Applied Science, Faculty of
Materials Engineering, Department of
DSpace
UBCV
Zuniga Sanchez, Pablo Andres
Master of Applied Science - MASc
University of British Columbia
Thiourea (Tu) has been widely studied and claimed to be used in many applications in medicine, industry, and analytical chemistry. Although, the significant discrepancies in the results reported have rendered a lack of consensus with regards to the mechanism and reaction pathway for the oxidation of Tu. Therefore, the main goal of the study was to improve the understanding of the chemical stability and oxidation of Tu in acidic ferric media. Using experimental data from both batch reactor and electrochemical tests, the sub-processes involved, their mechanism and kinetics were thoroughly examined to identify the rate-limiting sub-processes and the overall Tu oxidation rate. Of the four factors tested (pH, temperature, Tu concentration, and ferric concentration), the effects of the temperature and the pH were the most significant. Increasing the temperature over 35°C, in acidic ferric media, results in an average of 75% Tu consumption during the first 48 h. A direct dependence between the Tu and the ORP measurements was observed in the tests with 10 mM Fe³⁺ and under various [Tu]₀. These results confirm the assumption that in the presence of Tu, the ORP is not solely controlled by the Fe³⁺/Fe²⁺ and the Tu/FDS couple may play an important role. This investigation into the chemical stability and oxidation of Tu in ferric media demonstrated that Tu presents a rich and dynamic behavior. In this highly complex system, the oxidation reactions occurring in both series/parallel manner seem to play a key role in the formation of intermediate species, which influences the final concentrations. The proposed rate expressions are the first serious attempt at integrating the two main processes occurring in solution, oxidation of Tu in the presence of ferric ions and the hydrolysis of FDSH₂²⁺, into a single expression. Therefore, the findings of this study just begin to unravel the influence that different factors present in solution exert on Tu stability, besides establishing general guidelines for future research.
FUNDAMENTAL STUDY OF THE CHEMICAL STABILITY AND OXIDATION OF THIOUREA IN ACIDIC FERRIC MEDIA by Pablo Andres Zuniga Sanchez B.Sc., University of Concepción, 2014 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Materials Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2020 ©Pablo Andres Zuniga Sanchez, 2020 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for the acceptance, the thesis entitled: Fundamental study of the chemical stability and oxidation of thiourea in acidic ferric media Submitted by Pablo Andres Zuniga Sanchez in partial fulfillment of the requirements for the degree of Master of Applied Science in Materials Engineering Examining Committte: Dr. David G Dixon, Materials Engineering Supervisor Dr. Wenying Liu, Materials Engineering Supervisory Committee Member Dr. Edouard Asselin, Materials Engineering Supervisory Committee Member iii Abstract Thiourea (Tu) has been widely studied and claimed to be used in many applications in medicine, industry, and analytical chemistry. Although, the significant discrepancies in the results reported have rendered a lack of consensus with regards to the mechanism and reaction pathway for the oxidation of Tu. Therefore, the main goal of the study was to improve the understanding of the chemical stability and oxidation of Tu in acidic ferric media. Using experimental data from both batch reactor and electrochemical tests, the sub-processes involved, their mechanism and kinetics were thoroughly examined to identify the rate-limiting sub-processes and the overall Tu oxidation rate. Of the four factors tested (pH, temperature, Tu concentration, and ferric concentration), the effects of the temperature and the pH were the most significant. Increasing the temperature over 35°C, in acidic ferric media, results in an average of 75% Tu consumption during the first 48 h. A direct dependence between the Tu and the ORP measurements was observed in the tests with 10 mM Fe3+ and under various [Tu]0. These results confirm the assumption that in the presence of Tu, the ORP is not solely controlled by the Fe3+/Fe2+ and the Tu/FDS couple may play an important role. This investigation into the chemical stability and oxidation of Tu in ferric media demonstrated that Tu presents a rich and dynamic behavior. In this highly complex system, the oxidation reactions occurring in both series/parallel manner seem to play a key role in the formation of intermediate species, which influences the final concentrations. The proposed rate expressions are the first serious attempt at integrating the two main processes occurring in solution, oxidation of Tu in the presence of ferric ions and the hydrolysis of FDSH22+, into a single expression. Therefore, the findings of this study just begin to unravel the influence that different factors present in solution exert on Tu stability, besides establishing general guidelines for future research. iv Lay Summary Thiourea, also called thiocarbamide, is a sulfur-organic compound that has received considerable attention over the years. Despite being widely studied and claimed to be used in many applications in medicine, industry, and analytical chemistry, variable results and conclusions have been published because of the different conditions employed. The motivation of this study was to improve the understanding of the chemical stability of thiourea and to determine the key controlling factors influencing its behavior in acidic ferric media. In an attempt to shed some light into the mechanism of oxidation of thiourea, a kinetic model was developed using the empirical data from reactor tests. The proposed rate expressions show predictive capabilities allowing the tracking of the reaction progress in terms of their main constituents over a wide range of conditions. Therefore, the findings of this research may contribute to an optimum industrial operation design by avoiding non-productive losses of thiourea. v Preface This thesis is an original, unpublished, intellectual work of the author Mr. Pablo Zuniga under the supervision of Dr. David Dixon. Mr. Pablo Zuniga carried out all the testing and wrote the manuscripts regarding the present study. vi Table of Contents Abstract ....................................................................................................................................................... iii Lay Summary ............................................................................................................................................. iv Preface .......................................................................................................................................................... v Table of Contents ....................................................................................................................................... vi List of Tables ............................................................................................................................................... ix List of Figures .............................................................................................................................................. x List of Symbols ......................................................................................................................................... xvi List of Abbreviations ............................................................................................................................... xvii Acknowledgements ................................................................................................................................. xviii 1 Introduction ......................................................................................................................................... 1 1.1 Background ................................................................................................................................... 1 1.2 Problem Definition ........................................................................................................................ 2 1.3 Objective of the study ................................................................................................................... 2 2 Oxidation and stability of thiourea in acidic water .......................................................................... 3 2.1 Literature review ........................................................................................................................... 3 2.1.1 General aspects of thiourea ....................................................................................................... 3 2.1.2 Determination of thiourea ......................................................................................................... 4 2.1.3 Tautomerism and protonation behavior of thiourea ................................................................. 4 2.1.4 Oxidation and stability of thiourea in acidic water ................................................................... 5 2.2 Experimental ................................................................................................................................. 8 2.2.1 Experimental considerations ..................................................................................................... 8 2.2.2 Materials ................................................................................................................................... 8 2.2.3 Instrumentation ......................................................................................................................... 8 2.2.4 Analytical techniques ............................................................................................................... 9 2.2.5 Oxidation and stability of thiourea and formamidine disulfide tests ........................................ 9 2.2.6 Electrochemical oxidation of thiourea tests .............................................................................. 9 2.3 Results and discussions ............................................................................................................... 10 2.3.1 Thiourea characterization ....................................................................................................... 10 2.3.2 Oxidation and stability of thiourea in acidic water ................................................................. 12 vii 2.3.3 Oxidation and stability of formamidine disulfide in acidic water .......................................... 14 2.3.4 Effect of pH on the oxidation kinetics of formamidine disulfide in acidic water .................. 19 2.3.5 Effect of temperature on the stability of thiourea in acidic water .......................................... 20 2.3.6 Thiourea and formamidine disulfide oxidation mechanisms in acidic water ......................... 21 3 Oxidation and stability of thiourea in acidic ferric sulfate media ................................................ 24 3.1 Literature review ......................................................................................................................... 24 3.1.1 Oxidation of thiourea in the presence of an oxidant ............................................................... 24 3.1.2 Oxidation and stability of thiourea in ferric sulfate media ..................................................... 24 3.2 Experimental ............................................................................................................................... 29 3.2.1 Materials ................................................................................................................................. 29 3.2.2 Instrumentation ....................................................................................................................... 29 3.2.3 Analytical techniques ............................................................................................................. 29 3.2.4 Oxidation and stability of thiourea and formamidine disulfide tests ...................................... 30 3.3 Preliminary results ....................................................................................................................... 30 3.3.1 Thiourea behavior in acidic ferric sulfate media at room temperature ................................... 30 3.3.2 Formamidine disulfide behavior in acidic ferric sulfate media at room temperature ............. 32 3.3.3 Thiourea behavior in acidic ferric sulfate media at different temperatures ............................ 34 3.4 Results and discussion ................................................................................................................. 35 3.4.1 Effect of initial thiourea concentration on its oxidation and stability in acidic ferric sulfate media……. .......................................................................................................................................... 36 3.4.2 Effect of ferric on the oxidation and stability of thiourea in acidic ferric sulfate media ........ 38 3.4.3 Effect of pH on the oxidation and stability of thiourea in acidic ferric sulfate media ........... 39 3.4.4 Effect of temperature on the stability of thiourea in acidic ferric sulfate media .................... 41 3.5 Data analysis and significance of factors .................................................................................... 42 4 Proposed mechanism and kinetic model for the oxidation of thiourea in acidic ferric media ... 50 4.1 Analysis of the stoichiometric coefficients on the oxidation of thiourea in acidic ferric media . 50 4.2 Techniques and mathematical approach used for the interpretation of the data ......................... 58 4.3 Constraints and limitations of the experimental design and analytical methods ........................ 60 4.4 Constraints and limitations of the mathematical approach ......................................................... 60 4.5 Kinetic model of the oxidation of thiourea in the presence of ferric sulfate ............................... 61 4.6 Proposed mechanism and kinetic model validation of FDSH22+ hydrolysis ............................... 69 4.7 Kinetic model of the oxidation of thiourea and hydrolysis of formamidine disulfide in the presence of ferric ions ............................................................................................................................. 76 viii 4.7.1 Temperature dependence of kinetic parameters for the oxidation of thiourea and hydrolysis of FDSH22+ in the presence of ferric ions ................................................................................................ 89 4.7.2 Kinetic model summary .......................................................................................................... 91 5 General conclusions .......................................................................................................................... 95 5.1 Conclusions and overall significance of the research ................................................................. 95 5.2 Recomendations for future work ................................................................................................. 97 References .................................................................................................................................................. 98 Appendix A .............................................................................................................................................. 106 Appendix B ............................................................................................................................................... 108 Appendix C .............................................................................................................................................. 110 Appendix D .............................................................................................................................................. 113 ix List of Tables Table 1. Unit-cell parameters ...................................................................................................................... 10 Table 2. FDSH22+ hydrolysis rate constant at different pH and room temperature, assuming first-order reaction ........................................................................................................................................................ 20 Table 3. Summary of tests conditions and final concentrations (all in mM) for the statistical analysis ..... 43 Table 4. Statistical summary ....................................................................................................................... 44 Table 5. Analysis of variance (Anova table) for significance of the thiourea regression model ................ 44 Table 6. Summary of thiourea regression model outputs ............................................................................ 45 Table 7. Analysis of variance for significance of the FDS regression model ............................................. 45 Table 8. Summary of FDS regression model outputs ................................................................................. 45 Table 9. Analysis of variance for significance of the ferric regression model ............................................ 46 Table 10. Summary of ferric regression model outputs .............................................................................. 46 Table 11. Summary of the ratio values of final concentration per species ................................................. 52 Table 12. m ratio of thiourea and Fe3+ under indicated [Tu]0 concentrations ............................................. 54 Table 13. m average ratio of thiourea and Fe3+ for each effect under study ............................................... 55 Table 14. Effect of initial thiourea concentration on the calculated rate constant, assuming irreversible bimolecular-type second-order reaction ...................................................................................................... 56 Table 15. Power-law relationship of ki values at 20°C ............................................................................... 62 Table 16. Kinetic parameters for the overall rate of reaction ...................................................................... 66 Table 17. FDSH22+ overall hydrolysis rate constant at different pH and room temperature ....................... 73 Table 18. Linear relationship of ki values at 20°C, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+ ................................................................................................................................. 78 Table 19. Apparent activation energies for the chemical oxidation of thiourea and hydrolysis of FDSH22+ in the presence of ferric ions ....................................................................................................................... 90 x List of Figures Figure 1. Chemical structure of thiourea. Sulfur is shown in yellow, carbon in black, nitrogen in blue, and hydrogen in white. ......................................................................................................................................... 3 Figure 2. EMF diagram of thiourea in water (ÓShanmugaprabha et al., 2017. Reproduced with permission from Springer Nature) ................................................................................................................................... 6 Figure 3. Rietveld refinement plot of sample PZ-1a (blue line-observed intensity at each step; red line-calculated pattern; solid grey line below-difference between observed and calculated intensities; vertical bars-positions of all Bragg reflections). Colored lines are individual diffraction patterns of all phases. ... 11 Figure 4. Thiourea species concentrations at 20°C in acidic water, with 2 mM [Tu]0 and initial pH 1.7. . 12 Figure 5. (a) ORP and pH measurements at 20°C in acidic water, with 2 mM [Tu]0 and initial pH 1.7. Plot (b) presents a close-up of the ORP and pH measurements for the first 24 h. ............................................. 13 Figure 6. HPLC measurement of peak-areas of thiourea species at 20°C in acidic water, with 2 mM [Tu]0 and initial pH 1.7. ........................................................................................................................................ 13 Figure 7. Thiourea species concentrations at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. ............................................................................................................................................................... 15 Figure 8. HPLC chromatographs of FDS species at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. ......................................................................................................................................................... 16 Figure 9. HPLC measurements of the peak-areas of thiourea species at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. ..................................................................................................................... 17 Figure 10. ORP and pH measurements at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. ..................................................................................................................................................................... 17 Figure 11. XRD pattern of solid precipitate found as a result of the stepwise addition of FDS in acidic water pH 1.7 (blue line), reference pattern (red line) from ICDD, PDF 00-008-0247 database. ......................... 18 Figure 12. Effect of pH on the hydrolysis of FDS at 20°C in acidic water, with 1 mM [FDSH22+]0 under the indicated pH values. Curves with filled (hollow) symbols represent the thiourea (FDSH22+) concentrations. ..................................................................................................................................................................... 19 Figure 13. Linear relationship of the hydrolysis of FDS over time under indicated initial pH. ................. 20 Figure 14. Effect of temperature on the stability of thiourea in acidic water with 2 mM [Tu]0 and initial pH 1.7. ............................................................................................................................................................... 21 Figure 15. Eh-pH diagram of the Fe-SC(NH2)2-H2O ternary system for different ferric concentration. [Fe3+] (a) 2.8 ´ 10-4 M, (b) 4.6 ´ 10-4 M; [SC(NH2)2] 3.9 ´ 10-2 M; [Fe[SC(NH2)2]3+], (a) 2.3 ´ 10-2 M, (b) 3.9 ´ 10-2 M;[Fe2+], (a) 1.3 ´ 10-1 M, (b) 5.8 ´ 10-2 M; [[SC(NH)(NH2)]2], (a) 4.9 ´ 10-3 M, (b) 8.8 ´ 10-3 (ãTremblay et al., 1996. Reproduced with permission from Elsevier). ..................................................... 25 xi Figure 16. Degree of thiourea decomposition at various Fe2(SO4)3/thiourea molar ratio over time at room temperature and atmospheric pressure (ã Orgül & Atalay, 2002. Reproduced with permission from Elsevier). ..................................................................................................................................................... 27 Figure 17. Degree of ferric consumption at various Fe2(SO4)3/thiourea molar ratio over time at room temperature and atmospheric pressure (ã Orgül & Atalay, 2002. Reproduced with permission from Elsevier). ..................................................................................................................................................... 27 Figure 18. Arrhenius plot for thiourea oxidation by ferric ion (ã Kai et al., 1997. Reproduced with permission from American Chemical Society). .......................................................................................... 28 Figure 19. Thiourea species concentrations at 20°C with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7 ... 31 Figure 20. ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7. ......... 31 Figure 21. Thiourea species concentrations at 20°C with 40 mM Fe3+, 1 mM [FDSH22+]0, and initial pH 1.7. ..................................................................................................................................................................... 33 Figure 22. ORP and pH measurements at 20°C with 40 mM Fe3+, 1 mM [FDSH22+]0, and initial pH 1.7. 33 Figure 23. Effect of temperature on the stability of thiourea with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7. ............................................................................................................................................................... 34 Figure 24. Effect of temperature on the stability of FDSH22+ with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7. ............................................................................................................................................................... 35 Figure 25. Thiourea concentrations at 20°C with 10 mM Fe3+ under indicated [Tu]0 concentrations, and initial pH 1.7. ............................................................................................................................................... 37 Figure 26. FDSH22+ concentrations at 20°C with 10 mM Fe3+ under indicated [Tu]0 concentrations, and initial pH 1.7. ............................................................................................................................................... 37 Figure 27. Thiourea concentrations at 20°C with 2 mM [Tu]0 under indicated [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................................................... 38 Figure 28. FDSH22+ concentrations at 20°C with 2 mM [Tu]0 under indicated [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................................................... 39 Figure 29. Thiourea concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0, under indicated initial pH. .. 40 Figure 30. FDSH22+ concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0, under indicated initial pH. .. 40 Figure 31. Thiourea concentrations with 10 mM Fe3+, 2 mM [Tu]0 under indicated temperatures, and initial pH 1.7. ......................................................................................................................................................... 41 Figure 32. FDSH22+ concentrations with 10 mM Fe3+, 2 mM [Tu]0, under indicated temperatures, and initial pH 1.7. ......................................................................................................................................................... 42 Figure 33. Regression model fitting for the response variables at different [Tu]0 concentrations. ............. 48 Figure 34. Regression model fitting for the response variables at different [Fe3+]0 concentrations. .......... 48 xii Figure 35. Regression model fitting for the response variables at different initial pH. .............................. 49 Figure 36. Regression model fitting for the response variables at different temperatures. ......................... 49 Figure 37. Ratio of final concentrations between the species in solution at 20°C with 10 mM Fe3+ under different [Tu]0 concentrations, and initial pH 1.7. ...................................................................................... 51 Figure 38. Mathematical model fitting for thiourea concentration at 20°C under indicated [Tu]0 concentrations. ............................................................................................................................................. 53 Figure 39. Mathematical model fitting for Fe3+ concentration at 20°C under indicated [Tu]0 concentrations. ..................................................................................................................................................................... 53 Figure 40. m ratio values at 20°C with 10 mM Fe3+ under different [Tu]0 concentrations, and initial pH 1.7. ..................................................................................................................................................................... 54 Figure 41. Test for irreversible bimolecular-type second-order reaction at 20°C with 10 mM Fe3+ under the indicated [Tu]0 concentrations and initial pH 1.7. ....................................................................................... 56 Figure 42. Effect of initial thiourea concentration on the calculated k values assuming irreversible bimolecular-type second-order reaction. ..................................................................................................... 57 Figure 43. Model fitting for thiourea concentrations assuming power-law rate reaction at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7. .................................................................... 58 Figure 44. Power-law relationship of ki values at 20°C with 10 mM Fe3+ under different [Tu]0 concentrations, and initial pH 1.7. ............................................................................................................... 62 Figure 45. Reaction scheme for the oxidation of thiourea in the presence of ferric. .................................. 63 Figure 46. Model fitting for thiourea concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7, based on the rate expression obtained using co-factors. ....................... 66 Figure 47. Model fitting for FDSH22+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7. ................................................................................................................ 67 Figure 48. Model fitting for Fe3+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7, based on the rate expression obtained using co-factors. ....................... 67 Figure 49. Concentration of thiourea species that satisfy sulfur mass balance at 20°C, in acidic water with 1 mM. Hollow symbols in black (red) represent the TuOH/TuO (FDSH+) scenario. ................................ 70 Figure 50. Model fitting for thiourea species at 20°C in acidic water with 1 mM [FDSH22+]0 concentration and initial pH 1.7. ........................................................................................................................................ 72 Figure 51. Linear relationship of the hydrolysis rate of FDSH22+ at different initial pH. ........................... 73 Figure 52. Schematic representation of the hydrolysis of FDSH22+. ........................................................... 74 xiii Figure 53. Model fitting for thiourea species at 20°C, in acidic water, with 1 mM [FDSH22+]0 under indicated initial pH. Filled (hollow) symbols represent thiourea (FDSH22+), solid line (dash line) represent simulated thiourea (FDSH22+) concentrations. ............................................................................................................. 75 Figure 54. Normalized instantaneous rate of thiourea at 20°C with 10 mM Fe3+, under indicated [Tu]0 and initial pH 1.7. (a) Experimental rate values, (b) simulated rate values considering mathematical model presented in section 4.1. .............................................................................................................................. 79 Figure 55. Linear relationship of the initial rate of FDSH22+ formation at different initial conditions. (a) rate of formation with respect to [Tu]0, (b) rate of formation with respect to [Fe3+]0 concentration. ................ 79 Figure 56. ORP measurements and [H+] concentration at 20°C with 10 mM Fe3+, 1 mM [Tu]0, and initial pH 1.7. ......................................................................................................................................................... 82 Figure 57. Model fitting for proton concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations. ............................................................................................................................................. 84 Figure 58. Experimental rate constant values at 20°C with 10 mM Fe3+, 2 mM Tu, and different initial proton concentration. Red line represents the calculated values, the blue star represents the value used for the simulation of the concentration profile. (a) illustrate the rate constant for Tu, (b) presents the rate constant for FDSH22+. .................................................................................................................................. 86 Figure 59. Model fitting for thiourea concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. .................. 87 Figure 60. Model fitting for FDSH22+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. .................. 88 Figure 61. Model fitting for Fe3+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. .................. 88 Figure 62. Arrhenius plot for the chemical oxidation of thiourea and hydrolysis of FDSH22+ in the presence of ferric ions. ............................................................................................................................................... 89 Figure 63. Model fitting for thiourea concentration at indicated temperatures with 10 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. ..................................................................................................................................................................... 90 Figure 64. Model fitting for FDSH22+ concentration at indicated temperatures with 10 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. ..................................................................................................................................................................... 91 Figure 65. Model fitting for thiourea concentration at indicated temperatures with 40 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. ..................................................................................................................................................................... 93 xiv Figure 66. Model fitting for FDSH22+ concentration at indicated temperatures with 40 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. ..................................................................................................................................................................... 93 Figure 67. Model fitting for thiourea species and ferric concentrations at 20°C with 40 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. ...................................................................................................................................................... 94 Figure A - 1. Cyclic voltammograms of thiourea in acidic solutions, pH 1.7, at different scan rates. ..... 106 Figure A - 2. ORP and pH measurements at 20°C, in acidic water with 2 mM [TuO2]0 and initial pH 1.7. ................................................................................................................................................................... 106 Figure A - 3. ORP and pH measurements at 20°C, in acidic water with 2 mM [Cy]0 and initial pH 1.7. 107 Figure A - 4. Effect of temperature on the stability of thiourea in acidic water with 2 mM [Tu]0 and initial pH 1.7. ....................................................................................................................................................... 107 Figure B - 1. ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [Cy]0, and initial pH 1.7 .... 108 Figure B - 2. ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [TuO2]0, and initial pH 1.7. 108 Figure B - 3. ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [Urea]0, and initial pH 1.7. 109 Figure C - 1. Measured ferric concentrations at 20°C with 10 mM Fe3+, under the indicated [Tu]0 concentrations, and initial pH 1.7. ............................................................................................................. 110 Figure C - 2. ORP measurements at 20°C with 10 mM Fe3+, under the indicated [Tu]0 concentrations, and initial pH 1.7. ............................................................................................................................................. 110 Figure C - 3. Measured ferric concentrations at 20°C with 2 mM [Tu]0, under indicated [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................. 111 Figure C - 4. ORP measurements at 20°C with 2 mM [Tu]0, under indicated [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................................................. 111 Figure C - 5. Measured ferric concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0 and under indicated initial pH. ................................................................................................................................................... 112 Figure C - 6. Measured ferric concentrations with 10 mM Fe3+, 2 mM [Tu]0, under indicated temperatures and at initial pH 1.7. .................................................................................................................................. 112 xv Figure D - 1. Ratio of final concentrations at 20°C with 2 mM [Tu]0 under different [Fe3+]0 concentrations, and initial pH 1.7. ...................................................................................................................................... 113 Figure D - 2. Ratio of final concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0, and under different [H+]0 concentrations. ........................................................................................................................................... 113 Figure D - 3. m ratio values at 20°C with 2 mM [Tu]0, under different [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................................................................. 114 Figure D - 4. m ratio values at 20°C with 10 mM Fe3+, 2 mM [Tu]0, and under different [H+]0 concentrations. ................................................................................................................................................................... 114 Figure D - 5. Model fitting for FDSH22+ concentration assuming power-law rate reaction at 20°C under indicated [Tu]0 concentrations. ................................................................................................................. 115 Figure D - 6. Linear relationship of ki values at 20°C with 2 mM [Tu]0, under different [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................. 115 Figure D - 7. Linear relationship of ki values at 20°C with 10 mM Fe3+, under different [H+]0 concentrations, and 2 mM [Tu]0. ........................................................................................................................................ 116 Figure D - 8. Model fitting for thiourea concentration at 20°C, under indicated [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................................................. 116 Figure D - 9. Model fitting for FDSH22+ concentration at 20°C, under indicated [Fe3+]0 concentrations, and initial pH 1.7. ............................................................................................................................................. 117 Figure D - 10. Model fitting for Fe3+ concentration at 20°C, under indicated [Fe3+]0 concentrations and initial pH 1.7 .............................................................................................................................................. 117 Figure D - 11. Model fitting for thiourea concentration at 20°C with 10 mM Fe3+ under indicated initial pH. ................................................................................................................................................................... 118 Figure D - 12. Model fitting for FDSH22+ concentration at 20°C with 10 mM Fe3+ under indicated initial pH. ............................................................................................................................................................. 118 Figure D - 13. Model fitting for Fe3+ concentration at 20°C, under indicated initial pH. ......................... 119 xvi List of Symbols atm Standard atmosphere equal to 101,325 Pa d Particle size (µm) E0 Standard reduction potential E Reduction potential (V) Ea Activation energy (Jmol-1) F Faraday’s constant (96,485 Cmol-1electrons) Fe3+ Ferric ion Fe2+ Ferrous ion ΔG0 Standard Gibbs free energy g Grams h Hour J Joules K Kelvin L Liter M Molarity m Mass mol Mole P80 80% mass passing particle size R Ideal gas constant (8.314 Jmol -1K-1) s Second T Absolute temperature (K) t Time xvii List of Abbreviations EDX Energy-Dispersive X-ray Spectroscopy EW Electrowinning FDS Formamidine disulfide HPLC High-Performance Liquid Chromatography ICP Inductively Coupled Plasma OFAT One Factor at a Time ORP Oxidation Reduction Potential PLS Pregnant Leach Solution PPM Parts Per Million PSD Particle Size Distribution RPM Revolutions per Minute SEM Scanning Electron Microscope SHE Standard Hydrogen Electrode SX Solvent Extraction Tu Thiourea XRD X-ray Diffraction xviii Acknowledgements First and foremost, I would like to express my sincere gratitude to my supervisor Dr. David Dixon for his valuable guidance, trust, and support throughout the study and during the preparation of this manuscript. This work has also benefited from the insightful comments and suggestions made by the members of my committee, Dr. Edouard Asselin and Dr. Wenying Liu. I take this opportunity for conveying thanks for their valuable assistance with this work. I gratefully acknowledge the financial support provided by Jetti Services Canada Inc. and Mitacs, through the Mitacs Accelerate Initiative. Finally, a special thanks to all of those members of the Materials Department with whom I have had the pleasure to work during my journey both as a Master student and working in other related projects. 1 1 Introduction 1.1 Background Over the past years, the mining industry has been facing an imbalance between copper supply and world demand. The lack of new high-grade deposits along with increased delays in production due to higher industry standards and extensive permitting requirements have encouraged the search and development of more efficient alternatives for copper extraction. Chalcopyrite is the most abundant and wide-spread copper-bearing sulfide ore that accounts for 70% of the world known copper reserves (Córdoba et al., 2008). Hydrometallurgical alternatives for the treatment of chalcopyrite, including the sulfate-based processes, have received considerable attention, mainly due to the fact that the leaching chemistry is generally simpler, better understood, and copper recovery from sulfate media is straightforward (Hackl, 1995). A substantial amount of research has been undertaken and a significant amount of alternative leaching agents have been tested to overcome the low dissolution rate of chalcopyrite. However, the key controls of the aqueous oxidation process under both environmental and industrially relevant conditions are poorly understood. According to the literature available, the main reason for the slow and incomplete leaching of chalcopyrite is the formation of secondary reaction products, elemental sulfur (Dutrizac, 1989), ferric hydroxides (Stott et al., 2000) or copper rich polysulfides (Hackl et al., 1995), forming what are termed as passivation layers on chalcopyrite surfaces. Although it is held that the passivation layer is the main hindrance for the chalcopyrite dissolution, there is still a lack of consensus on its exact composition (Hackl et al., 1995). One of the new alternatives for the leaching of chalcopyrite currently under study by the UBC group has shown promising results indicating a positive effect overcoming the main hindrance for the commercial application of chalcopyrite heap leaching, the slow copper dissolution rate (Dixon et al., 2015). This patented technology uses thiourea, hereinafter referred as Tu, an organic reagent, which serves as the catalyst for low-temperature chalcopyrite leaching in acidic media, using ferric ions (Fe3+) as an oxidant. 2 In the copper mining industry, the most important role of the Tu is its ability to act as a copper cathode leveling and brightening agent (Turner & Johnson, 1962). On the other hand, in the gold industry, Tu was found to dissolve gold effectively and could be a potential substitute for cyanide leaching solution. Leaching with Tu has several advantages over the cyanidation process, including leaching rates that are up to 10 times higher. However, large consumptions of Tu make the overall cost of the process very high, which hindered its application in a large-scale (Orgül & Atalay, 2002). Relevant work has been reported by researchers with regards to the interactions of Tu with different ions in solutions and the surface of the minerals, although some ambiguities still remain. 1.2 Problem Definition The lack of consensus with regards to the mechanism and reaction pathway for the oxidation of Tu will become an important problem to be faced during the implementation of the patented technology. A major factor contributing to the problem is the different conditions employed which have rendered to significant discrepancies, variable results, and conclusions between the published studies. This has made direct comparisons somewhat difficult. 1.3 Objective of the study Whilst it is known that Tu will react in the presence of ferric, forming a clear picture of the mechanism for the oxidation of Tu is difficult at the present time. This fundamental study employs a rigorous systematic method to gather empirical information for the determination of key parameters influencing the oxidation and stability of Tu in solution. The chief objective of this thesis is to improve the understanding of the chemical stability and oxidation of Tu in acidic ferric media. To do so, the approach is threefold; first to elucidate the mechanism for the oxidation of Tu in the presence of ferric under acidic conditions; secondly, to validate and weigh the influence of the hydrolysis of FDSH22+ in the oxidation of Tu in acidic ferric media; and lastly, to find a suitable representation of this process that could be incorporated into a kinetic model. Given the multiple tasks at hand, the rationale to support the final findings of this work is constructed from the ground up. Each chapter expands on the previous ones, exploring the implications of the empirical data attained, with the special emphasis on the logical train of thoughts, that instigate further analysis in subsequent sections. 3 2 Oxidation and stability of thiourea in acidic water 2.1 Literature review 2.1.1 General aspects of thiourea Thiourea (Tu), also called thiocarbamide, is a sulfur-organic compound that resembles urea but contains sulfur instead of oxygen, as shown in Figure 1. The chemical formula is CS(NH2)2 while that of urea is CO(NH2)2. Despite being the analog compound to urea, the properties of Tu differ significantly because of the difference in electronegativity between sulfur and oxygen (Alkherraz, Lusta, & Zubi, 2014). Tu has a molecular weight of 76.12 g/mol and a density of 1.44 g/cm3 (Sahu et al., 2011). The synthesis of Tu was first reported by Reynolds in (1869) from the partial isomerization of solid ammonium thiocyanate (ammonium rhodanide; NH4SCN) at 170°C, after which he used this new compound as a source of sulfur in the synthesis of metal sulfides (Reynolds, 1869). Over the years, with the development of better routes for the synthesis, Tu became the preferred sulfur source for the synthesis of metal sulfides by chemical solution deposition (García-Valenzuela, 2017). Nowadays, the method of preparation more commonly used consists of the addition of hydrogen sulfide to cyanamide (Cy). Figure 1. Chemical structure of thiourea. Sulfur is shown in yellow, carbon in black, nitrogen in blue, and hydrogen in white. 4 2.1.2 Determination of thiourea Tu has been widely studied and claimed to be used in many applications in medicine, industry, and analytical chemistry. Therefore, its determination has received considerable attention. Several methods have been reported in the literature such as; titrimetric with iodine (Amin, 1985; Singh & Verma, 1962) N-bromosuccinimide (Thibert & Sarwar, 1969), Raman spectroscopy (Bowley, Crathorne, & Gerrard, 1986), voltammetry (Kirchnerová & Purdy, 2007; Sparatu, Sparatu, & Fujishima, 2005), high-performance liquid chromatography (Dikunets, Elefterov, & Shpigun, 2004; Grigorova & Wright, 1986; Rethmeier et al., 2001), ion-selective electrodes (Calokerinos & Hadjiioannou, 1983), and FTIR (Kargosha et al., 2001; Madhurambal et al., 2011). HPLC has been reported as a highly sensitive, selective, and accurate detection method to quantify the Tu concentration present at different levels (Abbasi et al., 2009), from pharmacokinetic studies (Chen & Uckun, 1999), human biological fluids (Balkhi, Sandouk, & Galliot-Guilley, 2005), and industrial process solutions (Rethmeier et al., 2001). The chromatographic separation of Tu species is performed using a C18-bonded silica column with acetonitrile-water as an eluent. The retention factor on the C18-bonded silica column correlates with the growth of the sorbate hydrophobicity (Dikunets, Elefterov, & Shpigun, 2004). According to Rethmeier et al. (2001), using HPLC for the determination of Tu minimizes the requirement of additional equipment to the lowest level, since sample preparation is not necessary, using a simple C18 phase can provide high sample throughput with minimum costs. Further, the selection of the optimum conditions for spectrophotometric detection is governed by the wavelength at which the absorbance of the studied compounds is maximum. The maximum absorption of the majority of Tu species is in the range of 230-250 nm (Dikunets et al., 2004). 2.1.3 Tautomerism and protonation behavior of thiourea The structure and properties of Tu have been extensively studied both experimentally and theoretically. However, because of the strong coordinative and adsorptive properties of the sulfur atom, Tu was categorized as a catalyst poison for a long time, hindering the use of Tu to its full potential (DuBois, 1989; Kondo & Mitsudo, 2000). 5 Madarász et al. (2016) stated that Tu derivatives represent a privileged class of organocatalyst that often involve hydrogen bond donor functionalities to promote asymmetric transformations. Thus, the catalytic activity of these compounds is generally associated with the ability to form double hydrogen bonds with substrates, which can favorably reorganize and activate the reactive partners. Furthermore, Rostkowska et al. (2003) reported that Tu is one of the simplest molecules that can exhibit a tautomeric thiol-thione equilibrium. Various factors such as pH of the medium and nature of the solvent have the greatest influence on the shift of the tautomeric in either direction, as tautomeric transitions caused prototropic binary equilibrium (Smirnova et al., 2015). The protonation of Tu at the nitrogen atom has been widely discussed in the literature, however, most of the authors (Felder et al., 2008; Sahu et al., 2011; Schiessl et al., 2005) found that the protonation on sulfur is more reliable, which it has been confirmed by NMR studies (Vold & Correa, 1970). 2.1.4 Oxidation and stability of thiourea in acidic water Although many studies have been conducted to establish the factors controlling the behavior and possible interactions of Tu with ions in solution, variable results and conclusions have been published because of the different conditions employed. This has made direct comparisons somewhat difficult. The significant discrepancies in the results reported have rendered a lack of consensus with regards to the mechanism and reaction pathway for the oxidation of Tu. The work of many authors shows that Tu itself is not stable under oxidizing conditions (Calla, Nava‐Alonso, & Fuentes‐Aceituno, 2016; Gupta, 1963; Orgül & Atalay, 2002; Preisler & Berger, 1947; Zhu, 1992). The first products from Tu oxidation depend on the oxidants used and the composition of the solutions. Gupta (1963) found that Tu may be oxidized in successive stages to form a number of products. The first product is formamidine disulfide (FDS), which is formed easily in acidic solution by the action of oxidants, such as hydrogen peroxide or ferric sulfate at room temperature. FDS further oxidizes to produce cyanamide, hydrogen sulfide, and elemental sulfur according to the following reactions (Orgül & Atalay, 2002). NH2(NH)CSSC(NH)NH2 ® NH2CSNH2 + Sulfinic Compounds Eq. 1 Sulfinic Compound ® CNNH2 + S0 Eq. 2 6 Tu, which is the simplest and one of the most reactive sulfur compounds, when oxidized shows a complex nonlinear behavior (Shubba & Puttaswamy, 2009). According to the literature, when being oxidized either through a chemical approach or via an electrochemical method, Tu has exhibited extremely rich dynamical behavior such as variable stoichiometries, oligooscillations (Simoyi, 1986), autocatalysis and autoinhibition in a batch reactor (Xu et al., 2017), mixed-mode oscillations (Chinake & Simoyi, 1994), bistability (Yan-Ru et al., 2008), birhythmicity, quasiperiodicity, and chaos in a continuous-flow stirred tank reactor (CSTR) (Doona, Blittersdorf, & Schneider, 1993), and travelling wave and fingering patterns in a reaction-diffusion medium (Feng et al., 2008). Only a few chemical systems are known to be able to exhibit such rich dynamics. Yet, whether the rich nonlinear dynamics arise from sulfur chemistry or the oxidant remains to be understood (Yan-Ru et al., 2008). Effect of pH on the stability and oxidation of thiourea Shaw and Walker (1956) found that the decomposition of Tu in aqueous media is independent of hydrogen ion concentration over a wide range of pH values (0 to 11). However, in recent years, Schielssl et al. (2005) reported that solutions of Tu are not indefinitely stable and tend to decompose slowly especially at a lower pH or can undergo catalyzed oxidation reactions. They also found that in acidic media, Tu undergoes an acid-catalyzed protonation which was confirmed by NMR data by Vold and Correa (1970). H2S and SCN– are two of the final products of the hydrolysis of Tu. Schielssl and co-workers (2005) also found that the decomposition reactions of Tu derivatives depend on the H+ and on the oxidant concentrations. Further, Tu also can be used to consume protons and make the system display complex pH-oscillations (Yuan et al., 2014). The EMF diagram of the Tu behavior in water reported by Shanmugaprabha et al. (2017) is shown in Figure 2. These authors presented the scheme aiming to illustrate the changes in terms of both proton and electron transfer of Tu in solution. Figure 2. EMF diagram of thiourea in water (ÓShanmugaprabha et al., 2017. Reproduced with permission from Springer Nature) 7 Kozin and Bogdanova (2001) stated that the propensity of Tu to undergo protonation in aqueous solutions can be described as follows: SC(NH2)2 + H+ ® [HSC(NH2)2]+ Eq. 3 According to Golovnev and Zorina (1998) in the presence of chloride the ratio of concentrations of protonated Tu molecules to non-protonated (initial) Tu molecules is described by the equation: 𝑙𝑜𝑔 $[𝐻𝑆𝐶(𝑁𝐻!)!]"[𝑆𝐶(𝑁𝐻!)!] - = 𝑝𝐾# −𝐻# Eq. 4 where H0 is the Hammett acidity function and pK0 is the Tu protonation constant, which was determined to lie between 1.55 and 1.59. The equilibrium constant for Eq. 3 at pH 1 is represented by: 𝐾$% = $ [𝐻𝑆𝐶(𝑁𝐻!)!]"[𝑆𝐶(𝑁𝐻!)!][𝐻"]- = [0.257 𝑡𝑜 0.282] Eq. 5 Consequently, the concentration of the protonated Tu molecules ([HSC(NH2)2]+) is much smaller than the concentration of Tu molecules ([HSC(NH2)2]+ < [SC(NH2)2]) (Kozin & Bogdanova, 2001). Thermal decomposition The decomposition of Tu and Tu-complexes of transition metals have been studied with TGA and DSC analysis at various temperatures (Stradella & Argentero, 1993), TG-FTIR (Madarász & Pokol, 2007) and the products have been analyzed with FT-IR spectroscopy (Wang, Gao, & Wang, 2005). Wang and his co-workers (2013), pointed out that whilst all the known experimental results indicate the formation of NH4SCN, H2S, NH3, CS2, HNCS, and guanidinium thiocyanate, cyanoamine (NH2CN) has not been detected from the decomposition of Tu. In recent years, Wang et al. (2013) reported that Tu starts to isomerize to ammonium thiocyanate (NH4SCN) at temperatures ranging from 140 to 180°C, with an equilibrium ratio of Tu to NH4SCN at 1 : 3. They concluded that the decomposition of Tu comprises two stages: the isomerization of Tu and its subsequent thermal decompositions. Their theoretical calculations showed that the endothermic decomposition of Tu is characterized by the following kinetics (Wang et al., 2013): 𝑑𝛼𝑑𝑡 = 2 × 10&.(( × exp$−86.99 × 10)𝑅𝑇 - (1 − 𝛼)[−𝑙𝑛(1 − 𝛼)]#.* Eq. 6 where a represents the relative weight loss. 8 2.2 Experimental A general description of the experimental considerations, materials, instrumentation, experimental procedures, and characterization methods employed throughout the tests presented in this chapter are outlined in this section. 2.2.1 Experimental considerations Since the main objective of this study was to provide a better understanding of the oxidation of Tu for the atmospheric leaching of chalcopyrite, is important to bear in mind the following experimental considerations: ü The temperature range of the study was from 20°C to 65°C ü The range of Tu concentration varied from 0 to 2 mM ü The initial pH range of the study was from 1.3 to 1.7 in the feed solution ü The stirring speed for the reactor tests was set to 500 rpm 2.2.2 Materials All the chemicals used for the preparation of the solutions were reagent grade: sulfuric acid, H2SO4 (Fisher Scientific, 95-98%); thiourea, CS(NH2)2 (Alfa Aesar, 99%); formamidine disulfide dihydrochloride, C₂H₆N₄S₂(HCl)2 (as FDSH22+2Cl–) (Sigma Aldrich, 97 %); formamidinesulfinic acid, NH2C(=NH)SO2H (Sigma Aldrich, 98%); cyanamide, CH2N2 (Sigma Aldrich, 99%); urea, NH2CONH2 (Sigma Aldrich, 98.5%) and tetrabutylammonium hydrogen sulfate, C16H37NO4S (Tokio Chemical Industry, 98%). 2.2.3 Instrumentation All the tests were conducted in sealed Applikon Dependable Instruments 2-L jacketed glass reactors fitted with a single six-blade Rushton turbine impeller and three baffles made of 316 stainless steel. Redox potential and pH probe were connected to a digital 1030 Bio-Controller and were used to monitor and measure ORP and pH for the duration of the experiments. The data outputs of these probes were recorded in a computer using LabVIEW software. 9 2.2.4 Analytical techniques Samples of 2 mL from the aqueous solutions were taken at regular intervals to assay and quantify catalyst concentration, Tu oxidation products, and various ions using high-performance liquid chromatography (HPLC). The concentration of the Tu species was assayed using a Waters 600 E HPLC, which includes a Waters 717plus autosampler, an automatic eluent degassing device, and a Waters 2487 dual λ absorbance detector. The separation was performed on a Restek C18 column (5 μm, 250 × 4.6 mm i.d.). To achieve better separation the mobile phase was prepared by mixing methanol and 1 mM of tetrabutylammonium hydrogen sulfate (TBA-HS) solution in a volumetric ratio of 5:95. The pH was set to 1.7, and the flow rate was set to 1.2 mL/min. The total injection volume was kept constant at 10 µL, and detection wavelengths of 233 and 214 nm were chosen for the determination of Tu and FDS species, respectively. Standard solutions of Tu and FDS were prepared from reagent grade materials described in section 2.2.2. After separation, Tu and FDS were identified from their retention times, and the calculation of the species concentrations was performed by the integration of their peak areas. 2.2.5 Oxidation and stability of thiourea and formamidine disulfide tests To study the stability and oxidation of Tu and FDS in acidic water, tests were conducted at pH 1.7 using and an initial 2 mM and 1 mM of Tu and FDS, respectively. Samples were taken at regular time intervals to measure the concentration of the Tu and FDS species in solution, and values of pH and ORP were closely monitored throughout the duration of the tests. 2.2.6 Electrochemical oxidation of thiourea tests Additional tests were performed in order to ascertain the presence in solution of Tu oxidation products such as TuO2. The electrochemical measurements were carried out in a 250 mL conventional three-electrode glass cell. A saturated calomel electrode (SCE) and a glassy carbon electron were used as a reference electrode (RE) and counter-electrode (CE), respectively. The working electrode was platinum wire, and its surface was electrochemically cleaned before each test. The electrochemical experiments were performed using a PARSTAT model 2273 potentiostat, at 25°C. The potentials reported are referred to the SCE potential scale (+ 0.24 V vs SHE). Cyclic voltammetry tests were conducted from 0 mV to 1500 mV at various scan rates. The scan rates used were 1, 10, 20, and 50 mV s-1. 10 2.3 Results and discussions In this section, the results are presented quantitatively only in terms of free Tu and FDSH2+. Species from the further oxidation reactions of FDS to yield cyanamide, elemental sulfur and any other intermediate products are not considered in the quantification of the species present in solution. 2.3.1 Thiourea characterization A solid sample of Tu was submitted for solid characterization. The X-ray diffractograms were analyzed using the International Centre for Diffraction Database PDF-4+ and Search-Match software by Bruker. X-ray powder-diffraction data of the samples were refined with Rietveld program Topas 4.2 (Bruker AXS). The Rietveld refinement plot is shown in Figure 3 and Table 1 summarizes the unit-cell parameters obtained from the Rietveld analysis. Table 1. Unit-cell parameters Reference SG a (Å) b (Å) c (Å) V (Å^3) Thiourea 200408 Pnma 7.66 8.59 5.48 361.07 PZ-1a Pnma 7.67 8.56 5.49 361.07 Thiourea 200408: Corresponds to the reference values reported in the International Centre for Diffraction Database PZ-1a: Corresponds to the commercial sample of thiourea provided by Sigma Aldrich Pnma: Orthorhombic primitive space group 11 Figure 3. Rietveld refinement plot of sample PZ-1a (blue line-observed intensity at each step; red line-calculated pattern; solid grey line below-difference between observed and calculated intensities; vertical bars-positions of all Bragg reflections). Colored lines are individual diffraction patterns of all phases. 12 2.3.2 Oxidation and stability of thiourea in acidic water The concentration of Tu species was determined using HPLC measurements. The retention time for Tu was found to be at 3.9 min under the test conditions discussed in this section. The results presented Figure 4 show that Tu remains fairly stable (± 0.03 mM) over time, as would be expected based on the reported literature (Orgül & Atalay, 2002; Shaw & Walker, 1956). An abrupt change in pH presented in Figure 5 was observed once Tu is added to the reactor. Further, Figure 6 illustrates the formation of the protonated forms of FDS. Based on these results, one could argue that in the first 24 h the reaction responsible for the change in ORP and pH, is not the oxidation of Tu but the interactions between Tu species, the protons, and the dissolved oxygen in solution. On the other hand, after the first 24 h, there are not significant oxidation nor reduction reactions occurring hence the value of ORP, pH, and concentration of species remained unchanged. Figure 4. Thiourea species concentrations at 20°C in acidic water, with 2 mM [Tu]0 and initial pH 1.7. 13 Figure 5. (a) ORP and pH measurements at 20°C in acidic water, with 2 mM [Tu]0 and initial pH 1.7. Plot (b) presents a close-up of the ORP and pH measurements for the first 24 h. Figure 6. HPLC measurement of peak-areas of thiourea species at 20°C in acidic water, with 2 mM [Tu]0 and initial pH 1.7. Over the course of the experiment, less than 1.5% of the initial Tu concentration reacted to yield intermediate FDS species. For this reason, it seems valid to consider that in acidic media spontaneous protonation and deprotonation reactions occur in solution, Eq. 7, which are responsible for the changes in pH, shown in Figure 5 (b). 14 The Tu protonation and deprotonation reactions, where the protonation takes place on the sulfur rather than the nitrogen atoms, have been supported by previous studies, where it has been claimed that the proton transfer/nucleophilic attack process occurring on the sulfur head is more reliable (Felder et al., 2008; Schiessl et al., 2005). Eq. 7 Similar results have been reported by Salman et al. (2007) and Yuan et al. (2014), with regards to the influence of pH. These findings referred to as “proton consumption” of Tu, make the system display complex pH-oscillations. Moreover, it can be observed in Figure 5 (b) that after reaching a maximum pH, the reaction presented in Eq. 7 is favored towards the deprotonation of Tu, hence the formation of free Tu. 2.3.3 Oxidation and stability of formamidine disulfide in acidic water The results presented in Figure 7 show that once FDSH22+ is added to the solution, an immediate reaction occurs, dropping the concentration from the initial 1 mM to 0.83 mM. According to the literature, it is held that Tu is one of the products of the FDS hydrolysis (Shaw & Walker, 1956; Sahu et al., 2011). As the hydrolysis reaction proceeds, it is noticed that FDSH22+ reacts to form different species. The chromatograms recorded during the FDS hydrolysis, presented in Figure 8, show that besides the reactant (FDSH22+) detected at a retention time of 2.6 min, and Tu at 3.9 min, other peaks with retention times of 2.9, 3.1, and 4.4 min were also detected. The determination of these “unknown” species was conducted preparing pure solutions of the expected products, based similar results reported in the literature (Gyula & Mihaly, 1985; Hu et al., 2011; Sahu et al., 2011), and the subsequent comparison of their retention times. Later, these species were identified to be Tu dioxide (TuO2) and cyanamide (Cy) for the 3.1- and 4.4-min retention times, respectively. In the case of the 2.9 min retention time, the two possible candidates are TuOX and FDSH+, and for simplification purposes it is assumed to correspond to FDSH+. A detailed discussion with regards to this assumption will be presented in section 4.6. Additionally, it is important to note that due to the complexity of the system, given the low intensities and non-linear relations at low concentrations (<2 mM), the determination of accurate calibration curves for these species, and hence the quantification of the species in terms of concentration was not attempted. However, the results presented in Figure 9 provide the necessary information to assess the behavior of the different species in solution and illustrate the evolution of the oxidation process. 15 Figure 7. Thiourea species concentrations at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. According to the HPLC measurements reported in Figure 9, TuO2 was fairly stable throughout the duration of the tests. This could imply that the oxygen present in solution, whether in the form of dissolved oxygen, water or hydroxide might be involved in the formation of the FDS-oxidation products as suggested by Zhou et al. (2008). Also, further oxidation and hydrolysis reactions of the TuOX species produce another H+ and induce complex pH oscillations. In order to assess the presence of Tu/FDS oxidation products in solution, electrochemical measurements were carried out, Figure A - 1 shows a second peak, that confirms the further oxidation of the preceding Tu/FDS oxidation products which occurs at a higher potential, > 1000 mV (+ 0.24 V vs SHE). Moreover, additional tests were conducted, shown in Figure A - 2 and Figure A - 3, starting with an initial 2 mM TuO2 and 2 mM Cy, respectively, as an attempt to illustrate and establish the dependence of these species on the proton activity. Based on these results, it is assumed that the TuOX is a key intermediate product, which might elucidate the decomposition pathway of Tu-FDS, facilitating the consumption of protons. More experimental proof is required, however, to validate this assumption. The aforementioned results highlight the importance of the protonation-deprotonation process of the main species in solution, FDSH22+. Moreover, the abrupt change of pH and ORP shown in Figure 10 could also suggest a fast reaction between the FDS species. In simple terms, the chemical reactions considering the pathway and the intermediate components can be expressed as follows: FDSH22+ ® FDSH+ ® FDS ® Products Eq. 8 16 Figure 8. HPLC chromatographs of FDS species at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. 214 nm 214 nm 214 nm 214 nm 17 Figure 9. HPLC measurements of the peak-areas of thiourea species at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. Figure 10. ORP and pH measurements at 20°C in acidic water, with 1 mM [FDSH22+]0 and initial pH 1.7. 18 Elemental sulfur has been reported by several authors (Groenewald, 1975; Rabai & Beck, 1985) to be a final product of the FDS oxidation. Under the experimental conditions followed in this study, cloudiness was observed in the aged solution (144 h) of the test with a 1mM initial concentration of FDSH22+. This phenomenon could be caused by the precipitation of a yellowish fine powder which suggests the formation of sulfur. In order to confirm, without ambiguity, the formation of a sulfur precipitate, the initial concentration of FDSH22+ had to be increased. Therefore, an extra test was performed preparing 1 L of the solution, at pH 1.7 with a total of 12 mM of FDSH22+. The approach taken differs from the one described before. After every 1 h interval, an additional 2 mM FDSH22+ was added. Once a total of 12 mM FDSH22+ was reached, the solution was aged for 48 h and filtered to collect the residues for further characterization analysis. Figure 11 shows the XRD pattern of the precipitate formed, which confirms that the main phase found in the residue corresponds to elemental sulfur. Therefore, it is proposed that sulfur is one of the final decomposition products of Tu-FDS in acidic solutions. Figure 11. XRD pattern of solid precipitate found as a result of the stepwise addition of FDS in acidic water pH 1.7 (blue line), reference pattern (red line) from ICDD, PDF 00-008-0247 database. 19 2.3.4 Effect of pH on the oxidation kinetics of formamidine disulfide in acidic water The hydrolysis kinetics of 1 mM FDSH22+, the 2 mM Tu equivalent, was studied at room temperature, in acidic water at different pH values. The results presented in Figure 12 show that the final concentration of Tu increases with the pH, however, the equivalent 2 mM Tu is not attained. Thus, the stability of the protonated forms of FDS was enhanced by the high concentration of protons in solution. These results further support the observation stated in section 2.3.3 regarding the formation of different species, besides Tu, during the hydrolysis of FDS, contrary to the reversibility theory proposed by Li and Miller (2002). Figure 12. Effect of pH on the hydrolysis of FDS at 20°C in acidic water, with 1 mM [FDSH22+]0 under the indicated pH values. Curves with filled (hollow) symbols represent the thiourea (FDSH22+) concentrations. The linear relationship between the initial FDS concentration and instant concentration at specific times for FDSH22+, shown in Figure 13, suggest that the hydrolysis reaction of FDS in acidic water is first-order with respect to 1 mM initial concentration of FDSH22+. The slope values of the linear approximation at different pH are presented in Table 2. Based on these results, it is concluded that the reaction rate increases with the increase of pH, which has already been observed by Rio and co-workers (1996), who found that the increasing of pH yielded an increase on the measured rate constant. 20 Figure 13. Linear relationship of the hydrolysis of FDS over time under indicated initial pH. Table 2. FDSH22+ hydrolysis rate constant at different pH and room temperature, assuming first-order reaction pH Rate constant R2 1.3 9.2E -03 0.98 1.5 1.1E-02 0.99 1.7 1.5E-02 0.99 2.3.5 Effect of temperature on the stability of thiourea in acidic water The effect of temperature on the stability of Tu is shown in Figure 14. As observed the Tu concentration remains fairly stable even after 10 days. There results illustrate that in acidic water, at pH 1.7, increasing the temperature from 25 to 65°C has no apparent effect on the stability of Tu. Moreover, it is important to note that the fluctuations observed on the respective FDSH22+ measured concentrations for these tests, shown in Figure A - 4, can be attributed to analytical error due to the low values detected. 21 Figure 14. Effect of temperature on the stability of thiourea in acidic water with 2 mM [Tu]0 and initial pH 1.7. 2.3.6 Thiourea and formamidine disulfide oxidation mechanisms in acidic water In light of the intrinsic properties of the Tu structure and using experimental data presented in the previous chapters, a mechanism for the oxidation of Tu in acidic water can be proposed. A hypothesis is formulated considering the formation of a tautomeric form of Tu. The chemical structure of Tu presents two donor sites, on the sulfur and nitrogen atoms, and is capable of the formation of N-H and S-H bonding units, which ensures the flexibility of the intermolecular interaction patterns. This unique behavior has been reported by Madarász et al. (2016), Schiessl et al. (2005), and Shanmugaprabha et al. (2017). A three-step mechanism can be proposed, which comprises the formation of the tautomeric form of Tu, followed by the release of a proton from the structure forming a “free radical”. The electron transfer takes place during the deprotonation process and the subsequent combination of the “free radicals” yields to the formation of FDSH22+. The mechanism’s steps are illustrated in Eq. 9, Eq. 10, and Eq. 11. Step 1: Formation of tautomeric form of Tu Eq. 9 22 Step 2: Formation of a free radical during the charge-transfer, redox reaction, and deprotonation process Eq. 10 Step 3: Combination of the free radicals to form formamidine disulfide (dimerization of 2 molecules of Tu) Eq. 11 From the experimental results presented in section 2.3.2, it is believed that the protonation and deprotonation process might play an important role in the charge transfer by facilitating the redox reaction. Based on these findings, an additional two-step of protonation and deprotonation of Tu can be proposed. These steps are illustrated in Eq. 12 and Eq. 13: Step 1: Formation of the protonated form of Tu Eq. 12 Step 2: Deprotonation of the protonated form of Tu Eq. 13 FDS is formed as a product of the dimerization of two Tu radicals. According to the HPLC measurements FDS was not detected during the experiments. The only species present in solution as “FDS species” were FDSH22+ and FDSH+ which may indicate that FDS is a transition species suggesting that FDS itself is not stable under the experimental conditions tested, pH = 1.7 and 25°C. Further, the hydrolysis of FDSH22+ is highly dependent on pH and the protonation process that is taking place in solution, as shown in Eq. 14, Eq. 15, and Eq. 16. 23 Step 1: Combination of the free radicals to form formamidine disulfide (dimerization of 2 molecules of Tu) Eq. 14 Step 2: First protonation of FDS Eq. 15 Step 3: Second protonation of FDS Eq. 16 24 3 Oxidation and stability of thiourea in acidic ferric sulfate media 3.1 Literature review 3.1.1 Oxidation of thiourea in the presence of an oxidant Initial studies of the electrochemical oxidation of Tu revealed that the reaction is quite a complex process, yielding species with oxidation states from -1 to +6 (Gao et al., 2008). Therefore, the kinetic studies of the oxidation of Tu and Tu derivatives have attracted a great deal of attention in the past decades in which various oxidants such as iodate (Rabai & Beck, 1985), bromate (Simoyi, 1986), permanganate (Szebelledy & Madis, 1983), monopersulfate (Fell & Meunier, 2000), chlorite (Alamgir & Epstein, 1985), chlorine dioxide (Rabai, Wang, & Kustin, 1993), ferrate (VI) (Sharma, Luther, & Millero, 2011), and hydroxyl radicals (Wang et al., 1999) have been characterized. These investigations lead to a general conclusion that the oxidation of Tu goes through S-oxygenation to form sulfenyl, then sulfinic and sulfonic acids, and finally sulfate ions (Zhou, Peng, & Tao, 2007). 3.1.2 Oxidation and stability of thiourea in ferric sulfate media Considering that ferric is widely used as the oxidant for the leaching of chalcopyrite, the reaction between Tu and ferric deserves some detailed attention. Having a clear understanding of the reaction between ferric sulfate and Tu will facilitate an accurate estimation of the Tu consumption levels for the leaching process. It should be pointed out that the standard redox potential for FDS/Tu is E0 = 0.42 V (Preisler & Berger, 1947) and the standard redox potential for the ferric (III)/ferrous (II) half-cell is E0 = 0.771 V (Tagirov et al., 2000). Thus, it is clear that ferric may oxidize Tu if it is used as the oxidant for chalcopyrite leaching. Gupta (1963) reported that Tu is easily oxidized by ferric ion in acidic solution producing formamidine disulfide: 2 CS(NH2)2 + 2 Fe3+ ® (CS(NH2)(NH))2 + 2 H+ + 2 Fe2+ Eq. 17 Formamidine disulfide is not stable in acidic solutions and decomposes irreversibly producing elemental sulfur and cyanamide: (CS(NH2)(NH))2 ® CS(NH2)2 + NH2CN + S Eq. 18 The loss of Tu due to the formation of a ferric sulfate complex, described by Eq.19, was first reported by Hiskey (1984), Groenewald (1976), and Pyper & Hendrix (1980): Fe3+ + SO42- + CS(NH2)2 ® (FeSO4(CS(NH2)2)+ Eq. 19 25 More recently, Li & Miller reported the thermodynamic data for the formation of Fe(III)-Tu complexes described as follows: Fe3+ + SO42- + Tu ® (FeSO4(Tu))+ b = 4.26 ´ 106 Eq. 20 Fe3+ + Tu ® Fe(Tu)+ b = 1.58 ´ 102 Eq. 21 Fe3+ + 2 Tu ® Fe(Tu)23+ b = 2.75 ´ 108 Eq. 22 Having a Pourbaix diagram would allow us to identify the predominant species in solution and serve as a guideline in selecting appropriate pH and potential values to optimize the stability of Tu. Unfortunately, there is very limited information available regarding the Fe-SC(NH2)2-H2O system. To the present author’s knowledge, the representation shown in Figure 15, proposed by Tremblay et al. (1996), can only be used as a guide, considering the insufficient information provided to support their assumptions and that the thermodynamic values used to construct the diagram have not been reported elsewhere. Figure 15. Eh-pH diagram of the Fe-SC(NH2)2-H2O ternary system for different ferric concentration. [Fe3+] (a) 2.8 ´ 10-4 M, (b) 4.6 ´ 10-4 M; [SC(NH2)2] 3.9 ´ 10-2 M; [Fe[SC(NH2)2]3+], (a) 2.3 ´ 10-2 M, (b) 3.9 ´ 10-2 M;[Fe2+], (a) 1.3 ´ 10-1 M, (b) 5.8 ´ 10-2 M; [[SC(NH)(NH2)]2], (a) 4.9 ´ 10-3 M, (b) 8.8 ´ 10-3 (ãTremblay et al., 1996. Reproduced with permission from Elsevier). 26 Örgül and Atalay (2002) studied the degree of Tu decomposition and Fe2(SO4)3 consumption after successive reaction between Tu and Fe3+. They found that more than 80% of Tu was consumed or decomposed by the end of 6 h of agitation for the molar ratio of Fe2(SO4)3/Tu:2/1, whilst in the same period of agitation only 40% of Tu decomposition was observed for the 1/2:Fe2(SO4)3/Tu molar ratio, as shown in Figure 16 (Orgül & Atalay, 2002). They also observed that approximately 80% of the initial Fe2(SO4)3 remains in solution, whilst Tu decomposes in the first 15 minutes of agitation regardless of the Fe2(SO4)3/Tu molar relationship, Figure 17. They suggested that the consumption of ferric sulfate is inversely proportional to the concentration of ferric present in solution. Thus, only a certain fraction of ferric sulfate was used for the oxidation of the available Tu. Li and Miller (2006) noted that the critical factor for Tu consumption was leaching potential or ferric sulfate concentration. They also found that to reduce Tu consumption in the gold leaching application, a few precautionary measures can be made, including pre-treatment of the ore and the addition of reducing agents (SO2, Na2SO3 and Na2S2O5) and ferrous salt to adjust the potential during the leaching process. Similarly, Deng et al. (2001) reported that consumption of Tu in the leaching of gold sulfide ore decreased significantly from 12 to 3 kg/tonne and the extraction time was shortened from 6 h to 1 h at pH 2 aided by the addition of 4.5 g/L of sodium sulfite (Na2SO3). In an attempt to minimize the effect of ferric, Kenna (1991) patented a Tu gold extraction method in which di and tri-carboxylic acids, fluorides, fluosilicic acid, fluosilicate salt, and EDTA salts are used to complex the ferric ions to reduce Tu consumption. For the gold leaching application, washing the ore with water and with varying concentrations of sulfuric acid prior to Tu leaching has been found advantageous by several workers (Deng et al., 2001; Lacoste-Bouchet et al., 1998; Kavanagh et al., 1994; Tremblay et al., 1996; Urbano & Lapidus, 2014). The value of this approach varies from ore to ore, however, pre-treatment with acid has been shown not only to remove easily leachable metals but also allow the Tu system to stabilize more quickly and to prevent unnecessary reagent consumption due to the precipitation of base metals (Adams, 2016). 27 Figure 16. Degree of thiourea decomposition at various Fe2(SO4)3/thiourea molar ratio over time at room temperature and atmospheric pressure (ã Orgül & Atalay, 2002. Reproduced with permission from Elsevier). Figure 17. Degree of ferric consumption at various Fe2(SO4)3/thiourea molar ratio over time at room temperature and atmospheric pressure (ã Orgül & Atalay, 2002. Reproduced with permission from Elsevier). 28 Effect of temperature on the stability and oxidation of thiourea An apparent activation energy of 73 kJ/mol was calculated according to the Arrhenius equation to measure the influence of temperature changes on the rate of oxidation of Tu with Fe(III) at initial concentrations of both Fe3+ and Tu of 1 mM, and over temperatures ranging from 279 K to 305 K. The kinetic expression for the reaction between Tu and Fe(III) can be written as follows (Zhu, 1992): 1[𝐹𝑒)"] = 1[𝐹𝑒)"]# + $𝑘+𝐾+ [𝐻]+.*[𝐻]+.* + 𝐾, + 𝑘!𝑃- 𝑡 Eq. 23 where: k1 = 1.2 x 10-4 kmol-1m-3s-1 k2 = 7.7 x 10-4 kmol-1m-3s-1 P: correction coefficient of activity of Fe3+ to account for hydrolysis and polymerization defined as P = K 5-5 + (pH)2.L0.5 K1: equilibrium constant for the formation of the co-ordination compound given by: Fe3+ + Tu ® FeTu3+ In approaching the problem of the high Tu consumption, Kai et al. (1997) determined the oxidation rate of Tu by ferric ions in the absence of ore. They reported that the consumption rate of Tu was first-order dependent on Tu and ferric concentrations. Based on the reaction rate constants at various temperatures, the authors found an apparent activation energy of 79 kJ/mol, Figure 18. These results agree with those observed by Zhu (1992). Figure 18. Arrhenius plot for thiourea oxidation by ferric ion (ã Kai et al., 1997. Reproduced with permission from American Chemical Society). 29 3.2 Experimental Given that the main objective of this study was to provide a better understanding of the oxidation of Tu for the atmospheric leaching of chalcopyrite, is important to bear in mind the following experimental considerations: ü The temperature range of the study was from 20°C to 65°C ü The range of Tu concentration varied from 0 to 6 mM ü The initial pH in the feed solution was from 0.8 to 1.7 ü The stirring speed for the reactor tests was set to 500 rpm 3.2.1 Materials All the chemicals used for the preparation of the solutions were reagent grade: sulfuric acid, H2SO4 (Fisher Scientific, 95-98%); thiourea, CS(NH2)2 (Alfa Aesar, 99%); formamidine disulfide dihydrochloride, C₂H₆N₄S₂(HCl)2 (as FDSH22+2Cl–) (Sigma Aldrich, 97 %); formamidinesulfinic acid, NH2C(=NH)SO2H (Sigma Aldrich, 98%); cyanamide, CH2N2 (Sigma Aldrich, 99%); urea, NH2CONH2 (Sigma Aldrich, 98.5%) and tetrabutylammonium hydrogen sulfate, C16H37NO4S (Tokio Chemical Industry, 98%). 3.2.2 Instrumentation All the tests were conducted in sealed Applikon Dependable Instruments 2-L jacketed glass reactors fitted with a single six-blade Rushton turbine impeller and three baffles made of 316 stainless steel. Redox potential and pH probe were connected to a digital 1030 Bio-Controller and were used to monitor and measure ORP and pH for the duration of the experiments. The data outputs of these probes were recorded in a computer using LabVIEW software. 3.2.3 Analytical techniques Samples of 2 mL from the aqueous solutions were taken at regular intervals to assay and quantify catalyst concentration, Tu oxidation products, and various ions using high-performance liquid chromatography (HPLC). The concentration of Tu species and Fe3+ were assayed using a Waters 600 E HPLC, which includes a Waters 717plus autosampler, an automatic eluent degassing device, and a Waters 2487 dual λ absorbance detector. 30 The separation was performed on a Restek C18 column (5 μm, 250 × 4.6 mm i.d.). To achieve better separation the mobile phase was prepared by mixing methanol and 1 mM of tetrabutylammonium hydrogen sulfate (TBA-HS) solution in a volumetric ratio of 5:95. The pH was set to 1.7, and the flow rate was set to 1.2 mL/min. The total injection volume was kept constant at 10 µL, and detection wavelengths of 233 and 214 nm were chosen for the determination of Tu and FDS species, respectively. Standard solutions of Tu FDS, and Fe3+ were prepared from reagent grade materials described in section 3.2.1 After separation, Tu, FDS, and Fe3+ were identified from their retention times, and the calculation of the species concentrations was performed by the integration of their peak areas. 3.2.4 Oxidation and stability of thiourea and formamidine disulfide tests To study the stability and oxidation of Tu and FDS in acidic ferric sulfate media, tests were conducted at pH 1.7 using an initial 2 mM and 1 mM of Tu and FDS, respectively. Samples were taken at regular time intervals to measure the concentration of the Tu and FDS species in solution, and values of pH and ORP were closely monitored for the duration of the tests. 3.3 Preliminary results 3.3.1 Thiourea behavior in acidic ferric sulfate media at room temperature Figure 19 shows a drastic change in Tu concentration during the first 24 h. It is believed that this drop implies that the redox reaction is taking place rapidly as it can be seen from the change in the ORP measurements, Figure 20. The results presented in Figure 19 indicate that the maximum FDSH22+ concentration is reached at 24 h. Thus, the decrease in the ORP observed in Figure 20 could be attributed to different reactions, besides the redox couple Tu/Fe3+, occurring in parallel/series. Further oxidations of FDS and protonation processes in acidic media, as described in section 2.3.2, are good candidates to explain this behavior. Unfortunately, it was not possible to detect species such as FDSH+ or TuOX due to their low intensity and the background contribution in the presence of ferric 40 mM Fe3+, which results in a broader peak between Tu and FDSH22+. The pH of the solution decreased from 1.7 to 1.45. This drop and posterior fluctuations seem to validate previous assumptions of protonation and deprotonation of FDS species. It is important to note that the Fe3+/Fe2+ couple and FDSH22+/Tu co-exist in the system, and the potential in the solution is a mixed potential of these couples. 31 Figure 19. Thiourea species concentrations at 20°C with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7 Figure 20. ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7. 32 3.3.2 Formamidine disulfide behavior in acidic ferric sulfate media at room temperature In the presence of 40 mM Fe3+, 1 mM FDSH22+ forms Tu rapidly, as shown in Figure 21. Throughout the duration of the test, there is a continuous decline in the concentration of FDSH22+. The maximum Tu concentration is reached at 8 h, 0.32 mM, after which the concentration remains fairly stable. The results shown in Figure 22 indicate that during the first 8 h the ORP is greatly influenced by the reaction, despite the large Fe3+:FDSH22+ molar ratio of 40:1. The pH fluctuations after the first 8 h could be attributed to the deprotonation of FDSH22+ and the formation of TuOX, cyanamide, and urea, as shown in Figure B - 1 to Figure B - 3. Based on previous studies reported by Sahu et al. (2011) these products are concomitant to hydrolysis reactions. The behavior observed in the FDSH22+ concentration profile after the first 8 h, Figure 21, may indicate the presence of intermediate species involved in the transition from FDSH22+ to Tu. One could argue that these intermediate species influence the “reversibility” of FDS to Tu. All the information presented thus far suggests that FDSH22+/Tu in ferric media might not be a direct step, but the nature of this transition is still unknown. The presence of ferric ions can increase the hydrolysis rate of FDSH22+ and consequently the stability of the forming species might differ from what was observed in the acidic media. A more detailed study must be considered in order to shed some light on the behavior of Tu in ferric sulfate media. 33 Figure 21. Thiourea species concentrations at 20°C with 40 mM Fe3+, 1 mM [FDSH22+]0, and initial pH 1.7. Figure 22. ORP and pH measurements at 20°C with 40 mM Fe3+, 1 mM [FDSH22+]0, and initial pH 1.7. 34 3.3.3 Thiourea behavior in acidic ferric sulfate media at different temperatures Figure 23 shows that ferric is an effective oxidant over the entire range of temperature under study. After 48 h the average Tu consumption is over 75% for temperatures above 35°C. It is noted that the reaction rate is greatly influenced by temperature, decreasing the time to reach the inflection point faster. After the inflection point, the Tu concentration profile reaches a steady state, dCTu/dt » 0. During the initial hours the formation of FDSH22+, shown in Figure 24, is somewhat proportional to the Tu consumption. Once FDSH22+ reaches the maximum concentration, the system starts to behave in a chaotic manner. It is noteworthy to mention that the formation of precipitates was noticed throughout the duration of the experiment. The aforementioned maximum concentration of FDSH22+ could be related to a supersaturation point where the precipitates start to form. The main culprit is sulfur, which was proven to be one of the final products of the hydrolysis of FDSH22+ in acidic media. Additionally, it should be noted that given the molar ratio of Fe3+/Tu = 40/2 used in the experiments, the effect of temperature on the ferric solution may play a major role, since the hydrolysis of ferric in solution is highly influenced by the increase of temperature, generating an array of changes in proton concentration and the potential (Yue et al., 2014) that could eventually overshadow the influence of temperature on the behavior of Tu. Figure 23. Effect of temperature on the stability of thiourea with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7. 35 Figure 24. Effect of temperature on the stability of FDSH22+ with 40 mM Fe3+, 2 mM [Tu]0, and initial pH 1.7. 3.4 Results and discussion This chapter intends to provide a better understanding of the Tu-Fe3+ system aiming to elucidate the chemical reaction pathway of Tu-species in ferric media. To ensure appropriate interpretation of the data, the ferric concentration was decreased to a maximum of 10 mM. It was observed that at 20 mM or higher Fe3+ concentrations, the background and peak contribution of these species on the HPLC measurements are not linear. Therefore, by lowering the ferric concentration any under- or overestimation of the organic species in solution could be minimized and the ferric profile could be monitored while the reaction proceeds. Further, based the results presented in section 3.3, the behavior of Tu oxidation and the ultimate concentration in solution is determined by the reactions occurring during the first 24 h. Thus, focusing on those interactions might provide a good insight in terms of the reaction pathway, and possible factors controlling the chemical oxidation processes in the system. 36 3.4.1 Effect of initial thiourea concentration on its oxidation and stability in acidic ferric sulfate media Figure 25 shows that by decreasing the initial ferric concentration to 10 mM Fe3+ it is possible to obtain smother Tu profiles compared with the preliminary experiments conducted using 40 mM Fe3+. In terms of Tu consumption, it was found that the lowest consumption was at 6 mM Tu, 51%, and the highest consumption, 66 %, at 1 mM. These results can be explained by the molar ratios Fe3+/Tu of each test and the amount of oxidant available in solution. Conversely to what we observed in terms of Tu concentration, the ferric profiles illustrated in Appendix C, Figure C - 1 show that as one increases the initial Tu concentration, the final concentration of Fe3+ decreases. Moreover, the results presented in Figure C - 2 suggest the ORP of the solutions strongly depends on the initial Tu concentration added to the system. The interpretation of these results from an industrial standpoint, where the goal is to maintain a set concentration in solution, should note that whilst 6 mM shows a slight decrease in the consumption compared to 1 mM, the reagent consumption needs to be considered in order to optimize the process in terms of both the chemical performance and economic attractiveness. Over the first 2 h a correlation can be observed between the average oxidation rate and the increase of initial Tu concentration being -0.03, -0.06, -0.14, -0.44 for 1, 2, 4, and 6 mM, respectively. However, Figure 25 shows that at higher Tu concentrations, 4 and 6 mM, the inflection point is shifted to the right, the curve plateaued after 96 h compared 48 h for 6 and 1 mM, respectively. As expected, the formation of FDSH22+ increases with the initial Tu concentration illustrated in Figure 26. After reaching a maximum, 0.3, 0.6, 1.1, 1.6 mM for 1, 2, 4, and 6 mM Tu, respectively the concentration of FDSH22+ decreases. After 48 h the average dCTu/dt » -0.001, for the test at 1 and 2 mM whilst at 4 and 6 mM the average dCTu/dt is -0.005 and -0.007, respectively. 37 Figure 25. Thiourea concentrations at 20°C with 10 mM Fe3+ under indicated [Tu]0 concentrations, and initial pH 1.7. Figure 26. FDSH22+ concentrations at 20°C with 10 mM Fe3+ under indicated [Tu]0 concentrations, and initial pH 1.7. 38 3.4.2 Effect of ferric on the oxidation and stability of thiourea in acidic ferric sulfate media Figure 27 shows that the oxidation of Tu increases with the initial ferric concentration. The change in Fe3+ concentration from 2.5 to 10 mM increases by 25% the amount of Tu being oxidized. At a concentration higher than 7.5 mM Fe3+ the response, in terms of Tu oxidation, is not proportional to the change in ferric. All the information presented thus far suggests that the oxidation of Tu is not strictly dependent on the concentration of ferric in the entire range of this study. Figure 27. Thiourea concentrations at 20°C with 2 mM [Tu]0 under indicated [Fe3+]0 concentrations, and initial pH 1.7. A higher FDSH22+ concentration was expected at 10 mM Fe3+. The results presented in Figure 28 show the same pattern described in previous sections, where after reaching a maximum after 48 h the FDSH22+ concentration starts to decrease. 39 Figure 28. FDSH22+ concentrations at 20°C with 2 mM [Tu]0 under indicated [Fe3+]0 concentrations, and initial pH 1.7. 3.4.3 Effect of pH on the oxidation and stability of thiourea in acidic ferric sulfate media Based on the Tu concentration profiles presented in Figure 29 it appears that by having a lower pH in solution, 1.3 and 0.8, the inflection point is shifted to the right causing a continuous decrease in the Tu concentration as opposed as what is observed in the test with pH 1.7 and 1.5. During the first 2 h of the experiment the reaction rates are dCTu/dt = -0.09, -0.10, -0.09, -0.06 for pH 0.8, 1.3, 1.5 and 1.7, respectively. After 8 h the curves start to separate from each other. After 72 h the curves have plateaued for the test at pH 1.5 and 1.7. There is a proportional relationship between the proton concentration and the stability of FDSH22+. From the FDSH22+ profile, Figure 30, it appears that at lower pH the inflection point, where the concentration reaches its maximum, is shifted to the right. Hence it is possible to achieve higher FDSH22+ concentrations, 35% over the baseline conditions. The presence of intermediate FDS species such as FDSH+ could also be a suitable explanation for this phenomenon. Thus, one could argue that at lower pH the reaction is being pushed towards the formation of FDSH22+. 40 Figure 29. Thiourea concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0, under indicated initial pH. Figure 30. FDSH22+ concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0, under indicated initial pH. 41 3.4.4 Effect of temperature on the stability of thiourea in acidic ferric sulfate media An increase in temperature enhances the oxidation rate of Tu as observed in Figure 31. Raising the temperature above 50°C resulted in a loss of Tu of 98% compared to the 59% under baseline conditions, 20°C. Over the first 2 h the reaction rates dCTu/dt are: -0.06, -0.2, -0.26, and -0.37 for 20°C, 35°C, 50°C, and 65°C, respectively. Moreover, the results presented in Figure 32 show that the highest concentration of FDSH22+, 0.6 mM, was obtained after 48 h at 20°C, whilst at 35°C the concentration was 0.2 mM, and almost nil for higher temperatures. Among all the variables comprised in this study, temperature presents the strongest effect on the oxidation of Tu. This considerable temperature dependence agrees with previous studies conducted under similar conditions by Zhu (1992). The assessment of the effect of temperature and the rest of the variables in the study will be referred to and analyzed in greater depth in the following sections. Figure 31. Thiourea concentrations with 10 mM Fe3+, 2 mM [Tu]0 under indicated temperatures, and initial pH 1.7. 42 Figure 32. FDSH22+ concentrations with 10 mM Fe3+, 2 mM [Tu]0, under indicated temperatures, and initial pH 1.7. 3.5 Data analysis and significance of factors The results outlined in this section aim to provide information on the oxidation kinetics of Tu in ferric media. By using an experimental design approach reliable information is obtained, in terms of the significance of each variable included in this study. The regression results presented in this chapter are not designed to model nor predict the oxidation of Tu in ferric media. Instead, they will be used as a starting point to find a more suitable explanation regarding the interaction of species in solution and the various reaction pathways. The “One Factor At a Time” experimental design (OFAT) was used to investigate the significance of the effects of different parameters and to determine the fluctuation of the output response, the final concentration of species. The experimental domain was established based on the results obtained for the preliminary tests, section 3.3. Table 3 shows the experimental conditions and final concentration results used for the statistical analysis. 43 Table 3. Summary of tests conditions and final concentrations (all in mM) for the statistical analysis Experiments Initial conditions Final concentrations # [Fe3+]0 [Tu]0 [H+]0 Temp. oC [Tu]F [FDSH22+]F [Fe3+]F 1 2.5 2.0 0.18 20 1.33 0.28 1.17 2 5.0 2.0 0.18 20 1.14 0.34 2.74 3 7.5 2.0 0.18 20 0.95 0.40 4.94 4b 10.0 2.0 0.18 20 0.82 0.43 7.61 5 10.0 1.0 0.18 20 0.31 0.17 8.73 6b 10.0 2.0 0.18 20 0.82 0.43 7.61 7 10.0 4.0 0.18 20 1.82 0.53 4.17 8 10.0 6.0 0.18 20 3.31 0.72 2.72 9 10.0 2.0 0.45 20 0.46 0.88 6.43 10 10.0 2.0 0.27 20 0.62 0.62 7.25 11 10.0 2.0 0.22 20 0.74 0.53 7.72 12b 10.0 2.0 0.18 20 0.90 0.43 7.61 13b 10.0 2.0 0.18 20 0.82 0.43 7.61 14 10.0 2.0 0.18 35 0.53 0.13 6.12 15 10.0 2.0 0.18 50 0.08 0.04 6.20 16 10.0 2.0 0.18 65 0.04 0.04 6.46 b: baseline conditions for OFAT 44 To determine the significance of factors, the F-test method at 95% confidence level has been applied. The output of the regression model for each species, the standard error, and R2 are presented in Table 4. These results show that the standard error for Fe3+F was found to be 54%. Thus, one could argue that the factor responsible for this abrupt increase, compared to TuF and FDSH22+F being 10% and 11% respectively, could be the change in the proton concentration. Conversely, to what was observed for the standard error, the calculated R2 and adjusted R2 values were 96% and 94%, respectively. Table 4. Statistical summary Regression statistics TuF FDSH22+F Fe3+F Multiple R 0.99 0.95 0.98 R square 0.99 0.90 0.96 Adjusted R square 0.98 0.86 0.94 Standard error 0.11 0.1 0.54 Observations 13 13 13 Further, the analysis of variance and the summary of the regression model outputs for each species (TuF, FDSH22+F, and Fe3+F) are presented from Table 5 to Table 10. Using the results generated from the statistical analysis it is possible to determine the coefficients for each variable to assess its respective correlation with the final outputs (concentrations). Table 5. Analysis of variance (Anova table) for significance of the thiourea regression model TuF df SS MS F Significance F Regression 4 8.99 2.25 183.20 6.74E-08 Residual 8 0.09 0.01 Total 12 9.08 45 Table 6. Summary of thiourea regression model outputs Coefficients Standard error t-Stat P-value Lower 95% Upper 95% Lower 95% Upper 95% Intercept 0.71 0.14 5.19 8.28E-04 0.40 1.03 0.40 1.03 [Fe3+]0 -0.07 0.01 -4.97 1.10E-03 -0.11 -0.04 -0.11 -0.04 [Tu]0 0.60 0.03 22.48 1.63E-08 0.54 0.67 0.54 0.67 [H+]0 -2.45 0.89 -2.74 0.03 -4.51 -0.39 -4.51 -0.39 Temp. oC -0.02 0.00 -7.59 6.36E-05 -0.02 -0.01 -0.02 -0.01 Table 7. Analysis of variance for significance of the FDS regression model FDSH22F+ df SS MS F Significance F Regression 4 0.70 0.18 19.03 3.78E-04 Residual 8 0.07 0.01 Total 12 0.77 Table 8. Summary of FDS regression model outputs Coefficients Standard error t-Stat P-value Lower 95% Upper 95% Lower 95% Upper 95% Intercept 0.17 0.14 1.21 0.26 -0.15 0.50 -0.15 0.50 [Fe3+]0 0.03 0.01 2.31 0.05 0.00 0.06 0.00 0.06 [Tu]0 0.09 0.02 3.99 3.98E-03 0.04 0.15 0.04 0.15 [H+]0 0.47 0.40 1.19 0.27 -0.44 1.39 -0.44 1.39 Temp. oC -0.01 0.00 -5.87 3.76E-04 -0.02 -0.01 -0.02 -0.01 46 Table 9. Analysis of variance for significance of the ferric regression model Fe3+F df SS MS F Significance F Regression 4 59.34 14.83 51.05 9.80E-06 Residual 8 2.32 0.29 Total 12 61.66 Table 10. Summary of ferric regression model outputs Coefficients Standard error t-Stat P-value Lower 95% Upper 95% Lower 95% Upper 95% Intercept 1.80 0.65 2.77 0.02 0.30 3.30 0.30 3.30 [Fe3+]0 0.82 0.07 12.19 1.90E-06 0.67 0.98 0.67 0.98 [Tu]0 -1.23 0.13 -9.66 1.10E-05 -1.53 -0.94 -1.53 -0.94 [H+]0 0.07 0.01 4.66 1.62E-03 0.04 0.10 0.04 0.10 Temp. oC -0.02 0.01 -1.42 0.19 -0.05 0.01 -0.05 0.01 The mathematical expression based on the regression analysis for Tu, Eq. 24, shows the coefficients for each one of the variables in this study. Albeit, the highest standard error of the regression, 0.89, corresponds to the proton concentration, the P-value is 0.03, Table 6, which indicates that the variable is statistically significant. [𝑇𝑢]! = −0.07[𝐹𝑒"#]$ + 0.6[𝑇𝑢]$ − 2.45[𝐻#]$ − 0.02[𝑇𝑒𝑚𝑝. ] + 0.71 Eq. 24 Similarly, the equation for the final FDS concentration based on the regression analysis can be expressed as: [𝐹𝐷𝑆𝐻%%#]! = 0.03[𝐹𝑒"#]$ + 0.09[𝑇𝑢]$ + 0.47[𝐻#]$ − 0.01[𝑇𝑒𝑚𝑝. ] + 0.17 Eq. 25 47 As observed in the Tu analysis, the highest standard error of the regression, 0.40, corresponds to the proton concentration. Although given the P-value is 0.27 >> 0.05 it is suggested that the changes in the proton concentration are not associated with the changes in the final concentration of FDS. Lastly, the equation to predict the final ferric concentration is given by: [𝐹𝑒"#]! = 0.82[𝐹𝑒"#]$ − 1.23[𝑇𝑢]$ + 0.07[𝐻#]$ − 0.02[𝑇𝑒𝑚𝑝. ] + 1.80 Eq. 26 Following the same analysis described before, Tu presents the highest standard error but since its respective P-value is 1.10E-05 << 0.05, Table 10, it can be concluded that the variable has an effect on the final response. As shown on curves in Figure 33 to Figure 36, depending on the output being analyzed, the resulting model from the regression analysis fails to yield a perfect fit. Further, from Figure 35 and Figure 36 it may be concluded that the regression model (represented by the hollow symbols) deviates from the experimental data, most markedly in the presence of various pH and increasing temperature. The failure of the model to perform accurate predictions of the data could be explained by the non-linear behavior of ferric at higher temperatures, perhaps because the hydrolysis of ferric is increased by increasing the temperature. Thus, it can be concluded that misfit of the model at the highest proton concentration supports the assumption that the chemical pathway of Tu to FDSH22+ cannot be solely described by the oxidation of Tu in the presence of ferric. Rather, in this highly complex system the reactions occurring in both series and parallel play a key role in the formation of intermediate species, which influences the final concentrations. 48 Figure 33. Regression model fitting for the response variables at different [Tu]0 concentrations. Figure 34. Regression model fitting for the response variables at different [Fe3+]0 concentrations. 49 Figure 35. Regression model fitting for the response variables at different initial pH. Figure 36. Regression model fitting for the response variables at different temperatures. 50 4 Proposed mechanism and kinetic model for the oxidation of thiourea in acidic ferric media Tu is not stable in the presence of ferric under acidic conditions. This point is well made in this current work and is substantiated from the literature available, as it has already been noted in previous chapters. Whilst it is known that Tu will react in the presence of ferric, forming a clear picture of the mechanism for the oxidation of Tu is difficult at the present time. The explicit purpose of this chapter is threefold; first to elucidate the mechanism for the oxidation of Tu in the presence of ferric under acidic conditions; secondly, to validate and weigh the influence of the hydrolysis of FDSH22+ in the oxidation of Tu in acidic ferric media; and lastly, to find a suitable representation of this process that could be incorporated into a kinetic model. Undoubtedly, this will give rise to a more thorough understanding of the behavior of Tu and the role of different variables in its oxidation. Additionally, one of the questions set out to be answered in this chapter is whether the measurement of concentrations obtained as a function of time, over a finite window (0, 144 h), provides sufficient information to determine the reaction rates of the Tu-Fe3+ system. 4.1 Analysis of the stoichiometric coefficients on the oxidation of thiourea in acidic ferric media This section explores the non-linear behavior of the system, discussed in Chapter 3, based on a macroscopic observation standpoint. The objective is to find a correlation between the components of the reactions, in an attempt to propose a general rate equation and stoichiometric coefficients that will enable the incorporation of the oxidation process in the development of a kinetic model, using standardized methods such as the integral method and/or power-law rate approach for an nth-order reaction. An arbitrary chemical reaction illustrated by Eq. 27 is considered: a A + b B ® c C + d D + … + n N Eq. 27 where the capital letters from A to C correspond to the concentrations of Tu, ferric ions, and FDSH22+, respectively. The non-capital letters, a to c correspond to the stoichiometric coefficients for each compound and the terms D to N represent the products that were not measured nor quantified during the tests. Considering the regression model, presented in section 3.5, yields to satisfactorily predict the final concentration of species and aiming to facilitate the determination of the stoichiometric coefficients, the final concentration used in this analysis were obtained from the regression analysis. 51 The working hypothesis articulates that if there is a correlation between the quotient of the final concentrations of the species in solution, the value of said quotient should remain fairly stable, regardless the change of the initial conditions of the system. Figure 37 shows the ratio of final concentration between the species in solution for the experiments where the initial Tu concentration was varied. A linear behavior with respect to the initial Tu concentration was found in both cases. The ratio between [Tu]F and [FDSH22+]F is greatly influenced by changing the initial Tu concentration, having a 2.36x factor, in comparison with the slope of [Tu]F/[Fe3+]F. Figure 37. Ratio of final concentrations between the species in solution at 20°C with 10 mM Fe3+ under different [Tu]0 concentrations, and initial pH 1.7. The same linear behavior was found when the initial concentration of ferric and protons were varied, Figure D - 1 and Figure D - 2. Table 11 summarizes the slope values for the ratios of final concentrations. The change in the sign of the slope further demonstrates the complexity of the system and highlights the influence the initial conditions exert on the behavior of the species in solution. Based on the results discussed thus far, the working hypothesis is proven to be unfounded. Hence, is not possible to describe the system in a stoichiometric fashion which is in agreement with the results reported by Simoyi (1986) regarding the variable stoichiometries observed for Tu oxidation reactions. 52 Table 11. Summary of the ratio values of final concentration per species Effect studied [Tu]F/[FDSH22+]F [Tu]F/[Fe3+]F Slope R2 Slope R2 [Tu]0 0.64 0.96 0.27 0.90 [Fe3+]0 -0.44 0.97 -0.15 0.78 pH0 -6.12 0.99 -0.34 1.00 Further, a second attempt is taken using a simplistic mathematical approach that will help elucidate the behavior of the Tu- Fe3+ species, as a function of the reaction time. The natural logarithm function is found to provide the best fit for the empirical data. Given the logarithm function is not defined for zero and that the independent term converges to the initial concentration values, the expression has been altered as a function of the initial concentrations for the stoichiometric analysis. The modified expressions can be defined as follows: [𝑇𝑢] = −𝑚/0 ln(𝑡) + [𝑇𝑢]# Eq. 28 [𝐹𝑒)"] = −𝑚1$!" ln(𝑡) + [𝐹𝑒)"]# Eq. 29 Figure 38 and Figure 39 illustrate the fitting comparison between the predicted data points using Eq. 28 and Eq. 29 and the corresponding experimental data. Moreover, defining the ratio of consumption between Tu and ferric concentration could facilitate the tracking of the reactants as the reaction proceeds. Thus, if we consider the quotient of the concentration change of Tu with respect to Fe3+ at a specific time, (ti), the resulting expression is just a function of the m values as described by Eq. 41: [𝑇𝑢]# − [𝑇𝑢]2#[𝐹𝑒)"]# − [𝐹𝑒)"]2# = 𝑚/0ln (𝑡3)𝑚1$!"ln (𝑡3) = 𝑚/0𝑚1$!" Eq. 30 53 Figure 38. Mathematical model fitting for thiourea concentration at 20°C under indicated [Tu]0 concentrations. Figure 39. Mathematical model fitting for Fe3+ concentration at 20°C under indicated [Tu]0 concentrations. 54 As expected, the change of initial Tu concentration exerts great influence in the change of the m values, Figure 40. It should be noted that the calculated m values also show a linear relationship in the case of changing initial ferric and proton concentration, Figure D - 3 and Figure D - 4. Figure 40. m ratio values at 20°C with 10 mM Fe3+ under different [Tu]0 concentrations, and initial pH 1.7. Table 12 summarized the m ratios calculated using Eq. 41. One could argue that, from an overall standpoint, the reactants are being consumed in an average ratio of 0.48 when the initial Tu concentration is varied. Similarly, the changing initial ferric concentration renders an m ratio of 0.49. However, the values in Table 13 show that these ratios drastically change for the tests with different initial pH. Table 12. m ratio of thiourea and Fe3+ under indicated [Tu]0 concentrations [Tu]0 m Tu/m Fe3+ 1.0 0.49 2.0 0.51 4.0 0.43 6.0 0.47 55 Table 13. m average ratio of thiourea and Fe3+ for each effect under study Effect studied m Tu/m Fe3+ [Tu]0 0.48 [Fe3+]0 0.49 pH0 0.19 Assuming the chemical oxidation of Tu in the presence of ferric is the only reaction taking place in the system, the value of the ratios, regardless of the change in the initial conditions, should be 1. Moreover, the difficulty defining a unique m value, that could represent the entire dataset, further supports the working hypothesis that the system cannot be described as one general stoichiometric chemical reaction. This point can be further illustrated with a preliminary kinetic study following both the integral method and a power-law rate approach, where the rate of the overall reaction is just a function of the reactants. In the case of the integral method an irreversible bimolecular-type second-order reaction is considered, where: Tu + Fe3+ ® Products Eq. 31 with corresponding rate equation 𝑟 = 𝑘𝐶/0𝐶1$!" Eq. 32 𝑟 = −𝑑𝐶/0𝑑𝑡 = −𝑑𝐶1$!"𝑑𝑡 Eq. 33 After the integration and rearrangement of the ordinary equation, the final expression can be written as: 𝑙𝑛 $[𝑇𝑢][𝐹𝑒)"]#[𝑇𝑢]#[𝐹𝑒)"]- = ([𝐹𝑒)"]# − [𝑇𝑢]#)𝑘𝑡 Eq. 34 If the data yields a straight line, it is assumed that the system is well represented by the rate equation and the rate constant can be estimated from the slope values. The effect of initial Tu concentration is shown in Figure 41, where the initial concentration of Fe3+ was always higher than the Tu concentration. Therefore, any change in the sign of the slope is attributed to the rate constant in the final expression. The goodness of the fit is determined by the coefficient of determination, R2, Table 14. 56 An interesting feature of these results is the change in the slope sign as the initial concentration of Tu decreases resulting in a negative value for the test with 1 mM and 2 mM of Tu. Since the value of the slope is given by Eq. 35, and 0 < [Fe3+]0 > [Tu]0, the change in the sign of the slope indicates that the behavior of the system is influenced by the change in the initial conditions. Further, the observed k values, Figure 42, indicate that at specific conditions the rate expressions attribute a higher weight to the initial conditions, [Tu]0 and [Fe3+]0 concentrations. ln $[𝑇𝑢][𝐹𝑒)"]#[𝑇𝑢]#[𝐹𝑒)"]- = ([𝐹𝑒)"]# − [𝑇𝑢]#)𝑘𝑡 Eq. 35 Figure 41. Test for irreversible bimolecular-type second-order reaction at 20°C with 10 mM Fe3+ under the indicated [Tu]0 concentrations and initial pH 1.7. Table 14. Effect of initial thiourea concentration on the calculated rate constant, assuming irreversible bimolecular-type second-order reaction [Tu]0 1 mM 2 mM 4 mM 6 mM Slope -6.62E-03 -4.64E-03 2.96E-04 4.26E-03 R2 0.92 0.88 0.88 0.94 k -7.36E-04 -5.80E-04 4.93E-05 1.06E-03 57 Figure 42. Effect of initial thiourea concentration on the calculated k values assuming irreversible bimolecular-type second-order reaction. Lastly, in the case of the power-law rate, the overall reaction is considered to be the as follows: 2 Tu + 2 Fe3+ ® FDSH22+ + 2 Fe2+ Eq. 36 𝑟 = −12𝑑𝐶/0𝑑𝑡 = −12𝑑𝐶1$!"𝑑𝑡 = 𝑘[𝑇𝑢]4[𝐹𝑒)"]5 Eq. 37 where a, b are fitting parameters. The kinetic parameter found after minimization of error between the model and experimental values are: k0 = 1.08E-03, the order of reaction with respect to Tu is a = 0.90 and with respect to ferric concentration is b = 1.46. The concentration profiles for both empirical and the predicted values are shown in Figure 43. As it can be observed, using a unique k value leads to an overestimation of Tu consumption over time. Similar results were found with respect to the formation of FDSH22+ as illustrated by the comparison between the empirical and predicted data in Figure D - 5. Based on the findings presented above, a more comprehensive analysis to represent the system is deemed necessary. Both stoichiometric and preliminary kinetic studies suggest that the chemical reactions are being catalyzed at different rates depending on the initial conditions. Which leads to the inconsistencies of the observed k and m values, misfit of the model, and the inexplicable changes of the final concentration ratio found in mathematical fitting approach. 58 Figure 43. Model fitting for thiourea concentrations assuming power-law rate reaction at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7. 4.2 Techniques and mathematical approach used for the interpretation of the data Considering the experimental evidence presented in Chapter 2, Chapter 3, and the discussion in section 4.1, it seems appropriate to describe the system from a microscopic standpoint. This would allow the assessment of the molecular interactions between the species in solution and the study of different hydrolysis pathways considering the formation of intermediate species such as FDSH+/FDS and TuO/TuOH, stated in section 2.3.3, as the possible hydrolysis products of FDSH22+. Therefore, this work is limited to study unimolecular and binary reactions of the following type: a A + b B ® c C + d D Eq. 38 and the specific reaction rates associated with each reaction, where it is assumed that the dynamics of the concentration profiles obey the law of mass action and their concentrations satisfy the following: 𝑟3 = −1𝑎 𝑑𝐶6𝑑𝑡 = −1𝑏 𝑑𝐶7𝑑𝑡 = 1𝑐 𝑑𝐶8𝑑𝑡 = 1𝑑 𝑑𝐶9𝑑𝑡 Eq. 39 𝑟3 = 𝑘3[𝐴]:[𝐵]; Eq. 40 59 where a and b represent the molecularity of the elementary reaction Eq. 38 and shall not be construed as the reaction order by species. Hence, these values are independent of the experimental data. The system can be written in a more compact vector matrix, facilitating the analysis of the error and model misfit per species. The kinetic reactions of the species under study can be described by a set of ODEs as shown in Eq. 41: 𝑑𝐶3𝑑𝑡 = 𝑓(𝑘3 , 𝐶3) 𝐶3(𝑡#) = 𝐶3# Eq. 41 Where Ci is the vector of state variable compositions as a function of time, ki is the vector of kinetic rate constants, and Ci0 is the array of initial concentrations. The approach taken to determine the reaction rates of the experimental data encompasses a numerical differentiation of the concentration versus time to obtain an approximation to the actual reaction rates. The unknown kinetic parameters were determined by solving the constrained non-linear dynamic minimization problem. The solution is a set of unknown parameters, ki, that leads to the minimization of the error between the experimental data and the model predictions, as expressed in Eq. 42: min< 𝑓(𝑘3 , 𝐶3) =[$\𝑑𝐶3𝑑𝑡 ]9:2: − \𝑑𝐶3𝑑𝑡 ]=>?$@-! × 𝑤3A3B+ 𝑘 = 𝑘3 (𝑓𝑜𝑟 𝑖 = 1, 2, … , 𝑛) Eq. 42 where m refers to the total number of observed discrete experimental data points. This number is equal to the number of sampling times multiplied by the number of target species collected at each sampling event; whilst n is the number of kinetic rate constants to be identified. The weighting factor, wi, represents the level of importance given to an individual experimental data point. In this work, all data points are assumed of equal importance (i.e., wi = 1) unless indicated otherwise. To simulate and compare the predicted and experimental concentrations, a numerical integration algorithm was used solving the system of ODEs simultaneously, using Runge-Kutta iterative methods to assure that the concentration profile of Tu species involved followed the law of mass action. The mass balance was assessed by element. Depending on the mechanism studied, additional species such as FDSH+/FDS and TuO/TuOH were added to the tracking of organic sulfur species in the mass balance equation described in Eq. 43: [𝑇𝑢]# = [𝑇𝑢] + 2[𝐹𝐷𝑆𝐻!!"] + [𝑇𝑢𝑂!] Eq. 43 60 Elemental sulfur was proposed, and later validated with experimental evidence, to be one of the final products of the FDSH22+ hydrolysis in acidic water, section 2.3.3. However, non-experimental evidence of sulfur precipitation was found in tests conducted in ferric media at room temperature. Rate constants were determined using the experimental data under baseline conditions. Similarly, the effect of the temperature was studied independently to assess the variation of the rate constants as the temperatures changes. 4.3 Constraints and limitations of the experimental design and analytical methods Before focusing on the restrictions of the algorithms, attention must be drawn to the limitations of the experimental design of the tests and the analytical methods used in this study. The experimental matrix was initially developed with the objective of monitoring the concentration profiles of Tu-FDSH22+ species at different initial ferric concentrations. This was to ensure that the experiments conducted in this work will allow us to find any correlations between the species involved in the system. Later, the analysis performed in section 3.5, where a non-linear behavior was observed from the experimental data of the tests with Tu:Fe3+ and Tu:FDSH22+, provided the impetus for attempting to develop a kinetic model, which could allow us to explain in a more comprehensive manner the evolution of these species over time, from both a chemical and mathematical standpoint. Batch experiments were carried out using 4 different conditions to assess the effect of initial concentrations of [Fe3+]0, [Tu]0, and [H+]0, respectively. Samples were taken at regular intervals and analyzed using HPLC to measure the absorbance of each species. The total retention time was set to 5 min, with a previous 2 min washing and conditioning of the HPLC column; this delay in the instantaneous measurement of the concentration might have influenced the accuracy of the readings later used in the calculation of rate constants by species. This phenomenon was accentuated in the case of shorter sampling intervals, especially at times when the reaction is fast as observed at the beginning of the test (first 2 h). Once the sampling interval is increased, the uncertainties arising from the concentration measurements are minimized, given the small variation observed in concentration values. 4.4 Constraints and limitations of the mathematical approach The approach taken to solve the inverse problem was first to calculate the gradient of the empirical concentration values. A large variation in the calculated gradient may hamper numerical convergence, due to the unknown kinetic rates, k, which generally differ by orders of magnitude. 61 The integration of the large set ODEs was subject to the assumption that there is no denaturation of the organic phase, and the formation of inorganic species was neglected. As a result of this, the species considered in the reaction mechanism could potentially be over or underestimated, in order to satisfy the law of mass action. Moreover, if the influence of the species that are not being considered in the chemical reaction network is higher than expected, this previous assumption will potentially lead to discrepancies between the experimental data and the simulated values. 4.5 Kinetic model of the oxidation of thiourea in the presence of ferric sulfate Considering that the dominant chemical process in the presence of ferric ions is the chemical oxidation of Tu, and based on the oxidation pathway of Tu proposed in Chapter 2 which results in a Fe3+/Tu molar ratio of 1:1, the overall reaction scheme and its reaction rate can be described by Eq. 44, Eq. 45, and Eq. 46, respectively. 2 Tu + 2 Fe3+ ® FDSH22+ + 2 Fe2+ Eq. 44 𝑟3 = −12𝑑𝐶/0𝑑𝑡 = −12𝑑𝐶1$!"𝑑𝑡 = 𝑑𝐶19CD$$"𝑑𝑡 = 12𝑑𝐶1$$"𝑑𝑡 Eq. 45 𝑟3 = 𝑘>;E[𝑇𝑢]![𝐹𝑒)"]! Eq. 46 The first attempt to find the constituents of the rate expression was to minimize the error of the empirical data using an overall rate constant. This rate constant, calculated as kobs = 6.35E-05, was later used as the first guess in the study of the evolution of Tu species in solution. This approach is reasonable in light of the fact that using the overall rate constant as an intelligent initial guess will assure convergence and further minimize the total sum of square error on the new ki values evaluated to assess the influence of changing the initial conditions. A linearization approach is followed by calculating the natural logarithm of the initial concentrations, as illustrated in Figure 44. Similarly, the effect of changing [Fe3+]0 and [H+]0 plots are shown in Appendix D, Figure D - 6 and Figure D - 7. Given that the rate at which the reaction is proceeding is being catalyzed by the change of the initial conditions of the tests, the observed rate constants are a function of the conditions of the system. The values of the slope of the natural logarithms between the new ki values and the initial conditions correspond to the weight attributed to the effect of each variable under the initial conditions studied, Table 15. 62 Figure 44. Power-law relationship of ki values at 20°C with 10 mM Fe3+ under different [Tu]0 concentrations, and initial pH 1.7. Table 15. Power-law relationship of ki values at 20°C Effect Slope R2 [Fe3+]0 -1.23 0.99 [Tu]0 -0.83 0.99 [H+]0 0.60 0.92 Having individual ki values for each experiment permits finding the best fit values to minimize the error of the system, and to evaluate the dependence of the kobs values with the empirical data. In order to find an overall rate expression, and to verify the assumed mechanism, it is imperative to reduce the mathematical complexity of the system. By assuming steady state and following the method introduced by Christiansen (1953), the chemical pathway, illustrated by Figure 45, can be simplified as follows: 63 Tu ⇄ X1 Eq. 47 X1 + Fe3+ ® X2 + Fe2+ + H+ Eq. 48 X2 + X2 ⇄ X3 Eq. 49 X3 + H+ ⇄ X4 Eq. 50 X4 + H+ ⇄ FDSH22+ Eq. 51 X1: Tautomeric form of Tu, as shown in Eq. 9 X2: Oxidation product of Tu, as shown in Eq. 10 X3: FDS, as shown in Eq. 14 X4: FDSH+, as shown in Eq. 15 Figure 45. Reaction scheme for the oxidation of thiourea in the presence of ferric. And their respective rates can be written as: 𝑟+ = 𝑘+[𝑇𝑢]! − 𝑘F+[𝑋+]! Eq. 57 𝑟! = 𝑘![𝑋+]![𝐹𝑒)"]! Eq. 58 2𝑇𝑢 +<%&⇄<& 2𝑋+ Eq. 52 2𝑋+ + 2𝐹𝑒)" <%$⇄<$ 2𝑋! + 2𝐹𝑒!" + 2𝐻" Eq. 53 2𝑋! <%!⇄<! 𝑋) Eq. 54 𝑋) +𝐻" <%'⇄<' 𝑋G Eq. 55 𝑋G +𝐻" <%(⇄<( 𝐹𝐷𝑆𝐻!!" Eq. 56 X4 X1 X1 X2 X2 X3 64 𝑟) = 𝑘)[𝑋!]! − 𝑘F)[𝑋)] Eq. 59 𝑟G = 𝑘G[𝑋)][𝐻"] − 𝑘FG[𝑋G] Eq. 60 𝑟* = 𝑘*[𝑋G][𝐻"] − 𝑘F*[𝐹𝐷𝑆𝐻!!"] Eq. 61 Moreover, the rate contribution for a generic reaction can be defined as: Xj + B ® Xk (−𝑟H)H→< = (𝑟<)H→< = 𝑘H<𝐶H𝐶7 Eq. 62 Following this method, the rate of reaction is written instead as, (−𝑟H)H→< = (𝑟<)H→< = 𝜆H<𝐶H 𝜆H< = 𝑘H<𝐶7 Eq. 63 Thus, with this convention any reaction with or without co-reactants and co-products and with a rate coefficient kjk, becomes mathematically equivalent to one composed with the co-factor ljk. Moreover, for Eq. 57 to Eq. 61, the co-factors are defined as follows: 𝜆+ = 𝑘+ 𝜆F+ = 𝑘F+ Eq. 64 𝜆! = 𝑘![𝐹𝑒)"]! 𝜆F! = 𝑘F! = 0 Eq. 65 𝜆) = 𝑘) 𝜆F) = 𝑘F) Eq. 66 𝜆G = 𝑘G[𝐻"] 𝜆FG = 𝑘FG Eq. 67 𝜆* = 𝑘*[𝐻"] 𝜆F* = 𝑘F* Eq. 68 After elimination of the concentration of all the intermediates species, (Xj with j = 1 to 6), by the Bodenstein approximation, the set of rate equations, Eq. 57 to Eq. 61, can be reduced to a single rate equation: −12 𝑟/0 = 𝑟19CD$$" = Λ/019CD$$"[𝑇𝑢]! − Λ19CD$$"/0[𝐹𝐷𝑆𝐻!!"]! Eq. 69 Where Λ/019CD$$" = Π/019CD$$"𝐷/019CD$$" , Λ19CD$$"/0 = Π19CD$$"/0𝐷/019CD$$" Eq. 70 The numerator of Λ/019CD$$", is the product of all the co-factors of the forward reactions: 65 Π/019CD$$" = 𝜆+𝜆!𝜆)𝜆G𝜆*[𝑇𝑢]! Eq. 71 Given that the 𝜆F! represents an electrochemical reaction driven to the forward direction, its value is equal to 0. Thus, Π19CD$$"/0 = 0. Lastly, 𝐷/019CD$$" is defined as: D/019CD$$" =[ij𝜆3,3F+HF+3B+ j𝜆3,3"+<F+3BH k<HB+ Eq. 72 Which is equivalent to: 𝐷/019CD$$" = (𝜆!𝜆)𝜆G𝜆*) + (𝜆F+𝜆)𝜆G𝜆*) Eq. 73 Therefore, the reaction rate is equal for Tu and FDSH22+ can be expressed as: 𝑟/0 = −2Λ/019CD$$" Eq. 74 𝑟19CD$$" = Λ/019CD$$" Eq. 75 To obtain the final rate equation for the chemical pathway proposed, the co-factors are replaced by the true rate coefficients and co-reactants or co-products, which results in Eq. 76 and Eq. 77 for Tu and FDSH22+, respectively. 𝑟/0 = −2𝑘+𝑘![𝑇𝑢]![𝐹𝑒)"]!𝑘! + 𝑘F+ Eq. 76 𝑟19CD$$" = 𝑘+𝑘![𝑇𝑢]![𝐹𝑒)"]!𝑘! + 𝑘F+ Eq. 77 Similarly, if the protonation is considered as the initiation step the final rate equation can be written as: 𝑟/0 = −2𝑘+𝑘!𝑘)[𝑇𝑢]![𝐹𝑒)"]![𝐻"]!𝑘)[𝐹𝑒)"]!(𝑘! + 𝑘F+) + 𝑘F+𝑘F![𝐻"]! Eq. 78 𝑟19CD$$" = 𝑘+𝑘!𝑘)[𝑇𝑢]![𝐹𝑒)"]![𝐻"]!𝑘)[𝐹𝑒)"]!(𝑘! + 𝑘F+) + 𝑘F+𝑘F![𝐻"]! Eq. 79 By re-arrangement of the constant terms, and considering the reaction order as variable, Eq. 78 and Eq. 79 become: 𝑟/0 = −2𝑘:[𝑇𝑢]A[𝐹𝑒)"]K[𝐻"]L𝑘;[𝐹𝑒)"]% + 𝑘M[𝐻"]N Eq. 80 66 𝑟19CD$$" = 𝑘:[𝑇𝑢]A[𝐹𝑒)"]K[𝐻"]L𝑘;[𝐹𝑒)"]% + 𝑘M[𝐻"]N Eq. 81 The kinetic parameters estimated by the least square minimization technique, considering the protonation of Tu as the initial step, are summarized in Table 16. Table 16. Kinetic parameters for the overall rate of reaction Kinetic parameters ka 1.42E-02 kb 3.33E+01 kc 6.23E-02 m 1.12 n 2.32 p 0.27 q 0.85 r 0.64 Figure 46. Model fitting for thiourea concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7, based on the rate expression obtained using co-factors. 67 Figure 47. Model fitting for FDSH22+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7. Figure 48. Model fitting for Fe3+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations and initial pH 1.7, based on the rate expression obtained using co-factors. 68 The species concentrations are calculated from the integration of the overall rate expression by species, when the [Tu]0 was changed, as shown in Figure 46, Figure 47, and Figure 48. For the remaining concentration profiles, please refer to Appendix D, Figure D - 8 to Figure D - 13. The calculated concentrations presented in Appendix D, show that the model fails to describe the behavior of this system over the entire duration of the tests. It can be seen that the model overestimates the Tu consumption in order to satisfy the restriction of the mass balance by species. Thus, given the irreversibility of the reaction, the simulated Tu concentration are lower values than the experimental data observed. Furthermore, due to the extent of the reaction Eq. 44, up to 48 h, where the FDSH22+ starts to accumulate, it can be observed that the model predicts satisfactorily the experimental concentrations. This might indicate that the assumption used to construct the model is valid when the chemical oxidation is the main chemical process in solution. On the other hand, besides the deviation of the empirical to the simulated values, attention must be drawn to the shape of the experimental concentration profiles. To throw some light into this matter, one should take into consideration the need to provide additional feedback in terms of formation of Tu and consumption of FDSH22+. Thus, as a working hypothesis, it would seem appropriate to incorporate the hydrolysis of FDSH22+ into the rate expression by species. In the case of Fe3+ concentration, Figure 48, a possible explanation for the higher consumptions observed, generating the misfit between simulated and experimental concentrations, is given by the fact that the hydrolysis of iron (III) species in solution could speed up in the presence of these organic species. Hence the consumption of Fe3+ will be increased. Further, as discussed in section 2.3.3 and considering Figure B - 1 to Figure B - 3, having additional organic compounds in solution has a strong influence on the pH. Moreover, the presence of more reductant organic species such as TuO2 could contribute to the further reduction of Fe3+ ions. 69 4.6 Proposed mechanism and kinetic model validation of FDSH22+ hydrolysis In order to determine the chemical pathway of FDSH22+ hydrolysis, both the identification and quantification of the species involved are imperative. Based on the findings described in Chapter 2 section 2.3.3, two species stand out as possible candidate “intermediate species” of FDSH22+ hydrolysis. To evaluate the influence of these intermediate species, a simplistic approach was taken. Given the lack of HPLC standards, the concentrations of TuOH/TuO and FDSH+ could not be quantified. However, the HPLC areas attributed to the unknown species and TuO2 should provide sufficient information to explain to some extent the imbalance in terms of the sulfur mass balance. Hence, assuming that the species tracked through the duration of the tests are the main species involved in the process; the sum of these species should be close enough to the initial concentration added to the system. 𝑇𝑜𝑡𝑎𝑙 𝑆𝑢𝑙𝑓𝑢𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑜𝑟𝑔𝑎𝑛𝑖𝑐 𝑓𝑜𝑟𝑚 = 2[𝐹𝐷𝑆𝐻!!"]# Eq. 82 Two scenarios are proposed, where the unquantified species are considered to follow a linear behavior between absorbance, measured with concentrations, and the correlation factor between the absorbance and concentration, e. For the unknown species, this can be calculated by forcing the system to follow the law of mass action. 2[𝐹𝐷𝑆𝐻!!"]# = [𝑇𝑢] + [𝐹𝐷𝑆𝐻!!"] + [𝐹𝐷𝑆𝐻"] + [𝑇𝑢𝑂!] Eq. 83 2[𝐹𝐷𝑆𝐻!!"]# = [𝑇𝑢] + [𝐹𝐷𝑆𝐻!!"] + [𝑇𝑢𝑂𝐻/𝑇𝑢𝑂] + [𝑇𝑢𝑂!] Eq. 84 This assumption attributes a certain weight to the unknown values and allows us to evaluate the concentration profiles of the monitored species, illustrated in Figure 49. The chosen scenario does not necessarily exclude the presence of the neglected species in the system. Instead, it highlights the influence the chosen candidate exerts on the transition from FDSH22+ to Tu. The sum of square error found on the FDSH+ scenario presents a 2.4x factor compared with the TuOH/TuO. The presence of TuOH/TuO species also contributes to the TuO2 feedback, which is considered as one of the possible reactants of the reaction responsible for the formation of TuO2. Similarly, if FDSH+ was the unknown species the analysis of data should have shown a correlation between FDSH22+ and FDSH+ given the chemical reaction illustrated by Eq. 16 which demonstrates that the formation of FDSH+ is a necessary step for the formation of Tu during the hydrolysis process, yet no correlation was detected. That said, the presence of FDS species shall not be neglected, but its transition is going to be assumed to be fast enough that they could not be accurately detected under the conditions studied. 70 Figure 49. Concentration of thiourea species that satisfy sulfur mass balance at 20°C, in acidic water with 1 mM. Hollow symbols in black (red) represent the TuOH/TuO (FDSH+) scenario. Therefore, the unknown peak found at 2.9 min of retention time is attributed to TuOH/TuO. From now on, for simplification purposes, the transition of FDSH22+ to Tu is going to be considered as a single-step reaction. This reasoning is supported by the lack of experimental evidence that could allow the calculation of any kinetic parameters for the formation of FDSH+ and FDS. Thus, their net rate is considered to be zero, which, from a mathematical standpoint, means that the influence of these species can be neglected. Two-reaction mechanisms are proposed for the species selected, which generate the same rate by species and consequently the same overall reaction. The net rate of the intermediate species is zero. Hence, these two species are mathematically equivalent in terms of their kinetic rate parameters. The reaction mechanism considering TuOH as an intermediate can be written as follows: 2 FDSH22+ + 2 H2O ® 2 Tu + 2 TuOH + 2 H+ R1 Eq. 85 2 TuOH ® Tu + TuO2 + 2 H+ R2 Eq. 86 2 FDSH22+ + 2 H2O ® 3 Tu + TuO2 + 4 H+ (Overall reaction) Eq. 87 𝑟+ = −12𝑑𝐶19CD$$"𝑑𝑡 = 12𝑑𝐶/0𝑑𝑡 = 12𝑑𝐶/0OD𝑑𝑡 𝑟+ = 𝑘+[𝐹𝐷𝑆𝐻!!"]! Eq. 88 71 𝑟! = −12𝑑𝐶/0OD𝑑𝑡 = 𝑑𝐶/0𝑑𝑡 = 𝑑𝐶/0O$𝑑𝑡 𝑟! = 𝑘![𝑇𝑢𝑂𝐻]! Eq. 89 Similarly, the reaction mechanism considering TuO as an intermediate can be expressed as: 2 FDSH22+ + 2 H2O ® 2 Tu + 2 TuO + 4 H+ R1 Eq. 90 2 TuO ® Tu + TuO2 R2 Eq. 91 2 FDSH22+ + 2 H2O ® 3 Tu + TuO2 + 4 H+ (Overall reaction) Eq. 92 𝑟+ = −12𝑑𝐶19CD$$"𝑑𝑡 = 12𝑑𝐶/0𝑑𝑡 = 12𝑑𝐶/0O𝑑𝑡 𝑟+ = 𝑘+[𝐹𝐷𝑆𝐻!!"]! Eq. 93 𝑟! = −12𝑑𝐶/0O𝑑𝑡 = 𝑑𝐶/0𝑑𝑡 = 𝑑𝐶/0O$𝑑𝑡 𝑟! = 𝑘![𝑇𝑢𝑂]! Eq. 94 To validate the reaction mechanism, the net kinetic rate by species were integrated and compared with the empirical data. The calculated values for Tu and FDSH22+ satisfactorily predict the experimental concentrations, as shown in Figure 50. On the other hand, the model fails to accurately predict the behavior of TuOH/TuO. These results might suggest the presence of an alternative chemical pathway, which comprises TuOH/TuO species. However, given the exemplary predictive capabilities of the model towards Tu and FDSH22+, it is concluded that this unknown chemical pathway does not have a significant influence on the system. In the case of TuO2, a substantial increase in the simulated concentrations is observed in comparison with the experimental data. A possible explanation for this phenomenon is the low absorbance of this species at the wavelength analyzed with the HPLC, 214 nm. This hindrance could increase the uncertainties and affect the accuracy of the concentrations measured during the experiments. Considering that the entire chemical reaction network has yet to be elucidated, one can speculate that the accumulation of TuO2 showed by the simulated data is an indication that these species continue to react in the system. 72 Figure 50. Model fitting for thiourea species at 20°C in acidic water with 1 mM [FDSH22+]0 concentration and initial pH 1.7. Having in mind the rationale of this chapter, a more general approach needs to be considered that would allow proper representation of the hydrolysis process and the determination of the kinetics parameters based solely on the concentration of Tu and FDSH22+ in the presence of ferric ions. Considering the overall reaction, Eq. 95, as the main chemical pathway in solution, it is expected that the fitting by species would deviate from the observed values, because the net rate of intermediate species, dTuOH/TuO/dt, is considered equal to zero. 2 FDSH22+ + 2 H2O ® 3 Tu + TuO2 + 4 H+ (Overall reaction) Eq. 95 𝑟+ = −12𝑑𝐶19CD$$"𝑑𝑡 = 13𝑑𝐶/0𝑑𝑡 = 𝑑𝐶/0O$𝑑𝑡 𝑟+ = 𝑘+[𝐹𝐷𝑆𝐻!!"]! Eq. 96 To assess the simplicity and predictive capabilities of the overall reaction model, the effect of changing pH was studied. As previously mentioned in section 2.3.4, the change of pH exerts a great influence on the rate at which FDSH22+ is being consumed. This behavior was attributed to the deprotonation of FDSH22+ as a reaction step in the chemical transformation of FDSH22+ to Tu. However, considering the reaction mechanism proposed in this chapter, the presence of TuOH/TuO might play a significant role. 73 The results presented in Figure 12, section 2.3.4, permits one to conclude that the hydrolysis rate of FDSH22+ is being catalyzed by the change in the initial concentration of acid. Therefore, following the same approach of section 4.5, it is possible to calculate the kinetic parameters, summarized in Table 17. Further, using the method proposed by Christiansen (1953), the chemical pathway, shown in Figure 52, can be expressed by Eq. 97. Table 17. FDSH22+ overall hydrolysis rate constant at different pH and room temperature kH Slope -0.69 R2 9.95E-01 k0 1.40E-03 Figure 51. Linear relationship of the hydrolysis rate of FDSH22+ at different initial pH. 74 Figure 52. Schematic representation of the hydrolysis of FDSH22+. 𝑟19CD$$" = 𝑘+[𝐹𝐷𝑆𝐻!!"]!𝑘! + 𝑘)[𝐻"]! + 𝑘G[𝐻"]G Eq. 97 Considering the overall reaction, Eq. 95, as the main chemical reaction, the predicted values shown in Figure 53 follow the trend of the experimental data. As expected, the fitting of the model is being compromised by mathematical constraints of the system to satisfy the restriction that the net rate of intermediate species is equal to zero. Nonetheless, this section aims to explore the nature of the hydrolysis process from a simplified conceptual and fundamental point of view, rather than a strictly predictive one. Thus, the kinetic parameters found in this section will be as an intelligent initial guess in the kinetic model for the oxidation of Tu in the presence of ferric ions. 75 Figure 53. Model fitting for thiourea species at 20°C, in acidic water, with 1 mM [FDSH22+]0 under indicated initial pH. Filled (hollow) symbols represent thiourea (FDSH22+), solid line (dash line) represent simulated thiourea (FDSH22+) concentrations. 76 4.7 Kinetic model of the oxidation of thiourea and hydrolysis of formamidine disulfide in the presence of ferric ions In light of the discussions presented in sections 4.5 and 4.6, the development of a comprehensive kinetic model that includes the two main chemical processes in solution, oxidation of Tu due to the presence of ferric ions and the hydrolysis of FDSH22+ was attempted. The Tu-Fe3+ system, is comprised of the chemical oxidation of Tu and the “overall” FDSH22+ hydrolysis reaction, can be described by Eq. 98 and Eq. 99, respectively. 2 Tu + 2 Fe3+ ® FDSH22+ + 2 Fe2+ R1 Eq. 98 2 FDSH22+ + 2 H2O ® 3 Tu + TuO2 + 4 H+ R2 Eq. 99 𝑟+ = −12𝑑𝐶/0𝑑𝑡 = −12𝑑𝐶1$!"𝑑𝑡 = 𝑑𝐶19CD$$"𝑑𝑡 = 12𝑑𝐶1$$"𝑑𝑡 𝑟+ = 𝑘+[𝑇𝑢]![𝐹𝑒)"]! Eq. 100 𝑟! = −12𝑑𝐶19CD$$"𝑑𝑡 = 13𝑑𝐶/0𝑑𝑡 = 𝑑𝐶/0O$𝑑𝑡 𝑟! = 𝑘![𝐹𝐷𝑆𝐻!!"]! Eq. 101 The net rate by species is defined by r1 and r2. The characteristic behavior and evolution of species in solution, where FDSH22+ species present an inflection point, at which ?[19CD$$"]?2 = 0, will help us constrain the system in terms of the determination of initial guesses and kinetics parameters. 𝑑𝐶/0𝑑𝑡 = −2𝑘+[𝑇𝑢]![𝐹𝑒)"]! + 3𝑘![𝐹𝐷𝑆𝐻!!"]! Eq. 102 𝑑𝐶1$!"𝑑𝑡 = −2𝑘+[𝑇𝑢]![𝐹𝑒)"]! Eq. 103 𝑑𝐶19CD$$"𝑑𝑡 = 𝑘+[𝑇𝑢]![𝐹𝑒)"]! − 2𝑘![𝐹𝐷𝑆𝐻!!"]! Eq. 104 𝑑𝐶/0O$𝑑𝑡 = 2𝑘![𝐹𝐷𝑆𝐻!!"]! Eq. 105 Using the inflection point of the FDSH22+concentration profile, where [FDSH22+] = [FDSH22+]tmax, a new correlation can be expressed as follows: 𝑑𝐶19CD$$"𝑑𝑡A:R = 𝑘+[𝑇𝑢]2A:R! [𝐹𝑒)"]2A:R! − 2𝑘![𝐹𝐷𝑆𝐻!!"]2A:R! = 0 Eq. 106 𝑘+[𝑇𝑢]2A:R! [𝐹𝑒)"]2A:R! = 2𝑘![𝐹𝐷𝑆𝐻!!"]2A:R! Eq. 107 77 𝑘+𝑘! = 2𝑘![𝐹𝐷𝑆𝐻!!"]A:R!𝑘+[𝑇𝑢]A:R! [𝐹𝑒)"]A:R! Eq. 108 Considering these constraints, it is possible to alter the model into an expression that describes the characteristic behavior of the FDSH22+ species. Due to the discrete information available from experimental observation, it is necessary to find a range where this assumption can be valid. Therefore, the approach followed was to calculate k1/k2 using empirical data and find the min and max boundaries using Eq. 108. Assuming that the system is accurately described by the oxidation of Tu and the overall hydrolysis of FDSH22+ it is also possible to define the rate of species as a function of the rest of species in solution. By doing so, we can have a sense of the rate at which the species are changing with respect to each other. Using the rate laws described in Eq. 102 through Eq. 105 the quotient of the rate by species can be written as: 𝑑[𝑇𝑢]𝑑[𝐹𝑒)"] = 1 − 3𝑘![𝐹𝐷𝑆𝐻!!"]!2𝑘+[𝑇𝑢]![𝐹𝑒)"]! Eq. 109 𝑑[𝑇𝑢]𝑑[𝐹𝐷𝑆𝐻!!"] = −2𝑘+[𝑇𝑢]![𝐹𝑒)"]! + 3𝑘![𝐹𝐷𝑆𝐻!!"]!𝑘+[𝑇𝑢]![𝐹𝑒)"]! − 2𝑘![𝐹𝐷𝑆𝐻!!"]! Eq. 110 Considering the initial conditions as a reference point, at t = 0, [Tu] = [Tu]0, [Fe3+] = [Fe3+]0, a domain in which the assumption is valid can be found: 𝑑[𝑇𝑢]𝑑[𝐹𝑒)"] ≤ 1 Eq. 111 𝑑[𝑇𝑢]𝑑[𝐹𝐷𝑆𝐻!!"] ≥ −2 Eq. 112 These correlations are going to be used later to explain the misfit between the experimental data and the simulated values. Table 18 summarizes the kinetic parameters that were found to minimize the sum of square error and satisfy the constraints, and were calculated following the same linearization approach described in section 4.5. 78 Table 18. Linear relationship of ki values at 20°C, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+ Effect Slope R2 k1 k2 k1 k2 [Fe3+]0 –1.42 –0.41 9.93E-01 8.30E-01 [Tu]0 –1.00 –1.48 9.95E-01 9.90E-01 [H+]0 0.26 –0.75 9.68E-01 9.66E-01 The results presented in Table 18 indicate a concentration-dependency of the observed rate constants, considered in the model for the overall oxidation and hydrolysis of Tu and FDS. This behavior could be explained by the intermediate species that are forming as a result of the conditions present in the system, and the transition from Tu to FDSH22+, or vice versa, no longer being a one-step reaction process. Moreover, if the concentration of intermediate species is high, side reactions coupled with another mechanism or chemical pathway are also possible and would influence the overall conversion of Tu to FDSH22+. Thus, under certain conditions, the system could be comprised of self-accelerating reactions, commonly called autocatalysis, through product-promoted or reactant-inhibited reactions. Therefore, the focus of the analysis is on the altered behavior due to the presence of intermediate species and the influence they exert, in terms of the variables measured throughout the durations of the tests. To further illustrate this point, Figure 54 presents the normalized instantaneous rates of Tu, for the experiments under different [Tu]0. In the case of the empirical normalized rates, Figure 54 (a), it is observed that the normalized rate follows a consistent trend, regardless of the [Tu]0. Moreover, by using the mathematical model presented in section 4.1, the normalized rate of Tu can be recalculated. The results presented in Figure 54 (b), shows that the normalized rate of Tu decreases monotonically as the Tu conversion progresses for all the [Tu]0 tested. The dependence of the rate of reaction with the components of the system can also be exemplified with the initial rate of FDSH22+ formation at different initial conditions. Figure 55, shows a linear dependency of the initial rate with respect to [Tu]0 (a), and [Fe3+]0 (b). The slope values indicate that the change in [Tu]0 exerts a pronounced effect on the initial rate, 5.3x factor, compared to the test where the [Fe3+]0 was varied. A more detailed discussion of the behavior observed in the test where the initial pH was changed is analyzed in greater depth in the following sections in this chapter. 79 Figure 54. Normalized instantaneous rate of thiourea at 20°C with 10 mM Fe3+, under indicated [Tu]0 and initial pH 1.7. (a) Experimental rate values, (b) simulated rate values considering mathematical model presented in section 4.1. Figure 55. Linear relationship of the initial rate of FDSH22+ formation at different initial conditions. (a) rate of formation with respect to [Tu]0, (b) rate of formation with respect to [Fe3+]0 concentration. (a) (b) (a) (b) 80 Considering the chemical pathway proposed in section 4.5 and section 4.6 for the chemical oxidation of Tu in ferric media and the hydrolysis of FDSH22+ in acidic water, the system can be defined by: 2 Tu + 2 Fe3+ ® FDS + 2 Fe2+ + 2 H+ Eq. 113 2 FDS + 2 H2O ® 2 Tu + 2 TuO Eq. 114 2 TuO ® Tu + TuO2 Eq. 115 2 FDS + 2 H+ ⇄ 2 FDSH+ Eq. 116 2 FDSH+ + 2 H+ ⇄ 2 FDSH22+ Eq. 117 𝑟+ = 𝑘+[𝑇𝑢]![𝐹𝑒)"]! Eq. 118 𝑟! = 𝑘![𝐹𝐷𝑆]! Eq. 119 𝑟) = 𝑘)[𝑇𝑢𝑂]! Eq. 120 𝑟G = 𝑘G[𝐹𝐷𝑆]![𝐻"]! − 𝑘FG[𝐹𝐷𝑆𝐻"]! Eq. 121 𝑟* = 𝑘*[𝐹𝐷𝑆𝐻"]![𝐻"]! − 𝑘F*[𝐹𝐷𝑆𝐻!!"]! Eq. 122 Assuming that the intermediate species follows the steady-state approximation, dCi/dt » 0, with the exception of TuO2, which is considered as the end-product of the oxidation/hydrolysis process, as stated in section 4.6, and the rate for the intermediate species can be expressed as: 𝑑[𝐹𝐷𝑆]𝑑𝑡 = 𝑟+ − 2𝑟! − 2𝑟G = 0 Eq. 123 𝑑[𝐹𝐷𝑆𝐻"]𝑑𝑡 = 2𝑟G − 2𝑟* = 0 Eq. 124 𝑑[𝑇𝑢𝑂]𝑑𝑡 = 2𝑟! − 2𝑟) = 0 Eq. 125 Applying the steady-state approximation allows to re-define the intermediate species in terms of Tu, Fe3+, H+, and FDSH22+, which were measured during the experiments. Therefore, the instantaneous concentration of the transient species can be written as: [𝐹𝐷𝑆]! = 𝑘+[𝑇𝑢]![𝐹𝑒)"]! + 2𝑘FG[𝐹𝐷𝑆𝐻"]!2(𝑘! + 𝑘G[𝐻"]!) Eq. 126 81 [𝐹𝐷𝑆𝐻"]! = 𝑘+𝑘G[𝐻"]![𝑇𝑢]![𝐹𝑒)"]!2𝑘!𝑘FG + 2𝑘!𝑘*[𝐻"]! + 2𝑘G𝑘*[𝐻"]G + 2𝑘F*(𝑘! + 𝑘G[𝐻"]!)[𝐹𝐷𝑆𝐻!!"]!2𝑘!𝑘FG + 2𝑘!𝑘*[𝐻"]! + 2𝑘G𝑘*[𝐻"]G Eq. 127 [𝑇𝑢𝑂]! = 𝑘![𝐹𝐷𝑆]!𝑘) Eq. 128 After algebraic rearrangement and substitution of the transient species the final rate expression can be obtained for Tu, FDSH22+, and TuO2: 𝑑[𝑇𝑢]𝑑𝑡 = −2𝑘+[𝑇𝑢]![𝐹𝑒)"]! + 3𝑘+𝑘![𝑇𝑢]![𝐹𝑒)"]!2(𝑘! + 𝑘G[𝐻"]!)+ 3𝑘+𝑘!𝑘G𝑘FG[𝑇𝑢]![𝐹𝑒)"]![𝐻"]!2(𝑘! + 𝑘G[𝐻"]!)(𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!))+ 3𝑘!𝑘FG𝑘F*[𝐹𝐷𝑆𝐻!!"]!𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) Eq. 129 𝑑[𝐹𝐷𝑆𝐻!!"]𝑑𝑡 = 𝑘+𝑘G𝑘*[𝑇𝑢]![𝐹𝑒)"]![𝐻"]G𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) + 2𝑘!𝑘*𝑘F*[𝐹𝐷𝑆𝐻!!"]!𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!)+ 2𝑘G𝑘*𝑘F*[𝐹𝐷𝑆𝐻!!"]![𝐻"]!𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) − 2𝑘F*[𝐹𝐷𝑆𝐻!!"]! Eq. 130 𝑑[𝑇𝑢𝑂!]𝑑𝑡 = 𝑘+𝑘![𝑇𝑢]![𝐹𝑒)"]!2(𝑘! + 𝑘G[𝐻"]!) + 𝑘!𝑘FG[𝑇𝑢]![𝐹𝑒)"]![𝐻"]!2(𝑘! + 𝑘G[𝐻"]!)(𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!))+ 𝑘!𝑘FG𝑘F*[𝐹𝐷𝑆𝐻!!"]!𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) Eq. 131 To facilitate the comparison between the results discussed in the previous sections in this chapter, all the terms associated with Tu or FDSH22+ will be rearranged and defined as one term, illustrated by Eq. 132 and Eq. 133, respectively. 𝑑[𝑇𝑢]𝑑𝑡 = −2𝑘+,/0[𝑇𝑢]![𝐹𝑒)"]! + 3𝑘!,/0[𝐹𝐷𝑆𝐻!!"]! Eq. 132 𝑑[𝐹𝐷𝑆𝐻!!"]𝑑𝑡 = 𝑘+,19CD$$"[𝑇𝑢]![𝐹𝑒)"]! − 2𝑘!,19CD$$"[𝐹𝐷𝑆𝐻!!"]! Eq. 133 Where k1, Tu, k2, Tu, k1, FDSH22+, and k2, FDSH22+ are defined by: 𝑘+,/0 = 𝑘+ − 3𝑘+𝑘!4(𝑘! + 𝑘G[𝐻"]!) − 𝑘+𝑘!𝑘G𝑘FG[𝐻"]!4(𝑘! + 𝑘G[𝐻"]!)(𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!)) Eq. 134 82 𝑘!,/0 = 𝑘!𝑘FG𝑘F*𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) Eq. 135 𝑘+,19CD$$" = 𝑘+𝑘G𝑘*[𝐻"]G𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) Eq. 136 𝑘!,19CD$$" = 𝑘F* − 𝑘!𝑘*𝑘F*𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) − 𝑘G𝑘*𝑘F*[𝐻"]!𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) Eq. 137 The experimental rate constant expressions, shown in Eq. 134 to Eq. 137, are strongly influenced by the proton concentration in solution. Significant fluctuations in the pH values measured were observed during the experiments, even at the lowest [Tu]0, 1 mM, illustrated in Figure 56. Further, the change of pH increased with increasing ferric concentration, as discussed in Chapter 3. Another supporting explanation for the changes in pH was made in the section 3.3.1 and 3.3.2, stating that species such as TuO2, Cy, and urea can be responsible for pH fluctuations. Therefore, more reliable proton concentration values are required to assure the convergence of the system and avoid local solutions. Figure 56. ORP measurements and [H+] concentration at 20°C with 10 mM Fe3+, 1 mM [Tu]0, and initial pH 1.7. 83 To adjust the proton concentration, it becomes imperative to minimize the contribution made by other species in the system that could influence the observed fluctuations. The approach chosen was to find an algebraic expression comprising the variables used to define the system. Thus, assuming the change in pH is due to the interaction of all the species and protons that play a role in the reaction network, the net rate of proton concentration can be defined as: 𝑑[𝐻"]𝑑𝑡 = 2𝑟+ − 2𝑟G − 2𝑟* Eq. 138 𝑑[𝐻"]𝑑𝑡 = 2𝑘+[𝑇𝑢]![𝐹𝑒)"]! − 2𝑘G[𝐹𝐷𝑆]![𝐻"]! + 2𝑘FG[𝐹𝐷𝑆𝐻"]! − 2𝑘*[𝐹𝐷𝑆𝐻"]![𝐻"]!+ 2𝑘F*[𝐹𝐷𝑆𝐻!!"]! Eq. 139 After substitution and algebraic rearrangement, the net rate for proton concentration can written as: 𝑑[𝐻"]𝑑𝑡 = 2𝑘+[𝑇𝑢]![𝐹𝑒)"]! − 2𝑘+𝑘G𝑘*[𝑇𝑢]![𝐹𝑒)"]![𝐻"]G𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!)+ 4𝑘!𝑘FG𝑘F*[𝐹𝐷𝑆𝐻!!"]!𝑘!𝑘FG + 𝑘*[𝐻"]!(𝑘! + 𝑘G[𝐻"]!) Eq. 140 The purpose of defining the proton concentration net rate was to facilitate the analysis solely in terms of the organic species. However, from a mathematical standpoint, an additional level of complexity is introduced to the system by considering the proton concentration net rate. By considering an additional expression the difficulty to minimize the error of the ODE system and converge to a global solution increases significantly. Therefore, the rate expressions must be simplified to ensure the convergence of the system and obtain a mathematical solution. A weighted overall k value was used as an approximation of the numerical solution for the instantaneous proton concentration. The simulated values obtained for the test where the initial concentration of Tu was varied, Figure 56, are lower than the experimental proton concentration detected. These results support the previous assumption with regards to the influence of intermediate species in fluctuation of the pH measurements. Moreover, the analysis of the proton dependence on the experimental rate constants is facilitated by the lack of fluctuations of the simulated concentration profiles, illustrated by the smooth curves in Figure 57. 84 Figure 57. Model fitting for proton concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations. The aforementioned analysis regarding the dynamic behavior of the main species in solution when the initial conditions of the system are varied demonstrates that even if the ODE system is integrated, having a unique mathematical expression that represents the Tu-Fe3+ system and the determination of an individual rate constant is not possible. In contrast, it is necessary to devote attention to specific limiting conditions, exhibited by the system, which could potentially shed some light on how the reaction regime is shifted as the composition of the solution changes. The variation was assessed by enforcing a rate-determining step. If one step is slower than others, the weight of the slower step does not influence the overall value of the experimental rate constant and the algebraic expression of the rate constant (k1, Tu, k2, Tu, etc.), can be simplified. Six scenarios were proposed to determine if using a rate-controlling step could be used to simplify the overall constant rate expressions. Case 1: Assuming that (k2 + k4[H+]2) >> k5[H+]2 k5[H+]2(k2 + k4[H+]2) » (k2 + k4[H+]2) 85 Case 1.1: Assuming that (k2 + k4[H+]2) >> k5[H+]2 k5[H+]2(k2 + k4[H+]2) » (k2 + k4[H+]2) and k4[H+]2 >> k2 k2 + k4[H+]2 » k4[H+]2 Case 1.2: Assuming that (k2 + k4[H+]2) >> k5[H+]2 k5[H+]2(k2 + k4[H+]2) » (k2 + k4[H+]2) and k2 >> k4[H+]2 k2 + k4[H+]2 » k2 Case 2: Assuming that k5[H+]2 >> (k2 + k4[H+]2) k5[H+]2(k2 + k4[H+]2) » k5[H+]2 Case 2.1: Assuming that k5[H+]2 >> (k2 + k4[H+]2) k5[H+]2(k2 + k4[H+]2) » k5[H+]2 and k4[H+]2 >> k2 k2 + k4[H+]2 » k4[H+]2 Case 2.2: Assuming that k5[H+]2 >> (k2 + k4[H+]2) k5[H+]2(k2 + k4[H+]2) » k5[H+]2 and k2 >> k4[H+]2 k2 + k4[H+]2 » k2 86 Interestingly, Case 2.1 was found to simplify the experimental rate constant for the test where the initial ferric concentration was varied. The analysis reveals that the increase of ferric concentration would facilitate the second protonation step of FDS, Eq. 16. This kinetic feature should follow saturation kinetics, after reaching a certain ferric concentration, the net rate of FDSH22+ formation will be independent of the ferric concentration. The experimental constant rate values converge using Case 1.1, for the tests when the initial concentration of Tu was varied. Under this scenario, the stability of the intermediate species is being enhanced, reaching the highest concentration levels for the maximum [Tu]0 tested in the study, 6 mM. It should be noted that under 6 mM, the calculated data deviates most markedly from the expected behavior of the experimental rate constants. As depicted by Figure 58, the experimental rate constant for the tests when initial pH was varied are best described using Case 2.2. Moreover, the experimental evidence presented in section 2.3.4 further supports this observation. By enhancing the stability of FDSH22+, due to the higher weight of the step k5[H+]2, the rate of formation of Tu from the hydrolysis of FDS is hindered. Therefore, the simulated values of the simplified rate constant yield to satisfactorily predict the dependence of the experimental rate constant with the change in proton concentration present in the system. Figure 58. Experimental rate constant values at 20°C with 10 mM Fe3+, 2 mM Tu, and different initial proton concentration. Red line represents the calculated values, the blue star represents the value used for the simulation of the concentration profile. (a) illustrate the rate constant for Tu, (b) presents the rate constant for FDSH22+. (a) (b 87 The simulated concentration profiles for the tests where the initial Tu concentration was varied are shown from Figure 59 through Figure 61. From an overall perspective, incorporating the hydrolysis of FDSH22+ to the model for the oxidation of Tu in the presence of ferric ions leads to a model that accurately describes the behavior of the system. The simulated values, presented in Figure 60, accurately depict the inflection point of the FDSH22+ species, which is attenuated in the test containing the highest [Tu]0, 6mM. The fact that the values of Tu concentration reached a plateau after 48 h, Figure 59, whilst the ferric concentration continued to decrease, Figure 61, can be attributed to the occurrence of side reactions with the hydrolysis products of FDSH22+, such as TuO2, or the hydrolysis of ferric ions. These discrepancies between the simulated and experimental values can be attributed to the uncertainties in the quantification method used or to a competitive side reaction that contributes to the formation of FDSH22+. Figure 59. Model fitting for thiourea concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. 88 Figure 60. Model fitting for FDSH22+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. Figure 61. Model fitting for Fe3+ concentration at 20°C with 10 mM Fe3+, under indicated [Tu]0 concentrations, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. 89 4.7.1 Temperature dependence of kinetic parameters for the oxidation of thiourea and hydrolysis of FDSH22+ in the presence of ferric ions The temperature-dependent term that will be included in the rate constant for the oxidation of Tu and hydrolysis of FDSH22+ over the range of temperatures studied can be determined using Arrhenius’ law: 𝑘(𝑇) = 𝑘#𝑒FS) TU \1𝑇 − 1𝑇#] Eq. 141 where k0 is the rate constant at the baseline conditions. The linearization of Eq. 141 yields to a fit of the experimental values, which gives a good approximation of the true temperature dependence. The slope for the hydrolysis of FDSH22+ (k2), shown in Figure 62, has a higher value, meaning that the reaction is more sensitive to the change in temperature compared to the chemical oxidation of Tu (k1). The apparent activation energies calculated from experimental data are presented in Table 19. Figure 62. Arrhenius plot for the chemical oxidation of thiourea and hydrolysis of FDSH22+ in the presence of ferric ions. 90 Table 19. Apparent activation energies for the chemical oxidation of thiourea and hydrolysis of FDSH22+ in the presence of ferric ions Effect Slope R2 EA (kJ mol-1) k1 -7092.97 9.97E-01 58.97 k2 -13749.16 9.38E-01 114.31 The concentration profiles of the simulated and experimental data for Tu and FDSH22+ are presented in Figure 63 and Figure 64, respectively. It can be observed that the model deviates from the experimental data most markedly at 50°C. The two main culprits to explain this behavior are the analytical error and the denaturation of the organic phases that could result in the formation of sulfur precipitates as discussed in section 2.3.3. Figure 63. Model fitting for thiourea concentration at indicated temperatures with 10 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. 91 Figure 64. Model fitting for FDSH22+ concentration at indicated temperatures with 10 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. 4.7.2 Kinetic model summary The key fundamental observations outlined in sections 4.3 and 4.4 regarding the limited capabilities of the analytical method must be addressed to overcome the shortcomings of the current model. For instance, the tracking of species comprised in the system was solely based on the quantification of Tu and FDSH22+concentrations given the experimental data available. In general, any fit can always be improved with a larger number of estimated parameters. Having an analytical technique that would allow us to determine the concentration profiles of all the species present in the system could conceivably improve the predictive capabilities of the model. Further, the least-square minimization approach is error-prone, especially in the presence of noisy experimental data. It is often difficult to ascertain if the parameters that are searched for (adjusted kinetic parameters) are uniquely found. Thus, even if the solution is unique may not depend continuously on the data. Even a small deviation in the data, due to the uncertainties of the experimental measurements, might be significantly amplified once the error of the system is minimized to calculate the kinetic parameters. 92 To improve the predictive capabilities of the model, the effect of the FDSH22+ hydrolysis in ferric media should be studied in a more comprehensive manner. Thus, it is imperative to develop an analytical procedure for accurate detection and quantification of the intermediate species, such as TuO/TuOH, in the presence of ferric. Moreover, the preliminary results from sections 3.3.1 and 3.3.3 were used to demonstrate the relevance of the findings discussed thus far and to assess the validity of the model whilst challenging its predictive capabilities under a wider range of conditions. Is noteworthy to remember that these experiments were carried out with an initial 40 mM Fe3+ concentration, which is 4 times the highest value used for the estimation of the kinetic parameters in the model, and 2 mM Tu. Figure 65 and Figure 66 show the predictive capabilities of the model for Tu and FDSH22+ concentrations, where the only parameters needed as inputs, to predict the data, were the initial conditions such as [Tu]0, [Fe3+]0, initial pH, and the temperature at which the experiments were carried out. As can be observed from Figure 65, the behavior of Tu in ferric media is successfully described by the kinetic rate expressions developed in this study under baseline conditions. As the temperature increases, the differences between the measured and predicted data can be attributed to a number of reasons, including the fact that the denaturation of the organic phase is accentuated at higher temperatures which could lead to formation/precipitation of sulfur. 93 Figure 65. Model fitting for thiourea concentration at indicated temperatures with 40 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. Figure 66. Model fitting for FDSH22+ concentration at indicated temperatures with 40 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. 94 Another reason for discrepancies between the model and experimental data is the fact that in the presence of over 2 g/L of Fe (40 mM Fe3+) the hydrolysis of ferric in solution is highly influenced by the increase of temperature, generating an array of changes in proton concentration and the potential precipitation of ferric hydroxide compounds such as jarosite. The formation of precipitates and the indirect loss of Tu due to co-precipitation or adsorption on the surface are important topics that the model does not yet address. Regardless of these considerations, the models developed herein provide an adequate fit of the trace data. In fact, in the absence of meaningful experimental data pertaining to the tests at high ferric concentration, due to its contribution in terms of the absorbance values that result in broader peaks which limit the quantification of species, the systematic approach followed to develop the kinetic rate expressions by species allows to accurately predict the progression of the reaction in terms of their main constituents as shown in Figure 67. The proposed rate expressions are the first serious attempt at integrating the two main processes occurring in solution into a single expression. The findings of this study just begin to unravel the influence that different factors present in solution exert on the catalyst stability, besides establishing general guidelines for future research. Figure 67. Model fitting for thiourea species and ferric concentrations at 20°C with 40 mM Fe3+, 2 mM [Tu]0 concentration, initial pH 1.7, including the chemical oxidation of thiourea and the hydrolysis of FDSH22+. 95 5 General conclusions 5.1 Conclusions and overall significance of the research The research work presented in this study addresses the lack of information of the behavior of thiourea in ferric sulfate media. To do so, the analysis focuses exclusively on the less well understood non-linear aspect of the whole chemical pathway for the oxidation of Tu in the presence of ferric and the concomitant process, the hydrolysis of FDSH22+. The oxidation kinetics of Tu have been studied using standard batch reactor tests. Of the four factors tested (pH, temperature, Tu concentration, and ferric concentration), the effects of temperature and the change in pH were the most significant. Increasing the temperature over 35°C, in acidic ferric media, results in an average 75% of Tu consumption during the first 48 h. Further, the significance of these factors was well defined by statistical means. Based on the regression model, pH was the key factor enhancing the oxidation of Tu with an estimated weight factor of -2.45. In the case of FDSH22+ the Tu concentration has a positive effect with an estimated weight of 0.09, whilst the ferric concentration was predicted to be 0.03. A direct dependence between the Tu and the ORP measurements was observed in the tests with 10 mM Fe3+ and under various [Tu]0. These results confirmed the assumption that in the presence of Tu, the ORP is not solely controlled by the Fe3+/Fe2+ and the Tu/FDS couple may also play an important role. This investigation into the chemical stability and oxidation of Tu in ferric media demonstrated that Tu presents a rich and dynamic behavior. In this highly complex system, the oxidation reactions occurring in a series/parallel manner seem to play a key role in the formation of intermediate species which influences the final concentrations. Further, the evidence suggests that the stability traits of Tu in acidic ferric media can be greatly influenced by specific conditions of the system. With this in mind, a simplification of the system by assuming rate-determining steps is now a valid approach to determine the rate of oxidation of Tu. It could be argued that the lack of a single expression to define the system gives less credibility to the predictive capabilities of the model. However, despite the absence of meaningful experimental data pertaining to the tests performed at high ferric concentration, 40 mM, the systematic approach followed to develop the kinetic rate expressions by species, allows to accurately predict the progression of the reaction in terms of their main constituents. The proposed rate expressions are the first serious attempt at integrating the two main processes occurring in solution, oxidation of Tu and hydrolysis of FDSH22+, into a single expression. Therefore, the 96 findings of this study just begin to unravel the influence that different factors present in solution exert on the stability of Tu, besides establishing general guidelines for future research. 97 5.2 Recomendations for future work Based on the results presented in this study, the following ideas are suggested for further investigation: In this project, the stability of Tu was studied in both acidic and ferric sulfate media. However, the quantification of all the possible oxidation products was not attained. Thus, it is imperative to develop an analytical procedure for accurate detection and quantification of the intermediate species, such as TuO/TuOH, in the presence of ferric. 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ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [Cy]0, and initial pH 1.7 Figure B - 2. ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [TuO2]0, and initial pH 1.7. 109 Figure B - 3. ORP and pH measurements at 20°C with 40 mM Fe3+, 2 mM [Urea]0, and initial pH 1.7. 110 Appendix C Figure C - 1. Measured ferric concentrations at 20°C with 10 mM Fe3+, under the indicated [Tu]0 concentrations, and initial pH 1.7. Figure C - 2. ORP measurements at 20°C with 10 mM Fe3+, under the indicated [Tu]0 concentrations, and initial pH 1.7. 111 Figure C - 3. Measured ferric concentrations at 20°C with 2 mM [Tu]0, under indicated [Fe3+]0 concentrations, and initial pH 1.7. Figure C - 4. ORP measurements at 20°C with 2 mM [Tu]0, under indicated [Fe3+]0 concentrations, and initial pH 1.7. 112 Figure C - 5. Measured ferric concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0 and under indicated initial pH. Figure C - 6. Measured ferric concentrations with 10 mM Fe3+, 2 mM [Tu]0, under indicated temperatures and at initial pH 1.7. 113 Appendix D Figure D - 1. Ratio of final concentrations at 20°C with 2 mM [Tu]0 under different [Fe3+]0 concentrations, and initial pH 1.7. Figure D - 2. Ratio of final concentrations at 20°C with 10 mM Fe3+, 2 mM [Tu]0, and under different [H+]0 concentrations. 114 Figure D - 3. m ratio values at 20°C with 2 mM [Tu]0, under different [Fe3+]0 concentrations, and initial pH 1.7. Figure D - 4. m ratio values at 20°C with 10 mM Fe3+, 2 mM [Tu]0, and under different [H+]0 concentrations. 115 Figure D - 5. Model fitting for FDSH22+ concentration assuming power-law rate reaction at 20°C under indicated [Tu]0 concentrations. Figure D - 6. Linear relationship of ki values at 20°C with 2 mM [Tu]0, under different [Fe3+]0 concentrations, and initial pH 1.7. 116 Figure D - 7. Linear relationship of ki values at 20°C with 10 mM Fe3+, under different [H+]0 concentrations, and 2 mM [Tu]0. Figure D - 8. Model fitting for thiourea concentration at 20°C, under indicated [Fe3+]0 concentrations, and initial pH 1.7. 117 Figure D - 9. Model fitting for FDSH22+ concentration at 20°C, under indicated [Fe3+]0 concentrations, and initial pH 1.7. Figure D - 10. Model fitting for Fe3+ concentration at 20°C, under indicated [Fe3+]0 concentrations and initial pH 1.7 118 Figure D - 11. Model fitting for thiourea concentration at 20°C with 10 mM Fe3+ under indicated initial pH. Figure D - 12. Model fitting for FDSH22+ concentration at 20°C with 10 mM Fe3+ under indicated initial pH. 119 Figure D - 13. Model fitting for Fe3+ concentration at 20°C, under indicated initial pH.
Thesis/Dissertation
eng
Materials Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Fundamental study of the chemical stability and oxidation of thiourea in acidic ferric media
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