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The Reactions of Osmium(VIII) in Hydroxide Medium By Theodor Earl Geswindt Submitted in fulfilment of the requirements for the degree of Magister Scientiae at the Nelson Mandela Metropolitan University January 2009 Supervisor: Prof. H. E. Rohwer I ACKNOWLEDGEMENTS I am deeply grateful to my supervisor, Professor H. E. Rohwer, for his encouragement, advice, guidance and thoughtful discussions. I would also like to express my sincere thanks to: Dr Willem Gerber for his time, effort and knowledgeable insight. Dr Eric Hosten and Henk Schalekamp – my poor proof-readers. Anglo Platinum Research Centre, the Nelson Mandela Metropolitan University and the Inorganic Chemistry Department for financial assistance. My parents for all their love and support. Evron for all her love and endless moral support. God for making all things possible. II TABLE OF CONTENTS Acknowledgements I Table of Contents II List of Figures VI List of Tables XI Abbreviations XII Summary XIII CHAPTER 1 Introduction 1.1 History of osmium 1 1.2 Extraction of osmium 2 1.3 Applications of osmium 4 1.4 General coordination chemistry 5 1.4.1 The Common oxidation states of osmium 6 1.4.2 Coordination numbers 7 1.4.3 Coordinating ligands 8 1.5 Aims and objectives 9 CHAPTER 2 Experimental 2.1 Apparatus 10 2.1.1 UV-Vis spectrophotometric recordings 10 2.1.2 Mole ratio titrations 11 2.1.3 Potentiometric titrations 12 2.1.4 pH measurements 12 2.1.5 Potentiometric measurements 12 2.1.6 Preparation of solutions 12 2.2 Computer hardware and software 13 2.3 Reagents utilised 14 2.4 Standardisation methods 16 III 2.4.1 Standardisation of acids 16 2.4.2 Preparation of a standard sodium hydroxide solution 16 2.5 Preparation and storage of osmium tetroxide 16 2.5.1 Introduction 16 2.5.2 Preparation procedure 17 2.5.3 Preparation of aqueous osmium tetroxide 19 2.6 Preparation of potassium osmate 19 2.7 Determination of osmium concentration – the thiourea colourimetric method 20 2.7.1 Introduction 20 2.7.2 The effect of varying thiourea concentration on the formation of the [Os(NH2CSNH2)6]3+ species 22 2.7.2.1 Literature review 22 2.7.2.2 Experimental procedures 22 2.7.2.3 Results and discussion 23 2.7.3 The effect of varying hydrochloric acid concentration on the formation of the [Os(NH2CSNH2)6]3+ species 25 2.7.3.1 Literature review 25 2.7.3.2 Experimental procedures 26 2.7.3.3 Results and discussion 28 2.7.4 The osmium – thiourea calibration curve 36 2.7.4.1 Literature review 36 2.7.4.2 Experimental procedures 36 2.7.4.3 Results and discussion 37 CHAPTER 3 The alcohol reduction of osmium(VIII) in hydroxide medium 3.1 Introduction 37 3.2 Isosbestic points 46 3.3 The stability of osmium(VIII) in a 2M hydroxide matrix 47 3.3.1 Literature review 47 3.3.2 Experimental procedures 50 IV 3.3.3 Results and discussion 51 3.4 The reduction of osmium tetroxide by aliphatic alcohols in a 2M hydroxide matrix 55 3.4.1 Literature review 55 3.4.2 Experimental procedures 56 3.4.3 Results and discussion 59 3.5 The geometrical analysis of kinetic data using Mauser diagrams 67 3.5.1 Literature review 67 3.5.2 Experimental procedures 71 3.5.3 Development of computational software for data analysis 71 3.5.4 Results and discussion 73 3.6 The osmium(VIII) – alcohol kinetic model 77 3.6.1 Literature review 77 3.6.2 Experimental procedures 78 3.6.3 Computational software utilised for kinetic modelling 79 3.6.4 Results and discussion 81 CHAPTER 4 The osmium(VIII)-osmium(VI) equilibrium reaction 4.1 Introduction 93 4.2 The stability of osmium(VI) in a 2M hydroxide matrix 94 4.2.1 Literature review 94 4.2.2 Experimental procedures 94 4.2.3 Results and discussion 96 4.3 The osmium(VIII) – osmium(VI) reaction 4.3.1 Literature review 100 100 4.3.1.1 Job’s method of continuous variation 100 4.3.1.2 Mole ratio titrations 104 4.3.2 Experimental procedures 104 4.3.2.1 Job’s method of continuous variation 104 4.3.2.2 Mole ratio titrations 105 4.3.3 Computer software used for simulating mole ratio titrations 106 V 4.3.4 Results and discussion 107 4.3.4.1 Job’s method of continuous variation 107 4.3.4.2 Mole ratio titrations 113 4.4 Conclusion 116 CHAPTER 5 Conclusion 5.1 Determination of osmium concentration 117 5.2 The osmium(VIII) – alcohol reaction 117 5.3 The osmium(VIII) – osmium(VI) complexation 120 APPENDIX Development of the program GP2 A.1 Introduction 123 A.2 Listing of the program GP2 126 REFERENCES 127 VI LIST OF FIGURES Chapter 1 Figure 1.1: Page Extraction of four of the platinum group metals from platinum ore concentrates; a simplified overall scheme. The path highlighted in red indicates the reaction investigated during this study. 3 Chapter 2 Figure 2.1: Illustration of the experimental system employed to record UV-Vis spectra at constant temperatures Figure 2.2: 11 Illustration of the experimental setup used during the preparation of a pure OsO4 solution Figure 2.3: 18 UV-Vis spectra illustrating the formation of the [Os(NH2CSNH2)6] 3+ species as a function of thiourea concentration. The direction of the solid arrows indicates increasing thiourea concentration. [HCl] = 5.091 mol/L; -4 [Osmium] = 1.051 × 10 mol/L; solutions were equilibrated for 8 days at 25°C Figure 2.4: 23 The change in absorbance at 490 nm as a function of thiourea concentration, indicating the large excess of thiourea required for the complete conversion of 2- 3+ [OsCl6] to the [Os(NH2CSNH2)6] species. The ratio of thiourea:osmium should 2- 3+ be at least 4300:1 in order for full conversion of [OsCl6] to [Os(NH2CSNH2)6] . Figure 2.5: UV-Vis spectra of the [OsCl6] reduction by thiourea as a function of HCl -4 concentration. [Thiourea] = 0.657 M; [Osmium] = 1.871 × 10 M Figure 2.6: 28 The change in absorbance at selected wavelengths as a function of HCl -4 concentration. [Thiourea] = 0.657 M; [Osmium] = 1.871 × 10 M Figure 2.7: 24 2- 29 2- UV-Vis spectra depicting the reduction of [OsCl6] by thiourea as a function of HCl concentration at an ionic strength of 6 M. The solid arrows indicate the direction of increasing [HCl]. The [HCl] ranges from 0.750 M to 5.250 M; -4 2- [Osmium] = 2.103 × 10 M. The spectrum of pure [OsCl6] is included for comparison. Figure 2.8: 30 - The absorbance at selected wavelengths as a function of the mole fraction Cl - ClO4 ] Figure 2.9: The absorbance at selected wavelengths as a function of [mole Cl / mole Figure 2.10: UV-Vis spectra depicting the reduction of osmium tetroxide by thiourea as a 31 31 function of HCl concentration at an ionic strength of 6 M. [Thiourea] = 0.657 M; -5 [Osmium] = 6.554 × 10 M; [HCl] ranges from 0.500 M to 6.000 M Figure 2.11: 33 The change in absorbance at selected wavelengths as a function of HCl concentration 33 VII Figure 2.12: UV-Vis spectra of the standard ammonium hexachloroosmium(IV)-thiourea solutions recorded after 8 days at 25°C. [Thiourea] = 0.657 M; [HCl] = 5.091 M; the respective osmium concentrations are noted in the figure. Figure 2.13: 37 The calibration curve obtained through the thiourea colourimetric method. Calibration curve constructed from the absorbance data at 490 nm 38 Figure 3.1: The generally accepted mechanism for the oxidation of alkenes to cis-diols 40 Figure 3.2: (a) syn- and (b) anti- dimeric monoesters, (c) monomeric diester 41 Figure 3.3: Proposed pathways (a and b) for the reaction of organic reductant (R) with osmium Chapter 3 tetroxide Figure 3.4: 42 The mechanism proposed by Sharpless et al involving nucleophillic attack by the C – C double bond on the electropositive osmium 43 Figure 3.5: Proposed reaction scheme for the oxidation of alcohols by osmium tetroxide 43 Figure 3.6: Mechanism of alcohol oxidation by chromic acid (Westheimer’s “ester mechanism”) 45 Figure 3.7: The UV-Vis spectra of OsO4 in both CCl4 and water, obtained during this study. The spectrum of gaseous OsO4 is included for comparison 48 Figure 3.8: Species distribution diagram for OsO4 as a function of pH 49 Figure 3.9: The change in the UV-Vis spectrum of osmium(VIII) in 2 mol/L NaOH as a function of time, from t = 0 hour to t = 625 hours. The spectra change in the direction of the -4 solid arrows over time. [Osmium] = 1.305 × 10 mol/L Figure 3.10: 51 Progress curve depicting the rate of change of absorbance at 370 nm. -4 [Osmium] = 1.305×10 mol/L; [NaOH] = 2 mol/L Figure 3.11: 52 -4 The spectra isolated during the reduction of 1.305 × 10 mol/L osmium(VIII) in -4 2 mol/L NaOH. The spectrum of a 1.305 × 10 mol/L osmium(VI) solution in 2 mol/L NaOH is included for comparison. Figure 3.12: 54 The change in the osmium(VIII) optical spectrum as a function of time, from t = 0 to -3 t = 986 minutes, upon addition of 1.00 × 10 mol/L methanol. The spectra denoted by A, B, and C respectively refer to the spectra recorded at t = 0, t = 34 and t = 986 minutes. The solid arrow indicates the direction of absorbance change with time. The solid and dashed lines indicate the occurrence of two isosbestic points. -4 - [Osmium] = 1.305 × 10 mol/L; [OH ] = 2 mol/L Figure 3.13: 59 Illustration of the isosbestic points formed during the reduction of osmium tetroxide by methanol in 2 mol/L hydroxide medium. (a) The first transient isosbestic point occurs at 274 nm as indicated by the dashed line; (b) the second isosbestic point occurs at 258 nm as indicated by the solid line Figure 3.14: 60 Progress curves demonstrating the rate of change of the absorbance at 370 nm at -4 different methanol concentrations. [Osmium] = 2.631 × 10 mol/L; [NaOH] = 2 mol/L; Methanol concentrations are denoted by the legend. 62 VIII Figure 3.15: (a) Spectra isolated at various times during the reduction of osmium(VIII) by -4 -3 methanol. [Osmium] = 2.631 × 10 mol/L; [Methanol] = 1.00×10 mol/L; [NaOH] = 2 mol/L. (b) A comparative reduction reaction conducted in the absence -4 of methanol. [Osmium] = 1.305 × 10 mol/L; [NaOH] = 2 mol/L. In both figures the times at which these spectra were recorded are denoted in the legend. Figure 3.16: 63 Progress curves indicating the rate of change of the absorbance at 370 nm for various methanol concentrations. The progress curve depicting the reaction of osmium(VIII) with 0 mol/L methanol was superimposed onto the progress curves for those reactions involving varying methanol concentrations. -4 [Osmium] = 2.631 × 10 mol/L; [NaOH] = 2 mol/L; methanol concentrations are denoted by the legend. Figure 3.17: 64 Progress curves illustrating the change in absorbance at 370 nm as a function of time for the reaction between osmium tetroxide and varying ethanol -4 concentrations. [Osmium] = 2.590 × 10 mol/L; [NaOH] = 2 mol/L; ethanol concentrations are denoted in the legend. Figure 3.18: 65 Progress curves illustrating the change in absorbance at 370 nm as a function of time for the reaction between osmium tetroxide and varying propan-1-ol -4 concentrations. [Osmium] = 2.285 × 10 mol/L; [NaOH] = 2mol/L; propan-1-ol concentrations are denoted by the legend. Figure 3.19: 65 Progress curves illustrating the change in absorbance at 370 nm as a function of time for the reaction between osmium tetroxide and varying butan-1-ol -4 concentrations. [Osmium] = 2.212 × 10 mol/L; [NaOH] = 2 mol/L; butan-1-ol concentrations are denoted by the legend. ↔B↔C Figure 3.20: Typical 2-dimensional Mauser diagram for the general reaction A Figure 3.21: The change in the Osmium (VIII) optical spectrum as a function of time, upon 66 70 -3 addition of 1.00 × 10 mol/L methanol. The spectra denoted by A, B and C respectively refer to the spectra recorded at t = 0, t = 34 and t = 986 minutes. The solid arrow indicates the direction of increasing time. -4 - [Osmium] = 1.305 × 10 mol/L; [OH ] = 2 mol/L Figure 3.22: 73 [a] 3D Mauser diagram of A370 vs. A240 vs. A280 (the indices indicate the wavelengths used). [b] Rotation of part [a]. The curve lies on a single plane, and is viewed along the edge of this plane. The result is a straight line indicating the case s = 2. 74 Figure 3.23: A 2D Mauser diagram constructed from the data presented in Figure 3.21. 75 Figure 3.24: Molar extinction spectrum for the Os(VII)-Intermediate species, calculated using the program GP2. 76 IX Figure 3.25: Comparison between the theoretical fits obtained for [a] methanol and [b] propan1-ol, based on Model 4. The comparison illustrates the pronounced effect that a loss of kinetic data has on the theoretical fit. Symbols = Experimental data; -4 Lines = Theoretical fit. [a] [Osmium] = 2.631 × 10 mol/L; -3 -4 [Methanol] = 15 × 10 mol/L. [b] [Osmium] = 2.285 × 10 mol/L; [Propan-1-3 ol] = 15 × 10 mol/L. 87 Figure 3.26: 2D Mauser diagram interpreted in terms of the proposed kinetic model, Model 4. 89 Figure 3.27: The E2 C – H bond cleavage reaction mechanism 90 Figure 3.28: The hydride transfer reaction mechanism – from the associative reaction of the primary alcohol molecule with the osmium(VIII) centre, leading to the formation of the osmate ion and the aldehyde. 91 Chapter 4 Figure 4.1: 2- The change in the UV-Vis spectrum of [OsO2(OH)4] upon exposure to an oxygen atmosphere, as a function of time. The dashed arrows respectively depict the spectra recorded at t = 0 min and t = 2868 min. The solid arrow indicates the -4 direction of increasing time. [Osmium] = 5.278 × 10 mol/L; [NaOH] = 2 mol/L Figure 4.2: The change in absorbance at 300 and 350 nm as a function of time under oxygen -4 atmosphere. [Osmium] = 5.278 × 10 mol/L; [NaOH] = 2 mol/L Figure 4.3: 97 2- The change in the UV-Vis spectrum of [OsO2(OH)4] upon exposure to a nitrogen -4 atmosphere. [Osmium] = 4.578 × 10 mol/L; [NaOH] = 2 mol/L Figure 4.4: 98 The change in absorbance at 300 and 350 nm as a function of time under nitrogen -4 atmosphere. [Osmium] = 4.578 × 10 mol/L; [NaOH] = 2 mol/L Figure 4.5: 96 98 The change in absorbance spectra as a function of increasing [Os(VI)]i / [Os(VIII)]i ratio at pH 14.3. The spectra denoted [1], [14] and [29] corresponds to the [Os(VI)]i / [Os(VIII)]i ratios 0.03, 0.94 and 30.00 respectively. -4 [Os(VI)] + [Os(VIII)] = 3.485 × 10 mol/L Figure 4.6: 107 -4 The UV-Vis spectra of 3.485 × 10 mol/L OsO4 in a 2 mol/L NaOH matrix; -4 3.485 × 10 mol/L potassium osmate in a 2 mol/L NaOH matrix; the experimentally -4 observed spectrum obtained from the reaction between 1.799 × 10 mol/L -4 osmium(VIII) with 1.686 × 10 mol/L potassium osmate in a 2 mol/L NaOH matrix; the theoretically calculated addition spectrum between osmium(VIII) and potassium osmate; and a comparison of the intermediate species’ spectrum obtained by reacting osmium(VIII) with methanol in a 2 mol/L NaOH matrix. Figure 4.7: 108 Non-equimolar Job diagram illustrating complex formation between osmium(VIII) and osmium(VI) in a 2 mol/L NaOH matrix. -4 -4 [Os(VI)] + [Os(VIII)] = [1] 3.485 × 10 mol/L; [2] 7.000 × 10 mol/L 109 X Figure 4.8: Job diagram depicting the complex formation between osmium(VIII) and osmium(VI) in a 2 mol/L NaOH matrix. The theoretical fits were simulated on a 1:1 -4 complexation model. [Os(VI)] + [Os(VIII)] = 3.485 × 10 mol/L. Symbols = experimental data; Lines = calculated fits. Figure 4.9: 110 Correcting a Job plot for the absorbance of the reacting components, as reported in literature. Lines [2] and [3] is subtracted from plot 1 to obtain plot 4. Experimental data are from an osmium(VIII) – osmium(VI) Job plot at pH 14.3. -4 [Os(VI)] + [Os(VIII)] = 3.485 × 10 mol/L Figure 4.10: 111 Absorbance curves from several osmium(VIII) vs. osmium(VI) mole ratio titrations in a 2 mol/L NaOH matrix. Linear regressions were drawn though the linear regions of the curves to obtain the point of intersect. The initial osmium(VIII) concentration is denoted in the legend. Figure 4.11: 113 Volume corrected absorbance curves from osmium(VIII) vs. osmium(VI) mole ratio titrations in a 2 mol/L NaOH matrix. The calculated curves were simulated on a 1:1 complexation model. The initial osmium(VIII) concentrations are denoted in the figure. Symbols = experimental data; Lines = calculated fits Figure 4.12: Species distribution curves of an osmium(VIII) vs. osmium(VI) titration in a 2 mol/L -4 Figure 4.13: 114 NaOH matrix. [Os(VIII)] = 2.327 × 10 mol/L 115 The formation of the dimeric osmium(VII) species 116 Program interface after data selection 124 Appendix Figure A 1: XI LIST OF TABLES Chapter 1 Table 1.1: Page The more unusual coordination numbers for osmium 7 Chapter 2 Table 2.1: Computer platform used for kinetic and equilibrium calculations 13 Table 2.2: Reagents utilised during this study 14 Chapter 3 Table 3.1: The second order rate constants for the oxidation of several alcohols by -4 osmium(VIII) in a hydroxide matrix; [Osmium] = 3.16 × 10 mol/L, - [OH ] = 0.05 mol/L, Temp = 305 K Table 3.2: Reactant volumes and concentrations for the reaction of osmium tetroxide with methanol in a 2 mol/L hydroxide matrix Table 3.3: 58 Calculated rate constants and molar extinction coefficients for the reduction of osmium(VIII) by several primary alcohols at pH 14.3, based on Model 4 Table 3.4: 44 87 Comparison between the molar extinction coefficient (at various wavelengths) of the Os2(VII) species calculated from a least squares [LS] method and Mauser diagrams [MD] 88 Chapter 4 Table 4.1: The molar extinction coefficients and averaged equilibrium constant calculated at various wavelengths through Job’s method of continuous variation. Table 4.2: 112 Comparison of the molar extinction coefficients and equilibrium constant obtained from mole ratio studies and Job diagrams at 400 nm 115 Chapter 5 Table 5.1: Comparison of the equilibrium constant and molar extinction coefficients calculated through several computational methods. MD = Mauser diagrams; LS = Least square analysis; JD = Job diagrams; MR = Mole ratio titrations 121 XII ABBREVIATIONS ETAAS electrothermal atomic absorption spectroscopy HCl hydrochloric acid HClO4 perchloric acid ICP-MS inductively coupled plasma mass spectrometry m/v mass per volume mL millilitre M mol per litre mol/L mol per litre NaOH sodium hydroxide UV-Vis ultraviolet – visible v/v volume per volume XIII SUMMARY Spectrophotometric techniques were used to elucidate the discrepancies surrounding the reduction of osmium tetroxide by several primary alcohols in a hydroxide matrix. In contrast to the documented literature, this reaction was observed to occur in two consecutive reaction steps. Geometrical and computational analysis of kinetic data revealed that the reaction proceeds by the following reaction model: Os(VIII) + RCH2OH Os(VIII) + Os(VI) k1 k+2 k-2 Os(VI) + RCHO Os2(VII) The conditional rate constants and molar extinction coefficients were calculated using custom written software. A hydride transfer mechanism, coupled with the synchronous removal of the hydroxyl proton of the alcohol, was postulated. The complexation between osmium(VIII) and osmium(VI) was investigated. Mole ratio titrations and mole fraction plots show that at pH 14.3 a 1:1 complexation occurs between osmium(VIII) and osmium(VI). The equilibrium constants and molar extinction coefficients calculated by these methods were found to be consistent with the parameters obtained from the reduction of osmium tetroxide by primary alcohols at pH 14.3. The formation of a mixed oxidation state dimeric osmium complex (denoted Os2(VII)) has been proposed. Key words: Spectrophotometric techniques, osmium tetroxide, osmium(VIII), primary alcohols, osmium(VI). 1 CHAPTER 1 Introduction 1.1 History of Osmium Osmium, so named by its discoverer Smithson Tennant, from the characteristic odour of its tetroxide (derived from the Greek word osme – smell, odour). Tennant, who was Professor of Chemistry at the University of Cambridge, discovered the new element in 1803 and announced it in 1804. He had heated (to red heat with caustic soda) the insoluble black residues which were left after the digestion of native platinum by aqua regia, and dissolved the resulting mass in water. The yellow filtrate was acidified, which led to the evolution of a white, volatile oxide, of which Tennant wrote[1]: “It stains the skin of a dark colour which cannot be effaced… (it has) a pungent and penetrating smell… from the extrication of a very volatile metal oxide… this smell is of its most distinguishing characters, I should on that account incline to call the metal Osmium” In this latter statement, it is interesting to note that Tennant had earlier proposed to call the element ptène (from ptenos – meaning volatile), but was persuaded to abandon this idea [1]. The “volatile metal oxide” Tennant referred to was osmium tetroxide, which is now known to have highly toxic effects, as documented by Brunot [2], who exposed himself to the toxic vapours in order to ascertain its toxicity. Upon exposure to the osmium tetroxide vapour he noticed a metallic taste in his mouth and found that smoking was unpleasant; after 30 minutes his eyes were smarting and tearing; after three hours his chest was constricted and he had difficulty breathing and on going outside he noticed large haloes around street lights. Subsequent research into the toxicity of osmium tetroxide revealed that the unpleasant side effects experienced by Brunot were a result of the reduction of osmium tetroxide onto the eyes, skin, and mucosa of the airways. 2 Concentrations in the air as low as 10-7 g.m-3 can cause lung congestion, skin and severe eye damage[3]. Due to its toxicity, every care must be taken when working with osmium in all its forms, since it can be oxidised by atmospheric oxygen to the tetroxide. 1.2 Extraction of Osmium The modern method for extracting the element does not differ greatly from the Tennant’s original procedure[1]. Platinum bearing concentrates are extracted with aqua regia and the insoluble portion heated in an oxidising flux such as sodium peroxide. The residue is extracted with water. The insoluble fraction is treated for rhodium and iridium while the soluble fraction contains perosmate, [OsO4(OH)2]2-, and ruthenate, [RuO4]2-, ions. At this stage, the osmium is removed with nitric acid, producing the volatile tetroxide. Alcohol can be added to the alkaline solution, which precipitates the ruthenium as the hydrated dioxide and reduces the perosmate to the soluble violet potassium osmate, K2[OsO2(OH)4]. This reaction route is highlighted in Figure 1.1. The potassium osmate can be precipitated by the addition of concentrated potassium hydroxide, which can be acidified to produce the volatile osmium tetroxide. Potassium osmate can also be treated with an alcohol-hydrochloric acid-ammonium chloride mixture to produce the ammonium hexachloroosmate(IV). The latter species may then be heated in an inert atmosphere in a graphite vessel to give the pure metal, which could also be obtained by reduction of osmium tetroxide in hydrogen. Figure 1.1 depicts a simplified overview of the industrial separation of four platinum group metals (rhodium, osmium, ruthenium and iridium) from platinum metal concentrates. The highlighted path indicates the reaction which would be under investigation during this study. 3 Insoluble residue from treatment of platinum metal concentatrates with aqua reagia is smelted with lead carbonate and then treated with nitric acid to remove silver as the nitrate. For ores of low rhodium content the bisulphate step is omitted Insoluble residue Fuse with NaHSO4 (500°) Insoluble Soluble Fuse with Na2O2 (500°) Rh2(SO4)3•aq Soluble NaOH Rh(OH)3•aq Insoluble residue of IrO2•aq [OsO4(OH)2]2- + [RuO4]2- HCl KOH C2H5OH H3[RhCl6]•aq Soluble NaNO2 + NH4Cl (NH4)3[Rh(NO2)6] [OsO2(OH)4]2- HCl NH4+ HNO3 (NH4)3[RhCl6] OsO4 H.COOH H2 at 1000° HCl, NH4+ C2H5OH Rhodium (NH4)2[OsCl6] H2 at 1000° Osmium HCl, HNO3, NH4+ Insoluble RuO2•aq HCl H2[RuCl6]•aq Cl2 (NH4)2[IrCl6] H2 at 1000° Iridium RuO4 HCl, NH4+ (NH4)3[RuCl6] H2 at 1000° Ruthenium Figure 1.1: Extraction of four of the platinum group metals from platinum ore concentrates; a [1] simplified overall scheme . The path highlighted in red indicates the reaction investigated during this study. 4 1.3 Applications of Osmium Due to its density (22.587 ± 0.009 g.cm-3), osmium is frequently used in small quantities in alloys where frictional wear must be minimised. These alloys are typically used in ballpoint pen tips, fountain pen tips, record player needles, electrical contacts and high pressure bearings. It is therefore not surprising that osmium is no longer considered industrially important, considering this list of applications. A less dated application of osmium is in the platinum/osmium (in a 90:10 ratio) alloy used in implants such as pacemakers and replacement valves[4]. This alloy is used predominantly due to its resistance to corrosives, but is difficult and expensive to manufacture. Osmium tetroxide, although highly toxic, is still used as a biological fixative, for the preservation of biological tissue and its delineation for optical and electronic microscopy[5]. The most useful application of osmium tetroxide is its ability to act as a catalyst in organic oxidation reactions. The most famous of these reactions is the industrially important cis-hydroxylation of alkenes; in which osmium tetroxide selectively cis-hydroxylate unsaturated organic compounds. 5 1.4 General Coordination Chemistry Osmium is considered as the most versatile of all the platinum group metals, even more so than Rhenium and Ruthenium. This is exhibited through the wide array of oxidation states (VIII to –II) displayed by its complexes. The major reason for its versatility is primarily due to the position that osmium assumes within the group of transition metals in the period table[6]. As a member of the third row of transition metals, the outer 5d orbitals are fairly exposed, effectively increasing the susceptibility of the electronic occupancy of the 5d orbitals to the coordinating ligands. In addition, its central position within the third row transition metals implies the attainment of[6]: o the d0 electronic configuration typical of the elements to the left of osmium in the periodic table o the d10 electronic configuration typical of the elements to the right of osmium in the period table Osmium can thus be classified as a metal which adopts various oxidation states through the nature of the coordinating ligands, making the chemistry of osmium unique and dynamic. High oxidation state osmium (the VIII, VII and VI oxidation states) is associated with strong σ- and π-donor ligands such as F-, O2- and N3-, since these ligands tend to form stable complexes with ions possessing few or no d-electrons. Medium oxidation state osmium (the V, IV and III oxidation states) is associated with ligands having σ-donating capabilities such as NH3, halides (F-, Cl-, Br- and I-) and ethylenediamine[6]. Low oxidation state osmium (the II to -II oxidation states) is associated with ligands having strong π-acceptor capabilities such as CO and NO+, while ligands with moderate πacceptor capabilities (e.g. CN-) will tend to favour the osmium(II) (d6) oxidation state. 6 1.4.1 The Common Oxidation States of Osmium[6] Osmium(II) Osmium(II) is a d6 ion, generally with a spin-paired (t2g6) electron configuration and is therefore considered as diamagnetic. Generally, octahedral complexes are formed, although five- and seven-coordinate complexes are known to exist. Osmium(II) complexes are easily oxidised through atmospheric oxygen, although it can be stabilised through the coordination of mild π-acceptor ligands such as phosphines, cyano-groups, CO, and aromatic amines. Osmium(III) Osmium(III) is a spin-paired d5 ion (t2g5) with an octahedral geometry exhibited by its complexes. This oxidation state illustrates extensive reactions with σ-donor, π-acceptor ligands such as N -, O -, S - and P -donor ligands. However, due to the single, unpaired electron within the t2g sub-shell, osmium(III) is prone to oxidation to the tetravalent oxidation state or reduction to the divalent oxidation state. Osmium(IV) The tetravalent oxidation state of osmium is its most common oxidation state, owing its stability to the coordination of good σ-donor, π-acceptor ligands to the metal ion. The osmium(IV) ion is spin-paired when existing in an octahedral milieu. Although the ion has two unpaired electrons in the t2g sub-shell, its magnetic properties are anomalous due to the quenching of electron spin by orbital spin. Most of its complexes are anionic or neutral (e.g. OsCl62-) although a few cationic species does exist (e.g. [Os(diars)2X2]2+, where X = Cl-, Br- and I-). Osmium(VI) The hexavalent oxidation state is frequently associated with σ-donor, π-donor ligands such as F-, O2- and N3-. The chemistry of these complexes are dominated by the oxospecies (more specifically, the octahedral trans-[OsO2(OH)4]2- species) and the nitridospecies (the octahedral [OsNCl5]2- species). It has been reported that the nitrido- species are more readily formed with osmium than with any other metal ion. 7 Osmium(VIII) The most important complex in this oxidation state is the stable, tetrahedral osmium tetroxide, OsO4. However, the fluoro-complex, [OsO3F3]-), and nitrido-complex, ([OsO3N]-), do also exist. The osmium(VIII) species is strongly oxidising, but not nearly as oxidising as its ruthenium analogue. Coordination Numbers[6] 1.4.2 In terms of its coordination numbers, platinum group metals show very little versatility, and osmium is no exception. The majority of the osmium complexes exhibit octahedral geometries. Table 1.1 illustrates the more unusual coordination numbers and geometries. The table contains some examples of eight- and seven-coordination, in addition to certain complexes that exhibit geometries ranging from square-based pyramidal (primarily displayed by higher oxidation state osmium ions) to bipyramidal (displayed by lower oxidation state osmium ions) geometries. Although the tetrahedral geometry is displayed by osmium tetroxide, it is still considered as a rare geometrical structure for osmium. Table 1.1: The more unusual coordination numbers for osmium Coordination number 8 [6] Examples Geometry Os(PMe2Ph)2H6 Unknown Os(edta)(H2O) Monocapped Octahedron OsF7 Pentagonal bipyramidal Os(Pet2Ph)4H3 Distorted Pentagonal bipyramidal Os2O4(O2R)2 Square-based pyramidal Os(CO)5 Trigonal bipyramidal 7 5 - 4 OsO4, [OsO4] Tetrahedral Os(NO)2(PPh3)2 Distorted Tetrahedral 8 1.4.3 Coordinating Ligands[6] Group VII donor ligands All of the halide ions (F-, Cl-, Br- and I-) form octahedral complexes with osmium ions. Fluorides are associated with the VIII, VII, VI and V oxidation states while Cl-, Br- and Iare associated with the IV and III oxidation states. Group VI donor ligands The coordination chemistry of high oxidation state osmium (the VIII, VII and VI states) are dominated by the oxo-species, of which the tetrahedral osmium tetroxide, OsO4, is the most important. There are also a number of sulphur-donor complexes which forms with these metal ions. Group V donor ligands Several nitrido complexes of osmium(VI) and osmium(IV) as well as the “osmiamate” ion ([OsVIIIO3N]-) are now known to exist. Considerable work has been conducted on the bipy, phen and terpy complexes of osmium. The ammine and ethylenediamine ligands, which do not exhibit π-acceptor capabilities, form stable complexes with osmium(IV) and osmium(III). On the other hand, phosphorous, arsenic and antimony, with their good π-acceptor capabilities, form stable complexes with osmium(III) and osmium(II) Group IV donor ligands This group is dominated by the osmium cluster carbonyl chemistry. As an exceptional σdonor, mild π-acceptor ligand, cyanide forms a rather stable complex with divalent osmium, forming the Os(CN)64- species. In the trans-[OsO2(CN)4]2- complex, the high oxidation state of osmium is stabilised by the oxo-ligands with its strong σ-, π-donor capabilities. 9 1.5 Aims and Objectives Osmium is of little use industrially (compared to other platinum group metals), which is owed chiefly to its expense of refining and also the considerable difficultly of working with the metal. Even though not as valuable, the mining industry still faces the task of separating and stabilising osmium during the refining processes associated with the procurement of the more valuable platinum group metals, including platinum and palladium, amongst others. In addition, this industry also has to deal with the environmental and occupational health threats that osmium poses. It is therefore essential to acquire experience and knowledge in the chemical behaviour and handling of osmium. Osmium tetroxide catalysed oxidations of organic molecules are important in many organic syntheses, and although these reactions have been investigated in the past, there does not seem to be a consensus regarding the mechanism by which these reactions proceed. This study stems from a process used in the platinum refining industry during which osmium tetroxide is reduced in an alkaline medium to osmium(VI) using industrial ethanol as a mild reducing agent. Spectrophotometric techniques, in conjunction with several computational methods, were used to investigate the kinetics and equilibria surrounding the reduction of osmium tetroxide by several primary alcohols in a hydroxide matrix. Through these investigations a mechanism explaining the acquired data is proposed. This mechanism allows a greater understanding of the fundamental chemical behaviour associated with these species. 10 CHAPTER 2: Experimental 2.1 Apparatus 2.1.1 UV-Vis Spectrophotometric Recordings UV-Vis spectra were recorded using a Perkin-Elmer Lambda 12, double beam UV-Vis spectrophotometer, interfaced with the UV WinLab (Version 1.22) software package. The spectra were recorded using the following settings: o cycle time (where applicable): 120 seconds o scan rate: 240 nm/min o slit width: 1 nm In aid of consistency, paired quartz cuvettes, with a 1 cm path length, were used in all spectral recordings made. Kinetic investigations were conducted at 25°C. In order to maintain a constant room temperature, a Samsung SH 122KG external air-conditioning unit was employed. This unit showed ± 0.5°C deviation from the desired temperature. In addition, a Grant KD100 circulating thermostat controller, mounted onto a Grant W6 water bath equipped with a cooling coil, was used to maintain the temperature of the spectrophotometer cuvette holder at 25°C (± 0.1°C). A pump, attached to the thermostatic water bath, was used to circulate water through the rubber tubing, as illustrated in Figure 2.1. The tubing extended through the cuvette-containing chamber of the spectrophotometer, and is attached to a thermostatic beaker which contains the sample solutions. This ensured that the contents of the beaker and the cuvettes were at equal temperature. The contents of the beaker were magnetically agitated with a Metrohm 128 stirrer. 11 Cuvette Chamber Beaker Circulating Pump Magnetic Stirrer Thermostatic Water bath Computer Aluminium-covered Rubber Tubing UV-Vis Spectrophotometer Figure 2.1: Illustration of the experimental system employed to record UV-Vis spectra at constant temperatures 2.1.2 Mole Ratio Titrations The absorbance measurements for mole ratio titrations were recorded with a Metrohm 662 photometer. This photometer consists of a probe connected to the main unit with two light guides. The first light guide relays light to the probe, which reflects light back to the photometer unit through the second light guide. The end of the probe is immersed into the reaction solution, therefore allowing titrations to be performed without the removal of samples from the reaction solution. The light path through the solution is 1 cm. The photometer was connected via its analogue output to a titroprocessor. This enables photometric titrations to be performed automatically, making it possible to record titrations with a large number of data points. The main disadvantage of the photometer is that the absorbance can only be measured at a single wavelength during a titration. 12 2.1.3 Potentiometric Titrations Titrations were performed and recorded using a Metrohm 780 pH meter and Metrohm 665 Dosimat. These titrations were performed automatically, with the measured aliquots of titrant being delivered via the dosimat. 2.1.4 pH Measurements pH was measured with a Metrohm 780 pH meter using a Metrohm 6.0232.100 combined pH glass electrode. The electrode was calibrated with pH 4.00 (Metrohm 6.2307.100) and pH 7.00 (Metrohm 6.2307.110) buffer solutions. 2.1.5 Potentiometric Measurements Potential was measured with a Metrohm 780 pH meter using a Metrohm 6.0402.100 combined platinum-wire electrode. 2.1.6 Preparation of Solutions The stock solutions used in this study were all prepared in a constant temperature room set at 25°C (± 0.2°C). The room temperature was maintained by means of a Bürisch thermostatic circulator linked to a Carel temperature control unit. Type 1 quality water, achieved by employing a Millipore Simplicity water purification system, was used for the preparation of aqueous solutions. The system provides polishing of water, removing any remaining contaminants from distilled water[7]. The water used throughout this study was produced in this manner, and will hereafter be referred to as distilled water. 13 2.2 Computer Hardware and Software Table 2.1: Computer platform used for kinetic and equilibrium calculations Processor Motherboard 1.86 GHz Intel Asus Deluxe P5B Pentium Core 2 SLI, 1066 MHz Duo, at 2.2 GHz Front Side Bus Processing Platform 64 Bit Memory Module 2 GB DDR2 The Windows XP compatible software used during this study include: o Word 2003 o Excel 2003 o SigmaPlot 9.0.1 o ChemDraw Version 8 o Visual Basic.Net o SimpleGraph (Author: Dr E C Hosten) o SPC-V-MR (Author: Dr E C Hosten) o KinEqui (Author: Dr W J Gerber) o GP 2 (Author: Mr T E Geswindt) The programs written during this study are listed in Appendix 1 and are discussed in the relevant chapters where they are applied. These programs were employed for the simulation of experimental kinetic data. 14 2.3 Reagents Utilised Osmium, in the form of the potassium osmate salt (K2[OsO2(OH)4]), was obtained in a crude form from the Anglo Platinum Research Centre. The crude potassium osmate salt was oxidised to the volatile osmium tetroxide during the preparation of a pure osmium tetroxide solution. Due to the solubility of osmium tetroxide in carbon tetrachloride, carbon tetrachloride was used to trap the volatile tetroxide. Pure potassium osmate salt was prepared through the recrystallisation procedure described in Chapter 2.6. Table 2.2: Reagents utilised during this study Salts Reagent Chemical Formula Percentage Purity Supplier Thiourea CH4NS2 98 Associated Chemical Enterprises (Pty) Ltd Potassium hydroxide KOH 88 Minema Laboratory Supplies (Pty) Ltd Sodium hydroxide NaOH 98 Merck Chemicals (Pty) Ltd Sodium tetraborate Na2B4O7·10H2O 99 May & Baker Liquids Reagent Chemical Formula Butan-1-ol CH3CH2CH2CH2OH Percentage Composition 99 Supplier Merck Chemicals (Pty) Ltd 15 Carbon tetrachloride CCl4 99.5 Ethanol CH3CH2OH 99.9 Hydrochloric acid HCl 32 Methanol CH3OH 99.9 Merck Chemicals (Pty) Ltd Minema Laboratory Supplies (Pty) Ltd SMM Instruments (Pty) Ltd Merck Chemicals (Pty) Ltd Associated Chemical Enterprises (Pty) Ltd Associated Chemical Enterprises (Pty) Ltd Nitric Acid HNO3 55 Orthophosphoric acid H3PO4 85 Perchloric acid HClO4 70 Merck Chemicals (Pty) Ltd Propan-1-ol CH3CH2CH2OH 99 Merck Chemicals (Pty) Ltd 99.99 Spectrascan Elemental Standard, TeknoLab A/S Ammonium hexachloroosmium(IV) (NH4)2[OsCl6] 16 2.4 Standardisation Methods 2.4.1 Standardisation of Acids Acid solutions were standardised against freshly prepared borax1 (sodium tetraborate) solutions. The exact concentrations of the prepared acid and base solutions were in the order of 1 × 10-3 mol/L. In order to retain the maximum number of significant figures, the total volume of the titrant at the endpoint was 25 mL. Titrations were repeated until concordant results were obtained. 2.4.2 Preparation of a Standard Sodium Hydroxide Solution Sodium hydroxide pellets were dissolved in distilled water and the freshly prepared solutions were titrated against standardised hydrochloric acid solutions. In order to retain the maximum number of significant figures, the total volume of the titrant at the endpoint was at least 25 mL. Titrations were repeated until concordant results were obtained. 2.5 Preparation and Storage of Osmium Tetroxide 2.5.1 Introduction Pure osmium tetroxide solutions were prepared through the oxidation of potassium osmate. The volatile osmium tetroxide was then trapped in carbon tetrachloride. Carbon tetrachloride is the ideal solvent for the storage of osmium tetroxide due to the fact that: o osmium tetroxide is significantly more soluble in carbon tetrachloride than in water o the UV-Vis spectrum of osmium tetroxide in carbon tetrachloride does not change as a function of time, indicative of the stability of osmium tetroxide in carbon tetrachloride. During preparatory procedures, it was found that only a limited number of oxidising agents resulted in the production of a pure osmium tetroxide solution. In most instances, the reduced product of the oxidising agent, and occasionally the oxidising 1 Borax was used as a primary standard 17 agent itself, contaminated the solution. Oxidising agents that proved to be inappropriate included sodium chlorate and chlorine, both of which produced contaminating chlorine species in the scrub solution. The presence of the oxidising agent as a contaminant in the scrub solution leads to an increase in the oxidising capabilities of the tetroxide solution. Due to the aforementioned contamination factors, hydrogen peroxide was selected as the oxidising agent. The hydrogen peroxide was acidified with orthophosphoric acid in order to enhance its oxidising capacity. 2.5.2 Preparation Procedure An illustration of the experimental system employed for the preparation of a pure osmium tetroxide solution is shown in Figure 2.2. Approximately 240 mL carbon tetrachloride was transferred to Dreschel flask 2 and approximately 6 g of crude potassium osmate was transferred to Dreschel flask 1. A hydrogen peroxide solution, consisting of the following components: o 45 mL distilled water o 45 ml 85% orthophosphoric acid o 10 ml 30% hydrogen peroxide was then carefully transferred to flask 1. Immediately following the addition of the hydrogen peroxide solution, the glass tubes were connected to the Dreschel flasks. 18 Figure 2.2: Illustration of the experimental setup used during the preparation of a pure OsO4 solution Hydrogen peroxide oxidised the potassium osmate to the volatile osmium tetroxide (Dreschel flask 1). With the aid of a stream of air purging the contents of flask 1, the tetroxide formed in this flask was forced through the glass attachments into Dreschel flask 2, which contained the carbon tetrachloride trap solution. This procedure was allowed to proceed over a period of 8 - 10 hours. Once the required time had elapsed, the osmium tetroxide solution in flask 2 was transferred to a stoppered dark glass container. 19 2.5.3 Preparation of Aqueous Osmium Tetroxide Aqueous osmium tetroxide solutions were prepared by extracting osmium tetroxide from a carbon tetrachloride stock solution into distilled water. The extraction process was allowed to proceed for at least 1 hour prior to separation of the organic and aqueous phases. Constant agitation of the mixture was provided by an automated orbital shaker. Once the extraction period had elapsed and the two phases were allowed to separate, the organic phase was removed. The aqueous phase was filtered through Whatman 41 filter paper (which was wetted with distilled water) in order to remove residual carbon tetrachloride present in the aqueous phase. 2.6 Preparation of Potassium Osmate Potassium osmate was originally obtained as a crude salt, used as a source of osmium during the preparation of pure osmium tetroxide solutions. However, during specific investigations it was imperative that the potassium osmate salt be of high purity. This was achieved by dissolving the crude potassium osmate in a warm, 2 mol/L potassium hydroxide solution. This solution was then filtered under vacuum, allowing for the removal of impurities. The filtrate was allowed to cool in an ice bath and pure potassium osmate was recrystallised through the addition of potassium hydroxide pellets. In certain instances ethanol was added to the filtrate containing excess potassium hydroxide, to facilitate crystal formation by lowering the dielectric constant of the filtrate solution. Pure potassium osmate was also prepared by the reduction of aqueous osmium tetroxide in the presence of excess potassium hydroxide in ethanol. Once in crystalline form, the potassium osmate was filtered and dried under vacuum for 3 - 5 days. 20 2.7 Determination of Osmium Concentration – The Thiourea Colourimetric Method 2.7.1 Introduction Since the discovery of osmium in 1804, nearly a century and a half would have passed before acceptable methods for its analysis were developed. During this period various methods were proposed, including[9]: o osmium separation as a sulphide species, followed by ignition in hydrogen o reduction of osmium(VIII) with alcohol o separation as hydrous oxide, followed by reduction in hydrogen o the precipitation of osmium as an ammonium or potassium chloro-osmate species o iodometric determination through the reduction of osmium(VIII) with iodide o the precipitation of osmium with strychnine sulphate o potentiometric titrations These methods proved laborious and the results obtained through these methods displayed significant discrepancies. A viable method was presented in 1918 when Chuguaev[11] found that an aqueous solution of osmium tetroxide, upon treatment with thiourea and hydrochloric acid, produced a brilliant, rose-red coloured solution. Continued investigations resulted in the isolation of red crystals from the reaction mixture, which had a percentage composition corresponding to either the trivalent [Os(NH2CSNH2)6]Cl3·H2O species or the tetravalent [Os(NH2CSNH2)6]OHCl3 species. During his earlier work, Chuguaev proposed that the composition of the red solid was composed of the [Os(NH2CSNH2)6]OHCl3 species. The tetravalent species was widely accepted until 1953, when Sauerbrunn and Sandell rejected the claims made by Chuguaev by conclusively proving that the composition of the red solid was in fact the trivalent hexathioureaosmium(III) cation[8]. Even with the advancement of technology in the 21st century, assaying of osmium still proves to be problematic. Inductively coupled mass spectrometry (ICP-MS) seems, at first glance, to be an attractive method for the assay of osmium. This method does, however, present problems including: 21 o the replacement of all plastic components of the spectrometer which would possibly exposed the osmium samples, for example plastic tubing, spray chamber etc. This is due to osmium, in the form of osmium tetroxide, reacting with the plastic components it comes into contact with. In order to prevent the formation of osmium tetroxide, all osmium samples should be reduced to a single, stable lower oxidation state without the loss of any osmium during the process. The entire procedure itself proves to be rather cumbersome. o to find a single matrix which does not oxidise, reduce nor volatilise the osmium samples Electrothermal atomic absorption spectrometry (ETAAS) is another analytical technique which could not be used for the assay of osmium, as it suffers from the same problems as ICP-MS, namely the need for replacement of plastic components. In addition, ETAAS illustrates a lack of reproducibility of results, with some authors reporting the relative standard deviation across three replicates as 19%[12]. These authors ascribed the lack of reproducibility to the high volatility and the ease of decomposition of osmium tetroxide and the Os – O bonds, which presumably decompose during the drying and ashing stages. Due to the aforementioned problems associated with ICP-MS and ETAAS, and the lack of reproducibility of results these techniques suffer from, it was opted to investigate only the thiourea colourimetric method for the assay of osmium samples. 22 2.7.2 The Effect of Varying Thiourea Concentration on the Formation of the [Os(NH2CSNH2)6]3+ Species 2.7.2.1 Literature Review Osmium tetroxide, upon treatment with excess thiourea in an acidic medium, reacts according to the following relation[8]: 2OsO4 + 22NH2CSNH2 + 6H+ → 2[Os(NH2CSNH2)6]3+ + 5(NH2)(NH)CS2(NH)(NH2) + 8H2O … 2.1 According to Relation 2.1, thiourea acts as both the reductant as well as the coordinating ligand, with each osmium equivalent reacting with eleven equivalents of thiourea and three equivalents of acid[8]. Sauerbrunn and Sandell[8] reported that the reaction depicted by Relation 2.1 occurred rapidly (approximately three days at 25°C) when osmium tetroxide was used. However, in strict contrast to osmium tetroxide, the reaction between hexachloroosmium(IV), [OsCl6]2-, and thiourea under identical conditions was found to be extremely slow (approximately eight days at 25°C). 2.7.2.2 Experimental Procedures A 1.095 mol/L thiourea stock solution was prepared in an 8.484 mol/L HCl matrix. Varying volumes of this stock solution was used to prepare thiourea solutions consisting of the following concentrations in 25 mL: o 0.0657, 0.1314, 0.2627, 0.3941, 0.4598, 0.5253, 0.5912, 0.6569, 0.7882 and 0.9196 mol/L Concentrated HCl (32% m/v) was used to maintain the HCl concentration of these solutions at 5.091 mol/L. To each of these solutions, 0.500 mL ammonium hexachloroosmium(IV) elemental standard was added to maintain the total osmium concentration at 1.051 × 10-4 mol/L. These solutions were equilibrated at 25°C, and the UV-Vis spectra of the solutions recorded daily until no significant changes in these spectra were observed. The results are based on the final spectra recorded. 23 2.7.2.3 Results and Discussion Figure 2.3 depicts the UV-Vis spectra of solutions containing a range of thiourea concentrations, while the osmium and HCl concentrations were kept constant. thiourea concentrations exceeding 0.394 mol/L, the At characteristic hexathioureaosmium(III), [Os(NH2CSNH2)6]3+, cations’ spectra are observed. These spectra illustrate a broad band at 550 nm and a sharp peak at 480 nm, with the absence of the peaks at 370 and 325 nm. The spectra of the solutions containing lower thiourea concentrations (less than 0.263 mol/L) illustrate two additional peaks at 370 nm and 325 nm. 1.0 0.0000 M 0.0657 M 0.1314 M 0.2627 M 0.3941 M 0.4598 M 0.5253 M 0.5912 M 0.6578 M 0.7889 M Absorbance 0.8 0.6 0.4 0.2 0.0 300 350 400 450 500 550 600 Wavelength /nm Figure 2.3: UV-Vis spectra illustrating the formation of the [Os(NH2CSNH2)6] 3+ species as a function of thiourea concentration. The direction of the solid arrows indicates increasing thiourea -4 concentration. [HCl] = 5.091 mol/L; [Osmium] = 1.051 × 10 mol/L; solutions were equilibrated for 8 days at 25°C 24 The peaks at 370 nm and 335 nm are ascribed to the presence of the hexachloroosmium(IV) species. This conclusion is based on the spectrum of the pure hexachloroosmium(IV) species, obtained from the solution prepared in the absence of thiourea. Figure 2.3 illustrates that the spectrum of the pure hexachloroosmium(IV) species display only two peak maxima, at 370 and 325 nm respectively. This correlates with the presence of similar peaks in the spectra of solutions of low thiourea concentration. 0.5 Absorbance at 490nm 0.4 0.3 0.2 0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 -1 [Thiourea] /mol.L Figure 2.4: The change in absorbance at 490 nm as a function of thiourea concentration, indicating the large excess of thiourea required for the complete conversion of [OsCl6] [Os(NH2CSNH2)6] 3+ 2- to the species. The ratio of thiourea:osmium should be at least 4300:1 in order for full 2- 3+ conversion of [OsCl6] to [Os(NH2CSNH2)6] . The [Os(NH2CSNH2)6]3+ cations’ spectra illustrated in Figure 2.3 stabilises only once the thiourea concentration is truly in vast excess over osmium, and the spectra remain relatively constant once a thiourea concentration of 0.460 mol/L or greater have been reached. This observation is further illustrated in Figure 2.4, where the absorbance at 490 nm remains constant once the thiourea concentration reaches 0.460 mol/L. This 25 fact was used in the selection of the optimal thiourea concentration for preparation of all subsequent analytical solutions. 2.7.3 The Effect of Varying Hydrochloric Acid Concentration on the Formation of the [Os(NH2CSNH2)6]3+ Species 2.7.3.1 Literature Review According to Sauerbrunn and Sandell[8] and as illustrated by Relation 2.1, in the presence of excess thiourea, one equivalent of osmium tetroxide reacts with three equivalents of acid: 2OsO4 + 22NH2CSNH2 + 6H+ → 2[Os(NH2CSNH2)6]3+ + 5(NH2)(NH)CS2(NH)(NH2) + 8H2O …Relation 2.1 Relation 2.1 depicts the reaction as being dependent only on the thiourea and acid concentrations. However, as observed by Cristiani et al[10] the kinetics of this reaction also depends on the type of acid used. These authors found that different acids resulted in different observed rate constants being obtained, and concluded that the kinetics of the reaction indicated a specific acid catalysis. In addition, Cristiani et al found that, when using perchloric acid as the source of H+, Relation 2.1 proceeds according to four main processes. All of these are acid dependent and only two of these processes are thiourea dependent. The two thiourea dependent processes were found to be faster than the two thiourea independent processes[10]. In contrast to the rapid reaction between osmium tetroxide and thiourea in HCl medium (at 25°C), the reaction between hexachloroosmium(IV) and thiourea was found to be exceedingly slow under identical experimental conditions. To date, no reports in the literature have been obtained discussing the reduction of hexachloroosmium(IV) with thiourea in the presence of perchloric acid. Reference has only been made to the reduction of hexachloroosmium(IV) in HCl solutions[8]. 26 2.7.3.2 Experimental Procedures This investigation was performed in three parts: a) The reduction of [OsCl6]2- by thiourea as a function of HCl concentration. b) The reduction of [OsCl6]2- by thiourea as a function of HCl at constant ionic strength. c) The reduction of osmium tetroxide as a function of HCl concentration at constant ionic strength. a) The following stock solutions were prepared in 250 mL volumetric flasks: o 1.095 mol/L thiourea in distilled water o 1.095 mol/L thiourea in a 6.753 mol/L HCl matrix o 1.095 mol/L thiourea in an 8.484 mol/L HCl matrix Solutions containing constant thiourea and osmium concentrations, with varying HCl concentrations, were prepared in 25 mL volumetric flasks adding the following volumes of reagents and filling with distilled water: • • solutions varying in HCl concentrations from 0 to 3.000 mol/L o 15 mL of the 1.095 mol/L thiourea stock solution prepared in distilled water o 0.890 mL ammonium hexachloroosmium(IV) o varying volumes of 32% HCl to obtain the desired HCl concentrations solutions varying in HCl concentrations from 4.052 to 4.500 mol/L o 15 mL of the 1.095 mol/L thiourea stock solution prepared in a 6.753 mol/L HCl matrix • o 0.890 mL ammonium hexachloroosmium(IV) o varying volumes of 32% HCl to obtain the desired HCl concentrations solutions varying in HCl concentrations from 5.091 to 7.000 mol/L o 15 mL of the 1.095 mol/L thiourea stock solution prepared in an 8.484 mol/L HCl matrix o 0.890 mL ammonium hexachloroosmium(IV) o varying volumes of 32% HCl to obtain the desired HCl concentrations 27 The UV-Vis spectra of these solutions were recorded daily until no significant changes in the spectra were observed, which usually occurred after a period of approximately eight days. The results are based on the final spectral recordings. b) A 1.642 mol/L thiourea stock solution was prepared with distilled water in a 250 mL volumetric flask. This solution was used to maintain the thiourea concentration at 0.657 mol/L, by transferral of 10 mL of the stock solution to 25 mL volumetric flasks. Varying volumes of 32% HCl was added to these flasks in order to obtain the required HCl concentrations. The ionic strength of these solutions was adjusted to 6 mol/L by addition of the required volume of 70% HClO4. The osmium concentration was fixed at 2.103 × 10-4 mol/L by addition of 1.000 mL of a 1000 mg/L ammonium hexachloroosmium(IV) elemental standard to each of the volumetric flasks. The flasks were filled to the mark with distilled water. The solutions were allowed to equilibrate over an eight day period at 25°C prior to the recording of UV-Vis spectra. c) Osmium tetroxide was obtained as a freshly prepared aqueous solution through the extraction from a carbon tetrachloride stock solution into distilled water, as described in Chapter 2.5.3. A 1.642 mol/L thiourea stock solution was prepared in a 250 mL volumetric flask. This solution was used to maintain the thiourea concentration at 0.657 mol/L by transferral of 10 ml of the stock solution to 25 ml volumetric flasks. Varying volumes of 32% HCl was added to these flasks to obtain the final HCl concentrations ranging from 0.500 mol/L to 6.000 mol/L. Ionic strength adjustments were made through the addition of the required volumes of 70% perchloric acid. The ionic strength of each of these solutions was fixed at 6.000 mol/L. The osmium concentration was -5 maintained at 6.554 × 10 mol/L throughout the series by addition of the extracted aqueous osmium tetroxide solution. These solutions were allowed to equilibrate for three days at 25°C prior to the recording UV-Vis spectra. 28 2.7.3.3 Results and Discussion The UV-Vis spectra depicting the reduction of hexachloroosmium(IV) by thiourea as a function of HCl concentration is illustrated in Figure 2.5. At increased HCl concentrations, the characteristic [Os(NH2CSNH2)6]3+ species’ spectra are observed This observation is based on the presence of the broad band at 550 nm and the narrow peak at 480 nm as well as the absence of the peaks at 370 and 325 nm. The peaks at 370 and 325 nm are ascribed to the incomplete conversion of the hexachloroosmium(IV) species to the [Os(NH2CSNH2)6]3+ species, which occurs at HCl concentrations lower than 5.091 mol/L. 0.489 M 0.998 M 1.507 M 3.034 M 4.052 M 5.091 M 6.089 M 7.107 M 1.4 1.2 Absorbance 1.0 0.8 0.6 0.4 0.2 0.0 300 350 400 450 500 550 600 Wavelength /nm Figure 2.5: UV-Vis spectra of the [OsCl6] 2- reduction by thiourea as a function of HCl -4 concentration. [Thiourea] = 0.657 mol/L; [Osmium] = 1.871 × 10 mol/L The degree of conversion of hexachloroosmium(IV) to the [Os(NH2CSNH2)6]3+ species as a function of hydrochloric acid concentration is also illustrated in Figure 2.6. At an HCl concentration of 5.091 mol/L, the absorbance at 490 nm reaches a plateau. This 29 implies the total conversion of hexachloroosmium(IV) to the [Os(NH2CSNH2)6]3+ cation at these HCl concentrations. 1.4 370 nm 490 nm 1.2 Absorbance 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 [HCl] /mol.L 5 6 7 8 -1 Figure 2.6: The change in absorbance at selected wavelengths as a function of HCl concentration. -4 [Thiourea] = 0.657 mol/L; [Osmium] = 1.871 × 10 mol/L The reaction between hexachloroosmium(IV) and thiourea to form the [Os(NH2CSNH2)6]3+ cation could also be observed by the dramatic decrease in the absorbance at 370 nm (a wavelength which have been established to represent the presence of hexachloroosmium(IV) in solution) as the HCl concentration is increased. It is interesting to note that the absorbance at 490 nm decreases at HCl concentrations exceeding 5.500 mol/L. This trend could be ascribed to the formation of the [Os(NH2CSNH2)5Cl]2+ and [Os(NH2CSNH2)4Cl2]+ cations, based on the existence of the iridium and rhodium analogues, which have been reportedly isolated as their respective salts[8]. 30 1.8 1.6 Pure [OsCl6]2- 1.4 Absorbance 1.2 1.0 0.8 5.250M HCl 0.6 0.4 0.750M HCl 0.2 0.0 300 350 400 450 500 550 600 Wavelength /nm Figure 2.7: UV-Vis spectra depicting the reduction of [OsCl6] 2- by thiourea as a function of HCl concentration at an ionic strength of 6 mol/L. The solid arrows indicate the direction of increasing -4 [HCl]. The [HCl] ranges from 0.750 mol/L to 5.250 mol/L; [Osmium] = 2.103 × 10 mol/L. The 2- spectrum of pure [OsCl6] is included for comparison. The UV-Vis spectra of the reduction of hexachloroosmium(IV) by thiourea as a function of HCl concentration at constant ionic strength is illustrated by Figure 2.7. Since the total H+ concentration of each of the solutions were adjusted to 6.000 mol/L, it was expected that the hexachloroosmium(IV) species in all the solutions would be converted to the [Os(NH2CSNH2)6]3+ species at the same rate, if the reaction occurs via a similar mechanism to that depicted by Relation 2.1. However, the presence of peaks at 370 and 325 nm at HCl concentrations lower than 4.000 mol/L, indicates the presence of hexachloroosmium(IV). Only at HCl concentrations exceeding 4.000 mol/L do these peaks disappear. 31 0.9 370 nm 490 nm 0.8 Absorbance 0.7 0.6 0.5 0.4 0.3 0.0 0.2 0.4 0.6 0.8 1.0 Mole Fraction Cl- Figure 2.8: The absorbance at selected wavelengths as a function of the mole fraction Cl 0.9 370 nm 490 nm 0.8 Absorbance 0.7 0.6 0.5 0.4 0.3 0 2 4 6 8 mole Clmole ClO 4 mole Cl- - mole ClO 4 Figure 2.9: The absorbance at selected wavelengths as a function of 32 Figure 2.8 illustrates the absorbance at the selected wavelengths as a function of the mole fraction of Cl-. The absorbance at 490 nm shows a linear increase as a function of the increasing mole fraction of Cl-, implying an increase in the formation of the [Os(NH2CSNH2)6]3+ species. Correspondingly, the increase in the Cl- mole fraction results in a decrease in absorbance at 370 nm, correlating to the decrease in hexachloroosmium(IV) as it is reduced to form the [Os(NH2CSNH2)6]3+ cation. This conclusion is supported by Figure 2.9, which depicts the absorbance at the indicated wavelengths as a function of the mole ratio, mole ClAs the mole ratio increases - . mole ClO4 (effectively implying an increase in HCl), the absorbance at 490 nm increase correspondingly as the [Os(NH2CSNH2)6]3+ species is formed. At the same time the absorbance at 370 nm decreases as the hexachloroosmium(IV) species is reduced to the [Os(NH2CSNH2)6]3+ species. At first glance it seemed as if the reaction between hexachloroosmium(IV) and thiourea is dependent on the chloride ion concentration, but further scrutiny reveals that it is the type of acid employed that drives this reaction, with the rate of reduction of hexachloroosmium(IV) by thiourea increasing with increasing HCl concentrations and decreasing HClO4 concentrations. The reaction at constant ionic strength was repeated with osmium tetroxide as the osmium source, the results of which are illustrated in Figures 2.10 and 2.11. 33 0.35 0.30 Absorbance 0.25 0.20 0.15 0.10 0.05 0.00 320 360 400 440 480 520 560 600 Wavelength /nm Figure 2.10: UV-Vis spectra depicting the reduction of osmium tetroxide by thiourea as a function of HCl concentration at an ionic strength of 6 mol/L. [Thiourea] = 0.657 mol/L; -5 [Osmium] = 6.554 × 10 mol/L; [HCl] ranges from 0.500 mol/L to 6.000 mol/L 0.30 370 nm 490 nm 0.25 Absorbance 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 -1 [HCl] /mol.L Figure 2.11: The change in absorbance at selected wavelengths as a function of HCl concentration 34 The reaction between osmium tetroxide and thiourea do not exhibit any significant differences between the UV-Vis spectra obtained over the range of HCl concentrations investigated, as illustrated in Figure 2.10. In addition, the absorbance at 370 and 490 nm remains relatively constant, irrespective of the HCl concentration (Figure 2.11). This is due to the fact that the reduction of osmium tetroxide by thiourea is predominantly dependent on the total H+ concentration, which was kept constant at 6.000 mol/L. This is also reflected by the rate at which equilibrium is established when osmium tetroxide is reacted with thiourea, in comparison to the reaction between hexachloroosmium(IV)- and thiourea; which was found to be three days for osmium tetroxide, compared to the eight day period required by the hexachloroosmium(IV) species. These results are in contrast to those obtained from the reaction between hexachloroosmium(IV) and thiourea. The predominant reason for these differences could the dissimilar fundamental properties of hexachloroosmium(IV) and osmium tetroxide with the former exhibiting greater kinetic and thermodynamic stability than the latter species. Thiourea, in the presence of excess H+, would thus reduce these species through different mechanisms, although the final product in both mechanisms would be the trivalent hexathioureaosmium(III) cation. This would also account for the longer equilibration time required for the reduction of hexachloroosmium(IV) by thiourea as compared to the reduction of osmium tetroxide. The reduction and ligand exchange for hexachloroosmium(IV) would be slower due to its aforementioned enhanced stability. Although there are uncertainties surrounding the hexachloroosmium(IV) reduction by thiourea, when compared to analogous reactions involving osmium tetroxide (in addition to the poor establishment of the type of bonding which occurs in the resultant products) the thiourea colourimetric method remains an accurate, consistent and efficient method for the assay of osmium. The use of hexachloroosmium(IV) as a standard can be considered as a more accurate (and less hazardous) alternative to the classical thiourea colourimetric method, in which osmium tetroxide was used. The reason for the increased accuracy of the method when using hexachloroosmium(IV) is due to the 35 decrease in the loss of osmium during sample preparation. In contrast, osmium tetroxide is partially lost as the tetroxide vapour during sample preparation. The optimum thiourea and HCl concentrations were respectively found to be 0.657 and 5.091 mol/L, and duly selected for the determination of the total osmium concentration for subsequent samples. 36 2.7.4 The Osmium-Thiourea Calibration Curve 2.7.4.1 Literature Review The formation of the [Os(NH2CSNH2)6]3+ species as a function of both thiourea and HCl concentration was established in Chapters 2.7.2 and 2.7.3. During these investigations it was observed that the formation of the [Os(NH2CSNH2)6]3+ species requires a vast excess of thiourea and HCl. Subsequently, the optimal thiourea and HCl concentrations were found to be 0.657 and 5.091 mol/L, respectively. Furthermore, it was established that at 25°C, an equilibration period of eight days is required for the complete conversion of hexachloroosmium(IV) to [Os(NH2CSNH2)6]3+, as opposed to the three day equilibration period required for the conversion of osmium tetroxide to [Os(NH2CSNH2)6]3+. According to Ayres and Wells[9], the osmium concentration range best exhibiting linearity was 8 mg/L (4.210 × 10-5 mol/L) to 40 mg/L (5.257 × 10-4 mol/L). During this study, the linear range was extended from 1 mg/L (5.257 × 10-5 mol/L) to 50 mg/L (2.628 × 10-4 mol/L), by using an adaptation of the classic thiourea method. 2.7.4.2 Experimental Procedures Standard solutions were prepared using an ammonium hexachloroosmium(IV) standard [Spectrascan standard for spectroscopy by Teknolab A/S]. This elemental standard is maintained in a 4.9% (1.559 mol/L) HCl matrix. Several standard solutions were -3 prepared using the 1000 mg/L (5.257 × 10 mol/L) osmium standard such that the final thiourea and HCl concentrations were 0.657 and 5.091 mol/L, respectively. The total osmium concentrations of the standard solutions were: 5.257 × 10-6, 1.051 × 10-5, 1.577 × 10-5, 2.628 × 10-5, 5.257 × 10-5, 7.885 × 10-5, 1.051 × 10-4, 1.577 × 10-4, 2.103 × 10-4 and 2.628 × 10-4 mol/L These solutions were equilibrated over a period of eight days after which the UV-Vis spectra of the solutions were recorded. 37 2.7.4.3 Results and Discussion 2.0 -6 5.257×10 M -5 1.051×10 M -5 1.577×10 M -5 2.628×10 M -5 1.5 5.257×10 M -5 7.885×10 M -4 Absorbance 1.052×10 M -4 1.577×10 M -4 2.103×10 M -4 2.628×10 M 1.0 0.5 0.0 300 350 400 450 500 550 600 Wavelength /nm Figure 2.12: UV-Vis spectra of the standard ammonium hexachloroosmium(IV)-thiourea solutions recorded after 8 days at 25°C. [Thiourea] = 0.657 mol/L; [HCl] = 5.091 mol/L; the respective osmium concentrations are noted in the figure. The UV-Vis spectra of the standard solutions are depicted in Figure 2.12. These spectra illustrate peak maxima at 480 nm. Conventionally, the wavelength at which the greatest change in absorbance occurs (in this case 480 nm) is employed during the construction of a calibration curve. However, in this investigation the absorbance at 490 nm was used for the construction of an osmium calibration curve. This is due to the fact that the calibration curve constructed from the data at 480 nm yields a larger positive y-intercept in comparison to the curve constructed from absorbance data at 490 nm; the former being approximately eleven times greater than the latter. 38 1.2 y = 3750x + 9.0264 × 10 -5 R 2 = 0.9999 Standard Error = 0.0029 Absorbance at 490nm 1.0 0.8 0.6 0.4 0.2 0.0 0 50x10-6 100x10-6 150x10-6 200x10-6 250x10-6 300x10-6 [Osmium] /mol.L-1 Figure 2.13: The calibration curve obtained through the thiourea colourimetric method. Calibration curve constructed from the absorbance data at 490 nm The osmium concentration range demonstrating linearity was extended from 5.257 × 10-6 to 2.628 × 10-4 mol/L (Figure 2.13). At 490 nm, the [Os(NH2CSNH2)6]3+ species exhibits a molar extinction coefficient of 3750.6 L mol-1 cm-1. 39 CHAPTER 3 The Alcohol Reduction of Osmium(VIII) in Hydroxide Medium 3.1 Introduction There is fairly extensive literature on the use of osmium tetroxide in the oxidation of organic molecules. In these examples, osmium tetroxide acts as a catalyst with the use of a co-oxidant to regenerate the reduced osmium product back to osmium(VIII). Notably, the literature centres on the economically important oxidation of alkenes to cisdiols. There has been renewed interest in these reactions since the 2001 Nobel Prize in Chemistry was awarded to Barry K. Sharpless, amongst others, for his work on “chirally catalyzed oxidation reactions”[17], which features the catalysis by osmium tetroxide of an asymmetric dihydroxylation. However, many of the reports in the literature on the oxidation of alcohols are out-dated. This fact, together with the interesting nature of some of the preliminary data obtained in this study prompted a fresh look at the oxidation of aliphatic alcohols by osmium tetroxide. Further studies were undertaken to understand the equilibria and kinetics of the high oxidation state osmium species, rather than the role of the organic molecules in the reaction. This study focuses on a process used in the platinum refining industry during which osmium tetroxide is reduced in a basic medium to osmium(VI) using industrial ethanol. It is therefore to be expected that a detailed understanding of the relevant osmium species in solution is of interest to this industry. This review provides a general background to the osmium tetroxide – alcohol reaction, discussing previous studies in this field as well as related studies into the oxidation of other organic molecules by osmium tetroxide. 40 Due to its industrial importance, the oxidation of alkenes to cis-diols by osmium tetroxide is covered extensively in the literature. The reactions between osmium tetroxide and alcohols are, however, not well documented. Singh et al made a comprehensive as study of the use of osmium tetroxide a catalyst with hexacyanoferrate(III) as a co-oxidant; using various substrates such as alcohols, diols, carboxylic acids and ketones[1, 6, 18-24]. In spite of many published reports, there does not seem to be consensus on the mechanisms of either the alkene or alcohol/carbonyl reactions. As yet unresolved issues include the mechanism of the formation of an osmium – substrate complex as well as the nature of this complex; although other parameters such as the hydroxide ion concentration should also be considered. A discussion on the alkene hydroxylation reaction will serve to open the discussion at hand. Criegee[25] performed crucial work for this important reaction, showing that alkenes react with osmium tetroxide to yield the osmium(VI) complexes, OsO2(O2R) and, in some instances, OsO(O2R)2. Subsequent IR and X-ray crystallographic studies formulated these complexes as dimeric species[25]. The rate of these reactions was increased with the addition of organic bases such as pyridine; an early example of ligand accelerated catalysis[26]. Hydrolysis of any of these complexes produced the cis-diol, R(OH)2 [6]. A generally favoured mechanism for this reaction is attack by the oxygen attached to the osmium(VIII) centre on the unsaturated double bond of the alkene leading to a sixelectron transition state[23, 27] . The reaction then proceeds to a five-membered ring which, upon hydrolisation, accounts for the exclusively cis-product. C C O + OsO4 C O 6π Os C O O C O C O C O Os Os O O O C Figure 3.1: The generally accepted mechanism for the oxidation of alkenes to cis-diols O O 41 VeeraSomaiah et al[28] conducted kinetic studies on the oxidation of unsaturated organic compounds by osmium tetroxide in a sulphuric acid/acetic acid medium. These investigators found evidence for a single reaction with a single rate constant and proposed a mechanism similar to that depicted in Figure 3.1, in which the six-electron complex is suggested as a transient transition state. There is no evidence for the formation of a stable five-membered ring which is to be expected. This is in agreement with the results reported by Singh[23], since the five-membered ring proposed in Figure 3.1 would at best be transient due to unfavourable angular strain on the fivemembered ring, since third row transition metals have no d2 tetrahedral stereochemistry. As tetra-substituted alkenes, or those having electron-withdrawing groups, generally form monomeric diester complexes in non-reducing organic solvents, one could expect to find a stable intermediate osmium(VI)-ester complex. Alkenes such as cyclohexene form dimeric monoester complexes[23]. O CH O O O O Os CH O O CH CH CH CH O Os Os O O (a) O O CH Os O (b) O CH O O O O CH O CH Os CH O O CH (c) Figure 3.2: (a) syn- and (b) anti- dimeric monoesters, (c) monomeric diester In contrast to the belief that only the osmate ester would be produced in an organic medium, Subbaraman et al[29] claimed to have followed the kinetics of formation of this ester in aqueous medium. Two separate rate constants were reported for this reaction – one for the formation of an osmate ester and one for the hydrolysis of the ester[29]. The results were obtained in three independent steps: (1) the kinetics of formation of the ester was followed spectrophotometrically in basic medium; (2) the osmate ester was 42 prepared in organic medium, and (3) the kinetics of the ester’s hydrolysis was followed in basic aqueous medium. In addition, it is worthy to mention the monodentate nature of the organic moiety of the osmate esters, which were formulated as (RO)2OsO2L2 where L represents various monodentate ligands. These authors did not postulate on a reaction mechanism. The conventionally accepted mechanism depicted by Figure 3.1 was challenged by Sharpless et al[30]. Low temperature experiments with chromyl chloride oxidation of olefins yielded organic products that were not easily accounted for by the previously accepted mechanism. A new reaction mechanism for this reaction was postulated by Sharpless et al, which was to include other d0 oxo-transition metal species. It was argued that for the conventionally accepted mechanism, the reaction must proceed via direct attack by the organic reductant on the oxygen end of the oxo moiety (path b below) implying the resonance form indicated in 2. However, the resonance structure is better represented by 1 below, indicating the preferred reaction pathway, a. Os 1 O Os a O R Os 2 O b Figure 3.3: Proposed pathways (a and b) for the reaction of organic reductant (R) with osmium tetroxide This mechanism is analogous to the nucleophillic attack in carbonyl compounds that occurs exclusively at the electropositive carbon atom, and not the oxygen atom. This implies the formation of an organometallic osmium(VIII) intermediate. This intermediate subsequently undergoes rearrangement during the rate-determining step (possibly to a dimeric cyclic ester) which, on rapid hydrolysis, yields the product. As opposed to the alternative mechanism, this scheme reduces angular strain on the intermediate ester ring in the first step in the absence of pyridine. Attack by pyridine results in the reductive insertion of the Os – C bond of the metallacycle into an oxo group giving an ester which, on reacting with more pyridine, produces OsO2(O2R)L2. This mechanism has yet to be conclusively proven. 43 R R O C O O + OsO4 C N Os O N R O N Os R O O O O [30] Figure 3.4: The mechanism proposed by Sharpless et al N Os N O R O O N Os N O R R O O O R involving nucleophillic attack by the C – C double bond on the electropostive osmium It can therefore be seen that two mechanisms were proposed, each involving the formation of intermediate species of undetermined composition. There is similar uncertainty regarding the oxidation of alcohols by osmium tetroxide. A study into the kinetics of the oxidation of various organic substrates including alcohols, diols and α-hydroxy acids by osmium tetroxide in alkaline medium conducted by VeeraSomaiah et al[28] concluded that the reaction was first order in osmium and substrate. Whilst no evidence was found for the formation of a stable intermediate complex, a mechanism involving an osmium(VIII) – alcohol transition state was proposed. This mechanism was followed by hydride ion abstraction by the osmium(VIII) in a slow step, as illustrated by the reaction scheme in Figure 3.5. OsO4(OH)H2O + OH- [OsO4(OH)2]2- + H2O H R OH + OsO4* C H H R ... 1 H R C H OH O C OH O O O ... 2 Os O O K Slow Os R C O + OsO3 + H2O ... 3 O O H *[OsO4(OH)2] 2- H written as OsO4 as per original authors Figure 3.5: Proposed reaction scheme for the oxidation of alcohols by osmium tetroxide [28] 44 These investigators found that an increase in hydroxide concentration caused an increase in the rate of the reaction and that the order of the reaction in hydroxide concentration was less than unity. The products of the oxidised substrates were identified as the corresponding aldehydes and ketones. The rate constants for the various alcohols were determined and a selection is reproduced in Table 3.1. Table 3.1: The second order rate constants for the oxidation of several alcohols by osmium(VIII) in -4 - a hydroxide matrix; [Osmium] = 3.16 × 10 mol/L, [OH ] = 0.05 mol/L, Temp = 305 K Subtrate 3 -1 [28] -1 k / ×10 L.mol .s Methanol 4.85 Ethanol 51.2 Chloroethanol 15.3 n-propanol 54.8 2-propanol 69.8 n-butanol 102.3 Isobutabol 83.4 Benzyl alcohol 16100 These authors’ proposed hydride ion abstraction mechanism was substantiated by the trends exhibited by the rates of the oxidation of various alcohols by osmium tetroxide, where electron-donating substituents at the α-carbon should increase the rate of oxidation, while electron-withdrawing substituents should retard it. This hypothesis was backed by a Taft plot with ρ* = -1.91, the negative value of which the authors claim supports their hydride ion transfer mechanism[28]. The reaction scheme proposed by these authors is illustrated in Figure 3.5. The same authors found that, although in acidic medium all organic substrates with double bonds reacted, there was no reaction between osmium tetroxide and alcohols. However, they did not propose any explanation for this phenomenon[28]. Even though none of these studies found evidence for a stable osmium – alcohol complex, it should be noted that the olive-green osmium(VI) complex, K2[OsO2(Ome)4], has been synthesised by the reaction of osmium tetroxide and potassium hydroxide in methanol and characterised by infra-red and UV-VIS spectroscopy[6]. In addition, 45 Subbaraman et al found evidence for the formation of an osmium(VI)-thymine glycol complex upon reaction of osmium(VI)-pyridine complexes with thymine glycols[31]. Glycols, however, would be expected to form more stable esters with osmium(VI) than alcohols because of the cyclic, bidentate nature of the ester. At this point it would be instructive to review the oxidation of alcohols by other oxidants. It is of particular interest to determine whether the reaction is initiated by C – H or O – H cleavage. Westheimer[32], for example, proved that the alcohol oxidation by chromic acid required the initial participation of the O – H bond, i.e. chromate ester formation. This was deduced from the observation that the rate of oxidation of 2-propanol is approximately 1500 times faster than that of diisopropyl ether. H H2CrO4 R1 O R1 O C C O Cr OH R2 H H R2 O R1 O O C + H3O+ + Cr R2 OH O O H H Figure 3.6: Mechanism of alcohol oxidation by chromic acid (Westheimer’s “ester mechanism”) [32] In contrast to chromic acid, ruthenium tetroxide is assumed to react via abstraction of the α-hydrogen without interaction with the O-H bond[33]. In addition, it reacts with alcohols and ethers at approximately the same rate, thus providing further evidence for the above mentioned mechanistic interpretation. This argument was employed by Rankin et al[34] for the oxidation of alcohols by permanganate. The proposed mechanism involved C – H bond cleavage on the basis of a similarity in rates of various substituted benzyl alcohols and their equivalent benzyl methyl ethers. The rationale behind these assumptions was that oxidation proceeding via a C – H bond cleavage mechanism would exhibit similar rates for equivalent alcohols and ethers, since the α-hydrogens in alcohols and ethers are electronically identical - in each, the hydrogen atom is attached to a carbon atom that is attached to an oxygen and other carbons or hydrogen atoms). 46 This concludes an extensive review of the literature on the oxidation of alcohols and ketones by osmium tetroxide. In addition, this review served to include a broad variety of closely related studies in order for comparative conclusions to be drawn. 3.2 Isosbestic Points Isosbestic points arise when two or more absorbing species have equal molar extinction coefficients at the same wavelength when the total concentration of the said species is constant. The presence of an isosbestic point is usually ascribed to the presence of only two absorbing species. This is due to the fact that the probability of more than two species having equal molar extinction coefficients at the same wavelength is very small. This is not to say that other species are completely absent, but these species might be present in low concentrations such that it does not interfere with the absorbance measured at that wavelength. In other instances it is possible that multiple species could be present at appreciable concentrations with molar extinction coefficients that are similar in magnitude to the isosbestic wavelength, or the molar extinction coefficients are multiples of each other, or that some species have comparatively low molar extinction coefficients. In these cases isosbestic points would not be very useful, and the assumption that only two absorbing species are present in appreciable concentrations during the formation of an isosbestic points would be incorrect. These cases are normally difficult to evaluate; however, careful experimentation and data analysis could reveal such anomalies. Throughout this study, it is assumed that only two light absorbing species are present in appreciable concentrations when reference is made to an isosbestic point. 47 3.3 The Stability of Osmium(VIII) in a 2M Hydroxide Matrix 3.3.1 Literature Review Due to its central position within the third row of transition metals, osmium can attain various oxidation states through the nature of the coordinating ligands, rendering its chemistry both unique as well as dynamic. Due to the fact that the alcohol-osmium tetroxide reactions are conducted in a hydroxide matrix, it only seems fitting to discuss the stability of osmium tetroxide in basic medium. Osmium tetroxide exists as a clear translucent solid, which sublimes at room temperature (melting point = 40.25°C). It is known for its high solubility in non- coordinating media such as CCl4 (375 g per 100 g CCl4) and its moderate solubility in water (7.24 g per 100 g water)[13]. Figure 3.7 illustrates the UV-Vis spectrum of osmium tetroxide in both CCl4 and water. The complete spectrum of osmium tetroxide in CCl4 is not shown due to the fact that CCl4 interferes with the osmium tetroxide spectrum at lower wavelengths, creating background noise. This is ascribed to the symmetrical structure shared by CCl4 and osmium tetroxide (i.e. both molecules are tetrahedral). The spectrum of gaseous osmium tetroxide is included for comparison[14, 15]. 48 3.0 Water CCl4 2.5 Gaseous Phase Absorbance 2.0 1.5 1.0 0.5 0.0 220 240 260 280 300 320 340 Wavelength /nm Figure 3.7: The UV-Vis spectra of OsO4 in both CCl4 and water, obtained during this study. The spectrum of gaseous OsO4 is included for comparison [14, 15] The spectra of osmium tetroxide in CCl4 and in water are similar to that of gaseous osmium tetroxide. The spectra of gaseous osmium tetroxide display structured absorptions indicative of a highly symmetrical species with a low density of vibrational states[35]. Absorption spectra of aqueous osmium tetroxide also illustrate vibrational structure; however, the individual bands are broader than the spectra of gaseous osmium tetroxide and osmium tetroxide in CCl4. In alkaline media, osmium tetroxide expands its coordination number to form the [OsO4(OH)]- and cis - [OsO4(OH)2]2- species[35]. Various studies have been reported to establish the reaction equilibria of osmium tetroxide with hydroxide. These studies, having examined the speciation of osmium tetroxide as a function of pH, are in general concurrence, if not in quantitative agreement[16, 35]. 49 According to these authors, the following reaction equilibria were established: Ka1 OsO4·2H2O [OsO4(OH)]-·H2O + H3O+ Ka2 [OsO4(OH)]-·H2O …3.1 …3.2 [OsO4(OH)2]2- + H3O+ The reported acid dissociation constants for the osmium(VIII) acid, OsO4·2H2O, are Ka1 = 8.69×10-13 and Ka2 = 7.58×10-15 M[35]. These values were used to construct a species distribution diagram (Figure 3.2), from which predictions could be made to establish which species would be present at a specified pH. 1.0 OsO4 - [OsO4(OH)] Mole Fraction Osmium 0.8 [OsO4(OH)2] 2- 0.6 0.4 0.2 0.0 8 10 12 14 16 pH Figure 3.8: Species distribution diagram for OsO4 as a function of pH. The distribution diagram depicted by Figure 3.8 was based on the rapid equilibrium between osmium tetroxide and hydroxide, the latter acting as the coordinating ligand. Figure 3.8 illustrates that an increase in pH leads to increased formation of the [OsO4(OH)]- species. Significant amounts of the cis - [OsO4(OH)2]2- species only forms at pH > 14, and under these conditions this species spontaneously decomposes to form 50 the trans-[OsO2(OH)4]2- species, which is considered as the dominant osmium(VI) species in aqueous solutions above pH = 5 [35]. 3.3.2 Experimental Procedures An aqueous osmium tetroxide solution was prepared by extracting osmium tetroxide from a CCl4 stock solution, as described in Chapter 2.5.3. A 1.305 × 10-4 mol/L osmium(VIII) solution was prepared through the addition of 20 mL of the extracted osmium tetroxide to a reaction vessel containing 230 mL of a 2.174 mol/L NaOH solution, such that the final hydroxide concentration was 2 mol/L (pH = 14.3). The NaOH solution was prepared using degassed water and the solution was purged with nitrogen prior to the addition of the aqueous osmium tetroxide solution. After the addition of osmium tetroxide, the solution was maintained under inert conditions for the duration of the experiment. This was done in order to exclude carbon dioxide from the solution, thus preventing the formation of carbonates. Carbonate formation would lead to a lowering in pH in addition to possible side-reactions involving the produced carbonates. The first UV-Vis spectrum was recorded immediately following the addition of osmium tetroxide to the reaction vessel. Subsequent spectra were recorded by periodic sampling of the solution over a period of 625 hours. A 100 mL stock osmium(VI) solution was prepared by dissolving 0.3339 g K2[OsO2(OH)4] in 2 mol/L NaOH solution such that the total osmium concentration was 9.062 × 10-3 mol/L. In order to attain a 1.305 × 10-4 mol/L osmium(VI) solution, 720 µL of the stock osmium(VI) solution was transferred to a 50 mL volumetric flask which was then filled with 2 mol/L NaOH solution. The total osmium concentration of each individual solution was determined through the thiourea method. 51 3.3.3 Results and Discussion As illustrated in Figure 3.9 there is a substantial change, over time, in the optical spectrum of osmium(VIII) in a 2 mol/L hydroxide matrix. The dashed arrow indicates the initial osmium(VIII) spectrum at t = 0 hours, while the solid arrows indicates the direction of increasing time. 0.5 Absorbance 0.4 0.3 0.2 0.1 t=0 0.0 300 400 500 600 Wavelength /nm Figure 3.9: The change in the UV-Vis spectrum of osmium(VIII) in 2 mol/L NaOH as a function of time, from t = 0 hour to t = 625 hours. The spectra change in the direction of the solid arrows over -4 time. [Osmium] = 1.305 × 10 mol/L In Chapter 3.3.1, it was concluded that the predominant osmium(VIII) species present at pH = 14.3 is the cis - [OsO4(OH)2]2- species. This species has a characteristic UV-Vis spectrum, which shows two peak maxima at 260 and 320 nm. As the reaction proceeds as a function of time, these maxima show a general increase. This increase is also associated with a shift in the peak maximum from 320 nm to 341 nm, and the eventual disappearance of the peak at 260 nm. The absorbance in wavelength region 320 – 475 nm shows a general increase to the point where a plateau is reached, after which 52 the absorbance slowly decreases. In addition, the spectra also indicate two sets of isosbestic points; the first being formed at 274 nm, which shifts to 258 nm as the reaction progresses. 0.40 Absorbance 370nm 0.35 0.30 0.25 0.20 0.15 0 100 200 300 400 500 600 Time /Hours Figure 3.10: Progress curve depicting the rate of change of absorbance at 370 nm. -4 [Osmium] = 1.305×10 mol/L; [NaOH] = 2 mol/L Figure 3.10 illustrates the change of absorbance at 370 nm as the reaction progresses. This figure suggests that the absorbance increases, reaches a plateau, and then decreases slowly until equilibrium is reached. This general trend illustrates two important points – (a) the reaction follows a distinct two-step process, and (b) there must be at least three absorbing osmium species present in appreciable concentrations. To elaborate on these points, various osmium species would have different molar extinction coefficients at a single wavelength (excepting the isosbestic wavelengths). The formation of an intermediate species, with a molar extinction coefficient larger than the initial osmium(VIII) species would therefore result in an increase in the absorbance at said wavelength; provided that the intermediate species is present in appreciable 53 concentration. This corresponds to the first step in the reaction process. The second step in the reaction would correspond to the formation of a third species with a molar extinction coefficient comparatively smaller than both that of the initial osmium(VIII) and that of the intermediate species, thus leading to the observed decrease in absorbance. However, it can also be argued that the observed changes in the optical spectrum is only due to a combination of two species, namely the initial osmium(VIII) and the final osmium product. This uncertainty could be resolved experimentally. Figure 3.11 illustrates UV-Vis spectra of the initial osmium(VIII) species and the experimentally obtained “intermediate” species. Since the reduction of osmium(VIII) leads to the formation of osmium(VI) as the final product, the spectrum of a pure osmium(VI) solution was recorded and is illustrated in Figure 3.11. 54 0.6 Os(VI) Os(VIII) Os-Intermediate Addition Spectrum 0.5 Absorbance 0.4 0.3 0.2 0.1 0.0 300 400 500 600 Wavelength /nm -4 Figure 3.11: The spectra isolated during the reduction of 1.305 × 10 mol/L osmium(VIII) in 2 mol/L -4 NaOH. The spectrum of a 1.305 × 10 mol/L osmium(VI) solution in 2 mol/L NaOH is included for comparison. Since the Beer-Lambert law is additive, a theoretical addition spectrum between pure osmium(VIII) and pure osmium(VI) can be constructed, as shown in Figure 3.11. If the experimentally observed spectral changes were only due to the simultaneous presence of osmium(VIII) and osmium(VI), then the theoretical addition spectrum would correspond to that of the experimentally obtained “intermediate” species. From Figure 3.11 it is evident that this is not the case. It can thus be concluded that the reduction reaction proceeds via a distinct intermediary species, which supports the earlier hypothesis that the reduction of osmium(VIII) to osmium(VI) follows a distinct two-step process involving at least three species. 55 3.4 The Reduction of Osmium Tetroxide by Aliphatic Alcohols in a 2M Hydroxide Matrix 3.4.1 Literature Review H.S Sing et al[18], who performed much of the early work on the kinetics of osmium tetroxide catalysed oxidation of alcohols by hexacyanoferrate(III), found evidence for the occurrence of only a single reaction with a single rate constant. The flaw in many of these early investigations was the fact that the first concentration recordings were made only approximately 5 to 10 (and sometimes as much as 20) minutes after initiation of the reaction, therefore excluding data during these first crucial minutes. They found that the order of the reaction with respect to osmium, 1- and 2-propanol and hydroxide (at hydroxide concentrations lower than 0.01 mol/L) was unity. At hydroxide concentrations greater than 0.01 mol/L the rate became independent of hydroxide concentration. These authors based their reaction scheme on the observation quoted from Cotton and Wilkinson[36], that “OsO4(OH)22- is the only reactive species”. However, at the low hydroxide concentrations at which they were working there would be no OsO4(OH)22present. Even at the highest hydroxide concentration used (0.01 mol/L) there would be approximately equal quantities of OsO4(OH)- and OsO4, but no OsO4(OH)22-. attempt was made to explain why the OsO4(OH)22- No is named as the only reactive species. This assertion is repeated without explanation in other studies[21, 37] . The proposed reaction scheme involves a seven-coordinate osmium(VIII)-propanol transition state (rare, in itself), which decomposes to the aldehyde and OsO2(OH)42-. The aldehyde is subsequently oxidised to the carboxylic acid. These authors extended their work from propanol to cover many other alcohols, with similar results and conclusions to the above study[19, 20, 23]. The derived rate laws were similar for all these studies: d[Fey] 2k 1K 1K 2[S][OH − ][Os(VIII) ]T = dt 1 + K 1[OH − ] where: Fey is the hexacyanoferrate(III) co-oxidant; S is the alcohol substrate 56 The rate and equilibrium constants refer to the following reaction scheme: [OsO4(H2O)(OH)]- + OH[OsO4(OH)2]2- + S Complex k1 K2 K1 [OsO4(OH)2]2- + H2O Complex Os(VI) + Intermediate Products Work with diethylene glycol monomethyl ether, diethylene glycol monoethyl ether, methoxyethanol and ethoxyethanol[23] prompted them to conclude that the reaction proceeds either by: a) activated complex formation between osmium tetroxide and the organic substrate as discussed above; or b) activated complex formation between osmium tetroxide and an anion derived from the alcohol molecule. 3.4.2 Experimental Procedures This section serves to introduce the experimental procedure of a typical kinetic reaction during which osmium tetroxide was reduced by several aliphatic alcohols at pH = 14.3. Methanol was used as the representative alcohol. The progress of the kinetic reactions was recorded using a Perkin-Elmer Lambda 12 UV-Vis spectrophotometer, interfaced with the UV WinLab software package. Reactants were mixed in a thermostatic reaction vessel maintained at 25.0°C ± 0.1°C, such that the final reagent volume was 25 mL. The reaction progress was followed in one of two ways, depending on the reaction rate: 1) scanning the wavelength region from 600 nm to 200 nm at a cycle time of 2 minutes and a scan speed of 240 nm/min. This method was used to follow the reaction at low methanol concentrations, during which the progress of the reaction proceeded at a slow rate. 2) recording single wavelength absorbance data at 370 nm (the wavelength based on the analysis of spectral curves that produced optimal progress curves). Absorbance data was recorded at 0.5 second intervals over a period of 30 minutes. This method was used for reactions with a high methanol concentration that resulted in faster reaction rates. 57 Prior to each kinetic reaction, a reaction “blank” was obtained, where the osmium(VIII) spectrum in a 2 mol/L hydroxide was recorded in the absence of methanol. This was required in order to obtain the initial osmium(VIII) spectrum at time equals zero minutes. Osmium tetroxide was obtained as a freshly prepared aqueous stock solution, as described in Chapter 2.5.3. The osmium tetroxide was extracted from a carbon tetrachloride stock solution into distilled water. Due to the volatile nature of osmium tetroxide, coupled with its moderate solubility in water, the osmium tetroxide concentration of the stock aqueous solution was expected to decrease over time. For this reason, the total osmium concentration of each solution prepared for the kinetic investigations were respectively determined by the thiourea method. In this manner the recorded absorbance data for a series of alcohol concentrations could be normalised in order to compensate for the gradual decrease in the osmium tetroxide concentration of the stock aqueous solution. All reactions were conducted in 2 mol/L hydroxide matrix. This concentration was achieved by the addition of an appropriate volume of a 6 mol/L sodium hydroxide solution to the reaction vessel. A 0.1716 mol/L stock methanol solution was prepared in a 2 mol/L sodium hydroxide matrix. The solution was prepared in this manner in order to avoid a substantial change in the pH of the osmium solution upon addition of the stock methanol solution. Table 3.2 shows the reagent volumes and concentrations for a typical kinetic investigation. investigation. All reagents were freshly prepared prior to commencement of the 58 Table 3.2: Reactant volumes and concentrations for the reaction of osmium tetroxide with methanol in a 2 mol/L hydroxide matrix Reaction Number Reagent Volume /Concentration (1) (2) (3) (4) (5) (6) (7) Volume 6M NaOH / M 8.285 8.188 8.091 7.945 7.848 7.605 7.362 Volume H2O / mL 14.570 14.375 14.181 13.890 13.695 13.210 12.724 0.146 0.437 0.728 1.166 1.457 2.185 2.914 2.000 2.000 2.000 2.000 2.000 2.000 2.000 1.000 3.000 5.000 8.000 10.00 15.00 20.00 2.558 2.558 2.558 2.558 2.558 2.558 2.558 Volume 0.1716 M methanol in 2 M NaOH / M Volume aqueous OsO4 / mL [Methanol] -3 / × 10 M [Osmium] -4 / × 10 M † No more than 30 seconds elapsed from initiating the reaction to the first spectral recording made. This procedure was repeated for several aliphatic alcohols, including ethanol, propan-1ol, and butan-1-ol. † The calculated total osmium concentration after normalisation of UV-Vis data 59 3.4.3 Results and Discussion Figure 3.12 illustrates the change in the osmium(VIII) UV-Vis spectrum as a function of time; a trend typical of the osmium tetroxide-methanol reaction. indicates the direction of increasing time. The solid arrow The spectra denoted by A, B and C respectively refer to the spectra recorded at t = 0 minutes, t = 34 minutes and t = 986 minutes. This figure shows the change in the shape of spectra, from the initial osmium(VIII) spectrum to the spectrum obtained once equilibrium has been achieved. 0.6 B A 0.5 Absorbance 0.4 0.3 0.2 C 0.1 0.0 240 280 320 360 400 440 480 520 560 600 Wavelength /nm Figure 3.12: The change in the osmium(VIII) optical spectrum as a function of time, from t = 0 to -3 t = 986 minutes, upon addition of 1.00 × 10 mol/L methanol. The spectra denoted by A, B, and C respectively refer to the spectra recorded at t = 0, t = 34 and t = 986 minutes. The solid arrow indicates the direction of absorbance change with time. The solid and dashed lines indicate the -4 - occurrence of two isosbestic points. [Osmium] = 1.305 × 10 mol/L; [OH ] = 2 mol/L 60 [a] 0 .5 A b s o rb a n c e 0 .4 0 .3 0 .2 0 .1 0 .0 230 270 310 350 390 430 470 510 550 590 510 550 590 W a v e le n g th /n m [b] 0 .5 A b s o rb a n c e 0 .4 0 .3 0 .2 0 .1 0 .0 230 270 310 350 390 430 470 W a v e le n g th /n m Figure 3.13: Illustration of the isosbestic points formed during the reduction of osmium tetroxide by methanol in 2 mol/L hydroxide medium. (a) The first transient isosbestic point occurs at 274 nm as indicated by the dashed line; (b) the second isosbestic point occurs at 258 nm as indicated by the solid line 61 The occurrence of two sets of isosbestic points is also evident in Figure 3.12. The first transient isosbestic point occurs at 274 nm, which changes to the second isosbestic point at 258 nm, respectively indicated by the solid and dashed lines in Figure 3.12. Figures 3.13 (a) and (b) aims to provide a clearer illustration of these isosbestic points. The occurrence of these isosbestic points hint at the establishment of at least two equilibria involving a minimum of three high oxidation state osmium species. Figure 3.14 shows the progress curves of the reactions reported in Table 3.2. The absorbance data of the reaction with the lowest methanol concentration was recorded by scanning the 600 nm to 200 nm wavelength region, at 2 minute cycle intervals over a period of 986 minutes. The absorbance data of all the subsequent reactions reported in Table 3.2 was recorded at a fixed wavelength (370 nm) at 0.5 second intervals. It is clear that the absorbance at 370 nm initially increased as a function of time, reached a plateau, and then gradually decreased until the reaction reached equilibrium; a trend consistent with the reaction proceeding via a distinct two-step process. An identical trend was established in Chapter 3.3.3 where the spontaneous reduction of osmium(VIII) in a 2 mol/L hydroxide matrix was investigated. Once again it can be proposed that the trend exhibited by Figure 3.8 implies that the reduction of osmium(VIII) by methanol in a 2 mol/L hydroxide matrix proceeds via two consecutive reactions which involves a minimum of three osmium species; a conclusion that was drawn from the presence of isosbestic points. 62 0.65 -3 1.00×10 M -3 3.00×10 M -3 5.00×10 M -3 8.00×10 M -3 10.0×10 M -3 15.0×10 M -3 20.0×10 M Absorbance at 370nm 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0 500 1000 1500 2000 2500 Time /s Figure 3.14: Progress curves demonstrating the rate of change of the absorbance at 370 nm at -4 different methanol concentrations. [Osmium] = 2.631 × 10 mol/L; [NaOH] = 2 mol/L; Methanol concentrations are denoted by the legend. In addition, the similarities demonstrated by the spectral changes observed during this investigation and that observed from the reduction of osmium(VIII) in a 2 mol/L hydroxide matrix implies that the reduction of osmium(VIII) proceeds via identical osmium species, irrespective whether the reducing agent is methanol or water. Therefore, the same conclusions made in during Chapter 3.3.3 would be valid for this reaction. Figure 3.15 (a) illustrates three spectra isolated at various times during the reduction of osmium(VIII) in the presence of methanol. The spectra depicted in Figure 3.15 (a) were respectively recorded at a time where these spectra most closely represent: 1) the initial osmium(VIII) species (species A) 2) the product of the first reaction (species B) 63 3) the final product of the reaction For clarity, these species were respectively labelled species A, species B and species C. [a] [b] 0.6 0.6 Species A 0.5 t = 0 min t = 34 min t = 986 min Species B 0.5 Species A Species B 0.4 Absorbance 0.4 Absorbance t = 0 hours t = 262.3 hours t = 624.1 hours Pure Os(VI) 0.3 0.2 0.3 0.2 Species C 0.1 0.1 0.0 0.0 240 280 320 360 400 440 480 520 560 600 240 Wavelength /nm 280 320 360 400 440 480 520 560 600 Wavelength /nm Figure 3.15:(a) Spectra isolated at various times during the reduction of osmium(VIII) by methanol. -4 -3 [Osmium] = 2.631 × 10 mol/L; [Methanol] = 1.00×10 mol/L; [NaOH] = 2 mol/L. (b) A comparative -4 reduction reaction conducted in the absence of methanol. [Osmium] = 1.305 × 10 mol/L; [NaOH] = 2 mol/L. In both figures the times at which these spectra were recorded are denoted in the legend. Figure 3.15 is a comparison between those spectra obtained in Chapter 3.3.3 for the reduction of osmium(VIII) in the absence of organic substrates. The similarities between these figures identified the observed spectra as osmium species as these spectra could not be ascribed to the presence of any organic species nor its reaction products. This prompts the question whether the spontaneous reduction of osmium(VIII) in the absence of methanol influenced the kinetics of the reaction in which methanol was present. Although this question will be addressed more rigorously in subsequent chapters, preliminary assessments reveal that the reaction between osmium tetroxide and hydroxide would not influence the validity of the kinetic reactions significantly. In Figure 3.16, the reaction of osmium tetroxide with hydroxide is superimposed on the progress curves obtained for the reduction of osmium tetroxide by methanol in a 2 mol/L hydroxide matrix. 64 0.65 0.00 M -3 1.00×10 M -3 3.00×10 M -3 5.00×10 M -3 8.00×10 M -3 10.0×10 M -3 15.0×10 M -3 20.0×10 M Absorbance at 370nm 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0 500 1000 1500 2000 2500 Time /s Figure 3.16: Progress curves indicating the rate of change of the absorbance at 370 nm for various methanol concentrations. The progress curve depicting the reaction of osmium(VIII) with 0 mol/L methanol was superimposed onto the progress curves for those reactions involving -4 varying methanol concentrations. [Osmium] = 2.631 × 10 mol/L; [NaOH] = 2 mol/L; methanol concentrations are denoted by the legend. During the 30 minute period allowed for the osmium(VIII)-methanol experiments, there is a noteworthy, albeit small, increase in the absorbance of the reaction conducted in the absence of methanol. In terms of the kinetics of the reaction, the influence of the spontaneous reduction osmium(VIII) in hydroxide matrix is negligible since the rate of the methanol reduction would be orders of magnitude greater than that reaction conducted in the absence of methanol. However, this is only a qualitative observation and more accurate comparisons could only be made in subsequent chapters once the rate constants of the various reactions had been established. Figures 3.17 – 3.19 illustrate the progress curves obtained for the osmium-alcohol reaction for the organic substrates used, i.e. ethanol, propan-1-ol and butan-1-ol. 65 0.65 -3 1.00×10 M -3 3.00×10 M -3 5.00×10 M -3 8.00×10 M -3 10.0×10 M 15.0×10-3 M -3 20.0×10 M Absorbance at 370nm 0.55 0.45 0.35 0.25 0.15 0 500 1000 1500 2000 2500 Time /s Figure 3.17: Progress curves illustrating the change in absorbance at 370 nm as a function of time for the reaction between osmium tetroxide and varying ethanol concentrations. -4 [Osmium] = 2.590 × 10 mol/L; [NaOH] = 2 mol/L; ethanol concentrations are denoted in the legend. 0.55 -3 1.00×10 M -3 5.00×10 M -3 8.00×10 M -3 10.0×10 M -3 15.0×10 M 20.0×10-3 M 0.50 Absorbance at 370nm 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0 500 1000 1500 2000 2500 Time /s Figure 3.18: Progress curves illustrating the change in absorbance at 370 nm as a function of time for the reaction between -4 osmium tetroxide and varying propan-1-ol concentrations. [Osmium] = 2.285 × 10 mol/L; [NaOH] = 2mol/L; propan-1-ol concentrations are denoted by the legend. 66 0.55 -3 1.00×10 M -3 3.00×10 M -3 5.00×10 M -3 8.00×10 M -3 10.0×10 M 15.0×10-3 M -3 20.0×10 M 0.50 Absorbance at 370nm 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0 500 1000 1500 2000 2500 Time /s Figure 3.19: Progress curves illustrating the change in absorbance at 370 nm as a function of time for the reaction between osmium tetroxide and varying butan-1-ol concentrations. -4 [Osmium] = 2.212 × 10 mol/L; [NaOH] = 2 mol/L; butan-1-ol concentrations are denoted by the legend. Preliminary (qualitative) assessment of Figures 3.16 – 3.19 reveal that the oxidation of alcohols by osmium tetroxide proceeded at a faster rate along the trend methanol < ethanol < propan-1-ol < butan-1-ol. This trend can be explained in terms of the increased electron donicity of the substituents on the α-carbon of the alcohols which increases with increasing alcohol chain length (methanol < ethanol < propan-1ol < butan-1-ol), resulting in the observed reaction rate increase along this trend. 67 3.5 The Geometrical Analysis of Kinetic Data using Mauser Diagrams 3.5.1 Literature Review In virtually all aspects of physical chemistry the kinetics of chemical reactions is treated only on the level of concentration equations. Furthermore, most of these chemical reactions in liquid phase are investigated via UV-Vis spectrophotometry, where the measured output used is absorbance data, which generally obey the Beer-Lambert law. In contrast to concentration determinations, absorbance data leads to a loss of kinetic information due to its inherent limited sensitivity[38]. Mauser diagrams are a powerful tool used for the evaluation of absorbance data. These diagrams are the collective name given to the absorbance (A), absorbance difference (AD) and absorbance difference quotient (ADQ) diagrams. These are typically two-dimensional diagrams, with the so-called Mauser space being multidimensional (n ≥ 2)[39], which allow for the determination of the number (s) of linearly independent reaction steps of a chemical reaction. By definition, a linear reaction system consists of first-order reaction steps; while linearly independent reactions are those reactions which are independent of the reaction order. Each reaction mechanism consists of a distinct number (s) of linearly independent reaction steps that can be determined through Mauser diagrams. Recently it has been established that, in addition to obtaining the number of linearly independent reaction steps, the geometric analysis of the “Mauser space” (or absorbance space) could provide new routes for the kinetic evaluation of chemical reactions. The absorbance (or absorbance differences) of n wavelengths establishes the axes of the absorbance space. A straight line in this space is obtained when the reaction system consists of a single linearly independent reaction step (s = 1), with the reaction order of the resultant curve being independent of the reaction order. A reaction system being described by two linearly independent steps (s = 2) would lead to a bent curve in 68 the Mauser space, which lies on a single plane. Since the curve lies on a single plane, a two-dimensional coordinate system can be introduced which lies in this plane. The coordinates of the Mauser curve with regard to the established two-dimensional coordinate system can thus be evaluated[39-43]. The reaction systems described by three linearly independent reaction steps (s = 3) also leads to a bent curve in the Mauser space. However, these systems differ from reaction systems with two linearly independent reaction steps in that the absorbance curve obtained does not lie on a single plane, and thus a two-dimensional coordinate system cannot be introduced. These reaction systems are evaluated on the basis of three-dimensional absorbance diagrams (i.e. Ai versus Aj versus Ak; where the subscripts refer to the respective wavelengths), using the concept of parallel projection[42], during which three-dimensional absorbance diagram is geometrically projected onto a two-dimensional coordinate system. In this manner, the eigenvalues describing the reaction mechanism can be determined. Furthermore, the reaction system s = 3 is reduced to a system which is described by only two linearly independent concentration variables[42]. The principles for the evaluation of the n-dimensional Mauser space is generally applicable to reactions where s = 1, s = 2 and s = 3 for linear and non-linear reaction systems. The following relations illustrate examples of the reaction systems which could be evaluated through the geometric analysis of the absorbance space[39, 42]: for s = 1 for s = 2 A B A A+B B A A A+B A ; A C C B B ; C C D C+D ;E B ;B+C F+D D 69 for s = 3 A A A A A B D C B C D D; E B; C B; C D; E B + C; D E; F F F G E A B; C D F Mauser diagrams provide particularly attractive routes for the elucidation of reaction models and consequently reduce the number of unknown parameters associated with the reaction. This is due to the fact that knowledge of the molar extinction coefficients of the absorbing species is not a prerequisite for the application of the theory. The only requirement for this type of evaluation is that a sufficient number of species absorb in the region of interest, i.e. that the single reactions of the system are individually registered spectrophotometrically. It should be noted that reaction models defined by a specific number of linearly independent steps cannot be distinguished from one another by purely spectroscopic means; e.g. for the system s = 3 the reaction model A → B → C → D cannot be distinguished from the reaction model A → B; C → D; E → F. To elaborate on the evaluation of Mauser diagrams, consider the following general consecutive reactions which are described by two linearly independent reaction steps: A k1 k-1 B k2 k-2 C … 3.3 From Relation 3.3 it could be assumed that, at any given time, only two absorbing species are present in appreciable concentrations. Figure 3.20 depicts a general Mauser diagram for a reaction system consisting of two linearly independent steps, such as the reaction represented by Relation 3.3. The bent curve illustrated in Figure 3.20, consists of two linear regions, denoted by regressions [1] and [2]. Using the aforementioned assumption (i.e. that only two absorbing species 70 are present in appreciable concentrations at any given time) into consideration, two important conclusions could be derived from Figure 3.20[44], namely: o the linear region denoted by the regression line denoted [1] represents the reaction A ↔ B o the linear region denoted by the regression line denoted [2] represents the reaction B ↔ C 2.2 C 2.0 B [2] 1.8 [3] Absorbance j 1.6 1.4 1.2 1.0 B 0.8 0.6 A [1] 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Absorbance i Figure 3.20: Typical 2-dimensional Mauser diagram for the general reaction A ↔B↔C Extrapolation of the regression lines [1] and [2] results in a point where the two regression lines intersect, which is denoted [3] in Figure 3.20. Effectively, this point represents the absorbance of species B, at the respective wavelength i and j. At this point the species in solution exists solely as species B, which implies that the concentration of species B at this point would equal the concentration of species A at the start of the reaction[44]. Since the concentration of species A at the start of the reaction is usually known, the molar extinction coefficient of species B can be calculated (at various wavelengths) using the Beer-Lambert law. 71 3.5.2 Experimental Procedures An aqueous osmium tetroxide solution was prepared through extraction from a CCl4 stock solution into distilled water, as described in Chapter 2. The total osmium concentration of this solution was determined by the thiourea method. Aqueous osmium tetroxide was transferred to a thermostatic reaction vessel containing NaOH to give a final hydroxide concentration of 2 mol/L. This solution was prepared in order to attain an initial osmium(VIII) spectrum (at time = 0 minutes), in the absence of alcohol. A second solution was prepared, in which aqueous osmium tetroxide was added to a reaction vessel containing a mixture of NaOH and methanol, such that the final hydroxide and methanol concentrations were 2 mol/L and 1.00×10-3 mol/L, respectively. Once sufficient agitation had been achieved, the UV-Vis spectra of this solution were recorded as a function of time. The time elapsed between the addition of osmium tetroxide and the first spectral recording did not exceed 32 seconds. The instrumental settings used for recording UV-Vis spectra were: o wavelength range scanned: 600 – 200 nm o cycle time: 2 minutes o scan speed: 240 nm/min The reaction was stopped after 998 minutes. 3.5.3 Development of Computational Software for Data Analysis The program GP2 was developed specifically for the geometric analysis of twodimensional Mauser diagrams. This program allows for the absorbance of data acquired at each wavelength to be plotted against the absorbance data of subsequent wavelengths. For instance, the absorbance data at wavelength i is plotted against the absorbance data acquired at every wavelength from wavelength (i + a) [where a = 1; 2; 3; …) to wavelength j; resulting in a total of [j - (i + 1)] Mauser diagrams being analysed for wavelength i. Employing a linear least-squares algorithm, the program fits two regression lines to user-defined series for each of the Mauser diagrams generated at 72 wavelength i, in an analogous manner to the diagram depicted in Figure 3.20. The coordinates for the point of intersect between the regression lines are then calculated for each of the diagrams, and an average absorbance value is calculated at each wavelength. The process is repeated for all subsequent wavelengths. As previously mentioned, Mauser diagrams that produce a straight line in the Mauser space describes a reaction system consisting of a single linearly independent reaction step. In certain cases, reaction systems described by two linearly independent reaction steps also produce Mauser diagrams in which a straight line is obtained in the Mauser space. This phenomenon typically occurs when the wavelengths used to construct the diagram are so close to each other (e.g. absorbance at i versus absorbance at (i + 1)) that the absorbance values of the respective wavelengths are indistinguishable from each other. Consequently, the data obtained from these Mauser diagrams should be considered as outliers, and should not contribute to the average absorbance returned by the program. For this reason the program has an “angle filter” which excludes these outlier values. In essence, the angle filter determines the angle formed at the point at which the regression lines intersect. If the calculated angle does not fall within a userdefined range, the absorbance determined at that point is excluded and has no contribution to the final average absorbance returned by the program for that particular wavelength. Consider Relation 3.3: A k1 k-1 B k2 k-2 C …3.3 The values returned by the GP2 program in this instance would represent the absorbance of species B, since the species present at the point of intersect would be in the form of species B. Since the concentration of species A at the start of the reaction equals the concentration of species B at this point, the molar extinction coefficient of species B at various wavelengths can be determined through the use of the BeerLambert law. The source code of the GP2 program is detailed in Appendix 1. 73 3.5.4 Results and Discussion Figure 3.21 illustrates the change in the UV-Vis spectra as a function of time for the methanol reduction of osmium tetroxide in a hydroxide medium. indicates the direction of increasing time. The solid arrow The spectra denoted by A, B and C respectively refer to the spectra recorded at t = 0 minutes, t = 34 minutes and t = 986 minutes. This figure illustrates the general shape of the various spectra, from the initial osmium(VIII) spectrum, to the final spectrum once the solution had reached equilibrium (t = 986 minutes). 0.6 B A 0.5 Absorbance 0.4 0.3 0.2 C 0.1 0.0 240 280 320 360 400 440 480 520 560 600 Wavelength /nm Figure 3.21: The change in the Osmium (VIII) optical spectrum as a function of time, upon addition -3 of 1.00 × 10 mol/L methanol. The spectra denoted by A, B and C respectively refer to the spectra recorded at t = 0, t = 34 and t = 986 minutes. The solid arrow indicates the direction of increasing -4 - time. [Osmium] = 1.305 × 10 mol/L; [OH ] = 2 mol/L 74 Figure 3.22 [a] and [b] shows a three dimensional Mauser diagram which was constructed from the data presented in Figure 3.21. The rotation of [a] results in the formation of a straight line (as illustrated by [b]) which lies on a single plane, implying that the number of linearly independent reaction steps equal two, i.e. s = 2. [b] [a] 0.38 0.38 0.36 0.36 0.34 0.28 0.26 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.28 0.26 0.24 0.35 0.30 Absorba 0.25 0.20 nce 370 0.15 0.10 nm 0.20 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 ce 3 an 0.40 or b 0.20 0.22 0.9 0.8 0.7 0.6 or b an ce 24 0.22 70 n 0n m 0.24 0.30 m 0.30 0.32 0.5 Absorbance 240nm 0.4 0.3 Ab s Absorbance 280nm 0.32 Ab s Absorbance 280nm 0.34 Figure 3.22: [a] 3D Mauser diagram of A370 vs. A240 vs. A280 (the indices indicate the wavelengths used). [b] Rotation of part [a]. The curve lies on a single plane, and is viewed along the edge of this plane. The result is a straight line indicating the case s = 2. Since the bent curve observed in Figure 3.22 lies on a single plane, a two dimensional coordinate system can be introduced which lies in this plane, as illustrated by Figure 3.23. Figure 3.23 illustrates a two-dimensional Mauser diagram for the reduction of osmium(VIII) by methanol at pH = 14.3. This diagram hints at the occurrence of two consecutive reduction reactions, as depicted in Figure 3.23. However, as will be seen during the remainder of this chapter, the reduction reactions are not as simple as the relations depicted in Figure 3.23. 75 1.0 i = 240nm i = 280nm Os( VI ) Absorbance at i 0.8 Os -In 0.6 0.4 Os(VIII) t Os-Int 0.2 0.0 0.15 0.25 0.35 0.45 0.55 Absorbance at 370nm Figure 3.23: A 2D Mauser diagram constructed from the data presented in Figure 3.21. The advantage of this type of analysis is that, irrespective of the nature of the intermediate species, the molar extinction coefficient of the intermediate species could easily be obtained, as described in Chapter 3.5.1. By employing the program GP2, the molar extinction coefficients of the intermediate osmium species was calculated at various wavelengths. A molar extinction coefficient spectrum of the intermediate species could thus be constructed, which is illustrated by Figure 3.24. 76 Molar extinction coefficient /L.mol-1.cm-1 7000 6000 5000 4000 3000 2000 1000 0 270 290 310 330 350 370 390 410 430 Wavelength /nm Figure 3.24: Molar extinction spectrum for the Os(VII)-Intermediate species, calculated using the program GP2. It can be seen that this type of data analysis eliminates tedious experimental procedures for the determination of the Os(VII)-intermediate species’ molar extinction coefficient. In addition, Mauser diagrams also aid in the elucidation of proposed reaction models for the reduction of osmium(VIII) by methanol at pH = 14.3. The values for the molar extinction coefficients obtained from this method would be compared to those obtained using other methods of analysis in subsequent chapters. 77 3.6 The Osmium(VIII) – Alcohol Kinetic Model 3.6.1 Literature Review The evaluation of kinetic data plays an important role in this study and it is thus essential to briefly describe the theory behind some of the results. The osmium(VIII) – alcohol reaction can be represented as: x Os(VIII) + y RCH2OH → Products …3.4 The rate of this reaction can therefore be written as: Rate = - d [RCH 2 OH] d [Os(VIII)] =− = k [Os(VIII)] x [RCH 2 OH] y dt dt …3.5 This rate equation can be reduced to a pseudo-first order rate equation by maintaining the alcohol concentration in sufficient excess, thus incorporating the alcohol term into the rate constant. Equation 3.5 can thus be reduced to: Rate = - d [Os(VIII)] = k obs [Os(VIII)] x dt …3.6 If x = 1, the reaction is first order with respect to Os(VIII) and can thus be written as: d [Os(VIII)] = −k obs dt [Os(VIII)] …3.7 Equation 3.7 can now be integrated between time = 0 and time = t, using the Os(VIII) concentration at time = 0 and time = t: [ Os(VIII)] t t d [Os(VIII )] = −k obs dt [Os(VIII )] 0 [ Os(VIII)] 0 ∫ ∫ …3.8 Upon integration, equation 3.8 becomes: ln [Os(VIII)] = kt – ln [Os(VIII)]0 …3.9 78 In an analogous manner, the linear rate equations for zero and second order reactions (represented by equations 3.10 and 3.11, respectively) can be derived: [Os(VIII)] t = [Os(VIII)] 0 − kt …3.10 1 1 − = kt [Os(VIII)] t [Os(VIII)] 0 …3.11 The complexities of the osmium(VIII) – alcohol reaction prevents the plotting of kinetic data in terms of equations 3.9 - 3.11. straight forward single-step reactions demonstrated by Therefore, kinetic modelling software was utilised in order to evaluate the kinetic data for the osmium(VIII) – alcohol reaction. The fact that two consecutive reduction reactions occur, imply that the equations cannot be plotted in terms of two variables since, if the reactions occur simultaneously, there would be a minimum of three absorbing species, each contributing to the total absorbance in varying degrees at any given time. Thus, the utilisation of KinEqui kinetic modelling software enabled fitting more complex reaction models to the experimentally obtained kinetic data. This section describes the challenges in proposing an appropriate reaction model that fits the experimental data within acceptable statistical error. A number of kinetic models were proposed; however, only four models that best fit the experimental data are illustrated. A single theoretical model was chosen to represent the experimental data. Reasons for this choice will be provided. 3.6.2 Experimental Procedures Kinetic reactions were performed as previously discussed in Chapter 3.4.2, using several aliphatic alcohols including methanol, ethanol, propan-1-ol and butan-1-ol. 79 3.6.3 Computational Software Utilised for Kinetic Modelling [45] The program KinEqui (Visual Basic 6) was developed for the integration of rate equations and the least squares fitting of the rate equations to experimental data. The user interface of the program allows the user to tweak a number of parameters. The program accesses a reaction model bank from which the user can select the appropriate kinetic model. Reaction models not present in the model database could be incorporated by introducing a new Visual Basic Script into the program without having to recompile the entire program. The calculation scheme for fitting spectrophotometric data is summarized below. The program has two main components that work in tandem; namely a routine to integrate the differential equations and a routine to do the least squares fitting, i.e. function minimization. The least squares routine can be set to optimize only the rate constants, only the extinction coefficients, or both simultaneously. A Runge-Kutta algorithm[46] was used to integrate a set of rate equations (viz. equation 3.12) numerically. The local truncation error at a specified step is a measure of the amount by which the difference equation being used for the approximation fails to satisfy the exact solution of the differential equation. The Runge-Kutta method is equivalent to a fourth order Taylor expansion method with the added advantage that the functions do not need to be differentiated four times. The most dominant parameter affecting the accuracy of the numerical solution is the time step (or space step) size, i.e. the spacing of the mesh points where the true function is approximated. Instead of defining local truncation error functions to test the accuracy of solutions, the technique of decreasing step size is employed. The decrease in step size in each calculation produces a more accurate approximation. This has the effect that the predicted solution curve converges to a unique curve. This unique curve is an accurate representation of the true solution curve within a negligibly small truncation error. 80 Let P be a set of first order differential equations. P = { f1( t, x 1, x 2 ,........, x n ) , f2 ( t, x1, x 2 ,........, x n ) ,..........., fn ( t, x1, x 2 ,........, x n ) } …3.12 dx i = fi ( t, x 1, x 2 ,....., x i ,......., x n ) dt …3.13 fi ( t ) = x i initial condition for species i …3.14 where: x = concentration t = time Integration of each function fi in Set P is represented in general by equation 3.15. The differential equations in Set P are integrated simultaneously as described by Burden et al[46]. y i (t ) = t =n ∫ f ( t, x , x i 1 2 ,........, x n )dt …3.15 t =1 In the program, the function yi(t) is not obtained analytically as equation 3.15 suggests, but by using the Runge-Kutta difference equations. The function yi(t) is, however, useful to define here in order to facilitate further discussions relating to the least squares calculation. The predicted concentration yi(t) obtained from the numerical integration is compared with the experimental absorbance or concentration data for minimization using a least squares formulation as shown by equation 3.16. S = ∑ ( A exp − ( A theo (1) + A theo ( 2 ) + A theo ( 3 ) + ......))2 …3.16 where S = error sum, yi(t) = ci ATheo(i) = l∈ yi(t) for absorbance data i ATheo(i) = yi(t) for chromatography data set parameters, l = 1 and ∈ = 1 i 81 The Simplex algorithm was employed for the minimization of equation 3.16. The unknowns in the calculation are the molar extinction coefficients and the rate constants. Each time the rate constants are updated in the least squares routine during a particular iteration, it implies that a constant in the integration routine also changes. This has the effect that the integration must be re-evaluated to calculate the new concentration values of the species with different rate constants. Termination of the calculation is controlled by the user who checks that a unique solution curve is obtained by decreasing the step sizes and other tolerance parameters. 3.6.4 Results and Discussion Models 1 – 4 reported below shows the theoretical fit of the models that were proposed. A number of kinetic models were proposed; however, only four models that best fit the experimental data is illustrated. The best fit for each model returned a set of corresponding molar extinction coefficients and rate constants. The molar extinction coefficients and rate constants should, by definition, be constant across the entire range of alcohol concentrations investigated. Due to possible experimental error, or because of an inappropriate theoretical model being chosen, these parameters varied from one alcohol concentration to another. Thus, the best-fit parameters were averaged across the entire alcohol concentration range and the theoretical fit produced by these parameters was superimposed onto the experimental data. The results reported below only show that of methanol, although the data for all the alcohols that was investigated were treated in an analogous manner. In each of the presented figures, the symbols represent the experimental data and the lines represent the simulated kinetic fits. 82 Model 1 Os(VIII) + RCH2OH Os(VII) + RCH2OH k1 Os(VII) + RCHO k2 Os(VI) + RCHO 5.00×10-3mol.L-1 Methanol 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm 3.00×10-3mol.L-1 Methanol 0.65 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 Time /s 1500 2000 10.00×10-3mol.L-1 Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm 8.00×10-3mol.L-1 Methanol 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 Time /s 1000 1500 2000 Time /s 15.00×10-3mol.L-1 Methanol 20.00×10-3mol.L-1 Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm 1000 Time /s 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 Time /s 1000 1500 2000 Time /s k1 k2 εOs(VIII) εOs(VII) εOs(VI) 0.665 8.470×10-2 1.140 × 103 2.694 × 103 1.185 × 103 83 Model 2 Os(VIII) + RCH2OH Os(VII) + RCH2OH -3 k+1 k-1 k2 Os(VII) + RCHO Os(VI) + RCHO -1 -3 0.60 0.60 0.55 0.55 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 0 2000 500 -3 -1 -3 8.00×10 mol.L Methanol 1500 2000 -1 10.00×10 mol.L Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm 1000 Time /s Time /s 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 0 2000 500 -3 1000 1500 2000 Time /s Time /s -1 -3 15.00×10 mol.L Methanol -1 20.00×10 mol.L Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm -1 5.00×10 mol.L Methanol 0.65 Absorbance 370nm Absorbance 370nm 3.00×10 mol.L Methanol 0.65 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 1000 1500 2000 Time /s Time /s k+1 k-1 k2 εOs(VIII) εOs(VII) εOs(VI) 0.202 30.348 7.134×10-2 1.193 × 103 4.971 × 103 0.753 × 103 84 Model 3 Os(VIII) + RCH2OH Os(VI) + RCHO k2 Os(VIII) + Os(VI) Os2(VII) + RCH2OH -3 k1 Os2(VII) k3 2Os(VI) + RCHO -3 -1 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm 0.65 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 1000 -3 -1 -3 8.00×10 mol.L Methanol 2000 -1 10.00×10 mol.L Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm 1500 Time /s Time /s 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 1000 Time /s -3 1500 2000 Time /s -1 -3 15.00×10 mol.L Methanol -1 20.00×10 mol.L Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm -1 5.00×10 mol.L Methanol 3.00×10 mol.L Methanol 0.65 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 Time /s 500 1000 1500 2000 Time /s k1 k2 k3 εOs(VIII) εOs2(VII) εOs(VI) 0.423 440.079 4.815×10-2 1.197 × 103 4.879 × 103 0.926 × 103 85 Model 4 Os(VIII) + RCH2OH Os(VI) + RCHO k+2 k-2 Os(VIII) + Os(VI) -3 k1 Os2(VII) -1 -3 0.60 0.60 0.55 0.55 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 Time /s -3 -1 1500 2000 -3 -1 10.00×10 mol.L Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm 1000 Time /s 8.00×10 mol.L Methanol 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 500 Time /s -3 1000 1500 2000 Time /s -1 -3 15.00×10 mol.L Methanol -1 20.00×10 mol.L Methanol 0.65 0.65 0.60 0.60 0.55 0.55 Absorbance 370nm Absorbance 370nm -1 5.00×10 mol.L Methanol 0.65 Absorbance 370nm Absorbance 370nm 3.00×10 mol.L Methanol 0.65 0.50 0.45 0.40 0.50 0.45 0.40 0.35 0.35 0.30 0.30 0.25 0.25 0 500 1000 1500 2000 0 Time /s 500 1000 1500 2000 Time /s k1 k+2 k-2 εOs(VIII) εOs2(VII) εOs(VI) 0.275 2154.47 8.697×10-2 1.151 × 103 6.397 × 103 0.908 × 103 86 The presented models represent the sum of the models fitted using KinEqui kinetic modelling software. These models produced the best theoretical fits, while other models produced noticeably poor theoretical fits that were consequently discarded. At this stage it is important to emphasize that there are certain components resulting in experimental error that is inherent in these reactions. These errors include natural experimental error inherent in measurement and agitation of each solution. In addition, there is also an inherent error in the determination of the total osmium concentration. However, it can be seen that these factors does not play a significant role, since the average of the rate constants and molar extinction coefficients for Model 4 produced exceptionally good theoretical fits across all methanol concentrations. Based on the good theoretical fit obtained from this model, in addition to reasons which will become apparent in this discussion, Models 1 – 3 were excluded and only Model 4 accepted. Model 4 is mechanistically reasonable, in that one molecule of osmium(VIII) reacts with one molecule of alcohol to exchange two electrons. The complexation reaction is in a dynamic equilibrium, with a conditional equilibrium constant defined by: K eq = [Os 2 (VII)] k = +2 [Os(VIII)] × [Os(VI)] k −2 …3.27 This equilibrium constant will be quoted in Chapter 4 since it is an easily comparable parameter, more so than forward and reverse reaction rate constants that may vary within a set of experimental parameters. This equilibrium reaction will favour the products if the osmium(VIII) concentration is high. As the reaction proceeds, however, the osmium(VIII) concentration becomes depleted and thus the equilibrium would tend to favour the reactants. The magnitude of Keq is high, implying that the concentration of the osmium(VIII) ascribed to this reaction will always be low. The time elapsed from initiation of the reaction to the first spectral recording made (on average 30 seconds) also produces a relative error margin, since it leads to a loss of kinetic data during this time. This effect is negligible when methanol and ethanol are used as reductants, but becomes more profound when propan-1-ol and butan-1-ol are used since the rate of the reaction increases by orders of magnitude when using these alcohols. Therefore, the theoretical fits obtained for Model 4 are not as good for propan-1-ol and butan-1-ol when compared to the fits obtained for methanol and 87 ethanol, which is illustrated by Figure 3.25 [a] and [b]. Table 3.3 summarises the kinetic parameters obtained for all the alcohols investigated in this study. [b] [a] 0.5 0.65 0.60 0.4 Absorbance 370nm Absorbance 370nm 0.55 0.50 0.45 0.40 0.3 0.2 0.35 0.1 0.30 0.25 0.0 0 500 1000 1500 2000 0 500 1000 Time /s 1500 2000 Time /s Figure 3.25: Comparison between the theoretical fits obtained for [a] methanol and [b] propan-1ol, based on Model 4. The comparison illustrates the pronounced effect that a loss of kinetic data has on the theoretical fit. Symbols = Experimental data; Lines = Theoretical fit. [a] [Osmium] = 2.631 × 10 -4 mol.L ; [Methanol] = 15 × 10 -1 [b] [Osmium] = 2.285 × 10 -4 mol.L ; [Propan-1-ol] = 15 × 10 -1 -3 -1 mol.L . -3 -1 mol.L . Table 3.3: Calculated rate constants and molar extinction coefficients for the reduction of osmium(VIII) by several primary alcohols at pH 14.3, based on Model 4 Extinction coefficient / Rate Constants Substrate k1 k2 3 -1 × 10 L.mol .cm k3 -1 ε Os(VIII) ε Os2 (VII) ε Os(VI) 8.732×10 1.151 6.397 0.908 34299.1 1.1417 1.109 6.392 0.932 1.206 93601.3 3.956 1.134 6.395 0.923 1.476 167279.6 7.971 1.134 6.392 0.929 -1 -1 -1 -1 -1 / L.mol .s / L.mol .s /s Methanol 0.275 2154.5 Ethanol 1.070 Propan-1-ol Butan-1-ol -2 The molar extinction coefficient of the dimeric osmium(VII) intermediate species calculated from Mauser diagrams are also in good agreement with that obtained using a least squares fit, supporting the proposed reaction model. These results are compared in Table 3.4. 88 Table 3.4: Comparison between the molar extinction coefficient (at various wavelengths) of the Os2(VII) species calculated from a least squares [LS] method and Mauser diagrams [MD] ε Os2 (VII) [LS] / Wavelength / nm 3 -1 × 10 L.mol .cm ε Os2 (VII) [MD] / -1 3 -1 × 10 L.mol .cm 350 6.957 6.570 360 6.635 6.214 370 6.397 5.641 380 5.499 4.762 390 4.674 3.744 400 3.105 2.834 -1 The two dimensional Mauser diagrams can now be fully explained in according to the proposed kinetic model. Figure 3.23 is reproduced here for more clarity. 1.0 i = 240nm i = 280nm Os( V Absorbance at i 0.8 Os -Int 0.6 0.4 I) Os(VIII) Os-Int 0.2 0.0 0.15 0.25 0.35 0.45 0.55 Absorbance at 370nm Figure 3.23: A 2D Mauser diagram constructed from the data presented in Figure 3.21. In Chapter 3.5, it was reported that a bent curve lying on a single plane typically represents the consecutive reaction A → B → C. Figure 3.26 aims to provide an 89 interpretation of the two dimensional Mauser diagram which is more consistent with the proposed kinetic model. 1.0 i = 240nm i = 280nm Absorbance at i 0.8 [2] Os (VI) 0.6 + O s2 (V II) Os 2(VII) [1] Os(VIII) + 0.4 0.2 0.0 0.15 0.25 0.35 0.45 0.55 Absorbance at 370nm Figure 3.26: 2D Mauser diagram interpreted in terms of the proposed kinetic model, Model 4. The bent curve illustrated by Figure 3.26 can be interpreted in terms of the kinetic model by considering that immediately following the formation of osmium(VI) in the first reaction step, the produced osmium(VI) would react with osmium(VIII) to form a dimeric osmium(VII) species. The first linear region of in Figure 3.26 would therefore correspond to the simultaneous presence of osmium(VIII) and the dimeric osmium(VII) species. As the reaction proceed, the dimeric osmium(VII) complex is reduced to form osmium(VI) and since osmium(VIII) becomes depleted, the predominant species would now be the dimeric osmium(VII) complex and osmium(VI). The second linear region of the Mauser diagram would thus correspond to the simultaneous presence of the osmium(VII) dimer and osmium(VI). Although the alcohol reduction of osmium(VIII) does not proceed via typical consecutive reduction reactions, the results obtained from 90 Mauser diagrams remain viable, and is corroborated by the good correlation with the least squares analysis of kinetic data. The next aspect of the reaction that must be decided is the reaction mechanism, i.e. whether the reaction is initiated by C – H bond cleavage (as depicted in Figure 3.27) or O - H bond cleavage (as depicted in Figure 3.28). 2- OH O 3- OH O O O O Os OH + R Os O OH H 2- O H O OH H2O C O HO OH Os OH HO O H C R O H OH- Figure 3.27: The E2 C – H bond cleavage reaction mechanism At first glance, there are certain aspects that impact negatively on the O – H bond cleavage mechanism. Firstly, the RO- species would illustrate greater reactivity toward the osmium(VIII) centre when compared to the ROH species. CH3O-, for example, is approximately 20 000 times more reactive as a nucleophile when compared to CH3OH. There is thus a definitive correlation between the rate of the reaction and the acidity of the reacting nucleophile. The more acidic a nucleophile, in this case the alcohol, the faster the rate of the reaction. In other words, since the acidity of the alcohols increases in the order secondary alcohol < primary alcohol < methanol, the rate of the reaction should increase in this order. In contrast to this prediction, the observed reaction rates illustrate quite the opposite trend, with the methanol reaction being by far the slowest. This reason led to the initial conclusion that the reaction might proceed via C – H bond cleavage as illustrated in Figure 3.27. The osmium(VIII) centre, being a d0 species and a strong electrophile, abstracts a hydride ion from the alcohol in an E2 reaction, leading to an instant rearrangement of the hydrogen atom to an oxygen atom in the second step of the proposed reaction 91 mechanism. This leads to further interaction with water in the final step to form the osmium(VI) product. High oxidation state osmium species are normally associated with strong σ - and π – donor ligands, since these ligands would form stable complexes with ions possessing few or no d-electrons. Oxygen is thus an excellent ligand for the d0 osmium(VIII) ion and the initial association of the alcohol through the oxygen atom is far more favourable than through a hydrogen atom. 2- OH O O O Os O O O O Os HO OH H H + R Os C OH O H H C H OH HO HO O 2- O H2O O H O 2- OH C H OH- R R Figure 3.28: The hydride transfer reaction mechanism – from the associative reaction of the primary alcohol molecule with the osmium(VIII) centre, leading to the formation of the osmate ion and the aldehyde. The increase in the reaction rate, despite the decreasing acidity of the alcohol, can be envisaged if the first step in the reaction mechanism depicted in Figure 3.28 is not the rate limiting step of the reaction mechanism. If the second step of the depicted reaction mechanism is considered as the rate limiting step, then the parameters governing its rate will be manifested through empirical studies. The second part of the O – H bond cleavage model depicts the association of the osmium(VIII) centre with the alcohol molecule through an Os – O bond to form a large, low-charge molecule. Subsequently, this molecule undergoes hydride ion transfer to the osmium centre, in which the hydride attached to the α – carbon is transferred to the osmium with the resultant formation of a C – O double bond and the reduction of osmium(VIII) to osmium(VI). There is a rapid rearrangement of the hydrogen atom to an oxygen atom in the second step of the O 92 depicted reaction mechanism, and then further interaction with water in the final step, resulting in the formation of the osmium(VI) product. The fact that the hydride ion transfer is considered to be the rate limiting step of this reaction mechanism, infers that the more stable molecule in the absence of the hydride ion would result in an increase in the reaction rate. Abstraction of the hydride ion results in the establishment of a positive charge on the α – carbon of the alcohol molecule. The larger and more polarisable alkyl groups attached to the α – carbon, the more the electron density can shift toward that transient positive charge, resulting in a lower energy transition state. This interpretation also elucidates the increase in the reaction rate with the increasing number of alkyl groups attached to the α – carbon. 93 CHAPTER 4 The Osmium(VIII) – Osmium(VI) Complexation Reaction 4.1 Introduction The oxides of osmium in oxidation states VI or VIII act as a catalyst (in aqueous alkaline medium) in the oxidation of alcohols by oxidants such as oxygen[60], or hexacyanoferrate(III)[18]. In these reactions, the transformation can be interpreted as a cyclical process involving the reduction of osmium(VIII) by alcohol to osmium(VI), followed by re-oxidation of the latter species to osmium(VIII). Reports in literature suggests the involvement of a monomeric osmium(VII) species[59]. In the previous chapter, least-squares fits to experimental kinetic data excluded the possibility of the involvement of a monomeric osmium(VII) species. This was based on the poor fits obtained from models which included the monomeric osmium(VII) species as an intermediate species during the oxidation of primary alcohols by osmium(VIII). In addition, the best fit model for the osmium(VIII) – alcohol reaction was given by: Os(VIII) + RCH2OH Os(VIII) + Os(VI) k1 k+2 k-2 Os(VI) + RCHO Os2(VII) In none of the reviewed literature was reference made to the possibility of the formation of a dimeric osmium(VII) intermediate species. It was therefore decided to investigate the relationship between osmium(VIII) and osmium(VI) in greater detail, with the aim of gaining further insight into the identity of the intermediate osmium(VII) species. It should be noted that the spectrophotometric techniques discussed here cannot determine the oxidation state of the intermediate species. 94 4.2 The Stability of Osmium(VI) in a 2M Hydroxide Matrix 4.2.1 Literature Review During the preparation of potassium osmate solutions in a 2 mol/L sodium hydroxide matrix, it was observed that the colour of the osmate solution changed from purple to brown as a function of time. This prompted the investigation into the stability of potassium osmate at pH 14.3 as a function of time. In addition to the observed colour change, potassium osmate was also observed to have a greater solubility in a hydroxide matrix than in water. The reported solubility of potassium osmate in a potassium hydroxide matrix is 2 × 10-2 mol/L in 0.7 mol/L potassium hydroxide at 276 K [47]. A change in the electronic spectrum of an osmate solution, as a function of hydroxide concentration, was documented by Mouchel and Bremard[48]. This was interpreted as a change in the species from the osmate ion, [OsO2(OH)4]2-, in less alkaline solutions to the trioxo ion, [OsO3(OH)3]3-, in more alkaline solutions. These authors subsequently calculated the electronic spectra of both these species and the value of the acid constant at 298 K was calculated to be 9.64 × 10-16. 4.2.2 Experimental Procedures K2[OsO2(OH)4] was purified and recrystallised from crude potassium osmate using the method described in Chapter 2.6. A 1.320 × 10-2 mol/L osmate solution was prepared by weighing and quantitatively transferring 1.2233 g of purified K2[OsO2(OH)4] salt to a 250 mL volumetric flask. A 500 mL 2 mol/L sodium hydroxide solution was prepared with degassed water. The sodium hydroxide solution was subsequently purged with nitrogen prior to its use. The K2[OsO2(OH)4] salt was dissolved and diluted to 250 mL by addition of the freshly prepared 2 mol/L sodium hydroxide stock solution. 95 A study of the stability of K2[OsO2(OH)4] in a 2 mol/L sodium hydroxide matrix was conducted in two parts: a) the stability of K2[OsO2(OH)4] in an oxygen atmosphere b) the stability of K2[OsO2(OH)4] in a nitrogen atmosphere a) Approximately 10.00 mL of the stock osmate solution was transferred to a reaction vessel containing 240 mL of a 2 mol/L sodium hydroxide solution. The sodium hydroxide solution was prepared with degassed water, and the solution was purged with oxygen for at least 15 minutes prior to the addition of the osmate stock solution. The solution was continuously purged with oxygen over a six hour sampling period. b) Approximately 10.00 mL of the stock osmate solution was transferred to a reaction vessel containing 240 mL of a 2 mol/L sodium hydroxide solution. The sodium hydroxide solution was prepared with degassed water, and the solution was purged with nitrogen for at least 15 minutes prior to the addition of the osmate stock solution. The solution was continuously purged with nitrogen over a six hour sampling period. UV-Vis spectra of the respective solutions were recorded immediately following the addition of the osmate stock solution to the reaction vessels. Thereafter, spectra were periodically recorded over a six hour period. Following the initial six hour sampling period, these vessels were sealed, ensuring that the solutions were kept saturated with oxygen and nitrogen, respectively. This was done to minimise the loss of solution due to evaporation; while keeping the solutions under oxidising and inert conditions, respectively. Subsequent spectra were recorded by periodic sampling of the solution over a period of 48 hours. The total osmium concentration of both solutions was determined by the thiourea method as described in Chapter 2. 96 4.2.3 Results and Discussion Figure 4.1 illustrates the change in the UV-Vis spectrum of osmium(VI) upon exposure to an oxygen atmosphere as a function of time. Initially there is a significant increase in the in absorbance, after which the absorbance increases very slowly. The figure demonstrates an overall change in the shape of the osmium(VI) spectrum, with the peak maxima at both 300 and 350 nm increasing in intensity. However, the peak at 350 nm undergoes a larger change with time. Figure 4.2 illustrates the change in absorbance at 300 and 350 nm as a function of time. This figure clearly show a significant initial increase in the absorbance at these wavelengths, which is followed by a comparatively slow increase in absorbance as the reaction reaches equilibrium. 2.0 t = 2868 min Absorbance 1.5 1.0 0.5 t = 0 min 0.0 250 300 350 400 450 500 550 600 Wavelength /nm Figure 4.1: The change in the UV-Vis spectrum of [OsO2(OH)4] 2- upon exposure to an oxygen atmosphere as a function of time. The dashed arrows respectively depict the spectra recorded at t = 0 min and t = 2868 min. The solid arrow indicates the direction of increasing time. -4 [Osmium] = 5.278 × 10 mol/L; [NaOH] = 2 mol/L 97 2.0 300 nm 350 nm 1.8 Absorbance 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0 500 1000 1500 2000 2500 3000 Time /min Figure 4.2: The change in absorbance at 300 and 350 nm as a function of time under oxygen -4 atmosphere. [Osmium] = 5.278 × 10 mol/L; [NaOH] = 2 mol/L A comparative study was conducted under inert conditions (a nitrogen atmosphere), the results of which is illustrated by Figures 4.3 and 4.4. From these figures it is evident that the osmium(VI) species remain stable, under inert conditions, since no change in its UV-Vis spectrum was observed over time. The fact that no changes were observed in the UV-Vis spectrum of the osmium(VI) species under inert conditions, implies that the exposure of osmium(VI) to oxygen results in the oxidation of osmium(VI) to, presumably, the osmium(VIII) species, [OsO4(OH)2]2-. The pH at which this investigation was conducted (pH 14.3) makes it unlikely that the osmium(VI) species disproportionate; a finding corroborated by Galbacs et al[47]. These authors asserts that disproportionation of osmium(VI) only occurs at a pH below 10. In addition, the disproportionation of osmium(VI) is also accompanied by the formation of a black precipitate[47] that was not observed in this study. 98 2.0 Absorbance 1.5 1.0 0.5 0.0 250 300 350 400 450 500 550 600 wavelength /nm Figure 4.3: The change in the UV-Vis spectrum of [OsO2(OH)4] 2- upon exposure to a nitrogen -4 atmosphere. [Osmium] = 4.578 × 10 mol/L; [NaOH] = 2 mol/L 300 nm 350 nm 1.6 Absorbance 1.4 1.2 1.0 0.8 0.6 0.4 0 500 1000 1500 2000 2500 3000 Time /min Figure 4.4: The change in absorbance at 300 and 350 nm as a function of time under nitrogen -4 atmosphere. [Osmium] = 4.578 × 10 mol/L; [NaOH] = 2 mol/L 99 The qualitative assessments made in this investigation provided invaluable information surrounding the experimental procedures required to prepare a stable osmium(VI) species in a 2 mol/L sodium hydroxide matrix. All the osmium(VI) solutions were subsequently prepared under inert conditions, ensuring that the osmate was not oxidised by exposure to atmospheric oxygen. 100 4.3 The Osmium(VIII) – Osmium(VI) Reaction 4.3.1 Literature Review 4.3.1.1 Job’s Method of Continuous Variation[49-54] Job’s method of continuous variation is a commonly used procedure for the determination of the composition of complexes in solution. It is thus necessary to describe the theory surrounding this experimental procedure in addition to deriving analytical functions for determining conditional equilibrium constants as well as the molar extinction coefficients of the various reacting species. Continuous variation diagrams are of a physical property related to the concentration of an equilibrium two-component complex against volume fraction (χv) or mole fraction (χm) of one of the two components. Consider the following reaction: A+B where: Keq AB …4.1 A = Osmium(VIII) B = Osmium(VI) AB = Os2(VII) Intermediate species A series of solutions can be prepared such that the sum of the concentration of the respective components remains constant, while the concentration of the individual components is continuously varied, i.e.: [A] + [B] = [T] …4.2 where [T] = The total concentration of the individual components and is constant The mole fraction of either component can be calculated through the following equations: mole A mole A + mole B …4.3 mole B = 1 - χ (A) mole A + mole B …4.4 χ (A) = χ (B) = 101 The equilibrium concentrations of the species are thus given by: [ A] eq = [T] × χ (A) - [AB] …4.5 [B] eq = [T] × (1 - χ (A) ) - [AB] …4.6 In dilute solutions, the thermodynamic equilibrium constant (Keq) for relation 4.1 can be approximated by the concentration equilibrium constant, Kc: K eq ≅ K c = [AB] [A]eq [B] eq …4.7 Substitution of equations 4.5 and 4.6 yields the following equation: K eq = ([T] χ [AB] (A) - [AB] )([T] × (1 - χ (A) ) - [AB] ) …4.8 Equation 4.9 is obtained when equation 4.8 is rearranged as a quadratic equation with respect to [AB]: ( K 1eq + [T]) − ( K 1eq + [T]) 2 − [ 4 × [T] 2 × ( χ ( A ) − χ ( A ) )] 2 [ AB] = …4.9 2 For the general reaction depicted by relation 4.1, the theoretical absorbance of each component (A, B and AB) at equilibrium could be calculated using the Beer-Lambert law, provided that the molar extinction coefficient of each species is known: Abs (A) = ε (A) × [A]eq × l …4.10 Abs (B) = ε (B) × [B]eq × l …4.11 Abs (AB) = ε (AB) × [AB]eq × l …4.12 o ε = molar extinction coefficient of the respective absorbing species o [A]eq, [B]eq, [AB]eq = equilibrium concentration of the respective absorbing species o l = optical path length of the cuvette 102 Since the Beer-Lambert law is additive, the contribution of each species’ theoretical absorbance (assuming that all three species are considered to be absorbing species in the wavelength region chosen for this study) to the overall theoretical absorbance is: Abs (Theo) = Abs (A) + Abs (B) + Abs (AB) …4.13 The numerical values obtained for Abs (Theo) (for each solution in the series) could be used to ascertain the validity of the estimated values of the parameters Keq, ε (A), ε (B) and ε (AB). This is achieved using a non-linear least-squares method, which is based on the assumption that the best estimate for the values of the parameters are those values that minimise the sum of the squared deviations between the experimentally observed absorbance data and the theoretically calculated absorbance data. Essentially, this implies the minimisation of the sum of the squared deviations between the experimentally observed absorbance data and the theoretical absorbance data calculated form the proposed equilibrium model (equation 4.9). Theoretically, the function minimum (denoted φ2) is represented by: ϕ2 ≡ M ∑ [Abs (Theo) i - Abs (Obs)i ] 2 …4.14 i =1 o M = Number of data points o Abs (Theo)i = Calculated absorbance (at a single wavelength) for the ith spectral curve o Abs (Obs)i = Observed absorbance (at a single wavelength) for the ith spectral curve The values assigned to each parameter should therefore be done in a manner which result in the value of φ2 reaching a minimum. To calculate the value of Abs (Theo)i, the values of the parameters Keq, ε (A), ε (B) and ε (AB) are required, which is (in most cases) unknown. It is assumed here that all three species have overlapping absorbances and that the molar extinction coefficient of species AB cannot be measured directly. However, the molar extinction coefficient of species A can be estimated by obtaining spectra of free A (i.e. in the absence of species B). Since the concentration and absorbance of species A is known, the molar extinction coefficient of species A can be approximated by using the Beer-Lambert law. 103 The molar extinction coefficient of species B can be approximated in an analogous manner. The evaluation of Keq and ε (AB) can be achieved through a least-squares method in combination with an iterative minimum-searching routine. Firstly, an initial estimate of Keq is made, for which a corresponding value of ε (AB) is calculated using the equation: ∆ε = ε ( AB) - ε ( A) - ε (B) …4.15 When equation 4.15 holds, equation 4.12 can be written as: ∆Abs = Abs ( obs) − Abs0 …4.16 where: Abs 0 = [(ε (A) − ε (B) ) × χ (B) + ε (B) ] × [T] By estimating the initial value of Keq, the corresponding value of ε (AB) that would minimise φ2 for this initial estimate would be given by: ∆ε = ∑ ( ∆Abs ) ×([AB] i ) ∑ [AB] 2 …4.17 i Equation 4.17 was derived by setting the partial derivative of φ2 (equation 4.14) with respect to ∆ε equal to zero[49 – 54]. From the initial estimate of Keq, the best corresponding value for ∆ε (and consequently ε (AB)) as well as the corresponding φ2 value can be determined. After each iteration, the value by which Keq is varied decreases (since there is a decrease in the value of φ2) and the procedure is stopped when a change in Keq produces a φ2 value that is smaller than a predetermined value. 104 4.3.1.2 Mole Ratio Titrations One of the limitations to Job’s method of continuous variation is the number of data points obtained, being dependent on the number of solutions prepared. Due to this reason, mole ratio titrations were performed, which has the advantage of obtaining a greater number of data points. Although not used in this study, it is possible to convert mole ratio titration data to a Job plot. In this manner, Job plots with many data points can be obtained and less reagent solution is used[55, 56]. The mole ratio method involves keeping the concentration of one reagent constant while varying the concentration of the other reagent. The resulting absorbances at specific wavelengths are plotted against the mole ratio of the two reagents. The shape of the absorbance curve at a particular wavelength depends on the values of the molar extinction coefficients of the reagents and complexes, and the value of the equilibrium constant. 4.3.2 Experimental Procedures 4.3.2.1 Job’s Method of Continuous Variation A 3.172 × 10-3 mol/L aqueous osmium tetroxide stock solution was prepared in distilled water using the method outlined in Chapter 2.5.3. A 2 mol/L sodium hydroxide solution was prepared under a nitrogen atmosphere by dissolving the appropriate amount of sodium hydroxide pellets in degassed water. This solution was used to dissolve 0.3501 g of purified K2[OsO2(OH)4] crystals in a 250 mL volumetric flask. This osmium(VI) stock solution was stored under a nitrogen atmosphere in order to prevent the oxidation of osmium(VI) by atmospheric oxygen. The osmium concentration of this stock was determined by the thiourea method, and was found to be 3.172 × 10-3 mol/L. Once the concentrations of the osmium(VI) and osmium(VIII) stock solutions were established, a series of solutions were prepared in 50 mL volumetric flask where the total molar osmium concentration was maintained at 3.485 × 10-4 mol/L, while the 105 [osmium(VI)]initial/[osmium(VIII)]initial ratio was varied by mixing different volumes of the osmium(VI) and osmium(VIII) solutions. A constant reaction volume and hydroxide concentration were achieved by diluting each solution in the series with specific volumes of 6 mol/L sodium hydroxide and distilled water, such that the final hydroxide concentration throughout the series was 2 mol/L. Following its preparation, each solution in the series was allowed to equilibrate for approximately 45 seconds after which its UV-Vis spectrum was recorded. The experiment was repeated for a total osmium concentration of 7.000 × 10-4 mol/L. 4.3.2.2 Mole Ratio Titrations Absorbance measurements for the mole ratio titrations were recorded with a Metrohm 662 photometer, which was described in Chapter 2.1.2. A mole ratio titration was performed in which 4.065 mL of a 1.431 × 10-3 mol/L osmium tetroxide stock solution, 12.602 mL distilled water and 8.333 mL of a 6 mol/L sodium hydroxide solution was transferred to a reaction vessel, such that the total volume of the solution was 25 mL. The final osmium(VIII) concentration of this solution was 2.327 × 10-4 mol/L and the sodium hydroxide concentration was 2 mol/L. This solution was titrated against a 7.636 × 10-3 mol/L potassium osmate solution prepared in a 2 mol/L sodium hydroxide matrix under nitrogen atmosphere. Delivery of the potassium osmate solution to the reaction vessel was achieved using a Metrohm 665 titroprocessor. During these titrations, the reaction solution was continuously agitated, but not vigorously to prevent splashes and air bubbles being trapped in the light path of the photometer probe. Following each addition of potassium osmate, the reaction solution was allowed to equilibrate for 15 seconds, after which its absorbance at 400 nm was recorded. Subsequent titrations were performed with slightly differing osmium(VIII) concentrations. The addition of titrant (in this case, potassium osmate) causes the volume of the reaction solution to increase. As a result the concentration of the initial reagent, osmium(VIII), decreases. However, since both the initial reagent as well as the titrant is osmium species, the absorbance increased continually. It is desirable to show only the 106 changes in absorbance due to reactions of the reagents, and not due to the effect of changing volume. This was achieved by “correcting” the absorbance data. The corrected absorbance, A, of the reaction solution was calculated from the observed absorbance, A0, as follows: A= where: A 0 × Vt Vi Vi = initial volume Vt = total volume of the reaction solution All the spectra and absorbance curves illustrated in this study were corrected in this manner, except if stated otherwise. 4.3.3 Computer Software Used for Simulating Mole Ratio Titrations The SPC-V-MR program was used to simulate mole ratio titrations where the mole ratios between various reagents change. Different reaction models could be simulated and formation constants and molar extinction values calculated from the experimental data. The SPC-V-MR program was written by Dr E. Hosten using Borland Turbo Pascal V6.0[57]. The program can simulate one or more equilibria. From estimates of the formation constants of each equilibrium and the total reagent concentrations, the program uses an iterative Gauss-Newton algorithm to calculate the free reagent (unreacted) concentrations. Together with the free reagent concentrations, the estimated formation constants and the molar extinction values, the program can then calculate the total absorbance. By comparing the calculated absorbance with the experimental absorbance, the program uses another iterative Gauss-Newton algorithm to calculate better estimates for reagent concentrations, formation constants and molar extinction values. These iterative cycles then continue until the changes to all the constants become statistically insignificant. During all the calculations the change in volume during the titrations due to the addition of titrant, is taken into account. This program simulates the following type of equilibria: aA + bB + cC β= [A aB b C c ] [A] a [B] b [C]c β A a Bb C c 107 4.3.4 Results and Discussion 4.3.4.1 Job’s Method of Continuous Variation Figure 4.5 illustrates the change in the UV-Vis spectra as the [Os(VI)]i / [Os(VIII)]i ratio was gradually increased at a constant total osmium concentration. The figure illustrates the presence of at least three absorbing osmium species, based on the observation that, at wavelengths greater than 320 nm, the absorbance initially increases and then decreases. An identical trend was established in Chapter 3. 1.4 1.2 [14] [1] Absorbance 1.0 0.8 0.6 0.4 0.2 [29] 0.0 230 270 310 350 390 430 470 510 550 590 Wavelength /nm Figure 4.5: The change in absorbance spectra as a function of increasing [Os(VI)]i / [Os(VIII)]i ratio at pH 14.3. The spectra denoted [1], [14] and [29] corresponds to the [Os(VI)]i / [Os(VIII)]i ratios -4 0.03, 0.94 and 30.00 respectively. [Os(VI)] + [Os(VIII)] = 3.485 × 10 mol/L The possibility that the observed absorbance spectrum, produced by reacting osmium(VIII) with osmium(VI), was simply due to a combination of the respective species’ absorbance spectra was excluded experimentally. Since absorbance is additive, the sum of the pure osmium(VIII) and osmium(VI) absorbance spectra would produce an addition spectrum if no reaction occurred. 108 1.4 Os(VIII) Os(VI) Os2(VII) Intermediate 1.2 Addition spectrum Intermediate from MeOH reduction Absorbance 1.0 0.8 0.6 0.4 0.2 0.0 245 295 345 395 445 495 545 595 Wavelength /nm -4 Figure 4.6: The UV-Vis spectra of 3.485 × 10 mol/L OsO4 in a 2 mol/L NaOH matrix; -4 3.485 × 10 mol/L potassium osmate in a 2 mol/L NaOH matrix; the experimentally observed spectrum obtained from the reaction between -4 1.799 × 10 mol/L osmium(VIII) with -4 1.686 × 10 mol/L potassium osmate in a 2 mol/L NaOH matrix; the theoretically calculated addition spectrum between osmium(VIII) and potassium osmate; and a comparison of the intermediate species’ spectrum obtained by reacting osmium(VIII) with methanol in a 2 mol/L NaOH matrix. It is evident from Figure 4.6 that the theoretical addition spectrum does not correspond with the experimentally observed absorbance spectrum. This implies that the observed absorbance spectrum is not simply due to a combination of the osmium(VIII) and osmium(VI) species’ absorbance spectra. For comparison, the absorbance spectrum of the intermediate species formed during the reaction of osmium(VIII) with methanol is included in Figure 4.6. It can be seen that these spectra are identical. Thus, it is clearly observed that the osmium species produced during the reaction of osmium(VIII) with osmium(VI) is the same osmium species produced during the reduction of osmium(VIII) by all the organic substrates used in this study. 109 Figure 4.7 illustrates a non-equimolar Job diagram which indicates complex formation between osmium(VIII) and osmium(VI) in a 2 mol/L sodium hydroxide matrix. The relatively sharp point at mole fraction 0.5, as well as the fact that the sides of the curve is virtually linear, is indicative of a 1:1 complex formation between osmium(VIII) and osmium(VI). In addition, the sharp point obtained at mole fraction 0.5 would imply a relatively high equilibrium constant. The formation of a 2:2 complex was negated based on the fact that the sides of the Job plot for this type of complex would become concave under the current experimental conditions. Thus, the Job plot also allows for the discrimination between the formation of 1:1 and 2:2 complexes. 1.8 [2] Absorbance at 370nm 1.6 1.4 1.2 1.0 [1] 0.8 0.6 0.4 0.2 0.0 0.2 0.4 Mole fraction 0.6 [Os(VI)] [Os(VI)] + [Os(VIII)] 0.8 1.0 Figure 4.7: Non-equimolar Job diagram illustrating complex formation between osmium(VIII) and -4 osmium(VI) in a 2 mol/L NaOH matrix. [Os(VI)] + [Os(VIII)] = [1] 3.485 × 10 mol/L; -4 [2] 7.000 × 10 mol/L Figure 4.8 depicts the Job plot of the complex formation between osmium(VIII) and osmium(VI), which was simulated based on a 1:1 complex formation, as described in Chapter 4.3.1.1. The proposed 1:1 stoichiometry produces complelling theoretical fits, as illustrated by Figure 4.8. 110 1.0 Exp Data Os(VIII)Theo Os(VI)Theo Absorbance at 370nm 0.8 Os2(VII)Theo Theo Fit 0.6 0.4 0.2 0.0 0.0 0.2 0.4 Mole Fraction 0.6 0.8 1.0 [Os(VI)] [Os(VI)] + [Os(VIII)] Figure 4.8: Job diagram depicting the complex formation between osmium(VIII) and osmium(VI) in a 2 mol/L NaOH matrix. The theoretical fits were simulated on a 1:1complexation model. -4 [Os(VI)] + [Os(VIII)] = 3.485 × 10 mol/L. Symbols = experimental data; Lines = calculated fits. The theoretical curves shown in Figure 4.8 can be used to correct the Job plot for absorbance of the uncomplexed reagent at the specified wavelength. The corrected absorbance is defined as the measured absorbance minus the sum of the absorbance of the reagents if no complexation had occurred[58]. 111 Absorbance at 370nm 1.0 0.8 [1] 0.6 [4] 0.4 [2] [3] 0.2 0.0 0.0 0.2 0.4 Mole fraction 0.6 0.8 1.0 [Os(VI)] [Os(VI)] + [Os(VIII)] Figure 4.9: Correcting a Job plot for the absorbance of the reacting components, as reported in [58] literature . Lines [2] and [3] is subtracted from plot 1 to obtain plot 4. Experimental data are from -4 an osmium(VIII) – osmium(VI) Job plot at pH 14.3. [Os(VI)] + [Os(VIII)] = 3.485 × 10 mol/L Graphically, this involves subtracting the line drawn from the 0.00 mole fraction data point to the 1.0 mole fraction point from the Job plot. According to the reported literature [58] Figure 4.9 illustrates this. , the assumption made by drawing a line between the first and last points, is that no complexation occurs. This is incorrect, even with complexes with a low equilibrium constant. As a result, the “corrected” plot may be a better graphical presentation of a Job plot, but it becomes unsuitable for the determination of constants and stoichiometry by non-linear methods of analysis. None of the Job pots in this study were corrected in this manner. The analytical functions described in Chapter 4.3.1.1 take into account the absorbance from uncomplexed reagents by considering the data as the sum of absorbance of the reagents and complexes, as illustrated in Figure 4.8. Figure 4.8 clearly shows that the absorbance contribution to the unreacted reagents is non-linear with mole fraction. 112 Table 4.1 shows the constants calculated at several wavelengths by using Job’s method of continuous variation. Table 4.1: The molar extinction coefficients and averaged equilibrium constant calculated at various wavelengths through Job’s method of continuous variation. Molar extinction coefficient / 3 -1 × 10 L.mol .cm Wavelength / nm -1 ε Os(VIII) ε Os(VI) ε Os2 (VII) 340 1.080 1.195 6.633 350 1.572 1.076 6.689 360 1.276 0.971 6.488 370 1.184 0.778 5.631 380 1.073 0.651 4.947 390 0.990 0.484 3.903 0.897 0.351 2.882 400 3 -1 Keq / × 10 L.mol 24.37 113 4.3.4.2 Mole Ratio Titrations The results of several osmium(VIII) versus osmium(VI) mole ratio titrations in a 2 mol/L sodium hydroxide matrix are illustrated in Figure 4.10. -4 1.163×10 M 2.327×10-4 M 3.490×10-4 M Absorbance at 400nm 0.5 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 Mole Ratio [Os(VI)] [Os(VIII)] 5 6 7 Figure 4.10: Absorbance curves from several osmium(VIII) vs. osmium(VI) mole ratio titrations in a 2 mol/L NaOH matrix. Linear regressions were drawn though the linear regions of the curves to obtain the point of intersect. The initial osmium(VIII) concentration is denoted in the legend. This figure illustrates a relatively sharp endpoint, indicative of the stability of the complex. The mole ratio of the endpoint indicates the composition of the complex. The approximate position of the endpoints can be obtained graphically by looking at the intersection of the lines drawn from the experimental points before and after the endpoint, as depicted in Figure 4.10. The average of the intercepts was calculated from Figure 4.10 and gives a mole ratio value at the endpoint of the titration of 1.07 (i.e. a 1:1 complex). This corresponds to the reaction: Os(VIII) + Os(VI) Os2(VII) 114 The program, SPC-V-MR was used to analyse the osmium(VIII) versus osmium(VI) mole ratio titration data, the results of which is illustrated in Figure 4.11. The simulation of a single equilibrium with a 1:1 complex results in good absorbance curve fits across all concentration range investigated. The corresponding species distribution curves are shown in Figure 4.12. 0.4 Corrected Absorbance at 400nm 3.490×10-4 M 0.3 2.327×10-4 M 0.2 1.163×10-4 M 0.1 0.0 0 1 2 3 Mole Ratio 4 [Os(VI)] [Os(VIII)] 5 6 7 Figure 4.11: Volume corrected absorbance curves from osmium(VIII) vs. osmium(VI) mole ratio titrations in a 2 mol/L NaOH matrix. The calculated curves were simulated on a 1:1 complexation model. The initial osmium(VIII) concentrations are denoted in the figure. Symbols = experimental data; Lines = calculated fits 115 1.0 Os2(VII) Os(VIII) Mole fraction (Os(VIII)) 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 Mole Ratio 5 [Os(VI)] [Os(VIII)] 6 7 Figure 4.12: Species distribution curves of an osmium(VIII) vs. osmium(VI) titration in a 2 mol/L -4 NaOH matrix. [Os(VIII)] = 2.327 × 10 mol/L Table 4.2 shows the constants calculated at 400 nm from mole ratio studies. These results are compared to that obtained from Job calculations. Table 4.2: Comparison of the molar extinction coefficients and equilibrium constant obtained from mole ratio studies and Job diagrams at 400 nm Mole ratio studies / Wavelength / nm 400 Keq / 3 × 10 L.mol -1 3 -1 × 10 L.mol .cm Job diagrams / -1 3 -1 × 10 L.mol .cm -1 ε Os(VIII) ε Os(VI) ε Os2 (VII) ε Os(VIII) ε Os(VI) ε Os2 (VII) 0.880 0.345 2.840 0.897 0.351 2.882 25.74 24.37 116 4.4 Conclusion Job method and osmium(VIII) – osmium(VI) mole ratio titrations confirmed that there is complex formation between osmium(VIII) and osmium(VI) in the ratio 1:1. The molar extinction coefficients and equilibrium constants obtained from these methods were in good correlation with each other. On the basis of results obtained, it is possible to postulate the following reaction between osmium(VIII) and osmium(VI): 2- OH O O Os O 2- O HO Os + O OH OH HO OH O Keq HO O Os HO O OH + 2OH- Os O O 2- O OH O Figure 4.13: The formation of the dimeric osmium(VII) species The formation of the mixed oxidation state dimeric species proceeds with the evolution of two hydroxide ions. 117 CHAPTER 5 Conclusion 5.1 Determination of Osmium Concentration The thiourea method for determining osmium was tested exhaustively and proved to be a consistent method for the assay of osmium. The sample preparation and analysis method was simple. The osmium-thiourea complex formation occurred rapidly in the case of osmate ([OsO2(OH)4]2-), perosmate ([OsO4(OH)2]2-) and osmium tetroxide, but was slow in the case of hexachloroosmium(IV). It was established that a vast excess of thiourea (at least 4300 times) was required before consistent spectra were obtained. Using these parameters, it was possible to develop an analysis method to fit all the criteria. A linear calibration curve was obtained over the osmium concentration range 5.257 × 10-6 to 2.628 × 10-4 mol/L. 5.2 The Osmium(VIII) – Alcohol Reaction Since the osmium(VIII) – alcohol reactions were conducted in a 2 mol/L sodium hydroxide matrix, the stability of osmium tetroxide in this matrix was investigated. It was found that at a pH of 14.3, osmium(VIII) spontaneously reduced over time to form osmium(VI). The progress curves obtained from this investigation suggested that the spontaneous reduction of osmium(VIII) in a 2 mol/L sodium hydroxide matrix followed a distinct two-step process, with at least three absorbing species being present, i.e. the initial osmium(VIII) species, an osmium(VII) intermediate species and the final osmium(VI) product. Various studies have reported to have established the reaction equilibrium of osmium tetroxide with hydroxide. These studies, having examined the speciation of osmium tetroxide as a function of pH are in general concurrence. At pH 14.3 it was reported that two osmium(VIII) species were present, namely the [OsO4(OH)]- and [OsO4(OH)2]2- 118 species, present in a 40%:60% ratio. It has also been reported[16] that an increase in the hydroxide concentration led to an increase in the rate at which osmium(VIII) was reduced by alcohol. In a 3 mol/L sodium hydroxide matrix, the two osmium(VIII) species would be present in the ratio 30% [OsO4(OH)]- to 70% [OsO4(OH)2]2-. It therefore seemed that there was a correlation between the concentration of the [OsO4(OH)2]2species and the rate of the reaction. However, this is not necessarily the case. It should be borne in mind that, at a pH > 14, the [OsO4(OH)2]2- species reduces to form the [OsO2(OH)4]2- species. This process would become more pronounced at higher hydroxide concentrations, which could lead to the false correlation that an increase in the [OsO4(OH)2]2- species’ concentration leads to an increase in the rate of the oxidation of alcohols by this species. The results obtained from the reduction of osmium(VIII) by several primary alcohols suggests that this reaction proceeds via a distinct two-step process, identical to the trend observed for the spontaneous reduction of osmium(VIII) at pH 14.3. The influence that the spontaneous reduction of osmium(VIII) has on the kinetics of the osmium(VIII) - alcohol reaction was found to be negligible, since the rate of the alcohol reduction of osmium(VIII) is orders of magnitude greater than the reaction conducted in the absence of organic substrate. The rate at which osmium(VIII) was reduced was found to increase along the trend methanol < ethanol < propan-1-ol < butan-1-ol. Two-dimensional Mauser diagrams were used to analyse the kinetic data obtained from the reduction of osmium(VIII) with alcohol in a hydroxide matrix. These diagrams indicated the occurrence of two consecutive reduction reactions, and allowed for the calculation of the calculation of the postulated osmium(VII) intermediate species. Kinetic modelling software was used to fit several theoretical models to the experimentally obtained kinetic data. The model that produced the best theoretical fit was given by: Os(VIII) + RCH2OH Os(VIII) + Os(VI) k1 k+2 k-2 Os(VI) + RCHO Os2(VII) 119 This model is mechanistically feasible, in that one molecule of osmium(VIII) reacts with one molecule of alcohol to exchange two electrons. In terms of the reaction mechanism, it was postulated that the reaction is initiated by an O – H bond cleavage, as illustrated by Figure 3.28. 2- OH O O O Os O O O O Os HO OH H H + R Os HO O H OH HO C OH O H H C 2- O H2O O H O 2- OH C H OH- R R Figure 3.28: The hydride transfer reaction mechanism – from the associative reaction of the primary alcohol molecule with the osmium(VIII) centre, leading to the formation of the osmate ion and the aldehyde This conclusion is based on the fact that osmium(VIII), being a d0 species, is normally associated with strong σ- and π-donor ligands, since these ligands form stable complexes with ions possessing few or no d-electrons. Oxygen would therefore be an excellent ligand for stabilising the d0 osmium(VIII) ion and the initial association of the alcohol through the oxygen atom would be far more favourable. Despite the increasing acidity of the alcohol in the order primary alcohol < methanol, the rate of osmium(VIII) reduction was found to increase in the order methanol < primary alcohol. This trend can be explained if the first step in the depicted reaction mechanism is not considered to be the rate limiting step. The fact that the hydride ion transfer is considered to be the rate limiting step of this reaction mechanism, infers that the more stable molecule in the absence of the hydride ion would result in an increase in the reaction rate. Abstraction of the hydride ion results in the formation of a positive charge on the α – carbon of the alcohol molecule. The larger and more polarisable the substituent alkyl groups attached to the α – carbon, the more electron density would be shifted toward that transient positive charge, which would result in a lower energy O 120 transition state. This interpretation elucidates the increase in the reaction rate with the increasing number of alkyl groups attached to the α – carbon. 5.3 The Osmium(VIII) – Osmium(VI) Complexation The complexation between osmium(VIII) and osmium(VI) at pH 14.3 was investigated spectrophotometrically using Job’s method of continuous variation and mole ratio titrations. Mole fraction plots and mole ratio titrations at pH 14.3 indicate that only a single 1:1 complex forms at this pH. Using the analytical functions described in Chapter 4.3.1.1 and custom written software, the equilibrium constant and molar extinction coefficients of the three postulated species were determined. The results of these calculations are summarised in Table 5.1. In addition, this table compares the data obtained from mole fraction plots and mole ratio titrations to that obtained from Mauser diagrams and least squares analysis of the kinetic data obtained from the osmium(VIII) – alcohol reaction. Table 5.1 illustrates an excellent correlation of the equilibrium constants and molar extinction coefficients for all the computational methods used. 121 Table 5.1: Comparison of the equilibrium constant and molar extinction coefficients calculated through several computational methods. MD = Mauser diagrams; LS = Least square analysis; JD = Job diagrams; MR = Mole ratio titrations Wavelength Molar extinction coefficient / / nm × 10 L.mol .cm 3 MD JD 1.466 1.572 6.957 6.689 ε Os(VI) 1.101 1.076 ε Os(VIII) 1.329 1.276 6.635 6.488 ε Os(VI) 0.966 0.971 ε Os(VIII) 1.199 1.184 6.397 5.631 ε Os(VI) 0.780 0.778 ε Os(VIII) 1.024 1.073 5.499 4.947 ε Os(VI) 0.676 0.651 ε Os(VIII) 0.990 0.990 4.674 3.903 ε Os(VI) 0.479 0.484 ε Os(VIII) 0.859 0.897 0.880 3.104 2.882 2.840 0.348 0.351 0.345 24.67 24.37 25.74 ε Os2 (VII) ε Os2 (VII) 360 ε Os2 (VII) 370 ε Os2 (VII) 380 ε Os2 (VII) 390 ε Os2 (VII) 400 ε Os(VI) 3 -1 LS ε Os(VIII) 350 -1 -1 Keq / × 10 L.mol 6.570 6.214 5.641 4.762 3.744 2.834 MR 122 On the basis of the results acquired, it was possible to postulate the following reaction between osmium(VIII) and osmium(VI): 2- OH O O Os O HO OH Os + O OH 2- O HO OH O Keq HO O Os HO O OH + 2OH- Os O O 2- O OH O Figure 4.13: The formation of the dimeric osmium(VII) species. In order to conclusively prove the existence of the dimeric osmium(VII) species, more rigorous techniques would be required, including: electron spin resonance (ESR) spectroscopy, mass spectrometry and osmium nuclear magnetic resonance (NMR) spectroscopy. Osmium NMR would be a particularly problematic technique to employ under the current set of experimental conditions, since large concentrations (in excess of 5 × 10-2 mol/L) osmium would be required in order to obtain the required signal intensity. 123 APPENDIX Development of the Program GP2 A.1 Introduction The program GP2 was developed specifically for the geometric analysis of twodimensional Mauser diagrams. This program allows for the absorbance of data acquired at each wavelength to be plotted against the absorbance data of subsequent wavelengths. For instance, the absorbance data at wavelength i is plotted against the absorbance data acquired at every wavelength from wavelength (i + a) [where a = 1; 2; 3; …] to wavelength j; resulting in a total of [j - (i + 1)] Mauser diagrams being analysed for wavelength i. Employing a linear least-squares algorithm, the program fits two regression lines to user-defined series for each of the Mauser diagrams generated at wavelength i, in an analogous manner to the diagram depicted in Figure 3.20. The coordinates for the point of intersect between the regression lines are then calculated for each of the diagrams, and an average absorbance value is calculated at each wavelength. The process is repeated for all subsequent wavelengths. 124 2.2 C 2.0 B [2] 1.8 [3] Absorbance j 1.6 1.4 1.2 1.0 B 0.8 0.6 A [1] 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Absorbance i Figure 3.20: Typical 2-dimensional Mauser diagram for the general reaction A Figure A 1: Program interface after data selection 1.6 ↔B↔C 125 Figure A 1 depicts the user interface of the program GP2 after the data have been imported as a tab delimited text file. Once the required data was has been imported, the user can select the data required for the construction of the linear regressions. DataSet 1 corresponds to the construction of regression [1] depicted in Figure 3.20, while DataSet 2 corresponds to regression [2]. In certain cases, reaction systems described by two linearly independent reaction steps also produce Mauser diagrams in which a straight line is obtained in the Mauser space (i.e. describing a system with a single linearly independent reaction step). Therefore, the program features an angle filter, which can be varied as required by the user. The angle filter prevents the inclusion of outliers in the average absorbance values returned by the program. These outliers typically occur when the wavelengths used to construct the diagram are so close to each other (e.g. absorbance at i versus absorbance at (i + 1)) that the absorbance values of the respective wavelengths are indistinguishable from each other. In essence, the angle filter determines the angle formed at the point at which the regression lines intersect. If the calculated angle does not fall within a userdefined range, the absorbance determined at that point is excluded and has no contribution to the final average absorbance returned by the program for that particular wavelength. 126 A.2 Listing of the Program GP2 The following is the listing of the Visual Studio.Net[54] code from the program GP2 used for the analysis of the osmium(VIII) – alcohol kinetic data through Mauser diagrams. Imports System.IO Imports System.Data Imports System.Data.OleDb Imports System.Collections Public Class Form1 Public myFile As String = "" Public dTable As DataTable Public finalTable As DataTable Public regArray(1, 3) As Double Public mVal As Double Public interC As Double Public mVal2 As Double Public interC2 As Double Public tempTable As New DataTable Public tempTable2 As New DataTable Public err As Boolean = False Public finalSet As New DataSet Public dSet As New DataSet Public tempSet As New DataSet Public tempSet2 As New DataSet Public meanTable As New DataTable Public meanSet As New DataSet Public emptyTable As New DataTable Private Sub OpenFile() With OpenFileDialog1 .Filter = "TextFiles (*.txt)|*.txt|All Files (*.*)|*.*" .DefaultExt = "txt" .InitialDirectory = "" If .ShowDialog() = Windows.Forms.DialogResult.OK Then myFile = .FileName() Else myFile = "" End If '========================================================' If myFile <> "" Then Dim detRecord As New System.Text.StringBuilder() Dim rec As String Dim recNbr As Integer Dim myDataTable As New DataTable("myTable") Dim myDataCol As DataColumn Dim myDRow As DataRow Dim myArray As String() 127 Try recNbr = 0 If File.Exists(myFile) And myFile.Length > 0 Then Dim srDetails As StreamReader = New StreamReader(myFile) rec = srDetails.ReadLine() myArray = rec.Split(ControlChars.Tab) Dim s As String For Each s In myArray myDataCol = New DataColumn myDataCol.DataType = System.Type.GetType("System.String") myDataCol.ColumnName = s myDataTable.Columns.Add(myDataCol) Next dSet.Tables.Add(myDataTable) grid.DataSource = dSet.Tables("myTable").DefaultView Do Until srDetails.Peek = -1 rec = srDetails.ReadLine() myArray = rec.Split(ControlChars.Tab) myDRow = myDataTable.NewRow() Dim i As Integer = 0 While i < myArray.Length() myDRow(i) = myArray.GetValue(i) i += 1 End While myDataTable.Rows.Add(myDRow) grid.Item(0, recNbr).Value = recNbr + 1 recNbr += 1 Loop srDetails.Close() Else MessageBox.Show("File does not exist") End If Catch ex As Exception MessageBox.Show(ex.ToString) End Try dTable = myDataTable End If End With End Sub Private Sub btnExit_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnExit.Click Me.Close() End Sub Private Sub btnSelectD1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnSelectD1.Click Dim n, i As Integer 128 Dim a, b As Integer a = System.Convert.ToInt32(txb1.Text.ToString) b = System.Convert.ToInt32(txb2.Text.ToString) i = grid.CurrentCell.ColumnIndex Dim dRow As DataRow Dim dCol As DataColumn Dim dCol2 As DataColumn Dim dCol3 As DataColumn For n = 0 To dSet.Tables.Item(0).Columns.Count - 1 dCol = New DataColumn() dCol2 = New DataColumn() dCol3 = New DataColumn() dCol.DataType = System.Type.GetType("System.String") dCol2.DataType = System.Type.GetType("System.String") dCol3.DataType = System.Type.GetType("System.String") dCol.ColumnName = dSet.Tables.Item(0).Columns.Item(n).ColumnName dCol2.ColumnName = dSet.Tables.Item(0).Columns.Item(n).ColumnName dCol3.ColumnName = dSet.Tables.Item(0).Columns.Item(n).ColumnName tempTable.Columns.Add(dCol) tempTable2.Columns.Add(dCol2) meanTable.Columns.Add(dCol3) Next tempSet.Tables.Add(tempTable) tempSet2.Tables.Add(tempTable2) meanSet.Tables.Add(meanTable) dRow = meanTable.NewRow() meanTable.Rows.Add(dRow) Dim k As Integer For n = a - 1 To b - 1 dRow = tempTable.NewRow() For k = 0 To dSet.Tables.Item(0).Columns.Count - 1 dRow(k) = dSet.Tables(0).Rows(n).Item(k) Next tempTable.Rows.Add(dRow) Next gridTemp.DataSource = tempSet.Tables(0).DefaultView grid2.DataSource = tempSet2.Tables(0).DefaultView gridMean.DataSource = meanSet.Tables(0).DefaultView End Sub Private Sub btnSelectD2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnSelectD2.Click Dim n, i As Integer Dim a, b As Integer a = System.Convert.ToInt32(txb3.Text.ToString) b = System.Convert.ToInt32(txb4.Text.ToString) i = grid.CurrentCell.ColumnIndex Dim dRow As DataRow Dim k As Integer For n = a - 1 To b - 1 dRow = tempTable2.NewRow() For k = 0 To dSet.Tables.Item(0).Columns.Count - 1 dRow(k) = dSet.Tables(0).Rows(n).Item(k) Next tempTable2.Rows.Add(dRow) Next End Sub 129 Private Sub OpenToolStripMenuItem1_Click(ByVal sender System.EventArgs) Handles OpenToolStripMenuItem1.Click OpenFile() End Sub As System.Object, ByVal e As Private Sub btnClearD1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnClearD1.Click End Sub Private Sub btnClearD2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnClearD2.Click End Sub Public arrayBase(tempTable.Rows.Count) As Double Public arrayTemp(tempTable.Rows.Count) As Double Public arrayBase2(tempTable2.Rows.Count) As Double Public arrayTemp2(tempTable2.Rows.Count) As Double Public arrayAns(tempTable.Columns.Count) As Double Public ansCount As Integer = 0 Public arrayAll(0) As Double Public arrayAllTemp(0) As Double Private Sub btnCalcMean_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnCalcMean.Click Dim ParrayBase(tempTable.Rows.Count) As Double Dim ParrayTemp(tempTable.Rows.Count) As Double Dim ParrayBase2(tempTable2.Rows.Count) As Double Dim ParrayTemp2(tempTable2.Rows.Count) As Double Dim ParrayAns(tempTable.Columns.Count - 1) As Double Dim ParrayAll(dTable.Rows.Count) As Double Dim ParrayTempAll(dTable.Rows.Count) As Double 'populate base array Dim n As Integer 'Dim k As Integer = 0 Dim base As Integer Dim i As Integer For base = 0 To tempTable.Columns.Count - 1 For n = 0 To dTable.Rows.Count - 1 ParrayAll.SetValue(System.Convert.ToDouble(dTable.Rows(n).Item(base).ToString), n) Next arrayAll = ParrayAll For n = 0 To tempTable.Rows.Count - 1 ParrayBase.SetValue(System.Convert.ToDouble(tempTable.Rows(n).Item(base).ToString), n) Next For n = 0 To tempTable2.Rows.Count - 1 ParrayBase2.SetValue(System.Convert.ToDouble(tempTable2.Rows(n).Item(base).ToString), n) Next arrayBase = ParrayBase arrayBase2 = ParrayBase2 For i = 0 To tempTable.Columns.Count - 1 If i = base Then Else For n = 0 To dTable.Rows.Count - 1 130 ParrayTempAll.SetValue(System.Convert.ToDouble(dTable.Rows(n).Item(i).ToString), n) Next arrayAllTemp = ParrayTempAll For n = 0 To tempTable.Rows.Count - 1 ParrayTemp.SetValue(System.Convert.ToDouble(tempTable.Rows(n).Item(i).ToString), n) Next For n = 0 To tempTable2.Rows.Count - 1 ParrayTemp2.SetValue(System.Convert.ToDouble(tempTable2.Rows(n).Item(i).ToString), n) Next arrayTemp = ParrayTemp arrayTemp2 = ParrayTemp2 calculateRegression1() calculateRegression2() If (calcAngle() < System.Convert.ToDouble(txbA1.Text) System.Convert.ToDouble(txbA2.Text)) Then Else ParrayAns(ansCount) = calcintercept() ansCount += 1 End If End If Next Dim sum As Double = 0 Dim p As Integer For p = 0 To ParrayAns.Length - 1 sum += ParrayAns(p) Next ansCount = 0 meanTable.Rows(0).Item(base) = sum / (ParrayAns.Length - 1) Dim b As Double = calcBiSection(base) Next MessageBox.Show("calculation comlete") End Sub Public Sub calculateRegression1() Dim x As Double Dim y As Double Dim sumP As Double = 0 Dim sumX As Double = 0 Dim sumY As Double = 0 Dim sumSq As Double = 0 Dim totalSumSq As Double Dim n As Integer Dim m As Double Dim b As Double Dim count As Integer = 0 n = arrayBase.Length - 1 For count = 0 To arrayBase.Length - 2 x = arrayBase(count) y = arrayTemp(count) sumP += x * y sumX += x sumY += y sumSq += x * x Or calcAngle() > 131 Next totalSumSq = sumX * sumX '=================================== 'calculate slope m = ((n * sumP) - (sumX * sumY)) / ((n * sumSq) - totalSumSq) 'round m = Math.Round(m, 4) mVal = m 'calculate intercept b = (sumY - (m * sumX)) / n 'round b = Math.Round(b, 4) interC = b End Sub Public Sub calculateRegression2() Dim x As Double Dim y As Double Dim sumP As Double = 0 Dim sumX As Double = 0 Dim sumY As Double = 0 Dim sumSq As Double = 0 Dim totalSumSq As Double Dim n As Integer Dim m As Double Dim b As Double Dim count As Integer = 0 n = arrayBase2.Length - 1 For count = 0 To arrayBase2.Length - 2 x = arrayBase2(count) y = arrayTemp2(count) sumP += x * y sumX += x sumY += y sumSq += x * x Next totalSumSq = sumX * sumX '=================================== 'calculate slope m = ((n * sumP) - (sumX * sumY)) / ((n * sumSq) - totalSumSq) m = Math.Round(m, 4) mVal2 = m 'calculate intercept b = (sumY - (m * sumX)) / n b = Math.Round(b, 4) interC2 = b End Sub Public Function calcintercept() As Double Dim x As Double Dim b As Double Dim ans As Double x = mval - mval2 b = interc2 - interc If x <> 0 Then ans = b / x 132 Else ans = 1000 err = True End If Return ans End Function Private Sub CloseToolStripMenuItem_Click(ByVal sender System.EventArgs) Handles CloseToolStripMenuItem.Click As System.Object, ByVal e As ByVal e As End Sub Private Sub ExitToolStripMenuItem_Click(ByVal sender System.EventArgs) Handles ExitToolStripMenuItem.Click Me.Close() End Sub As System.Object, Public angX1, angX2, angX3 As Double Public angY1, angY2, angY3 As Double Public d1, d2, d3 As Double Private Function calcAngle() As Double angX1 = arrayBase(1) angX2 = arrayBase2(arrayBase2.Length - 2) angY1 = mVal * angX1 + interC angY2 = mVal2 * angX2 + interC2 angX3 = calcintercept() angY3 = mVal * angX3 + interC d1 = Math.Sqrt(((angX1 - angX2) * (angX1 - angX2)) + ((angY1 - angY2) * (angY1 - angY2))) d2 = Math.Sqrt(((angX3 - angX2) * (angX3 - angX2)) + ((angY3 - angY2) * (angY3 - angY2))) d3 = Math.Sqrt(((angX1 - angX3) * (angX1 - angX3)) + ((angY1 - angY3) * (angY1 - angY3))) Dim f, f4 As Double Dim t1, t2 As Double t1 = d3 * d3 + d2 * d2 - d1 * d1 t2 = 2 * d3 * d2 ''f = Math.Cos((t1) / (t2)) ''f3 = Math.Cosh(t1 / t2) f4 = Math.Acos(t1 / t2) f = f4 * (180 / Math.PI) ''f2 = 1 / f If angX3 = 1000 Then Return System.Convert.ToDouble(txbA1.Text) + 0.0001 Else Return f End If End Function Private Function calcTrapesium(ByVal Count As Double, ByVal startX As Double, ByVal startY As Double) As Double Dim h, b1, b2 As Double Dim initX As Double = startX 'arrayAll(0) Dim initY As Double = startY 'arrayAllTemp(0) Dim Sum As Double = 0 Dim finY, finX As Double 133 Dim PrevX As Double = arrayAll(0) Dim PrevY As Double = arrayAllTemp(0) 'calc base line finX = finalArray(Count) finY = mVal2 * finX + interC2 If (initX < finX) Then If (initY > finY) Then Dim grad As Double = ((initY - finY) / (initX - finalArray(Count))) b1 = 0 Dim i As Integer = 0 For i = 1 To arrayAll.Length - 2 Dim nextX As Double = arrayAll(i) Dim nextY As Double = arrayAllTemp(i) Dim C As Double = nextY - (nextX * ((1 / grad) * -1)) 'Dim C As Double = nextY - (nextX * 6) Dim crossX As Double Dim ans As Double crossX = grad - ((1 / grad) * -1) Dim tempVal As Double = initY - grad * initX 'crossX = grad - 6 Dim b As Double = C - tempVal '50 'arrayAllTemp(0) If crossX <> 0 Then ans = b / crossX Else ans = 1000 'err = True End If h = Math.Sqrt(Math.Pow((PrevX - ans), 2) + Math.Pow((PrevY - (((1 / grad) * -1) * ans + C)), 2)) b2 = Math.Sqrt(Math.Pow((nextX - ans), 2) + Math.Pow((nextY - (((1 / grad) * -1) * ans + C)), 2)) Sum = Sum + (0.5 * h * (b1 + b2)) b1 = b2 PrevX = ans PrevY = ((1 / grad) * -1) * ans + C Next Else initY = finY initX = finX finY = startY '[arrayTemp(0) finX = startX 'arrayBase(0) Dim grad As Double = ((initY - finY) / (initX - finalArray(Count))) Dim tempVal As Double = initY - grad * initX b1 = 0 Dim i As Integer = 0 For i = 1 To arrayAll.Length - 2 Dim nextX As Double = arrayAll(i) Dim nextY As Double = arrayAllTemp(i) Dim C As Double = nextY - (nextX * ((1 / grad) * -1)) 'Dim C As Double = nextY - (nextX * 6) Dim crossX As Double 134 Dim ans As Double crossX = grad - ((1 / grad) * -1) 'crossX = grad - 6 Dim b As Double = C - arrayAllTemp(0) If crossX <> 0 Then ans = b / crossX Else ans = 1000 'err = True End If h = Math.Sqrt(Math.Pow((PrevX - ans), 2) + Math.Pow((PrevY - (((1 / grad) * -1) * ans + C)), 2)) b2 = Math.Sqrt(Math.Pow((nextX - ans), 2) + Math.Pow((nextY - (((1 / grad) * -1) * ans + C)), 2)) Sum = Sum + (0.5 * h * (b1 + b2)) b1 = b2 PrevX = ans PrevY = ((1 / grad) * -1) * ans + C Next End If Else If (initY > finY) Then 'Next Else initY = finY initX = finX finY = startY 'arrayAllTemp(0) finX = startX 'arrayAll(0) Dim grad As Double = ((initY - finY) / (initX - finX)) Dim tempVal As Double = initY - grad * initX b1 = 0 Dim i As Integer = 0 PrevX = initX PrevY = initY For i = arrayAll.Length - 3 To 0 Step -1 Dim nextX As Double = arrayAll(i) Dim nextY As Double = arrayAllTemp(i) Dim C As Double = nextY - (nextX * ((1 / grad) * -1)) Dim crossX As Double Dim ans As Double crossX = grad - ((1 / grad) * -1) 'crossX = grad - 6 Dim b As Double = C - tempVal '160 'arrayAllTemp(arrayAll.Length - 2) If crossX <> 0 Then ans = b / crossX Else ans = 1000 'err = True End If h = Math.Sqrt(Math.Pow((PrevX - ans), 2) + Math.Pow((PrevY - (((1 / grad) * -1) * ans + C)), 2)) b2 = Math.Sqrt(Math.Pow((nextX - ans), 2) + Math.Pow((nextY - (((1 / grad) * -1) * ans + C)), 2)) Sum = Sum + (0.5 * h * (b1 + b2)) 135 b1 = b2 PrevX = ans PrevY = ((1 / grad) * -1) * ans + C Next End If End If Return Sum End Function End Class 136 REFERENCES 1) Griffith, WP. In: The Chemistry of the Rarer Platinum Metals (Os, Ru, Ir & Rh). Chapter 3. 1967, Interscience. 2) Brunot, FR. J. Ind. Hyg. & Tox. 1933, 136-143. 3) McLaughlin, AIG, Milton, R and Perry, KMA. British J of Ind. Med. 1946, 183186. 4) http://www.webelements.com/webelements/elements/text/Os/ 5) Griffith, W.P. Platinum Metals Review. 2004, 48(4), 182-189. 6) Griffith W.P., Osmium. In: Comprehensive Coordination Chemistry. The synthesis, reactions, properties and applications of coordination compounds. 1987. Vol. 4. Ed. G. Wilkinson. Pergamon Press, Oxford. 7) Millipore Simplicity Water Purification System: Operating and Maintenance Manual 8) Sauerbrunn, RD and Sandell, EB. J. Am. Chem. Soc. 1953, 75, 3554 9) Ayres, GH and Wells, WN. Anal. Chem., 1950, 22, 317-320 10) Cristiani, F, Devillanova, FA, Diaz, A and Verani, G. Inorg. Chim. Acta, 1981, 50, 251-255 11) Chugaev, L and Gritzmann, EZ. Anorg. Allg. Chem. 1928, 172, 213 12) Suzuki, T, Miyada, M, Ohta, K, Kaneco, S and Mizuno, T. Microchim. Acta, 1998, 129, 259-263 13) Anderson, LH and Yost, DM. J. Am. Chem. Soc., 1938, 60, 1822-1825 14) Wells, EJ, Jordan, AD, Alderdice, DS and Ross, IG. Aust. J. Chem., 1967, 20, 2315-2322 15) Roebber, JL, Wiener, RN, Russel, CA. J. Phys. Chem., 1974, 60, 3166-3173 16) McFadzean, BJ. PhD Dissertation, 2008, NMMU, South Africa 17) The Royal Swedish Academy of Sciences. Advanced information on the Nobel Prize in Chemistry 2001. http://nobelprize.org/nobel_prizes/chemistry/laureates/2001/chemadv.pdf. 18) Singh, HS, Singh, SP, Singh, SM, Singh, RK and Sisodia, AK. J. Phys. Chem. 1975, 79(18), 1920-1924. 137 19) Singh, NP, Singh, VN and Singh, MP. Aust. J. Chem. 1968, 21, 2913-8. 20) Singh, NP, Singh, VN, Singh, HS, Singh, MP. Aust. J. Chem. 1970, 23, 921-8. 21) Singh, VN, Singh, HS and Saxena, BBL. J. Am. Chem. Soc. 1969, 91(10), 2643-8 22) Singh, B, Singh, BB and Singh, RP. J Inorg. Nucl. Chem. 1981, 43, 1283-6. 23) Singh, H.S. Oxidation of Organic Compounds with Osmium Tetroxide. In: Organic synthesis by oxidation with metal compounds. 1986. Ed. W.J. Mijs & C.R.H. de Jonge. Plenum Press, New York. 24) Lay,PA and Harman, WD. Recent advances in inorganic chemistry. 1991, 37, 219-379 25) Criegee, R. Liebigs Ann. Chem. 1936, 522. 26) http://www.acros.com/_Rainbow/pdf/AO_Oxidation_OSMIUM_DEF.pdf. 27) McMurray, J. Organic Chemistry – 4th Ed. 1996. Brooks/Cole Publishing Company, Pacific Grove, USA. 28) Veerasomaiah, P, Reddy, KB, Sethuram, B and Navaneeth Rao, T. J Indian Chem. Soc. 1989, 66, 755-8. 29) Subbaraman, LR, Subbaraman, J and Behrman, EJ. Inorganic Chemistry. 1972, 11(11), 2621-7. 30) Sharpless, KB, Teranishi, AY and Backvall, JE. J. Am. Chem. Soc. 1976, 99(9), 3120-7. 31) Subbaraman, LR, Subbaraman, J and Behrman, EJ. J. Org. Chem. 1973, 38(8), 1499-1504. 32) Westheimer, FH and Watanaba, W. J. Chem. Phys. 1949, 17, 61 33) Jordan, RB. Reaction mechanisms of inorganic and organometallic systems. 2nd ed. 1998. Oxford University Press, Oxford. 34) Rankin, KN, Qing Liu, JH, Yee, H, Nazih, A, Noureldin, A and Lee, DG. Tetrahedron Letters. 1998, 39, 1095-1098. 35) Dehestani, A, Lam, WH, Hrovat, DA, Davidson, ER, Borden, WT, Mayer, JM. J. Am. Chem. Soc., 2005, 127, 3423-3432 36) Cotton, FA and Wilkinson, G. Advanced Inorganic Chemistry. 4th Ed. 1980, Wiley-Interscience, New York. 37) Uma, KV and Mayanna, SM. Journal of Catalysis. 1980, 61, 165-9. 138 38) Polster, J and Mauser, H. Talanta, 1992, 39 (10), 1355-1359 39) Polster, J and Dithmar, H. Phys. Chem. Chem. Phys. 2001, 3, 993-991 40) Polster, J. Chemical Physics, 1999, 240, 331-351 41) Polster, J. Phys. Chem. Chem. Phys. 1999, 1, 4791-4795 42) Polster, J. Chemical Physics. 2001, 263, 69-81 43) Polster, J and Dithmar, H. Chemical Physics, 2002, 283, 473-480 44) Geswindt, TE, Gerber, WJ, Rohwer, HE and Hosten, EC. A kinetic approach to determine the activity coefficients of Rhodium(III) species in an HCl matrix, Unpublished work, 2006 45) Gerber, WJ. Rhodium(III) Speciation: A Chromatographic Study with ICP-MS, PhD dissertation, NMMU, Port Elizabeth, 2006 46) Burden, RL and Faires, JD. 6th Ed, Brookes/Cole Publishing Company, 1997 47) Galbacs, ZM, Zsednai, A and Csányi, LJ. Transition metal chemistry. 1983, 8, 328-332. 48) Mouchel, B and Bremard, CJ. Chem. Research (S). 1978, 312-313. 49) Bruneau, E, Lavabre, D, Levy, G and Micheau, JC. J. Chem. Educ., 1992, 69 (10), 833-837 50) Gil, VMS and Oliveira, NC. J. Chem. Educ., 1990, 67 (6), 473-478 51) Hill, ZD and MacCarthy, P. J. Chem. Educ., 1986, 63, 162-167 52) Long, JR and Drago, RS. J. Chem. Educ., 1982, 59 (12), 1037-1039 53) MacCarthy, P. Anal. Chem., 1978, 50 (14), 2165 54) Likussar, W and Boltz, DF. Anal. Chem., 1971, 43 (10), 1265-1272 55) Momoki, K, Sekino, J, Sato, H, Yamaguchi, N. Anal. Chem., 1969, 41 (10) 1286-1299 56) Inczèdy, J. Analytical Applications of Complex Equilibria, Ellis Horwood, Chichester, 1976 57) Hosten, EC. Complexing Interactions with Arsenazo(III), PhD dissertation, NMMU, Port Elizabeth, 1996 58) Klausen, KS, Langmyhr, F. J., Anal. Chim. Acta., 1963, 28, 335-340 59) Beaufils, JP. Bull. Soc Chim, 1969, 4, 1066 60) Beaufils, JP and Coussemant, F. Bull. Soc Chim., 1968, 1, 27 139 61) Doke, ER, Satzinger, JW, Williams, SR and Douglas, DE. Object-Orientated Application Development Using Microsoft Visual Bascic.NET, 2003, Course Technology