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Kinetics of selenium and tellurium removal with cuprous ion from copper sulfate-sulfuric acid solution Mokmeli, Mohammad 2014

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  Kinetics of selenium and tellurium removal with cuprous ion from copper sulfate-sulfuric acid solution   by  Mohammad Mokmeli    A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Materials Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)  April 2014    © Mohammad Mokmeli, 2014  ii Abstract  Dissemination of selenium and tellurium in pyritic ores and many of the sulphide minerals results in the contamination of pregnant leach solutions and electrolytes in hydrometallurgical treatment of sulphide ores and residues. In an effort to reduce the detrimental effects of selenium and tellurium, it has been of great interest to remove selenium and tellurium from contaminated solutions to lower levels than allowed in regulations, product specifications or process requirements. The selenium and tellurium content of the solution may be reduced into insoluble precipitates of copper selenides and tellurides using cuprous ion. Cuprous ion has uses as a reducing agent in hydrometallurgical applications and can be specifically used to remove selenium and tellurium ions from copper sulphate-sulfuric acid solutions.  In this study, the chemistry and kinetics of the removal of selenium and tellurium from copper sulfate-sulfuric acid solutions by cuprous ion reduction and precipitation was pursued. At first, a study of equilibrium cuprous concentrations for the cupric–copper metal reaction was performed and an empirical function capable of predicting the saturated [Cu+] was suggested at different temperatures, cupric and sulfuric acid concentrations. Secondly, the kinetics of the selenium removal with cuprous was studied and the mechanism of the reduction reaction and the rate law was determined over a wide range of acidity and temperature. The effects of temperature, acidity, cupric concentration and ionic strength on selenium removal rate were also studied. Subsequently, rate constants as functions of temperature, acidity and ionic strength were suggested. Thirdly, the tellurium reduction chemistry and reaction kinetics by means of cuprous in a wide range of conditions were investigated. The mechanism of the reaction, rate  iii constants and activation energies were also determined. Similarly to selenium, effects of temperature and acidity on tellurium removal rate were also studied and rate constants as a function of temperature and acidity were suggested. Selenium and tellurium reduction reaction times can be estimated at different acidities and temperatures using the suggested rate laws and rate constant functions.                     iv Preface  Much of the work presented in this thesis has been previously published in Hydrometallurgy journal, or is under review for publication or has been presented at the conference. The overall supervision of this research was provided by Dr. Dreisinger and Dr. Wassink.   The experimental apparatus and some of the experimental procedures have been developed by Dr. Wassink. All the testing, data analysis and manuscript writing were conducted by the candidate. All publications were prepared by the candidate and edited by Dr. Dreisinger and Dr. Wassink, prior to submission for publication.  This thesis manuscript is mainly composed of the publications listed below:  Mokmeli M., Wassink B., Dreisinger D. B., (2012), Equilibrium cuprous concentrations in copper sulfate–sulfuric acid solutions containing 50–110 g/L Cu2+ and 10–200 g/L H2SO4 at 50–95 °C, Hydrometallurgy, Volume 121-124, pp. 100–106. Portions of this paper appear in sections 2.1, 3.2 and 4.1.  Mokmeli M., Wassink B., Dreisinger D. B., (2013), Cuprous sulfate thermodynamics and cuprous perchlorate oxidation kinetics, European Metallurgical Conference 2013, Weimar, Germany, pp. 69-84. Portions of this paper appear in sections 1.1, 3.2, 4.1 and 4.2.   v Mokmeli M., Wassink B., Dreisinger D. B., (2013), Kinetics study of selenium removal from copper sulfate-sulfuric acid solution, Hydrometallurgy, Volume 139, pp 13-25. Portions of this paper appear in section 2.2 and chapter 5.  Mokmeli M., Dreisinger D. B., Wassink B., (under consideration), Thermodynamics and kinetics study of tellurium removal with cuprous ion, submitted to Hydrometallurgy journal, September 26, 2013. Parts of this manuscript appear in section 2.3 and chapter 6.   Mokmeli M., Dreisinger D. B., Wassink B., (2014) Fundamental studies in selenium and tellurium removal from copper sulphate-sulphuric acid solutions with application to industrial purification circuits, Hydrometallurgy Conference 22-25 June 2014, Victoria, Canada                  vi Table of Contents Abstract...........................................................................................................................ii Preface ...........................................................................................................................iv Table of Contents ...........................................................................................................vi List of Tables .................................................................................................................ix List of Figures .................................................................................................................x List of Symbols and Abbreviations...............................................................................xiii Acknowledgments........................................................................................................xiv Dedication....................................................................................................................xvi Chapter 1 Introduction .................................................................................................1 1.1 Background......................................................................................................1 1.2 Problem Definition...........................................................................................5 1.3 Objectives of the Research ...............................................................................6 Chapter 2 Chemistry and Kinetics of Cuprous, Selenium and Tellurium.......................7 2.1 Thermodynamics and Kinetics of Cuprous Generation Reaction ......................7 2.2 Selenium Chemistry.......................................................................................12 2.2.1 Selenium Reduction Chemistry and Kinetics ..........................................16 2.2.2 Selenium Reduction Chemistry and Kinetics in Copper Sulfate-Sulfuric Acid Solutions .......................................................................................................19 2.2.3 Chemistry of Cuprous Selenide Reaction with Cupric Ion ......................22 2.3 Tellurium Chemistry......................................................................................25 2.3.1 Tellurium-Copper -Water System...........................................................30 2.3.2 Tellurium Reduction Chemistry and Kinetics .........................................35 2.4 Selenium and Tellurium Removal at VALE (Canada) ....................................40 2.5 Summary .......................................................................................................45 Chapter 3 Experimental..............................................................................................49 3.1 Materials........................................................................................................49 3.2 Experimental Procedures................................................................................50 3.2.1 Generation, Sampling and Analysis of Cuprous Ion................................50 3.2.2 Determination of Equilibrium Cuprous Concentration............................52 3.2.3 Kinetics of Cuprous Oxidation with Perchlorate .....................................54 3.2.4 Kinetics Study of Selenium Reduction ...................................................55 3.2.5 Kinetics Study of Tellurium Reduction...................................................58 3.2.6 Repeatability and Accuracy of the Thermodynamics and Kinetics Experiments...........................................................................................................59 Chapter 4 Cuprous Sulfate Thermodynamics and Cuprous Perchlorate Oxidation Kinetics……….. ...........................................................................................................61 4.1 Equilibrium Cuprous Concentrations in Copper Sulfate-Sulfuric Acid Solutions…................................................................................................................61 4.1.1 Objectives ..............................................................................................61 4.1.2 Experimental..........................................................................................62 4.1.3 Results and Discussion...........................................................................62 4.2 Kinetics of Cuprous Oxidation with Perchlorate.............................................68 4.2.1 Objectives ..............................................................................................68 4.2.2 Experimental..........................................................................................69 4.2.3 Results and Discussion...........................................................................69  vii 4.3 Summary .......................................................................................................75 Chapter 5 Kinetics Study of Selenium Removal from Copper Sulfate-Sulfuric Acid Solutions…. ..................................................................................................................77 5.1 Objectives......................................................................................................77 5.2 Experimental..................................................................................................77 5.2.1 Stoichiometry of the Reduction of Biselenate with Cuprous ...................78 5.2.2 Verification of the Rate Law at Constant Acidity, Temperature and Ionic Strength…… .........................................................................................................78 5.2.3 Cuprous Selenide Reaction with Cupric..................................................78 5.2.4 Effect of Acidity, Temperature, Cupric Concentration and Ionic Strength on Selenium Removal Rate....................................................................................79 5.3 Results and Discussion...................................................................................81 5.3.1 General Rate Law Based on Suggested Mechanism................................81 5.3.2 Cuprous Selenide Reaction with Cupric..................................................86 5.3.3 Stoichiometry of the Reduction of Biselenate .........................................88 5.3.4 Verification of the Rate Law at Constant Acidity, Temperature and Ionic Strength… .............................................................................................................89 5.3.5 Effect of Acidity on Rate Constants and Rate Law ...............................100 5.3.6 Effect of Temperature on Selenium Rate of Removal with Cuprous .....106 5.3.7 Cupric Sulfate Concentration Effect on Rate Constants ........................109 5.3.8 Effect of Ionic Strength on Selenium Removal Rate .............................111 5.4 Summary .....................................................................................................116 Chapter 6 Thermodynamics and Kinetics Study of Tellurium Removal with Cuprous Ion…………. ..............................................................................................................121 6.1 Objectives....................................................................................................121 6.2 Experimental................................................................................................121 6.2.1 Cuprous Telluride Reaction with Cupric...............................................122 6.2.2 Stoichiometry of the Reduction of Tellurate/Tellurite with Cuprous .....123 6.2.3 Investigation of the Reaction Order as a Function of Acidity and Temperature ........................................................................................................123 6.2.4 Verification of the Rate Law ................................................................124 6.2.5 Effect of Acidity and Temperature on Tellurium Removal Rate ...........124 6.3 Results and Discussion.................................................................................125 6.3.1 Stoichiometry of the Reduction of Tellurate with Cuprous ...................125 6.3.2 Reaction Order of TeVI Reduction with Cu+ as a Function of Acidity and Temperature ........................................................................................................126 6.3.3 Kinetics Study of TeIV reduction with Cuprous.....................................130 6.3.4 Coupled Reduction of TeVI and TeIV with Cuprous...............................134 6.3.5 Mechanism of TeVI Reduction and General Rate Law...........................138 6.3.5.1 Verification of the Rate Law at Constant Acidity and Temperature ......142 6.3.6 Effect of Acidity on Rate Constant and Rate Law.................................145 6.3.7 Effect of Temperature on Tellurium Rate of Removal ..........................147 6.3.8 Selenium and Tellurium Species Rate of Reduction..............................150 6.4 Summary .....................................................................................................151 Chapter 7 Conclusions and Recommendations .........................................................154 7.1 Industrial Applications of the Findings.........................................................160  viii 7.2 Recommendations for Future Work..............................................................166 References...................................................................................................................168 Appendices..................................................................................................................179 Appendix 1: Thermodynamic data used to draw Se-Cu-H2O Eh-pH diagrams. ............179 Appendix 2: Thermodynamic data used to draw Te-Cu-H2O Eh-pH diagrams. ............180 Appendix 3: Te-Cu-H2O Eh-pH diagram activity of Te ions = 0.01 and 1 M ...............181 Appendix 4: Cupric sulfate-sulfuric acid solution densities..........................................182 Appendix 5: Cuprous concentrations in molal units for initial CuSO4/H2SO4 concentrations. ............................................................................................................187 Appendix 6: General kinetics equation for reduction of SeVI and TeVI based on mechanism 2 ...............................................................................................................188                          ix List of Tables Table  2-1: Selenium oxidation states. ............................................................................13 Table  2-2: CuxSe standard Gibbs free energy data.........................................................23 Table  2-3: CuxSe thermodynamic data at 25°C and 95°C. .............................................24 Table  2-4: Tellurium oxidation states. ...........................................................................26 Table  2-5: Cu-TeIV thermodynamic data. Criss Cobble method was used to calculate higher temperature data for Cu-H2O ionic species. ........................................................31 Table  2-6: Average concentration of species in Se-Te removal circuit (Qin, 2005). .......43 Table  4-1: Cuprous concentrations in g/L units for initial CuSO4/H2SO4 concentrations.......................................................................................................................................63 Table  4-2: Constants for equation ( 4-2) used to estimate cuprous concentrations. ..........65 Table  4-3: Cuprous oxidation rate constants with first order rate law assumption at different sodium perchlorate and initial cuprous concentration.......................................72 Table  4-4: Cuprous oxidation rate constant with nominal ionic strength, HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C..............................................................................................73 Table  5-1: Verification of suggested rate law at different initial cuprous and selenate concentrations at T = 95.1 ± 0.1°C, [H2SO4] = 100 g/L, [Cu2+] = 50 g/L........................91 Table  5-2: rate constants at different cupric concentrations at I = 6 molal, T = 95.1°C, [H2SO4] = 50 g/kg solution............................................................................................92 Table  5-3: Rate constants at different acidities at 95.1°C and 86.2°C and [Cu2+] = 50 g/L in sulphuric acid solution.............................................................................................100 Table  5-4: Rate constants at different acidities at 95.1°C and [Cu2+] = 50 g/L in perchlorate medium at I = 4.35 molal. .........................................................................104 Table  5-5: k1 and k-1/k2 values at different temperatures, Cu2+ = 75 g/L and H2SO4 = 100. g/L ..............................................................................................................................106 Table  5-6: k1 and k-1/k2 values for different cupric concentrations at T = 95.2°C and H2SO4 = 100 g/L. ........................................................................................................109 Table  5-7: Selenate reduction rate constant with nominal ionic strength, HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C............................................................................................112 Table  5-8: Biselenate reduction rate constant by addition of sulphate salts, T = 95.1 °C.....................................................................................................................................116 Table  6-1: Verification of suggested rate law at different initial cuprous and tellurate concentrations at T = 95.2 °C, [H2SO4] = 50 g/L, [Cu2+] = 50 g/L. ..............................143 Table  6-2: Rate constants at different acidities at 95.2 °C and [Cu2+] = 50 g/L.............145 Table  6-3: k1 values at different temperatures, Cu2+ = 50 g/L and H2SO4 = 50 g/L.....148         x List of Figures Figure  1-1: Thermodynamic possibility of reduction of selenium and tellurium species with different reducing agents at pH = 0, [Se] = 10-3 M, [Te] = 3×10-4 M, T = 25°C, P SO2 = 1atm, total sulphate = 1 M.....................................................................................3 Figure  2-1: Stable range of Se, Te, Fe oxidation states at pH = 0.5, [Se] =10-3 M, [Te] = 3×10-4 M, T = 100°C. ......................................................................................................9 Figure  2-2: Eh-pH diagram for the Se-H2O system with activity of selenium ions = 10-3 M, P = 1atm, 25°C.........................................................................................................14 Figure  2-3: Se-Cu-H2O Eh-pH diagram with activity of selenium ions = 10-3 M and activity of Cu ions = 0.8 M, 100°C. ...............................................................................15 Figure  2-4: Eh-pH diagram for the Te-H2O system with activity of Te ions = 3×10-4 M, P = 1atm, 25°C. ................................................................................................................27 Figure  2-5: Influence of pH on the solubility of TeO2 at 25°C. × Kasarnowsky`s experimental values (Deltombe et al., 1956). .................................................................30 Figure  2-6: Te-Cu-H2O Eh-pH diagram with activity of Te ions = 3×10-4 M and activity of Cu ions = 0.8 M, 25°C...............................................................................................32 Figure  2-7: Te-Cu-H2O Eh-pH diagram with activity of Te ions = 3×10-4 M and activity of Cu ions = 0.8 M, 100°C.............................................................................................33 Figure  2-8: Superimposed Eh-pH diagram of Se-Cu-H2O and Te-Cu-H2O at 100°C and ionic activates of Se = 10-3 M and Te = 3×10-4 M. .........................................................43 Figure  2-9: Selenium and tellurium removal circuit at VALE-Canada. ..........................44 Figure  3-1: Schematic illustration of the experimental apparatus. ..................................51 Figure  4-1: Measured cuprous concentrations as a function of temperature for varying [Cu2+] and 100 g/L H2SO4 at specified initial temperatures, fitted to the empirical correlation of equation ( 4-2). .........................................................................................66 Figure  4-2: Effect of acidity on cuprous concentration as a function of temperature for (A): [Cu2+] = 50 g/L and (B): [Cu2+] = 110 g/L, fitted to the empirical correlation of equation ( 4-2)................................................................................................................67 Figure  4-3: Cuprous concentration in sulphate and perchlorate media versus time, Cu2+ = 50 g/L, H2SO4 and HClO4 = 100 g/L, T = 95.1°C. .........................................................70 Figure  4-4: log [Cu+] vs. voltage (vs. Cu/Cu2+) and calibration equations for Cu+ oxidation reactions with perchlorate species at 0, 2 and 3 molar NaClO4 and different [Cu+]0. (HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1°C). ....................................................71 Figure  4-5: Comparison of calculated and experimental cuprous concentrations with time at 0, 1, 2 and 3 M NaClO4 concentration  and HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1°C.......................................................................................................................................73 Figure  4-6: Rate constant k1 as a function of solution nominal ionic strength at HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C (Table  4-4)...............................................................74 Figure  5-1: Cuprous selenide dissociation reaction equilibrium at T = 98.6°C and Cu2+ = 90 g/L. Portions of Cu2Se were added to the CuSO4/H2SO4 solution at indicated times..87 Figure  5-2: Stoichiometry of the reduction of biselenate with cuprous at T = 95.1°C. ....88 Figure  5-3: Pseudo first order kinetics of biselenate reduction at nearly constant cuprous concentration, [Cu+]0 = 0.017M , [SeVI]0 = 0.00015M at 95.1°C. ...................................90 Figure  5-4: Suggested general rate law validation plot: 1/[Cu+] + A× (ln C+[Cu+]/[Cu+]) with time at [Cu+]0 = 0.014M and [SeVI]0 = 0.028M at 95.1°C. ......................................91  xi Figure  5-5: Cell voltage vs. Cu/Cu2+ reference electrode with time for kinetics test with [Cu+]0 = 0.014M and [SeVI] = 0.028M, T = 95.1°C........................................................93 Figure  5-6: log [Cu+] vs. voltage (vs. Cu/Cu2+) and calibration equation for kinetics test with [Cu+]0 = 0.014M and [SeVI] = 0.028M, T = 95.1°C. ...............................................94 Figure  5-7: Plot of a/[Cu+] – ln[Cu+] vs time for [Cu+]0 = 0.0141 M and [SeVI] = 0.0281 M, T = 95.1°C. ..............................................................................................................95 Figure  5-8: Comparison of calculated and experimental cuprous and biselenate concentrations with time for kinetics test with [Cu+]0 = 0.014M and [SeVI] = 0.028M T = 95.1°C. ..........................................................................................................................96 Figure  5-9: Comparison of calculated and experimental cuprous and biselenate conc. with time for kinetics test with [Cu+]0 = 0.017 M and [SeVI] = 0.00015 M T = 95.1°C...........97 Figure  5-10: Deviation of kinetics data from a simple second order rate law at low [Cu+]. f([Cu+]) =  ++++++−][][ln][1][221CuCuCACukCuk and ][][ln+++CuCuC for general rate law and second order rate law, respectively at [Cu+]0 = 0.0075 M, [SeVI] = 0.0023 M,          95.1 ± 0.1°C, [H2SO4] = 100 g/L and [Cu2+] = 50 g/L....................................................99 Figure  5-11: Effect of acidity on cuprous concentration with time on the biselenate removal reaction ([Cu+]0= 0.015, [Cu+]final = 0.00005 M, [SeVI]0 = 0.03M) at 95.1°C. Details of the first 1.5 hours are shown in the insert.....................................................101 Figure  5-12: Effect of acidity on cuprous concentration with time on the biselenate removal reaction ([Cu+]0= 0.0125, [Cu+]final = 0.00005 M, [SeVI]0 = 0.025 M) at 86.2 °C. The data points are shown along with the model fit of the suggested rate law. .............102 Figure  5-13: power law relationship between rate constant and sulfuric acid concentration at T=95.1 °C (k1 = 0.00581 [H2SO4]1.25 (M-1s-1))..........................................................103 Figure  5-14: power law relationship between rate constant and sulfuric acid concentration at T = 86.2 °C (k1= 0.00301[H2SO4]1.21 (M-1s-1)). ........................................................103 Figure  5-15: power law relationship between rate constant and perchloric acid concentration at T = 95.1°C and I = 4.35 (k1 = 0.0159 [H+]0.9). ....................................105 Figure  5-16: Effect of temperature on cuprous concentration with time on biselenate removal rate ([Cu+] initial = 0.015, [SeVI]initial = 0.03M) at Cu2+ =75 g/L and H2SO4 = 100 g/L. The curves are calculated based on the proposed rate law.....................................107 Figure  5-17: Activation energy and prefactor values for k1 at Cu2+ = 75 g/L and H2SO4 = 100 g/L........................................................................................................................107 Figure  5-18: Activation energy and prefactor values for k-1/k2 at Cu2+ = 75 g/L and H2SO4 = 100 g/L. ........................................................................................................109 Figure  5-19: Effect of cupric concentration on cuprous concentration with time on biselenate removal rate ([Cu+]initial = 0.015, [SeVI]initial = 0.03M) at [H2SO4] = 100 g/L and T= 95.1 °C. The data points are shown along with the model fit of the suggested rate law. Details of the first 0.5 hour are shown in the insert. .....................................................110 Figure  5-20: Comparison of calculated and experimental cuprous concentrations with time for HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C. ..................................................113 Figure  5-21: Rate constant k1 as a function of solution nominal ionic strength at HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C (Table  5-7).............................................................114 Figure  6-1: Stoichiometry of the reduction of tellurate with cuprous at T = 95.1°C and [H2SO4] = 50 g/L.........................................................................................................125  xii Figure  6-2: Cuprous reaction order in reduction of TeVI with cuprous ion at T = 95.2°C and Cu2+ = 50 g/L, [H2SO4] = 10, 50 g/L, [Cu+]0 = 0.005M , [TeVI]0 = 0.003 M...........126 Figure  6-3: Tellurium reaction order in reduction of TeVI with cuprous ion at T = 95.2°C and Cu2+ = 50 g/L, [H2SO4] = 10, 50 g/L, [Cu+]0 = 0.0174 M, [Cu+]f = 0.0161 M........127 Figure  6-4: Cuprous reaction order in reduction of TeVI with cuprous ion as a function of temperature at Cu2+ = 50 g/L, [H2SO4] = 50 g/L, ([Cu+]0 = 0.0153 M , [TeVI]0 = 0.030 M at T = 95.1°C), ([Cu+]0 = 0.0126 M , [TeVI]0 = 0.025 M at T =86.1°C), ([Cu+]0 = 0.0081 M , [TeVI]0 = 0.016 M at T =75.1°C) . .........................................................................128 Figure  6-5: [Cu+] with time in reduction of TeIV and TeVI with cuprous ion at T = 95.1°C and Cu2+ = 50 g/L. Lines are representing the continuous cuprous concentration calibrated and calculated based on the solution voltage and data points are analysed cuprous concentration. Details of the first 3 hours are shown in the insert....................129 Figure  6-6: Stoichiometry of the reduction of TeIV with cuprous at T = 95.1°C, Cu2+ = 50 g/L and [H2SO4] = 50 g/L............................................................................................131 Figure  6-7: Cuprous reaction order in reduction of TeIV with cuprous ion at T = 95.1 °C and Cu2+ = 50 g/L, [H2SO4] = 50 g/L, [Cu+]0 = 0.0180 M , [TeIV]0 = 0.030 M. ............132 Figure  6-8: Tellurium reaction order in reduction of TeIV with cuprous ion at T = 95.1 °C and Cu2+ = 50 g/L, [H2SO4] = 50 g/L, [Cu+]0 = 0.0177 M, [TeIV]0 = 0.0004 M. ...........133 Figure  6-9: Calculated TeVI, TeIV and Cu2Te concentration with time for kinetics test with [Cu+]0 = 0.0172 M and [TeVI]0 = 0.000137 M (17.5) ppm at T = 95.1°C. .....................136 Figure  6-10: Comparison of calculated and experimental tellurium concentrations with time for kinetics test with [Cu+]0 = 0.0172 M and [TeVI]0 = 0.000137 M at T = 95.1°C.....................................................................................................................................137 Figure  6-11: Comparison of calculated and experimental tellurium reaction order in reduction of TeVI with cuprous ion at [Cu+]0 = 0.0172 M and [TeVI]0 = 0.000137 M at T = 95.1°C. ........................................................................................................................138 Figure  6-12: Comparison of calculated and experimental cuprous and tellurium concentrations with time for kinetics test with [Cu+]0 = 0.016 M and [Te6+]0 = 0.001M, H2SO4 = 50 g/L, Cu2+  = 50 g/L, T = 95.2°C................................................................144 Figure  6-13: Effect of acidity on cuprous concentration with time on tellurium removal reaction at 95.2 °C. Lines are representing the suggested rate law and data points are analysed cuprous concentration. ..................................................................................146 Figure  6-14: power law relationship between rate constant and sulfuric acid concentration at T= 95.2 and low and high acidity range: (k1 = 0.0297×[H2SO4]1.35 at 10 g/L < [H2SO4] < 100 g/L.....................................................................................................................147 Figure  6-15: Effect of temperature on cuprous concentration with time on tellurium removal rate at H2SO4 = 50 g/L and Cu2+ = 50 g/L. Lines are representing the suggested rate law and data points are analysed cuprous concentration. .......................................148 Figure  6-16: Activation energy and prefactor values for k1 at H+ = 50 g/L and Cu2+ = 50 g/L. .............................................................................................................................149 Figure  6-17: Cuprous concentration depletion in reaction with SeIV, SeVI, TeIV and TeVI at [H2SO4] = 100 g/L, [Cu2+] = 50 g/L and T = 95.1°C. Points are analyzed [Cu+] and lines represent [Cu+] as determined by potentiometry. .........................................................150    xiii List of Symbols and Abbreviations  Symbols  A Prefactor in Arrhenius equation E0 Standard reduction potential E Reduction potential  Ea Activation energy ∆E Potential difference F Faraday’s constant (96485 C/mol) g Gram ∆G0 Standard Gibbs free energy ∆G0f Standard Gibbs free energy of formation ∆G0 Gibbs free energy hr Hour ∆H°rxn,298  Standard heat of reaction ∆H°f 298 Standard heat of formation I Ionic strength k  Rate constant k0 Rate constant at infinite dilution K  Equilibrium constant Ksp Solubility product constant L Litre m Molality M Molarity MΩ Megaohm [M]0 Initla concentration of M  N Normality P Pressure pKa Acid dissociation constant psi Pressure (pound force) per square inch R Ideal gas constant s Second  S°298 Standard molar entropy  ∆S° 298 Entropy change at standard conditions t Time T Temperature (K or °C) V Volt zA charge of ion A [electron charge units]  Abbreviations  EPA Environmental Protection Agency ICP-MS Inductively Coupled Plasma-Mass Spectrometry  SHE Standard Hydrogen Electrode  xiv Acknowledgments  I would like to gratefully acknowledge my supervisor, Dr. David Dreisinger and my co-supervisor Dr. Berend Wassink for their guidance, constant support and advice. It has been an honor to be their student. I would also like to thank Dr. Wassink for all his help in the lab and countless hours of discussion.  I wish to thank VALE Canada for their financial support of this project. Many thanks are due to Timothy Le Roy, who helped me on analyzing selenium and tellurium samples.  I wish to thank all my colleagues and friends in the Hydrometallurgy lab and the Materials Engineering Department who made my time here enjoyable and enriched learning environment. I am especially grateful to Renaud Daenzer, Alexander Burns and Bethan Mckevitt.   دو    	     دو   از ا                                                                                                                                                                                                                              و اب       م   ا         ! #ّ $ن      '&ر)    * +, ل و  ?< =>    د;:9 45678  از 23 01. دارم و از /.د-رA B را CD E FGH8و  IJKم و اJLM N.O   ّP QRST وU رV ا$ از  WXاJY و  WXZ[  <= ات]^_ +`ab .defgh بiار jkl رmno * Jpi  qrs و Jteو    ا  B    uv9  رwx 9       ازyz{|     ید   JKر~ .  ]/ €‚ƒ ض… †     زi    JK†                                                                                                                                                                                                                                                                                                                                                            <‡Sˆ *    را    <‰Š‹ +ŒŽ <                     <‘J’“” .•†   $روز    uvر B                                                                                                                                                                                                                                                                                                                                                          JL–      <‰ ن دaXو رV     xv <= +Œ—˜h ™U š رم›œ   J   رŸ>  و 01. ž’رت[      B   ن  یدi ¡ ن  یرانt¢ل  و م دوJ›£  ن  وi¤£   ¥M م * :   ن§ Jteاق اU ل©¥ J” B .O  †      دو     و                                                                                                                                                                                                                                            ª©¥ 9« ن ¬ن§  W­L®¯£   ین و ±°$ روز-رانL²~ اقU * ³وت    ~ن B  9´€µ ار1نJو     دی     dM… +¶·ا de¸¹   Qº»S¼ dM½¾ و  ¿À0† و        <ÁÂ9« B     ر1نtÃÄ ÅÆ  و روان Çb:  9´È£ <É  +`tÊ£  *     $رËs B   ،ق—Íو ا   ÎÏ 	      رV   Ðرا   ! 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"#$ $دم از †%.اœ â *                                           NوJKا   Zا +&Ã'( اران  ی از   دل)  $J*  QRS+­ $ ¡ روز-ران B  â  ان /.د  ,9ون >                                                                                                                                                                                                                                                                              دل-  Zروز-ران    ا B    JKاوJ. س/¢  <É  tÊ£     ا    راû  *     Qé£   و    او  از    $ B   او .    xvi Dedication                   To my lovely wife, Somayeh           And          My adorable children, Negar and Mohammad Ali       1 Chapter 1 Introduction  1.1 Background  The presence of selenium and tellurium in base metal sulphide minerals contained in  copper-sulphide ores and concentrates and the pyrometallurgical products of the treatment of sulphide ores and residues results in down-stream contamination of leach solutions and electrolytes in hydrometallurgical treatment of these materials (Zigaro et al., 1974). It was reported that 40-60 percent of the selenium and 30 to 40 percent of the tellurium in copper matte smelting find their way into the blister copper and finally to the copper anode slimes (Cooper, 1971 and Zigaro et al., 1974). Anode slimes usually contain copper, nickel, selenium, tellurium, gold, silver and trace amounts of platinum group metals. The copper, selenium and tellurium content of the slime may vary from 3-35, 0.6-18 and 0.5 to 8 percent respectively (Morrison, 1963). Copper, selenium and tellurium need to be separated from the slimes prior to precious metal extraction. In most cases, copper and nickel are removed by oxidation and sulphuric acid leaching (Morrison, 1963). The selenium and tellurium content of the copper sulphide residues and copper anode slimes dissolves in the form of SeIV/VI and TeIV/VI species during acid pressure oxidation leaching resulting in a contaminated copper sulphate solution (Qin, 2005 and Morrison 1963). Selenium and tellurium must be removed from the leach solution before copper electrowinning to prevent contamination of the copper cathode. Contamination of copper metal by selenium and tellurium adversely affects the physical properties of electroplated copper (Cooper, 1985). Selenium and tellurium can have marked deleterious effects on annealability and the recrystalization temperature of electrorefined  2 copper. For instance, wire-bars produced from cathodes with selenium content between 6 to 10 ppm contained cracks (Charles et al., 1970). Tellurium has a greater adverse effect on annealability of copper than selenium. The detrimental effect on the annealability of copper metal is increasingly affected by the following elements in the order of: tellurium > selenium > bismuth > antimony > arsenic (Braun et al., 1976). Therefore, the total combined concentration of tellurium, selenium and bismuth must be kept to less than 3 ppm in grade 1 Electrolytic Copper Cathode (ASTM B115-00, 2004) and accordingly must be maintained much lower than 1 mg/L in the electrowinning electrolyte. In addition to being harmful impurities in copper cathode, selenium and tellurium are valuable by-products of electrolytic copper refining and anode slimes that may be recovered. It is thus of interest to investigate effective methods to extract selenium and tellurium from the copper bearing solutions prior to copper metal recovery.  Copper metal or cuprous ion may be used to remove impurities in higher oxidation states such as SeVI, TeVI, SeIV and TeIV from solutions containing cupric ion. In addition to copper metal and cuprous ion, metals with reduction potentials below those of SeVI/IV and TeVI/IV or SeIV/0 and TeIV/0 couples may also have the thermodynamic possibility of reducing selenate/selenite and tellurate/tellurite to elemental selenium/tellurium or selenide/telluride. The stability region of selenium and tellurium species as a function of solution potential at pH = 0, [Se] = 10-3 M, [Te] = 3×10-4 M and T = 25°C are shown in Figure  1-1. According to the graph, the Fe2+/Fe3+ couple can only reduce SeVI/TeVI to SeIV/TeIV. However, the couples Cu/Cu2+, Cu+/Cu2+ and SO2/HSO4- have the thermodynamic ability to reduce selenate/selenite and tellurate/tellurite to elemental  3 selenium/tellurium, and the base metal couples Fe/Fe2+, Ni/Ni2+ and Zn/Zn2+ can further reduce elemental selenium/tellurium to hydrogen selenide/telluride.   SO2/HSO4- Cu/Cu2+ H2SeO3 HSeO4- 1.5 1.0 0.5 0.0 -0.50 Eh (V) Se H2Se Cu+/Cu2+ Fe2+/Fe3+ Fe/Fe2+ Ni/Ni2+  Oxidation half reactions: Zn/Zn 2+  Stability region of Se and Te species at pH = 0 H6TeO6 TeO(OH)+ Te H2Te  Figure  1-1: Thermodynamic possibility of reduction of selenium and tellurium species with different reducing agents at pH = 0, [Se] = 10-3 M, [Te] = 3×10-4 M, T = 25°C, P SO2 = 1atm, total sulphate = 1 M.  Nevertheless, in cupric-bearing solutions, couples with electrochemical potentials below that of the cupric-copper couple will precipitate the copper as well. It was also shown by Ladriere (1973) that copper metal does not directly reduce SeVI species to SeIV but cuprous ion does. Distinct advantages of using cuprous as a reducing agent rather than using metals such as Fe, Co, Ni, Zn and sulfur dioxide gas are as follows:  4 Cuprous ion adds no impurities to copper EW electrolytes (the only soluble reactant and final product is cupric ion) while other metals as reductants would dissolve to their respective metal ions. The reduction of selenium and tellurium ions with cuprous is an environmentally cleaner process whereas SO2 gas may result in contamination of the workplace (Stewart et al., 1985). The precipitation of SeVI and TeVI with sulfur dioxide requires an autoclave and is favoured at low acidity, while SeIV/VI and TeIV/VI reduction reactions are favoured at high acidities. In contrast with SO2 gas, the reduction reaction with cuprous effectively occurs at low pH (refined solution may transfer to copper electrowinning tank house without further acidity adjustment), atmospheric pressure and low temperature. The disadvantages of using cuprous are the slow reaction kinetics for reduction of SeVI and TeVI with cuprous, the high air sensitivity of cuprous and the low saturated concentrations of cuprous in solution. Vale’s CRED plant in Sudbury, Canada (Stewart et al., 1985),  Naoshima’s smelter and refinery in Kagawa, Japan (Shibasaki et al., 1991), Freeport’s refinery in El Paso, USA (Wang et al., 2003) and the Luilu metallurgical plant in Katanga, Congo (Charles et al., 1970) are examples of industrial plants where a process of selenium and tellurium removal in the presence of copper metal (cuprous ion) from acidic copper sulphate solution are practiced. The Luilu plant (Katanga mining), as the world’s largest cobalt producer, had the first published use of cuprous to remove selenium and tellurium form electrolyte solution. Considering the advantages of cuprous and the reduction of reagent costs, usage of sulphur dioxide has been replaced with cuprous in the selenium and tellurium removal circuit at the Copper Refinery Electrowinning Department (CRED) plant of Vale (Canada) since 1976. Since then, Vale uses cuprous sulfate to remove selenium and  5 tellurium impurities from copper sulfate-sulfuric acid electrolyte prior to electrowinning. Selenium and tellurium removal from copper solutions has been practiced by contact with metallic copper in a fixed bed reactor followed by a solution ageing step (Stewart et al., 1985). High pressure oxidative leaching of a copper sulfide residue at the Vale Sudbury facility dissolves the selenium content of the residue in the form of SeIV/VI and TeIV/VI species into the electrolyte (Qin, 2005). The SeIV/VI and TeIV/VI species are reduced in the presence of copper metal to form insoluble copper selenides/tellurides. Cuprous is generated by contacting the electrolyte with copper metal at a temperature between 95-99°C and sulphuric acid concentration of 125 g/L (Stewart et al., 1985). Copper is recovered by electrowinning after selenium and tellurium removal from the leach solution. An environmentally clean process and minimal introduction of impurities into process streams are the main advantages of this process. On the other hand, a long reaction time is the drawback of the process (12-23 hours for a typical processing rate of 150 to 450 L/min).  1.2 Problem Definition  Selenium and tellurium must be removed from the cupric electrolyte before copper electrowinning and be kept below 1 mg/L in the electrolyte. Cuprous ion is industrially used as a reducing agent to remove selenium and tellurium ions from copper sulphate-sulfuric acid solutions as it is advantageous over other reducing reagents. However, the removal rate of selenium and tellurium by cuprous ion reduction and precipitation is slow. Kinetics of the reduction of selenium and tellurium with cuprous and removal rate  6 enhancing factors are not well known. The slow kinetics of selenium and tellurium removal from cupric bearing electrolytes results in a long processing time before electrowinning. This could lead to a decline in the annual production rate of copper metal and precious metals from solution and precipitates, respectively.   1.3 Objectives of the Research  The objective of this research is to provide a better understanding of the selenium and tellurium reduction chemistry and reaction kinetics. This can lead to a more efficient process. Knowing the selenium and tellurium reduction kinetics with cuprous facilitates the optimization of the residence time. This is an important consideration in the design and economics of the removal process to achieve the desired selenium and tellurium concentrations.   In this study, the chemistry and kinetics of selenium and tellurium removal by cuprous ion precipitation and the effects of acidity, cupric concentration, temperature and ionic strength on the removal rate were investigated.          7 Chapter 2 Chemistry and Kinetics of Cuprous, Selenium and Tellurium  2.1 Thermodynamics and Kinetics of Cuprous Generation Reaction  Cuprous is an important oxidation state of copper which is of interest both in the area of fundamental chemistry and industry. Cuprous ion may be generated in the presence of a cupric salt and copper metal. Aqueous cuprous ion has uses as a reducing agent in hydrometallurgical applications such as leaching of ores (Hyvärinen et al., 2005) or scraps (Oishi et al., 2007) or in purification processes (Stewart et al., 1985 and Shaw et al., 2006). Certain ligands of cuprous salts (chloride, halides, cyanide) have useful applications in industry due to their property to form stable coordination compounds of cuprous, enhancing its solubility (Parker et al., 1977).  Cuprous ion in sulfate or chloride media have been studied and used in the leaching of chalcopyrite concentrates by reducing it to chalcocite (Avraamides et al., 1980). The Outokumpu Hydrocopper process is an industrial example of chloride leaching of copper concentrate (Hyvärinen et al., 2005). Cuprous is also generated in either fabrication or recycling of electronic printed circuit boards. Copper in the waste may dissolve as cuprous ammine complexes and metallic copper is then electrowon from the solution with 2-4 times lower power consumption than conventional cupric-sulfuric acid electrowinning (Oishi et al., 2007). Electrowinning of cuprous ion has been studied widely due to the low theoretical decomposition voltage of copper metal from monovalent state. Some preliminary investigations have been conducted to electrorefine copper using acid cuprous sulfate solutions containing organic nitriles (Muir et al. 1975).   8 Cuprous may be used to remove impurities in higher oxidation states such as SeVI, TeVI, SeIV, TeIV from solutions containing cupric ion. In highly acidic solutions (0 < pH < 2) inorganic SeVI, SeIV, TeVI and TeIV mainly exists as biselenate (HSeO4-), selenious acid (H2SeO3), telluric acid (H6TeO6) and telluryl ion (TeO(OH)+), respectively. Cuprous ion may react with SeIV/VI and TeIV,VI in acidic solution and form cuprous selenide/telluride according to following overall reactions:  HSeO4- + 10Cu+ + 7H+ = Cu2Se + 8Cu2+ + 4H2O                                                         ( 2-1)   H2SeO3 + 8Cu+ + 4H+ = Cu2Se + 6Cu2+ + 3H2O                                                           ( 2-2) H6TeO6 + 10Cu+ + 6H+ = Cu2Te + 8Cu2+ + 6H2O                                                        ( 2-3) TeO(OH)+ + 8Cu+ + 3H+ = Cu2Te + 6Cu2+ + 2H2O                                                      ( 2-4)  The distinct advantages of using cuprous generated by reaction between cupric salts and copper metal for removal of selenium and tellurium are that it is an environmentally clean process and it adds no impurities to copper EW electrolytes; the only soluble reactant and final product is cupric ion. Industrially, cuprous is generated by contacting the electrolyte with copper metal at temperature near 100°C (Stewart et al., 1985). Cuprous sulfate solutions have also been applied to strip ferric ion from phosphonic acid ion exchange resins, which are used to purify copper sulfate-sulfuric acid electrowinning electrolytes in a technology that has been commercialized by Fenix Hydromet of Australia (Shaw et al., 2006). Ferric ion loads strongly onto the resin and cannot be displaced by conventional acid stripping. However, cuprous readily reduces ferric to ferrous, which in turn can be readily displaced from the functional group by acid at temperatures of up to 85°C. The  9 thermodynamic basis for Vale’s selenium and tellurium purification circuit and Fenix Hydromet’s ferric removal process at low pH and high temperature is depicted in Figure  2-1. The standard reduction potential for the Cu2+/Cu+ couple was estimated to be 0.26 V at 100°C using the Criss-Cobble method (Criss et al., 1964).            Figure  2-1: Stable range of Se, Te, Fe oxidation states at pH = 0.5, [Se] =10-3 M, [Te] = 3×10-4 M, T = 100°C.  According to the graph, the oxidation of cuprous to cupric can thermodynamically reduce SeIV/VI and TeIV/VI species and ferric ion to form copper selenide and copper telluride and ferrous ion (∆E > 0), respectively. However, the possibility of using cuprous to reduce SeIV/VI and TeIV/VI in a copper sulfate-sulfuric acid solution must be studied further, particularly the reaction kinetics.   TeO(OH)+ → Cu2Te  H2SeO3 → Se HSeO4-→ H2SeO3 0.86 1.07 1.5 1.0 0.5 E/V Cu+ → Cu2+ Reduction Half Reaction Oxidation Half Reaction 1.22 H6TeO6 → TeO(OH)+ 0.0 0.56 0.50 Se → CuSe 0.26 Fe3+→ Fe2+ 0.65 CuSe → Cu2Se   10 It was shown by Ladriere (1973) that cuprous generation is a diffusion-controlled reaction with an activation energy of 14.5 kJ/mol and with a rate proportional to the solution diffusion coefficient of Cu2+ and copper metal surface area. By increasing the temperature, both cuprous concentration (cuprous generation is an endothermic reaction ∆H = 75 kJ/mol) and the rate of its formation will increase (diffusion coefficients will increase with increasing temperature). Strong agitation can also increase the rate constant by improving mass transfer.   The accurate determination of cuprous ion involves significant challenges. In sulfate solution the reaction between cuprous and oxygen is extremely rapid. Secondly, concentrations of cuprous also may be quite low (<30 mM). Further, higher concentration solutions at temperatures above ambient tend to rapidly disproportionate as they cool, forming cupric ion and copper metal (Cotton et al., 1972). In perchlorate solution cuprous reacts slowly with perchlorate ions and oxidizes to cupric.  The equilibrium,                                                                                                                                              Cu2+aq + Cu s = 2Cu+aq   ( 2-5)  has been the subject of several investigations in sulfate and perchlorate media at 25°C. Fenwick (1926) determined a concentration (molar scale) equilibrium constant of       (1.91 ± 0.22)×10-7 over a range of 0.22-0.67 M cupric sulfate in 0.26-0.79 M sulfuric acid solution. She also estimated the equilibrium constant in perchlorate solution to be 1×10-6.  11 Endicott et al. (1965) determined the equilibrium constant to be (1.15 ± 0.15)×10-6 at infinite dilution, again using cupric perchlorate. Cuprous concentrations were determined indirectly by spectrophotommetry. Tindall et al. (1968) determined the equilibrium concentration of cuprous in a solution containing 4×10-4 M cupric sulfate and 0.2 M sulfuric acid using a copper rotating disk electrode. The concentration equilibrium constant was found to be 5.8×10-7 (molar scale). Ciavatta et al. (1980) measured the cuprous concentration by constant current coulometry. They found a K value of (1.86 ± 0.13)×10-6 at infinite dilution in perchlorate medium, and (1.91 ± 0.13)×10-6 in sulfate solution. Utilizing specific interaction theory, they re-determined K values at infinite dilution from the data of numerous other authors and in most cases found very good agreement with their own determination in perchlorate solution. The equilibrium constant increases substantially with increasing temperature because reaction ( 2-5) is endothermic.  Heinerth (1931) and Ladriere (1973) are the only workers who have reported studies of the reaction in copper sulfate-sulfuric acid solutions at high temperatures. Heinerth (1931) studied the equilibrium constant in 0.04-1 M CuSO4 and 0.04-1 M H2SO4 solutions at 20-60°C by potentiometric titration. Ladriere (1973) determined the concentration of cuprous in 0.5 M H2SO4 and 0.1-1 M CuSO4 solution by potentiometric titration with Ce(IV) at 25-100°C. The two sets of results differ significantly; in general Ladriere's results were lower than Heinerth's.   Knowing the thermodynamics and kinetics of cuprous ion reaction with various species in acidic solutions is of critical importance. However, data for the equilibrium cuprous  12 concentrations in copper sulfate-sulfuric acid solutions over a suitably wide range of composition and temperature are not available.  The kinetics of the reduction of biselenate with cuprous ion have been studied in both perchlorate and sulphate medium and are reported in chapter 5. In perchlorate media, perchloric acid oxidizes cuprous ion slowly. Hence, studying the concentration of cuprous in perchlorate solution especially at high temperature is impossible without considering the oxidation rate of cuprous by perchlorate. Since no studies were reported on the cuprous oxidation rate in perchlorate solution, the kinetics of cuprous oxidation in perchloric acid solution need to be investigated.   2.2 Selenium Chemistry  Selenium is in group VIb of the periodic table along with sulfur. Accordingly these two elements show similar chemical properties and selenium occurs in many kinds of sulphide ores. Selenium, has four different common oxidation states (Table  2-1): Selenide (Se2-), elemental selenium (Se0), selenite (SeIV) and selenate (SeVI); selenium five (SeV) is an unstable short-lived state (Klaning, 1986). Selenate is predominant at high electrochemical potentials, while at moderate potentials selenite is the major species. In acidic solutions inorganic selenium mainly exists as biselenite/selenite and biselenate/selenate ions which, therefore, cannot be precipitated as simple hydroxide/sulphide salts (Zigaro et al., 1974). Unstable oxoradicals of selenium, SeO3- and HSeO42- were observed as SeV species in aqueous solution (Klaning, 1986). SeV species are very short lived intermediate species. The SeO3- radical (∆G0f = -201.6 kJ/mol) is produced by the oxidation of SeIV species at pH below 11. At pH higher than  13 11, HSeO42- with ∆G0f = -358.2 kJ/mol is formed (Klaning, 1986).  The electrochemical reduction of SeIV in acidic media gives two forms of elemental selenium, one form in a direct electroreduction and the other one in a subsequent chemical reaction between Se-2, produced at more negative potential, and SeIV present in the system.  Table  2-1: Selenium oxidation states. Oxidation states Compounds pKa Comment H2SeO4 (selenic acid) -1.9 HSeO4- (biselenate) 1.9 SeVI SeO42- (selenate)  Strong oxidant, but reacts quite slowly SeO3-  SeV HSeO42-   Very short lived intermediate species   H2SeO3 (selenious acid) 2.6 HSeO3-  (biselenite) 7.3 SeIV SeO32-  (selenite)  Reacts relatively fast Se0 Gray (hexagonal)  Red (amorphous)    Se2- H2Se, HSe-, MetalxSe (2 > x > 1)  Superscripted Roman numerals, e.g. SeV, refer to all 5+ selenium cations.  Espinosa (1991) has shown that SeIV in sulfuric acid media is reduced to gray selenium and after that to Se-2, and at more negative potentials (-450 mV) to red selenium:  H2SeO3 + 4H+ + 4e- = Segray + 3H2O                                                                              ( 2-6) 2Se gray + 4H+ + 4e- = 2H2Se                                                                                          ( 2-7) 2H2Se + H2SeO3 = 3Sered + 3H2O                                                                                  ( 2-8)  In reducing environments, water insoluble elemental selenium is predominant over a wide pH range. As it will be shown, CuSe and Cu2Se don’t require as strongly reducing  14  conditions to form in copper sulfate-sulfuric acid medium as for H2Se in water.  An Eh–pH diagram for the Se-H2O system at 25°C and ionic activities of 10-3 M selenium is depicted in Figure  2-2. This selenium activity would be typical of selenium concentration in copper electrowinning solution. Thermodynamic data that were used are summarized in Appendix 1.  -1-0.500.511.52-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11pHEh (V)H2SeO3H2SeSe(0)HSe-SeO32-SeO42-O2H2OHSeO4-H2H+HSeO3-H2SeO4 Figure  2-2: Eh-pH diagram for the Se-H2O system with activity of selenium ions = 10-3 M, P = 1atm, 25°C.  Four oxidation states of selenium are presented in the diagram. Selenic acid is thermodynamically dominant at very high acidic concentration. In the pH range 0-1, biselenate, selenious acid, elemental selenium and hydrogen selenide are dominant species depending on potential.  15 An Eh–pH diagram for the Se-Cu-H2O system at elevated temperature and ionic activities of 10-3 M Se and 0.8 M Cu is depicted in Figure  2-3. These activities would be typical of an impure copper electrowinning solution.  Figure  2-3: Se-Cu-H2O Eh-pH diagram with activity of selenium ions = 10-3 M and activity of Cu ions = 0.8 M, 100°C.  The Criss-Cobble method was used to calculate higher temperature data (HSC chemistry 7.1 data base). Contrary to the Se-H2O system, either copper metal or cuprous can thermodynamically reduce biselenate to selenide (ie, Cu2Se) in the presence of cupric ion (copper selenide/telluride don’t require as strongly reducing conditions to form in copper sulphate solution as for H2Se/H2Te in water, comparing Figure  1-1 and Figure  2-1). Copper selenide is present at Eh < 0.58 V. Hydrogen selenide cannot be formed from Cu+ or copper metal reacting with biselenate (∆E < 0). A plausible selenate reduction  -1-0.500.511.50 1 2 3 4 5 6 7 8 9pHEh (V)H2SeO3H2SeSe(0)HSe-SeO32-SeO42-OH2OHSeO4-H2H+HSeO3-Cu2SeCuSeO3Cu 2+CuOCu 2 OCuSeCu 16 sequence by cuprous ion in pH range of 0-1 (Vale solution pH range) has the order:  HSeO4-→ H2SeO3 → Se → CuSe → Cu2Se.   Neither amorphous nor crystalline precipitates of any mixture of SeO42- and Cu2+ form up to a concentration of 1 M in an aqueous medium. No sparingly soluble SeVI-Cu+ complexes have been reported. Contrary to selenate, selenite can react with Cu2+ to form the sparingly soluble (log Ksp = -7.8) CuSeO3 compound (Devoy et al., 2002). In the presence of copper metal as a reductant and in the absence of strong acid (figure  2-3), CuSeO3 forms, resulting in a coating on the copper metal and its passivation (Ladriere, 1972). At higher acidity, it is necessary to remove copper selenide precipitate, which is a reduction product of the SeIV/VI reaction with cuprous. Charles et al. (1970) suggested using a fluidized bed reactor rather than the fixed bed reactor to prevent the reactor bed clogging with the fine solid precipitates of Cu2Se in the reduction process of SeIV with granulated copper metal.   2.2.1 Selenium Reduction Chemistry and Kinetics  A possible reaction sequence through which biselenate is reduced to selenide under acidic conditions (pH = 0.5, [Se] =10-3 M at 25°C for example) is as follows (figure  2-2):  HSeO4- + 3H+ + 2e- = H2SeO3 + H2O (E0 = 1.04 V)                                                      ( 2-9) H2SeO3 + 4H+ + 4e- = Se + 3H2O (E0 = 0.66V)                                                           ( 2-10) Se + 2H+ + 2e- = H2Se (E0 = -0.06V)                                                                           ( 2-11)   17 Selenate or selenite removal from solutions has been practiced in either heterogeneous or homogenous type of reduction reactions. In order for heterogeneous reduction to occur, selenate or selenite must first adsorb onto the surface of the metal or metal oxide and then be reduced by electrons donated from the metal/metal oxide. According to Figure  1-1, Zn, Fe, Ni and SO2 gas all have the possibility of reducing selenate to lower oxidation states. As a matter of fact, it was shown by Mondel et al. (2004) that among the transition metals Ni, Fe, Co and Cu, copper powder has the lowest selenate removal efficiency in neutral solution. However, in cupric-bearing solutions, couples with electrochemical potentials below that of the cupric-copper couple can precipitate the copper as well.  Koyama et al. (2000) tried copper, iron, zinc and aluminum powder as a selenate reductant in HCl at pH = 2. He found iron was the most effective metal among these four with 98.5% removal efficiency. Copper with 2.5% efficiency had the lowest removal efficiency. Elemental iron was also tested in an effort to remove dissolved selenium from waste waters. It is cheap and the reaction products are not environmentally harmful (Qiu et al., 2000). In fact, ferrihydrite precipitate (amorphous iron oxide and goethite) was selected by the U.S. EPA as the “Best Demonstrated Available Technology” for selenium removal in the form of selenite from industrial waste waters. However, the selenate removal efficiency is insignificant by means of amorphous iron oxide (<10%).  Koyama et al. (2000) investigated selenate removal by chemical reduction with iron powder and found the reduction rate of selenite to be much greater than that of selenate under the same conditions. For selenate/selenite removal with copper metal, copper selenide does not adhere to the copper metal surface (Ladriere, 1973). Very similar chemical properties of selenate and sulfate ions make selenate removal particularly difficult in sulfate  18 solutions by heterogeneous reactions in adsorption processes (Zhang et al., 2005). Selenite has a higher adsorption affinity than selenate on metal surfaces and it was confirmed that adsorbed selenate can be easily replaced by other solution anions such as sulphate. Chlorides, nitrates and sulphates are smaller anions compared to the oxyanions of selenium and they compete effectively for adsorption at the active sites of metals (Zhang et al., 2005). For instance, it was shown that SeVI removal rate by elemental iron is slower than SeIV in the sulphate solution, while in the chloride solution the removal rate is equal. It was also observed that the presence of 2.5 g/L sulphate greatly reduces the selenate removal by NiFe powder from 100% to 71.5% (Mondel et al., 2004). Mondel showed that selenate reduction reactions with Fe and Fe-Ni powders are first order with respect to selenate concentration in neutral solution and at low selenate concentrations. However, the reaction kinetics was observed to shift toward zeroth-order with respect to selenate concentration when the initial concentration of selenate was greater than 50 mg/L. This indicated that the concentration of selenate ions in the aqueous solution was significantly greater than the sites available for reaction on the solid surface (Mondel et al., 2004).  Sulfur dioxide gas or sulfite may also be used to remove selenate and selenite from solutions containing cupric ion (Newman et al., 2004). To achieve adequate SeVI removal with sulphur dioxide, reduction reactions should occur above 140°C in autoclaves (Weir et al., 1982). Furthermore, sulfur dioxide tends to reduce some of the copper in copper sulphate solution into the cuprous form. Subsequently, cuprous tends to disproportionate to metallic copper when it exits the autoclave and tends to precipitate on the walls of the equipment, valves and heat exchangers causing blockage (Hofirek, 1983). Strong  19 reducing agents such as sodium borohydride (NaBH4) may also effectively remove SeVI from natural copper sulphate solutions but not from acidic solutions as borohydride will react and decompose with acid (Chou et al., 1985).   2.2.2 Selenium Reduction Chemistry and Kinetics in Copper Sulfate-Sulfuric Acid Solutions  Few studies have been reported on the removal of selenate from H2SO4-CuSO4 solution in the presence of cuprous ion. It was found by Qin (2007) that the reduction rate of selenite to lower oxidation states in the presence of copper metal is much greater than the reduction rate of biselenate to selenite. Selenite can be easily and rapidly removed in the presence of copper powder in sulfuric acid-copper sulfate solution (99% within 1 minute using 45µm copper particles). On the other hand, the rate of biselenate removal is much slower and is significantly affected by temperature (70% within 120 minutes at 99°C).  Ladriere (1973) showed that selenate reduction to selenite is the rate determining step and that all subsequent steps have faster rates.  Walcarius et al. (2004) determined the mechanism responsible for the immobilization of selenate and selenite from aqueous solution by the addition of cuprite (Cu2O) particles at various pH values (in the range of 5-12). It was shown that at pH below 8 the amount of removed selenate was much greater than the total surface area of Cu2O available for selenate binding, suggesting the participation of cuprite dissolution and selenate reduction by cuprous; Cu+ generated by Cu2O likely reduces SeVI to SeIV by the following overall reaction:   20 Cu2Os + SeO42- + 4H+ = CuSeO3 s + Cu2+ + 2H2O (pH = 4.5-5.5)                              ( 2-12)  Chalcomenite (CuSeO3) was detected as the sole reaction product. Neither elemental selenium nor copper selenide were detected. Stewart (1985) measured the rate of selenium removal from (formerly INCO) CRED plant solution without considering the coexistence of selenate and selenite ion in the solution and suggested a second order rate law (-d[Se]/dt = k[Se]2) with varying rate constants (varying from 0.01 hr-1 to 0.09 hr-1 depending on the solution redox potential) in the ageing towers and in the presence of cuprous. She showed that the selenium removal rate decreased with increasing solution redox potential in the ageing towers and increased with increasing solution acidity.   Ladriere (1972) found that electrochemical reduction of selenious acid (H2SeO3) is controlled by providing H2SeO3 to a cathode surface. Ladriere set up selenious acid reduction experiments electrochemically on a platinum electrode in sulfuric acid-copper sulphate solutions. Depending on the cathodic current density, several copper selenides can precipitate (CuxSe, 1 < x < 1.8, x = 1.8 at limiting current density). Ladriere suggested that the selenite electrochemical reduction reaction occurs according to:   H2SeO3+ 1.8Cu2+ +4H+ + 7.6e- = Cu1.8Se + 3H2O                                                      ( 2-13)   The apparent activation energy was reported to be 21 kJ/mol for selenite reduction on platinum. Ladriere also suggested a selenite reduction reaction with copper metal in sulfuric acid-copper sulphate solutions:   21 H2SeO3 + 2H2SO4 + 3.8Cu = Cu1.8Se + 2CuSO4 aq + 3H2O                                         ( 2-14)   The apparent activation energy was reported to be 23 kJ/mol for selenite reduction on copper metal, which is in a good agreement with the assumption of a reaction controlled by diffusion in the liquid phase.   Ladriere (1972) found that the selenite reduction rate on copper metal is directly proportional to the concentration of H2SeO3 raised to the power of 1.25 (dSeIV/dt = k[Se]1.25 ) at T = 50°C, H2SO4 = 50 g/L, CuSO4 = 0.63M with rate constant equal to k = 0.0047 mol-0.25L 1.25hr-1cm-2.   Biselenate is reduced to   Cu2-xSe (0 < x < 0.2) in the presence of copper metal and cupric in solution (Ladriere 1973). He showed that copper metal does not directly reduce biselenate and it is actually cuprous ion which reduces biselenate homogenously (Ladriere, 1973). Similarly, it was noted by Charles et al. (1970) that copper metal does not directly reduce selenious acid (SeIV) and that it was probably the cuprous ion, which is generated in the presence of copper metal and cupric, that reduces selenious acid. According to the Se-Cu-H2O Eh-pH diagram and Ladriere’s (1973) results on copper selenide composition, biselenate as the dominant species at pH < 3 can be reduced into Cu2-xSe at temperatures higher than 50°C:  Reduction: HSeO4- + (2-x)Cu2+ + 7H+ + (10-2x)e- = Cu2-xSe + 4H2O                        ( 2-15) Oxidation: (10-2x)Cu+ = (10-2x)Cu2+ + (10-2x)e-                                                       ( 2-16) Overall reaction: HSeO4- + 7H+ + (10-2x)Cu+ = Cu2-xSe + 4H2O + (8-x)Cu2+ ( 2-17)   22 The rate equation suggested by Ladriere (1973) was a second order rate law, first order in activity of both Cu+ and SeVI with an activation energy of about 100 kJ/mol:                                                                           ))((][ 1 VIVISeCukdtSed +=−  ( 2-18)   However, as will be shown in chapter 5, selenate reduction with cuprous deviates from simple second order rate law at sufficiently low cuprous concentration and/or high cupric concentration. Hence, understanding the biselenate reduction chemistry and reaction kinetics by means of cuprous in a wider range of conditions, suggesting the mechanism of the reaction and determining the rate constants and activation energies are among the main objectives of this research.   2.2.3 Chemistry of Cuprous Selenide Reaction with Cupric Ion  The composition of electrodeposited copper selenide (CuxSe) varies by changing the concentration of Cu2+ and SeIV in potentiostatic deposition of copper selenide from H2SeO3-CuSO4-H2SO4 solution. Besides the composition of the solution, solution temperature also affects the composition of CuxSe layers. Cu3Se2 is mainly deposited at room temperature and Cu2Se deposition occurs at temperatures above 70°C (Lippkow et al., 1998). It was also shown by Ladriere (1973) that biselenate is reduced to Cu2-xSe (0 < x < 0.2) in the presence of copper metal and cupric. Non-stoichiometric copper selenide, Cu2-xSe (0 < x < 0.2), precipitated over a temperature range of 50°C to 100°C and the  23 composition was determined by X-ray diffraction.  When cuprous selenide particles are present in solution with cupric ion, the cuprous concentration in the solution will be affected by reaction of Cu2Se with cupric ion forming a non-stoichiometric compound as shown by reaction ( 2-19):  Another possible mechanism for the formation of the non-stoichiometric compound of copper selenide is through an incomplete reaction of CuSe with cuprous ion. In fact, the CuSe particles precipitate as an intermediate solid product of biselenate reduction with cuprous (see Figure  2-3, pH range 0-1). Subsequently, the non-stoichiometric Cu1+xSe compounds form through reaction of cuprous with the intermediate CuSe (reaction ( 2-20)):   Thermodynamic data for Cu0.5Se, CuSe, Cu1.5Se and Cu2Se are available (Mills 1974). There is an almost linear relationship between Gibbs free energy of formation of copper selenide and the Cu:Se ratio (Table  2-2).  Table  2-2: CuxSe standard Gibbs free energy data. Cu/Se ratio ∆G0 kJ/mole (25°C ) calculated based on Glazov et al. (2000) data Cu0.5Se -21.54 CuSe -40.66 Cu1.5Se -55.98 Cu2Se -70.86 Cu2Se + xCu2+aq = 2xCu+aq + Cu2-xSes 0 < x ≤ 1 ( 2-19) 2xCu+aq + CuSes = Cu1+xSe + xCu2+aq         0 < x ≤ 1 ( 2-20)  24 Based on these equations (∆G025°C (kJ/mol) = -32.65×Cu/Se – 6.448 and ∆G095°C (kJ/mol) =       -34.30×Cu/Se – 6.16), ∆G0f of Cu2-xSe species can be estimated at the desired temperature.  The equilibrium constant for the reaction ( 2-21)  5Cu2Se + Cu2+aq = 2Cu+aq + 5Cu1.9Ses ( 2-21)  is equal to K = (Cu+)2/(Cu2+) = 3.1×10-9 at 95°C (Table  2-3). Therefore, for example, at [Cu2+] = 50 and 90 g/L with the assumption of activity coefficients equal to one, the reaction is favourable at cuprous activity concentrations lower than [Cu+] = 0.00005 M and 0.00007 M respectively.   Table  2-3: CuxSe thermodynamic data at 25°C and 95°C. Reaction ∆G0R(25°C) ∆G0R(95°C) K(25°C) K(95°C) Cu2Se + Cu2+ = 2Cu+ + CuSe 65.012 55.528 4.07×10-12 1.32×10-8 2Cu2Se + Cu2+ = 2Cu+ + Cu3Se2 69.482 61.475 6.71×10-13 1.89×10-9 5Cu2Se + Cu2+ = 2Cu+ + 5Cu1.8Se 67.099 58.92 1.75×10-12 4.36×10-9 10Cu2Se + Cu2+ = 2Cu+ + 10Cu1.9Se 66.729 59.97 2.04×10-12 3.10×10-9  The maximum equilibrium constant was obtained for the precipitation of CuSe (first reaction in Table  2-3) with K = (Cu+)2/(Cu2+) = 1.32×10-8 at 95°C. Accordingly, at [Cu2+] = 50 and 90 g/L, the equilibrium cuprous concentration can be calculated giving [Cu+] = 0.00010 M and 0.00014 M, respectively. Since the selenate removal rate and kinetics are based on the cuprous concentration, the effect of this reaction on the reaction stoichiometry needed to be experimentally investigated. Then all kinetics tests were designed so that the lowest cuprous concentration in the kinetics tests were above the minimum [Cu+] below which Cu2Se dissociation begins.   25 2.3 Tellurium Chemistry  Tellurium, a silvery-white semimetal, bears a definite resemblance to selenium and sulfur in many of its properties. Tellurium, like sulfur and selenium, readily forms oxides which can be hydrolyzed to produce oxyacids (Dutton et al., 1966).   Tellurium, has several oxidation states (Table  2-4): Telluride (Te2-), Te-, elemental tellurium, TeII, TeIV, TeV and TeVI; TeII and TeV are unstable states. In addition, however, tellurium can exist in the oxidation states of I and III, as well as fractional oxidation states but there are uncertainties regarding the existence and the thermodynamic stability of these species (Holleman, 2005).  The differing properties of selenium and tellurium in aqueous solution are based on differences in the relative ease of oxidation and reduction of their various valence states, their stability and differences in the solubility of their respective oxides, oxyacids and salts. For instance, in aqueous solution, tetravalent tellurium passes through a minimum solubility in water at pH 4.5 (solubility 6.3×10-6 mol/L TeO2 at 25°C) while tetravalent selenium is freely soluble throughout the pH range 0-14. TeIV is relatively soluble in acid media, sparingly soluble in neutral media, and soluble in alkaline media. Tellurium is soluble as tellurite and bitellurite ions in alkaline media but hydrolyzes and precipitates as tellurium dioxide or its hydrated form, H2TeO3 on acidification.  Most tellurium-selenium separation processes are based on this property (Dutton, 1971). If the neutralization of sodium tellurite is carried out near the boiling point, a cruddy precipitate of tellurous acid, H2TeO3, is first formed; this soon changes to crystalline tellurium dioxide. The product is white when it is pure.  26  Table  2-4: Tellurium oxidation states. Oxidation state Compounds pKa Comment H6TeO6 7.7 H5TeO6- 11 TeVI  H4TeO62- 14.5 Aqueous H6TeO6 exists in the form of simple molecules in dilute solution or polymerised in concentrated solution (Dutton, 1971). H2TeO4-  Very short lived species (Klaening et al., 2001). TeO3-  Very short lived. (formed by reduction of H6TeO6) HTeO42-  Very short lived. (formed by reduction of H5TeO6-) TeV TeO43-  Very short lived. (formed by reduction of H4TeO62-) Te4+  Dominant at very low pH (Awad, 1968) TeO(OH)+   TeO2 (s)  pH dependent solubility, most stable oxide (Dutton, 1971). H2TeO3   Readily loses water; forms TeO2 above 0°C (Dutton, 1971). HTeO3-   TeIV TeO32-   TeII Te2+  Unstable in aq. solution (2Te2+ = Te + Te4+) (Havezov et al., 1974) Te0    Te1- Te22-  Dominant at pH > 8 and high Te concentrations (Myers, 2007). H2Te  Decomposes at > 0°C (Dutton, 1971). HTe-   Te2- Te2-   Superscripted Roman numerals, e.g. TeIV, refer to all 4+ tellurium cations.  At lower temperatures, transformation from tellurous acid to tellurium dioxide may not take place (Dutton, 1971)  An Eh–pH diagram for the Te- H2O system at 25°C and ionic activities of 3×10-4 M Te is depicted in Figure  2-4. This tellurium activity would be typical of tellurium concentrations in impure copper electrowinning solution. Thermodynamic data that were used are summarized in Appendix 2.    27 -1.5-1-0.500.511.5-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14pHEh (V)TeO2H2TeTe(0)HTe-TeO32-H4TeO62-O2H2OH5TeO6-H2H+HTeO3-H6TeO6Te2-Te22-TeO(OH)+Te4+ Figure  2-4: Eh-pH diagram for the Te-H2O system with activity of Te ions = 3×10-4 M, P = 1atm, 25°C.  Four oxidation states of tellurium are presented in the diagram. In the pH range 0-2, telluric acid, telluryl ion (TeO(OH)+), elemental tellurium and hydrogen telluride are dominant species depending on potential.   There have been disputes over the aqueous chemistry of tellurium since tellurium speciation has been investigated. Deltombe et al. (1956) were the first to publish an Eh-pH diagram for the system Te-H2O at 25°C. Aqueous species present in the Deltombe diagram included H2TeO4, HTeO4-, TeO42-, Te4+, HTeO2+, HTeO3-, TeO32-, Te22-, H2Te, HTe- and Te2-. It was found later that the known TeVI species are not H2TeO4, HTeO4- and TeO42- and simple tetrahedral telluric acid or simple tetrahedral tellurate anions do not  28 exist. Andersson et al. (1981) confirmed the octahedral, monomeric structure of telluric acid in the crystal form and aqueous solution. The Te-OH distance found in solution is somewhat longer than those in crystals, which indicates that Te-OH bond is slightly weaker in solution than in the solid state (Andersson et al., 1981). In other words, TeVI does not form a simple tetrahedral MO42- ion in contrast with selenic and sulphuric acid which exist only in the tetrahedral form. Telluric acid formulas, then, may be written as H6TeO6 or Te(OH)6. Telluric acid is very soluble in water (about 2 mol/L) (Deltombe et al., 1956).  Only the first three dissociation constants of the acid are known. The values recommended for the first three dissociation constants of telluric acid have been estimated as: K1 = 2×10-8, K2 = 1×10-11, and K3 = 3×10-15 (Dutton et al, 1966).   Tellurium(V) species are very short lived intermediate species. Four different tellurium(V) oxoradicals, are formed in aqueous solution: H2TeO4-, TeO3-, HTeO42- and TeO43-(Klaening et al., 2001). TeV species may be formed by reduction of telluric acid, bitellurate and tellurate or oxidation of bitellurite and tellurite. For instance, TeO3-, HTeO42- and TeO43- are formed by reduction of H6TeO6, H5TeO6- and H4TeO62- respectively. HTeO42- and TeO43- are the dominant species in strongly alkaline solutions.   Te4+, TeO(OH)+ or H3TeO3+, TeO2, H2TeO3, HTeO3- and TeO32- are the main TeIV species in aqueous solution (McPhail, 1995). Te4+ is limited to very low pH (depending on the differences at ∆G0f it may vary from pH of -0.15 to -0.4 at 25°C). Awad (1968) showed that an elemental tellurium anode dissolves as Te4+ ion in solutions of pH < 0 (1, 4.5 N HClO4 and 5, 10 N H2SO4). Schumann (1925) showed that TeIV exists in the form  29 of ions such as Te(OH)3+ or TeO(OH)+ in 0.103, 0.292 and 0.737 N perchloric acid concentrations. Later Marhenke et al. (1967) concluded that the predominant TeIV species in mineral acid solutions is the cation TeO(OH)+. Formation of TeO(OH)+, in the pH range 0–0·8 in HClO4, H2SO4 and HNO3 was also confirmed by Awad (1968). Havezov et al. (1974) summarized the most probable ionic species of TeIV as TeO(OH)+, H2TeO3, HTeO3- and  TeO32-.   Like selenium, tellurium forms oxides which can be hydrolysed to oxyacids. Of the oxides TeO, TeO2, Te2O5 and TeO3, tellurium dioxide is the most stable oxide (Dutton, 1971). TeO has only transient existence and supposed compounds thought to be tellurium monoxide, have turned out to be the mixtures of tellurium and tellurium dioxide (Dutton, 1971). TeO2 is a white (α) or yellow (β) non-volatile solid. The solubility of tellurium dioxide is pH dependent. Solubility is relatively high in increasingly acidic or basic solutions while the minimum solubility is attained in water at room temperature (3.75×10-5 M at 18°C, pH = 6.5). The solubility increases sharply on heating above 40°C. Tellurium dioxide gives definite solubility values in sulphuric acid solution: 0.05 M in 20% H2SO4, 0.065 M in 30% H2SO4 and 0.383 M at 50% H2SO4 (Dutton, 1971). Influence of pH on the solubility of TeO2 is depicted in Figure  2-5.   30           Figure  2-5: Influence of pH on the solubility of TeO2 at 25°C. × Kasarnowsky`s experimental values (Deltombe et al., 1956).  Elemental tellurium has only one crystalline form. Anodic polarization of tellurium in sulfuric acid solution, leads to formation of TeO2 and its dissolution to telluryl ion (TeO(OH)+ ) at low pH. Cathodic polarisation of tellurium leads to formation of H2Te in acidic medium (Barbier et al., 1978).   2.3.1 Tellurium-Copper -Water System  In the system of TeO2-H2O-CuSO4, it was found that crystalline tellurium dioxide does not react with an aqueous copper sulphate solution, whereas tellurous acid does, forming a green solid of variable composition, xTeO2·yCuTeO3·zCuSO4 (where x > y > z)  31 (Dutton, 1971). CuTeO3, CuTe2O5 and CuO·CuTeO3 are the known copper tellurite species that form by interaction of Cu2+ with alkaline tellurites (Gospodinov, 1991). In this study the thermodynamic data for CuTeO3, CuTe2O5 and CuO.CuTeO3 was calculated based on Gospodinove study on ∆H°rxn,298  and S°298 CuTeO3, CuTe2O5 and CuO.CuTeO3 (Gospodinov 1983,1984, 1994). For example, for CuTeO3, ∆H°298 was calculated based on ∆H°rxn,298 CuTeO3 (CuO + TeO2 = CuTeO3) reported by Gaspodinove as well as McPhail (1995) and HSC Chemistry 7.11 (2011) data on ∆H°f 298 CuO and TeO2. ∆S°298 was also calculated based on S°298 CuTeO3 as well as S°298 Cu, Te and O2. ∆G°f 298 was calculated then by:   ∆G°f 298 = ∆H° 298 -T ∆S° 298                                                                                        ( 2-22)  Molar heat capacity data suggested by Gospodinove was also used to calculate G°373 for CuTeO3, CuTe2O5 and CuO·CuTeO3. Gibbs free energy data at T = 298.15 and 373.15 K are tabulated in Table  2-5. An Eh–pH diagram of the Te-Cu-H2O system at 25°C and ionic activities of 3×10-4 M Te and 0.8 M Cu is depicted in Figure  2-6. Thermodynamic data from McPhail (1995) was used as the most recent complete available data along with calculated values using the Gospodinove (Table  2-5) data to draw the Eh-pH diagram.  Table  2-5: Cu-TeIV thermodynamic data. Criss Cobble method was used to calculate higher temperature data for Cu-H2O ionic species.  Compound ∆G0f 298 kj/mol ∆G0f 373.15 kj/mol CuTeO3  -339.73 -374.65 CuO·CuTeO3 -563.19 -495.03 CuTe2O5  -692.86 -644.52   32 The Te-Cu-H2O system is very sensitive to changes in temperature and tellurium concentration which consequently may cause significant differences in the Eh-pH diagram. At 25°C, CuTe2O5 and CuO·CuTeO3 are widely dominant as shown in Figure  2-6. At tellurium concentrations higher than 0.003M, the TeO2(s) region appears in the diagram close to the TeO(OH)+ stability region and is expanded by increasing the tellurium concentration to  0.048 M at Cu2+ = 0.8 M (see Appendix 3 for [Te] = 0.01 M).  Figure  2-6: Te-Cu-H2O Eh-pH diagram with activity of Te ions = 3×10-4 M and activity of Cu ions = 0.8 M, 25°C.  At concentrations higher than 0.048 M, TeO(OH)+ does not appear and TeO2(s) will be dominant. The Eh-pH diagram at Te ionic activity of 0.01 M and 1 M at T = 25°C and 100°C is depicted in Appendix 3. -1.5-1-0.500.511.52-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14pHEh (V)CuTe2O5H2TeCu2TeHTe-TeO32-H4TeO62-O2H2OH5TeO6-H2H+CuO·CuTeO3H6TeO6Te2-Te4+CuCu 2 OCuOCu 2+CuTeTeO(OH)+Te 33  In Figure  2-7, an Eh–pH diagram of Te-Cu-H2O system at elevated temperature and ionic activities of 3×10-4 M Te and 0.8 M Cu is depicted. Tellurium activity was chosen to simulate Vale’s process solution composition. The species CuTeO3, CuTe2O5 and CuO·CuTeO3 are not stable at 100°C.   Figure  2-7: Te-Cu-H2O Eh-pH diagram with activity of Te ions = 3×10-4 M and activity of Cu ions = 0.8 M, 100°C.  Thermodynamic data of aqueous Te species at 100°C were taken from the McPhail (1995) study. The Criss Cobble (1964) method was used to calculate higher temperature data for Cu-H2O species. CuTe is not a dominant species in the above-mentioned conditions. According to the Eh-pH diagram a plausible tellurate reduction sequence at low pH and at T = 100°C could be: H6TeO6→ TeO(OH)+→ Cu2Te. The Te-Cu-H2O  -1.5-1-0.500.511.5-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14pHEh (V)TeO2H2TeCu2TeHTe-TeO32-H4TeO62-O2H2OH5TeO6-H2H+HTeO3-H6TeO6Te2-TeO(OH)+Te4+CuCu 2 OCuOCu 2+Te 34 system is different from what was observed in the Se-Cu-H2O system where the only dominant SeIV species in sulphuric acid concentration of 10 to 200 g/L was H2SeO3 (Figure  2-3). At higher pH, the reduction sequence may occur through reduction of TeO2(s) to Cu2Te: H6TeO6→ TeO2(s)→ Cu2Te.  The mechanism of reduction of TeVI species to TeIV species and TeIV species to copper telluride may consist of a number of electron transfer steps to form short lived intermediate species. By increasing the concentration of tellurium in Figure  2-7, the TeO2 stability region is expanded from both sides. Increasing the tellurium concentration by one order of magnitude results in the expansion of the TeO2 stability region from pH = 1.92 to pH = 0.92. As a result, TeO(OH)+ stability region shrinks towards the right until it disappears from the Eh-pH diagram at a tellurium concentration of 0.0125 M (see Appendix 3 for [Te] = 1 M, T = 100°C). Consequently, at lower acidity and/or higher tellurium concentration the dominant species shifts from TeO(OH)+ ion to TeO2 solid.  This may change the rate law considering the fact that the solid TeO2 phase will react heterogeneously with cuprous whereas the reduction of TeO(OH)+ occurs homogeneously. Therefore, the reduction rate of tellurium may be dependent on which species of tellurium are present. In case of the presence of both TeO(OH)+ ion and TeO2 solids, the rate is then expected to be governed by the proportion of the dominant phase over the minority phase. To avoid complication of the reduction of H6TeO6 through TeO2 or mixture of the TeO2-TeO(OH)+ species, the concentration of the initial tellurium and solution acidity in this work were chosen much below the saturated TeO2 concentration in all tests.  35 2.3.2 Tellurium Reduction Chemistry and Kinetics  2.3.2.1 TeIV Reduction Chemistry and Kinetics  Tellurite reduced rapidly and conveniently with copper powder results in formation of copper telluride, Cu2Te, near the boiling point; contrary to selenite which reduces at the ambient temperature (Dutton, 1966):  H2TeO3 + 4Cu + 2H2SO4 = Cu2Te + 2CuSO4 + 3H2O                                                ( 2-23)  It was shown that at least 50 g/L of sulphuric acid is needed for the complete precipitation of tellurium (Cooper, 1971).   Pressure reduction of tellurium ions with sulfur dioxide is also practiced (Western Platinum Ltd, South Africa) to separate tellurium from the copper-tellurium acid leach solution (Lottering et al., 2012). Sulfur dioxide may be used to remove impurities in higher oxidation states such as selenate and selenite and tellurate and tellurite from solutions containing cupric ions. It was shown by Hamada (1961) that H+ ions act as a negative catalyst in the reduction of tellurious acid in a sulfuric acid medium. Hence, tellurite may be reduced by sulfur dioxide in very weak acid solutions. He found that in a sulfuric acid medium the rate of reduction is first order with respect to [H2TeO3] and proportional to [H+]-2. Conversely, he showed that in hydrochloric acid solution the rate constant of tellurium reduction with SO2 is proportional to [H+]2.   36 Morrison (1963) showed that the reduction of TeIV and TeVI with sulfur dioxide is inhibited by adding sulphuric acid such that precipitated tellurium percentage decreased from almost 100% at pH = 6 to 20 % at pH = 0.5. The precipitation of TeVI with sulfur dioxide requires an autoclave. A partial pressure of 45-50 psi SO2 and a temperature of 105-120°C can precipitate tellurium as Cu2Te at low concentrations of sulfuric acid (Jennings et al., 1969 and Morrison 1963). The mechanism for the reduction of tellurium with sulfur dioxide in the presence of cupric ion is not clearly understood. The precipitate appeared to be cuprous telluride with a minor amount of metallic copper (Morrison 1963). Based on observations of produced copper metal, it was suggested by Wang et al. (2003), that it is probable that the SO2 reduced the cupric to cuprous and then the cuprous disproportionated to copper metal and cupric. Subsequently, the tellurium would be cemented on to the surface of the fine copper particles. However, this mechanism wasn’t proven and a more likely mechanism involves the reduction and precipitation of tellurium species with the cuprous ions followed by direct reduction of cupric and cuprous to copper metal by SO2 gas. Direct reduction of TeVI/IV and SeIV/VI with cuprous rather than sulphurous acid was also suggested by Newman et al. (2004) in the selenium and tellurium removal circuit of Stillwater. For the Stillwater base metal refinery process, selenium and tellurium are removed by pressure feeding of the sulphurous acid (mixture of SO2 gas and water) into a reactor containing a copper pregnant leach solution with selenium and tellurium ions.      37 2.3.2.2 TeVI Reduction Chemistry and Kinetics  Precipitation of TeVI to Cu2Te may occur at low concentration of sulfuric acid with sulfur dioxide at SO2 partial pressure of 45-50 psi and temperature of 105-120°C (Jennings et al., 1969 and Morrison, 1963).  Hexavalent tellurium can be precipitated from solution by treatment with copper powder at temperatures not lower than 90°C, producing copper telluride according to the reaction:  H6TeO6 + 5Cu + 3H2SO4 = Cu2Te + 3CuSO4 + 6H2O                                                ( 2-24)  It was shown that for complete precipitation of tellurium with copper metal, at least 50 g/L sulphuric acid must be present. The reaction rate has been reported to be slow with sulfuric acid concentration lower than 25 g/L (Cooper, 1971). Jennings et al. (1968) used various forms of metallic copper such as copper powder (20 microns), copper sheet and copper shot in attempts to find a satisfactory procedure. A coating of copper telluride rendered the sheet inactive, showing that copper metal can be used if the Cu2Te is continuously removed from the surface. Using copper shot and tumbling it with the heated solution in a drum reactor was found satisfactory. It was shown that operating below the boiling point causes higher consumption of copper and acid and consequently decreasing cuprous telluride precipitation rate. Operating at the boiling point increases the rate of precipitation and provides an inert atmosphere of steam preventing copper metal reaction with oxygen. Total consumption of copper and  38 sulphuric acid increases in the presence of oxygen, either from copper oxide on the surface of the shot or as air entering into the reactor:  Cu2O + H2SO4 = CuSO4 + Cu + H2O                                                                          ( 2-25) Cu + H2SO4 + 1/2O2 = CuSO4 + H2O                                                                          ( 2-26)   The effect of temperature, acid concentration, copper loading (4-8 mesh) and the rotation speed on the rate constant were studied by Jennings (1969) in a rotary drum. Drum rotation speed had a small effect in the range of 31-105 rpm on the reduction rate. Temperature had a very pronounced effect on reduction rate and corresponded to an apparent activation energy of 125 kJ/mol. It was shown that the rate of precipitation increased moderately as the sulphuric acid concentration is raised from 50 to 100 g/L, but remained constant when increasing to 140 g/L (Jennings et al., 1968). Jennings (1969) found a nearly linear relation between tellurium concentration and reaction time with a rate constant of 0.0030 s-1 at T = 103°C, [H2SO4] = 123 g/L [Cu2+] = 105 g/L, copper shot = 1880 g/L in reduction of 14.86 g/L TeVI and under nitrogen gas flow. The reaction rate increases with an increase in the copper shot loading from 95 g/L to 1880 g/L. The reaction rate stays almost constant at higher copper shot loading of 7500 g/L.  The independence of the tellurium reduction rate from copper surface area at high loadings of copper metal might be attributed to the fact that cuprous ion concentration reaches its equilibrium constant when the copper loading is equal or greater than 1880 g/L. Hence, it can be suggested that similar to SeVI, the reduction of TeVI actually occurs  39 by homogeneous reaction with cuprous ion rather than directly on the surface of the copper metal.  At Naoshima smelter and refinery, tellurium removal with copper cuttings takes 48 hours at 85°C. Pilot plant tests were conducted by Shibasaki (1992) to determine design parameters of a fixed bed reactor packed with copper choppings. Shibasaki (1992) showed that copper telluride strips easily from a copper metal surface when it forms at 80-90°C in a fixed bed reactor. He showed that the tellurate elimination rate is first order with respect to tellurium concentration:   ][Tekdt][Ted VIVI−=                                                                                                      ( 2-27)  The reaction rate constant was reported 0.0057 s-1 at T = 90°C where copper choppings with specific surface area of 3560 m2/m3 (acid concentration not mentioned) was used. He found that the rate constant is almost proportional to the specific surface area of the copper cuttings when it is increased. Increasing the specific surface area of the cuttings in constant volume from 639 m2/m3 to 3560 m2/m3 (5.6 times increase) increases the rate of the reaction from 0.0010 to 0.0057 s-1 (5.7 times increase). This result would not apply to the fixed column reactor (static bed) as the copper telluride would block the surface of the copper metal in this application. Considering the results from Jennings (1969), the dependence of the tellurium reduction rate with copper surface area can be attributed to the fact that cuprous ion concentration did not yet reach its saturated concentration at 3560 m2/m3 copper choppings specific surface area.   40 Few studies were referenced (Shibasaki 1992, Jennings 1969) on the kinetics of reduction of tellurate in the presence of copper metal, but as was mentioned, tellurate reduction most likely occurs homogeneously by reacting with cuprous ion rather than reacting directly on the surface of the copper metal. The kinetics of reduction of TeVI and TeIV with cuprous is not known. It is therefore an objective of this research to investigate the TeVI and TeIV reduction reaction kinetics with cuprous ion in acidic solution and identify factors enhancing the removal rate. In chapter 6 of this study, the chemistry and kinetics of tellurium removal by cuprous ion precipitation and the effects of acidity and temperature on the removal rate are reported.  2.4 Selenium and Tellurium Removal at VALE (Canada)   Chalcopyrite concentrate, pyrrhotite concentrate and a mixed pentlandite-pyrrhotite-chalcopyrite concentrate are the three products of Vale’s Sudbury mining and flotation process. The mixed pentlandite- chalcopyrite concentrate undergoes flash smelting which after matte slow cooling and separation yields copper sulphide, nickel sulphide and a magnetic nickel-copper alloy. The nickel-copper alloy is refined at Vale’s Copper Cliff Nickel Refinery using the INCO Pressure Carbonyl (ICP) process and the porous granular residue is treated at CRED (Copper Refinery Electrowinning Department). As described by Tyroler et al. (1988), the resulting ICP residue which contains copper (55-60%), nickel (6-10%), cobalt (4-8%), selenium (0.06-0.1%), tellurium (0.06-0.1%) and precious metals (41 tons/day) is pressure leached in two stages at CRED. In the first stage nickel, cobalt and iron are leached under non-oxidative conditions at 150°C, 100-200 g/L  41 H2SO4 and 5.6 kg/cm2 steam pressure. The purpose of the first stage is to dissolve nickel, cobalt and iron in order to separate them from selenium, tellurium and precious metals, all of which remain in a substantially Cu2S residue. In the second stage copper, selenium and tellurium are oxidatively dissolved from the first stage leach residue. The first stage leach residue which contains Cu2S as a major component, is batch leached under oxygen pressure of 150 psi and a temperature of 115°C to convert the chalcocite to copper sulphate. The second stage leaching is divided into two steps: oxidative pressure leaching in an autoclave in acid deficient environment to produce a solid of basic copper sulphate (antlerite) in a solution of copper sulphate according to the following exothermic reaction:   2Cu2S (S) + 5O2 + 2H2O = CuSO4 + CuSO4.2Cu(OH)2                                               ( 2-28)  The equilibrium between cupric sulphate and basic copper sulphate buffers the solution pH between 2 and 3 (Vanlier R. 1995). Afterwards, releaching of basic copper sulphate slurry with spent electrolyte dissolves the basic copper sulphate according to the following reaction:   CuSO4.2Cu(OH)2 (S) + 2H2SO4 = 3CuSO4 + 4H2O                                                     ( 2-29)     Selenium and tellurium are also dissolved in this stage. After solid/liquid separation, the solution is forwarded to the selenium and tellurium removal circuit.  The solution passing to the removal circuit has a typical composition presented in Table  2-6 (Qin, 2005). Information has been received recently from VALE (Wong M., 2010)  42 indicating the removal circuit feed solution typical composition as 50-100 ppm selenium and 100-150 ppm tellurium. Tellurium concentration of up to 200 ppm was also observed. According to this report, 15 to 20% of selenium and tellurium in the solution are in the +6 oxidation state and the rest are in +4 state. In case of insufficient addition of copper shot, which consequently causes lower cuprous concentration, Te was reported as the first element that leaves the aging towers at elevated concentration (> 5 ppm) rather than selenium.  High pressure oxidative leaching of the chalcocite residue at the CRED plant can generally dissolve selenium and tellurium content of the residue in the form of SeIV/VI and TeIV/VI species into electrolyte. Superimposed Eh-pH diagrams of Se-Cu-H2O and Te-Cu-H2O at 100°C and ionic activates of Se = 10-3 M and Te = 3×10-4 M are depicted in Figure  2-8. CRED plant solution pH range is also shown in the shaded area in the diagram. Dotted lines define domains of predominance of Se-Cu-H2O system.   According to the diagram, the dominant selenium and tellurium species at the +4 and +6 oxidation states in the CRED plant solution are biselenate (SeVI), selenious acid (SeIV) and telluric acid (TeVI), telluryl ion (TeIV) respectively. Biselenate and telluric acid are both strong oxidizing agents but kinetically slow. Hence, the main drawback of the Se-Te removal circuit is the long reaction time for reducing SeVI and TeVI to copper selenide and telluride. Copper can be recovered by electrowinning after selenium and tellurium removal from the leach solution. This is accomplished by elevating the temperature of second stage leach solution to 95-99°C. The solution then up flows through a fixed bed column containing copper wire cuttings.   43 -1.5-1-0.500.511.5-1 0 1 2 3 4pHEh (V)TeO2H2TeCu2TeHTe-O2H2OH2H+H6TeO6TeO(OH)+Te4+TeHSeO 4 -H 2 SeO 3Se CuSeO 3 HSeO 3 -CuSeCu 2 SeH 2 SeVALE solution pH rangeSeO 4 2- Figure  2-8: Superimposed Eh-pH diagram of Se-Cu-H2O and Te-Cu-H2O at 100°C and ionic activates of Se = 10-3 M and Te = 3×10-4 M.  Work by Qin (2005) reported that typically 91% of the selenium and 96% of the tellurium are removed after direct contact with copper metal (Table  2-6). During contact with copper metal, the solution potential is reduced from almost 690 mV to 340 mV vs. SHE (Cu/Cu2+ couple is dominant over other interacting impurities).   Table  2-6: Average concentration of species in Se-Te removal circuit (Qin, 2005).  Species  SeVI (mg/L) SeIV (mg/L) Te (mg/L) Cu (g/L) Ni (g/L) Co (g/L) FeII (g/L) FeIII (g/L) H2SO4 (g/L) Feed solution 3 34 142 115 16.5 19 5 9 137 column overflow 3 0.3 5 126 17 19 13.3 ------ 144 Aged solution 0.4 0.1 1 114 17 19 12.7 ------- 147  44 All other species in solution then tend to adjust their speciation to conform to 340 mV potential versus the hydrogen electrode (virtually all ferric in solution goes to ferrous). The higher the contact time with copper metal the lower the redox potential. For instance at 100°C the solution potential reduces from 371 mV to 361 mV when the contact time is increased from 1 minute to 2.5 minutes (Stewart D. A. et al., 1985).  The copper selenide and telluride are precipitated as fine black particles. The solution and solids of copper selenide and copper telluride then overflow the column through four consecutive aging towers. Solids from aging towers 2, 3 and 4 are recycled to aging tower one (Figure  2-9).   Figure  2-9: Selenium and tellurium removal circuit at VALE-Canada. Second stage leach solution  Steam Heater 95-99°C Aging Towers Copper Contact Column Pressure Filter Purified solution to electrowinning circuit Vacuum Filter Se, Te Residue  45 The solids are settled and collected in the bottoms of the aging towers. The reactions proceed until the selenium and tellurium concentrations have been reduced to less than 1 mg/L. During solution aging, the redox potential of the solution increases by 30 mV. The purified copper sulphate solution enters the electrowinning circuit to produce copper cathode. The rate of selenium removal during contact with copper is a function of solution temperature, copper surface area and contact time. The rate of selenium removal during solution aging is a function of the temperature, redox potential of the solution and the sulfuric acid concentration (Stewart D. A. et al., 1985). The settled solids from the aging towers are recovered to a small vacuum drum filter and transferred to the silver refinery for selenium and tellurium recovery (Stewart D. A. et al., 1985).  2.5 Summary   Cuprous is an important oxidation state of copper which has uses as a reducing agent in hydrometallurgical applications such as purification processes. Industrially, cuprous is generated by contacting the cupric electrolyte with copper metal at temperature near 100°C (cuprous generation is an endothermic reaction ∆H = 75 kJ/mol). Cuprous may be used to remove impurities in higher oxidation states such as SeVI, TeVI, SeIV, TeIV in acidic solution containing cupric ion. Cuprous can thermodynamically reduce SeIV/VI and TeIV/VI species to form copper selenide and copper telluride in a copper sulfate-sulfuric acid solution. However, the kinetics of using cuprous for this purpose must be studied further.    46 The advantages of using cuprous for removal of selenium and tellurium are that it is an environmentally clean process and it adds no impurities to copper EW electrolytes; the only soluble reactant and final product is cupric ion. The disadvantages of using cuprous are the slow reaction kinetics for reduction of SeVI and TeVI with cuprous, the high air sensitivity of cuprous and the low saturated concentrations of cuprous in solution.  Vale’s CRED plant in Sudbury, Canada is an example of industrial plant where a process of selenium and tellurium removal with cuprous ion from acidic copper sulphate solution is practiced. Selenium and tellurium removal from copper solutions has been practiced by contact with metallic copper in a fixed bed reactor followed by a solution ageing step. The solution to the removal circuit has a typical composition of 40 mg/L selenium, 140 mg/L tellurium, 115 g/L cupric and 140 g/L sulphuric acid. Residence time in the aging towers may vary from 12-23 hours for a typical processing rate of 150 to 450 L/min.  Cuprous generation is a diffusion-controlled reaction with an activation energy of 14.5 kJ/mol and with a rate proportional to the solution diffusion coefficient of Cu2+ and copper metal surface area. In perchlorate solution cuprous reacts slowly with perchlorate ions and oxidizes to cupric. Hence, studying the concentration of cuprous in perchlorate solution especially at high temperature is impossible without considering the oxidation rate of cuprous by perchlorate. The equilibrium, Cu2+aq + Cu s = 2Cu+aq, has been the subject of several investigations in sulfate and perchlorate media at 25°C. However, data for the equilibrium cuprous concentrations at high temperature and over a suitably wide range of composition and temperature are not available.    47 When cuprous selenide particles are present in solution with cupric ion, the cuprous concentration in the solution will be affected by reaction of Cu2Se with cupric ion forming a non-stoichiometric compound of Cu2-xSe (0 < x < 0.2). Since the selenium and tellurium removal rate and kinetics are based on the cuprous concentration, the effect of this reaction on the reaction stoichiometry needs to be experimentally investigated.     In highly acidic solutions (0 < pH < 2) inorganic SeVI, SeIV, TeVI and TeIV mainly exists as biselenate (HSeO4-), selenious acid (H2SeO3), telluric acid (H6TeO6) and telluryl ion (TeO(OH)+), respectively. A plausible selenate reduction sequence by cuprous ion in pH range of 0-1 has most likely the order:  HSeO4-→ H2SeO3 → Se → CuSe → Cu2Se. A plausible tellurate reduction sequence at low pH and at T = 100°C could be: H6TeO6→ TeO(OH)+→ Cu2Te. At higher pH, the reduction sequence of tellurate may occur through reduction of TeO2(s) to Cu2Te: H6TeO6→ TeO2(s)→ Cu2Te. This may change the rate law considering the fact that the solid TeO2 phase will react heterogeneously with cuprous whereas the reduction of TeO(OH)+ occurs homogeneously.  Metals such as Al, Zn, Fe, Ni, Co and Cu have the possibility of reducing selenate to lower oxidation states (Cu has the lowest selenate removal efficiency). However, in cupric-bearing solutions, couples with electrochemical potentials below that of the cupric-copper couple can precipitate the copper as well. Very similar chemical properties of selenate and sulfate ions make selenate removal particularly difficult in sulfate solutions by heterogeneous reactions in adsorption processes. Sulfur dioxide or sulfite may be used to remove impurities in higher oxidation states such as selenate and selenite  48 and tellurate and tellurite from solutions containing cupric ions. A more likely mechanism in cupric solution involves the reduction and precipitation of selenium and tellurium species with the cuprous ions (generated in reduction of cupric with sulfite) followed by direct reduction of cupric and cuprous to copper metal by SO2 gas. The use of SO2 gas may result in contamination of the workplace, the reduction reaction is unfavoured at high acidities and reduction reactions should occur above 140°C in autoclaves.   Selenite can be easily and rapidly removed in the presence of copper powder in sulfuric acid-copper sulfate solution. On the other hand, the rate of biselenate removal is much slower and is significantly affected by temperature.  The apparent activation energy of 23 kJ/mol was reported for selenite reduction with copper metal in sulfuric acid-copper sulphate solution. Biselenate is reduced to Cu2-xSe (0 < x < 0.2) in the presence of copper metal and cupric in solution. However, the copper metal does not directly reduce biselenate and it is actually cuprous ion which reduces biselenate homogenously. The rate equation suggested by Ladriere (1973) on reduction of SeVI with cuprous was a second order rate law, first order in activity of both Cu+ and SeVI with an activation energy of about 100 kJ/mol. However, it will be shown in this study that the selenate reduction with cuprous deviates from simple second order rate law. It is suggested that similar to SeVI, the reduction of TeVI most likely occurs homogeneously by reacting with cuprous ion rather than reacting directly on the surface of the copper metal. However, the kinetics of reduction of TeVI and TeIV with cuprous is not well understood.    49 Chapter 3 Experimental  3.1 Materials  All chemicals used for preparation of cuprous-containing solutions were reagent grade or better: Na2SeO4 99% (Sigma-Aldrich), Na2SeO3 99% (Sigma-Aldrich), Cu2Se 99.5% (Alfa Aesar), Na2Te(OH)4O2.xH2O 51.42% Te (Alfa Aesar), Na2TeO3 57.44% Te (Alfa Aesar), CuSO4.5H2O 101.4% A.C.S. (Fisher Scientific), MgSO4 A.C.S. (Fisher Scientific), Al2(SO4)3.18H2O 101.4% A.C.S. (Fisher Scientific), Na2SO4 A.C.S. (Fisher Scientific), copper wire, 0.5 mm diameter, 99.9% (Alfa Aesar), H2SO4, 95-98% (Fisher Scientific), HClO4 61.2% A.C.S. (Fisher Scientific), NaClO4.H2O HPLC grade (Fisher Scientific) and Cu(ClO4)2.6H2O 99.2% (Acros). Chemicals used for analysis of cuprous were analytical grade: Cerium(IV) sulfate, 0.1 N  (Alfa-Aesar) and ferroin solution, 0.025 M (Fisher Scientific) or reagent grade: NH4Fe(SO4)2·12H2O, 99% (Sigma-Aldrich). All solutions were prepared with high purity water (18 MΩ cm) using a Nano Pure Diamond water purification system (Barnstead). Ultra high-purity argon 99.999% Ar (<3 ppm O2) was used to purge the reactor and protect cuprous solutions from oxygen. The concentration of the cerium(IV) solution was verified by titration (Vogel, 1989) with analytical grade As2O3, 99.96% (Sigma-Aldrich), and using OsO4 solution, 2% (Alfa Aesar). Copper sulfate was assayed by indirect EDTA titration using standardized zinc sulfate solution as titrant and xylenol orange as the indicator (Prĭbil, 1982). Standard EDTA, 0.0500 M (Ricca Chemical Co.), ZnSO4·7H2O, 99.5-103% (Fluka) and xylenol orange, >96% (BDH) were used. Concentrated sulfuric acid was standardized by titration with standard NaOH solution (Fisher Scientific). Thermometers were calibrated before  50 tests using an accurate certified thermometer at ice-water and boiling water temperatures (accounting for the effect of air pressure). A Radiometer auto-burette dispenser (ABU 80) was also checked for its accuracy by weighing dispensed volumes of water.   3.2 Experimental Procedures  3.2.1 Generation, Sampling and Analysis of Cuprous Ion  Cuprous ion was generated in a sealed 2 L five-neck, flat bottom flask. A schematic illustration of the experimental apparatus is shown in Figure  3-1. The reaction vessel was immersed in a thermostatted water bath. The temperature was maintained to within ±0.3°C. Argon gas was sparged through the initially chilled (minimizing water evaporation) copper sulfate-sulfuric acid/copper perchlorate-perchloric acid solution for 30 minutes to displace oxygen from solution. A slow flow of argon was maintained across the top of the apparatus. Argon was passed through copper tubing connected to the apparatus in order to minimize oxygen ingress; plastic lines proved inadequate. Solutions were prepared at known initial temperatures with known cupric and sulphuric/perchloric acid concentrations. A magnetic stirrer was used to agitate the solution. Cuprous was formed by contact of the solution with a coil of copper wire (about 16 g of 0.5 mm diameter wire) at the desired temperature. Potentiometry was used to follow the potential of a solution relative to a reference electrode (see 3.2.4.1 for details).    51  Figure  3-1: Schematic illustration of the experimental apparatus.  Sampling from the solution was accomplished by applying positive pressure of argon gas to the reactor and forcing solution to flow through a polypropylene filter (30 µm) and a heated Teflon tube into a 25 ml graduated cylinder containing a known mass of ~0.04 M (NH4)Fe(SO4)2·12H2O in 1 M sulfuric acid solution. This converted Cu+ into the more stable Fe2+, facilitating subsequent titration analysis (Fe3+ + Cu+ = Fe2+ + Cu2+). Heating of the sampling tube was necessary to avoid disproportionation of cuprous during sampling. The ferric solution was deaerated with argon gas for 10 minutes before  BubblerArgonBubblerRotameterBubblerSeptaTemperature controller95°CWater bathStirrerArgonBubblerCopper linesHeating tapeFilter95°CReference ElectrodePt Indicating Electrode Voltage controllerThermocouple thermometersArgonFe(III)aqArgonVycorStirrer 52 introducing the cuprous solution. The argon was pre-humidified by passage through an identical ferric/H2SO4 solution to minimize water vapour losses from the solution during deaeration. The mass change after deaeration was found to be at most 0.3%. During sampling the ferric solution was rapidly stirred. After sampling the solution was kept sealed and allowed to cool. The vessel and contents was again weighed to determine the mass of sample obtained. From the densities of the copper-containing solutions, the sample volume at temperature was determined. Ferrous ion was determined by titration with cerium(IV) using a Radiometer ABU 80 automatic burette with a resolution of 0.1 µL (Fe2+ + Ce4+ = Ce3+ + Fe3+). The endpoint was indicated by ferroin. The concentration of ferroin in the samples was on the order of 5 × 10-6 M. Blank titrations were used to correct for indicator error. The uncertainty in the cuprous determination was estimated to be ± 0.6% relative standard deviation. In order to verify the reliability of the procedures, a cuprous sample (~0.004 M) was generated, the copper coil was removed and then the solution was maintained at 95°C. The solution was allowed to stand for 20 hours and it was sampled periodically. The average concentration of Cu+ was 0.00412 M with a relative standard deviation of 0.56%. Deviations from the average cuprous concentrations appeared to be random and within the experimental uncertainty of the analysis, indicating that the methods used were adequate for protecting Cu+ from oxygen.   3.2.2 Determination of Equilibrium Cuprous Concentration   Copper sulfate and sulfuric acid solutions were reacted with copper metal at different temperatures to form Cu+ until equilibrium was attained. The same procedure as outlined  53 in section 3.2.1 was used for the determination of the cuprous as well as sampling and analysis. Equilibrium was usually attained within 1-1.5 hours. Copper wire coil was kept in the solution throughout the whole experiment including sampling period. Solution potential was monitored via the potential of a Pt wire in the solution relative to an Ag/AgCl reference electrode. This was used as a convenient means of indicating the time required to achieve equilibrium. Each equilibrated solution was analyzed in duplicate. The maximum deviation in the average cuprous concentration was ±1.4%.  3.2.2.1 Density Measurement of CuSO4-H2SO4 Solutions   In order to estimate the cuprous concentrations in g/L, as well as [Cu2+] and [H2SO4], for solutions at the reaction temperatures, the solution densities as a function of temperature were needed. There are a number of literature sources of density data for copper sulfate-sulfuric acid solutions (Price et al., 1980 and Hotlos et al., 1988). The work of Price et al. (1980) provided densities for solutions at temperatures of 50-70°C, but, these were stated for solution compositions in g/L known at 20°C only, while densities at 20°C were not given. Thus the concentrations at the higher temperatures cannot be determined from this data. The paper by Hotlos et al. listed compositions in molality. These data were used for solutions containing 25-70 g/L Cu2+ and 24-166 g/L H2SO4 at temperatures between 25°C and 60°C. However, many of the compositions and temperatures of interest in this study were beyond the ranges reported. Hence additional density measurements were necessary. In order to estimate solution compositions in volumetric units (e.g. g/L) the densities of the parent CuSO4-H2SO4 solutions at the reaction temperatures were used.  54 This was used as a good estimate of the densities of the cuprous-containing solutions. Copper sulfate-sulfuric acid solution densities were estimated at various temperatures, maintained to within ±0.3°C, using 1 L volumetric flasks. Known masses of assayed copper sulfate (as CuSO4·5H2O) and H2SO4 were added to a flask. Nominally 1 L solutions of known volume were prepared at an upper temperature. (The change in flask volume with temperature was incorporated into the determinations.) After weighing, the solution was cooled to a lower temperature and water was added until the required volume and temperature were achieved. The procedure was continued over the desired number of determinations. Density as a function of temperature and masses of CuSO4 and H2SO4 per kg of water was fitted to an empirical equation (Appendix 4). Density was also estimated based on known concentrations of Cu2+ and H2SO4 in g/L and temperature using an alternative correlation as described in Appendix 4.  3.2.3 Kinetics of Cuprous Oxidation with Perchlorate   The cuprous concentration in sulfate solution stays constant with time while it decreases in a perchlorate medium. Perchlorate medium was used to investigate effect of ionic strength on rates of reduction. Cuprous generation, sampling and analysis were accomplished according to the procedure outlined in section 3.2.1. After generation of a sufficient amount of cuprous (initial cuprous concentration) the copper coil was taken out from the solution and a series of cuprous samples were removed for analysis. The solution potential at sampling time was also recorded for further analysis. The cuprous concentration was analysed by titration. Continuous measurement of cuprous  55 concentration was carried out by potential monitoring between a copper metal/copper perchlorate reference electrode and the platinum electrode. Analytical results of cuprous concentration were used to calibrate the relationship between solution potential and cuprous concentration i.e. voltage versus log[Cu+] (see section 3.2.4.1). Then the Cu+ concentration with time was determined continuously by potentiometry. The voltage corresponds to the Cu2+/Cu+ couple, and was measured using a platinum electrode immersed in the test solution and a copper percholorate/copper metal reference electrode in a separate chamber and under the argon gas pressure. The copper salt/copper metal reference electrode was used to minimize the junction potential between reference and test solutions.   3.2.4 Kinetics Study of Selenium Reduction  To study the biselenate reduction kinetics with cuprous, the same procedure as outlined in section 3.2.1 was used for the cuprous generation, sampling and analysis. Typical experiments first involved placing a copper wire coil into solution. Cuprous ion was generated by the reaction of copper wire with cupric sulfate/perchlorate in the acidic solution. After generation of sufficient amounts of cuprous the copper coil was taken out from the solution and the initial concentration of cuprous was analysed by titration. The reaction was initiated by adding sodium selenate/selenite to the solution once the solution temperature stabilized at the desired value. Selenate addition was accomplished by addition of a weighed amount of Na2SeO4 powder. The Na2SeO4 powder was deaerated by vacuum. Na2SeO4 dissolves rapidly in copper sulfate sulfuric/perchloric acid solution  56 at high temperature. Selenite addition was accomplished by addition of a weighed amount of Na2SeO3 powder. During an experiment a series of samples were removed for analysis. The samples were filtered (in-line) using a fine polypropylene filter (30 µm) and after cuprous analysis the samples were sent to Vale-Canada’s laboratory for total selenium analysis by ICP-MS.   3.2.4.1 Potentiometric Monitoring in Kinetics Tests  Continuous measurement of [Cu+] was carried out by potentiometric monitoring. In potentiometry, the Cu+ concentration with time can be determined continuously by recording the voltage. The measured voltage corresponded to the Cu2+/Cu+ couple, and was measured using a platinum electrode (indicating electrode) immersed in the test solution and a Cu2+/Cu reference electrode. A reference electrode with a similar solution composition to that of the test solution was used to decrease the junction potential between solutions. The reference electrode was kept in a separate chamber and under argon gas pressure. The reference electrode chamber was connected to the test solution via a Vycor frit junction immersed in the test solution.   The Cu+/Cu2+ couple is the only reversible oxidation-reduction couple which exerts a potential in the solution. The only other oxidation reduction couple that may exist in the solution is the SeVI/SeIV (or TeVI/TeIV) couple. As was mentioned before, reduction of SeVI to SeIV is a very slow reaction in general. In addition, reduction of SeIV to lower oxidation states is very fast and it will be consumed as soon as it is generated. In other  57 words, the SeVI/SeIV redox reaction is highly irreversible on Pt electrode and it will not affect the potential measured on platinum electrode. Cu2Se precipitates could affect the potential, but they did not precipitate onto the Pt electrode. The cell voltage potential measured during biselenate reduction experiments is also much lower than SeVI/SeIV redox couple range and conforms to a cell voltage in the range of the Cu+/Cu2+ redox couple. (see Figure  5-5). Consequently, the potential difference is calculated as:  Reference electrode: 0.5Cu2+ + e- = 0.5Cu                                                                    ( 3-1) Indicating electrode: Cu2+ + e- = Cu+                                                                             ( 3-2) Cell overall reaction: 0.5Cu R + Cu2+I = 0.5Cu2+R + Cu+ I                                              ( 3-4)  [Cu2+]R and [Cu2+]I represent the cupric concentrations in the reference electrode chamber and test solution, respectively. Since [Cu2+]R and [Cu2+]I are essentially fixed (only a relatively small additional [Cu2+]I forms during reduction reaction) hence, there is a linear relationship between solution voltage and the logarithm of the cuprous concentration.   3.2.4.2 Cuprous Selenide Reaction with Cupric  To study the effect of the reaction: Cu2Se + xCu2+aq = 2xCu+aq + Cu2-xSes on the reaction stoichiometry, the rate of chemical reaction of reagent grade Cu2Se with cupric in solution was conducted under argon. Copper sulfate solutions were purified from iron ions by adding 0.02 g/L KOH to the solution (Perrin et al., 1988). The solutions were IIRICell CuFRTConstCuCuCuFRTEE ]log[303.2.][][][log303.2 25.020 ++++−=⋅−∆=∆   ( 3-3)  58 filtered after 2 weeks and then the solution acidity was adjusted. Known portions of de-aerated cuprous selenide powder were added to the solution in stages. The maximum possible cuprous concentration (below which Cu2Se dissociation begins), was measured by adding sufficient amounts of cuprous selenide powder to copper sulfate-sulfuric acid solution and monitoring the generated cuprous concentration. Below this concentration the dissociation reaction occurs and the stoichiometry of the overall reaction and eventually the rate constants deviate slightly from their initial values. Above this point the dissociation of Cu2Se becomes very small so that generated cuprous is not detectable by titration (Cu+ < 0.0001 M). This allowed determination of the minimum cuprous concentration in kinetics tests such that the copper selenide product would be essentially Cu2Se rather than Cu2-xSe. Tests were designed to avoid having cuprous concentrations go below this threshold.  3.2.5 Kinetics Study of Tellurium Reduction   Kinetics experiments to investigate tellurium reduction were conducted in the same apparatus described in section 3.2.1. Details of the cuprous generation, sampling and analysis were explained previously. Cuprous ion was generated by the copper wire-copper sulfate reaction in the acidic solution. After generation of sufficient amounts of cuprous the copper coil was taken out from the solution and the initial concentration of cuprous was analysed by titration. The reaction was initiated by adding sodium tellurate/tellurite to the solution once the solution temperature stabilized at the desired value. Tellurium addition was accomplished by addition of a weighed amount of sodium  59 tellurate/tellurite powder. The sodium tellurate/tellurite powder was deaerated by vacuum. Sodium tellurite concentrations were restricted to levels low enough to avoid formation of solid TeO2. During the experiment a series of samples were removed for analysis. Samples were sent to the Vale-Canada laboratory for tellurium analysis by ICP-MS. Continuous measurement of [Cu+] was carried out by potentiometric monitoring similar to the selenium reduction tests.   3.2.6 Repeatability and Accuracy of the Thermodynamics and Kinetics Experiments   In this work several tests were applied to verify that the cuprous equilibrium had been reached. The Cu2+/Cu+ couple potential on Pt was monitored during Cu+ generation, and once it was constant samples were taken. Two samples (occasionally three) were analyzed for each set of conditions, with good agreement as outlined in this Experimental chapter. In general cuprous saturation was approached by heating cupric solutions with copper metal. In one test equilibrium was also approached from cuprous supersaturation. This was done using a saturated cuprous solution prepared with 50 g/L Cu2+ and 10 g/L H2SO4 at 95°C and lowering the temperature to 75.2°C. Copper metal was seen to have precipitated upon cooling. The analyzed [Cu+] was found to be 0.5182 g/L, which was virtually identical to the result produced by heating the same test solution to the same temperature (0.5178 and 0.5180 g/L at 75.2°C). A test was done to verify that the sampling methodology was reliable. A solution containing 122.8 g CuSO4/kg H2O and 37.6 g H2SO4/kg H2O at 50.0°C (47.3 g/l Cu2+,  60 36.4 g/L H2SO4) was equilibrated with copper metal. The copper wire coil was then removed from the solution. Samples were removed and analyzed for Cu+. Next a known mass of excess aqueous NH4Fe(SO4)2·12H2O in 1 M H2SO4 (deaerated) was added to the entire remaining Cu+ solution. Large samples (~110 g each) of this solution were removed and titrated with CeIV to determine the Fe2+. In this way all the cuprous was first converted to cupric, which was then sampled under argon. Possible losses of Cu+ due to air ingress during sampling were thus prevented. The average cuprous concentration by the conventional sampling method was 0.1614 g/L and that obtained by the second method was 0.1634 g/L. The agreement was very good and within experimental uncertainty. Together these efforts suggest that the methodology was sound and accurate.  Efforts were also made to assure the accuracy and repeatability of the kinetics tests. Initial cuprous concentration was measured by taking at least two samples after the copper coil was taken out from the solution and before addition of selenium and tellurium. In some kinetics tests rate constants were measured separately as a concentration function of both cuprous and selenium/tellurium with time. Continuous measurements of [Cu+] with time in all kinetics tests also contributed to the accuracy of the rate constants measurements during the reduction reactions. The accuracy of the analysis of selenium and tellurium samples were verified by including blind standards of known concentration among the samples sent to VALE for ICP-MS analysis. Replicate experiments were also performed for some equilibrium and kinetics tests (see section 4.1.3.1 (Table  4-1) for equilibrium tests, 5.3.4 for kinetics of selenium reduction and 6.3.5.1 for kinetics of tellurium reduction).  61 Chapter 4 Cuprous Sulfate Thermodynamics and Cuprous Perchlorate Oxidation Kinetics   4.1 Equilibrium Cuprous Concentrations in Copper Sulfate-Sulfuric Acid Solutions   4.1.1 Objectives   As mentioned in chapter 1 and 2, aqueous cuprous ion has uses as a reducing agent in hydrometallurgical applications. Cuprous ion is formed by contacting an aqueous cupric salt with metallic copper. Hence, knowing the thermodynamics of cuprous ion reaction in a wide range of composition and temperature is of critical importance.  However, while some data are available for the equilibrium cuprous concentrations in copper sulfate-sulfuric acid solutions (Heinerth, 1931 and Ladriere, 1973), it does not cover a suitably wide range of composition and temperature. In addition, Heinerth, 1931 and Ladriere, 1973 results differ significantly. This and the desire to have a more extensive data set of cuprous concentrations for stronger CuSO4/H2SO4 solutions provided the impetus for this part of the work.   In this section, the equilibrium concentrations of cuprous ion in sulfate medium at 50-95°C were studied. Equilibrium cuprous concentration data were fit to a relationship as a function of [Cu2+], [H2SO4] and temperature. This function is of use in chapter 5 and 6 in using cuprous sulfate solutions derived from moderately high concentrations of CuSO4 and H2SO4.    62 4.1.2 Experimental  Copper sulfate (25-110 g/L Cu2+) and sulfuric acid (10-200 g/L) solutions were reacted with copper metal at temperatures between 50 and 95°C to form Cu+ until equilibrium was attained. Equilibrium was usually attained within 1-1.5 hours. Solution potential was monitored as a convenient means of indicating the time required to achieve equilibrium.  Details of the experimental apparatus and cuprous sampling and analysis were explained in 3.2.1 and 3.2.2.  4.1.3 Results and Discussion  4.1.3.1 Cuprous Concentrations  Cuprous concentrations for various Cu2+-H2SO4 compositions and temperatures were obtained. The cuprous generation reaction is an endothermic reaction and hence the cuprous concentration will increase with increasing temperature. Cuprous concentrations for various Cu2+-H2SO4 compositions and temperatures are reported in Table  4-1. Data for [Cu+] expressed on the g/L scale were estimated from the analytical results (mass of cuprous per g of sample) multiplied by the estimated density at the reaction temperature. The densities of the cuprous-bearing solutions were assumed to be equal to those of their parent CuSO4/H2SO4 solutions at specified temperatures. This introduces a small, but probably minor error; the additional mass of copper added to a solution upon formation of Cu+ was at most 0.07%. Replicate experiments (Table  4-1) were performed for four sets of conditions ([Cu2+]/[H2SO4], in g/L, approximately 25/100, 50/10, 75/100 and 110/200) with good agreement of 2.9% maximum deviation.  63 Table  4-1: Cuprous concentrations in g/L units for initial CuSO4/H2SO4 concentrations. Solution composition Temp. °C [Cu+] g/L a Solution composition Temp. °C [Cu+] g/L a 50.2 0.1174 50.2 0.2100 60.2 0.1852 60.2 0.3261 75.3 0.3605 75.3 0.6306 85.2 0.5346 85.2 0.9285 25 g/L Cu2+ (WCuSO4 = 65.70 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 104.6 g/kg H2O) at 22.4°C 95.1 0.7706 95.2 1.342 75 g/L Cu2+ (WCuSO4 = 199.4 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 105.9 g/kg H2O) at 22.4°C 98.2 1.502 50.2 0.1143 60.1 0.1823 60.2 0.3166 75.3 0.3599 75.2 0.6219 85.1 0.5321 85.3 0.9219 25 g/L Cu2+ (WCuSO4 = 65.73 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 104.7 g/kg H2O) at 22.2°C 95.1 0.7651 75 g/L Cu2+ (WCuSO4 = 199.5 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 105.9 g/kg H2O) at 22.2°C 95.2 1.325 50.2 0.1619 50.2 0.2291 60.2 0.2550 60.2 0.3649 75.3 0.5180 75.2 0.7053 50 g/L Cu2+ (WCuSO4 = 126.8 g/kg H2O), 10 g/L H2SO4 at (WH2SO4 = 10.10 g/kg H2O) 22.4°C 95.2 1.105 85.3 1.036 95.2 1.499 50.2 0.1604 90 g/L Cu2+ (WCuSO4 = 243.8 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 107.9 g/kg H2O) at 49.0°C 98.3 1.673 60.2 0.2577 75.3 0.5178 60.2 0.3815 50 g/L Cu2+ (WCuSO4 = 126.9 g/kg H2O), 10 g/L H2SO4 (WH2SO4 = 10.11 g/kg H2O) at 22.2°C 95.2 1.086 75.3 0.7859 85.2 1.170 50.2 0.1696 110 g/L Cu2+ (WCuSO4 = 287.4 g/kg H2O), 10 g/L H2SO4 (WH2SO4 = 10.40 g/kg H2O) at 58.9°C 95.2 1.723 60.2 0.2631 75.3 0.5102 60.2 0.4072 50 g/L Cu2+ (WCuSO4 = 132.1 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 105.2 g/kg H2O) at 22.4°C 95.2 1.085 75.2 0.7953 85.3 1.179 50.2 0.1738 110 g/L Cu2+ (WCuSO4 = 301.8 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 109.2 g/kg H2O) at 58.9°C 95.2 1.696 60.1 0.2673 75.3 0.5262 75.3 0.8430 50 g/L Cu2+ (WCuSO4 = 138.4 g/kg H2O), 200 g/L H2SO4 (WH2SO4 = 220.5 g/kg H2O) at 22.4°C 95.2 1.114 85.2 1.230 110 g/L Cu2+ (WCuSO4 = 322.2 g/kg H2O), 200 g/L H2SO4 (WH2SO4 = 233.3 g/kg H2O) at 73.6°C 95.3 1.751 50.2 0.1828 60.2 0.2881 75.3 0.8319 75.3 0.5584 85.2 1.227 85.2 0.8249 60 g/L Cu2+ (WCuSO4 = 158.9 g/kg H2O), 100 g/L H2SO4 (WH2SO4 = 105.4 g/kg H2O) at 22.4°C 95.2 1.191 110 g/L Cu2+ (WCuSO4 = 321.8 g/kg H2O), 200 g/L H2SO4 (WH2SO4 = 233.0 g/kg H2O) at 71.4°C 95.3 1.756 a At the specified temperatures.   64 Increasing the cupric concentration will shift the equilibrium to the right (Cu2+ + Cu (S) = 2Cu+) and generate more cuprous. To a rough approximation, cuprous concentration as a function of temperature can be estimated based on the Van’t Hoff equation. In this equation it is assumed that the ∆H reaction is independent of temperature (over a limited temperature range). Accordingly, the cuprous concentration would be expected to rise exponentially with temperature and to be approximately proportional to [Cu2+]0.5:  5.022 ][][ +∆−+ ×= CueCu RTH reaction  ( 4-1)  The data showed that cuprous concentration increased slightly at higher acidity. Hence the data were fitted to an empirical equation of the form,  where [Cu+], [Cu2+] and [H2SO4] are in g/L at temperature T (K), or are in molal, and V-Z are constants. Cupric and sulphuric acid concentrations at temperature T may be obtained by knowing the cupric and sulphuric acid concentrations at solution preparation temperature and using empirical density functions reported in Appendix 4. The constants V-Z are shown in Table  4-2. The difference between the calculated and measured [Cu+] was at most ±3.6% when expressed in g/L units. When [Cu+], [Cu2+] and [H2SO4] were expressed in molal units the difference was at most ±3.5%. The data and calculated values are shown in Figure  4-1 for solutions containing approximately 100 g/L H2SO4.  ( )1]Z[H]Y[H][Cue][Cu 42242X2T-W ++= ++ SOSOV    ( 4-2)  65 Table  4-2: Constants for equation ( 4-2) used to estimate cuprous concentrations.   Compositions at the temperatures at which the solutions were prepared are provided in the legend for ease of comparison with the data in Table  4-1. Equilibrium cuprous concentrations in molal units for initial CuSO4/H2SO4 concentrations were presented in Appendix 5.  4.1.3.2 Effect of Acidity on Cuprous Concentration  Varying acid concentrations (~10, ~100 and ~200 g/L H2SO4) were tested for ~50 g/L Cu2+ and ~110 g/L Cu2+. The data and calculated values are shown in Figure  4-2 A and B for solutions containing 50 and 110 g/L cupric. Sulfuric acid concentration has a modest effect on the equilibrium cuprous concentration. The difference between the highest and lowest [Cu+] for a given [Cu2+] and temperature was 7%. The effect is higher at lower temperatures and it decreases slightly at higher temperatures. For example, as it is illustrated in Figure  4-2 B, the cuprous concentration decreases by 5.7%, 4.7% and 1.8% with increasing acidity from 10 g/L to 200 g/L sulfuric acid at 75, 85 and 95°C, respectively. V W X Y Z Maximum error [Cu+] in g/L over: 25-110  g/L Cu2+, 10-200 g/L H2SO4, 50-95°C  145,906 5089.08 0.52162 2.400 × 10-6 -1.849 × 10-4 ± 3.6% [Cu+] in molal over: 0.41-2.0 m Cu2+, 0.10-2.4 m H2SO4, 50-95°C 22757 5128.95 0.5330 0.009462 0.02540 ± 3.5%  66  0.00.51.01.52.045 55 65 75 85 95Temperature °C[Cu+] g/L110/100 at 58.9°C90/100 at 49.0°C75/100 at 22.4°C60/100 at 22.9°C50/100 at 22.4°C25/100 at  22.4°CComposition, g/L: Cu2+/H2SO4 at specified temperature.  Figure  4-1: Measured cuprous concentrations as a function of temperature for varying [Cu2+] and 100 g/L H2SO4 at specified initial temperatures, fitted to the empirical correlation of equation ( 4-2).  Increasing acid concentration may be expected to convert more SO42- to HSO4-, thereby increasing the activity of Cu2+. This would be expected to enhance the formation of Cu+ (reaction ( 2-5) ). A detailed theoretical analysis would include consideration of the   Cu2+-SO42- ion pairing equilibrium, the HSO4- acid dissociation and reaction ( 2-5). The maximum cuprous concentration that can be generated at 95°C and cupric concentration of 110 g/L is about 1.75 g/L (Figure  4-2 B).   67          Figure  4-2: Effect of acidity on cuprous concentration as a function of temperature for (A): [Cu2+] = 50 g/L and (B): [Cu2+] = 110 g/L, fitted to the empirical correlation of equation ( 4-2).  There are two other reports on cuprous concentrations in copper sulfate-sulfuric acid solutions and at temperatures above room temperature. The first is by Heinerth (1931). This work used cupric concentrations of up to 65 g/L Cu2+ and up to 49 g/L H2SO4. Cuprous concentrations were referenced to solution compositions at 20°C. Where conditions of Heinerth’s work overlap with those of this work his results were higher by 3.0-8.4% (comparing the published results with the calculated values based on equation ( 4-2)). All of Heinerth’s data (2.5-65 g/L Cu2+, 2-50 g/L H2SO4 and 20-60°C) were fitted to equation ( 4-2) with quite different constants from those in Table  4-2. Where Heinerth’s conditions and those of this work overlap, the two correlations based on equation ( 4-2) 00.20.40.60.811.20 100 200[H2SO4] g/L[Cu+] g/L95 °C85 °C60 °C50 °C(A) Temperature, °C at specified [H2SO4] and Cu2+ = 50 g/L00.40.81.21.620 100 200[H2SO4] g/L[Cu+] g/L95 °C85 °C75 °C60 °C(B) Temperature, °C at specified [H2SO4] and Cu2+ = 110 g/L 68 were almost parallel; the difference was 0.013-0.016 g/L Cu+. This suggests a systematic error, though the reasons for the discrepancy are not clear.   The second report in the literature on cuprous concentration with varying [Cu2+] and temperature is the work of Ladriere (1973). His work used [Cu2+] between 6 and 64 g/L and a fixed H2SO4 concentration of 49 g/L with solutions prepared at 25°C. Cuprous concentrations were determined for these solutions reacted between 40 and 100°C. Under conditions where Ladriere’s work and this study overlap his results were 12-17% lower than those of this work, or in a couple of cases the same, within experimental uncertainty.  4.2 Kinetics of Cuprous Oxidation with Perchlorate  4.2.1 Objectives   Perchloric acid oxidizes cuprous ion slowly. Hence, studying the concentration of cuprous in perchlorate solution especially at high temperature is impossible without considering the oxidation rate of cuprous by perchlorate. Kinetics behaviour of the cuprous ion in perchlorate solution is not known. Perchloric acid is a strong acid which can fully dissociate and does not make a strong complex with cuprous ion, nor cupric ion. Hence, in principle, it can be used to investigate the true effect of ionic strength and acidity on reduction rate of SeIV, VI and TeIV, VI without weak acid buffering effect of HSO4- = H+ + SO42- or the ion pairing effect of CuSO4aq = Cu2+aq + SO42-aq in copper sulfate-sulfuric acid solution. Finally the fact that perchlorate can be reduced to lower  69 oxidation states by cuprous might afford a means of removing this rather toxic species. The kinetics of cuprous oxidation in perchloric acid solution was investigated at 95°C and four different ionic strengths.  4.2.2 Experimental  Experiments were conducted in a 2 L flask. Details of the experimental apparatus and cuprous generation, sampling and analysis were explained in section 3.2.1 and 3.2.2. Cupric concentration of 50 g/L and 100 g/L perchloric acid with sodium perchlorate salt concentration varying from 0 to 3 molar was used. Cupric perchlorate was used to provide cupric ion in the kinetics tests. Continuous measurement of cuprous concentration was carried out by potential monitoring between the copper/copper perchlorate reference electrode and the platinum electrode. After generation of sufficient amounts of cuprous (initial cuprous concentration) the copper coil was taken out from the solution and a series of cuprous samples were removed for analysis.   4.2.3 Results and Discussion  The cuprous concentration in sulfate solution stays constant with time while it decreases in a perchlorate medium. In Figure  4-3 the different behaviour of Cu+ in sulfate and perchlorate media is shown at 95.1°C and equal concentrations of Cu2+ (50 g/L), H2SO4 and HClO4 (100 g/L).  70 00.10.20.30.40.0 5.0 10.0 15.0 20.0Time (hr)[Cu+] g/LCuSO4-H2SO4 SolutionCu(ClO4)2-HClO4 Solution Figure  4-3: Cuprous concentration in sulphate and perchlorate media versus time, Cu2+ = 50 g/L, H2SO4 and HClO4 = 100 g/L, T = 95.1°C.  The average concentration of cuprous in copper sulphate-sulfuric acid solution deviates within the experimental uncertainty, as explained previously. Cuprous concentration decreases by 63% in perchlorate solution after 20 hours. The oxidation of cuprous to cupric may be achieved when coupled to one or more of the following reduction half reactions (E0 values were calculated based on the ∆G0 of the reactions using HSC 7.1 database):  ClO4- + 2H+ + 2e- = ClO3- + H2O (E0 =  1.23 V)                                                            ( 4-3) ClO3- + 2H+ + 2e- = ClO2- + H2O (E0 =  1.10 V)                                                            ( 4-4) ClO2- + 2H+ + 2e- = ClO- + H2O (E0 =  1.51 V)                                                              ( 4-5) ClO- + 2H+ + 2e- = Cl- + H2O (E0 =  1.72 V)                                                                  ( 4-6)   71 Cuprous concentration with time was determined continuously by recording the solution voltage (Equation ( 3-3)). Analytical data and cuprous calibration equations for solutions with 0, 2 and 3 M NaClO4 and [Cu+]0 = 0.019, 0.004 and 0.015 M are depicted in Figure  4-4. Calibration equations then were used to determine continuous [Cu+] versus time. Rate constants for reaction of ClO4- with Cu+ were measured by plotting ln[Cu+] or [Cu+] versus time and calculating the slope of the straight line using least squares method for first order and zero order rate equations, respectively. Cuprous oxidation rate in perchlorate media was measured for solutions containing 0, 1, 2 and 3 M NaClO4, [HClO4] = 100 g/L, [Cu(ClO4)2] = 50 g/L at 95.1°C. Figure  4-4: log [Cu+] vs. voltage (vs. Cu/Cu2+) and calibration equations for Cu+ oxidation reactions with perchlorate species at 0, 2 and 3 molar NaClO4 and different [Cu+]0. (HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1°C).  y = -0.0127x - 1.4936R2 = 0.9966y = -0.0126x - 1.4369R2 = 0.9971y = -0.0125x - 1.3299R2 = 0.9954-2.8-2.6-2.4-2.2-2-1.8-1.6-1.410 20 30 40 50 60 70 80 90 100Voltage (mV)log [Cu+] M□ NaClO4 = 0 M, Cu+0 = 0.019 M∆ NaClO4 = 2 M, Cu+0 = 0.004 MO NaClO4 = 3 M, Cu+0 = 0.015 M 72 Rate constant data with the assumption of an apparent first order rate law are tabulated in Table  4-3 at different initial cuprous concentrations. The data fit well to an apparent first order kinetics (equation ( 4-7)) with rate constants as per Table  4-3.   Table  4-3: Cuprous oxidation rate constants with first order rate law assumption at different sodium perchlorate and initial cuprous concentration.  [NaClO4] = 0 M [NaClO4] = 1 M [NaClO4] = 2 M [NaClO4] = 3 M [Cu+]0 M 0.007 0.019 0.009 0.019 0.004 0.009 0.010 0.016 First Order (s-1) 1.72×10-5 1.78×10-5 3.31×10-5 3.25×10-5 5.73×10-5 5.77×10-5 9.92×10-5 9.92×10-5 Average k first order 1.75×10-5 s-1 3.28×10-5 s-1 5.75×10-5 s-1 9.92×10-5 s-1  The model of zero order kinetics was rejected since the cuprous oxidation rate constants differed at different initial [Cu+]. Assuming first order kinetics, rate constants are almost identical at different initial cuprous and constant cupric-perchloric acid concentration:  kt0e][Cu][Cu][Cukdt][Cud ++++=⇒=   ( 4-7)   Rate constants increase significantly with addition of sodium perchlorate salt and consequently increasing the solution ionic strength. The data and calculated values are shown ( Figure  4-5) for solutions containing 0, 1, 2 and 3 molar sodium salt at different initial cuprous concentrations. The calculated [Cu+] with time matches the experimental data very well as shown in  Figure  4-5. Calculated curves are based on the suggested first order rate law and average rate constants at constant cupric-perchloric acid concentration (Table  4-3). Cuprous was oxidized almost six times faster in a solution containing 3 M  73 NaClO4 than a solution without NaClO4 addition and with similar initial cuprous-cupric compositions. Rate constant data along with nominal ionic strength of the solution are summarized in Table  4-4.   Figure  4-5: Comparison of calculated and experimental cuprous concentrations with time at 0, 1, 2 and 3 M NaClO4 concentration  and HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1°C.  Table  4-4: Cuprous oxidation rate constant with nominal ionic strength, HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C. NaClO4 [M] I [M] k (M-1s-1) 0 3.36 1.75×10-5 1 4.36 3.28×10-5 2 5.36 5.75×10-5 3 6.36 9.92×10-5  00.30.60.91.21.50 1 2 3 4 5Time (hr)[Cu+] g/L□ NaClO4 = 0 M, k = 1.77×10-5s-1  ◊ NaClO4 = 2 M, k = 5.75×10-5s-1  ∆ NaClO4 = 1 M, k = 3.28×10-5s-1  O NaClO4 = 3 M, k = 9.92×10-5S-1  74 The ionic strength increases from 3.35 to 6.35 M as the NaClO4 concentration varies from 0 M to 3 M. The rate constant data follows the modified Bronsted-Bjerrum (1922) equation (see section 5.3.8 for details) in the form of equation ( 4-8). According to the modified Bronsted-Bjerrum equation, the rate constant k1 is expected to increase by increasing the ionic strength in the solution concentration range tested. The product of the reacting ions charges and the rate constant at infinite dilution was found to be - 0.90 and 8.53×10-6 M-1s-1 from the slope and intercept of the straight line in Figure  4-6.   −+−−= IIIk 3.0190.007.5log21211   ( 4-8)  log k1 = -0.90 [I1/2/(1+I1/2)-0.3I]  - 5.07R2 = 1.00-5-4.5-4-3.5-1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1I1/2/(1+I1/2)-0.3Ilog k 12.0003.0004.0005.0006.0007.000I Figure  4-6: Rate constant k1 as a function of solution nominal ionic strength at HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C (Table  4-4).   75 The deviation of the calculated values from the modified Bronsted-Bjerrum equation can be attributed to the higher solution concentrations used in this study. Rate constant k1 values can be estimated accordingly, at different ionic strengths using the equation ( 4-8).   4.3 Summary    In this chapter, the equilibrium concentrations of cuprous ion for various Cu2+-H2SO4 compositions and temperatures were obtained at 50-95°C. Equilibrium cuprous concentration data were fit to a relationship as a function of [Cu2+], [H2SO4] and temperature. The cuprous concentration would be expected to rise exponentially with temperature following the Van’t Hoff equation as cuprous generation reaction is an endothermic reaction and would be expected to be approximately proportional to [Cu2+]0.5. This function is of use in chapter 5 and 6. The equilibrium cuprous concentration data were fitted to an empirical equation of the form,  where [Cu+], [Cu2+] and [H2SO4] are in g/L at temperature T (K), or are in molal, and V-Z are constants. The difference between the calculated and measured [Cu+] was at most ±3.6% when expressed in g/L units over the solution range of 50-110 g/L Cu2+ and 10-200 g/L H2SO4. Sulfuric acid concentration had a modest effect on the equilibrium cuprous concentration.  Kinetics behaviour of the cuprous ion in perchloric acid solution as a strong acid which does not make a complex with cuprous ion, nor cupric ion was studied at 95°C and four ( )1]Z[H]Y[H][Cue][Cu 42242X2T-W ++= ++ SOSOV   ( 4-2)  76 different ionic strengths. Perchloric acid solution, can be used to investigate the true effect of ionic strength and acidity on reduction rate of SeIV, VI and TeIV, VI without weak acid buffering effect of HSO4- = H+ + SO42- or the ion pairing effect of CuSO4aq = Cu2+aq + SO42-aq in copper sulfate-sulfuric acid solution. Cuprous reacts slowly with perchlorate in solutions with cupric perchlorate and perchloric acid. Cuprous oxidation rate in perchlorate media was measured for solutions containing 0, 1, 2 and 3 M NaClO4, [HClO4] = 100 g/L, [Cu(ClO4)2] = 50 g/L at 95.1°C. The rate of cuprous oxidation was apparent first order with respect to cuprous concentration ([Cu+] = [Cu+0] × e-kt) with the rate constants varying from 1.75×10-5 to 9.92×10-5 s-1 depending on the sodium perchlorate concentration. Rate constants increase significantly with addition of sodium perchlorate salt and consequently increasing the solution ionic strength. The rate constant data followed the modified Bronsted-Bjerrum equation in the form of:  −+−−= IIIk 3.0190.007.5log21211   ( 4-8)  where I is the solution ionic strength.         77 Chapter 5 Kinetics Study of Selenium Removal from Copper Sulfate-Sulfuric Acid Solutions  5.1 Objectives  Cuprous ion can be specifically used to remove higher oxidation states of selenium from copper sulphate-sulfuric acid solution. The main disadvantage of using cuprous is that the reduction of SeVI with cuprous is a slow reaction. Kinetics of the reduction of SeVI with cuprous is poorly understood. It is therefore an objective of this research to investigate the SeVI reduction reaction kinetics with cuprous ion in acidic solution and identify factors enhancing the removal rate. In this chapter, the chemistry and kinetics of selenium removal by cuprous ion precipitation and the effects of acidity, cupric concentration, temperature and ionic strength on the removal rate was investigated.  5.2 Experimental  Details of the experimental apparatus and cuprous analysis were explained previously (section 3.2.1 and 3.2.4). Typical experiments first involved placing a copper wire coil into copper sulfate/perchlorate solution. After generation of sufficient amounts of cuprous the copper coil was taken out and the reaction was initiated by adding a weighed amount of Na2SeO4 powder. During the experiment a series of samples were removed for cuprous and selenium analysis. Details of solutions concentration and test conditions varied for each experiment and are as following.   78 5.2.1 Stoichiometry of the Reduction of Biselenate with Cuprous  The stoichiometry of the overall reaction was investigated by running a kinetics test with initial cuprous and selenium concentration of 0.012 M and 0.001 M, respectively at 95.1°C. The ratio of cuprous-selenium consumed was measured by sampling and analysis. Consequently, the stoichiometric coefficient x in reaction ( 2-17) was measured in above mentioned conditions.  5.2.2 Verification of the Rate Law at Constant Acidity, Temperature and Ionic Strength  The dependence of rate constants on concentrations of biselenate, cuprous and cupric were investigated by running several tests at different initial concentrations of biselenate, cuprous and cupric but constant temperature (T = 95.1°C), acidity (H2SO4 = 100 g/L) and ionic strength.   5.2.3 Cuprous Selenide Reaction with Cupric  Chemical reaction of Cu2Se reagent with cupric at [Cu2+] = 50 and 90 g/L and [H2SO4] = 100 g/L was conducted under argon gas. Details of the experimental procedure are summarized in 3.2.4.2. Maximum possible cuprous concentration at which cuprous selenide dissociation reaction is not detected, was measured at 95.1 and 98.6°C. Below this concentration the dissociation reaction occurs and the stoichiometry of the overall reaction and eventually the rate constants deviate slightly from their initial values. Cupric  79 concentration of 90 g/L and 98.6°C temperature were the maximum concentration and temperatures which have been used in this research which consequently results in the maximum cuprous concentration from the dissociation reaction in all kinetics tests as per equation ( 2-19). This concentration represents the minimum cuprous concentration that should be formed in kinetics tests (at cupric concentrations lower than 90 g/L and temperatures below 98.6°C less cuprous will form). A similar test for cupric concentration of 50 g/L and temperature of 95.1°C was conducted and similarly the minimum cuprous concentration was determined.  5.2.4 Effect of Acidity, Temperature, Cupric Concentration and Ionic Strength on Selenium Removal Rate  The effect of acidity was investigated by running the reduction reaction at 95.1 and 86.2°C in a fixed cupric concentration of 50 g/L at sulfuric acid concentrations of 10, 50, 100, 150, 200 g/L and perchloric acid concentrations of 10, 50, 100, 150 g/L. Acidity has a direct contribution in the overall reaction (HSeO4- + 7H+ + 10Cu+ = Cu2Se + 4H2O + 8Cu2+) and is expected to have a significant effect on the selenate removal rate.  The effects of temperature on the kinetics of reaction at T = 98.6, 95.1, 90.3, 86.1°C and Cu2+ = 75 g/L and H2SO4 = 100 g/L was studied. Activation energy of biselenate reduction with cuprous was also measured via the Arrhenius equation (k = Ae-Ea/RT) and calculated rate constants.    80 Cupric concentration effect on biselenate removal rate was investigated through two sets of experiments in copper sulfate-sulfuric acid solution with and without keeping the ionic strength constant. In the first set, the effect of cupric concentrations of 30, 40, 50 and 60 g/L at constant nominal ionic strength of 6 molal was investigated on removal rate at 95.1°C and H2SO4 = 50 g/L. Ionic strength was kept constant by adding sufficient amounts of sodium sulfate to the solution. In the second set of experiments, the effect of cupric at concentrations of 40, 50, 75 and 90 g/L was investigated without controlling the solution ionic strength.  To investigate the true effect of ionic strength on biselenate reduction rate it is essential to use a salt without sulfate-bisulfate buffering effect (HSO4- = H+ + SO42-) or copper sulfate ion pairing effect (CuSO4 = Cu2+ + SO42-) in solution. In sulfate media usage of any kind of sulfate based salts will increase the sulfate ion concentration which consequently affects the free H+ ion concentration by changing the bisulfate dissociation equilibrium. As it will be shown later, any small change in H+ ion concentration and solution acidity will change the removal rate significantly and disrupt the effect of ionic strength. To prevent this problem, using a strong acid which can fully dissociate is recommended. Since hydrochloric acid can make a strong complex with cuprous    (CuCl2-), perchloric acid was chosen to investigate the effect of ionic strength on removal rate. Cupric perchlorate was also used to provide cupric ion in solution. Sodium perchlorate was used as a salt to adjust the ionic strength. The biselenate removal rate was measured at 95.1°C, NaClO4 concentrations of 0, 1, 2 and 3 M, cupric perchlorate and perchloric acid concentrations of 50 g/L Cu2+ and 100 g/L respectively.   81 5.3 Results and Discussion  5.3.1 General Rate Law Based on Suggested Mechanism  SeVI and SeIV are well known selenium species; SeV is a short-lived intermediate state (Klaning, 1986). Cu+3 ion is also known (Utter et al., 2004), as a strong oxidant (Cu3+/Cu2+ E0 = 1.80V). Reduction of SeVI with Cu+ may be expected to occur then according to two different mechanisms (Cannon Roderick, 1980): Initial one electron transfer with formation of intermediate SeV :  +→++↔+++++−IVkVVkkVISeCuCuSeSeCuSeCu22211    Mechanism 1  Or, initial two electron transfer with formation of intermediate Cu3+:  =+→++↔+++−++′+++′′+)96.1( 321102233VECuCuCuCuSeCuSeCuCuCukIVkkVIMechanism 2  Mechanism one is the most probable for two electron reagents with VI/IV oxidation states (CrVI, PuVI, UVI are known examples of this mechanism) with a known short lived intermediate of V oxidation state (Cannon Roderick, 1980). As it will be shown later the  82 kinetics fit this mechanism. The two electron transfer reduction of SeVI to SeIV with formation of intermediate Cu3+ (mechanism 2) is very unfavourable reaction (∆E0 < 0).   Mechanism 1 is based on initial one electron transfer to form the intermediate SeV, followed by applying the steady state criterion for SeV ie: 0][ =−dtSed V :  Rate determining step   SeCuCuSeSeCuCuSeSeCuSeCufastIVIVkVVkkVI222211→++→++↔++++++−   By writing and combining rate equations for the above three reactions and applying the  steady state criterion a general kinetics equation at constant acidity is derived as follows:  ]][[]][[]][[][]][[]][[][2112211VVIVVVVIVISeCukSeCukSeCukdtSedSeCukSeCukdtSed+−+++−+−+−=+−= ][][][][][][][][][][]][][[]][[][][][]][[][])[][]([]][[0][:ionapproximat stateSteady 22121221221221211122112211++−+++−+++−++−+++−+++−++−=+−=++−=⇒++=⇒++=+=CuCukkSeCukCukCukSeCukkCukCukCuSeCukkSeCukdtSedCukCukSeCukSeCukCukSeSeCukdtSedVIVIVIVIVIVIVVVIV                                  83  General kinetics equation: ][][][][][22121++−++=−CuCukkSeCukdtSed VIVI  ( 5-1)  Similarly, the derivation of the rate law based on mechanism 2 was shown in Appendix 6.  According to equation (5-1), the biselenate removal rate increases at higher concentrations of cuprous and biselenate while cupric functions as an inhibitor especially if k-1/k2 is high. If the overall reaction is stated as equation ( 2-17), then ][101][ +∆−=∆ CuxSeVI:  dtkkCudCuCCuCukCukdtCuCCukkCukCukCudCuCukkCuCCukdtCudCCuSexCuCukkCuSexCuCukdtCudCuCukkSeCuCuxCukdtCudxCuCukkSeCuCuxCukdtCudxdtSedSeCuCuxSeSeSeCuxSeCuCuCuandSeSeSeVIVIVIVIVIVIVIVIVIVIVIVIVI212221221221221210022100212210021221002100000][])[(][])[][(])[(][])[][]([][][])[(][][][])[10(][][])[][)10(]([][][][][][])[]([101][][101][][][])[]([101][][101][][])[]([101][][][][101][][][][][][][−=++⇒+−=+++−=⇒=−−+−−−=+−−−=−⇒+−−−=−=⇒+−−−=⇒−=∆−=∆−=∆−=∆+++++−++++−+++−++++++−++++++−++++++−++++++++++  84 By integrating the above equation:  )(][])[(][][][])[(][][02121][][][][2222100 0ttkkdtkkCudCuCCuCukCudCuCCuCukttCuCuCuCu−−=−=+++∫∫ ∫++++++++++++−  By assuming that [Cu2+] = Constant and t0 = 0:  tkkCuCCuCudkCuCCuCudCukCuCuCuCu21][0][][0][221 ])[]([][2])[(][][][ −=∫ ∫+++++++ +++++++−   We know that (by using partial fraction method):   xxCCxCxdxandxxCCCxxCxdx +−=+++−=+ ∫∫ ln1)(ln11)( 22    Then by integration:  ][][ln1)][][ln1][1]([]][][ln1)][][ln1][1]([222121][][2221 0++++++−++++++−+−++−⇒−=+−++− ++CuCuCCkCuCuCCCuCCuktkkCuCuCCkCuCuCCCuCCuk CuCu =+++−⇒+−++−+−=+++−+++++++++−][][ln][)][][ln1][1(][][ln1)][][ln1][1]([21200200202121CuCuCCukkCuCuCCCuCuCuCCkCuCuCCCuCCuktkk −+−+=+−++⇒+++−++−++++−+−++++++−++++−][1][][ln][1][][1][][ln][1][][ln][][][ln1][1][2120002121212002120002121CukkCCuCuCCuCukCtkkCukkCCuCuCCuCuCuCCukkCuCuCCCuCukCtkk  85  By substituting, the integrated form of the rate law would be:                                                     DBtCuCuCACu+=+++++ ][][ln][1 ( 5-2) 000001221212][])[10(ln][1][])[10(][1][+++−++−−+=−−==−=CuSexACuDCuSexCkCukCkBCCukkAVIVI By plotting  ][][ln][1+++++CuCuCACu versus time for a trial value of A and then calculating the slope and intercept of straight line by using least squares method, k1 and  k-1/k2 can be calculated. For high selenium concentrations such that [SeVI] remains almost constant ( averageVIfinalVIinitialVIVI SeSeSeSe ][2][][][ =+= ), the general rate law reduces to simpler form and drives as follows:    =+−=+⇒−−=−−=+−−=+⇒+=−−=−+++++++++++−+++++−++++−++++−++−++∫∫∫∫][][221][][2][][22112012][][2221122221221210000]]ln[][][][][][][][][)10(][)10(][][][][][)10(][][][][][][][][][101][CuCuCuCuCuCuaveVItaveVICuCuaveVIaveVIVICukCuCukCudCukCudCuCuktSekkxdtSekkxCudCuCukCukdtSekkxCudCuCukCukCuCukkSeCukdtCudxdtSed  86 ⇒−−=−++− +++−+++− tSekkxCukCuCukCukCuCukaveVI ][)10(]ln[][][]ln[][][1202021221                    022101221-][][]ln[][)10(][ln][k][Cuk++−++++−+−=−CukCukCuSetkxCuCu aveVI   ( 5-3)              By applying the same method, the rate law reduces to pseudo-first order kinetics at constant cuprous concentration:  0221201][][][ln++−++=CuCukktCukSeSeIVfinalVIinit ( 5-4)                                                                  5.3.2 Cuprous Selenide Reaction with Cupric  Results are depicted in Figure  5-1. The dissociation reaction of Cu2Se is very fast. Cuprous samples were taken when the solution potential was constant. The equilibrated cuprous concentration was then measured by titration at each stage. The average concentrations of analyzed cuprous and cuprous sampling time and frequency are shown on the graph. Cuprous selenide addition time and amount is also summarized in the insert table. The maximum concentration of cuprous was found to be 0.0027 M at 98.6°C and 90 g/L cupric which is almost 35 times higher than the expected thermodynamic level if based on formation of Cu1.9Ses (see Table  2-3 for thermodynamic data). The composition of the copper selenide precipitate was calculated at each stage based on the analysed cuprous concentration and added cuprous selenide concentration. The copper selenide  87 compositions obtained in this experiment are consistent with Ladriere’s (1973) work: Cu2-xSe (0 < x < 0.2) and this explains the non-stoichiometric nature of the precipitate as a function of cuprous concentration in solution.  Figure  5-1: Cuprous selenide dissociation reaction equilibrium at T = 98.6°C and Cu2+ = 90 g/L. Portions of Cu2Se were added to the CuSO4/H2SO4 solution at indicated times.   A cuprous concentration of 0.0017 M was found to be the maximum generated from the reaction at T = 95.1°C and with Cu2+ = 50 g/L. Cuprous concentrations of 0.0027 M and 0.0017M in contact with very high added cuprous selenide concentrations will not possibly occur in biselenate removal kinetics tests. For example, at the maximum attainable cuprous concentration of 0.02M (T = 98.6°C and Cu2+ = 90 g/L) at most 0.002 M of Cu2Se powder will be generated (based on reaction ( 5-5)) which can produce a 0 2 4 6 890110130150170190330350Time (hr)Voltage (mV)Cu+= 0.000928 MCu+= 0.00127 MCu+= 0.00211 MCu+= 0.00239 M Cu+= 0.00268 M Cu+= 0.00274 M0.02460.02090.01680.01190.005900.00391Cumulative Cu2Se (M)Cu1.94Se6.85Cu1.94Se5.37Cu1.93Se3.85Cu1.91Se2.66Cu1.89Se1.29Cu1.88Se0.16Composition ofCuxSe calculatedTime Cu2Se added (hr) 88 cuprous concentration of lower than 0.001 M according to Figure  5-1. Consequently, in this research, all kinetics tests were designed so that [Cu+] data below 0.001 were not used in kinetics calculations.   5.3.3 Stoichiometry of the Reduction of Biselenate  The biselenate reduction reaction with cuprous was studied at T = 95.1°C and initial cuprous and selenium concentrations of 0.012 M and 0.001 M respectively. Stoichiometry was calculated by measuring the concentration changes of the cuprous to the concentration changes of biselenate ∆∆ +][][VISeCu. Results are depicted in Figure  5-2.     Figure  5-2: Stoichiometry of the reduction of biselenate with cuprous at T = 95.1°C.  0246810120 2 4 6 8 10 12 14Time (hr)∆Cu+/∆SeVI ∆Cu+/∆SeVI = -0.003t + 9.981 89 The final concentration of cuprous was 0.002 M (above the dissociation concentration of Cu2Se) and the final concentration of selenium in the solution was 0.00014 M resulting in 88% of the SeVI being reacted. An average of ][][VISeCu∆∆ + ratio during the full reaction time (13 hours) was calculated as 9.96. Or, in essence the reaction stoichiometry is 10:1 of Cu+:SeVI under these conditions. According to the graph, stoichiometry of the overall reaction is written then as:                                                              HSeO4- + 10Cu+ aq + 7H+ = Cu2Se + 4H2O + 8Cu2+ ( 5-5)  5.3.4 Verification of the Rate Law at Constant Acidity, Temperature and Ionic Strength  Reduction of biselenate by cuprous was studied at constant temperature T = 95.1 ± 0.1 °C, acidity and ionic strength but variable cuprous, selenium and cupric concentrations. At the beginning, a test at nearly constant cuprous concentration (9% of [Cu+] was reacted) and low selenium concentration (0.00015M) was conducted to determine the reaction order with respect to selenium concentration.   Figure  5-3 shows a plot of ln[SeVI] with time over a three half-life change in the selenium concentration ([Se] decreased from 12 ppm to 1.2 ppm). The reaction obviously conforms to a first order rate equation. To validate the suggested rate law in its general form, equation ( 5-1), a least squares method was applied to the integrated form of the suggested rate law, equation ( 5-2). This was achieved by constructing a plot using equation ( 5-2) in the form of y = mx + b where x represents time for a test with [Cu+]0 = 0.014M and  90 [SeVI]0 = 0.028M at 95.1°C. Subsequently a value of 9568.56 for the constant A was found; which gave the best fit to the straight line. Based on the definition of A in equation ( 5-2), then the rate constant ratio k-1/k2 was calculated giving a value of 1.39×10-4. Lastly, the rate constant k1 was determined to be equal to k1 = 0.0057 M-1s-1 using the slope of the best fit straight line (Figure  5-4).  y = -0.3043x - 8.7395R2 = 0.9992-11-10-9-80 1 2 3 4 5 6 7Time (hr)Ln [SeVI] M Figure  5-3: Pseudo first order kinetics of biselenate reduction at nearly constant cuprous concentration, [Cu+]0 = 0.017M , [SeVI]0 = 0.00015M at 95.1°C.  91 Figure  5-4: Suggested general rate law validation plot: 1/[Cu+] + A× (ln C+[Cu+]/[Cu+]) with time at [Cu+]0 = 0.014M and [SeVI]0 = 0.028M at 95.1°C.  Seven kinetics tests were conducted to verify the independence of rate constants from cuprous and biselenate concentration by determining k1 and k-1/k2 values at different initial cuprous and selenium concentrations.   Table  5-1: Verification of suggested rate law at different initial cuprous and selenate concentrations at T = 95.1 ± 0.1°C, [H2SO4] = 100 g/L, [Cu2+] = 50 g/L. Initial cuprous [M] Initial selenate [M] k1 (M-1s-1) k-1/k2 0.0115 0.00107 0.00550 ------------- 0.0034 0.00813 0.00544 1.75×10-4 0.0141 0.0281 0.00565 1.39×10-4 0.0170 0.00015 0.00540 ------------- 0.0075 0.0023 0.00544 1.35×10-4 0.0171 0.00028 0.00536 ------------- 0.0171 0.00029 0.00546 ------------- Average  0.00546 1.50×10-4 y = 52807x + 28678R2 = 0.999920000250003000035000400004500050000550000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45Time (hr)1/[Cu+] + A (ln C+[Cu+]/[Cu+]) 92 Kinetics tests results are tabulated in Table  5-1. k-1/k2 values cannot be accurately determined when the initial concentration of selenium is low and hence are not reported in Table  5-1 for some tests. Rate constant values are consistent and quite close.  Four tests also were conducted to investigate if the rate constants depend on the cupric concentration ([Cu2+] = 30, 40, 50 and 60 g/kg). This was achieved by determining k1 and k-1/k2 values at different initial cuprous, selenium and cupric concentrations but T = 95.1°C, [H2SO4] = 50 g/kg solution and I = 6 molal (nominal). Solution ionic strength was kept constant by addition of sufficient amount of sodium sulfate. Results are summarized in Table  5-2.  Table  5-2: rate constants at different cupric concentrations at I = 6 molal, T = 95.1°C, [H2SO4] = 50 g/kg solution.   The rate constants increase slightly with increasing cupric concentration. The small increment of rate constant at higher cupric concentration might be attributed to total sulfate concentration. As shown in Table  5-2 the total sulfate concentration at Cu2+ = 60 g/kg is slightly lower than Cu2+ = 30 g/kg which consequently leads to more bisulfate dissociation and generation of more free H+ in solution. As it will be shown later, the rate constant k1 increases significantly at higher acidities.  Cu2+ (g/kg) Initial cuprous [M] k1 (M-1s-1) k-1/k2 Total Sulfate ion (molal) 30 0.0125 0.00105 2.32×10-4 1.84 40 0.0137 0.00115 2.25×10-4 1.79 50 0.0123 0.00138 2.17×10-4 1.74 60 0.0140 0.00153 2.07×10-4 1.69  93 5.3.4.1 Details of a Rate Constants Measurement   To clarify the applied method for determining the rate constants, the third test in Table  5-1 is chosen as an example and explained as follows:   The Cu+ concentration with time can be determined continuously by recording the voltage, WCell CuFRTCE ]log[303.2 +−=∆ , as explained in experimental procedure. A voltage-time plot is depicted in Figure  5-5 for test 3 of Table  5-1.  Figure  5-5: Cell voltage vs. Cu/Cu2+ reference electrode with time for kinetics test with [Cu+]0 = 0.014M and [SeVI] = 0.028M, T = 95.1°C.  Upon adding selenium to the solution cuprous concentration decreases and consequently the overall cell voltage increases until all the cuprous reacts with the selenium and the cell voltage finally reaches a constant value.  0501001502002500 0.5 1 1.5 2 2.5 3 3.5 4Time (hr)∆E cell (mV)Cuprous becomes less than 0.001 M at this pointSeVI added at this point 94 Initial cuprous concentration was measured by taking at least two samples after the copper coil was taken out of the solution at the test temperature and before the addition of selenium. Cuprous and selenium samples were taken before the cuprous concentration reached the concentration at which Cu2Se dissociation reaction started (0.001 M). The linear equation between cell voltage and the logarithm of cuprous concentration was then calibrated by means of known [Cu+]-voltage data points. The calibration equation is shown in Figure  5-6. Figure  5-6: log [Cu+] vs. voltage (vs. Cu/Cu2+) and calibration equation for kinetics test with [Cu+]0 = 0.014M and [SeVI] = 0.028M, T = 95.1°C.  When the selenium concentration is essentially constant ([Se] final > 90% [Se] initial) then the integrated form of the general rate law is in the form of a/[Cu+] - ln[Cu+]  =  Ct + constant (see equation ( 5-3)).  By plotting a/[Cu+] - ln[Cu+]  versus time for a trial value of a and  applying the least squares method, k1 and k-1/k2 can be calculated from the slope Log [Cu+] = -0.0140V - 1.5566R2 = 0.9991-2.6-2.4-2.2-2-1.8-1.6-1.410 20 30 40 50 60 70Voltage (mV)log [Cu+] MCu+ concentrationLinear (Cu+ concentration) 95 and intercept. In Figure  5-7 the plot of a/[Cu+] - ln[Cu+]  versus time is shown. Cuprous concentrations are calculated by means of log[Cu+] vs. voltage calibration equation.  4.55.05.56.06.57.07.50.0 0.1 0.2 0.3 0.4 0.5Time (hr)a/[Cu+]-ln[Cu+] Figure  5-7: Plot of a/[Cu+] – ln[Cu+] vs time for [Cu+]0 = 0.0141 M and [SeVI] = 0.0281 M, T = 95.1°C.  In Figure  5-8 the experimental and calculated concentrations of cuprous and selenium are plotted with time for this test. Calculated curves are based on the general rate law. There is good agreement between the model and the experimental data. k1 = 0.00565 M-1s-1  k-1/k2 = 1.39 ×10-4  96   Figure  5-8: Comparison of calculated and experimental cuprous and biselenate concentrations with time for kinetics test with [Cu+]0 = 0.014M and [SeVI] = 0.028M T = 95.1°C. 0.0000.0020.0040.0060.0080.0100.0120.0140.0160 0.5 1 1.5Time (h)[Cu+] MBased on rate equation[Cu+] titration`00.0050.010.0150.020.0250.030 0.5 1 1.5Time (h)[SeVI ] MBased on rate equationICP analysis 97  Comparison of the model and experimental cuprous and selenium concentrations for test 4 of Table  5-1 are also plotted in Figure  5-9 with time.  Figure  5-9: Comparison of calculated and experimental cuprous and biselenate conc. with time for kinetics test with [Cu+]0 = 0.017 M and [SeVI] = 0.00015 M T = 95.1°C. 0.000000.000030.000060.000090.000120.000150.000180 2 4 6 8Time (h)[SeVI] MBased on rate equationICP analysis0.01520.01560.0160.01640.01680.01720 2 4 6 8Time (h)[Cu+] MBased on rate equation[Cu+] titration 98 The general form of the rate equation can be reduced to a simple second order form when     k-1[Cu2+]/k2 << [Cu+]. Then the rate equation goes to:  ]][[][ 1 VIVISeCukdtSed +=−  ( 5-6)  ][ 221 +− Cukk is negligible when cuprous concentration is high. Since 21kk− is very small (on the order of 1 to 3×10-4) then the ][ 221 +− Cukkterm can be significant when the cupric concentration is high and cuprous concentration is small. This can cause deviation from a simple second order kinetics rate law. Deviation from a simple second order rate law is depicted in Figure  5-10 at [Cu+]0 = 0.0075 M, [SeVI]0 = 0.0023 M, 95.1 ± 0.1°C, [H2SO4] = 100 g/L and [Cu2+] = 50 g/L. As shown in Figure  5-10, a deviation occurred when the cuprous concentration decreased to low enough levels. Ladriere (1973) reported simple second order kinetics, however in fact the kinetics are more complex as was suggested in this study. The rate law suggested in this study is consistent with other well known metal oxo-anions reduction kinetics like CrVI, PuVI, UVI (Cannon Roderick, 1980).   Deviation of the kinetics data from a simple second order rate law and its conformation to the suggested general rate law, rejects the possibility of SeVI reduction based on mechanism 2 (see section 5.3.1). The rate law equation derived based on the mechanism 2 is presented in Appendix 6. As will be discussed later, during the reduction of SeVI, build up of the SeIV does not occur since the SeIV reacts extremely rapidly with cuprous, as it is generated in the solution (see Figure  6-17). Therefore, SeIV never attains a  99 significant concentration. As a result, the rate law (see Appendix 6) would simplify to a simple second order reaction as k-1[SeIV]/k2 approaches 0 and consequently, rejects the possibility of mechanism 2.   0501001502002500.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0Time hrf([Cu+])[Cu+] M titration Second order rate lawGeneral rate law Figure  5-10: Deviation of kinetics data from a simple second order rate law at low [Cu+]. f([Cu+]) =  ++++++−][][ln][1][221CuCuCACukCuk and ][][ln+++CuCuC for general rate law and second order rate law, respectively at [Cu+]0 = 0.0075 M, [SeVI] = 0.0023 M,          95.1 ± 0.1°C, [H2SO4] = 100 g/L and [Cu2+] = 50 g/L.     100 5.3.5 Effect of Acidity on Rate Constants and Rate Law  The effect of acidity in sulphate solution was investigated by running the reduction reaction at sulfuric acid concentrations of 10, 50, 100, 150 and 200 g/L at T = 95.1 and 86.2 °C. Cupric concentration was set to 50 g/l with initial cuprous and biselenate concentrations equal to 0.015 M and 0.03 M respectively. A summary of the rate constants calculated from these experiments is tabulated in Table  5-3.   Table  5-3: Rate constants at different acidities at 95.1°C and 86.2°C and [Cu2+] = 50 g/L in sulphuric acid solution.          The k-1/k2 values vary in the range of of 1×10-4 to 3×10-4 for all experiments. As expected, the rate constants decrease with temperature. In Figure  5-11 and Figure  5-12 the effect of acidity on cuprous oxidation rate with selenium are depicted at T = 95.1 °C and T = 86.2 °C, respectively. The curves are the suggested model equations fitted to the cuprous data. k1 (M-1s-1) k1 (M-1s-1) Sulfuric acid (g/L) at T = 95.1°C at T = 86.2 °C 10  0.000357 0.000203 50  0.00222 0.001225 100  0.005672 0.002868 150  0.010021 0.005036 200  0.01548 0.007898  101 0.0000.0020.0040.0060.0080.0100.0120.0140 0.5 1 1.50.0000.0020.0040.0060.0080.0100.0120.0140.0160 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Time (h)[Cu+] MH2SO4 = 10 g/LH2SO4 = 50 g/LH2SO4 = 100 g/LH2SO4 = 150 g/LH2SO4 = 200 g/L Figure  5-11: Effect of acidity on cuprous concentration with time on the biselenate removal reaction ([Cu+]0= 0.015, [Cu+]final = 0.00005 M, [SeVI]0 = 0.03M) at 95.1°C. Details of the first 1.5 hours are shown in the insert.  Acidity has a significant effect on the rate of selenium reduction with cuprous. The biselenate reduction reaction rate increases with increasing sulfuric acid concentration. As shown, at 10 g/L sulfuric acid concentration, it takes almost 14 hours for 0.015M cuprous to react with 0.03 M selenium and declines to 0.00005 M. This reaction occurs in less than 40 minutes in 200g/L sulfuric acid solution. At 86.2 °C the same reaction takes in 31 hours with [H2SO4] = 10 g/L and 86 minutes for 200 g/L sulfuric acid concentration.    102  Figure  5-12: Effect of acidity on cuprous concentration with time on the biselenate removal reaction ([Cu+]0= 0.0125, [Cu+]final = 0.00005 M, [SeVI]0 = 0.025 M) at 86.2 °C. The data points are shown along with the model fit of the suggested rate law.  There is an approximately linear correlation between ln k1 and ln [H2SO4]; k1 is very nearly proportional to [H2SO4]1.2:                                                                                                                     k1 = 0.00581 [H2SO4]1.25 (T = 95.1°C) M-1s-1  ( 5-7) k1 = 0.00301 [H2SO4]1.21 (T = 86.2 °C) M-1s-1  ( 5-8)  Results for T = 95.1°C and 86.2°C are depicted in Figure  5-13 and Figure  5-14. Equation ( 5-7) and ( 5-8) were used to determine the k1 values at sulphuric acid concentrations ranging from 10 to 200 g/L.  0.0000.0020.0040.0060.0080.0100.0120.0140 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32Time (h)[Cu+] MH2SO4 = 10 g/LH2SO4 = 50 g/LH2SO4 = 100 g/LH2SO4 = 150 g/LH2SO4 = 200 g/L 103  Figure  5-13: power law relationship between rate constant and sulfuric acid concentration at T=95.1 °C (k1 = 0.00581 [H2SO4]1.25 (M-1s-1)). y = 1.207x - 5.804R2 = 0.997-9-8-7-6-5-4-3-2-10-2.5 -2 -1.5 -1 -0.5 0 0.5 1Ln [H2SO4] MLn k 1 Figure  5-14: power law relationship between rate constant and sulfuric acid concentration at T = 86.2 °C (k1= 0.00301[H2SO4]1.21 (M-1s-1)). y = 1.250x - 5.148R2 = 0.997-9-8-7-6-5-4-3-2-10-2.5 -2 -1.5 -1 -0.5 0 0.5 1Ln [H2SO4] MLn k 1 104 The small difference in the power of acid concentration between temperatures may be partially attributed to the decrease of the bisulfate dissociation constant at higher temperature (Hovey et al., 1990). This increment in free H+ concentration at lower temperature results in a lower power of sulphuric acid concentration in equation ( 5-8), as it is expected that total H+ concentration in equation ( 5-7) and equation ( 5-8) are equal.    To determine the H+ dependence of the rate constant a strong acid without the weak acid buffering effect or ion pairing effect should be used. Hence, rate constants were measured in perchloric acid solution at 95.1°C. Sodium perchlorate was used as a salt to adjust the ionic strength to 4.35 molal at perchloric acid concentrations of 10, 50, 100 and 150 g/L (concentrations are at room temperature). Details of cuprous concentration measurement in perchlorate solution were described in section 4.2. The rate constant k1 is proportional to the 0.9 power of H+ concentration:                                                                                                               k1 = 0.0159 [H+] 0.9  ( 5-9)  Results and rate constant data are presented in Figure  5-15 and Table  5-4.   Table  5-4: Rate constants at different acidities at 95.1°C and [Cu2+] = 50 g/L in perchlorate medium at I = 4.35 molal. Acidity (g/L)  10 50 100 150 Acidity (molal) 0.103 0.539 1.072 1.669 k1 (M-1s-1) 0.00172 0.00698 0.01371 0.01931    105 Biselenate removal rate constants were calculated based on the net cuprous concentration change with time (see section 5.3.8 for details). Equation ( 5-9) may combine with general kinetics equation suggested at constant acidity, equation ( 5-1), to demonstrate all factors affecting the biselenate removal rate in one equation:  ][][][][][][22129.01++−+++′=−CuCukkSeCuHkdtSed VIVI                                                                            ( 5-10) Figure  5-15: power law relationship between rate constant and perchloric acid concentration at T = 95.1°C and I = 4.35 (k1 = 0.0159 [H+]0.9).  The effect of acidity on biselenate removal rate can be attributed to H+ contribution in the stoichiometry of the overall reduction reaction (equation ( 5-5)).  y = 0.898x - 4.140R2 = 1.000-9-8-7-6-5-4-3-2-1-3 -2.5 -2 -1.5 -1 -0.5 0 0.5Ln [HClO4] MLn k 1 106 5.3.6 Effect of Temperature on Selenium Rate of Removal with Cuprous  The effect of temperature was studied at constant cupric concentration of 75 g/L and constant acidity of H2SO4 = 100 g/L at 86.1, 90.3, 95.1 and 98.6°C. The initial cuprous and selenium concentrations were chosen equal to 0.015 M and 0.03 M respectively.   In Figure  5-16 the effect of temperature on cuprous concentration with time for all four temperatures is shown. The data are fitted to the model rate law equation. In Table  5-5, k1 and k-1/k2 values at different temperatures are summarized. The rate constant k1 and the ratio k-1/k2 values increase with increasing temperature.   Table  5-5: k1 and k-1/k2 values at different temperatures, Cu2+ = 75 g/L and H2SO4 = 100. g/L Temperature 98.6 95.1 90.3 86.1 k1 (M-1s-1) 0.00674 0.00509 0.00350 0.00255 k-1/k2 3.32×10-4 2.06×10-4 1.04×10-4 4.70×10-5  The inhibition effect of k-1/k2 also becomes increasingly important as temperature increases, especially at high cupric and low cuprous concentrations, according to equation ( 5-1). However, since k1 is an order of magnitude larger than k-1/k2 the effect of k-1/k2 is practically insignificant especially at high cuprous concentrations. By using the Arrhenius law for k1 values the activation energy and natural logarithm of the prefactor are calculated as 86.0 kJ/mol and ln A = 22.8 mol-1s-1 (Figure  5-17). This high activation energy confirms that the reaction of cuprous ion and biselenate are under chemical reaction rate control.   107 0.0000.0020.0040.0060.0080.0100.0120.0140.0160 1 2Time (h)[Cu+] M86.1°C90.3°C95.2°C98.6°C Figure  5-16: Effect of temperature on cuprous concentration with time on biselenate removal rate ([Cu+] initial = 0.015, [SeVI]initial = 0.03M) at Cu2+ =75 g/L and H2SO4 = 100 g/L. The curves are calculated based on the proposed rate law.  Figure  5-17: Activation energy and prefactor values for k1 at Cu2+ = 75 g/L and H2SO4 = 100 g/L.  y = -10343x + 22.812R2 = 0.9993-6.1-5.6-5.1-4.60.00268 0.0027 0.00272 0.00274 0.00276 0.00278 0.00281/T (K-1)Ln (k 1)Ea = 86.0 kJ/molLn A = 22.8 M-1s-1 108 Based on the thermodynamic information available for SeO3- species at 25°C (Klaning, 1986) and the following reaction where K25 is equilibrium constant at 25°C and equal to 6.395×10-6:  kJ/mol)28.99(∆∆OHSeOCuHHSeOCu 0298232kk411=++↔++ −++−+−   5-11  Rate constant k-1 can be calculated at 25°C using equation ( 5-12) and K= k1/k-1 formulas.  −=12aT2at1T1at1T1T1REexpkk  ( 5-12)  The rate constant k-1 values at higher temperatures are not known as the thermodynamic data for SeO3- is not available at these temperatures. Therefore, values of Ea2 and Ea-1 cannot be calculated separately. Instead, a value of Ea2 - Ea-1 may be calculated as the    k-1/k2 ratio is known at high temperature using the equation ( 5-13).   RTEEAALnkkLn 12 aa2121 −−+= −−   ( 5-13)  Figure  5-18 represents the application of Arrhenius law measuring the k-1/k2 activation energy and it’s prefactor. Activation energy and prefactor then were calculated as Ea-1- Ea2 = 171.9 kJ/mol and Ln (A-1/A2) = 47.6 M-1s-1. The main portion of the Ea-1- Ea2 value is expected to be possessed by Ea-1 since Ea-1 and Ea2 are positive numbers.   109  Figure  5-18: Activation energy and prefactor values for k-1/k2 at Cu2+ = 75 g/L and H2SO4 = 100 g/L.  5.3.7 Cupric Sulfate Concentration Effect on Rate Constants   The effect of cupric concentration without ionic strength adjustment was also investigated at T = 95.1 °C and H2SO4 = 100 g/L. Rate constant values are summarized in Table  5-6. Cuprous concentration depletion rate at different cupric concentrations are depicted in Figure  5-19 at T= 95.1 °C. The curves are calculated based on the proposed rate law. The data points are shown along with the model fit of the suggested rate law.  Table  5-6: k1 and k-1/k2 values for different cupric concentrations at T = 95.2°C and H2SO4 = 100 g/L.   Cu2+ (g/L) 40 50 75 90 Cu2+ (g/kg) 41.95 53.42 80.62 98.50 k1 (M-1s-1) 0.00604 0.00566 0.00509 0.00483 Total Sulfate  [molal] 1.65 1.81 2.20 2.44  y = -20680x + 47.647R2 = 0.9964-11-10-9-8-70.00268 0.0027 0.00272 0.00274 0.00276 0.00278 0.00281/T (K-1)Ln (k -1/k2)Ea-1- Ea2 = 171.9 kJ/molLn (A-1/A2) = 47.6 M-1s-1 110 Increasing the cupric concentration decreases the rate constant and slows the removal rate. This might be attributed to variation of free H+ ion concentration. Increasing sulfate ion in solution will increase concentration of undissociated HSO4- and consequently will decrease the free H+ ion in solution.   Figure  5-19: Effect of cupric concentration on cuprous concentration with time on biselenate removal rate ([Cu+]initial = 0.015, [SeVI]initial = 0.03M) at [H2SO4] = 100 g/L and T= 95.1 °C. The data points are shown along with the model fit of the suggested rate law. Details of the first 0.5 hour are shown in the insert.  Any small change in acidity can significantly affect the removal rate. Results of Table  5-6 are consistent with the results of Table  5-2 from the view point of sulphate concentration and its affect on rate constants. For example the rate constant k1 decreases approximately 0.0005 M-1s-1 from 30 to 60 g/kg cupric concentration change (Table  5-2) 0.0000.0020.0040.0060.0080.0100.0120.0140.0160 0.5 1 1.5 2 2.5Time (h)[Cu+] MCu2+ = 90g/LCu2+ = 75g/LCu2+ = 50g/LCu2+ = 40g/L0.0000.0020.0040.0060.0080.0100.0120 0.1 0.2 0.3 0.4 0.5 111 and 0.15 m of total sulphate concentration change whereas it decreases the similar (0.0004 M-1s-1) for cupric concentration change of 40 to 50 g/L (Table  5-6) but almost the same (0.16 M) of the total sulphate concentration change.   5.3.8 Effect of Ionic Strength on Selenium Removal Rate  The effect of ionic strength on the biselenate removal rate was measured in sulfate and perchlorate solution media. Perchloric acid oxidizes the cuprous very slowly. At lower HClO4 concentration this effect will decrease. To account for this effect while studying the biselenate removal rate with cuprous, the cuprous oxidation rate in different perchlorate compositions was measured. Biselenate removal rate constants were then calculated based on the net cuprous concentration change with time. The kinetics of cuprous oxidation with perchlorate in solutions containing 0, 1, 2 and 3 M NaClO4, [HClO4] = 100 g/L, [Cu2+] = 50 g/L (Cu(ClO4)2) and at 95.1°C was measured as explained in section 4.2. The rate of cuprous oxidation by perchlorate was apparently first order with respect to cuprous concentration ([Cu+] = [Cu+0] × e-kt). This rate equation was used to adjust the rate of biselenate reduction reaction in perchlorate medium. Analyzed cuprous concentration values ([Cu+]) were modified to higher values ([Cu+0]) using the [Cu+] = [Cu+0] × e-kt equation from the time selenium was added to the solution to account for cuprous oxidation with perchlorate. Biselenate reduction reaction measurements in perchlorate solution were conducted similarly to the tests in sulfate medium. Rate constants were measured considering the effect of perchloric acid oxidation at 95.1°C at NaClO4 concentrations of 0, 1, 2 and 3 M and cupric perchlorate  112 and perchloric acid concentrations of 50 and 100 g/L respectively. Rate constants data are summarized in Table  5-7.  Table  5-7: Selenate reduction rate constant with nominal ionic strength, HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C.  NaClO4 [M] I [M] k1 (M-1s-1) 0 3.36 0.0075 1 4.36 0.0134 2 5.36 0.0238 3 6.36 0.0412  Biselenate removal rate increased significantly by increasing the ionic strength of the solution. Rate constant k1 values vary from 0.0075 to 0.0412 M-1s-1 in solutions containing 0 to 3 M NaClO4 at 95.1°C and [HClO4] = 100 g/L, Cu2+ = 50 g/L. Comparison of calculated and experimental cuprous concentrations with time for above mentioned experiments are depicted in Figure  5-20.   The rate constant k1 increases from 0.0056 M-1s-1  in sulfate solution to 0.0075 M-1s-1 in perchlorate solution at H2SO4/HClO4 = 100 g/L, Cu2+= 50 g/L and 95.1°C. This increment may be attributed to the higher ionic strength in sulfate solution. The nominal ionic strength for sulfate solution and perchlorate solution at H2SO4/HClO4 = 100 g/L and Cu2+ = 50 g/L are 6.21 M and 3.36 M, respectively. It will be shown (Table  5-8) that contrary to the perchlorate system, in sulphate solutions, the rate constant decreases with increasing ionic strength of the solution. The ionic strength increases from 3.35 to 6.35 M as NaClO4 concentration varies from 0 M to 3 M.  113 0.0000.0050.0100.0150.0200.0250 0.1 0.2 0.3 0.4Time (hr)[Cu+] MNaClO4 = 0 MNaClO4 = 1 MNaClO4 = 2 MNaClO4 = 3 M Figure  5-20: Comparison of calculated and experimental cuprous concentrations with time for HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C.  Using rate constant data at different ionic strengths, a linear correlation between log k1 and I1/2/ (1+I1/2) – 0.3I was obtained as:  −+−−= IIIk 3.019.046.2log21211   ( 5-14)  This equation was obtained by substituting the revised form of the Davies equation for uni-univalent electrolytes (Davies, 1962) into the Bronsted-Bjerrum (1922) equation:   114 −++= IIIZZkk BA 3.01loglog212101   ( 5-15)  where ZA and ZB represent the reacting ion charges for the rate determining step. The product of the charges and the rate constant at infinite dilution are obtained from the slope and intercept of the straight line in Figure  5-21.  Based on the equation ( 5-14) and the rate determining step of the suggested mechanism,  OHSeOCuHHSeOCu 232kk411++↔++ −++−+−  ( 5-16)  log k1 = -0.902 [I1/2/(1+I1/2)-0.3I] - 2.456R2 = 0.998-3.00-2.50-2.00-1.50-1.00-0.500.00-1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1I1/2/(1+I1/2)-0.3Ilog k 12.0003.0004.0005.0006.0007.000 I Figure  5-21: Rate constant k1 as a function of solution nominal ionic strength at HClO4 = 100 g/l, Cu2+ = 50 g/l, T = 95.1 °C (Table  5-7).   115 ZAZB should be equal to -1 and, as was shown experimentally, the rate constant k1 is expected to increase by increasing the ionic strength. The rate constant at infinite dilution was found to be 0.00348 M-1s-1 and the product of the charges was -0.90. The Davies equation was reported to have an uncertainty not exceeding 2% at concentrations below 0.1 M (Davies, 1962). Therefore, the deviation of the calculated values for the product of the charges and presumably the rate constant at infinite dilution from ( 5-15) can be attributed to the higher solution concentrations used in this study. By changing the coefficient from 0.3 to 0.263, the product of the charges would be -1.000 via the following equation:  −+−−= IIIk 263.01000.1402.2log21211   ( 5-17)  Contrary to perchlorate system, in sulphate solutions, the rate constant decreases with increasing ionic strength of the solution. This can be attributed to the effect of the sulfate ion concentration which consequently decreases the free H+ ion concentration according to the bisulfate dissociation equilibrium.  In Table  5-8, the effect of addition of aluminum and magnesium sulfate salts to the solutions with identical sulphuric acid and cupric sulfate concentration on rate constant is shown. Free H+ concentration was estimated considering the sulfate ion pairing effect and bisulfate dissociation equilibrium reaction at 25°C (Medusa software was used). Decreasing the free H+ concentration, decreases the rate constant k1 although the ionic  116 strength is increasing. In fact, the rate constant k1 is independent of solution ionic strength at similar H+ concentrations in sulphate medium.  Table  5-8: Biselenate reduction rate constant by addition of sulphate salts, T = 95.1 °C.           5.4 Summary    The kinetics of selenium removal by cuprous ion precipitation and the effects of acidity, cupric concentration, temperature and ionic strength on the removal rate were investigated in chapter 5. Reduction of SeVI with Cu+ most likely occurs according to initial one electron transfer with formation of intermediate SeV. This mechanism is the most probable mechanism for reduction of two electron reagents with VI/IV oxidation states with a known short lived intermediate of V oxidation state. It was shown that the kinetics fit this mechanism. The general form of the rate law was determined based on the suggested mechanism and over a wide range of acidity and temperature:   ][][][][][22121++−++=−CuCukkSeCukdtSed VIVI  ( 5-1)  Salt type Al2(SO4)3 MgSO4 ------------ Salt concentration [M] 0.215 0.325 0 CuSO4 [M] 0.29 0.29 0.29 H2SO4 [M] 0.25 0.25 0.25 H+  at 25°C [M] 0.163 0.163 0.197 Nominal I [M] 5.14 3.21 1.91 k1 (M-1s-1) 0.0010 0.0010 0.0017  117 Accordingly, the biselenate removal rate increases at higher concentrations of cuprous and biselenate while cupric functions as an inhibitor especially if k-1/k2 is high. The general rate equation can be reduced to a simple second order form when k-1[Cu2+]/k2 << [Cu+]. Then the rate equation goes to:  ]][[][ 1 VIVISeCukdtSed +=−  ( 5-6)  Ladriere (1973) reported simple second order kinetics, however in fact the kinetics are more complex. The ][ 221 +− Cukkterm is significant when the cupric concentration is high and cuprous concentration is small. This caused deviation from a simple second order kinetics rate law. The rate law suggested in this study is consistent with other well known metal oxo-anions reduction kinetics like CrVI, PuVI, UVI. Deviation of the kinetics data from a simple second order rate law and its conformation to the suggested general rate law, rejects the possibility of SeVI reduction based on initial two electron transfer with formation of intermediate Cu3+ and SeIV mechanism.  Stoichiometry of biselenate reduction reaction with cuprous was calculated by measuring the ][][6++∆∆SeCu  at T = 95.1°C as:   HSeO4- + 10Cu+ aq + 7H+ = Cu2Se + 4H2O + 8Cu2+ ( 5-5)  Seven kinetics tests were conducted to verify the independence of rate constants from cuprous and biselenate concentration by determining k1 and k-1/k2 values at T =  118 95.1±0.1°C, [H2SO4] = 100 g/L, [Cu2+] = 50 g/L. The Cu+ concentration with time was determined continuously by recording the solution voltage and using the calibration equation:   The rate constants were estimated by using the integrated form of the rate law. Rate constant values were consistent and quite close. The average values of k1 and k-1/k2 were found to be 0.0055 M-1s-1 and 1.5×10-4 at T = 95.1°C, [H2SO4] = 100 g/L and [Cu2+] = 50 g/L. Rate constants were almost independent of cupric concentration at constant ionic strength but decreased slightly with increasing cupric concentration and increasing ionic strength.  The effect of acidity in sulphate solution was investigated by running the reduction reaction at sulfuric acid concentrations of 10, 50, 100, 150 and 200 g/L at T = 95.1 and 86.2 °C at Cu2+ = 50 g/l.  Acidity had a significant effect on the selenium reduction with cuprous. The biselenate reduction reaction rate increased with increasing sulfuric acid concentration. At 10 g/L sulfuric acid concentration and T = 95.1°C, it took almost 14 hours for 0.015 M cuprous to fully react with selenium whereas it was occurred in less than 40 minutes in 200g/L sulfuric acid solution. Nearly linear correlations were observed between ln k1 and ln [H2SO4] at T = 95.1 and 86.2 °C:  ICell CuFRTCE ]log[303.2 +−=∆   ( 3-3)  119 k1 = 0.00581 [H2SO4]1.25 (T = 95.1°C) M-1s-1  ( 5-7) k1 = 0.00301 [H2SO4]1.21 (T = 86.2 °C) M-1s-1  ( 5-8)  The H+ dependence of the rate constant was measured in perchloric acid solution at 95.1°C. The rate constant k1 was proportional to the 0.9 power of H+ concentration:             k1 = 0.0159 [H+] 0.9  ( 5-9)  The effect of temperature was studied at constant cupric concentration of 75 g/L and constant acidity of H2SO4 = 100 g/L at 86.1, 90.3, 95.1 and 98.6°C. The activation energy was calculated for k1 values as 86.0 kJ/mol. This high activation energy confirms that the reaction of cuprous ion and biselenate are under chemical reaction rate control.  The effect of ionic strength on the biselenate removal rate was measured in sulfate and perchlorate solution. In perchlorate medium, biselenate removal rate increased significantly by increasing the ionic strength of the solution. Rate constant k1 values vary from 0.0075 to 0.0412 M-1s-1 in solutions containing 0 to 3 M NaClO4 at 95.1°C, [HClO4] = 100 g/L and [Cu(ClO4)2] = 50 g/L. A linear correlation between log k1 and solution nominal ionic strength was found to be:   −+−−= IIIk 263.01000.1402.2log21211   ( 5-17)  in perchlorate medium at 95.1°C.   120 Contrary to the perchlorate system, in sulphate solutions, the rate constant decreases with increasing ionic strength of the solution. This can be attributed to the effect of the sulfate ion concentration which consequently decreases the free H+ ion concentration according to the bisulfate dissociation equilibrium. In sulfate medium, decreasing the free H+ concentration decreases the rate constant k1 although the ionic strength is increasing.                     121 Chapter 6 Thermodynamics and Kinetics Study of Tellurium Removal with Cuprous Ion  6.1 Objectives  The kinetics of reduction of TeVI and TeIV in the presence of copper metal and with cuprous is not well understood. Few studies were referenced in section 2.3 (Shibasaki 1992, Jennings 1969) on the kinetics of reduction of tellurate in the presence of copper metal, but as was mentioned, similar to selenate, tellurate reduction most likely occurs homogeneously by reacting with cuprous ion rather than reacting directly on the surface of the copper metal. It appears that there are no studies on the mechanism and kinetics of the tellurate reduction reaction with cuprous ion. Understanding the tellurium reduction chemistry and reaction kinetics by means of cuprous in a wide range of conditions and determining the mechanism of the reaction, rate constants and activation energies are the main objectives of the work presented in this chapter. Effects of acidity and temperature on the tellurium removal rate will be investigated and reported.  6.2 Experimental   Details of the experimental apparatus and experimental procedure were explained in section 3.2.1 and 3.2.5. Typical experiments involved generation of sufficient amounts of cuprous followed by adding a weighed amount of sodium tellurate/sodium tellurite powder. During the experiment a series of samples were removed for cuprous and tellurium analysis. Sodium tellurate dissolves rapidly in copper sulfate-sulfuric acid solution at T ≥ 75°C and concentrations below 0.03 M at [H2SO4] ≥ 50 g/L. At [H2SO4] <  122 50 g/L the sodium tellurate/tellurite concentration was confined to 0.003 M to avoid formation of solid TeO2.  6.2.1 Cuprous Telluride Reaction with Cupric  Similar to the copper selenide dissociation reactions (Table  2-3), the equilibrium constant (K = (Cu+)2/(Cu2+) ) and saturated cuprous concentration were obtained for the precipitation of Cu1.9Te by the reaction:  Cu2Te + 0.1 Cu2+ = 0.2Cu+ + Cu1.9Te   ∆G0R(95°C) = 55.60 kJ/mol  ( 6-1)  The equilibrium constant and cuprous concentration were subsequently measured as                     K = 1.29×10-8 and [Cu+] = 0.0001 M at T = 95°C and Cu2+ = 50 g/L, respectively. Therefore, by analogy to the dissociation of copper selenide (section 5.3.2) and considering the fact that the initial cuprous concentration in all tellurium experiments was always less than 0.018 M (at most 0.0018 M of Cu2Te will generate), all tellurium kinetics tests were designed such that the resulting [Cu+] in the kinetics tests were above 0.001 M. Kinetic tests with final Cuprous concentrations below 0.001 M were not considered for the kinetics calculations, stipulating that a drop in cuprous concentration in the products will drive the reaction forward (see equation ( 6-1)).      123 6.2.2 Stoichiometry of the Reduction of Tellurate/Tellurite with Cuprous  The stoichiometry of the overall reaction was investigated by running a kinetics test with initial cuprous and tellurium concentration of 0.015 M and 0.001 M respectively, at 95.1°C and [H2SO4] = 50 g/L for tellurate reduction. Initial cuprous and tellurium concentration for tellurite reduction reaction was 0.0171 M and 0.0031 M, respectively. The ratio of cuprous-tellurium consumed was measured by sampling and analysis. Consequently, the stoichiometric coefficient was measured in above mentioned conditions.  6.2.3 Investigation of the Reaction Order as a Function of Acidity and Temperature  The reaction order of TeVI and TeIV reduction with cuprous was determined with respect to cuprous and tellurium concentration at an acidity range of 10 to 100 g/L H2SO4 for TeVI reduction reaction and at [H2SO4] = 50 g/L for TeIV reduction reaction. The effect of temperature on the reaction order was investigated at T = 75.1, 86.1 and 95.2°C at [H2SO4] = 50 g/L for TeVI reduction reaction. Cuprous concentration with time was also monitored for reduction of TeVI and TeIV at T = 95.2°C and at [H2SO4] = 10, 50 and 100 g/L to identify the slow step of the reduction reaction.    124 6.2.4 Verification of the Rate Law  A mechanism of the reaction is suggested based on the results obtained from the reaction order and suggested rate determining step. The dependence of the rate constant on the concentrations of tellurate and cuprous were then investigated by running four tests at different initial concentrations of TeVI and cuprous at constant temperature (T = 95.1°C) and acidity (H2SO4 = 50 g/L). Rate constants then were calculated based on the suggested mechanism and general rate law at T = 95.2, 86.1 and 75.1 °C, [Cu2+] and [H2SO4] = 50 g/L.   6.2.5 Effect of Acidity and Temperature on Tellurium Removal Rate  The effect of acidity was investigated by running the reduction reaction at 95. 2°C in a fixed cupric concentration of 50 g/L at sulfuric acid concentrations of  10, 15, 50, 75 and 100 g/L. Acidity has a direct contribution in the overall reaction (H6TeO6 + 6H+ + 10Cu+ = Cu2Te + 6H2O + 8Cu2+) and is expected to have a significant effect on the tellurate removal rate. The effect of temperature was studied at constant cupric concentration of 50 g/L and sulphuric acid concentration of 50 g/L at 75.1, 86.1 and 95.2°C. The activation energy of tellurate reduction with cuprous then was calculated via using the Arrhenius equation (k = Ae-Ea/RT) for rate constants at [H2SO4] = 50 g/L.     125 6.3 Results and Discussion  6.3.1 Stoichiometry of the Reduction of Tellurate with Cuprous  The stoichiometry of TeVI reaction with Cu+ was determined by measuring the concentration changes of the cuprous to the concentration changes of tellurate ∆∆ +][][VITeCu at T = 95.1°C and initial cuprous and tellurium concentrations of 0.0155 M and 0.001 M, respectively. Results are depicted in Figure  6-1. The final concentrations of cuprous and tellurium was 0.0068 M and 0.00013 M resulting in 87% of the TeVI being reacted. An average of ][][VITeCu∆∆ + ratio during the full reaction time (6 hr) was calculated as 10.05.  0246810120 1 2 3 4 5 6 7Time (hr)∆Cu+/∆TeVI Figure  6-1: Stoichiometry of the reduction of tellurate with cuprous at T = 95.1°C and [H2SO4] = 50 g/L.  126  According to this, then stoichiometry of the overall reaction may be written as following at T = 95.1°C:                                                                               H6TeO6 + 6H+ + 10Cu+ = Cu2Te + 6H2O + 8Cu2+    ( 6-2)   6.3.2 Reaction Order of TeVI Reduction with Cu+ as a Function of Acidity and Temperature  The reaction order of TeVI reduction with cuprous with respect to cuprous and tellurium concentration was investigated at different acidities and temperatures. Results at T = 95.2°C and [H2SO4] = 10 and 50 g/L are depicted in Figure  6-2 and Figure  6-3.     Figure  6-2: Cuprous reaction order in reduction of TeVI with cuprous ion at T = 95.2°C and Cu2+ = 50 g/L, [H2SO4] = 10, 50 g/L, [Cu+]0 = 0.005M , [TeVI]0 = 0.003 M. R2 = 0.994R2 = 0.981-7.5-6.5-5.50 4 8 12 16 20 24 28 32 36 40 44Time (hr)ln [Cu+] MH+ = 10 g/LH+ = 50 g/L 127 A plot of ln[Cu+] over time was shown in Figure  6-2 where the cuprous concentration decreased from 0.005 M to 0.0009 M and about 14% of the initial tellurium has reacted. A plot of ln[Te] over time was also shown in Figure  6-3 over a three half-life change in the tellurium concentration ([Te] decreased from 18.4 ppm to 2.2 ppm at H+ = 10 g/L and from 17.3 ppm to 2.2 ppm at H+ = 50 g/L) where only 7.5% of the starting cuprous ion had reacted. The reaction order very nearly conforms to a first order rate equation with respect to cuprous and tellurium concentration at either [H2SO4] = 10 or 50 g/L at 95.2°C.    Figure  6-3: Tellurium reaction order in reduction of TeVI with cuprous ion at T = 95.2°C and Cu2+ = 50 g/L, [H2SO4] = 10, 50 g/L, [Cu+]0 = 0.0174 M, [Cu+]f = 0.0161 M.  A change in temperature had no effect on reaction order at [H2SO4] = 50 g/L and similar results were observed when the temperature was decreased to 86.1 and 75.1 °C (Figure  6-4 and Figure  6-15). The effect of acidity was also observed on the cuprous reaction R2 = 0.997R2 = 0.993-11.5-11.0-10.5-10.0-9.5-9.0-8.5-8.00 2 4 6 8 10 12Time (hr)Ln [ TeVI] MH+ = 10 g/LH+ = 50 g/L 128 order. It was found that the order of reaction as a function of [Cu+] was not affected by [H2SO4] of 50, 75 and 100 g/L (see Figure  6-13).  R2 = 0.998R2 = 0.998R2 = 0.999-8-7-6-5-4-30.0 0.5 1.0 1.5Time (hr)ln [Cu+] M T= 95.1° CT = 86.1° CT = 75.1° C Figure  6-4: Cuprous reaction order in reduction of TeVI with cuprous ion as a function of temperature at Cu2+ = 50 g/L, [H2SO4] = 50 g/L, ([Cu+]0 = 0.0153 M , [TeVI]0 = 0.030 M at T = 95.1°C), ([Cu+]0 = 0.0126 M , [TeVI]0 = 0.025 M at T =86.1°C), ([Cu+]0 = 0.0081 M , [TeVI]0 = 0.016 M at T =75.1°C) .                                           Accordingly, based on what was observed, the TeVI reduction reaction may be written as following:  at][][][ VIVITeCudtTed +− α 10 g/L < [H2SO4] < 100 g/L  ( 6-3)  To identify the slow step of the reduction of TeVI and TeIV with cuprous, cuprous concentration with time was monitored for [H2SO4] = 10, 50 and 100 g/L and initial TeVI  129 or TeIV concentration of 0.003 M. The data points on the graphs represent analysed cuprous concentration values and the lines are cuprous concentrations measured continuously as a function of solution potential. The potential was step changed over time resulting in jagged curves.  0.0010.0030.0050.0070.0090.0110.0130.0150.0170.0190 5 10 15 20 25 30 35 40Time (hr)[Cu+] M0.0010.0030.0050.0070.0090.0110.0130.0150.0170 0.5 1 1.5 2 2.5 3Te6+ , H2SO4 = 10 g/LTe4+ , H2SO4 = 10 g/LTe6+ , H2SO4 = 50 g/LTe4+ , H2SO4 = 50 g/LTe6+ , H2SO4 = 100 g/LTe4+ , H2SO4 = 100 g/L Figure  6-5: [Cu+] with time in reduction of TeIV and TeVI with cuprous ion at T = 95.1°C and Cu2+ = 50 g/L. Lines are representing the continuous cuprous concentration calibrated and calculated based on the solution voltage and data points are analysed cuprous concentration. Details of the first 3 hours are shown in the insert.  As depicted in Figure  6-5, the reduction of TeVI is slower than the TeIV for acid concentrations of 10, 50 and100 g/L H2SO4 solution. Therefore, to a first approximation  130 it may be assumed that the reduction of TeVI to TeIV is the rate determining step in the reduction of  TeVI to Cu2Te. Over this pH range, H6TeO6 slowly reduces to TeO(OH)+ ions. Subsequently, TeO(OH)+ is reduced at a faster rate to lower tellurium oxidation states and Cu2Te finally precipitates. The validity of the simplified assumption, that the reduction of TeVI to TeIV is considered a rate determining step, needs to be verified. This was achieved by studying the kinetics of the coupled reaction of TeVI and TeIV with cuprous.  At the beginning, the rate law was suggested for reduction of TeIV with cuprous. Then, the coupled kinetics equation for consecutive reduction reactions of TeIV and TeVI was derived. Finally it was shown that the rate constant of the coupled reaction is very close to the rate constant calculated based on the simplifying assumption that TeVI reduction is rate-determining step.  6.3.3 Kinetics Study of TeIV reduction with Cuprous  It was shown in Figure  6-5 that for a given acid level TeIV reduces about 3-4 times faster than TeVI. However, TeIV reduction is not fast enough compared to TeVI to say that TeVI reduction is definitely rate-determining. This means that the two reduction reactions are coupled and some build-up of TeIV concentration is expected especially at the beginning of the reduction reaction. The significance of this effect was investigated by studying the kinetics of the TeIV reduction with cuprous at T = 95.1°C, [Cu2+] = 50 g/L and [H2SO4] = 50 g/L as follows.    131 6.3.3.1 Stoichiometry of the Reduction of TeIV with Cuprous  The stoichiometry of TeIV reaction with Cu+ was determined by measuring the concentration changes of the cuprous to the concentration changes of tellurite ∆∆ +][][IVTeCu at T = 95.1°C and initial cuprous and tellurium concentrations of 0.0171 M and 0.0031 M, respectively. Results are depicted in Figure  6-6. The final concentrations of cuprous and tellurium was 0.0014 M and 0.0011 M resulting in 92% of the cuprous being reacted.  0246810120 0.2 0.4 0.6 0.8 1Time (hr)∆Cu+/∆TeIV Figure  6-6: Stoichiometry of the reduction of TeIV with cuprous at T = 95.1°C, Cu2+ = 50 g/L and [H2SO4] = 50 g/L.  An average of ][][IVTeCu∆∆ + ratio during the full reaction time (1 hr) was calculated as 8.05. According to this, then stoichiometry of the overall reaction may be written as follows at T = 95.1°C:                                                          132 TeO(OH)+ + 3H+ + 8Cu+ = Cu2Te + 2H2O + 6Cu2+    ( 6-4)  6.3.3.2 Reaction Order and Rate Law Equation of TeIV Reduction with Cuprous  The reaction order of TeIV reduction with cuprous with respect to cuprous and tellurium concentration was investigated in the pseudo-first order kinetics condition at [H2SO4] = 50 g/L and T = 95.1°C. Results are depicted in Figure  6-7 and Figure  6-8.   R2 = 0.991-10-9-8-7-6-5-4-3-20.00 0.02 0.04 0.06 0.08 0.10Time (hr)ln [Cu+] MH+ = 50 g/L Figure  6-7: Cuprous reaction order in reduction of TeIV with cuprous ion at T = 95.1 °C and Cu2+ = 50 g/L, [H2SO4] = 50 g/L, [Cu+]0 = 0.0180 M , [TeIV]0 = 0.030 M.  A plot of ln[Cu+] over time was shown in Figure  6-7 where the cuprous concentration decreased from 0.018 M to 0.0005 M and just about 6% of the initial tellurium has reacted. Similarly, a plot of ln[TeIV] with time was shown in Figure  6-8 over a three half-life change in the tellurium concentration ([Te] decreased from 0.0004 M to 0.00005 at  133 H+ = 50 g/L) where 15 % of the starting cuprous ion has reacted. The reaction order very nearly conforms to a first order rate equation with respect to cuprous and tellurium concentration at [H2SO4] = 50 g/L at 95.1 °C.   R2 = 0.993-12.0-11.0-10.0-9.0-8.0-7.0-6.00.0 0.2 0.4 0.6 0.8 1.0Time (hr)Ln [ TeIV] MH+ = 50 g/L Figure  6-8: Tellurium reaction order in reduction of TeIV with cuprous ion at T = 95.1 °C and Cu2+ = 50 g/L, [H2SO4] = 50 g/L, [Cu+]0 = 0.0177 M, [TeIV]0 = 0.0004 M.                                   Hence, based on what was observed, the reduction reaction may be written as follows:  ][][][ IVIVTeCudtTed +=−    ( 6-5)  By analogy to the TeVI case, the rate constant (k1) was calculated from the slope of the best-fit straight line to the kinetics data. Accordingly, an average rate constant k1 for reduction of TeIV was estimated as 0.0328 M-1s-1 at [H2SO4] = 50 g/L, Cu2+ = 50 g/L and  134 T = 95.1°C. An average rate constant for reduction of TeVI at sulphuric acid concentration of 50 g/L is 0.00771 M-1s-1 (Table  6-1). Therefore, the removal rate of TeIV is 4.2 times faster than the removal rate of TeVI at similar initial tellurium and cuprous concentration.  6.3.4 Coupled Reduction of TeVI and TeIV with Cuprous   Kinetics scheme of consecutive irreversible reductions of TeVI and TeIV with cuprous may be proposed as follows:  →+→+++TeCuCuTeTeCuTekIVIVkVI221  Pseudo-first order kinetics condition at almost constant cuprous concentration simplifies the TeVI and TeIV reduction rate laws as follows:  ≈≈−=+++aveVIVICuCuatCuTekdtTed01 ][][][][][ Constant  Therefore, the TeVI concentration with time is given by:  aveCutkVIVI eTeTe 01 ][0][][+−×=  ( 6-6)  According to the kinetics scheme, the differential rate equation for reduction of TeIV is written as:  135 aveIVCutkVIIVVIIVCuTekCueTekCuTekCuTekdtTedave02][0121 ][][][][][][][][][ 01 ++−++−×=−=+  The dependence of the TeIV on time can be obtained then by applying the integrating factor method (Connors K., 1990):   Then, the TeVI concentration with time is given by:  )(][][ 0201 ][][1201 aveave CutkCutkVIIVeekkTekTe++−−−−=  ( 6-7)  Accordingly, the total tellurium concentration is written as:  −−+=++++−−−12][][1][0)(][][][020101kkeekeTeTeTeaveaveaveCutkCutkCutkVIVIIV  ( 6-8)  Cu2Te concentration is then obtained by the mass balance relationship:  aveaveaveaveaveaveaveCutkCutkVICutkIVCutkCutkVICutkaveIVIVCutkVIaveIVIVeCueTekdteTedeCueTekeCuTekdtTedCueTekCuTekdtTed02010202010201][][01][][][01][02][0102])[][()]([])[][(][][][][][][][][+++++++−+−−−+−−++−+××= ×××=×+×=+ 136 −−+−=+++−−−12][][1][002)(][][][020101kkeekeTeTeTeCuaveaveaveCutkCutkCutkVIVI  ( 6-9)  Reduction reaction of TeVI with Cu+ at initial cuprous and telluruium concentrations of 0.0172 M and 0.000135 M (first row of the Table  6-1), was chosen to investigate the effect of the coupled reaction. In this test cuprous concentration was kept nearly constant (cuprous varies from 0.0172 M to 0.0158 M) while tellurium concentration reduces from 17.3 ppm to 1/8 of this concentration (2.2 ppm). The [TeIV], [TeVI] and [Cu2Te] were calculated based on equation ( 6-6), ( 6-7) and ( 6-9) for the kinetics test with [Cu+]0 = 0.0172 M and [TeVI]0 = 0.000137 M (17.5) ppm at T = 95.1°C where k1 and k2 were 0.00754 M-1s-1 and 0.0328 M-1s-1, respectively. Results are depicted in Figure  6-9.  00.000020.000040.000060.000080.00010.000120.000140.000160 5 10 15Time (hr)[Te] M[Te(VI)][Te(IV)][Cu2Te] Figure  6-9: Calculated TeVI, TeIV and Cu2Te concentration with time for kinetics test with [Cu+]0 = 0.0172 M and [TeVI]0 = 0.000137 M (17.5) ppm at T = 95.1°C.  137 Comparison of calculated and experimental total tellurium concentration with time for the above mentioned kinetics test is shown in Figure  6-10. There is suitably good agreement between the model and the experimental data.   00.000020.000040.000060.000080.00010.000120.000140.000160 5 10 15Time (hr)[TeVI +TeIV]  MCalculatedAnalyzed  Figure  6-10: Comparison of calculated and experimental tellurium concentrations with time for kinetics test with [Cu+]0 = 0.0172 M and [TeVI]0 = 0.000137 M at T = 95.1°C.  The rate constant values were calculated accordingly for both measured and calculated tellurium concentrations via the slope of the straight lines (see equation ( 6-6)) in Figure  6-11. The calculated rate constant considering the coupled reaction (k1 = 0.00718          M-1s-1) was just 5% below the rate constant considering the TeVI to TeIV as a rate determining step (k1 = 0.00754 M-1s-1). Hence, the data may be fit to a simple second order model for simplification. According to these results, a reaction mechanism in next section was proposed assuming the TeVI to TeIV reduction as a rate determining step.  138 k1 = 0.00718 M-1s-1R2 = 0.996k2 = 0.00754 M-1s-1R2 = 0.993-11.5-11-10.5-10-9.5-9-8.50 1 2 3 4 5 6Time (hr)ln [TeVI+TeIV] CalculatedAnalyzed  Figure  6-11: Comparison of calculated and experimental tellurium reaction order in reduction of TeVI with cuprous ion at [Cu+]0 = 0.0172 M and [TeVI]0 = 0.000137 M at T = 95.1°C.  6.3.5 Mechanism of TeVI Reduction and General Rate Law   The reduction of TeVI with Cu+ can occur via either initial one electron transfer with formation of cupric and intermediate TeV (mechanism 1), or initial two electron transfer with formation of Te IV and intermediate Cu3+ (mechanism 2) (Cannon Roderick, 1980). By analogy with selenium, the mechanism of TeVI reduction with cuprous is perhaps best based on initial one electron transfer to form the intermediate TeV:     139      TeVI and TeIV are well known tellurium species; TeV is a short-lived intermediate state (Klaening et al., 2001). This mechanism is the most probable mechanism for two electron reagents with VI/IV oxidation states like CrVI, PuVI, UVI with a known short lived intermediate of V oxidation state (Cannon Roderick, 1980). As it will be shown later (Figure  6-12), the kinetics data fit this mechanism. By analogy to the SeVI case, a general kinetics equation at constant acidity can be stated as follows:                                                                                       ][][][][][22121++−++=−CuCukkTeCukdtTed VIVI  ( 6-10)  According to this equation, the TeVI removal rate increases at higher concentrations of cuprous and tellurate. The derivation of the rate law based on mechanism 2 (two electron transfer with formation of Te IV and intermediate Cu3+) was shown in Appendix 6. The rate law based on mechanism 2 is given by:  ][][][][][2121+−++=−CuTekkTeCukdtTedIVVIVI  ( 6-11)   Rate determining step  TeCuCuTeCuTeCuTeCuTeCuTefastIVIVkVVkkVI222211→++→++↔++++++−   140 Over the solution concentration range studied, it appeared that k-1/k2 ratio effectively approaches to zero. As a result, in contrast with the SeVI reduction reaction, both mechanisms are possible in principle (formation of cupric and intermediate TeV, or formation of TeIV and intermediate Cu3+). The two cannot be distinguished, based on the available results. However, the two electron transfer reduction of TeVI to TeIV with formation of intermediate Cu3+ is very unfavourable reaction (∆E0 < 0).  If the overall reaction is stated as equation ( 6-2), ][101][ +∆=∆ CuTe VI , by substituting and integration of the general rate equation (equation ( 6-10)), the integrated form of the rate law would be:  DBtCuCuCACu+=+++++ ][][ln][1  ( 6-12) 000001221212][][10ln][1][][10][1][+++−++−+=−==−=CuTeACuDCuTeCkCukCkBCCukkAVIVI  By analogy to the SeVI (see section 5.3.1 for calculations), when TeVI concentration is high and approximately constant, the general rate law reduces to simpler form of pseudo-first order kinetics as follows:   141 022101221-][][]ln[][10][ln][k][Cuk++−++++−+=−CukCukCuTetkCuCu aveVI                                 ( 6-13)  By plotting a/[Cu+] - ln[Cu+]  versus time for a trial value of a (a = 221-k][Cuk + ) and  applying least squares method, k1 and k-1/k2 can be calculated from the slope of the best fitted straight line.   Similarly, the general form of the rate equation can be reduced to a simple second order form when k-1[Cu2+]/k2 << [Cu+]. Then the rate equation simplifies to:   ]][[][ 1 VIVITeCukdtTed +=−  ( 6-14)  As a matter of fact, it was observed (see section 6.3.5.1) that the best fit to the straight lines will be attained when the 221-k][Cuk + ratio approaches to zero. Therefore the k-1 value is very small; which might be an indication of irreversible reaction of TeVI with cuprous and generation of the intermediate TeV. This reduces the general form of the rate law to a simple second order rate law in the form of equation ( 6-14) that subsequently complies with the rate orders observed (equation ( 6-3)). Therefore, the integrated form of the rate law is given by:  001 ][][10ln][][ln++++=+CuTeCtkCuCuC VI                                                                              ( 6-15)  142 By plotting  ][][ln+++CuCuC versus time and then calculating the slope of the straight line by using least squares method, k1 can be calculated. The rate law equation as a function of tellurium concentration and based on the ][101][ +∆=∆ CuTeVI  reaction stoichiometry is written as: 001 ][][101ln][][10ln VIVIVITeCuCtkTeTeC ++−=+−                                                                        ( 6-16)  By applying the same method, the rate law reduces to pseudo-first order kinetics at constant cuprous concentration as follows:                                                                                                             tCukTeTefinalVIinitVI01 ][][][ln +=  ( 6-17)  6.3.5.1 Verification of the Rate Law at Constant Acidity and Temperature  Reduction of TeVI by cuprous was studied at T = 95.1±0.1 °C and at [H2SO4] = 50 g/L but variable cuprous and tellurium concentrations. Continuous measurement of [Cu+] was carried out by potentiometric monitoring. The linear equation between cell voltage and logarithm of cuprous concentration was then calibrated by means of known [Cu+]-voltage data points. The calibration equation (equation ( 3-3)) was then used to measure the cuprous concentration in 5 seconds intervals.   143 To validate the suggested rate law (equation ( 6-10)), independence of the rate constants from cuprous and tellurium concentration was verified by conducting four kinetics tests at different initial cuprous and tellurium concentrations. The value of A giving the best possible straight line for the function ][][ln][1+++++CuCuCACu was found using the least squares method. It was determined that A converges to zero. This results in k-1/k2 value equal to zero and reduces the general rate law to a simple second order rate law. Kinetics tests results are tabulated in Table  6-1.   Table  6-1: Verification of suggested rate law at different initial cuprous and tellurate concentrations at T = 95.2 °C, [H2SO4] = 50 g/L, [Cu2+] = 50 g/L.      The rate constant (k1) values are consistent and quite close. In Figure  6-12 the experimental and calculated concentrations of cuprous and tellurium are plotted with time for the third test in Table  6-1. There is a good agreement between the model and the experimental data.  Initial cuprous [M] Initial Tellurate[M] k (M-1s-1) 0.0172 0.000135 (17 ppm) 0.00754 0.0153 0.0243 (3770 ppm) 0.00764 0.0161 0.00103 (131 ppm) 0.00781 0.0173 0.00246 (314 ppm) 0.00784 Average  0.00771  144  Figure  6-12: Comparison of calculated and experimental cuprous and tellurium concentrations with time for kinetics test with [Cu+]0 = 0.016 M and [Te6+]0 = 0.001M, H2SO4 = 50 g/L, Cu2+  = 50 g/L, T = 95.2°C.  00.00020.00040.00060.00080.0010.00120 1 2 3 4 5 6 7Time (hr)[Te] MBased on rate equation[Te] ICP Analysis0.0000.0020.0040.0060.0080.0100.0120.0140.0160 1 2 3 4 5 6 7Time(hr)[Cu+] MBased on rate equation[Cu+] titration 145 6.3.6 Effect of Acidity on Rate Constant and Rate Law  The effect of acidity on the rate constant k1 in sulphate solution was investigated by running the reduction reaction at [H2SO4] = 10, 15, 50, 75 and 100 g/L at T = 95.2 °C. Cupric concentration was set to 50 g/l where initial cuprous concentrations were equal to 0.016-0.015M at most. Tellurate concentration was equal to ~0.003 M and 0.03 M at [H2SO4] = 10, 15 and 50, 75 and 100 g/L respectively. A summary of the rate constants calculated from these experiments data are shown in Table  6-2.   Table  6-2: Rate constants at different acidities at 95.2 °C and [Cu2+] = 50 g/L.  [H2SO4] g/L 10 15 50 75 100 k1 (M-1s-1) 0.00140 0.00231 0.00771 0.0205 0.0353   As was seen with SeVI, the rate constants are lower at lower acid concentrations. In Figure  6-13 the effect of acidity on cuprous oxidation rate with tellurium at [H2SO4] = 50, 75 and 100 g/L is depicted at T = 95.2 °C presenting the suggested rate law and analysed cuprous data points. Acidity has a significant effect on the rate of tellurium reduction with cuprous. The tellurate reduction reaction rate increases with increasing sulfuric acid concentration. For example, at 50 g/L sulfuric acid concentration, it takes almost 48 minutes for ~0.016M cuprous to react with 0.03 M tellurium and tellurium concentration drops to 0.00005 M (6 ppm). This reaction occurs in less than 6 minutes at 100 g/L sulfuric acid concentration.    146 Figure  6-13: Effect of acidity on cuprous concentration with time on tellurium removal reaction at 95.2 °C. Lines are representing the suggested rate law and data points are analysed cuprous concentration.  There is an approximately linear correlation between lnk1 and ln[H2SO4]. The rate constant k1 is approximately proportional to the 1.35-power of sulfuric acid concentration:  k1 = 0.0297 [H2SO4]1.352    (10 g/L < [H2SO4] < 100 g/L)  ( 6-18)  Results for T = 95.2 °C are depicted in Figure  6-14. Equation ( 6-18) can be used to estimate the rate constant k1 values at sulphuric acid concentrations ranging from 10 to 100 g/L.  0.0000.0020.0040.0060.0080.0100.0120.0140.0160 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Time (hr)[Cu+] MH2SO4 = 50 g/LH2SO4 = 75 g/LH2SO4 = 100 g/L` 147 Ln k1 = 1.35 Ln [H2SO4] - 3.52R2 = 0.98-7-6-5-4-3-2-2.5 -2 -1.5 -1 -0.5 0 0.5Ln [H2SO4] MLn k 1 (M-1 s-1 ) Figure  6-14: power law relationship between rate constant and sulfuric acid concentration at T= 95.2 and low and high acidity range: (k1 = 0.0297×[H2SO4]1.35 at 10 g/L < [H2SO4] < 100 g/L.  By substitution of equations ( 6-18) in the second order kinetics equation of ( 6-14), all factors affecting the tellurium removal rate can be included in one equation:  ]][[][][ 35.1421' VIVITeCuSOHkdtTed +=−      (10 g/L < [H2SO4] < 100 g/L)                 ( 6-19)  6.3.7 Effect of Temperature on Tellurium Rate of Removal   The effect of temperature was studied at constant cupric concentration of 50 g/L and [H2SO4] = 50 g/L at T = 75.1, 86.1 and 95.2°C. The initial cuprous concentrations were chosen equal to 0.0081, 0.0126 and 0.0153 M at T = 75.1, 86.1 and 95.2°C respectively.  148 Tellurium concentrations were chosen so that just 95% of tellurium reacted with cuprous over a three half-life change in the cuprous concentration. In Figure  6-15 the effect of temperature on cuprous concentrations with time is shown. The data are fitted to the model rate law equation. 0.0000.0020.0040.0060.0080.0100.0120.0140.0160 0.5 1 1.5 2 2.5 3Time(hr)[Cu+] MT = 75.1°CT = 86.1°CT = 95.2°C  Figure  6-15: Effect of temperature on cuprous concentration with time on tellurium removal rate at H2SO4 = 50 g/L and Cu2+ = 50 g/L. Lines are representing the suggested rate law and data points are analysed cuprous concentration.  In Table  6-3, k1 values at different temperatures are shown. The rate constant k1 values increased with increasing temperature.   Table  6-3: k1 values at different temperatures, Cu2+ = 50 g/L and H2SO4 = 50 g/L. Temperature °C 75.1 86.1 95.2 k1 (M-1s-1) 0.00202 0.00427 0.00771    149 By using the Arrhenius law, the activation energy and natural logarithm of the prefactor are calculated at [H2SO4] = 50 g/L.  Results are depicted in Figure  6-16. An activation energy of 70.9 kJ/mol and ln A1 = 18.3 mol-1s-1 were calculated for k1.  y = -8532.5311x + 18.2975R2 = 1.0000-6.5-5.5-4.50.0027 0.0027 0.0027 0.0028 0.0028 0.0028 0.0028 0.0028 0.0029 0.00291/T (K-1)Ln (k 1)Ea1= 70.9 kJ/molLn (A1) = 18.3 M-1s-1 Figure  6-16: Activation energy and prefactor values for k1 at H+ = 50 g/L and Cu2+ = 50 g/L.   This relatively high activation energy confirms that the reaction of cuprous ion and TeVI are under chemical reaction rate control. Therefore, TeVI reduction reaction with cuprous is expected to be faster than the SeVI reduction reaction as Ea TeVI < Ea SeVI (Ea SeVI = 86.0 kJ/mol).      150 6.3.8 Selenium and Tellurium Species Rate of Reduction   The reduction of SeVI, SeIV, TeVI and TeIV ions with cuprous ion was carried out individually under a single, standardized set of conditions by monitoring the continuous cuprous concentration at [H2SO4] = 100 g/L, [Cu2+] = 50 g/L, T = 95.1°C, [Cu+]0 = 1 g/L and [SeVI/IV]0 and [TeVI/IV]0 ~ 0.03 M.  Results are depicted in Figure  6-17. The data points on the graphs represent analysed cuprous concentration values and the lines are cuprous concentrations measured continuously as a function of solution potential. The potential was step changed over time resulting in jagged curves.    0.00.20.40.60.81.00 0.1 0.2 0.3 0.4 0.5 0.6Time (hr)[Cu+] g/LTe (VI)Se (VI)Te (IV)Se (IV) Figure  6-17: Cuprous concentration depletion in reaction with SeIV, SeVI, TeIV and TeVI at [H2SO4] = 100 g/L, [Cu2+] = 50 g/L and T = 95.1°C. Points are analyzed [Cu+] and lines represent [Cu+] as determined by potentiometry.   151 This shows that SeIV reacts extremely rapidly with cuprous, while it takes much longer for SeVI and TeVI to reduce to copper selenide/telluride with cuprous. Removal of SeVI is by far the slowest process. Accordingly, if SeVI is the highest-concentration species or even of comparable concentration to tellurium species, and it is removed to the required level, SeIV, TeVI and TeIV must also be at or below that concentration, assuming that the reduction reaction of all four species are independent of each other.   6.4 Summary   The kinetics of tellurium removal by cuprous ion precipitation and the effects of acidity and temperature on the removal rate were investigated over sulphuric acid concentration of 10 < [H2SO4] < 100 g/L in chapter 6. At first, stoichiometry of TeVI reduction reaction with cuprous was calculated by measuring the ][][VITeCu∆∆ +  at T = 95.1°C as:   H6TeO6 + 6H+ + 10Cu+ = Cu2Te + 6H2O + 8Cu2+    ( 6-2)  Similarly, an average of ][][IVTeCu∆∆ + was calculated and a ratio of 8:1 cuprous ions per TeIV ion was found to be required to generate cuprous telluride at 95.1°C and [H2SO4] = 50 g/L:   TeO(OH)+ + 3H+ + 8Cu+ = Cu2Te + 2H2O + 6Cu2+    ( 6-4)   152 The reduction of TeVI is 3-4 times slower than TeIV for acid concentrations of 10, 50 and100 g/L H2SO4 solution. Over this acidity range, H6TeO6 slowly reduces to TeO(OH)+ ions and subsequently, TeO(OH)+ is reduced at a faster rate to lower tellurium oxidation states and Cu2Te. However, TeIV reduction is not fast enough compared to TeVI to say that TeVI reduction is definitely rate-determining. This means that the two reduction reactions are coupled and some build-up of TeIV concentration is expected especially at the beginning of the reduction reaction. The significance of this effect was investigated by studying the kinetics of the TeIV reduction with cuprous at T = 95.1°C, [Cu2+] = 50 g/L and [H2SO4] = 50 g/L. It was shown that the measured rate constant of the coupled reaction was just 5% below the rate constant calculated based on the assumption that TeVI reduction is rate-determining. Hence, the kinetics data fit to a simple second order model for simplification and a reaction mechanism was proposed assuming the TeVI to TeIV reduction as a rate determining step.  The TeVI reduction found to be a second order reaction mechanism, first order with respect to both tellurium and cuprous concentration. The kinetics adequately fit the simple rate equation of:   ]][[][ 1 VIVITeCukdtTed +=−  ( 6-14)  for TeVI reduction reaction.  Both mechanisms of formation of cupric and intermediate TeV or formation of TeIV and intermediate Cu3+ were seen to be possible and not distinguishable by methods used in this study. The suggested rate law was validated by  153 verifying the independence of the rate constant k1 from cuprous and tellurium concentration. The average value of k1 was found to be 0.0077 M-1s-1 at T = 95.1°C, [H2SO4] = 100 g/L and [Cu2+] = 50 g/L.  Similar to TeVI reaction, the TeIV reaction followed a second order reaction kinetics, first order with respect to TeIV and Cu+ concentration:  ]][[1 IVIVTeCukdtdTe +=−  ( 6-5)  Acidity had a significant effect on tellurium reduction rate with cuprous. For example at 50 g/L sulfuric acid concentration, it took almost 48 minutes for ~0.016M cuprous to fully react with cuprous whereas, the reaction occurred in less than 6 minutes at 100g/L sulfuric acid concentration. It was shown that increasing solution acidity significantly increases the TeVI reduction reaction rate via an empirical correlation of:  k1 = 0.0297 [H2SO4]1.352    (10 g/L < [H2SO4] < 100 g/L)  ( 6-18)  over the range of 10 g/L < [H2SO4] < 100 g/L.   The effect of temperature on the TeVI reduction reaction was studied at constant cupric concentration of 50 g/L and [H2SO4] = 50 g/L at T = 75.1, 86.1 and 95.2°C and the activation energy of 70.9 kJ/mol was calculated for k1 values.   154 Chapter 7 Conclusions and Recommendations   The chemistry and kinetics of the removal of selenium and tellurium from copper sulfate-sulfuric acid solutions by cuprous ion reduction and precipitation was studied.   At first, a study of equilibrium cuprous concentrations for the cupric–copper metal reaction was performed and an empirical function capable of predicting the saturated [Cu+] was suggested at different temperatures, cupric and sulfuric acid concentrations. Hydrometallurgical applications of aqueous cuprous ion as a reducing agent were discussed in section 2.1. Cuprous ion was formed by contacting an aqueous cupric salt with metallic copper. Studies of cuprous ion used as a reducing agent to remove impurities such as SeVI, TeVI, SeIV and TeIV in solutions containing cupric ion were completed. The equilibrium concentrations of cuprous ion in sulfate media and the oxidation rate of cuprous in perchlorate media were reported in chapter 4. Equilibrium cuprous concentrations were determined for copper sulfate-sulfuric acid solutions with about 50-110 g/L Cu2+, 10-200 g/L H2SO4 (section 4.1). Copper sulfate and sulfuric acid solutions were reacted with copper metal at temperatures between 50 and 95°C to form Cu+ until equilibrium was attained. Samples were collected into an NH4Fe(SO4)2·12H2O solution to convert cuprous to ferrous, which were then titrated with standard Ce(IV) using very dilute ferroin as the indicator. A maximum cuprous concentration of 1.75 g/L was attained with 110 g/L Cu2+ and 200 g/L H2SO4. Equilibrium cuprous concentration data were fitted to the relationship:    155  where [Cu+], [Cu2+] and [H2SO4] are in g/L at specified temperature T (K) and V to Z are empirical constants. The empirical expression predicted the measured [Cu+] to within ±3.6%. Based on the empirical function fitted to the data a solution composed of 105-110 g/L Cu2+ and 10-200 g/L H2SO4 at 95°C (CRED plant solution concentrations) would be expected to support up to about 1.75 g/L Cu+. Acid concentrations of 10-200 g/L had only a modest effect on the equilibrium of cuprous concentrations. With 10-200 g/L H2SO4 and a given [Cu2+] the difference between the highest and lowest [Cu+] was 7% at most. The kinetics of the oxidation of cuprous by perchlorate in a perchloric acid solution at 95°C were also studied at NaClO4 concentrations of 0, 1, 2 and 3 molar, and Cu2+ and HClO4 concentrations of 50 and 100 g/L respectively. Cuprous reacts slowly with perchlorate in solutions with cupric perchlorate and perchloric acid. The rate of cuprous oxidation was apparent first order with respect to cuprous concentration                    ([Cu+] = [Cu+0] × e-kt) with the rate constants varying from 1.75×10-5 to 9.92×10-5 s-1 depending on the sodium perchlorate concentration. Rate constants increased with solution ionic strength. It was shown that cuprous can reduce perchlorate almost 6 times faster in a solution containing 3 molar NaClO4 than in a solution without it at similar initial cuprous-cupric compositions.  Secondly, the chemistry and kinetics of the removal of selenium from copper sulfate-sulfuric acid solution by cuprous ion reduction and precipitation was studied and discussed in section 2.2 and chapter 5. The kinetics were consistent with a well known mechanism common to similar redox reaction systems. The rate law was determined over ( )1]Z[H]Y[H][Cue][Cu 42242X2T-W ++= ++ SOSOV   ( 4-2)  156 a wide range of acidity and temperature. Continuous determination of [Cu+] with time contributed to the accuracy of the rate constants measurements during the reduction reactions. At first, the stoichiometry of the overall reaction was studied and found to be:   HSeO4- + 10Cu+ aq + 7H+ = Cu2Se + 4H2O + 8Cu2+ ( 5-5)  at 95.1°C so long as [Cu+] was > 0.001 M. The likely reduction reaction mechanism was based on initial one electron transfer, to form SeO3- radicals followed by reduction of SeO3- to selenious acid and ultimately cuprous selenide. The kinetics fit the rate law:     ][][][][][22121++−++=−CuCukkSeCukdtSed VIVI  ( 5-1)  at constant acidity. Therefore, the biselenate reduction rate was a function of acid concentration, cuprous, cupric and biselenate concentration. The effects of temperature, acidity, cupric concentration and ionic strength on selenium removal rate were also studied. By knowing the sulfuric acid and cupric sulfate concentration and temperature, it became possible to estimate the reduction reaction time using the integrated form of the rate law and rate constant k1 as a function of acidity. The values of k1 and k-1/k2 were found to be 0.0055 M-1s-1 and 1.5×10-4 at [H2SO4] = 100 g/L, [Cu2+] = 50 g/L and 95.1°C. Rate constants were almost independent of cupric concentration at constant ionic strength but decreased slightly with increasing cupric concentration and increasing ionic strength. An activation energy of 86.0 kJ/mol for k1 was calculated by varying the  157 temperature from 86.1 to 98.6°C. It was shown in section 5.3.2 that, cuprous selenide precipitates react with cupric ion and generate cuprous ion and form non-stoichiometric CuxSe solids (1.88 < x < 1.94). In sections 5.3.5 to 5.3.8, rate constants as functions of temperature, acidity, cupric concentration and ionic strength were suggested. It was shown that, increasing solution acidity significantly increases the biselenate reduction reaction rate. An empirical correlation of:  k1 = 0.00581 [H2SO4]1.25 (T = 95.1°C) M-1s-1  ( 5-7)  was found between the sulfuric acid concentrations in the range of 10 to 200 g/L and k1 at T = 95.1 °C. The biselenate reduction reaction was also investigated in the non-complexing perchlorate medium to study the effects of acidity and ionic strength without the complication of weak acid dissociation of HSO4- and ion pairing effects. Cuprous is oxidized slowly by perchlorate species. The rate of cuprous oxidation was used to modify the rate of biselenate reduction reaction in perchlorate medium. An empirical correlation of:  k1 = 0.0159 [H+] 0.9  ( 5-9)  was found between the H+ concentrations in the range of 10 to 150 g/L HClO4 and I = 4.35 m at 95.1°C. Biselenate removal rate was increased significantly by increasing the ionic strength of the solution. The k1 values varied from 0.0075 to 0.0412 M-1s-1 in solutions containing 0 to 3 M NaClO4, respectively, at 95.1°C, [HClO4] = 100 g/L and  158 [Cu(ClO4)2] = 50 g/L. A linear correlation between log k1 and solution nominal ionic strength was found to be:   log k = -2.402 - [I1/2 / (1+I1/2) – 0.263 I ]  ( 5-17)  in perchlorate medium at 95.1°C. In contrast to the results obtained in the perchlorate medium, biselenate removal rate was decreased in sulfate bearing solutions by addition of sulfate based salts.  This almost certainly has to do with decreasing free acid levels due to formation of bisulfate anion.   Thirdly, the tellurium reduction chemistry and reaction kinetics by means of cuprous was studied over a wide range of conditions as reported in section 2.3 and chapter 6. At first, the stoichiometry of the overall reaction was studied and a ratio of 10:1 cuprous ions per TeVI ion and 8:1 cuprous ions per TeIV ion was found to be required to generate cuprous telluride at 95.1°C and [H2SO4] = 50 g/L in reduction of TeVI and TeIV, respectively. Then, the TeVI reduction reaction order with respect to cuprous and tellurium concentration was investigated over an acidity range of 10 to 100 g/L H2SO4 and at temperatures of 75°C to 95°C. Similarly, the TeIV reduction reaction order with respect to cuprous and tellurium concentration was investigated at [H2SO4] = 50 g/L and at temperatures of 95.1°C. Coupled reduction of the TeVI and TeIV with cuprous was investigated and a total tellurium concentration function with time was given in a pseudo first order kinetics condition:   159 −−+=++++−−−12][][1][0)(][][][020101kkeekeTeTeTeaveaveaveCutkCutkCutkVIVIIV  ( 6-8)  The reduction reaction mechanism, a suggested rate determining step and a rate law was offered accordingly for reduction of TeVI with cuprous. The reduction reaction order followed second order reaction, first order with respect to both tellurium and cuprous concentration regardless of the solution temperature (T = 75.1, 86.1 and 95.2°C) and acidity (10 g/L < [H2SO4] < 100 g/L). The kinetics adequately fit the simple rate equation of:  ]][[][ 1 VIVITeCukdtTed +=−  ( 6-14)  A plausible TeVI reduction with cuprous was suggested via slow reduction of H6TeO6 to TeO(OH)+ following by faster reduction of TeO(OH)+ to lower tellurium oxidation states. The rate constant k1 was calculated at different sulphuric acid concentrations (10, 15, 50, 75, 100 g/L) at T = 95.2°C. Similarly to selenium, effects of temperature and acidity on tellurium removal rate were also studied and rate constants as a function of temperature and acidity were determined. It was shown in section 6.3.6 that increasing solution acidity significantly increases the tellurium reduction reaction rate. An empirical correlation of:  k1 = 0.0297 [H2SO4]1.352    (10 g/L < [H2SO4] < 100 g/L)  ( 6-18)   160 was found between the rate constants and the sulfuric acid concentration over the range of 10 g/L < [H2SO4] < 100 g/L. This equation was found to adequately estimate the rate constant k1 at different sulphuric acid concentrations in a range of 10 to 100 g/L. The k1 values at different temperatures can be determined by using the Arrhenius equation and experimental values of Ea1 = 70.9 kJ/mol and ln A1 = 18.3 M-1s-1. This activation energy was calculated by varying the temperature from 75 to 95°C. By knowing the sulfuric acid concentration and solution temperature, it became possible to estimate the reduction reaction time using the integrated form of the rate law and rate constants k1.   7.1 Industrial Applications of the Findings  Selenium and tellurium reduction reaction times can be estimated at different acidities and temperatures using the suggested rate laws and rate constants functions. The following calculations show the application of the suggested rate law and other empirical equations using the CRED plant’s selenium and tellurium removal circuit (Figure  2-9) conditions (Stewart et al., 1985). The solution sent to the removal circuit has a typical composition of 100 g/L cupric, 125 g/L sulphuric acid and, reporting at most 100 mg/L of selenium. It was reported by Qin (2005) that 20 to 40 % of the selenium to the removal circuit is in the SeVI oxidation state. The Copper Contact Column (CCC) inlet and outlet tellurium composition reported by Qin (2005) shows a large drop of total tellurium (TeIV and TeVI) concentration from 142 mg/L to 5 mg/L. There was no report on TeVI and TeIV composition ratio but it can be assumed that most of the remaining tellurium in the CCC outlet is TeVI. At the beginning the solution temperature is 95-99 °C and then the solution  161 up flows to copper contact column (CCC) containing copper wire cuttings. Residence time may vary from 1 to 3 minutes in CCC. The SeIV and TeIV fraction of the selenium and tellurium ions content of the solution reacts in the presence of copper wire cuttings in CCC and forms black particles of copper selenide/telluride. Copper selenide/telluride particles with solution containing biselenate/telluric acid overflow into four consecutive ageing towers and the biselenate/telluric acid reduction reaction with cuprous ion proceeds until the selenium and tellurium content of the solution reach below 1 mg/L. The equilibrium cuprous concentration of the solution generated in CCC can be estimated using the cuprous function equation ( 4-2). However, the presence of the metal ion impurities such as ferrous (9 g/L), nickel (17 g/L) and cobalt (19 g/L) ions may limit the utility of equation ( 4-2) due to increasing the solution ionic strength. At [Cu2+] = 100g/L, [H2SO4] = 125 g/L and T = 97°C the equilibrium cuprous concentration is:   ( ) ( )M0.0271.75g/L)1]251[10849.1]251[102.4(00]1[exp145906][Cu1]Z[H]Y[H][Cue][Cu426-0.52162273.1597-5089.0842242X2T-W==+××−×××=⇒++=−++++ SOSOV It is assumed that the residence time in CCC is sufficient for the cuprous generation reaction to reach equilibrium concentration. The harmful effect of oxygen in CCC and ageing towers was ignored (i.e., it is assumed no oxygen enters the aging towers). Therefore, it is expected that the CCC can continuously provide steady state concentration of 0.027 M cuprous. Hence, the general rate law simplifies to pseudo-first order reaction kinetics and selenium removal time can be calculated using equation ( 5-4) and ( 5-7). If it is assumed that the solution temperature stays at 95°C during the whole  162 reduction reaction in the ageing towers, then according to the calculations below, it would take 4.8 hours for a solution containing 40 mg/L biselante to reach a selenium concentration of 1 mg/L:   Equation ( 5-7):  k1 = 0.0058 [H2SO4]1.25 = 0.0058×(125/98)1.25 = 0.0079 M-1s-1   Equation ( 5-4):   Accordingly, if the solution acidity increases from 125 g/L to 150 g/L the removal rate respectively decreases from 4.83 hours to 3.87 hours.   Ferric input to a CCC was reported by Qin (2005) to be 9 g/L. Therefore, if cuprous ion concentration entering the aging towers drops below the saturated concentration (due to the partial reaction with oxygen or ferric ion), the removal time increases significantly. For example, assuming only one tenth of the ferric ion (0.0161 M) reacts with cuprous, then the final cuprous concentration entering the aging towers would be 0.0109 M (0.027-0.0161 = 0.0109). Using equation ( 5-4) at a cuprous concentration of 0.0109 M the removal time would increase to 12.1 hours. There is evidence for low cuprous concentration in the CRED plant according to the Copper Cliff Copper Refinery report (2001). It was shown that 7.20 mg/L of selenium concentration in the CCC over flow (T = 100°C, Cu2+ = 99.8 g/L and H2SO4 = 128 g/L) decreased to 2.25 mg/L in the aging tower No. 4 over flow (T = 84°C, Cu2+ = 99.4 g/L and H2SO4 = 123 g/L) after 12.8 hours. hrt 83.43600027.00079.0027.055.6310010140ln24=××+×=− 163 According to equations ( 5-4) and ( 5-7), and an average acidity of 125.5 g/L, [Cu2+] = 99.6 g/L and T = 95 °C the rate constant k1 and consequently [Cu+] can be calculated as:  Equation ( 5-7):  k1 = 0.0058 [H2SO4]1.25 = 0.0058× (125.5/98)1.25 = 0.0079 M-1s-1   Equation ( 5-4):       [Cu+] = 0.00334 M  It may be concluded that low cuprous concentrations are due to insufficient residence time at the CCC, reaction of ferric with cuprous and/or ingress of oxygen in the CCC and aging towers. The dissolution of oxygen in an electrolyte solution will decline with increasing temperature and the solution ionic strength in copper sulphate sulphuric acid solutions studied in this work (Tromans, 2000). The maximum oxygen concentration that may be present in the solution at an oxygen partial pressure of 0.2 atm (air pressure) will not exceed 0.0001 M in the 100 g/L copper sulphate solution at 97°C (Tromans, 2000). In acidic sulphate solutions the oxidation reaction of cuprous with oxygen is extremely fast (Cotton et al., 1972) and may be written as:  2Cu2SO4 + O2 + 2H2SO4 = 4CuSO4 + 2H2O  ( 7-1)  Accordingly, the maximum amount of cuprous ion concentration that may be consumed with oxygen will not be greater than 0.0004 M assuming a limited access of air to electrolyte solution. Good sealing of the CCC and aging towers and keeping the solution ⇒××+×=++−3600][0079.0][55.636.991025.220.7ln82.12 24CuCu 164 temperature near the boiling point can effectively minimize the ingress of the oxygen into CCC and aging towers following the consumption of dissolved oxygen with cuprous. The concentration of 0.0004 M cuprous corresponds to just 1.5% of the total saturated cuprous concentration that is supposed to be generated in the CCC at [Cu2+] = 100g/L, [H2SO4] = 125 g/L and T = 97°C. Therefore the low saturated concentration in the aging towers may be mostly attributed to either oxidation of cuprous with ferric ion inside the CCC or insufficient residence time for cuprous to reach equilibrium inside the CCC. An average ferric content of the solution entering the CCC was reported to be 0.16 M (Qin, 2005). This would have easily consumed all the cuprous that could be generated in the CCC if the direct reduction of ferric with copper metal is not considered. Hence, the possibility of generating cuprous in a separate reactor using a low ferric electrolyte and directly injecting the saturated cuprous into the aging towers to supplement the rate of reaction should be considered. Alternatively, the CCC could be redesigned in order to increase the residence time of the passing electrolyte solution. Routine analysis of the cuprous concentration at CCC outlet should be considered to check on performance of the CCC. This can decrease the selenium and tellurium removal time to the values predicted by the rate laws suggested in this study.   For tellurium, removal time can be calculated using equation ( 6-18) and ( 6-17) assuming that the reduction reaction of selenium and tellurium are independent of each other. It is assumed that the solution temperature stayed at 95°C during the whole reduction reaction in the ageing towers and final tellurium concentration decreased to 1 mg/L:    165 Equation ( 6-18): k1 = 0.0297 [H2SO4]1.352  = 0.0297×(125/98)1.352 = 0.04127 M-1s-1  Equation ( 6-17):    The use of equation ( 6-18) is based on the possibility of extrapolating the solution acidity to 125 g/L. Knowing the chemistry of the cuprous ion results in using it more efficiently as the removal of SeVI and TeVI takes place via the reduction with cuprous ion rather than copper metal. Preserving the cuprous from oxidation with oxygen may be achieved by minimizing the solution contact surface with air or operating near the boiling point to provide an inert atmosphere of steam. Keeping the solution temperature close to 100°C in the aging towers also prevents cuprous disproportionation when concentration is near saturation (first aging tower) and improves the reaction kinetics as was shown in this study. It was shown that cuprous concentration drop form 0.027M to 0.011 M (due to the insufficient residence time at the CCC, reaction of ferric with cuprous in the CCC and/or ingress of oxygen in the CCC and aging towers) significantly increased the selenium removal time from 4.8 hours to 12.1 hours. Comparison of the actual cuprous concentration at the CCC outlet with the expected cuprous concentration estimated by the suggested function (Equation 4.2) can verify if the required time for cuprous to reach to equilibrium is provided or not.  Knowing the selenium and tellurium reduction rate laws and rate constants over a wide range of acidity, temperature, cupric concentration and ionic strength facilitate the min2460027.00413.015ln=××=t 166 estimation of the residence time needed for removal of known amounts of selenium and tellurium. This can lead to a more efficient process by designing efficient reactors (CCC and aging towers) and/or controlling the solution flow rate, if possible. Therefore, if the removal time was much greater than what models are estimating, effects of other factors such as insufficient residence time at CCC, consumption of the cuprous ion by oxygen and/or ferric ion and temperature drop in aging towers should be investigated and corrected to the extent possible.  7.2 Recommendations for Future Work   The effect of impurities in the solution can be investigated further. Impurities with higher reduction potential than the cuprous-cupric couple such as ferric, especially at high concentration, can easily be reduced to ferrous with cuprous and consume the main portion of cuprous resource. Thus, the effect of ferrous on both equilibrium of the cuprous concentration and kinetics of the selenium and tellurium removal needs to be studied. Metal ion impurities at lower redox potential than the cuprous-cupric couple such as Ni2+ (17 g/L), Co2+ (19 g/L), Fe2+ (5 g/L) and Fe3+ (9 g/L) may change the rate constants by increasing the solution ionic strength. Accordingly, developing the rate law as a function of cuprous, cupric and selenium/tellurium activity and calculating the activity coefficients as a function of solution ionic strength may lead to a rate law that can predict the effect of the impurities in the solution. The possibility of interaction of selenium and tellurium on  167 rate laws and rate constants may be investigated, whereas they were investigated individually in this study.  It was shown in this study that the reduction of SeVI/TeVI with cuprous is under chemical reaction rate control with relatively high activation energies of 86.0 kJ/mol and 70.5 kJ/mol for selenium and tellurium, respectively. 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Compound ∆G0f  298 kj/mol ∆G0f  368.15 kj/mol ∆G0f  373.15 kj/mol H2SeO4aq -441.10 -401.06 -398.14 HSeO4-aq -452.16 -421.27 -419.02 SeO42-aq -441.29 -401.82 -398.83 H2SeO3aq -426.11 -407.30 -405.97 HSeO3-aq -411.48 -386.73 -384.92 SeO32-aq -369.70 -334.48 -331.79 Se(gray) 0.00  -3.41 H2Seaq 22.03 23.11 23.22 HSe-aq 43.81 51.30 51.90 Se2-aq 155.99 164.52 165.30     H2 (g) 0.00  -10.05 O2 (g) 0.00  -15.64 H+ 0.00  -1.143 H2O -237.14  -243.05     CuSe -42.63 -43.01 -43.04 CuSe2 -44.98 -44.27 -44.22 CuSeO3  -347.98 -328.42 -327.03 Cu3Se2 -111.39 -112.03 -112.01 Cu2Se -73.23 -74.97 --75.02     Cu 0.00  -2.70 Cu+ 49.98 44.54 44.13 Cu2+ 65.55 65.51 65.51 CuO -128.08 -121.60 -121.14 Cu2O -147.84 -142.50 -142.12  180 Appendix 2: Thermodynamic data used to draw Te-Cu-H2O Eh-pH diagrams.  Criss Cobble method was used to calculate higher temperature data for Cu-H2O species. thermodynamic properties of aqueous Te species at 100°C were calculated by McPhail.  * Data reported by Woods was used. ** Data reported by Mills was used. †  89.5 kJ was also reported by Woods. ‡ -436.6 kJ was also reported by Woods. †* Data was calculated based on Gospodinove71,72,73 study of ∆H°rxn,298  and S° 298 for CuTeO3, CuTe2O5 and CuO.CuTeO3.       Compound ∆G0f 298 kj/mol ∆G0f  373.15 kj/mol ∆G0f  298 kj/mol ∆G0f  298 kj/mol ∆G0f  298 kj/mol ∆G0f  298 kj/mol ∆G0f  298 kj/mol ∆G0f  298 kj/mol Reference Mc Phail Mc Phail Brookins Bard Woods Barnar Zhang Pashinkin H6TeO6  -964.75 -985.496   -1025.2    H5TeO6-  -920.8 -935.408       H4TeO62-  -858.3 -862.772       Te4+  *   219.16 219.16 219.2    H3TeO3+ -490.73 -503.486 -496.1   -496.2   TeO(OH)+ *   -258.49  -257.7    H2TeO3 (s)    -484.1 -478.5  -474.46  TeO2 (s) -266.11 -271.86 -270.29 -270.3 -269.7 -270.29   HTeO3-  -438.164 -441.831 -436.56 -436.56 -452.3‡  -452.29  TeO32-  -383.6 -372.222 -392.42 -392.42 -391.6  -391.20  Te(s) 0 -3.941 0      H2Te aq 90.89 86.862 142.67 142.7 142.7†  89.54  HTe- 105.93 108.335 157.74 157.7   104.6  Te22- 154.35 161.049  162.1 162.55  163.05  Te2- 175.35 189.44  220.05 174  174.05  CuTe(s) ** -26.37 -33.35      -25.10 Cu2Te(s) ** -47.57 -58.35      -48.10 CuTeO3 (S) †* -339.73 -374.65       CuO·CuTeO3†* -563.19 -495.03       CuTe2O5 †* -692.86 -644.52       Cu 0.00 -2.70       Cu2+ 65.55 70.49       CuO -128.08 -131.67       Cu2O -147.84 -155.35        181 Appendix 3: Te-Cu-H2O Eh-pH diagram activity of Te ions = 0.01 and 1 M   -1.5-1-0.500.511.52-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14pHEh (V)CuTe2O5H2TeCu2TeHTe-TeO32-H4TeO62-O2H2OH5TeO6-H2H+CuO·CuTeO3H6TeO6Te2-Te4+CuCu 2 OCuOCu 2+CuTeTeO(OH)+TeTeO2 Te-Cu-H2O Eh-pH diagram activity of Te ions = 0.01 M, activity of Cu ions = 0.8 M, 25°C            Te-Cu-H2O Eh-pH diagram activity of Te ions = 1 M, activity of Cu ions = 0.8 M, 100°C -1.5-1-0.500.511.5-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14pHEh (V)TeO2H2TeCu2TeHTe-TeO32-H4TeO62-O2H2OH5TeO6-H2H+H6TeO6Te2-Te4+CuCu 2 OCuOCu 2+CuTeTe 182 Appendix 4: Cupric sulfate-sulfuric acid solution densities  In order to estimate the cuprous concentrations in g/L, as well as [Cu2+] and [H2SO4], for solutions at the reaction temperatures, the densities as a function of temperature were needed. The density data for the various compositions and temperatures are shown in  Table 1-Appendix 4: Density data for copper sulfate-sulfuric acid solutions Temp. °C Wt. Cu2+  g a Wt. H2SO4 g a density g/L Vol.  mL b  Temp. °C Wt. Cu2+ g a Wt. H2SO4 g a density g/L Vol.  mL b 96.3 25 100 1076.8 1001.7  58.9 110 100 1292.8 1000.9 93.3 25 100 1078.9 1001.7  93.3 50 200 1191.3 1001.7 83.5 25 100 1085.5 1001.4  83.5 50 200 1197.3 1001.4 73.6 25 100 1091.5 1001.2  78.5 50 200 1200.4 1001.3 96.3 50 100 1133.1 1001.7  73.6 50 200 1203.3 1001.2 93.3 50 100 1135.1 1001.7  63.8 50 200 1209.2 1001.0 83.5 50 100 1141.7 1001.4  49.0 50 200 1217.8 1000.7 73.6 50 100 1147.9 1001.2  29.3 50 200 1229.1 1000.2 96.3 60 100 1156.1 1001.7  24.4 50 200 1231.9 1000.1 93.3 60 100 1158.1 1001.7  93.3 50 10 1088.7 1001.7 83.5 60 100 1164.7 1001.4  83.5 50 10 1095.0 1001.4 73.6 60 100 1170.6 1001.2  78.5 50 10 1098.3 1001.3 96.3 75 100 1189.7 1001.7  73.6 50 10 1101.2 1001.2 93.3 75 100 1191.8 1001.7  63.8 50 10 1106.9 1001.0 83.5 75 100 1198.5 1001.4  49.0 50 10 1114.8 1000.7 73.6 75 100 1204.5 1001.2  29.3 50 10 1123.8 1000.2 58.9 75 100 1213.4 1000.9  24.4 50 10 1125.8 1000.1 49.0 75 100 1219.1 1000.7  93.3 110 200 1320.9 1001.7 96.3 90 100 1222.9 1001.7  83.5 110 200 1326.9 1001.4 93.3 90 100 1225.2 1001.7  78.5 110 200 1330.0 1001.3 83.5 90 100 1231.9 1001.4  73.6 110 200 1333.0 1001.2 73.6 90 100 1237.9 1001.2  73.6 110 200 1335.3 1001.2 58.9 90 100 1246.6 1000.9  63.8 110 200 1338.7 1001.0 49.0 90 100 1252.5 1000.7  93.3 110 10 1226.6 1001.7 49.0 90 100 1253.9 1000.7  83.5 110 10 1233.0 1001.4 96.3 110 100 1267.3 1001.7  78.5 110 10 1236.1 1001.3 93.3 110 100 1269.7 1001.7  73.6 110 10 1239.1 1001.2 83.5 110 100 1276.4 1001.4  63.8 110 10 1244.8 1001.0 73.6 110 100 1281.9 1001.2  58.9 110 10 1248.6 1000.9 58.9 110 100 1290.7 1000.9  49.0 110 10 1252.8 1000.7 a Masses Cu2+ (as CuSO4·5H2O) or H2SO4 added to a 1 L volumetric flask. b Volume of flask corrected for expansion: V = 1000 mL + 0.02263(T - 20) mL/°C.   183 Table 1-Appenix 4. This data supplements data available in the literature (Price et al., 1980 and Hotlos et al., 1988). The masses of Cu2+ and H2SO4 added to 1 L volumetric flasks are reported. The masses of CuSO4 were calculated from the masses of assayed CuSO4·5H2O used. The mass of water present in each solution was determined as the difference between the total solution mass and the masses of CuSO4 and H2SO4. The masses (g) of CuSO4 and H2SO4 were normalized to those corresponding to 1000 g of water. The corresponding volumes (mL) of the solutions per kg of water were then calculated. The same quantities were determined for the literature data. The volumes per kg H2O were fitted to an empirical equation of the form,  2SOHCuSO eTdTcWbWaV 424 ++++=                          (1-Appendix 4)  where V is the volume in mL per kg H2O, WCuSO4 is the mass (g) of CuSO4 per kg H2O, WH2SO4 is the mass of H2SO4 per kg H2O and T is the temperature in °C, while a-e are empirical constants. Then the density (g/L) of a solution at a temperature of interest can be calculated according to the equation below:  V001.01000WWρ 424 SOHCuSO×++=                                                                         (2- Appendix 4)  The constants that gave the best fit are provided in Table 2-Appenix 4. The calculated volumes and densities differed from the experimental values by ±0.59% at most. The correlation is quite adequate for the purposes of this study. For given masses (g) of CuSO4 and H2SO4 per kg of water, at any temperature within the specified range, the  184 density of a solution can be estimated, and thence the volumetric concentrations at the reaction temperatures.  Table 2-Appendix 4: Empirical constants for estimation of volumes of solutions and mass of water per litre of solution over specified concentration and temperature ranges.  2SOHCuSO eTdTcWbWaV 424 ++++=  (mL/kg H2O)  a b c d e 66-326 g CuSO4/kg H2O 10-236 g H2SO4/kg H2O 25-95°C a 978.68 0.10451 0.46714 0.33120 0.002731 TEDT1]SOH[C]Cu[BAW 422L/OH2 ++−−=+  (g/L solution)  A B C D E 25-110 g/L Cu2+ 10-200 g/L H2SO4 25-95°C 1045.74 0.27016 0.48663 0.000835 0.3310 a Approximately 25-110 g/L Cu2+,10-200 g/L H2SO4.    However, some studies reported cuprous concentrations (mol/L) in CuSO4/H2SO4 solutions at temperatures above room temperature as a function of [Cu2+] and [H2SO4] (mol/L) at some initial, lower reference temperature (room temperature), at which the parent solutions were prepared. Thus the volumetric concentrations of the solutes in the solutions at higher temperatures were not known. This limits the utility of these data. (In this work the more concentrated solutions could not be prepared at room temperature due to saturation.) Nevertheless, in order to make use of such data and compare it to this work, it was deemed helpful to be able to estimate the [Cu2+] and [H2SO4] at the reaction temperatures, based on the compositions of the parent solutions at the preparation temperature. From the masses of CuSO4 and H2SO4 added to 1 L volumetric flasks and the known solution volumes at the various temperatures (this work), the [Cu2+] and  185 [H2SO4] in g/L were determined. These quantities were also readily obtained from the data of Hotlos et al., 1988. The masses of water in g per L of solution, termed WH2O/L, were known (this work) or calculated (from the data of Hotlos et al., 1988). These values were fitted to the equation below, where T is the temperature in °C and A-E are empirical constants:  TEDT1]SOH[C]Cu[BAW 422L/OH2 ++−−=+                                        (3- Appendix 4)  The constants A-E that gave the best fit are provided in Table 2-4. The error between known WH2O/L and calculated values was at most ±0.60%. For a given volumetric composition and temperature, the density is then given by:  O/LH424 2W]SO[H][CuSOρ ++=           (4-Appendix 4)  where [CuSO4] in g/L is calculated from [Cu2+]. The maximum error in densities calculated in this way was ±0.55%.   Next, for a given volumetric composition at a temperature at which the solution was prepared, the density of this same solution at some other temperature can be calculated using the correlation of equations (1-Appendix 4) and (2-Appendix 4). (The quantities WCuSO4 and WH2SO4 can be estimated from [Cu2+], [H2SO4] and WH2O/L.) Finally, knowing the volume of the solution per kg H2O at the new temperature (equation 1-Appendix 4),  186 the [Cu2+] and [H2SO4] can be found from WCuSO4 and WH2SO4. To summarize, density can be estimated in two ways. The first is from known masses of CuSO4 and H2SO4 per kg of water and the temperature of interest. Second, starting from known [Cu2+] and [H2SO4] in g/L for a solution prepared at some initial temperature the density at some other temperature can be found using equation (3-Appenix 4) and then equations (1-Appendix 4) and (2-Appendix 4). Densities determined in these two ways differed from each other by at most 0.14%.                    187 Appendix 5: Cuprous concentrations in molal units for initial CuSO4/H2SO4 concentrations.   Temp. °C [Cu2+] m [H2SO4] m [Cu+]  m  Temp. °C [Cu2+] m [H2SO4] m [Cu+]  m 50.2 0.4117 1.067 0.001954  50.2 1.249 1.079 0.003543 60.2 0.4117 1.067 0.003101  60.2 1.249 1.079 0.005542 75.3 0.4117 1.067 0.006098  75.3 1.249 1.079 0.01081 85.2 0.4117 1.067 0.009108  85.2 1.249 1.079 0.01603 95.1 0.4117 1.067 0.01323  95.2 1.249 1.079 0.02334 50.2 0.4118 1.067 0.001903  98.2 1.249 1.079 0.02619 60.1 0.4118 1.067 0.003053  60.2 1.250 1.080 0.005376 75.3 0.4118 1.067 0.006088  75.2 1.250 1.080 0.01066 85.1 0.4118 1.067 0.009065  85.3 1.250 1.080 0.01592 95.1 0.4118 1.067 0.01313  95.2 1.250 1.080 0.02305 50.2 0.7946 0.1030 0.002599  50.2 1.526 1.099 0.003886 60.2 0.7946 0.1030 0.004119  60.2 1.526 1.099 0.006226 75.3 0.7946 0.1030 0.008453  75.2 1.526 1.099 0.01215 95.2 0.7946 0.1030 0.01831  85.3 1.526 1.099 0.01797 50.2 0.7952 0.1031 0.002575  95.2 1.526 1.099 0.02620 60.2 0.7952 0.1031 0.004163  98.3 1.526 1.099 0.02931 75.3 0.7952 0.1031 0.008450  60.2 1.799 0.1060 0.006262 95.2 0.7952 0.1031 0.01799  75.3 1.799 0.1060 0.01303 50.2 0.8276 1.072 0.002842  85.2 1.799 0.1060 0.01955 60.2 0.8276 1.072 0.004437  95.2 1.799 0.1060 0.02899 75.3 0.8276 1.072 0.008687  60.2 1.889 1.113 0.006989 95.2 0.8276 1.072 0.01875  75.2 1.889 1.113 0.01378 50.2 0.8674 2.248 0.003062  85.3 1.889 1.113 0.02058 60.1 0.8674 2.248 0.004737  95.2 1.889 1.113 0.02981 75.3 0.8674 2.248 0.009411  75.3 2.015 2.374 0.01540 95.2 0.8674 2.248 0.02020  85.2 2.015 2.374 0.02262 50.2 0.9956 1.075 0.003073  95.3 2.015 2.374 0.03243 60.2 0.9956 1.075 0.004871  75.3 2.013 2.371 0.01521 75.3 0.9955 1.075 0.009533  85.2 2.013 2.371 0.02258 85.2 0.9955 1.075 0.01418  95.3 2.013 2.371 0.03253 95.2 0.9955 1.075 0.02064           188 Appendix 6: General kinetics equation for reduction of SeVI and TeVI based on mechanism 2  Mechanism 2 is based on initial two electron transfer to form the intermediate Cu3+, followed by applying the steady state criterion for Cu3+ ie: 0][3=−+dtCud :  Rate determining step  SeCuCuSeCuCuCuCuSeCuSeCufastIVkIVkkVI22233211→++→++↔++++′+++′′+−   By writing and combining rate equations for the above three reactions and applying the steady state criterion a general kinetics equation at constant acidity is derived as followings:  ]][[]][[]][[][]][[]][[][311323311IVVIIVVIVISeCukSeCukCuCukdtCudSeCukSeCukdtSed+−+++++−+−+−=+−= ][][][][][][][][][][]][][[]][[][][][]][[][])[][]([]][[0][:ionapproximat stateSteady 21212122121111211321313+−++−++−+−++−+++−++++−=+−=++−=⇒++=⇒++=+=CuSekkSeCukCukSekSeCukkCukSekSeSeCukkSeCukdtSedCukSekSeCukCuCukSekCuSeCukdtCudIVVIIVVIIVIVVIVIVIIVVIIVVI                                 189  General kinetics equation: ][][][][][2121+−++=−CuSekkSeCukdtSedIVVIVI    Similarly, the general kinetics equation for reduction of TeVI based on mechanism 2 is:  General kinetics equation: ][][][][][2121+−++=−CuTekkTeCukdtTedIVVIVI             

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