluded that the 1-1 electrolytes have two kind of behavior of activity coefficient versus molality. It is seen that the substances might either stabilize towards the 6.0 mol/kg (water) or they can first decrease dramatically and after reaching certain point they will begin to increase the value for activity coefficient. Based on all of the figures above, it is noticed that the deviation between the experimental data, calculated original Pitzer values and the simplified model is rather small with some exceptions.

29

When comparing the Pitzer calculated model to the simplified version presented by Simoes et al. (2016), it can be noted that the two models go well together and the deviation is not huge, as it is for the optimized model when comparing the two other models.

4.1.2 1-2 Electrolytes

For the 1-2 electrolytes only three examples were chosen for the results. These substances were chosen based on the applications. For example, lithium is used in the car batteries, therefore, it is interesting to find out, if it is possible to improve the solubility of lithium and therefore, gain it back to the production. The results for 1-2 electrolytes are presented in figures 15-17. Parameter values were from Pitzer (1991), Simoes et al (2016) and Kim & Frederick Jr. (1988a), and these parameter values were used in the calculations in order to gain activity coefficients, which were compared in the figures.

Na2SO4

1.0

- 0.8

0.6

0.4

Activity coefficient, 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. p. 179 Simoes et al. p. 14

Figure 15. Activity coefficient per molality for Na2SO4 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

30

Li2SO4

1.0

- 0.8

0.6

0.4

Activity coefficient, 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. p. 179 Simoes et al. p. 14

Figure 16. Activity coefficient per molality for Li2SO4 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

K2SO4

1.0

- 0.8

0.6

0.4

Activity coefficient, 0.2

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. p. 179 Simoes et al. p. 14

Figure 17. Activity coefficient per molality for K2SO4 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

31

As seen in figures 15-17, Pitzer theory predicts with a sufficient accuracy the behavior of 1-2 electrolytes, since the experimental data follows the calculated data within acceptable error range. In the 1-2 electrolytes can be noted that the Kim & Frederick Jr. optimized parameters are better and more consistent compared to 1-1 electrolytes. Compared to Simoes et al. simplified model, the values are set very similar compared to the original Pitzer calculations, and the deviation between the two is rather small.

Compared to 1-1 electrolytes, the 1-2 electrolytes have more similar behavior with each other than the 1-1 electrolytes. It can be noticed that all of the figures have first a drastic decrease in the activity coefficient versus molality, but after certain point the values stabilize. The deviation between the data points is rather small compared to 1-1 electrolytes.

32

4.1.3 2-1 Electrolytes

The next step was to model the 2-1 electrolytes. The results for these electrolytes are presented in figures 18-20. Three electrolytes were chosen based on their possibilities in industrial scale. For example, it is important to recycle both nickel and cobalt from the car batteries, since nickel is toxic for the environment and cobalt is a rare mineral to be found on Earth.

CoCl2

1.5 - 1.0

0.5 Activity coefficient,

0.0 0.0 0.5 1.0 1.5 2.0 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp. 180-181 Simoes et al. pp. 14-15

Figure 18. Activity coefficient per molality for CoCl2 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

33

NiCl2

1.5 - 1.0

0.5 Activity coefficient,

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp. 180-181 Simoes et al. pp. 14-15

Figure 19. Activity coefficient per molality for NiCl2 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

MgCl2

1.5 - 1.0

0.5 Activity coefficient,

0.0 0.0 0.5 1.0 1.5 2.0 Molality, mol/kg Pitzer model CRC p. 5-100 to 5-106 at 25°C CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. pp.180-181 Simoes etal. pp. 14-15

Figure 20. Activity coefficient per molality for MgCl2 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

34

From the results it can be seen that the 2-1 electrolytes have more similar behavior than compared to for example 1-1 electrolytes. When comparing the behavior of NaCl and NaOH, and KCl and KOH, the results were not predictable based on the earlier information gained for common ion substances. However, it can be noticed that for 2-1 electrolytes the behavior is very similar to each other having the common ion. In the 2-1 electrolytes can be noted that the Kim & Frederick Jr. optimized parameters behave similar way compared to 1-2 electrolytes. As seen in previous results, the results in 2-1 electrolytes follow the same pattern when it comes to comparing calculated Pitzer data to calculated simplified data.

Compared to previous electrolyte type, the 2-1 electrolytes behave similar to each other like 1-2 electrolytes do. However, compared to 1-2 electrolytes, the 2-1 electrolytes do not stabilize after the decreasing, but they begin to increase again.

35

4.1.4 2-2 Electrolytes

The last modellings were done for 2-2 electrolytes. The results for these pure electrolytes are presented in figures 21-24. The selection of the results presented in this section was made with similar principles as presented in the earlier sections.

CuSO4

1.0

- 0.8

0.6

0.4

Activity coefficient, 0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Molality, mol/kg

Pitzer model CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. p. 182 Simoes et al. p. 15

Figure 21. Activity coefficient per molality for CuSO4 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

36

CdSO4

1.0

- 0.8

0.6

0.4

Activity coefficient, 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Molality, mol/kg

Pitzer model CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. p.182 Simoes et al. p. 15

Figure 22. Activity coefficient per molality for CdSO4 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

MgSO4

1.0

0.8 -

0.6

0.4 Activity coefficient, 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Molality, mol/kg

Pitzer model CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. p. 182 Simoes et al. p. 15

Figure 23. Activity coefficient per molality for MgSO4 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

37

NiSO4

1.0

0.8 -

0.6

0.4 Activity coefficient, 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Molality, mol/kg

Pitzer model CRC p. 5-98 to 5-99 at 25°C Kim & Frederick Jr. p. 182 Simoes et al. p. 15

Figure 24. Activity coefficient per molality for NiSO4 at 25 °C (Haynes, 2016-2017; Kim & Frederick Jr., 1988a; Pitzer, 1991; Simoes et al, 2016).

From the results it can be seen that the activity coefficients are very low for 2-2 electrolytes and increasing the molality of the solution does not increase the activity coefficient. Just like 1-2 and 2-1 electrolytes, the behavior of 2-2 electrolytes are very similar to each other. In the figures it can be noted that the behavior of both the Pitzer model parameters and Kim & Frederick Jr. optimized parameter values give similar behaving and consistent results. The simplified model behaves just as well as in the previous chapters.

The results for pure electrolytes indicate that the calculated results are satisfactory and can be used within the molality range, since the calculated values follow the empirical data well.

38

4.2 Mixed Electrolytes

After modeling the pure electrolytes, it was possible to model the mixed electrolytes. The results for mixed electrolytes consist of similar figures as seen in the pure electrolytes part. In the figures it can be noticed that there are three or more values presented. Values for a simple Pitzer model and for the more accurate Pitzer model were calculated as presented in the modelling section.

Modelling of the pure electrolytes provided a base for calculations for mixed electrolytes, because studying the behaviour of pure electrolytes, it can be concluded if the model is working for these substances and therefore, if the model can be used reliable for mixed electrolytes. The Ksp values were for pure electrolytes, therefore, before calculating the solubility of the mixed electrolytes, it was valuable to calculate the pure electrolytes before calculating the mixed electrolytes.

With the calculated values there are presented the experimental values gained from the Stephen & Stephen books. The data obtained from the Stephen & Stephen books were in a table format, and the used table is mentioned in the figure.

39

NaCl-HCl 7.00

6.00

5.00

4.00

3.00

Molality of NaCl mol/kg 2.00

1.00

0.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 Molality of HCl mol/kg

Pitzer parameters Kim & Frederick Jr. p. 182 S&S values from table 964

Figure 25. Solubility of NaCl in the presence of HCl (Kim & Frederick Jr., 1988b; Pitzer, 1991; Stephen & Stephen, 1979).

40

NaCl-HCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of HCl mol/kg

Pitzer 1 Pitzer 2

Figure 26. Comparison of the values gained using Pitzer parameters (Pitzer, 1991).

NaCl-HCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of HCl mol/kg

Kim & Frederick Jr. (1) p. 182 Kim & Frederick Jr. (2) p. 182

Figure 27. Comparison of the parameters presented by Kim & Frederick Jr (Kim & Frederick Jr.; 1988b).

41

NaCl-HCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of HCl mol/kg

Pitzer parameters Kim & Frederick Jr. p. 182

Figure 28. Comparison of the values with two different models (Pitzer, 1991; Kim & Frederick Jr., 1988b).

Table 1. Molalities for NaCl-HCl mixture calculated using both simplified model and more complex model with Kim & Frederick Jr. parameter values and Pitzer values

m (NaCl) kg/mol, Kim & m (NaCl) kg/mol, Kim m (NaCl) kg/mol, m (NaCl) kg/mol, m (HCl), kg/mol Frederick Jr. (1) & Frederick Jr. (2) Pitzer (1) Pitzer (2)

6.24 6.16 6.24 6.16 0.00 5.67 5.59 5.67 5.59 0.50 5.10 5.03 5.11 5.04 1.00 4.55 4.48 4.56 4.50 1.50 4.01 3.95 4.03 3.97 2.00 3.50 3.44 3.52 3.47 2.50 3.01 2.96 3.04 2.98 3.00 2.55 2.51 2.58 2.53 3.50 2.13 2.09 2.16 2.12 4.00 1.75 1.71 1.78 1.74 4.50 1.41 1.38 1.44 1.41 5.00 1.12 1.09 1.15 1.12 5.50 0.88 0.85 0.91 0.88 6.00

42

In figures 26-28 is presented the comparison between different parameters with equation 24 and the simplified model from that equation. The “1” marks the simplified model and “2” marks the more complex equation. The table 1 presents the values gained for both of the parameter types calculated using both of the equations. As seen in the figures 26-28 and table 1, the values do not vary from each other significantly.

LiCl-NaCl 7.00

6.00

5.00

4.00

3.00

Molality of NaCl mol/kg 2.00

1.00

0.00 0.00 5.00 10.00 15.00 20.00 25.00 Molality of LiCl mol/kg

Pitzer 1 Pitzer 2 Kim & Frederick Jr. (1) p. 282 Kim & Frederick Jr. (2) p. 282 S&S table 1409 S&S table 1412

Figure 29. Solubility of NaCl in the presence of LiCl (Kim & Frederick Jr., 1988b; Pitzer, 1991; Stephen & Stephen, 1979).

43

LiCl-NaCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg

1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of LiCl mol/kg

Pitzer 1 Pitzer 2

Figure 30. Comparison of the models using Pitzer parameters (Pitzer, 1991).

LiCl-NaCl 7

6

5

4

3

2 Molality of NaCl mol/kg

1

0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of LiCl mol/kg

Kim & Frederick Jr. (1) p. 282 Kim & Frederick Jr. (2) p. 282

Figure 31. Comparison of the models using Kim & Frederick Jr. parameters (Kim & Frederick Jr., 1988b).

44

LiCl-NaCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg

1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of LiCl mol/kg

Pitzer parameters Kim & Frederick Jr. parameters p. 282

Figure 32. Comparison of the parameters and models (Kim & Frederick Jr.,1988b; Pitzer, 1991).

Table 2. Molalities for LiCl-NaCl mixture calculated using both simplified model and more complex model with Kim & Frederick Jr. parameter values and Pitzer values

45

Figures 29-32 present the calculations for LiCl-NaCl system. Comparing the data to NaCl-HCl, the experimental data does not follow as well in figure 29 as it does in figure 25. The deviation between the calculated data points and empirical points is big, and at some points it exceeds the acceptable error percentage, which in this work is 15 %.

Figures 30-32 presents the values for comparison between the Pitzer parameters and Kim & Frederick Jr. parameters. The behavior is similar to the NaCl-HCl system, since the deviation is much smaller than 15 %. Therefore, it can be said that the simplified model is enough for this electrolyte system.

Table 2 presents the calculated values for the mixture using both of the parameters. These values were gained by calculating the values for both of the models, the simplified and the more complex one, by using the parameters from the Pitzer theory and from the study by Kim & Frederick Jr.

HCl-KCl 6.00

5.00

4.00

3.00

2.00 Molality of KCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of HCl mol/kg

Pitzer 1 Pitzer 2 S&S values from table 995 Kim & Frederick Jr. (1) Kim & Frederick Jr. (2)

Figure 33. Solubility of KCl in the presence of HCl (Kim & Frederick Jr., 1988b; Pitzer, 1991; Stephen & Stephen, 1964).

46

HCl-KCl 6.00

5.00

4.00

3.00

2.00 Molality of KCl mol/kg

1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of HCl mol/kg

Pitzer 1 Pitzer 2

Figure 34. Comparison of the Pitzer parameters (Pitzer, 1991).

HCl-KCl 6.00

5.00

4.00

3.00

2.00 Molality of KCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of HCl mol/kg

Kim & Frederick Jr. (1) Kim & Frederick Jr. (2)

Figure 35. Comparison of the Kim & Frederick Jr. parameters (Kim & Frederick Jr., 1988b).

47

HCl-KCl 6.00

5.00

4.00

3.00

2.00 Molality of KCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of HCl mol/kg

Pitzer parameters Kim & Frederick Jr. parameters

Figure 36. Comparison between the Pitzer and Kim & Frederick Jr. parameters (Kim & Frederick Jr., 1988b; Pitzer, 1991).

Table 3. Molalities for HCl-KCl mixture calculated using both simplified model and more complex model with Kim & Frederick Jr. parameter values and Pitzer values

m (KCl), Kim & m (KCl), Kim & m (KCl) mol/kg, m (KCl) mol/kg, m (HCl), Frederick Jr. 1 Frederick Jr. 2 Pitzer 1 Pitzer 2 mol/kg 4.73 4.77 4.73 4.77 0.00 4.21 4.24 4.21 4.24 0.50 3.70 3.72 3.70 3.72 1.00 3.22 3.23 3.22 3.23 1.50 2.77 2.77 2.76 2.77 2.00 2.35 2.36 2.34 2.34 2.50 1.97 1.96 1.96 1.96 3.00 1.64 1.53 1.63 1.62 3.50 1.35 1.33 1.34 1.32 4.00 1.10 1.09 1.09 1.08 4.50 0.90 0.88 0.89 0.87 5.00 0.73 0.72 0.72 0.71 5.50 0.60 0.58 0.58 0.57 6.00

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Figures 33-36 present the same mixture with and without empirical data compared with calculated values. As seen in figure 33, the empirical and calculated data does not meet, since the empirical data points vary from the calculated values over 15 %.

Figure 34-36 presents the comparison between the simpler and more complex calculations. It can be noted that with this mixture the difference between the two models are negligible. However, since the calculated data points vary drastically compared to the empirical data points, for this electrolyte pair the calculations cannot be said to be good enough.

The table 3 presents the values used in figures 33-36. The table 3 values were gained using both Pitzer parameters and Kim & Frederick Jr. optimized mixing parameters. Both parameters were calculated using the simplified model and the more complex model.

KCl-NaCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of KCl mol/kg

Pitzer 1 Pitzer 2 S&S table 3678 Kim & Frederick Jr. (1) Kim & Frederick Jr. (2)

Figure 37. Solubility of KCl in the presence of NaCl (Kim & Frederick Jr., 1988b; Pitzer, 1991; Stephen & Stephen, 1964).

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KCl-NaCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of KCl mol/kg

Pitzer 1 Pitzer 2

Figure 38. Comparison of the Pitzer parameters (Pitzer 1991).

KCl-NaCl 7

6

5

4

3

2 Molality of NaCl mol/kg

1

0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of KCl mol/kg

Kim & Frederick Jr. (1) Kim & Frederick Jr. (2)

Figure 39. Comparison of the Kim & Frederick Jr. parameters (Kim & Frederick Jr., 1988b).

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KCl-NaCl 7.00

6.00

5.00

4.00

3.00

2.00 Molality of NaCl mol/kg 1.00

0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Molality of KCl mol/kg

Pitzer 1 Pitzer 2 Kim & Frederick Jr. (1) Kim & Frederick Jr. (2)

Figure 40. Comparison between the Pitzer and Kim & Frederick Jr. parameters (Kim & Frederick Jr., 1988b; Pitzer, 1991).

Table 4. Molalities for KCl-NaCl mixture calculated using both simplified model and more complex model with Kim & Frederick Jr. parameter values and Pitzer values

m (NaCl) kg/mol, Kim m (NaCl) kg/mol, Kim m (NaCl) kg/mol, m (NaCl) kg/mol, & Frederick Jr. 1 & Frederick Jr. 2 Pitzer 1 Pitzer 2 m KCl, Pitzer 1 6.24 6.16 6.24 6.16 0.00 5.99 5.91 5.98 5.90 0.50 5.74 5.67 5.71 5.64 1.00 5.50 5.43 5.45 5.39 1.50 5.27 5.20 5.20 5.14 2.00 5.04 4.98 4.95 4.89 2.50 4.82 4.77 4.70 4.65 3.00 4.61 4.57 4.46 4.42 3.50 4.41 4.38 4.22 4.19 4.00 4.22 4.20 3.99 3.97 4.50 4.04 4.03 3.77 3.76 5.00 3.87 3.87 3.55 3.55 5.50 3.71 3.72 3.34 3.36 6.00

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Figures 37-40 presents the behavior of the KCl-NaCl system. In those figures it can be noted that the values do not go linearly but have a change in approximately point 2.5 and 5.5, even though the calculated values behave linearly. Table 4 presents the values gained using the Pitzer parameters and the Kim & Frederick Jr. parameters.

The deviation between Pitzer parameters and the Kim & Frederick Jr. parameters are major, and the Pitzer values are much closer to the empirical data than the Kim & Frederick Jr. values. Since the Pitzer parameters give much more reliable results compared to the empirical data, it can be said that the original Pitzer mixing parameters are more suitable than the optimized parameters.

As stated before, the calculations show that the difference between the simpler and more complex model are rather small, therefore, it can be said that the simpler model works well enough for larger scale. If the need is for smaller and more accurate scale, it is recommended that the more complex calculations are taken into account.

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5 Discussion and Conclusions

One of the main goals of this thesis was to find out, if it is possible to use Pitzer model in order to predict the behavior of the substances for industrial applications, such as preventing the fouling on the bipolar membranes used in electrodialysis or increasing the solubility of the metals from the wastewaters produced in the mining industry. The aim was to calculate and model how the activity of the pure electrolytes changes when the molality is changed, and later use this knowledge in order to model the electrolytes when interfering with other electrolytes and compare the change in the solubility. First, the goal was to study the activity coefficients and Ksp values for pure electrolytes, and then proceed to the mixed electrolytes and the study of solubility of the target substance in presence of other substance.

By analyzing the results gained both from the pure and mixed electrolytes, it was possible to conclude that the model is working and can be used in an industrial scale within the guidelines limiting the use of the Pitzer model. With the mixed electrolytes model, it was possible to predict the behavior, if the molality of one substance in ternary system was changed. However, with some of the cases the deviation between the results was too big, therefore, it can be said that in order to get the precis results and the most reliable results, the use of empirical data points and the optimization of the parameters are crucial points. This thesis focused on ternary systems of aqueous solutions, but the indications gained from the results state that this model can also be used for other solvents and for multicomponent systems, because for multicomponent systems more terms are needed for the calculations to present all of the components in the system. However, adding more terms does not change the accuracy of the model, therefore, it can be used for more complex systems than for ternary systems.

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Pitzer model can be used to predict the behavior of the pure electrolytes regardless on the type of the electrolyte. In the results it can be seen that the calculated values and the experimentally gained values follow each other within a small error range. Since the error is smaller than 15 %, it can be said the model works very well for this purpose.

It can be also noted that the optimized values gained from Kim & Frederick Jr. does have a coherent behavior compared to each other for most of the studied cases. Studying the data from their study to the calculated values and data gained from CRC, it can be said that the optimized model works with wariness. As seen in the results presented for 1-1 electrolytes, the optimized values gave varying results for the electrolytes. However, as seen in the other pure electrolytes, the simplified results were as accurate as the results calculated using the original Pitzer theory parameters. It can be said that the optimized model gives a good idea about the substance, but for more accurate scale the optimized parameter model does not work with expected accuracy.

When using the Pitzer model for predicting the behavior of the substances, it must be taken into account that the principal for the model to work is that the molality does not exceed 6.0 mol/kg (water). If the molality exceeds 6.0 mol/kg (water), the Pitzer model loses its accuracy, as seen in the results in mixed electrolytes. However, for some of the cases the maximum molality, where the Pitzer model work, is much smaller than 6.0 mol/kg (water), which makes the prediction of the behavior more challenging.

The successfulness of simplification can be noticed in figure 25, since for mixed electrolytes both of the used models work within the suitable error range compared to the experimentally gained values. Therefore, it can be concluded that adding more accurate terms make the model more and more reliable, but the model works well enough even with the simple model. However, for industrial scale the more accurate

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calculations are recommended, since in larger scale even the minor changes in impurities might be a huge problem.

If the molalities are relatively low in the industry, the Pitzer model can be used in order to predict the behavior of the chemicals. The model is rather inexpensive way to check and therefore, it is a good tool for chemical auditing for example for plant designing, because it can be done mathematically and not by determine experimentally and running laboratory tests. For example, in bipolar membrane systems it might help to prolong the life of the membrane if the solubility can be increased in order to prevent the sediment formation on the membrane.

The results indicate that the optimization of the parameters is possible, however, it can be noted that the changes were minor compared to the original Pitzer parameters. All of the used models worked within the acceptable error range and the deviation between the all was small. As stated before, the Pitzer model can be used to have an idea about the behavior of the system with the simplified model, as seen with the results gained using the Simoes et al. (2016) parameter values and simplification.

The metal recovery is an important aspect in the future industry both for environmental point of view and industrial needs. The Pitzer model can be used for designing the metal recovery systems, because it can be used as a tool to model what substances could be used in order to increase the solubility of the environmentally hazard metals or those metals the industry is short of. When the solubility is increased, less of the needed substances is lost in the process, and therefore, can be used in further needs more efficient.

Pitzer model has been studied in many researches during the past decades and there are plenty of data of optimized parameters. However, one of the complicating factors is that the empiric data unfortunately has a majority of high molality values for some

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compounds. Since the Pitzer equations work trustworthy with the maximum molality of 6.0 mol/kg (water), the results might not be trustworthy if calculated with the higher molality values. For further studies the optimization process would be good to be done so that the molality would not be the limiting factor, or even to have the same maximum molality for all of the substances the Pitzer theory can be used to.

The second complicating factor is that the values for various substances were for salt hydrates. In the calculations this make them more complex since the salt hydrates must be taken into account in the calculations, therefore, calculations of the activity of the water must be added. Because of the first and second complicating factors, the comparison of the acids and bases, and how they change the solubility of the same substance, was not successful.

The third complicating factor is that the Pitzer parameter values are temperature dependent. If predicting the behavior for certain substance in different temperatures, the calculations must be done with specific parameters in correct temperature. It must be also taken into account that the solubility is also temperature dependent.

The biggest challenge was to find suitable experimental values for the calculations. Since the molalities are rather high for the various data sources, the calculations cannot be made within a satisfying error range. The lacking quantity and quality of the data points give rather narrow point of view for the issue. With larger quantity of suitable data with molality under 6 mol/kg (water), it would be possible to get more variety to the results, and with variety better idea of the behavior of the substance can be obtained. It must be remembered that the more data points there are to compare, the more reliable the results and therefore, the optimization would be.

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Even though Pitzer model has been studied for many decades, there are still many appliances where it could be used. For future work for this topic, studying the impacts of substances with water of crystallization in them. It would be important to know if the calculations could be simplified. The larger study including several empirical measurements in the laboratory would be important as well. The measurements would be critical for substances having a few empirical data for lower molalities, in order to gain enough data for better optimization process. Since the Pitzer model works generally for maximum molality of 6.0 mol/kg (water), the empirical data gathering would be extensive for the better optimization process. These gained data could be saved online data base. The lack of experimental data in various temperatures makes the use of the Pitzer model rather difficult, therefore, impacts the results in a negative way.

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Appendix A. Parameters used in the calculations for pure electrolytes and mixed electrolytes

Appendix B. Pure NaCl 1-1 electrolyte calculations

Appendix C. Pure Li2SO4 1-2 electrolyte calculations

Appendix D. Pure CoCl2 2-1 electrolyte calculations

Appendix E. Pure NiSO4 2-2 electrolyte calculations

Appendix F. Determination of the molality of NaCl by changing the molality of HCl