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Manufacture of sodium dithiouite from sodium-mercury amalgam and aqueous solution of sulfur dioxide 1972

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| 5 " I V ) MANUFACTURE OF SODIUM DITHIONITE FROM SODIUM- MERCURY AMALGAM AND AQUEOUS SOLUTION OF SULFUR DIOXIDE by RAMAN NAYAR B. Tech. (Hon.), I . I . T . , K h aragpur, 1967 A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department o f CHEMICAL ENGINEERING We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA November, 1972 In presenting t h i s thesis i n p a r t i a l fulfullment of the requirements for an advanced degree at the University of B r i t i s h Columbia/ I agree that the Libr a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the Head of my Department or by his representatives. I t i s understood that p u b l i c a t i o n , i n part or i n whole, or the copying of th i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. RAMAN NAYAR Department of Chemical Engineering The University of B r i t i s h Columbia Vancouver 8, Canada Date K^~ot Xo' \^ 7 3 i i ABSTRACT A r e l a t i v e l y d i l u t e (approximately 1 to 2%) water soluti o n of sodium d i t h i o n i t e was produced from sodium-mercury amalgam and aqueous s o l u t i o n of s u l f u r dioxide i n a simple "once through" reactor [proposed process]. The reactor could be run i n conjunction with the Castner-Kellner type c e l l . The manufactured solu t i o n could then be used d i r e c t l y for the brightening of groundwood pulp. The bench scale experiments were c a r r i e d out i n a continuous-flow-stirred-tank reactor where the aqueous and amalgam phases formed an i n t e r f a c e . The e f f e c t s of important process variables on the steady-state concentration of sodium d i t h i o n i t e i n the reactor and y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed and on sodium consumed i n a s i n g l e pass were determined. The above-mentioned y i e l d s are important i n assessing the economic f e a s i b i l i t y of the pro- posed process. The steady-state y i e l d of sodium d i t h i o n i t e on sodium i n the amalgam entering the reactor and'conversion of sodium to d i f f e r e n t products i n the reactor were also determined. The present i n v e s t i g a t i o n showed that the process variables can be c o n t r o l l e d to give approximately 2.3% sodium d i t h i o n i t e s o l u t i o n with steady-state Na2S20^ y i e l d s of about 21% on s u l f u r dioxide i n the aqueous feed and about 67% on sodium consumed. The y i e l d s obtained depend on the l e v e l s of process variables such as: 1. the concentration of sodium i n the amalgam enter- ing the reactor, 2. the concentration of t o t a l s u l f u r dioxide i n the aqueous feed s o l u t i o n , 3. the a g i t a t i o n i n the aqueous phase, 4. the a g i t a t i o n i n the amalgam phase, 5. the residence time i n the aqueous phase, 6. the residence time i n the amalgam phase, 7. the interfacial-area/aqueous-volume r a t i o , 8. the temperature of the aqueous phase, and 9. the pH of the aqueous phase. This experimental study indicates that i t may be economically f e a s i b l e for a pulp m i l l to change .from zinc d i t h i o n i t e produced in situ to sodium d i t h i o n i t e produced in situ by the proposed; process. Further, the proposed process compared to the manufacture of zinc d i t h i o n i t e i n situ avoids the discharge of zinc ions which act as b i o c i d a l agents when discharged into the e f f l u e n t r eceiving waters. The models suggested by Ketelaar (44) and Gerritsen (30) were found inadequate to explain the processes occurring i v i n the reacting system sodium-mercury amalgam and aqueous s u l f u r dioxide. A q u a l i t a t i v e model has been suggested on the basis of the experimental work and the information ava i l a b l e i n the l i t e r a t u r e . This work also sheds some l i g h t on the type of reactor which would be sui t a b l e f o r the proposed process. V ACKNOWLEDGEMENT The author wishes to express h i s thanks to the fac u l t y and s t a f f of the Chemical Engineering Department, The University of B r i t i s h Columbia. Special thanks are extended to Dr. F.E. Murray, who suggested the pro j e c t and under whose guidance t h i s work was undertaken. The author i s indebted to the Chemical Engineering Workshop personnel f o r t h e i r assistance i n assembling the experimental equipment. The author wishes to thank Mr. E. Rudischer, i n p a r t i c u l a r , for his assistance and cooper- ation . F i n a n c i a l support for th i s research was most g r a t e f u l l y received from the National Research Council of Canada and from the B r i t i s h Columbia Research Council. The author i s also indebted to his wife Jane for her invaluable help throughout t h i s work. v i TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION 1 I I . REVIEW OF PERTINENT PRIOR WORK 7 A. Manufacturing Processes for Sodium Di t h i o n i t e 7 1. Zinc dust: sodium carbonate process . . . 7 2. E l e c t r o l y t i c or cathodic reduction process 9 3. Sodium formate process 9 4. Sodium borohydride process 10 5. Sodium amalgam process 11 (a) Advantages of the sodium amalgam process 11 (b) Types of the sodium amalgam process . . . 12 (i) Sodium amalgam: S0 2-organic solvent process 12 ( i i ) Sodium amalgam: gaseous SO2 process and sodium amalgam: l i q u i d SO2 process 13 ( i i i ) Sodium amalgam: S02-NaHS03/Na2S03 buffer process 13 B. Recommended Conditions for Improving the Y i e l d of Sodium D i t h i o n i t e i n the Sodium Amalgam: S0 2-NaHS0 3/Na 2S0 3 Buffer Process . . 15 C. Mercury Contamination of Sodium D i t h i o n i t e Produced by the Sodium Amalgam: SOj-NaHSO,/ Na„S0 o Buffer Process . . . . . . 17 CHAPTER v i i PAGE D. Li g n i n Preserving Bleaching of Ground- wood Pulp by Sodium D i t h i o n i t e 19 1. D e f i n i t i o n of the terms "brightening" and "bleaching" . . . . . 19 2. C h a r a c t e r i s t i c s of the groundwood bleach- ing process . 20 3. E f f e c t s of groundwood brightening . . . 21 4. Conditions for groundwood brightening by sodium d i t h i o n i t e 21 E. Sodium-mercury Amalgam 24 1. Molecular structure of sodium-mercury amalgam . . . . . . . . . . 24 2. Surface tension of sodium-mercury amalgam 25 3. S e n s i t i v i t y to oxidation of sodium- mercury amalgam . . . . . . 25 4. Density of sodium-mercury amalgam . . . 26 F. Sulfur Dioxide Solution i n Water . . . . . 26 1. P r i n c i p a l e q u i l i b r i a . . . . . . . . . 26 2. D i f f u s i o n of s u l f u r dioxide i n water . . . . . . . . . . . . . . . . . 32 G. Important Reactions i n the Proposed Process . . . . . 33 1. The Sodium d i t h i o n i t e formation reaction . . . . . . 35 2. The water reaction 39 3. The sodium d i t h i o n i t e decomposition reactions . . . . . . . 43 (a) Homogeneous decomposition of sodium d i t h i o n i t e 43 (b) Heterogeneous decomposition of sodium d i t h i o n i t e 4 6 v i i i CHAPTER PAGE 4. The sodium d i t h i o n i t e oxidation reaction . . . . . 48 I I I . THEORETICAL MODELS 50 IV. EXPERIMENTAL 54 A. Experimental Materials . . . . 54 1. Sodium-mercury amalgam . . . . . 54 2. Aqueous s u l f u r dioxide solution 54 B. Experimental Apparatus . 55 1. Reactor 55 2. pH measurement of the aqueous phase . . . 64 3. Temperature measurement of d i f f e r e n t streams 65 4. Insulation of the equipment . . . . . . . 67 5. E l e c t r i c a l wiring diagram . . . . . . . . 67 C. C a l i b r a t i o n Curves . . . . . 67 D. An Experimental Run . . . . . . . . 69 E. A n a l y t i c a l Procedures and Errors . . . . . . 71 1. Sodium-mercury amalgam . . . . 71 (a) Analysis of sodium-mercury amalgam 71 (b) Accuracy and p r e c i s i o n of the a n a l y t i c a l procedure 72 2. Aqueous s u l f u r dioxide solution . . . . . 75 (a) Analysis of aqueous s u l f u r dioxide solution 75 (b) Accuracy and p r e c i s i o n of the a n a l y t i c a l procedure 76 3. Aqueous sodium d i t h i o n i t e solution . . . . 77 i x CHAPTER PAGE (a) Analysis of sodium d i t h i o n i t e i n the product stream 77 (b) Accuracy and p r e c i s i o n of the a n a l y t i c a l procedures 79 V. EXPERIMENTAL RESULTS 8 2 A. Batch Experiments 82 B. Introduction to Experiments i n the CFSTR . . . . . . . . . . 8 7 C. D e f i n i t i o n s of Some Important Quantities which are used for the Interpretation of Data . . . 90 D. Reproducibility of Experimental Runs i n the CFSTR 9 4 E. Data from CFSTR Experiments . . . . . . . . . 1 0 1 1. Concentration of sodium i n fresh amalgam 101 2. Concentration of " t o t a l " s u l f u r dioxide i n the aqueous feed s o l u t i o n 121 3. A g i t a t i o n i n the aqueous phase 133 4. Flow rate of aqueous s u l f u r dioxide so l u t i o n , i . e . residence time i n the aqueous phase . . . . . . 144 5. Interfacial-area/aqueous-volume r a t i o . . 153 6. Temperature of the aqueous phase 164 7. pH of the aqueous phase 168 8. Flow rate of fresh amalgam, i . e . residence time i n the amalgam phase . . . 168 VI. DISCUSSION I 7 0 A. Model for the Reacting System i n the Proposed Process 170 X CHAPTER PAGE 1. Development of the model 170 2. The model 185 B. Conditions for Improving the Yields of Sodium D i t h i o n i t e i n the Proposed Process 188 C. Economic F e a s i b i l i t y of the Proposed Process . . . . . . . 194 D. Reactor for the Proposed Process . . . . . . 198 VII. CONCLUSIONS 199 VIII. RECOMMENDATIONS FOR FURTHER WORK 203 IX. NOMENCLATURE 205 BIBLIOGRAPHY . . . . . . . . 208 APPENDIX A. EQUIPMENT SPECIFICATION A - l 1. pH measurement A - l 2. D i g i t a l temperature recording . . . . . . . . A - l 3. C a l i b r a t i o n curves . . . . . . . A-2 B. STATISTICAL EVALUATION OF ACCURACY AND PRECISION B - l 1. Error of a measurement process . . . . . . . B - l 2. Evaluation of accuracy B-3 3. Evaluation of p r e c i s i o n (or imprecision). . . B-4 4. Propagation of random error B-8 C. SODIUM-MERCURY AMALGAM C - l 1. Purity of the chemicals i n preparing amalgam C - l 2. Problems encountered i n preparation of amalgam . . . . . C-2 x i APPENDIX PAGE 3. Cal c u l a t i o n of sodium content i n an amalgam sample C-3 4. Estimation of the p r e c i s i o n of the a n a l y t i c a l procedure C-4 D. AQUEOUS SOLUTION OF SULFUR DIOXIDE D-l 1. Purity of the chemicals i n preparing aqueous su l f u r dioxide solu t i o n D-l 2. Ca l c u l a t i o n of the t o t a l s u l f u r dioxide con- centration i n an aqueous solution sample . . D-2 3. Estimation of the p r e c i s i o n of the a n a l y t i c a l procedure . . . . . D-3 E. SODIUM DITHIONITE IN THE PRODUCT STREAM . . . . . E - l 1. Deta i l s of the a n a l y t i c a l procedures and sample c a l c u l a t i o n s E - l (a) The iodine-formaldehyde method E - l (b) The Rubine-R method E-8 2. Estimation of the p r e c i s i o n of the Rubine-R E-16 method F. DATA PROCESSING F - l 1. Mathematical expressions for c a l c u l a t i n g C S 2 0 4 ' Y S 0 2 , YNa' C 0 N N A ' XNa a n d N a / S ° 2 < rate of sodium consumption, and sample calcu l a t i o n s 2. The 95 per cent confidence l i m i t s of the steady-state C8 Y , CONNA, X^, Na/S02 and rate of sodium consumption _ for an experimental run 3. Experimental data and r e s u l t s F-12 x i i LIST OF FIGURES Figure Page 1. Concentrations of free s u l f u r dioxide, b i s u l f i t e ions and s u l f i t e ions versus pH i n a 0.399 molar s u l f u r dioxide s o l u t i o n i n water at 25°C 2. E f f e c t i v e d i f f u s i o n c o e f f i c i e n t s for su l f u r dioxide i n aqueous ( ^ 4 ) 2 6 0 3 . 'Total* s u l f u r dioxide concentration = 1 gm mole/ 1 i ter 3. Schematic flow-sheet of the experimental apparatus 4. Reactor assembly 61 5. D i g i t a l temperature measurement (schematic). . 66 6. E l e c t r i c a l wiring diagram (schematic) 68 7. Reproducibility of the experimental runs i n the CFSTR 97 8. Reproducibility of the experimental runs i n the CFSTR 100 9. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/S02 r a t i o s entering the CFSTR for the experimental set: 65-77 . 103 10. Steady-state values of sodium d i t h i o n i t e con- centration and various y i e l d s versus concen- trations of sodium i n amalgam entering the CFSTR for the experimental set: 65-77 . . . . 11. Rates of sodium consumption versus Na/S02 r a t i o s entering the CFSTR for the experimental set: 65-77 107 12. Rates of sodium consumption versus concentra- tions of sodium i n amalgam entering the CFSTR for the experimental set: 65-77 . . . . 108 x i i i Figure Page 13. Rates of sodium consumption versus concen- trations of sodium i n amalgam entering the CFSTR for the experimental sets: 95-105, 23-28, 65-77 and 42-46 . . . . . I l l 14. Concentrations of sodium d i t h i o n i t e i n the product stream versus time for runs i n the experimental set: 4 2-46 . 115 15. Concentrations of sodium i n amalgam leaving the CFSTR versus time for runs i n the experimental set: 42-4 6 16. Concentrations of sodium d i t h i o n i t e i n the product stream versus time for runs i n the experimental set: 23-28 117 17. Concentrations of sodium i n amalgam leaving the CFSTR versus time for runs i n the experimental set: 23-28 118 18. Concentrations of sodium d i t h i o n i t e i n the product stream versus time for runs i n the experimental set: 65-77 119 19. Concentrations of sodium i n amalgam leaving the CFSTR versus time for runs i n the experi- mental set: 65-77 120 20. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/SC>2 r a t i o entering the CFSTR for the experimental set: 23-28 123 21. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/SC>2 r a t i o entering the CFSTR for the experimental set: 4 2-46 124 22. Steady-state sodium d i t h i o n i t e concentrations versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of su l f u r dioxide i n the aqueous feed ^25 23. Steady-state sodium d i t h i o n i t e concentrations versus concentrations of sodium i n amalgam entering the CFSTR at d i f f e r e n t concentrations of s u l f u r dioxide i n the aqueous feed . . . 127 xiv Figure Page 24. C r i t i c a l concentrations of sodium i n amalgam entering the CFSTR versus molar- i t y of su l f u r dioxide i n the aqueous solutions entering the CFSTR 128 25. Steady-state y i e l d s of sodium d i t h i o n i t e on sulfur dioxide i n the aqueous feed versus Na/SC>2 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of s u l f u r dioxide i n the aqueous feed 129 26. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of s u l f u r dioxide i n the aqueous feed 130 27. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of s u l f u r dioxide i n the aqueous feed . 131 28. Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/SC«2 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of s u l f u r dioxide i n the aqueous feed 132 29. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/S02 r a t i o s entering the CFSTR f o r the experimental set: 86-90 137 30. Steady-state sodium d i t h i o n i t e concentrations versus Na/SC^ r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed , 139 31. Steady-state y i e l d s of sodium d i t h i o n i t e on su l f u r dioxide i n the aqueous feed versus Na/SC>2 r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed . . 140 32. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR versus Na/SC>2 r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed 141 XV Figure Page 33. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/SC»2 r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed 142 34. Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed . 143 35. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/S0 2 r a t i o s entering the CFSTR for the experimental set: 94-104 145 36. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/SC>2 r a t i o s entering the CFSTR for the experimental set: 95-105 . 146 37. Steady-state sodium d i t h i o n i t e concentrations versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t flow rates of the aqueous feed . . 147 38. Steady-state y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed versus Na/S02 r a t i o s entering the CFSTR at d i f f e r - ent flow rates of the aqueous feed 14 8 39. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR ver- sus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t flow rates of the aqueous feed . . 149 40. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/SC>2 r a t i o s entering the CFSTR at d i f f e r - ent flow rates of the aqueous feed 150 41. Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t flow rates of the aqueous feed . . 151 XVI Figure Page 42. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/S02 r a t i o s entering the CFSTR for the experimental set: 122-134 . . . . . . . . . . 156 43. Steady-state values of sodium d i t h i o n i t e concentration and various y i e l d s versus Na/S02 r a t i o s entering the CFSTR for the experimental set: 123-135 157 44. Steady-state sodium d i t h i o n i t e concentra- tions versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t values of i n t e r f a c i a l - area/aqueous-volume r a t i o 158 45. Steady-state y i e l d s of sodium d i t h i o n i t e on sulfur dioxide i n the aqueous feed versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t values of interfacial-area/aqueous volume r a t i o 159 46. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t values of i n t e r f a c i a l - area/aqueous-volume r a t i o 160 47. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r - ent values of interfacial-area/aqueous- volume r a t i o 161 48. Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r -ent values of interfacial-area/aqueous- volume r a t i o 162 49. Steady-state values of sodium d i t h i o n i t e concentration and y i e l d of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed versus interfacial-area/aqueous-volume r a t i o s at d i f f e r e n t Na/S02 r a t i o s entering the CFSTR 163 50. Steady-state y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t steady-state temperatures of the aqueous phase 166 x v i i Figure Page 51. Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/SG^ ra t i o s entering the CFSTR at d i f f e r e n t steady-state temperatures of the aqueous phase . 167 A-I. Flow rate of mercury pumped by Moyno pump versus micrometer set t i n g on Graham transmission A~3 A - I I . Flow rate of aqueous s u l f u r dioxide versus reading on the rotameter scale A-4 A - I I I . Flow rate of cooling water versus reading on the rotameter scale . Ar-5 A - I V . M i l l i v o l t output of iron-constantan thermocouples versus temperature °C . . . . A-6 A - V . RPM of the propeller versus micrometer sett i n g on the thyratron c o n t r o l l e r f o r the v a r i a ble speed drive (Heller motor) . . x v i i i LIST OF TABLES TABLE PAGE 1. Conditions for Brightening Groundwood by N a 2 S 2 ° 4 23 2. P r e c i s i o n of the Amalgam A n a l y t i c a l Procedure . . . . . 74 3. Pr e c i s i o n of the Sulfur Dioxide A n a l y t i c a l Procedure 76 4. Process Variables and Their Units . . . . . . . 93 5. Levels of the Process Variables i n Set: 47-57 96 6. Levels of the Process Variables i n Set: 65-77 96 7. Levels of the Process Variables i n Set: 66-76 99 8. Levels of the Process Variables i n Set: 62-63 . . . . . . . . . . . 99 9. Levels of the Process Variables i n Set: 87-91 . . . . . . . . 99 10. Levels of the Process Variables i n Set: 95-105 . . . . . . . 110 11. Levels of the Process Variables i n Set: 23-28 110 12. Levels of the Process Variables i n Set: 42-46 110 13. Levels of the Process Variables i n Set: 86-90 1 3 g 14. Levels of the Process Variables i n Set: 94-104 1 3 g 15. Levels of the Process Variables i n Set: 122-134 . 155 xix TABLE PAGE 16. Levels of the Process Variables i n Set: 123-135 155 17. Levels of the Process Variables i n Set: 106-118 165 18. Levels of the Process Variables i n Set: 110-113 165 19. Levels of the Process Variables for the Run 44 195 C-I. Measured Values, Range of Random Errors and Variances of d i f f e r e n t measured quanties (amalgam a n a l y t i c a l procedure) C-7 F-I. Steady-State Data and Results f o r Experimental Set: 47-57 F-14 F-II. Steady-State Data and Results f o r Experimental Set: 65-77 F-15 F-I I I . Steady-State Data and Results for Experimental Set: 66-76 F-16 F-IV. Steady-State Data and Results f o r Experimental Set: 62-63 . . . . . F-17 F-V. Steady-State Data and Results for Experimental Set: 87-91 F ~ l 8 F-VI. Steady-State Data and Results for Experimental Set: 95-105 F ~ l 9 F-VII. Steady-State Data and Results for Experimental Set: 23-28 F ~ 2 0 F-VIII. Steady-State Data and Results for Experimental Set: 42-46 F-21 F-IX. Steady-State Data and Results f o r Experimental Set: 86-90 F-22 F-X. Steady-State Data and Results for Experimental Set: 94-104 F-23 X X TABLE PAGE F-XI. Steady-State Data and Results for Experimental Set: 122-134 F-24 F-XII. Steady-State Data and Results for Experimental Set: 123-135 F-25 F-XIII. Steady-State Data and Results for Experimental Set: 106-118 F-26 F-XIV. Steady-State Data and Results f o r Experimental Set: 110-113 . . . . . . . F-27 F-XV. Unsteady-State Results for Experimental Run 42 F-28 F-XVI. Unsteady-State Results for Experimental Run 43 F-28 F-XVII. Unsteady-State Results for Experimental Run 44 F-29 F-XVIII. Unsteady-State Results for Experimental Run 4 5 F-29 F-XIX. Unsteady-State Results f o r Experimental Run 46 F-30 F-XX. Unsteady-State Results for Experimental Run 23 F-30 F-XXI. Unsteady-State Results for Experimental Run 24 F-31 F-XXII. Unsteady-State Results for Experimental Run 25 F-31 F-XXIII. Unsteady-State Results for Experimental Run 26 F-32 F-XXIV. Unsteady-State Results for Experimental Run 27 F-32 F-XXV. Unsteady-State Results for Experimental Run 28 F-33 F-XXVI. Unsteady-State Results for Experimental Run 65 F-33 XXI TABLE PAGE F-XXVII. Unsteady-State Results for Experimental Run 67 . F-34 F-XXVIII. Unsteady-State Results for Experimental Run 69 F-34 F-XXIX. Unsteady-State Results for Experimental Run 71 F-35 F-XXX. Unsteady-State Results for Experimental Run 73 . F-35 F-XXXI. Unsteady-State Results for Experimental Run 75 F-36 F-XXXII. Unsteady-State Results for Experimental Run 77 F-36 1 CHAPTER I INTRODUCTION Groundwood pulps, e s p e c i a l l y those obtained from western softwood species, are dark i n colour and must be brightened for use i n newsprint manufacture. Brightening i s done usually with a so l u t i o n of zinc d i t h i o n i t e (ZnS 20^), manufactured on the m i l l s i t e from zinc dust and aqueous su l f u r dioxide s o l u t i o n , according to the reaction: Zn + 2S0 2 ZnS 20 4 This process i s economical and e f f i c i e n t but suffers from one serious drawback. That i s , the zinc ion which remains i n the spent bleach solu t i o n must be discharged to the available e f f l u e n t receiving waters. Since zinc ion i s an active b i o c i d a l agent (46, 37), th i s i s very object- ionable from the standpoint of water p o l l u t i o n c o n t r o l . Already the use of zinc d i t h i o n i t e i s prohibited i n some areas and i n others, pressure i s developing to p r o h i b i t i t s use. For a m i l l which can not use zinc d i t h i o n i t e , the availab l e a l t e r n a t i v e i s to purchase manufactured sodium 2 d i t h i o n i t e (^2820^). Sodium d i t h i o n i t e i s avai l a b l e i n the market as the anhydrous c r y s t a l l i n e s a l t . I t i s quite unstable i n aqueous solut i o n or when i t c a r r i e s water of c r y s t a l l i z a t i o n (Na 2S 20 4' 2H 20). T h e cost of ZnS 20 4 produced i n pulp m i l l s (62) i s approximately 16<:/lb of $2®^ Ion. The cost of c r y s t a l l i n e ^ 2 8 2 0 ^ bought i n the market (65) i s approximately 39<:/lb of $2°^ i° n« Preferred a p p l i c a t i o n of sodium d i t h i o n i t e f o r the brightening of ground- wood pulp i s 0.2 - 1.5% of the f i b r e weight (62, 106). For the following example, i t was assumed that i n the bleaching plant, the concentration of sodium d i t h i o n i t e i s 1% of the f i b r e weight. For a m i l l producing 500 tons per day of groundwood pulp, forced to change from ZnS20^ produced in s i t u to c r y s t a l l i n e ^2^2^^ bought i n the market, the extra cost involved would be about one m i l l i o n d o l l a r s per year. A good part of the cost i n purchased c r y s t a l l i n e sodium d i t h i o n i t e i s incurred i n the c r y s t a l l i z a t i o n and subsequent drying steps. I t would be possible to reduce s u b s t a n t i a l l y the cost of sodium d i t h i o n i t e for m i l l use i f i t could be manufactured in s i t u i n a simple "once through" reactor and the s o l u t i o n fed d i r e c t l y to the groundwood bleaching plant. One possible means of doing this would be by the sodium-mercury amalgam route (Chapter I I ) . In th i s process, a s o l u t i o n of s u l f u r dioxide (or sodium b i s u l f i t e ) i n water i s allowed to react with sodium dissolved i n mercury to produce a solut i o n of sodium d i t h i o n i t e . This approach may be of a spe c i a l i n t e r e s t to pulp m i l l s where chlorine and caustic soda are manufactured i n mercury c e l l s . Considering the f a c t that ^ 2 8 2 0 ^ (~39<Vlb of 4 ^ o n ^ n t n e a n n Y ^ r o u s c r y s t a l l i n e salt) i s a more valuable product than NaOH [-2.75C/lb(65)], sodium-mercury amalgam produced i n the brine e l e c t r o l y s i s unit could be used as a r e l a t i v e l y inexpensive source of sodium to produce sodium d i t h i o n i t e . In other words, i t might be advantageous to d i v e r t a part of the sodium-mercury amalgam to the proposed sodium d i t h i o n i t e manufacturing u n i t . The r e s t of the amalgam could go to the conventional "decomposer" to produce caustic soda. The sodium-depleted amalgam from the decomposer and the sodium d i t h i o n i t e manufacturing unit could be sent back to the brine e l e c t r o l y s i s u n i t . The sodium amalgam process for making sodium d i t h i o n i t e has been investigated quite extensively. A summary of the l i t e r a t u r e search i s given i n Chapter I I . Although a good deal of information has been developed on t h i s process, i t i s directed primarily at producing concentrated solutions of sodium d i t h i o n i t e f o r easy recovery of the s o l i d s a l t . The reason behind t h i s was probably to compete with the e x i s t i n g zinc dust: sodium carbonate method (Chapter I I ) , which has been used i n d u s t r i a l l y to manufacture anhydrous sodium d i t h i o n i t e c r y s t a l s . For the proposed sodium amalgam process, solutions obtained could be as d i l u t e as 1 to 2% Na^S-,0. . I t can be 4 shown from a mass-balance that i f an approximately 1% solut i o n of sodium d i t h i o n i t e i s manufactured, i t would not change appreciably the pulp consistency which i s employed i n the normal groundwood brightening process (62, 106). Based on the above discussion the problem for the present research was defined. I t was decided to investigate the e f f e c t of d i f f e r e n t process variables on the y i e l d s of sodium d i t h i o n i t e produced as a r e l a t i v e l y d i l u t e (approxi- mately 1-2%) water solut i o n from sodium-mercury amalgam and s u l f u r dioxide i n a simple "once through" reactor. The manufactured aqueous solut i o n would be used d i r e c t l y for the brightening of groundwood pulp. I t was also hoped that the i n v e s t i g a t i o n would lead to a better understanding of the sodium amalgam process and might y i e l d s u f f i c i e n t information for the design of a semi-commercial or a commercial plant. Since i t was decided to have no recycle of s u l f u r dioxide i n t h i s i n v e s t i g a t i o n , y i e l d s of sodium d i t h i o n i t e on * s u l f u r dioxide entering t and on sodium consumed i n a singl e pass must be economical. Y i e l d of sodium d i t h i o n i t e on t o t a l s u l f u r dioxide entering the reactor (%), (gm molar cone, of Na2S20^ i n product) x 2 x 100 Y — 2 (gm molar cone, of t o t a l SO- i n aqueous feed) 5 A rough economic assessment of a sodium amalgam process to produce sodium d i t h i o n i t e s o l u t i o n in s i t u can be made. In the manufacture of chlorine and caustic soda using mercury c e l l s , the cost of production may be apportioned to these two products on a weight basis (57). Thus, the cost of chlorine gas and caustic soda i s almost equal. The market value of caustic soda can be taken as approximately 2.75<Vlb (65). An evaluation of the sodium i n the amalgam would be approximately 5$ (40/23 x 2.75 = 5) per pound. The cost of crude s u l f u r varies depending on the market conditions but may be taken as 1.8£/lb (65). The cost of s u l f u r dioxide gas produced by oxidation of t h i s s u l f u r would be about 0.9$ plus processing cost for a t o t a l of about 1.5C/lb. The reaction between sodium and s u l f u r dioxide i s given s t o i c h i o m e t r i c a l l y by the equation: 2 Na + 2S0 2 -*• 2 Na + + * Y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (%) , (gm moles of Na^SpO. i n product/min) x 2 x 100 CONNA = gm moles of Na entering with fresh amalgam/min -gm moles of Na leaving with spent amalgam/min 6 If i t i s assumed that a 100% y i e l d of sodium d i t h i o n i t e on sodium consumed i s obtained and the y i e l d of sodium d i t h i o n i t e on sulf u r dioxide entering i s 100%, then the cost of sodium d i t h i o n i t e (chemical cost only) would be about 3.3<?/lb of S 20~ ion. This cost can be compared with the cost of anhydrous sodium d i t h i o n i t e c r y s t a l s bought i n the market (=39<:/lb of S 2 O 4 ion) as well as the cost of zinc d i t h i o n i t e produced in s i t u (~16<:/lb of ^>2Q~i ion) . I f reasonably high y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide entering and on sodium consumed could be obtained by the proposed sodium amalgam process, i t seems possible to decrease the cost of sodium d i t h i o n i t e s u b s t a n t i a l l y f o r m i l l use. I t i s also possible that the cost of d i t h i o n i t e ions produced by the proposed sodium amalgam process may not be very d i f f e r e n t from the cost of d i t h i o n i t e ions i n the zinc d i t h i o n i t e produced in s i t u . 7 CHAPTER II REVIEW OF PERTINENT PRIOR WORK A. Manufacturing Processes f o r Sodium D i t h i o n i t e A number of methods are a v a i l a b l e i n the l i t e r a t u r e describing preparation of sodium d i t h i o n i t e . A l l of them are based on the reduction of s u l f u r dioxide (or sodium b i s u l f i t e ) . The ones which could be used commercially are: 1. Zinc dust: sodium carbonate process 2. E l e c t r o l y t i c or cathodic reduction process 3. Sodium formate process 4. Sodium borohydride process 5. Sodium amalgam process. B r i e f outlines of these processes are given below. Special emphasis has been put on the sodium amalgam process because of i t s s i m i l a r i t y to the proposed process. 1. Zinc dust: sodium carbonate process Sodium d i t h i o n i t e i s manufactured by reacting an aqueous solut i o n of s u l f u r dioxide with a s t i r r e d suspension of zinc dust i n water and then converting the zinc s a l t into the sodium s a l t by the addition of sodium carbonate (8-10, 8 17, 19, 30, 73, 76, 78, 94, 98, 148). The chemical reactions involved are: Zn + 2S0 2 -> ZnS 20 4 ZnS 20 4 + Na 2C0 3 •*• ZnC0 3 + Na 2S 20 4 After the removal of the zinc carbonate by f i l t r a t i o n , Na 2S 20 4. 2H20 i s salted out by the addition of NaCI. Dehydration and drying steps follow to make the anhydrous s a l t , Na 2S 20 4. Badischen A n i l i n - und Sodafabrik (Germany) used t h i s method i n d u s t r i a l l y (9, 10). A 20% sol u t i o n of sodium d i t h i o n i t e was c r y s t a l l i z e d , dehydrated, then d r i e d . This German firm obtained a y i e l d of 65-75% based on s u l f u r dioxide feed and about 70% on zinc. V i r g i n a Chemical Inc. of the U.S.A. has also been reported to use t h i s method i n d u s t r i a l l y . Some of the disadvantages of the zinc dust:sodium carbonate process to produce sodium d i t h i o n i t e are: (a) The market for zinc oxide, which i s a by-product, i s contracting. Zinc dust i s quite expensive, and the i n i t i a l cost incurred i n the raw material i s not compensated by revenue from the sale of zinc oxide. (b) The process i s discontinuous and involves the extra steps (compared to the other processes) of pre- c i p i t a t i n g zinc carbonate and c a l c i n i n g the p r e c i p i - tated carbonate to obtain zinc oxide. 9 (c) Zinc i s always present as an impurity i n the N a 2S 20 4 and zinc ions, as mentioned e a r l i e r , are a p o l l u t i o n hazard i f released with m i l l e f f l u e n t . (d) Dehydration and drying steps to make stable anhydrous Na2S204 are complicated and expensive. 2. E l e c t r o l y t i c or cathodic reduction process In t h i s method d i t h i o n i t e ion i s produced c a t h o d i c a l l y (8, 10, 21, 39, 40, 61, 71, 75, 131, 132, 135, 136, 139, 142- 144, 147) according to the reaction: 2HSO~ + 2H + + 2e -»• S 2 0 = + 2H 20 Although the cathodic reduction of s u l f u r dioxide (or b i s u l - f i t e ) s o l u t i o n i n water has been studied repeatedly since 1904, t h i s method has never been used i n d u s t r i a l l y . The process i s reported to give low y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide and low current e f f i c i e n c i e s . However, i n a recently published i n v e s t i g a t i o n based on laboratory experiments, Oloman (67, 68) claims that ^28204 produced by t h i s method could compete with ZnS20^ produced in s i t u . 3. Sodium formate process This process was invented by Kinzlberger & Co. (122, 123). In t h i s process s u l f u r dioxide i s dissolved i n a solu- 10 t i o n of sodium hydroxide i n methanol. The s u l f u r dioxide i s reduced i n turn, by a suspension of sodium formate i n aqueous methanol at a temperature of about 70°C according to the reaction: HCOONa + NaOH + 2S0 2 * 2Na + + S ^ + C0 2 + H 20 The product i s f i l t e r e d , washed with methanol and then dried to give anhydrous sodium d i t h i o n i t e . According to Gerritsen (30) t h i s process was commer- c i a l l y used i n the past, but i t was dropped because the product was a very f i n e l y divided powder and therefore not very stable to oxidation. Recently some investigators (128, 141, 146, 151, 152), on the basis of laboratory experiments, have reported high y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide (=80%) and high p u r i t y of the product (==90%) from the formate process. 4. Sodium borohydride process In t h i s process an aqueous solut i o n of s u l f u r dioxide (or sodium b i s u l f i t e ) i s reduced by sodium borohydride (140, 150) according to the reaction: NaBH. + 8 NaHSO- -*• NaB0o + 6 H„0 + 4 Na oS„0. So f a r thi s method has not been used i n d u s t r i a l l y . 11 5. Sodium amalgam process In t h i s process sodium metal dissolved i n mercury i s used to reduce s u l f u r dioxide to give sodium d i t h i o n i t e . The o v e r a l l reaction can be written as follows: 2 Na + 2S0 2 •*• Na 2S 20 4 The standard oxidation p o t e n t i a l of pure sodium metal i s greater than that of sodium i n sodium-mercury amalgam (35, 36, 57). The overvoltage of hydrogen gas on sodium-mercury amalgam i s high (57) . Thus i t i s possible to bring about a controlled reaction between sodium i n mercury solut i o n and various other reactive compounds i n aqueous s o l u t i o n , with l i t t l e loss due to reaction of the sodium with water. (a) Advantages of the sodium amalgam process (i) Compared to the zinc dust: sodium carbonate process, which i s used i n d u s t r i a l l y , extra steps are avoided such as separation of zinc carbonate and c a l c i n i n g the p r e c i p i t a t e d carbonate to obtain zinc oxide. ( i i ) Sodium d i t h i o n i t e obtained by t h i s process i s not contaminated by the zinc ions as i s the d i t h i o n i t e obtained by the zinc dust: sodium carbonate method. 12 ( i i i ) The reactor could work as the decomposer i n con- junction with mercury c e l l s which may be used for chlorine manufacture at a m i l l s i t e . (iv) As the reducing agent i s a sol u t i o n , continuous reduction can be e a s i l y c a r r i e d out. (v) Sodium-mercury amalgam i s an inexpensive source of sodium met a l , p a r t i c u l a r l y i f the sodium i s produced i n a mer- cury c h l o r - a l k a l i c e l l . (b) Types of the sodium amalgam process Sulfur dioxide i n a number of forms may be reacted with sodium-mercury amalgam to produce sodium d i t h i o n i t e . Some of these forms are: (i) Sulfur dioxide dissolved i n organic solvents ( i i ) Gaseous or l i q u i d s u l f u r dioxide ( i i i ) Sulfur dioxide introduced into aqueous buffer containing NaHSO^ and Na2S0.j. (i) Sulfur dioxide dissolved i n organic solvents (sodium amalgam: SG^ - organic solvent process) A number of investigators (49, 83, 117, 126) have pre- pared sodium d i t h i o n i t e from sodium-mercury amalgam and s u l f u r dioxide dissolved i n non-aqueous media such as hydrocarbons, ethers, amides, alcohol and kerosene. They have claimed high 13 yi e l d s of the anhydrous product which i s obtained d i r e c t l y . According to the information a v a i l a b l e , t h i s process has never been used i n d u s t r i a l l y . ( i i ) Gaseous or l i q u i d s u l f u r dioxide (sodium amalgam: gaseous process and sodium amalgam: l i q u i d S O 2 process) Rougeot (89) reported finding Na2S20^ i n the reaction mass when S O 2 was bubbled through sodium-mercury amalgam f o r 7 to 8 hours, or when l i q u i d s u l f u r dioxide was i n contact with sodium amalgam f o r 2 to 3 hours at room temperature. According to the information a v a i l a b l e , t h i s method has never been used i n d u s t r i a l l y . ( i i i ) Sulfur dioxide introduced into aqueous buffer containing NaHS03 and Na 2S0 3 (Sodium amalgam: S0 2-NaHS0 3/Na 2S0 3 buffer process) This method has been a subject of i n t e r e s t f o r many investigators (10, 18, 19, 26, 56, 64, 69, 120, 121, 124, 129, 130, 132-134, 137, 145). In t h i s process sodium metal dissolved i n mercury reduces the s u l f u r dioxide added to an aqueous buffer solution of NaHS03 and Na2S0 3, at a pH of about 5 to 6 and at a temperature of about 15 to 30°C, to give a concentrated solu t i o n of sodium d i t h i o n i t e . Hydrated sodium d i t h i o n i t e c r y s t a l s (Na 2S20 4« 2H20) are salted out by the addition of sodium chloride and the s l u r r y i s taken to a 14 f i l t r a t i o n u n i t where the c r y s t a l s are removed and the mother l i q u o r i s sent back to the reactor. These hydrated c r y s t a l s are then dehydrated by heating them r a p i d l y to a temperature of about 60 to 65°C/ a f t e r which they are f i l t e r e d , washed with alcohol and dried under vacuum. High y i e l d s of sodium d i t h i o n i t e and high pu r i t y of the product have been reported. Some other investigators (74, 125, 138, 149) have recommended that a c e r t a i n percentage of water-miscible alcohol should be added to the aqueous buffer s o l u t i o n to improve the recovery of anhydrous sodium d i t h i o n i t e . The steps i n the reaction f o r t h i s process are as follows: Formation reaction 2Na + 2NaHSO_ Na oS o0. + 2NaOH Neutralization reaction NaOH + NaHSO, + Na-SO-, + H o0 Overall formation and n e u t r a l i z a t i o n reaction 2Na + 4NaHSO_ -»• Na^S-O. + 2Na~SO., + 2Ho0 Regeneration reaction 2Na 2S0 3 + 2S0 2 ->- 4NaHSO 15 Overall reaction 2Na + 2S0 2 Na 2S 20 4 This method of preparation of sodium d i t h i o n i t e was used i n d u s t r i a l l y (30 to 40 tons Na 2S 20 4/month) from 1923 to 1930 by Farbenfabriken Bayer i n Leverkusen (9) but i t was plagued by poor y i e l d s and formation of unwanted by-products. As l a t e as the early 1940's they had concluded that the zinc dust: sodium carbonate process was the most economical route to sodium d i t h i o n i t e unless the pri c e of zinc were unusually high and provided that the by-product zinc oxide could be sold (26) . J . Olmestead (66) reported that R.B. MacMullin Associates of Niagara F a l l s , N.Y. had b u i l t a sodium d i t h i o n i t e plant some years ago, using the sodium-mercury amalgam route, for the Marathon Paper Company, but that t h i s operation was discontinued for some unknown reason. B. Recommended Conditions f o r Improving the Y i e l d of Sodium D i t h i o n i t e i n the Sodium Amalgam: S0 2-NaHS0 3/Na 2S0 3 Buffer Process A b r i e f d e s c r i p t i o n of t h i s process has been given on pp. 13-15.Although the objective of the proposed i n v e s t i g a t i o n (study of the sodium-mercury amalgam process f o r the manufacture 16 of a r e l a t i v e l y d i l u t e water solu t i o n of sodium d i t h i o n i t e ) i s quite d i f f e r e n t from the aim of most of the previous investigations (manufacture of a s o l u t i o n of sodium d i t h i o n i t e , generally 15-25% so l u t i o n , for e f f i c i e n t recovery of the s o l i d s a l t ) , i t was f e l t important to consider the recommended le v e l s of process variables for the l a t t e r case as they might y i e l d some useful information f o r the proposed i n v e s t i g a t i o n . A number of investigators (10, 18, 19, 26, 56, 64, 69) have spelled out conditions for increasing the y i e l d of sodium d i t h i o n i t e by the sodium amalgam: SG^ - NaHS02/Na2SO.j buffer process. Their conclusions are given below. I t was generally recognized that conditions of extreme a c i d i t y and high temperatures i n the reactor increase the rate of decomposition of sodium d i t h i o n i t e . Therefore, to obtain reasonable y i e l d s of sodium d i t h i o n i t e , i t was found necessary to maintain the reactor pH between 5 and 6 and the reactor temperature i n the range 15 to 30°C. I t was also found that sodium d i t h i o n i t e i s r a p i d l y oxidized by atmospheric oxygen; therefore, an i n e r t atmosphere of nitrogen (or carbon dioxide) was provided i n the e n t i r e apparatus. The concentration of sodium i n the inlet-sodium amalgam was kept i n the range .01% to .05% (by weight) and s u l f u r dioxide was introduced i n stoichiometric proportions to the sodium fed from the amalgam. The residence time of the aqueous solu t i o n * The word " y i e l d " has not been defined very c a r e f u l l y i n the a v a i l a b l e l i t e r a t u r e . In most cases i t appears that the authors considered the y i e l d of sodium d i t h i o n i t e on sodium consumed. 17 i n the reactor was kept as short as possible to avoid the decomposition of sodium d i t h i o n i t e formed. The aqueous sol u t i o n was well agitated i n the reactor i n order to disperse the s u l f u r dioxide and to renew the soluti o n at the i n t e r f a c e . Some other investigators (74, 125, 138, 149) modified the process by using a 20-30% ethanol s o l u t i o n i n water rather than water alone as the solvent for NaHSO^- Na2S02 b u f f e r . The presence of ethanol helped i n the recovery of better c r y s t a l s of sodium d i t h i o n i t e . Most of the information mentioned above has been obtained from the patent l i t e r a t u r e and d i f f e r e n t investigators used varied experimental devices and contacting methods for amalgam and aqueous phases. Unfortunately, very l i t t l e e f f o r t has been made to improve understanding of the sodium amalgam process i n general. For the proposed "once through" process, recommen- dations such as the addition of 20 to 30% ethanol to the buffer solu t i o n were considered uneconomical. Some other recommen- dations provided guide l i n e s for the proposed i n v e s t i g a t i o n . C. Mercury Contamination of Sodium D i t h i o n i t e Produced by the Sodium Amalgam: S0 2 - NaHSO^/NaSO^ buffer process At l e a s t two investigators (10, 19) have reported that sodium d i t h i o n i t e obtained by the sodium amalgam: S0 9 - 18 NaHS0 3/Na 2S0 3 buffer process was contaminated with small amounts of mercury. However, i t i s not indicated whether the mercury was entrained i n the product stream or some chemical compounds of mercury were present. Farbenfabriken Bayer (10) manufactured sodium d i t h i o n - i t e i n d u s t r i a l l y i n a reactor where sodium-mercury amalgam was thoroughly mixed with the s u l f u r dioxide s o l u t i o n i n the presence of a buffer solution of NaHS03 and Na 2S0 3(pH 5-7). Sodium d i t h i o n i t e produced by t h e i r process was contaminated with mercury, but they reported that i t was possible to prepare a product with not more than 20 ppm mercury. At that time the mercury content of t h e i r product was not considered objectionable i n the bleaching of groundwood pulp. D i j s , Hoogland and Waterman (19) manufactured a 15% solution of sodium d i t h i o n i t e i n a packed bed (column packed with glass rods). Sodium-mercury amalgam entered the reactor at the top of the column, divided into f i n e droplets which, after i n t e r a c t i o n with s u l f u r dioxide i n the presence of a 5% NaHS03 and Na 2S0 3 buffer (pH 5-5.5), gathered at the bottom of the column. The buffer s o l u t i o n flowed up the column, counter current to the amalgam, and the product stream was recycled to the bottom of the reactor. The operation was made continuous by introducing an aqueous so l u t i o n of s u l f u r dioxide to the feed and bleeding o f f an equal volume of the product stream. According to D i j s et al • t n e product stream was sometimes contaminated with mercury. 19 Removal of small amounts of mercury from the product stream i s r e l a t i v e l y easy. D i j s et al, recommended a so l u t i o n of Na2S to p r e c i p i t a t e small amounts of mercury as HgS, which might be removed by f i l t r a t i o n . Recently, Imperial Chemical Industries, England, has patented (127) a process to remove mercury from the waste brine of mercury c e l l s . Generally, the waste brine contains 3 to 4 ppm of Hg and t h i s mercury can be removed by tre a t i n g the brine with a s o l u t i o n of NaHS and subsequently f i l t e r i n g the suspension to remove HgS. The same p r i n c i p l e can also be used to remove mercury from the sodium d i t h i o n i t e s o l u t i o n . D. L i g n i n Preserving Bleaching of Groundwood Pulp by Sodium Dithionite(62, 106) 1. D e f i n i t i o n of the terms "brightening" and "bleaching" When r e f e r r i n g to groundwood, the term "brightening 1 1 i s generally used to describe the whitening action of reducing agents such as the s u l f i t e s and d i t h i o n i t e s . The term "bleaching" generally r e f e r s to the action of o x i d i z i n g agents, such as peroxides, which modify the coloured substances of the wood pulp f o r a longer period of time. However, the term "bleaching" i s sometimes used to describe the action of both d i t h i o n i t e s and peroxides. 2. C h a r a c t e r i s t i c s of the groundwood bleaching process The essence of the groundwood bleaching process can be summarized as follows: (a) A major requirement i n groundwood bleaching, i n contrast to chemical pulp bleaching, i s that l i g n i n must be retained. (b) Unlike chemical pulp brightness, unbleached groundwood brightness varies widely with wood species and, f o r each species, varies with the condition of the wood being ground. Therefore, a great deal of care i n cleaning and s e l e c t i n g wood must be taken so that a l l groundwood produced can be rai s e d to the desired brightness by the a v a i l a b l e processes at an acceptable cost. (c) The brightness of groundwood a f t e r bleaching i s much more unstable than that of bleached chemical pulps. The b r i g h t - ness reversion rate i s greater a f t e r the reducing treatment by d i t h i o n i t e s than a f t e r the o x i d i z i n g action of peroxides. This i s understandable, considering that the oxygen of the a i r w i l l tend to reverse the reducing action of the d i t h i o n i t e s . For papers of l i m i t e d use, l i k e newsprint, groundwood brightening with d i t h i o n i t e gives j u s t adequate brightness gains [10-12 G.E. brightness points with 1-2% (by weight) d i t h i o n i t e on f i b r e ] . Since peroxide bleaching costs are between 5 and 10 times as high as for d i t h i o n i t e brightening, the l a t t e r has gained wide acceptance i n the production of newsprint. 21 3. E f f e c t s of groundwood brightening The action of d i t h i o n i t e on groundwood pulps has two major e f f e c t s ; (a) The sheet r e f l e c t s more l i g h t , and hence i t becomes bright e r . (b) The colour of the sheet s h i f t s appreciably from yellow- pink towards a bluer shade, and so i t becomes whiter. This i s because d i t h i o n i t e treatment a f f e c t s p a r t i c u l a r l y the substances which absorb strongly the blue components of l i g h t and are responsible for the yellow-pink appearance of unbleached pulps. 4. Conditions for groundwood brightening by sodium d i t h i o n i t e In the chemical action of d i t h i o n i t e during groundwood brightening, the oxidation state of the s u l f u r atom changes 3+ 4 + from S to S , that i s , from d i t h i o n i t e to s u l f x t e or b i - s u l f i t e (62). Depending on pH, the reaction can be written i n two ways. In acid s o l u t i o n , d i t h i o n i t e reacts as follows: 2H20 + HS 20~ :̂ =£ 2HS0~ + 3H + + 2e The standard oxidation p o t e n t i a l of t h i s reaction at 25°C on the hydrogen scale i s E° = + .08 v o l t s (51). In strongly a l k a l i n e s o l u t i o n the reaction i s : 22 S 2 0 4 + 40H ~ " 2S0 3 + 2H20 + 2e The standard oxidation p o t e n t i a l of t h i s reaction at 25°C on the hydrogen scale i s E° = + 1.12 v o l t s . Thus, d i t h i o n i t e i s a f a r stronger reducing agent i n a l k a l i n e than i n a c i d i c s o l u t i o n . However, high a l k a l i n i t y causes degradation and d i s - colouration of wood l i g n i n ; so, i n p r a c t i c e , i t i s necessary to carry out the d i t h i o n i t e treatment at pH l e v e l s 1 to 2 units below n e u t r a l i t y . The i n s t a b i l i t y of d i t h i o n i t e solutions to acids, oxygen and high temperature has been mentioned e a r l i e r and w i l l be discussed i n d e t a i l i n section I I . G. The mixing of the groundwood pulp with d i t h i o n i t e should be rapid, intimate and uniform; and the pulp should be as free of a i r as possible. Ranges for permissible and preferred conditions (62) f o r brightening groundwood from most species are shown i n Table 1. 23 TABLE 1 CONDITIONS FOR BRIGHTENING GROUNDWOOD BY Na oS o0 Process Variable Permissible Conditions Preferred Conditions Temperature Reaction Time pH Consistency D i t h i o n i t e Treatm % (by weight) of Fibre 32 to 82°C 1/2 to 8 hrs 5 to 7.5 3 to 18% tent .2 to 2% 50 to 74°C 1 to 2 hrs 5 to 5.6 3 to 6% .2 to 1.5% 24 E. Sodium-mercury Amalgam For the proposed continuous manufacture of sodium d i t h i o n i t e , i t would be necessary to use l i q u i d sodium- mercury amalgam. I t has been reported i n the l i t e r a t u r e (35, 36) that the s o l u b i l i t y of sodium i n mercury, at 25°C, i s about 0.6% by weight. I f the sodium d i t h i o n i t e manufactur- ing u n i t was to work i n conjunction with a mercury c e l l , sodium i n mercury would be av a i l a b l e at a c e r t a i n composition, and that would, without the use of some sp e c i a l equipment, put an upper l i m i t on the concentration that could be used. Normally, the maximum concentration of sodium i n the amalgam produced i n the mercury c e l l i s about .05 to .15% by weight (2, 28). In the proposed process, the maximum concen- t r a t i o n of sodium i n the inlet-amalgam would be about 0. 15% by weight. The following information a v a i l a b l e i n the l i t e r a t u r e on some of the important properties of l i q u i d sodium-mercury amalgam i s pertinent. 1. Molecular structure of sodium-mercury amalgam According to Vanstone (107-109) and Schuller (92), the d i s c o n t i n u i t i e s i n the freezing point diagram and i n the s p e c i f i c volume versus weight per cent curve, as well as the micrographic study of mixtures of sodium and mercury, indicate that there are six compounds of the two elements 25 i n s o l i d sodium-mercury amalgam. However, the molecular structure of l i q u i d sodium-mercury amalgam remains uncertain. Vanstone (107, 109) and Bent (7) determined the s p e c i f i c volume, e l e c t r i c a l conductivity, oxidation p o t e n t i a l , depres- sion of freezing point, lowering of vapour pressure and heat of formation of l i q u i d sodium-mercury amalgams. On the basis of t h e i r r e s u l t s , i t can be assumed that l i q u i d sodium- mercury amalgams are monoatomic, true solutions of sodium i n mercury. 2. Surface tension of sodium-mercury amalgam The surface tension of pure mercury has been deter- mined against a i r and vacuum at d i f f e r e n t temperatures (16). Schmidt (90) determined the surface tension of mercury against a i r at 20°C and reported a value of 435.5 dynes/cm. According to Hohn (35) the surface tension of mercury i s lowered when sodium i s dissolved i n i t . 3. S e n s i t i v i t y to oxidation of sodium-mercury amalgam Liquid sodium mercury amalgam i s highly s e n s i t i v e to oxidation by atmospheric oxygen. According to Hohn (35), when the l i q u i d sodium amalgam i s exposed to a i r i t i s immediately coated with a grey f i l m of oxide. A t h i n layer of p a r a f f i n o i l has been recommended to avoid oxidation. 26 4. Density of sodium-mercury amalgam Copious data on the s p e c i f i c volume of sodium- mercury amalgam, i n l i q u i d as well as s o l i d state, has been reported i n the l i t e r a t u r e (4, 58, 79, 107-109, 112). Maey's (58) data can be used to p l o t density of the l i q u i d amalgam at a temperature of 17°C against weight per cent of sodium i n the amalgam upto a concentration, of 0.3% sodium. A regression f i t on his data gives the following expression. Density of sodium amalgam at 17°C = 13.55 - .9986 x weight per cent of sodium i n amalgam I t can be seen from t h i s expression that the density of l i q u i d sodium-mercury amalgam decreases with increasing concentration of sodium i n the above-mentioned range. F. Sulfur Dioxide Solution i n Water 1. P r i n c i p a l e q u i l i b r i a On the basis of numerous investigations (5, 24, 25, 29, 31, 42, 96, 99-101, 115) i t can be concluded that when sulfur dioxide i s dissolved i n water, the following e q u i l i b r i a e x i s t . 27 SO- , %+ H-0 - 7 — S0-» H O -—»- HSO" + H +- SO- + 2H + 2 (g) 2 2 2 3 3 I t i s i n t e r e s t i n g to note that at very low pH's, an aqueous solution of su l f u r dioxide does not contain H 2S0 3 molecules; s u l f u r dioxide e x i s t s i n the molecular state. Simon and Waldmann (100) , working with Raman spectra and aqueous solu- tions of s u l f u r dioxide of concentration greater than 1 molar, detected l i n e s a t t r i b u t e d to S 2Og, SU(3<3es^n9 that another i o n i c equilibrium e x i s t s i n the system, namely 2HS03 - — ^ S 2 0 5 + H 20 Not much i s known about t h i s equilibrium, hence, the presence of S2OJT ions has been ignored i n the present i n v e s t i g a t i o n . Thus, the p r i n c i p a l e q u i l i b r i a may be written as follows: Khs S 0 2 ( g ) + H 2 ° — S 0 2 " H 2 ° K l  + S0 2« H 20 , H + HS0 3 K 2 HS0~ , H + + S0 3 where, = Thermodynamic equilibrium constant for S0 2-H 20 system 28 aS0 2'H 20 [S0 2'H 20] K h s = = ~Z * fS0 o-H o0 * * * x a T I „ P„„ 2 2 S 0 2 H 2 ° S 0 2 K.̂  = Thermodynamic i o n i z a t i o n constant for the f i r s t d i s s o c i a t i o n of S0 2» H 20 aH+ X aHSOl [H +][HSOl] f H + X fHSOl ± = . J . . . .(2) a S 0 2 « H 2 0 [S0 2«H 20] fS0 2*H 20 K0 Thermodynamic i o n i z a t i o n constant f o r the second d i s s o c i a t i o n of S0 2 • H 20 a H + X aS0= [H +][SOl] f H + X fS0= = ^ — • . . . . (3) aHSO~ [ H S 0 3 ] fHSO- In the equations (1), (2) and (3) 'a' i s the a c t i v i t y of the indicated species. [ ] i s the concentration i n gram ions or gram moles per l i t e r of the enclosed species. ' f i s the a c t i v i t y c o e f f i c i e n t of the indicated species. P i s the pressure of s u l f u r dioxide gas i n atm. b U 2 The values of , K 2 and K^g have been reported by several investigators (93, 111, 118). According to Scott 29 (93), at 25°C, K± = .0127; K 2 = 6.28 x 10~ 8; and K h g = 1.233 gm mo l e s / l i t e r atm. In the proposed i n v e s t i g a t i o n the concentration of t o t a l s u l f u r dioxide ( S 0 2 + HSO^ + SO3) i n the aqueous solutions used was i n the range 0.4 molar to 1.3 molar. No data i s availa b l e to-date on the molar a c t i v i t y c o e f f i c i e n t s of the s u l f u r dioxide molecules dissolved i n water and mean molar a c t i v i t y c o e f f i c i e n t s of hydrogen and s u l f i t e ions. Mean molar a c t i v i t y c o e f f i c i e n t s of hydrogen and b i s u l f i t e ions have been reported (34, 77) f o r very d i l u t e solutions -3 -3 of s u l f u r dioxide i n water (3.27 x 10 to 12.6 x 10 molar) . In the absence of any reasonable data, f o r the purposes of t h i s i n v e s t i g a t i o n , the a c t i v i t y c o e f f i c i e n t s were assumed to be unity. Hence, the p r i n c i p a l e q u i l i b r i a , at 25°C, could be written as follows: [S0 9'H,0] - - = 1.233 . . . .(4) [H+][HSO~] — = .0127 . . . .(5) [S0 2'H 20] [H ][SO"] [HSO3] = 6.28 x 10 -8 . . . . ( 6 ) The concentration of t o t a l s u l f u r dioxide i n the aqueous soluti o n could be written as follows: [S02] + [HSO~] + [SO3] = [S0 2 ] T O T A L . . . .(7 I f the concentration of t o t a l s u l f u r dioxide i n the aqueous solut i o n and the pH were known, the concentrations of a l l the i o n i c species and the dissolved s u l f u r dioxide i n molecular state could be calculated using the equations (5), (6) and (7). A computer program was written using these equations and for a t y p i c a l [S*-^ Total = molar, the concentrations of d i f f e r e n t species of s u l f u r dioxide i n the aqueous solution were ca l c u l a t e d . These concentrations are plotted against pH (.1 to 9) i n Figure 1. I t can be observed from t h i s figure that at very low pH (pH - 1) , most of the su l f u r dioxide i n the aqueous s o l u t i o n i s a v a i l - able as molecular s u l f u r dioxide; the remainder i s present as b i s u l f i t e ions. As the pH increases, the proportion of b i s u l f i t e ions increases and reaches a maximum at a pH of about 4.5. With further increase i n the pH the concentration of s u l f i t e ions s t a r t s b u i l d i n g up and above a pH of 9, most of the su l f u r dioxide i s avail a b l e as s u l f i t e ions. The conclusions a r r i v e d at by the author, agree with the following comments made by Eriksen (22), despite the l a t t e r s usage of s l i g h t l y d i f f e r e n t i o n i z a t i o n constants Figure 1 Concentrations of free s u l f u r dioxide, b i s u l f i t e ions and s u l f i t e ions versus pH i n a 0.39 9 molar su l f u r dioxide solution i n water at 25°C (K± = 1.54 x 10~ 2; K 2 = 6.9 x 10 1) . "More than 97 per cent of the sul f u r atoms i n the solutions were contained as s u l f u r dioxide molecules i n a solution of pH 0.3 and more than 99 per cent as b i s u l f i t e ions at pH 4.5 and as s u l f i t e ions at pH 9.0. This s e l e c t i o n of d i f f e r e n t pH values seems to be the closest one could come to achieving pure solutions of these molecules or ions." 2. D i f f u s i o n of s u l f u r dioxide i n water Eriksen (22, 23) investigated the s e l f - d i f f u s i o n of 35 s u l f u r dioxide i n aqueous solutions using S as a t r a c e r . He used Anderson and Saddington's (1) assumption that there was no i n t e r a c t i o n between the three d i f f u s i n g species, namely, SC^, HSO^ and SÔ ". He calculated the composition of a saturated solution of sul f u r dioxide i n water at 20°C and atmospheric pressure, finding 1.6 molar SG^ and 0.15 molar HSÔ ", i . e . about 11 per cent was ionized. Therefore, he concluded that the d i f f u s i o n c o e f f i c i e n t of s u l f u r dioxide i n water could not be ascribed to any one d i f f u s i n g species but might be treated as an " e f f e c t i v e d i f f u s i o n c o e f f i c i e n t . " He reported the i n t e g r a l concentration weighted (effective) d i f f u s i o n c o e f f i c i e n t of s u l f u r dioxide -5 i n a saturated aqueous solu t i o n at 20°C to be 1.45 x 10 2 cm /sec. This value of e f f e c t i v e d i f f u s i v i t y i s comparable to the values obtained by several other investigators (33, 48, 55, 72, 105, 113). 33 According to Eriksen the d i f f u s i v i t i e s of the d i f f e r - ent species of s u l f u r dioxide i n water are unequal, and the r e l a t i v e amounts of molecular SC^, HSO^ a n o ^ S0~ w i l l vary with pH f o r a fixed concentration of t o t a l s u l f u r dioxide i n the system. Hence, the " e f f e c t i v e d i f f u s i o n c o e f f i c i e n t " w i l l be a v a r i a b l e with pH. The e f f e c t i v e d i f f u s i o n c o e f f i c - i e n t for s u l f u r dioxide, i n aqueous (NH^^SO-j, as a function of pH i s shown i n Figure 2 (22). I t can be seen from Figure 2 that the e f f e c t i v e d i f f u s i v i t y of s u l f u r dioxide decreases with increasing pH of the s o l u t i o n . The e f f e c t of temperature, t o t a l i o n i c concentration and type of cations on the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t of s u l f u r dioxide i n aqueous solutions were also investigated by Eriksen. G. Important Reactions i n the Proposed Process Af t e r c a r e f u l l y studying d i f f e r e n t manufacturing processes for sodium d i t h i o n i t e (including the patent l i t e r a t u r e ) , i t was p o s s i b l e to o u t l i n e some of the major reactions that may take place i f a d i l u t e aqueous so l u t i o n of sodium d i t h i o n i t e were to be produced by contacting sodium-mercury amalgam and a s o l u t i o n of s u l f u r dioxide i n water (proposed process). These reactions are: Figure 2 E f f e c t i v e d i f f u s i o n c o e f f i c i e n t s for s u l f u r dioxide i n aqueous (NH^JoSC^. 1 T o t a l 1 s u l f u r dioxide concentration = I gm m o l e / l i t e r 35 1. The sodium d i t h i o n i t e formation reaction 2. The water reaction 3. The sodium d i t h i o n i t e decomposition reactions 4. The sodium d i t h i o n i t e oxidation reaction . Unfortunately, very l i t t l e information has been reported about the k i n e t i c s and mechanisms of these reactions. The a v a i l - able information i s as follows: 1. The sodium d i t h i o n i t e formation reaction Although the mechanism of d i t h i o n i t e formation on sodium-mercury amalgam i s not exactly known, i t can be postu- lated (44) that the atomic sodium i n the amalgam reduces b i s u l f i t e ion to give sodium d i t h i o n i t e according to the reaction: 2Na + 2HS0~ + 2Na + + + 20H~ The mechanism of the formation reaction has been i n - vestigated by several workers (32, 44, 48) using polaro- graphic techniques. They studied the reduction of s u l f u r dioxide i n aqueous solutions at a dropping mercury electrode. None of the investigators found reduction waves at dropping mercury electrodes with neutral or a l k a l i n e s u l f i t e solutions, but well-defined waves were observed i n acid medium. In other words, aqueous solutions of sulf u r dioxide were reduced 36 i n strong as well as weakly a c i d i c media. In strongly a c i d i c medium (pH 0 to 2) , the reduction of aqueous sulfur dioxide to d i t h i o n i t e takes place i n one step at a half-wave p o t e n t i a l , = -0.37 v o l t s (reduction p o t e n t i a l , at pH = 1 and temperature = 25°C, measured against a saturated calomel electrode) (32, 48). The reaction could be written as follows: 2S0 2 + 2e -* S 2 0 4 In weakly a c i d i c medium (pH 6), the polarograph shows two waves (32, 44, 48), one at E^y 2 = -0.67 v o l t and the other at E j y 2 = -1.23 v o l t s (reduction p o t e n t i a l s , at pH = 6 and temperature = 25°C, measured against a saturated calomel electrode). According to Ketelaar (44) , at both of these half-wave p o t e n t i a l s , d i t h i o n i t e i s formed e x c l u s i v e l y . This i s contradictory to the explanation of Kolthoff and M i l l e r (48), who reported that the step at -1.23 v o l t i s connected with the formation of t h i o s u l f a t e according to the empirical equation: 2HSO~ + 4H + + 4e -»• + 3 H 2 < J or 2HSO~ + H„0 + 4e + S„o!T + 40H~ Ketelaar concluded that t h i o s u l f a t e i s formed at s t i l l more negative p o t e n t i a l s , and hydrogen i s l i b e r a t e d at the same time (E-jy2 = v o l t s ) . At more negative p o t e n t i a l s , further reductions occur, which lead to the formation of s u l f i d e ions and other products. The s u l f i t e ions are not reducible at these p o t e n t i a l s . Ketelaar postulated that the reduction reaction at E^^ 2 = -0.67 v o l t may be written as: 2HSO~ + 2e S 2 0 4 + 20H" . . . .(8) However, the reaction based on the step at E j y 2 = -1-23 v o l t i s uncertain. According to Ketelaar, t h i s reaction could be written as follows: HS0 3 + S0 3 + 3H20 + 4e •*• 2HS02 + 50H HS0 2 + HS0 3 -»• S 2 0 4 + 2H20 The t o t a l reduction at ^^y2 = - 1 ' 2 3 v o l t s could be written: 3HS03 + S0 3 + H 20 + 4e 2S 20 4 + 50H . . . .(9) When the formation reaction (9) i s combined with the e q u i l i b - rium between HS0 3 and S0 3 ions i n the aqueous medium, HSO~ + OH~ S0 3 + H 20 38 the resultant formation reaction i s equivalent to equation (8) . Previous investigators (30, 44) assumed that when sodium-mercury amalgam i s brought i n contact with an aqueous solution of sulfu r dioxide,-the d i t h i o n i t e formation probably takes place at the inte r f a c e of the two phases. The author has attempted to explain t h i s assumption as follows: According to information a v a i l a b l e i n the l i t e r a t u r e , sodium cannot e x i s t i n aqueous solutions i n atomic form. Sodium, from the amalgam gets ionized at the i n t e r f a c e to give an electron: Na -*• Na + + e Free electrons or hydrated electrons (95) have not been known to e x i s t i n aqueous solutions for any measurable length of time. They would react with b i s u l f i t e ions and hydrogen ions r a p i d l y . This may be taken as a j u s t i f i c a t i o n of the assumption that the reduction by sodium-mercury amalgam probably does not take place i n s i d e the aqueous medium. No data has been reported on the s o l u b i l i t y of aqueous s u l f u r dioxide i n sodium-mercury amalgam or pure mercury. I t i s believed that the aqueous s o l u t i o n of s u l f u r dioxide i s insoluble i n the amalgam. Hence, the reduction reactions would not take place inside the amalgam phase. Having accepted the assumption that the d i t h i o n i t e formation takes place at the inte r f a c e of the two phases, attention was directed to determine i f the reaction i s rev e r s i b l e or i r r e v e r s i b l e . The equilibrium constant f o r the reaction 2Na + 2HSG~ •*• 2Na + + + 20H~ , at 25 °C, was calculated by using the standard free energy of formation values (51) of d i f f e r e n t atomic and i o n i c species for the reaction at 25°C. The value of the equilibrium 67 constant, at that temperature was approximately 10 . Such a high value of the equilibrium constant implies that the reaction can be considered an i r r e v e r s i b l e reaction at 25°C. No data i s avail a b l e i n the l i t e r a t u r e on the rate of the sodium d i t h i o n i t e formation r e a c t i o n . However, i t has been suggested by previous investigators (30, 44) that the rate of the d i t h i o n i t e formation on the amalgam surface i s excl u s i v e l y dependent on the mass-transfer . rate of b i s u l f i t e ions on the aqueous side and the supply of sodium from the amalgam to the i n t e r f a c e . This implies that compared to the mass-transfer rate i n the two phases, the chemical reaction rate i s i n f i n i t e l y f a s t . 2. The water reaction Avedikian (125), i n 1956, was granted a patent for the manufacture of sodium d i t h i o n i t e by the sodium amalgam process. He reported that, i n his process when the con- centration of sodium i n the amalgam was greater than .04% (by weight), some of the sodium was consumed i n what he c a l l e d the water reaction. This i s an unproductive reaction compared to d i t h i o n i t e formation, and produces sodium hydroxide and gaseous hydrogen thus lowering the y i e l d of sodium d i t h i o n i t e . According to him the water reaction may be written as follows: 2Na + 2H20 -»• 2 NaOH + H 2 The evolution of hydrogen has also been reported by Ketelaar (44) i n his i n v e s t i g a t i o n s . I t was f e l t necessary to investigate t h i s reaction at d i f f e r e n t pH values, for i t would compete with the sodium d i t h i o n i t e formation r e a c t i o n . The reactions of sodium- mercury amalgam with d i f f e r e n t acids, buffer solutions, water and sodium hydroxide have been studied by several i n v e s t i - gators (12, 20, 45). Unfortunately, none of the investigators studied the rate of the water reaction from the point of view of the modern approach to mass-transfer with chemical reaction as outlined by A s t a r i t a (3). D i f f e r e n t investigators experimented under e n t i r e l y d i f f e r e n t conditions, hence, i t i s d i f f i c u l t from the information a v a i l a b l e i n the l i t e r a t u r e , to formulate a mathematical model which would p r e d i c t the rate of the water reaction under a given set of conditions. 41 The most r e l i a b l e work has been done by Dunning and K i l p a t r i c k (20) and t h e i r conclusions are as follows: The rate of the water reaction i s proportional to the square root of concentration of sodium i n the amalgam, -4 independent of hydrogen ion concentration i n the range 10 to 1 0 - 1 ^ m o l e s / l i t e r , and proportional to the area of the i n t e r f a c e . Thus, the empirical equation could be written as follows: dC Na dt k . A V~Z water C . . . .(10) Na where, 'Na water Na dt Concentration of sodium i n the amalgam, gm m o l e s / l i t e r Surface area of the sodium-mercury amalgam 2 i n contact with water, cm Reaction rate constant Rate of d i s s o l u t i o n of sodium from the amalgam into water, gm m o l e s / l i t e r sec Presence of c e r t a i n e l e c t r o l y t e s i n the aqueous phase also a f f e c t s the rate of the water reaction; however, no quantitative r e l a t i o n s h i p has been proposed. Dunning and K i l p a t r i c k (20) and Fletcher and K i l - patrick (27) also showed that the rate of d i s s o l u t i o n of sodium (or lithium) from the amalgam into water increased very sharply when the concentration of hydrogen ions -4 increased above 10 m o l e s / l i t e r . The nature of the empirical rate equation (10) implies that, i n the pH range 4 to 10, the rate of the water reaction i s not controlled by the mass-transfer rate of sodium to the i n t e r f a c e . Dunning and K i l p a t r i c k suggested that the rate i s probably co n t r o l l e d by the rate of chemical reaction at the i n t e r f a c e . Like the sodium d i t h i o n i t e formation reaction, the water reaction probably also takes place at the i n t e r f a c e of the amalgam and aqueous phases. The equilibrium constant for the water reaction, Na + H 20 + Na + + 0H~ + 1/2 H 2 , at 25°C, was calculated by using the standard free energy of formation values (51) of the d i f f e r e n t atomic and i o n i c species i n the reaction. The equilibrium constant, for 3 2 the water reaction, at 25°C i s approximately 10 . This high value of the equilibrium constant indicates that the water reaction i s e s s e n t i a l l y i r r e v e r s i b l e . 43 3, The sodium d i t h i o n i t e decomposition reactions Two types of decomposition reactions should be con- sidered. The homogeneous decomposition reaction takes place i n a l l parts of the aqueous phase. Heterogeneous decomposition takes place at the int e r f a c e of the amalgam and aqueous phases where d i t h i o n i t e i s reduced by sodium of the amalgam. (a) Homogeneous decomposition of sodium d i t h i o n i t e Studies (40, 43, 53, 54, 59, 60, 70, 82, 116) of the decomposition of sodium d i t h i o n i t e i n various aqueous solu- tions, i n the absence of oxygen, have shown that at a pH of about 7, the main o v e r a l l reaction i s : 2Na 2S 20 4 + H 20 -»• 2NaHS03 + Na 2S 20 3 Several side reactions occur, however, and there has been l i t t l e agreement on t h e i r importance or products. The k i n e t i c s have been i n dispute and d i f f e r e n t mechanisms have been suggested. Spencer (102), i n 1967, reviewed most of the previous work and pointed out that the k i n e t i c studies by e a r l i e r workers had been i n dispute because the rate of decomposition i s a function of s o l u t i o n pH and the concentrations of b i - s u l f i t e , t h i o s u l f a t e and d i t h i o n i t e ions; a l l of which change during the decomposition react i o n . By the use of buffered 44 solutions containing high b i s u l f i t e concentrations, he avoided the k i n e t i c i r r e g u l a r i t i e s of the e a r l i e r work. He was also able to elucidate some features of the decomposition reaction mechanism. Sodium d i t h i o n i t e decomposition was followed i n standard solutions over a range of concentrations (.015 to .20 moles/liter) and temperature (15 to 40°C). In most of his experiments, the pH of the aqueous buffer containing NaHSO^ and Na 2S0 3 was about 5.2. According to Spencer, two sets of stable products, (Na 2S 20 3 + NaHS03) and Na 2S 30g are obtained. I t was also found that about 10% of the o v e r a l l decomposition reaction gives t r i t h i o n i t e ions, even when the concentrations of NaHS03 and Na 2S0 3 are low. Ketelaar (113) also reported the formation of t r i t h i o n i t e ions i n the homogeneous decomposition react i o n . According to Spencer, the decomposition reactions could be written as follows: 2Na 2S 20 4 + H 20 -»• 2NaHS03 + Na2S2C>3 . . . . (11) Na 2S 20 4 + 2NaHS03 N a ^ O g + Na 2S0 3+ H 20 . . . . (12) He also postulated that the i n i t i a l , rate-determining steps are common to both reactions (11) and (12), with the f i n a l product d i s t r i b u t i o n being determined by subsequent a l t e r n - ative routes. The mechanism of the rate determining step was also suggested. I t was found that the rate of decomposition i s f i r s t order i n [820^] and, of various solu t i o n components, b i s u l f i t e ion has the strongest influence on the decomposition rate. The e f f e c t s of pH, [HSO^] and [S0~] can not be separated rigorously, but i t seems probable that the decomposition rate i s f i r s t order i n [HSO3], variable f r a c t i o n a l order i n [H +] and zero order i n [S0~]. The presence of S2Q3 i ° n s accelerates the rate of decomposition. In most of the investigations (24, 121-129) on the rate of decomposition of sodium d i t h i o n i t e i n aqueous solutions, i t was found that an increase i n temperature increases the rate of decomposition. Thus, the rate of decomposition of sodium d i t h i o n i t e i n aqueous solutions can be given by the following expression. rhomo = k c [ S 2 O I ] 1 [ H S O P 1 [ S O 3 ] 0 [ H + ] X [ S 2 O 3 ] y ' ' * ' ( 1 3 ) where, k = Reaction rate constant; increases with an i n -c crease i n the temperature. No data has been reported on i t s value by Spencer, x = Variable. y = Not determined by Spencer Some idea about the rate of decomposition may be obtained from Spencer's experiments. In concentrated buffer solutions of b i s u l f i t e and s u l f i t e (2.38 moles NaHSO.,/liter; 0.25 moles N a 2 S 0 3 / l i t e r ) at a pH of 5.2 and a temperature of 20°C, sodium d i t h i o n i t e decomposed from a concentration of 0.135 to .02 mo l e s / l i t e r i n approximately 350 minutes. Decomposition of sodium d i t h i o n i t e i n the solutions at very low pH l e v e l s was investigated by Scholder and Denk (91). According to them, auto-decomposition of sodium d i t h i o n i t e i s very rapid i n strongly a c i d i c solutions and eventually elemental s u l f u r i s p r e c i p i t a t e d . The reaction can be written as follows: 2H 2S 20 4 -*> 3S0 2 + S + 2H20 . . . .(4) Decomposition of sodium d i t h i o n i t e i n highly a l k a l i n e aqueous solutions has also been investigated (10, 60). I t was suggested that the reac t i o n can be written as follows: 3Na 2S 20 4 + 6 NaOH 5Na 2S0 3 + Na 2S + 3H 20 Hence, for a sodium d i t h i o n i t e manufacturing process, the conditions of extreme a c i d i t y or a l k a l i n i t y and high temperatures must be avoided to obtain reasonable y i e l d s of the desired product. (b) Heterogeneous decomposition of sodium d i t h i o n i t e Chassain and Ostertag (14) reported that when sodium d i t h i o n i t e was prepared by bubbling gaseous s u l f u r dioxide through sodium-mercury amalgam i n the presence of traces of water, some of the d i t h i o n i t e was further reduced by sodium dissolved i n mercury according to the following r e a c t i o n : 3Na 2S 20 4 + 2Na -*• 2Na 2S 20 3 + 2Na 2S0 3 Kolthoff and M i l l e r (4 8) and Ketelaar (44) , from the polaro- graphic i n v e s t i g a t i o n of aqueous sulfu r dioxide solutions, also concluded that the d i t h i o n i t e ions can be further reduced according to the equation: S 2 0 4 + 2H + + 2e •*• S 2 0 3 + H 20 Ketelaar also observed that a t stronger reduction p o t e n t i a l s , S 2 0 4 ion i n the aqueous solut i o n was reduced to S~ ion. Thus, when sodium-mercury amalgam i s contacted with an aqueous sol u t i o n of s u l f u r dioxide,the heterogeneous decomposition of the d i t h i o n i t e ions formed at the i n t e r f a c e can be written schematically as follows: Reduction by Reduction by Reduction by 2 4 2 3 n . . . .(15) No data has been reported, i n the l i t e r a t u r e , on the rates or mechanisms of these reactions. Like the sodium d i t h i o n i t e formation and the water reaction, the heterogeneous 48 decomposition reaction probably also take place a t the i n t e r - face of the amalgam and aqueous phases. 4. The sodium d i t h i o n i t e oxidation reaction Since sodium d i t h i o n i t e i s a strong reducing agent, i t i s r a p i d l y attacked i n solution and more slowly as a hydrated s o l i d , by common oxidants such as atmospheric oxygen (13, 30, 38, 83) . Many investigations (6, 43, 54, 63, 80, 81) have been done on the k i n e t i c s and mechanism of a i r oxidation of the d i t h i o n i t e ions i n aqueous solutions. According to Jouan (43), the oxidation of sodium d i t h i o n i t e by oxygen i n aqueous solutions involves two reactions, and s u l f i t e and s u l f a t e ions are the products e x c l u s i v e l y . The f i r s t reaction i s very rapid and involves 82.4 per cent of the d i t h i o n i t e i n solu t i o n : H oS„0. + 0 o + H o0 -*• H o0'S0 o + HnSO. 2 2 4 2 2 2 2 2 4 Simultaneously, the remaining 17.6 per cent of the d i t h i o n i t e i s converted into an un i d e n t i f i e d compound of si m i l a r reducing power, presumably s u l f o x y l i c acid, which then oxidizes more slowly to s u l f i t e : • (H 2S0 2) + \ 0 2 H 2O.S0 2 49 According to Rinker et a l . (81), the rate of oxidation of sodium d i t h i o n i t e i n aqueous solutions by atmospheric oxygen under the conditions where d i f f u s i o n of a i r was not the rate c o n t r o l l i n g step, could be given by the following expression: = V 2 r o x i d a t i o n - k o [ S 2 ° 4 ] [ 0 2 ] A c o r r e l a t i o n of the rate constants with temperature was made by use of the Arrhenius equation. A value of 9.3 Kcal/mole was obtained for the a c t i v a t i o n energy and the frequency 5 - 1 / 2 - 1 factor was found to be 7.2 x 10 (moles/liter) (sec) In view of the information mentioned above, an i n e r t atmosphere should be provided i n an apparatus which i s used to manufacture sodium d i t h i o n i t e . 50 CHAPTER III THEORETICAL MODELS As outlined i n the Section II.G., when sodium-mercury amalgam i s contacted with an aqueous so l u t i o n of su l f u r dioxide to produce sodium d i t h i o n i t e , the following reactions should be considered: A. The Sodium D i t h i o n i t e Formation Reaction B. The Water Reaction C. The Heterogeneous Decomposition of Sodium D i t h i o n i t e D. The Homogeneous Decomposition of Sodium D i t h i o n i t e E. The Oxidation of Sodium D i t h i o n i t e . The l i t e r a t u r e c i t e d i n the Section I I . A . 5 , b . i i i . shows that, although several investigators have t r i e d to develop the sodium amalgam: S0 2 - NaHSO^/Na^O^ buffer process from the point of view of obtaining good y i e l d s of the s o l i d s a l t , none considered a l l of the reactions mentioned above. In most of the studies only the sodium d i t h i o n i t e formation reaction, the homogeneous decomposition reaction and the oxidation reaction were considered. Even f o r such a s i m p l i f i e d case, i n the absence of k i n e t i c data on the reactions considered, no mathematical models have been suggested which would predict the y i e l d s of sodium d i t h i o n i t e 51 on s u l f u r dioxide and on sodium consumed as a function of the process v a r i a b l e s . Ketelaar (44) suggested a mathematical model for the rate of sodium d i t h i o n i t e formation reaction on the basis of the d i f f u s i o n rates of the reactants i n the amalgam and the aqueous phases. He also discussed the importance of homogeneous decomposition of the d i t h i o n i t e b r i e f l y . Gerritsen (30) attempted to c o r r e l a t e some process variables to the y i e l d of sodium" d i t h i o n i t e on sodium consumed for a t h e o r e t i c a l l y i d e a l reactor (the amalgam and aqueous phases p e r f e c t l y mixed separately). He assumed no loss of d i t h i o n i t e due to oxidation and considered, p r i m a r i l y , the sodium d i t h i o n i t e formation reaction and the homogeneous decomposition of d i t h i o n i t e along with the mass-transfer of the reactants i n the two phases. In the absence of mass- transfer c o e f f i c i e n t s and k i n e t i c data, he a r r i v e d at the following general conclusions. According to Gerritsen, y i e l d s of sodium d i t h i o n i t e on sodium consumed could be improved by using large interfacial-area/aqueous-volume r a t i o s , large mass-transfer rates of s u l f u r dioxide, high concentrations of s u l f u r dioxide i n the aqueous phase and low rates of homogeneous decomposition of the d i t h i o n i t e . For the present i n v e s t i g a t i o n , where d i l u t e aqueous solutions of sodium d i t h i o n i t e were produced, mass-transfer of the d i f f e r e n t reacting species i n the amalgam and aqueous 52 phases along with a l l of the major reactions mentioned above should be considered to formulate a t h e o r e t i c a l model. The oxidation of sodium d i t h i o n i t e i n the aqueous s o l u t i o n could be avoided by providing an i n e r t atmosphere of nitrogen i n the e n t i r e apparatus used to manufacture sodium d i t h i o n i t e and by using fresh, oxygen-free d i s t i l l e d water to prepare the s u l f u r dioxide s o l u t i o n . Already, a l o t of information has been developed on the homogeneous decomposition of sodium d i t h i o n i t e i n a c i d i c , aqueous sol u t i o n , and a quantitative r e l a t i o n s h i p may be obtained by studying t h i s reaction i n the samples taken from the experimental reactor. Although some information (II.G.2.) i s a v a i l a b l e on the rate of the water reaction, i t i s not known how t h i s rate i s qu a n t i t a t i v e l y affected by the e l e c t r o l y t e s present i n the experimental reactor. I t would be very d i f f i c u l t to i s o l a t e the water reaction, the sodium d i t h i o n i t e formation reaction and the heterogeneous decomposition of d i t h i o n i t e for k i n e t i c i n v e s t i g a t i o n separately because they are p a r a l l e l - s e r i e s reactions. Other than lack of r e l i a b l e k i n e t i c data on the major reactions, the formulation of a t h e o r e t i c a l model i s further complicated by the following: 1. The d i f f u s i o n of i o n i c species i n the aqueous phase (50) may not be treated as molecular d i f f u s i o n . 2. The mass-transfer of sodium i n the amalgam may increase due to the Marangoni e f f e c t . 3. Some products may get adsorbed at the mercury surface. Thus, i t was d i f f i c u l t to suggest a t h e o r e t i c a l model for the proposed process from the information a v a i l a b l e . However, a q u a l i t a t i v e model has been postulated on the basis of the information i n the l i t e r a t u r e and the experiments c a r r i e d out by the author. This model w i l l be discussed i n Chapter VI. 54 CHAPTER IV EXPERIMENTAL A. Experimental Materials 1. Sodium-mercury amalgam A known quantity of d i s t i l l e d mercury was taken i n a s t a i n l e s s - s t e e l container and covered with a t h i n layer of p a r a f f i n o i l . Sodium metal was cut under p a r a f f i n o i l and cleaned to remove the layer of oxide formed on i t s surface.The desired amount of clean sodium metal was slowly added to the mercury with constant a g i t a t i o n , and was allowed to amalgamate. (The layer of p a r a f f i n o i l prevents oxidation of the sodium amalgam by the atmospheric oxygen). The p u r i t y of the chemicals and some problems involved i n the preparation of amalgam are presented i n Appendix C. 2. Aqueous s u l f u r dioxide s o l u t i o n Solutions of s u l f u r dioxide gas i n f r e s h l y d i s t i l l e d water were made by using an absorption column (2 1/2" x 30") f i l l e d with 1/2" Raschig Rings. This s o l u t i o n was always kept under an atmosphere of nitrogen to avoid oxidation • The absorption column could prepare solutions up to 1.4 molar s u l f u r dioxide i n water. When pH of the SC^ sol u t i o n required adjustment, a concentrated aqueous so l u t i o n of sodium hydroxide was added. The purity of chemicals used i n the preparation of aqueous sulfur dioxide solutions i s given i n Appendix D. B. Experimental Apparatus The experimental apparatus used i n t h i s study i s described schematically i n Figure 3. Legend f o r Figure 3 has been enclosed i n the following pages. For the sake of c l a r i t y , the types of valves used i n the apparatus have not been described i n the flow-sheet or the legend. For precise con- t r o l of flow rate (e.g. the flow rate of the aqueous s u l f u r dioxide s o l u t i o n ) , a needle valve made of s t a i n l e s s - s t e e l - 316 was used. For l e s s accurate control of flow rates, vee valves made of stainless-steel-316 were u t i l i z e d . When an on-off control of flow rates was required, toggle-operated valves made of stainless-steel-316 were employed. Some important features of the experimental apparatus are pre- sented below. 1. Reactor To obtain the desired information, a continuous-flow- stirred-tank reactor (CFSTR) was designed with aqueous and CYCLE Figure 3 Schematic flow-sheet of the experimental apparatus 57 LEGEND FOR FIGURE 3 A. Amalgam and Product Cycle: 1. Fresh amalgam storage, 8 l i t e r polyethylene b o t t l e 2. Moyno pump (Type 3M1, SSQ). Po s i t i v e displacement pump for pumping amalgam to the reactor (0-730 ml/ min) 3. Graham transmission; v a r i a b l e speed drive f o r Moyno pump (0-450 rpm) 4. Amalgam cooling heat-exchanger 5. Variable speed s t i r r e r i n the amalgam heat-exchanger (200-1400 rpm) 6. Plexigl a s s connector 7. Fresh amalgam sampling place 8. Stainless-steel-sheathed iron-constantan thermocouple 9. Pyrex CFSTR 10. Propeller mixer (1 1/2" dia) mounted on 5/16" s t a i n l e s s - s t e e l shaft 11. H e l l e r motor; v a r i a b l e speed drive (0-3000 rpm) 12. Thyratron c o n t r o l l e r for Heller motor 13. Plexiglass l e v e l c o n t r o l l e r f o r amalgam layer i n the reactor 14. Spent amalgam sampling place 15. Stainless-steel-sheathed iron-constantan thermocouple 16. Spent amalgam rese r v o i r (1" x 12" glass) 17. P l e x i g l a s s l e v e l c o n t r o l l e r for spent amalgam i n the reserv o i r 58 Legend for Figure 3 (continued) 18. Spent amalgam storage, 8 l i t e r polyethylene b o t t l e 19. Plexiglass connector 20. Product sampling place 21. Stainless-steel-sheathed iron-constantan thermocouple 22. Burette f i l l e d with the product 23. Erlenmeyer f l a s k with Rubine-R s o l u t i o n 24. N 2 gas cylinder 25. Combination pH electrode 26. Thermocompensator B. SO_2 Cycle: 27. D i s t i l l e d water storage tank, 10 g a l l o n polyethylene b o t t l e 28. Absorption column (2.1/2" x 30") packed with Raschig Rings 29. S0 2 solution storage tank, 20 g a l l o n polyethylene b o t t l e 30. Centrifugal pump; Eastern type D - l l 31. Rotameter (0-400 ml/min) 32. Plexi g l a s s connector 33. S0 2 s o l u t i o n sampling place 34. Stainless-steel"sheathed iron-constantan thermocouple 35. S0 2 s o l u t i o n cooling heat-exchanger 36. Variable speed s t i r r e r i n SC»2 s o l u t i o n heat-exchanger (200-1400 rpm) 37. S0 9 gas cyli n d e r 59 Legend for Figure 3 (continued) 38. N 2 gas cylinder C. Cooling Water Cycle 39. Cooling water storage tank, 10 g a l l o n enamelled container 40. Centrifugal pump, Eastern type E-1 41. Rotameter (0-3920 ml/min) 60 amalgam phases forming an i n t e r f a c e . This was selected rather than a packed, spray or a tubular reactor because a l l of the variables could be investigated independently and conveniently. This reactor might not be the i d e a l commercial reactor, but i t was convenient to provide information on the proposed process. One of the require- ments for the present i n v e s t i g a t i o n was to design a CFSTR that could be scaled-up, i f necessary, for a future semi-commercial or f u l l - s c a l e plant. The reactor consisted of a 4" x 6" Pyrex pipe section. The amalgam/aqueous so l u t i o n i n t e r f a c e was about 4 inches i n diameter. The reactor assembly i s shown i n Figure 4 along with the applicable legend. The major parts of the reactor are described i n the following paragraphs. I n i t i a l l y i t was planned to s t i r the two phases i n the reactor p e r f e c t l y but independently. This would have required separate s t i r r e r s and b a f f l e s f o r each phase. To simplify the reactor design for the present i n v e s t i g a t i o n , no s t i r r e r or baffles were provided i n the amalgam phase. Mixing i n the amalgam phase was due to flow of the amalgam. The part of the reactor which contained the aqueous phase was designed for perfect mixing using the recommended dimensions given by Sterbacek and Tausk (103) . I t was decided to use a c e n t r a l l y - l o c a t e d marine prop e l l e r (Part 2), fixed to a rota t i n g v e r t i c a l shaft (Part 3) and driven by a va r i a b l e speed drive (Heller F i g u r e 4 Reactor assembly 62 LEGEND FOR FIGURE 4 Part No. 1 4" x 6" Pyrex pipe section 2 1 1/2" diameter 3 blade s t a i n l e s s - s t e e l marine propeller; angle of tilt=42° from v e r t i c l e 3 5/16" s t a i n l e s s - s t e e l shaft 4 nylon bushing 5 s t a i n l e s s - s t e e l packing gland 6 t e f l o n washer 7 s t a i n l e s s - s t e e l c o l l a r for the t e f l o n washer 8 s t a i n l e s s c o l l a r 9 four b a f f l e s ( s t a i n l e s s - s t e e l ) 10 s t a i n l e s s - s t e e l slab 11 1/5" thick s t a i n l e s s - s t e e l d i s c mounted on part 10 12 1/5" thick s t a i n l e s s - s t e e l d i s c mounted on part 11 13 s t a i n l e s s - s t e e l bottom flange 14 polyethylene weir 15 s t a i n l e s s - s t e e l top flange 16 combination pH electrode 63 motor), i n the aqueous phase. The advantages of the propeller mixer were i t s high speed, a x i a l flow pattern and great pumping e f f e c t , which permits short mixing times. The aqueous sulfu r dioxide s o l u t i o n was introduced j u s t above the p r o p e l l e r . The flow patterns were such that the s o l u t i o n was forced to the i n t e r f a c e p r i m a r i l y by a x i a l flow, and then mixed with the r e s t of the aqueous medium by r a d i a l flow, a x i a l flow and tangential flow. The shaft of the propeller entered the reactor through a nylon bushing (Part 4) i n a s t a i n l e s s - s t e e l packing gland (Part 5). The lower end of the bushing was sealed by a t e f l o n washer (Part 6), held i n place by a s t a i n l e s s - s t e e l c o l l a r (Part 7) which, i n turn, rested on a c i r c l i p . Another s t a i n l e s s - s t e e l c o l l a r (Part 8) was mounted on the p r o p e l l e r shaft above the bushing, such that the distance between i t s lower face and the top end of the bushing was approximately 1/16". D i s t i l l e d water was injected into t h i s gap p e r i o d i c a l l y to l u b r i c a t e the shaft i n the bushing. This c o l l a r also r e s t r i c t e d any movement of the bushing i n the packing gland. Four b a f f l e s (Part 9) were provided i n the aqueous phase to promote perfect mixing conditions. To ensure that s t i r r i n g i n the aqueous phase did not agitate the amalgam phase s i g n i f i c a n t l y , the b a f f l e s i n the aqueous phase extended only to the i n t e r f a c e . The sodium-mercury amalgam entered at the bottom of the reactor c e n t r a l l y and then i t flowed outward r a d i a l l y over a s t a i n l e s s - s t e e l slab (Part 10). The hold-up of the amalgam i n the reactor could be changed, without changing the i n t e r f a c i a l area, by using 1/5 inch thick s t a i n l e s s - s t e e l d iscs (Parts 11 and 12). The surface area of the in t e r f a c e could be changed by opening the bottom flange (Part 13) of the reactor and introducing thin s t a i n l e s s - s t e e l d iscs with annular holes of various diameters. These discs were pressed against the bottom of the b a f f l e s . The product stream containing sodium d i t h i o n i t e flowed over a polyethylene weir (Part 14), thus f i x i n g the height of the aqueous medium. The weir rested on top of the Pyrex pipe section and i t was kept i n i t s p o s i t i o n by the top flange (Part 15) made of s t a i n l e s s - s t e e l . Holes were provided i n the top flange f o r i n s e r t i n g a pH electrode, the s u l f u r dioxide i n l e t tube, and the nitrogen i n l e t and o u t l e t tubes. Holes were provided i n the bottom flange for introducing fresh sodium-mercury amalgam and removing the spent amalgam. 2. pH measurement of the aqueous phase The combination pH electrode was located i n the reactor and the thermocompensator placed i n the product stream. The pH output was recorded continuously. The s p e c i f i c a t i o n s of the instruments used are presented i n Appendix A. When the combination pH electrode was placed i n the reactor, i t became contaminated repeatedly. This was prob- ably caused by entry of the aqueous so l u t i o n r e s u l t i n g from the greater pressure exerted on the reference-electrode l i q u i d junction by the aqueous phase i n the reactor than the hydro- s t a t i c pressure of KCl-solution inside the reference electrode. However, the combination pH electrode worked s a t i s f a c t o r i l y when the reference electrode was pressurized by about 15 psig N 2 through the r e f i l l aperture. 3. Temperature measurement of d i f f e r e n t streams The temperatures of the i n l e t s u l f u r dioxide s o l u t i o n , product stream, fresh amalgam and spent amalgam were measured by stainless-steel-sheathed iron-constantan thermo- couples. These temperatures were recorded d i g i t a l l y with the a i d of e l e c t r o n i c instruments including a d i g i t a l clock, d i g i t a l m i l l i v o l t meter, scanner, multiplexer and a p r i n t e r system (printer and p r i n t e r c o n t r o l l e r ) . The system used to measure the temperatures d i g i t a l l y i s out- l i n e d schematically i n Figure 5. The s p e c i f i c a t i o n s of the d i f f e r e n t temperature measuring instruments used are given i n Appendix A. 66 MAIN IRON-CONSTANTAN THERMOCOUPLES 115 V, 60 C/S S0 2 SOLN. FRESH AMALGAM SPENT AMALGAM DITHIONITE SOLN. DIGITAL CLOCK O U m t t t t SCANNER o o ca 1 DIGITAL m-VOLT METER o u 00 MULTIPLEXER BCD PRINTER SYSTEM T PRINT-OUT Figure 5 D i g i t a l temperature measurement (schematic) 67 4. Insulation of the equipment The heat of formation of the sodium d i t h i o n i t e at 25°C was calculated. A value of AH° = -88.29 Kcal/gm mole implies that the d i t h i o n i t e formation reaction i s highly exothermic. To maintain low temperatures i n the reactor, the i n l e t streams were cooled and most of the equipment was insulated with glass-wool. 5. E l e c t r i c a l wiring diagram A schematic wiring diagram for the experimental apparatus i s shown i n Figure 6. C. C a l i b r a t i o n Curves The following c a l i b r a t i o n s were done and the c a l i - bration curves have been attached i n Appendix A: 1. Flow rate of mercury pumped by the Moyno pump against micrometer se t t i n g on the Graham transmission. 2. Flow rate of aqueous s u l f u r dioxide against reading on the rotameter scale. 3. Flow rate of cooling water against reading on the rotameter. 208 V,60 C/S EASTE PUMP 2 A THYRATRON CONTROLLER -EXCHAN. "T^^^Y TIRRER-1 \ p r / 33 3 A Ar-/- HEAT S HEAT- EXCHAN. STIR RER-2 LIGHT BULB DIGITAL CLOC DIGITAL M-VOLT METER 'J3 SCANNE MULTIPLEXER P CONT RINTER "7^^" ROL J L y L n t e r 33 pH METER 3 A , A T - / - 1 A • 1 A A/- 1 A A T 1 A 1 A Ar- 1 A Ai- 1 A A/- 1 A •Ar- N1G 12 A r 3 A Figure 6 E l e c t r i c a l wiring diagram (schematic) 69 4. M i l l i v o l t output of iron-constantan thermocouples against temperature (°C). 5. RPM of the propeller against micrometer se t t i n g on the thyratron c o n t r o l l e r for the variable speed drive (Heller motor). D. An Experimental Run Sodium-mercury amalgam, the sodium content of which was known approximately, was prepared and stored i n the fresh amalgam storage b o t t l e under a th i n layer of p a r a f f i n o i l . A concentrated aqueous solut i o n of s u l f u r dioxide was prepared i n the absorption column and stored, under N 2, i n the s u l f u r dioxide storage b o t t l e . The concentration of t o t a l s u l f u r dioxide i n the solu t i o n was determined and then i t was d i l u t e d with d i s t i l l e d water, so that i t was s l i g h t l y above the desired concentration. The pH of t h i s s o l u t i o n was adjusted i n the desired range, by the addition of concentrated sodium hydroxide s o l u t i o n . The amalgam and s u l f u r dioxide solution streams were then c i r c u l a t e d through the heat-exchangers (closing the i n l e t s to the reactor) and cooled by water. Samples were taken from the amalgam and sulf u r dioxide-solution streams for analysis and t h e i r concentrations were determined. 70 The reactor was flushed with N 2 and kept under a s l i g h t pressure of nitrogen gas. The cooled amalgam was sent through the heat-exchanger to the reactor and the height of the amalgam layer i n the reactor ( s l i g h t l y above the bottom of the baffles) was adjusted by the mechanical l e v e l c o n t r o l l e r . The flow rate of the amalgam was adjusted by the micrometer screw oh -the Graham transmission which was d r i v i n g the Moyno pump. The pro p e l l e r i n the reactor, driven by the va r i a b l e speed drive (Heller motor), was started and i t s rpm was fix e d at the desired l e v e l with the help of a thyratron c o n t r o l l e r . The combination pH electrode was then introduced into the reactor and the pH meter was kept i n the "standby" p o s i t i o n . The cooled s u l f u r dioxide solution entered the reactor at a very high flow rate u n t i l the reactor was f i l l e d and then the flow rate was reduced and adjusted to the desired l e v e l , using a needle valve and a rotameter. Generally, the amalgam l e v e l c o n t r o l l e r had to be re-adjusted so that the amalgam ju s t touched the bottom of the b a f f l e s . The pH meter was turned on and pH of the aqueous phase i n the reactor was recorded continuously. The desired temperature of the aqueous phase i n the reactor was obtained by c o n t r o l l i n g the temperatures of the reactant streams. The temperatures of the reactant streams were controlled by the flow rate of the cooling water. The temperatures of the fresh amalgam, spent amalgam, i n l e t s u l f u r dioxide s o l u t i o n and the product stream were recorded p e r i o d i c a l l y . 71 Outlet amalgam samples were taken p e r i o d i c a l l y during the run from a sample point on the l e v e l c o n t r o l l e r . From time to time, the product stream was taken from the top of the reactor to the burette (under a N 2 atmosphere) and • t i t r a t e d against Rubine-R dye for i t s d i t h i o n i t e content. The experimental run was continued u n t i l the process attained steady-state. A steady-state was attained when successive t i t r a t i o n s with Rubine-R dye gave the same concentration of sodium d i t h i o n i t e i n the product stream. E. A n a l y t i c a l Procedures and Errors 1. Sodium-mercury amalgam (a) Analysis of sodium-mercury amalgam The a n a l y t i c a l procedure used was s i m i l a r to that employed by Rinker and Lynn (83) . The sodium-mercury amalgam sample was taken using a hypodermic syringe and injected under d i s t i l l e d water (to avoid oxidation by air) i n an Erlenmeyer f l a s k . A known volume of standard H^SO^ was pipetted into i t and the Erlenmeyer f l a s k was agitated thoroughly. The sodium dissolved i n mercury completely reacted with H^SO^ to give H 2 provided there was an excess of I^SO^. Excess of H-SO. was back-titrated with a standard solu t i o n of NaOH using phenolphthalein as an i n d i c a t o r . A sample c a l c u l a t i o n to determine the concentration of sodium i n amalgam i s presented i n Appendix C. (b) Accuracy and p r e c i s i o n of the a n a l y t i c a l procedure The theory behind the estimation of uncertainty i n the r e s u l t s obtained by an a n a l y t i c a l method i s discussed i n Appendix B. The most e f f i c i e n t way to t e s t the accuracy and p r e c i s i o n of the proposed a n a l y t i c a l method i n our laboratory, would have been to make an amalgam of known sodium concen- t r a t i o n and check i t s sodium content several times by the a n a l y t i c a l method. Unfortunately, i t was found d i f f i c u l t to prepare an amalgam of known sodium concentration s t a r t i n g with known quantities of mercury and sodium metal (Appendix C). Hence, i t was not possible to c a l c u l a t e the accuracy of the a n a l y t i c a l method by the above-mentioned approach. However, i t was evident from the information a v a i l a b l e i n the l i t e r a t u r e (52, 97, 104, 110) that the chemical reactions involved i n the a n a l y t i c a l procedure were i r r e v e r s i b l e and went to completion i n a very short time. Precautions were taken to avoid any systematic errors i n various steps of the procedure. Based on the above arguments, i t was assumed that the a n a l y t i c a l procedure, as applied i n the present i n v e s t i g a t i o n , provided accurate estimates of sodium content i n the amalgam. The p r e c i s i o n of the a n a l y t i c a l procedure was estimated by the method of "propagation of random er r o r " (Appendix B). In short, the p r e c i s i o n of measurement of d i r e c t l y measured qua n t i t i e s , i n various steps of the ana- l y t i c a l procedure, was known. From t h i s knowledge, the 95 per cent confidence l i m i t s (precision of the a n a l y t i c a l procedure) of the weight per cent of sodium i n the amalgam were estimated (Appendix C). In the instances where f a i r l y d i l u t e (- 0.1N) standard solutions of H^SO^ and NaOH were used and s u f f i c i e n t l y large samples (= 30 gms) of the amalgam were taken, the a n a l y t i c a l procedure was precise enough f o r the present i n - ve s t i g a t i o n . To i l l u s t r a t e t h i s , three amalgams of d i f f e r e n t sodium content were analysed by the proposed a n a l y t i c a l method. The sodium concentrations of these amalgams, covered the range of sodium content i n the amalgams used i n the present work. The pr e c i s i o n of the method, at 95 per cent confidence l e v e l , f o r determining the concentration of sodium i n these three amalgams was estimated (Appendix C) and the r e s u l t s are given i n Table 2. 74 TABLE 2 PRECISION OF THE AMALGAM ANALYTICAL PROCEDURE Amalgam Sample No. gm of Na/ 100 gm of Amalgam Prec i s i o n (95% C o n f i - dence l i m i t s ) Percentage Pr e c i s i o n I .0015 +.0005 -± 33 II .0383 +.0005 *± 1.3 III .1533 +.0005 -± .33 I t has been shown i n Appendix F that the large imprecision i n determining very small concentrations of sodium i n the amalgam (e.g. amalgam no. I) d i d not cause appreciable error i n the desired y i e l d s and conversions. To v e r i f y the estimated p r e c i s i o n mentioned above, several samples of spent amalgam were taken from the reactor a f t e r steady-state had been attained during an experimental run. These samples were analyzed f o r t h e i r sodium content by the a n a l y t i c a l method used. The scatter i n the data was caused by: (i) random errors involved i n various steps of the a n a l y t i c a l procedure, and ( i i ) the change of sodium content i n the spent amalgam depending on the reactor dynamics. 75 The variance was estimated from the experimental data using the equation (B-2). In almost a l l of the experimental runs, i t could be said with 95 per cent confidence that there was no s i g n i f i c a n t d i f f e r e n c e between the experimentally estimated variance and the variance estimated by the method of propagation of random er r o r . The variances were compared by the *F* t e s t . This conclusion also implied that the f l u c t u a t i o n s of sodium content i n the spent amalgam caused by reactor dynamics were i n s i g n i f i c a n t compared to the imprecision caused by the a n a l y t i c a l method. 2. Aqueous su l f u r dioxide s o l u t i o n (a) Analysis of aqueous s u l f u r dioxide s o l u t i o n The t o t a l s u l f u r dioxide (SC»2 + HSO^ + SO^) i n aqueous sol u t i o n was determined by iodometric analysis as outlined by Vogel (110) and Kolthoff and Belcher (47). A l i q u i d sample of the aqueous s u l f u r dioxide s o l u t i o n was inje c t e d , using a hypodermic syringe, into an excess of standard iodine s o l u t i o n . The excess of iodine i n the solut i o n was back-titrated with a standard s o l u t i o n of sodium t h i o s u l f a t e using a starch-solution as an i n d i c a t o r . The method used to c a l c u l a t e the concentration of t o t a l s u l f u r dioxide i n water i s presented i n Appendix D. 76 (b) Accuracy and p r e c i s i o n of the a n a l y t i c a l procedure The iodometric method to determine t o t a l s u l f u r dioxide i n aqueous so l u t i o n i s a standard text-book method (47/ 110) and i s considered to give accurate r e s u l t s by several investigators (22, 93). Three d i f f e r e n t concentrations of s u l f u r dioxide i n aqueous solutions were used i n the present i n v e s t i g a t i o n ; 0.40 molar, 0.655 molar and 1.30 molar. The method used to estimate the p r e c i s i o n of the a n a l y t i c a l procedure, at 95 per cent confidence l e v e l , i n determining the concen- t r a t i o n of t o t a l s u l f u r dioxide i n these three solutions has been outlined i n Appendix D. The r e s u l t s are presented i n Table 3. TABLE 3 PRECISION OF THE SULFUR DIOXIDE ANALYTICAL PROCEDURE Aqueous s u l f u r dioxide sol u t i o n No. Moles of Tot a l sulfur dioxide/ l i t e r P r e c i s i o n (95% Confidence l i m i t s ) Percentage P r e c i s i o n I 0.400 ±0.002 *± 0.5 II 0.655 ±0 .004 = ± 0.6 III 1.300 ±0.007 *± 0.5 77 3. Aqueous sodium d i t h i o n i t e s o l u t i o n When a i r oxidation was avoided, the product stream from the CFSTR contained mainly S.^^, S 20~ and HSO~ (or S0~ or S0 2 depending on pH) ions. (a) Analysis of sodium d i t h i o n i t e i n the product stream The assay of sodium d i t h i o n i t e has been thoroughly studied by a committee and th e i r findings have been published (114) . In i t s attempt to determine the most suitable method for sodium d i t h i o n i t e analysis, the committee reviewed about fourteen d i f f e r e n t methods. This committee concluded that i t i s possible to obtain precise and comparable r e s u l t s by f a i t h f u l a p p l i c a t i o n of the following three methods. (i) The iodine-formaldehyde method ( i i ) The Rubine-R method ( i i i ) The ammonical-copper method. The iodine-formaldehyde (47) and the Rubine-R (114, 119) methods were modified and then used i n the present i n v e s t i g a t i o n . A d e t a i l e d d e s c r i p t i o n of these a n a l y t i c a l procedures along with sample ca l c u l a t i o n s are presented i n Appendix E. The general p r i n c i p l e of the iodine-formaldehyde method i s as follows. The d i t h i o n i t e ions are oxidized q u a n t i t a t i v e l y to s u l f a t e ions by iodine according to the 78 following reaction: + 3 I 2 + 4H 20 -> 2S0J + 6I~ + 8H + However, the d i r e c t t i t r a t i o n i s of no p r a c t i c a l value since s u l f i t e ions (or b i s u l f i t e i o n s ) , which are always present with the d i t h i o n i t e ions, also react. This interference can be eliminated by the addition of an excess of formaldehyde which reacts with the d i t h i o n i t e to form formaldehyde-bisulfite and formaldehyde-sulfoxylate according to the rea c t i o n : S20^ + 2HCH0 + H 20 •*• HCHO'HSO" + HCHO»HSO~ Formaldehyde-bisulfite i s i n e r t to iodine, whereas the s u l - foxylate reacts r e a d i l y according to: HCHO'HSO" + 2 I 2 + 2H20 -*• SOj + HCHO + 4 l " + 5H + Rubine-R i s a bright red dye. A so l u t i o n of Rubine-R i s reduced instantaneously by the d i t h i o n i t e ions, to an amber coloured l i q u i d . Although, HSO-j and S^^" ions also reduce Rubine-R, the rate of reaction i s very slow and i t takes them weeks to reduce a small quantity of the dye so l u t i o n . Thus, Rubine-R can be considered s p e c i f i c f o r determination of d i t h i o n i t e ions. In the present i n v e s t i g a t i o n , the iodine-formaldehyde and the Rubine-R methods gave comparable r e s u l t s . The Rubine-R 79 method was used most of the time because of i t s s i m p l i c i t y and better p r e c i s i o n . The disadvantage of the Rubine-R method was that i t gave only S 2 0 4 ^ n t* i e product stream while S^^, S 20~ and HSO-j (or S0 3) could be determined by the iodine-formaldehyde method. (b) Accuracy and p r e c i s i o n of the a n a l y t i c a l procedures The most e f f i c i e n t way to t e s t the accuracy and p r e c i s i o n of the two a n a l y t i c a l methods used i n the present i n v e s t i g a t i o n would have been to make aqueous sodium d i t h i o n i t e solution of a known concentration and check i t s sodium d i t h i o n i t e content several times by both methods. I t was found impractical to prepare a s o l u t i o n of known Na 2S 20 4 content as a primary standard because reagent grade sodium d i t h i o n i t e purchased from the market contains an unknown amount of Na 2S 20 4. Fresh stock obtained from the market may contain as high as 90% Na 2S 20 4 while o l d stock may have les s than 60% Na 2S 20 4 due to the decomposition of Na 2S 20 4 to NaHS03 and Na2S2C<3. As mentioned i n the l a s t section, the iodine- formaldehyde and the Rubine-R methods have been accepted as the most accurate and precise methods fo r determining the concentration of Na 2S 20 4 i n a s o l u t i o n . A f t e r steady- state conditions had been obtained i n an experimental run, samples of the product stream were taken from the reactor, and were analyzed by both methods. The mean concentration 80 > (gm Na 2S 2O 4/100 ml) of Na 2S 20 4, determined by the Rubine-R method, was about 5 per cent higher than the mean concen- t r a t i o n determined by the iodine-formaldehyde method. The scatter i n the data for an a n a l y t i c a l method was caused by: (i) random errors involved i n various steps of the a n a l y t i c a l procedure, and ( i i ) the change of Na 2S 20 4 content i n the product stream depending on the reactor dynamics. From the experimental data, the p r e c i s i o n of the two a n a l y t i c a l methods at the 95 per cent confidence l e v e l , f o r determining the concentration of Na 2S 20 4 i n the product stream was estimated. In most of the cases, the p r e c i s i o n of the Rubine-R method derived from experimental data was within ± 1% and the p r e c i s i o n of the iodine-formaldehyde method was about ± 5%. The p r e c i s i o n of the Rubine-R method was also estimated by the method of propagation of random er r o r . Various steps involved i n the Rubine-R method f o r pr e c i s i o n c a l c u l a t i o n s have been outlined i n Appendix E. Using t h i s approach, the estimated p r e c i s i o n of the Rubine-R method was also found to be within approximately ± 1% for the concentrations of sodium d i t h i o n i t e analyzed i n the present i n v e s t i g a t i o n . The observation that, at 95 per cent confidence i n t e r v a l , there was no s i g n i f i c a n t difference between the experimentally estimated p r e c i s i o n and,the p r e c i s i o n estimated by the method of propagation of random e r r o r , implied that the fluctuations of ^ 2 8 2 0 ^ concentration i n the product stream caused by the reactor dynamics were i n s i g n i f i c a n t compared to the imprecision caused by the a n a l y t i c a l method. 82 CHAPTER V EXPERIMENTAL RESULTS A. Batch Experiments On the basis of information a v a i l a b l e i n the l i t e r a - ture, f i v e possible reactions were outlined i n Section I I . G that may take place i n the proposed process. Some batch experiments showed that, under the experimental conditions of the present i n v e s t i g a t i o n , almost a l l of these reactions would take place. 1. Presence of the sodium d i t h i o n i t e formation reaction Four 50 ml samples of an approximately 0.22% sodium-mercury amalgam (0.22 gms Na/100 gms of amalgam) were taken i n four separate beakers. An approximately 2.2 molar solut i o n of sodium b i s u l f i t e i n water was prepared and the solu t i o n was divided into four parts. The pH of the'four portions of the NaHSO^ soluti o n was adjusted to 0.8, 1.7, 4.0 and 9.0 respectively by the addition of concentrated ^SO^ or NaOH. Four 50 ml samples of the NaHSO^ solutions at the d i f f e r e n t pH's were added to the four amalgam samples respectively and the contents i n the beaker were s t i r r e d with a glass rod. An approximately 1 ml sol u t i o n of d i l u t e 83 Rubine-R dye was added to each of the beakers. The bright red colour of the Rubine-R dye disappeared almost immediately i n the beakers where NaHSO^ solutions at pH's 0.8, 1.7 and 4.0 were added. In a l l of the three cases, immediately a f t e r the Rubine-R was discoloured, the pH of the aqueous phase was below 7. In the fourth beaker, where the pH of the NaHSO^ sol u t i o n sample was 9, the Rubine-R dye was not discoloured. These experiments demonstrated that when sodium- mercury amalgam i s brought i n contact with an aqueous so l u t i o n of sodium b i s u l f i t e , sodium d i t h i o n i t e i s produced at a rapid rate. The r e s u l t s also agree with the l i t e r a t u r e information presented i n section II.G.l that the sodium d i t h i o n i t e formation reaction can take place only when the pH of the aqueous solut i o n i s i n the a c i d i c range. This reaction can be written as follows: 2Na + 2HSO~ -»• 2Na + + + 20H~ . . . . (16) 2. Presence of homogeneous decomposition of sodium d i t h i o n i t e i n an a c i d i c s o l u t i o n Approximately 20 gms of the anhydrous sodium d i t h i o n i t e (reagent grade salt) was dissolved i n a l i t e r of oxygen-free d i s t i l l e d water (this i s the maximum concentration of Na~S 90 4 expected i n the present investigation) and the s o l u - 84 t i o n was stored under an i n e r t atmosphere of N 2 gas. The concentration of sodium d i t h i o n i t e i n the solu t i o n was determined by the Rubine-R method. The solu t i o n was then divided into three parts and t h e i r pH was adjusted to 0.8/ 1.7 and 5.5 r e s p e c t i v e l y . A l l these solutions were kept at room temperature (20°C) and under a N 2 blanket to avoid oxidation of sodium d i t h i o n i t e . By taking samples from these solutions at d i f f e r e n t i n t e r v a l s of time and analyzing them f o r t h e i r sodium d i t h i o n - i t e content by the Rubine-R method, i t was concluded that the rate of homogeneous decomposition of sodium d i t h i o n i t e increased with decreasing pH. By varying the temperature of a sodium d i t h i o n i t e s o l u t i o n at a fixed pH, i t was observed that the rate of homogeneous decomposition of sodium d i t h i o n i t e increased with increasing temperature. These conclusions agree with the information a v a i l a b l e i n the l i t e r a t u r e (Section II.G.3.a). These experiments were not exhaustive enough to determine a quantitative expression for the rate of decomposition. The following observation of some s p e c i a l s i g n i f i c a n c e was obtained from the above-mentioned experiments. No elemen- t a l s u l f u r was observed i n any of the sodium d i t h i o n i t e solutions kept at 20°C and pH's of 0.8, 1.7 and 5.5 even a f t e r 48 hours. This implies that the rate of auto- decomposition of sodium d i t h i o n i t e according to the equation, 85 2H 2S 20 4 -»• 3S0 2 + S + 2H20 , i n the pH range 0.8 to 5.5 i s n e g l i g i b l y small. I t was thought that, i n the proposed i n v e s t i g a t i o n , the pH of the aqueous medium would not be less than 0.8 and the residence time of the product i n the aqueous medium would not be more than an hour, hence, the auto-decomposition of d i t h i o n i t e could be neglected. Thus, only the following homogeneous decomposition reactions, outlined by Spencer (10 2), were considered to occur. 2Na 2S 20 4 + H 20 2NaHS03 + Na 2S 20 3, and (11) Na oS o0. + 2NaHSO, •*• Na oS-0 c + Na oS0- + H o0 (12) 2 2 4 3 2 3 6 2 3 2 3 . Presence of the heterogeneous decomposition of sodium d i t h i o n i t e Approximately 50 ml of a 0.22% sodium-mercury amalgam was taken i n a beaker. A n approximately 5 ml sample of a 1% sodium d i t h i o n i t e s o l u t i o n i n water was added to the amalgam sample and the contents i n the beaker were s t i r r e d with a glass rod. Af t e r a short time H 2S gas was detected as one of the products by i t s d i s t i n c t i v e smell. The gas was confirmed to be H 2S when i t turned lead acetate paper black. The experiment was repeated with approximately 1 ml 86 of the 0.22% amalgam and a large excess (approximately 200 ml) of the 1% Na2S2C>4 solution; no H 2S was detected. These re s u l t s q u a l i t a t i v e l y agree with the reported (Section II.G.3.b) heterogeneous decomposition of sodium d i t h i o n i t e by sodium- mercury amalgam: Reduced by Reduced by Reduced by S 20= *a * S 20= £2 S= ^ * S = . . .(15) When the Na/Na 2S 20 4 r a t i o was very high, the reduc- ti o n of S 2 0 4 took place progressively and eventually S~ ions were obtained which reacted with the H + ions present i n the aqueous medium to give H 2S. On the other hand, when the Na/Na 2S 20 4 r a t i o was very small, the reduction probably stopped a f t e r the f i r s t or the second step and, therefore, no S _ ions were formed to produce H 2S. 4. Presence of the water reaction In the batch experiments, at low Na/NaHSO^ r a t i o s and low pH's of the so l u t i o n (pH 0.8 and 1.7), a gas evolving from the inte r f a c e could be seen. This gas was not H 2S. Most probably i t was hydrogen generated due to the water reaction (Section II.G.2) 2Na + 2H20 2 NaOH + H 2 . . . .(17) 87 At high Na/NaHSO^ r a t i o s , the water reaction probably also takes place. 5. Presence of the sodium d i t h i o n i t e oxidation reaction i n an aqueous solu t i o n Approximately 10 gms of reagent grade sodium d i t h i o n - i t e s a l t was dissolved i n 1 l i t e r of oxygen-free d i s t i l l e d water and the s o l u t i o n was neutralized by sodium hydroxide to avoid a c i d i c decomposition. This s o l u t i o n was stored under N 2 gas at 20°C. The Na2S2C>4 content of t h i s s o l u t i o n was accurately determined by the Rubine-R method. A sample of the standard s o l u t i o n was taken i n a beaker; the beaker was exposed to a i r and i t s contents were s t i r r e d with a glass rod. The concentration of Na 2S 20 4 i n the sample decreased with increasing time as has been reported i n the l i t e r a t u r e (Section II.G.4). B. Introduction to Experiments i n the CFSTR Nine process variables were i d e n t i f i e d f o r considera- t i o n . They were; 1. the concentration of sodium i n the fresh amalgam, 2. the concentration of t o t a l s u l f u r dioxide i n the aqueous feed s o l u t i o n , 88 3. the a g i t a t i o n i n the aqueous phase, 4. the a g i t a t i o n i n the amalgam phase, 5. the flow rate of the aqueous su l f u r dioxide s o l u t i o n (residence time i n the aqueous phase), 6. the flow rate of the sodium-mercury amalgam ( r e s i - dence time i n the amalgam phase), 7. the interfacial-area/aqueous-volume r a t i o , 8. the temperature of the aqueous phase, and 9. the pH of the aqueous phase. The e f f e c t of d i f f e r e n t process variables and t h e i r i n t e r a c t i o n s on y i e l d s of sodium d i t h i o n i t e , based on t o t a l s u l f u r dioxide entering the reactor and on sodium consumed i n the reactor could possibly be determined i f a f a c t o r i a l design of experiments were done at l e a s t at f i v e l e v e l s of o each v a r i a b l e . This would amount to doing (5) = 1953125 experimental runs. Since considerable time was required f o r preparing reagents and analyzing products f o r an experimental run, i t was d i f f i c u l t to do more than four to f i v e experi- mental runs a week. Doing a l l possible experiments would have taken an exceptionally long time, and many would not have produced reasonable d i t h i o n i t e y i e l d s or d i t h i o n i t e concentrations from the point of view of economics and use r e s p e c t i v e l y . Therefore, the e f f e c t s of process v a r i a b l e s considered of primary importance and t h e i r i n t e r a c t i o n s on the y i e l d s of sodium d i t h i o n i t e were investigated. For a l l the experimental runs the depth of the 89 amalgam and the volume of the aqueous layer i n the CFSTR were kept f i x e d . As a r e s u l t of t h i s arrangement, for the reactor of a sp e c i f i e d geometry (Section IV.B.l), the volume of the aqueous layer was approximately 980 ml and the volume of the amalgam layer was about 96 ml. I t was mentioned i n Section II.G. that probably none of the process reactions take place inside the amalgam phase. The sodium metal dissolved i n mercury i s transferred to the mercury/aqueous i n t e r f a c e where the sodium d i t h i o n i t e formation reaction, the water reaction and the hetrogeneous decomposition of sodium d i t h i o n i t e take place. A c r i t i c a l look at the l i s t of the process variables showed that the e f f e c t of variables (4), (6) and (1) should have a s i m i l a r e f f e c t on the rate of mass-transfer of sodium i n the amalgam. In other words, an increase i n the l e v e l of a g i t a t i o n i n the amalgam phase by introducing a mechanical s t i r r e r and b a f f l e s i n that phase, at a fix e d concentration of sodium i n the fresh amalgam entering the reactor, should increase the rate of mass-transfer of sodium to the i n t e r f a c e . S i m i l a r l y , an increase i n the volumetric flow rate of the fresh amalgam at a fix e d concentration of sodium i n fresh amalgam or an increase i n the concentration of sodium i n fresh amalgam at a fixed flow rate of fresh amalgam should also increase the rate of mass-transfer of sodium to the i n t e r f a c e . Therefore, an increase i n the l e v e l of any of these three variables should a f f e c t the y i e l d s of sodium d i t h i o n i t e i n the same manner. 90 In the present i n v e s t i g a t i o n , the e f f e c t of the rate of mass-transfer of sodium to the in t e r f a c e on the y i e l d s of sodium d i t h i o n i t e was investigated p r i m a r i l y by changing the concentration of sodium i n fresh amalgam and keeping the volumetric flow rate of the amalgam f i x e d . As mentioned i n Section IV.B.l, to simplify the reactor design, no s t i r r e r or b a f f l e s were provided i n the amalgam phase. Due to a l i m i t e d supply of mercury a v a i l a b l e for the experiments, the volumetric flow rate of the amalgam could not be changed s i g n i f i c a n t l y . In any case, i t was hoped that by a systematic i n v e s t i g a t i o n of the other process v a r i a b l e s , one could pre- d i c t the e f f e c t of a v a r i a t i o n i n the l e v e l of a g i t a t i o n i n the amalgam phase or the volumetric flow rate of the amalgam. The e f f e c t s of the remaining process variables on the y i e l d s of sodium d i t h i o n i t e are discussed i n the follow- ing sections. C. D e f i n i t i o n s of Some Important Quantities which are Used for the Interpretation of Data These quantities have been defined below. The mathe- matical expressions to ca l c u l a t e them and sample c a l c u l a t i o n s have been presented i n Appendix F. 1. Concentration of sodium d i t h i o n i t e i n the product stream, ° S 2 0 4 " (gms of sodium d i t h i o n i t e ) (100 ml of the product stream) 2. Y i e l d of sodium d i t h i o n i t e on t o t a l s u l f u r dioxide entering the reactor (%), (gm molar cone, of Na2S20^ i n product) x 2 x 100 ^SO ~~ 2 (gm molar cone, of t o t a l SG^ i n aqueous feed) 3. Y i e l d of sodium d i t h i o n i t e on sodium entering the reactor with the fresh amalgam (%), (gm moles of Na2S20^ i n product/min) x 2 x 100 N a (gm moles of Na entering with fresh amalgam/min) 4.Yield of sodium d i t h i o n i t e on sodium consumed i n the reactor (%), (gm moles of Na2S20^ i n product/min) x 2 x 100 CONNA = gm moles of Na entering with fresh amalgam/min1 -gm moles of Na leaving with spent amalgam/mini 92 5. Conversion of sodium from the amalgam to d i f f e r e n t products i n the reactor (%), gm moles of Na entering with fresh amalgam/min -gm moles of Na leaving with spent amalgam/min x X = — (gm moles of Na entering with fresh amalgam/min) 6. Na/SC>2 r a t i o entering the reactor, (gm moles of Na entering with fresh amalgam/min) (gm moles of t o t a l SC>2 entering with aqueous feed/min) 7. Rate of sodium consumption i n the reactor, = (gm moles of Na entering with fresh amalgam/min) -(gm moles of Na leaving with spent amalgam/min) For br e v i t y , symbols were used for the d i f f e r e n t process variables i n the following sections. These symbols along with t h e i r units have been described i n Table 4. TABLE 4 PROCESS VARIABLES AND THEIR UNITS SYMBOLS DESCRIPTION UNITS CHGF Concentration of sodium i n the fresh amalgam gm of Na/100 gm of the fresh amalgam STS0 2 Concentration of t o t a l s u l f u r dioxide i n the aqueous feed s o l u t i o n gm mole/liter (RPM)_ Aq Speed of the marine propeller in aqueous phase revolutions/min FLS0 2 Flow rate of the aqueous sulfu r dioxide solu- t i o n l i t e r / m i n FLHG Flow rate of the sodium-mercury amalgam ml/min <A/v)A q The interfacial-area/aqueous-volume r a t i o 2 3 cm /cm TEMP Temperature of the aqueous phase degree centigrade PH pH of the aqueous phase . , gm ions of H » CO 94 D. Reproducibility of Experimental Runs i n the CFSTR Before a det a i l e d experimental i n v e s t i g a t i o n could be started, i t was decided to check the r e p r o d u c i b i l i t y of the experimental runs i n the CFSTR. Unfortunately, the following problems made the task somewhat d i f f i c u l t . The sodium-mercury amalgam for the experimental runs was prepared i n a batch. I t i s explained i n Appendix C why i t was d i f f i c u l t to make an amalgam of a s p e c i f i e d sodium-concentration s t a r t i n g with known quantities of mercury and sodium. Generally, i t took over an hour to obtain steady-state conditions during an experimental run. The supply of mercury was l i m i t e d (- 7.5 l i t e r s ) , therefore, i t was not convenient to do more than two experimental runs, at the flow rate of the fresh amalgam considered, under i d e n t i c a l amalgam concen- t r a t i o n s . The r e s u l t s obtained from only two experimental runs under i d e n t i c a l l e v e l s of d i f f e r e n t process v a r i a b l e s would not o f f e r a very powerful s t a t i s t i c a l t e s t f o r re- p r o d u c i b i l i t y . Hence, the following scheme was used. A set of seven experimental runs (set: 47-57, expts. 47, 50, 52, 53, 54, 55 and 57) was performed under almost i d e n t i c a l l e v e l s of d i f f e r e n t process variables except the concentration of sodium i n the fresh amalgam which was varied i n the range .0403% to .0932%. The experimental conditions for the set: 47-57 have been presented i n Table 5. From the observations made, the steady-state C c n , S2 U4 , Y„ , CONNA and X.T and t h e i r 95 per cent confidence S0 2' Na Na r l i m i t s were calculated for each experimental run. Sample cal c u l a t i o n s for these quantities i n the experimental run 54 are shown i n Appendix F. For a l l the experimental runs i n the set: 47-57, the steady-state C g Q , Y g 0 , Y N a, CONNA and X N a were plot t e d 2 4 2 against the Na/S02 r a t i o entering the reactor i n each run. Thus, f i v e smooth curves were drawn as shown i n Figure 7. The 95 per cent confidence l i m i t s are not shown on the graphs. I t i s important to point out that the nature of the curves obtained by p l o t t i n g steady-state Cg Q , Y g 0 , v N a , CONNA 2 4 2 and X N a against the concentrations of sodium i n fresh amalgam would be s i m i l a r because the molarity of the s u l f u r dioxide solut i o n entering the reactor, STS0 2, during a l l of the experimental runs i n t h i s set was approximately the same. However, p l o t t i n g these quantities against Na/S0 2 r a t i o s offered c e r t a i n advantages i n the i n t e r p r e t a t i o n of data as discussed i n l a t e r sections. At a l a t e r date, another set of seven experimental runs ( set: 65-77, expts. 65, 67, 69, 71, 73, 75 and 77) was performed using d i f f e r e n t batches of reagents f o r the a n a l y t i c a l work. The l e v e l s of the process variables were nearly the same as for the set: 47-57, except that the concentration of sodium i n fresh amalgam was varied i n the range .0392 % to .1010 %. The experimental conditions f o r the set: 65-77 have TABLE 5 LEVELS OF THE PROCESS VARIABLES IN SET: 47 - 57 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF S T S 0 2 (RPM) j^q F L S O 2 FLHG (A/V) Aq TEMP PH .0403 - .0932 .639 -.656 673 .096 47.5 .0784 17 5.6 - 6.0 TABLE 6 LEVELS OF THE PROCESS VARIABLES IN SET: 6 5 - 7 7 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF STS02 (RPM) A q FLS0 2 FLHG (A/V) Aq TEMP pH .0392 - .1010 .650 -.658 673 .096 47.5 .0784 1 7 5.4 - 6.0 vo 97 J I I L •2 -3 -4 -5 Na/S0 2 Figure 7 Repr o d u c i b i l i t y of the experimental runs i n the CFSTR. See Tables 5 and 6 for the l e v e l s of the process variables 98 been presented i n Table 6. Once again, the steady-state C„ _ , Y„„ , Y„ , CONNA and X.T , calculated from the obser- 2 4 2 vations made for each experimental run, were plotted against t h e i r respective Na/S02 r a t i o s and are shown i n Figure 7. Figure 7 shows that, within the 95 per cent confidence l i m i t s there i s no s i g n i f i c a n t difference between the steady- state Cg 0 , Y g 0 , Y N a, CONNA and X N a curves f o r the two 2 4 2 sets: 47-57 and 65-77. Furthermore, for two experimental runs, run 55 and 73, which were performed under almost i d e n t i c a l conditions, i t can be said with 95 per cent confidence that there i s no s i g n i f i c a n t difference between the i r respective steady-state C_ _ , Y _ , Y , CONNA and X values. 2 4 2 Further confirmation of the r e p r o d u c i b i l i t y of the experimental runs was provided by the r e s u l t s obtained from the set: 66-76 (expts. 66, 68, 70, 72, 74 and 76), set: 62-63 (expts. 62 and 63) and set: 87-91 (expts. 87, 89 and 91). These sets used d i f f e r e n t batches of the reagents f o r the a n a l y t i c a l work but they b a s i c a l l y d i f f e r e d from the sets: 47-57 and 65-77 i n that the rpm of the propeller i n the aqueous phase was decreased from 673 to 225. The experimental con- d i t i o n s f o r the sets: 66-76, 62-63 and 87-91 are presented i n the Tables 7, 8 and 9 res p e c t i v e l y and the r e s u l t s are shown i n Figure 8. TABLE 7 LEVELS OF THE PROCESS VARIABLES IN SET: 6 6 - 7 6 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF S T S 0 2 (RPM) A q FLSO 2 FLHG (A/V) A q TEMP pH .0392 - .0892 .650 -.658 225 .096 47.5 .0784 17 5.35-5.95 TABLE 8 LEVELS OF THE PROCESS VARIABLES IN SET: 6 2 - 6 3 Range of the Changed Variable VALUES OF THE FIXED VARIABLES S T S 0 2 (RPM) Aq F L S 0 2 FLHG ( V V ) A q TEMP PH CHGF .0635 - .1012 .639 -.646 225 .096 47.5 .0784 17 5.7-6.15 TABLE 9 LEVELS OF THE PROCESS VARIABLES IN SET: 87 - 91 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF S T S 0 2 (RPM) A q FLSO 2 FLHG (A/V) Aq TEMP pH .0372 - .0986 .655 -.658 225 .096 47.5 .0784 17 5.35-5.85 vo vo 100 Figure 8 Reproducibility of the experimental runs i n the CFSTR. See Tables 7 , 8 and 9 for the lev e l s of the process variables 101 E. Data from CFSTR Experiments 1. Concentration of sodium i n fresh amalgam The general plan of the work involved a set of experi- mental runs at various concentrations of sodium i n fresh amalgam, and at chosen fi x e d l e v e l s of the other process v a r i a b l e s . The e f f e c t s of the concentration of sodium i n fresh amalgam on the steady-state values of C c _ , Y_ n , 2 4 2 Yr, , CONNA and X.T were determined at d i f f e r e n t l e v e l s of Na Na each v a r i a b l e . Generally, these calculated quantities were plotted against the Na/S0 2 r a t i o s entering the reactor. These quantities were also plotted against the concentration of sodium i n the fresh amalgam to obtain a d d i t i o n a l information. The nature of the curves obtained by p l o t t i n g the steady-state CS 0 ' YS0 ' YNa' C 0 N N A a n d XNa a 9 a i n s t t n e Na/S0 2 r a t i o s 2 4 2 (or the concentration of sodium i n the fresh amalgam) was found to be s i m i l a r for d i f f e r e n t sets of the experimental runs. During an experimental run, the unsteady-state concentration p r o f i l e s of sodium d i t h i o n i t e i n the product stream and sodium i n the spent amalgam, as well as the pH of the aqueous phase, were also investigated. The e f f e c t of varying the concentration of sodium i n fresh amalgam on the nature of these unsteady-state curves was also determined. 102 (a) The v a r i a t i o n of steady-state values of C S 20 4' Y S 0 2 / YNa' CONNA and X N a with change i n the Na/S0 2 r a t i o s entering the reactor The experimental set: 65-77 may be considered a t y p i c a l set of experimental runs where, as mentioned i n Section V.D., the concentration of sodium i n fresh amalgam was varied i n the range .0392 % to .1010 %. The experimental conditions for t h i s set are presented i n Table 6. the concentration of sodium i n fresh amalgam i n Figure 10. The curves i n Figure 9 and 10 were sim i l a r because the molarity of sul f u r dioxide s o l u t i o n entering the reactor during a l l of the experimental runs i n t h i s set was approximately the same. (i) The v a r i a t i o n of steady-state sodium d i t h i o n i t e concen- t r a t i o n i n the product stream, C_ n , with change i n Na/S0 2 r a t i o s entering the reactor Steady-state concentrations of sodium d i t h i o n i t e i n the product stream are of considerable importance i f t h i s product stream i s to be used for groundwood brightening. Figure 9 shows the e f f e c t on values of steady-state C n caused by changing Na/S0 2 r a t i o s . The concentration of sodium d i t h i o n i t e i n the product stream increases with increasing Na/SO- r a t i o s to a value of Na/S09 equal to 0.29* Steady-state values of C g Q , Y g 0 , Y N a, CONNA and X. 2 4 2 were plotted against Na/S0» r a t i o s i n Figure 9 and against Na 1 0 3 1 I I I I I I L •2 -3 -4 *5 Na/S0 2 Figure 9 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SO~ r a t i o s entering the CFSTR for the experimental set: 65-77. See Table 6 for the le v e l s of the process variables 104 100 9 0 - 80 CC * 70 o o CO 60 50 40 30 20 Figure 10 o - 19 - 15 - 11 o o CN C O CM cc E o CM C O o - 1-2 •8 - .4 • \ CONNA 05 •10 •15 20 CHGF (gm Na/100gmAmalgam) Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus concentrations of sodium i n amalgam entering the CFSTR for the experimental set: 65-77. See Table 6 for the l e v e l s of the process variables At t h i s point, steady-state C reaches i t s maximum value of 0.9%. At values of the Na/S02 r a t i o greater than 0.29, the concentration of d i t h i o n i t e drops sharply; then l e v e l s ,off to decrease slowly with further increase i n the Na/S02 r a t i o . For the set: 65-77, a Na/SC»2 r a t i o of about 0.29 corresponds to a sodium concentration i n fresh amalgam of .064% (molarity of s u l f u r dioxide i n the aqueous so l u t i o n was fixe d at about 0.65 molar) . ( i i ) The v a r i a t i o n of steady-state y i e l d of sodium d i t h i o n i t e on t o t a l s u l f u r dioxide entering the reactor, Y c n , with change i n Na/S02 r a t i o s entering the reactor Figure 9 shows the e f f e c t of Na/S0 2 r a t i o s on the y i e l d of sodium d i t h i o n i t e calculated on s u l f u r dioxide. The steady-state concentration of sodium d i t h i o n i t e when the Na/S02 r a t i o i s changed. Y i e l d on sulfu r dioxide reaches a maximum of 15.6% at the Na/S0 2 r a t i o of 0.29. ( i i i ) The v a r i a t i o n of steady-state conversion of sodium (from the amalgam) to d i f f e r e n t products i n the reactor, X^ a, with change i n Na/S0 2 r a t i o s entering the reactor 2 values of steady-state Y SO respond i n a way s i m i l a r to the As shown i n Figure 9, when the steady-state values of X M are plotted against the Na/SO- r a t i o s entering the 106 reactor, a curve i s obtained showing a maximum. A maximum . conversion of 94% i s obtained at a Na/SC^ r a t i o of 0.29. For the set: 65-77, the rate of sodium consumption by the aqueous phase (gm moles of sodium entering the reactor with fresh amalgam minus gm moles of sodium leaving the reactor with spent amalgam per minute) i s plotted against the Na/SG^ r a t i o s i n Figure 11 and against the concentration of sodium i n fresh amalgam i n Figure 12. These curves demonstrate that when the Na/SC^ r a t i o entering the reactor or the concentration of sodium i n fresh amalgam i s increased, keeping the l e v e l s of a l l of the other process variables f i x e d , the rate of sodium removal from the amalgam phase increases. Figures 11 and 12 also show that at Na/SC^ r a t i o s below 0.29 corresponding to sodium concentration i n fresh amalgam of less than .064%, the rate of sodium consumption i s l i n e a r l y related to the Na/SC^ r a t i o entering the reactor or the concentration of sodium i n fresh amalgam. However, at Na/SG^ r a t i o s above 0.29 the rate of sodium consumption i s not l i n e a r l y proportional to the Na/SC^ r a t i o s entering the reactor (Figure 11). A s i m i l a r r e s u l t i s obtained at CHGF above .064% when the rate of sodium consumption i s plotted against the concentration of sodium i n fresh amalgam (Figure 12). In Figure 12, when the curve i s extrapolated to zero rate of sodium consumption, the l i n e does not go through the o r i g i n . For the set: 65-77, i t appears that upto 107 "E co Q O C O L l . o L U 0 2 5 0 h o -0225 E E 3 ^ -0200 O h- Q_ 0175h O O -0150 0125h 0100 Figure 11 •2 -3 -4 Na/S0 2 Rates of sodium consumption versus Na/S0 o r a t i o s entering the CFSTR for the experimental set: 65-77. See Table 6 for the l e v e l s of the process variables 108 CHGF (gmNa/100 gm Amalgam) Figure 12 Rates of sodium consumption versus concentrations of sodium i n amalgam entering the CFSTR for the experimental set: 65-77. See Table 6 for the l e v e l s of the process variables 109 approximately 0.0035% sodium i n fresh amalgam, no sodium i s consumed by any rea c t i o n . A few s t a t i s t i c a l c a l c u l a t i o n s (95 per cent confidence l i m i t s ) show that t h i s deviation from the o r i g i n can be attributed neither to the errors i n the a n a l y t i c a l method nor to the c a l c u l a t i o n technique. To further v e r i f y the above-mentioned phenomena, the rate of sodium consumption i s plotted against the concentration of sodium i n fresh amalgam f o r d i f f e r e n t sets of the experi- mental runs. For the sets: 95-105 (expts. 95,97,99,103 and 105), 23-28 (expts. 23,24,25,26,27 and 28), 65-77 (expts. 65,67,69,71,73,75 and 77) and 42-46 (expts. 42,43,44,45 and 46), the plots are shown i n Figure 13 and the experimental conditions have been presented i n Tables 10,11,6 and 12 res p e c t i v e l y . Figure 13 shows that for each experimental set at values of CHGF below the steady-state sodium d i t h i o n i t e concentration maximum, the rate of sodium consumption i s l i n e a r l y r e l a t e d to the concentration of sodium i n the fresh amalgam (CHGF). But at values of CHGF above the steady-state Na2S204 concentration maximum, the rate of sodium consumption i s not l i n e a r l y proportional to the values of CHGF. Further, for none of the sets does the extrapolated l i n e pass through the o r i g i n . (iv) The v a r i a t i o n of steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor, CONNA, with change i n Na/S09 r a t i o s entering the reactor TABLE 10 LEVELS OF THE PROCESS VARIABLES IN SET: 95-105 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF S T S 0 2 (RPM) A q F L S 0 2 FLHG <Vv) A q TEMP PH .0439 - .0912 .653 -.660 673 .198 47.5 .07 84 17 5.20 - 5.65 TABLE 11 LEVELS OF THE PROCESS VARIABLES IN SET: 23-28 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF S T S 0 2 (RPM) A q FLSO 2 FLHG ( A / v ) A q TEMP PH ' .0173 - .0544 .397 -.403 673 .096 47.5 .0784 17 5.2 - 5.9 TABLE 12 LEVELS OF THE PROCESS VARIABLES IN SET: 4 2-46 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF S T S 0 2 (RPM) Aq FLSO 2 FLHG (A/V>Aq TEMP PH .0656 - .2127 1.270 -1.310 67 3 .096 47.5 .0784 17 5.0 - 5.75 I l l in ) E •048 CD O E E •040 w o lid •032 C O z: o •024 o O D  •016 C O LL. O LU i •008 < cr • A O V SET:95-105 SET:23-28 SET-.65-77 SET.-42-46 • 04 -08 -12 -16 -20 CHGF (gmNa/lOOgm Amalgam) Figure 13 Rates of sodium consumption versus concentrations of sodium i n amalgam entering the CFSTR for the experimental sets: 95-105, 23-28, 65-77 and 42- 46. See Tables 6, 10, 11 and 12 for the l e v e l s of the process variables 112 When the steady-state CONNA values were plotted against the Na/S02 r a t i o s f o r the set: 65-77, the curve shown i n Figure 9 was obtained. This curve shows no maximum. The steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor i s about 71% at a Na/S0 2 r a t i o of .176 (small- est Na/S02 r a t i o f o r the experimental set: 65-77). The steady-state value of CONNA decreases gradually with increas- ing Na/S0 2 r a t i o s to a value of Na/S0 2 equal to 0.29. At values of the Na/S02 r a t i o greater than 0.29, the y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor drops sharply then l e v e l s o f f to decrease slowly with further increase i n the Na/S©2 r a t i o . (v) The v a r i a t i o n of steady-state y i e l d of sodium d i t h i o n i t e on sodium entering the reactor with the fresh amalgam, YNa' w ^ t n change i n Na/S02 r a t i o s entering the reactor Figure 9 shows that the form of the curves obtained by p l o t t i n g steady-state Y N a versus Na/S02 r a t i o s and steady- state CONNA versus Na/S02 r a t i o s i s s i m i l a r ; the l a t t e r having been discussed i n the l a s t section. However, at a fixed Na/S02 r a t i o entering the reactor the steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (CONNA) i s always greater than the steady-state y i e l d of sodium d i t h i o n i t e on sodium entering the reactor with fresh amalgam, Y . 113 (b) The v a r i a t i o n of unsteady-state concentration p r o f i l e s with change i n Na/SC^ r a t i o s entering the reactor (i) Concentration of H +ions i n the aqueous phase For an experimental run, s t a r t i n g with s u l f u r dioxide i n water at pH = 3 to 3.5 and the system i n unsteady-state, the pH of the aqueous phase i n the CFSTR increases and then attains a steady-state value i n the range 5 to 6. Starting with an aqueous su l f u r dioxide s o l u t i o n of a fi x e d concentration and pH, when the Na/SC^ r a t i o entering the reactor i s increased (or the concentration of sodium i n fresh amalgam i s increased) , the steady-state pH of•< the aqueous phase i n the reactor also increases. ( i i ) Concentration of sodium d i t h i o n i t e i n the product stream and concentration of sodium i n spent amalgam For the following presentation 'M1 has been defined as the Na/SC^ r a t i o , for a set of experimental runs, at which maximum steady-state concentration of sodium d i t h i o n i t e i s obtained i n the product stream. The concentration of sodium d i t h i o n i t e i n the product stream versus time curves for two t y p i c a l sets, sets: 42-46 and 23-28, at various Na/SG^ r a t i o s entering the reactor are shown i n Figures 14 and 16 r e s p e c t i v e l y . The concen- t r a t i o n of sodium i n spent amalgam versus time curves f o r 114 these sets are shown i n Figures 15 and 17 r e s p e c t i v e l y . The l e v e l s of the d i f f e r e n t process v a r i a b l e s , under steady- state conditions, for these sets (42-46, 23-28) have been presented i n Tables 12 and 11 r e s p e c t i v e l y . At Na/S02 r a t i o s l e s s than M, for the experimental runs i n various sets including the sets: 42-46 and 23-28 (Figures 14 and 16), the concentration of sodium d i t h i o n i t e i n the product stream from the reactor increases with time and then attains a steady-state value. Figures 15 and 17 show that the concentration of sodium i n the spent amalgam decreases and also attains a steady-state value. At Na/SG^ r a t i o s above M, as can be seen from Figures 14 to 17, transient maxima (for sodium d i t h i o n i t e ) and minima (for sodium i n spent amalgam) are observed i n the unsteady-state concentra- t i o n p r o f i l e s . However, no such maximum i n pH i s observed on the pH versus time curves i n t h i s region. A better understanding of t h i s phenomenon i s obtained by examining the curve for concentration of sodium d i t h i o n i t e i n the product stream versus time (Figure 18) and the concen- t r a t i o n of sodium i n spent amalgam versus time curve (Figure 19) for the experimental runs i n the set: 65-77. The steady-state experimental conditions for t h i s set have been presented i n Table 6. As mentioned e a r l i e r , f o r t h i s set, M = 0.29. The experimental run 69 was done at a Na/SC^ r a t i o <0.29. The pH of the aqueous phase increased from 3.35 to 5.65 and as L_ I I I I I I i I 10 20 30 40 50 60 70 TIME ( min ) Figure 14 Concentrations of sodium d i t h i o n i t e i n the product stream versus time for runs i n the experimental set: 42-46. See Table 12 for the steady- state l e v e l s of the process v a r i a b l e s . See Tables F-XV to F-XIX for the unsteady-state r e s u l t s h J I I I I I l_ 10 20 30 40 50 60 70 TIME ( min) Figure 15 Concentrations of sodium i n amalgam leaving the CFSTR versus time for runs i n the experimental set: 42-46. See Table 12 for the steady-state l e v e l s of the process variables. See Tables F-XV to F-XIX for the unsteady-state r e s u l t s i 1 i 1 1 1 1 r TIME (min) Figure 16 Concentrations of sodium d i t h i o n i t e i n the product stream versus time for runs i n the experimental set: 23-28. See Table 11 for the steady- state l e v e l s of the process v a r i a b l e s . See Tables F-XX to F-XXV for the unsteady-state r e s u l t s RUN A - 23 0 - 28 • - 27 • - 24 A - 26 • - 25 Na/S02>M -A-A- = • 0 = 0 = •tQ= 1 1 -O Cr 30 40 50 60 TIME (min) 70 80 Figure 17 Concentrations of sodium i n amalgam leaving the CFSTR versus time for runs i n the experimental set: 23-28. See Table 11 for the steady-state l e v e l s of the process v a r i a b l e s . See Tables F-XX to F-XXV for the unsteady-state r e s u l t s RUN A -75 V -69 O -73 • -67 • -71 • -77 • - 65 1 Na/S0 2>M l _ 10 20 30 40 50 TIME (min) 60 70 Figure 18 Concentrations of sodium d i t h i o n i t e i n the product stream versus time for runs i n the experimental set: 65-77. See Table 6 for the steady- state l e v e l s of the process variables. See Tables F-XXVI to F-XXXII for the unsteady-state re s u l t s .A A A. RUN A - 75 ^ " 69 O - 73 • - 67 • - 71 A - 77 • -65 Na /S0 2>M L) '.Q—rrT^rCr—gfisQ l̂ rt 9 U V- 1 1 10 20 30 40 50 TIME (min) 60 70 Figure 19 Concentrations of sodium i n amalgam leaving the CFSTR versus time for runs i n the experimental set: 65-77. See Table 6 for the steady-state l e v e l s of the process vari a b l e s . See Tables F-XXVI to F-XXXII for the unsteady-state r e s u l t s 121 shown i n Figures 18 and 19 no maximum nor minimum i s observed i n the unsteady-state curves. The experimental run 73 was also done at a Na/S0 2 r a t i o <0.29/ however, the pH of the aqueous phase was fixed at about 5.8 during the unsteady-state as well as the steady-state periods. Again, no maximum nor minimum i s observed i n the unsteady-state concentration p r o f i l e s (Figures 18 and 19). The experimental run 65 was done at a Na/S0 2 r a t i o >0.29 and the pH of the aqueous phase increased from 3.53 to 6.0 at the steady-state. Figures 18 and 19 show that for th i s experimental run maximum and minimum are observed i n the unsteady-state curves. The experimental runs 71 and 77 were also done at Na/S0 2 r a t i o s >0.29, however, the pH of the aqueous phase was fi x e d at about 5.9 under the unsteady- state and the steady-state conditions. In these experimental runs, no maxima nor minima are observed i n the unsteady-state concentration p r o f i l e s (Figures 18 and 19). it >• 2. Concentration of t o t a l s u l f u r dioxide i n the aqueous feed s o l u t i o n To investigate the e f f e c t of v a r i a t i o n i n the concen- t r a t i o n of t o t a l s u l f u r dioxide i n the aqueous feed s o l u t i o n on the steady-state C„ , Y „ , Y.T , CONNA and X M at d i f f e r e n t Na/S0 2 r a t i o s entering the reactor, sets: 23-28, 65-77 and 4 2-46 were performed. The concentration of t o t a l s u l f u r dioxide i n these sets was about 0.4 molar, 0.65 molar and 1.30 molar r e s p e c t i v e l y . The l e v e l s of the other process variables for these sets, under steady-state conditions, are presented i n Tables 11, 6 and 12 r e s p e c t i v e l y . The steady-state C g Q , Y S Q , v N a , CONNA and X N a, for the sets: 2 4 2 23-28, 65-77 and 42-46, are plotted against the Na/S0 2 r a t i o s entering the reactor, i n Figures 20, 9 and 21 r e s p e c t i v e l y . (a) The v a r i a t i o n of steady-state sodium d i t h i o n i t e concen- t r a t i o n i n the product stream, C c , with change i n b2 u4 the concentration of s u l f u r dioxide i n the aqueous feed s o l u t i o n Figure 22 shows that the nature of the curves obtained by p l o t t i n g the steady-state concentration of sodium d i t h i o n i t e i n the product stream against the Na/S0 2 r a t i o s entering the reactor for sets: 23-28 and 4 2-46 was the same as f o r the set: 65-77, which has been discussed i n Section V . E . l . a . i . Figure 22 also shows that at a f i x e d Na/S0 2 r a t i o , when a l l of the other process variables are kept constant, an increase i n the concentration of t o t a l s u l f u r dioxide i n the aqueous feed s o l u t i o n increases the steady-state concentration of sodium d i t h i o n i t e i n the product stream. As the concentration of s u l f u r dioxide i n the aqueous feed for a l l of the experimental runs i n each set was f i x e d , the steady-state C c _ i s plotted against the concentration s2°4 of sodium i n fresh amalgam, CHGF, for the sets: 23-28, 65-77 123 •2 -3 -4 Na/S0 2 Figure 20 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SCu r a t i o entering the CFSTR for the experimental set: 23- 28. See Table 11 for the l e v e l s of the process variables 124 — m l)  — o o >^ d CM C O CM CM o >°° E CM O CM CO u - 19 - 2-4 — - 15 - 2-0 — - 11 - 1-6 — 7 - 1-2 — Figure 21 •2 -3 -4 Na/S0 2 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SO- r a t i o entering the CFSTR for the experimental set: 42- 46. See Table 12 for the l e v e l s of the process variables 125 T T 3-0 STS0 2 O- 1.30 MOLAR A-0-65 « • -0.40 " E 2-5 o o c5 2-o CM C O OJ CO E O ) 1-5 c? O 1-0- •5- 1 •3 -4 Na/S0 2 Figure 22 Steady-state sodium d i t h i o n i t e concentrations versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of su l f u r dioxide i n the aqueous feed. See Tables 6, 11 and 12 for the l e v e l s of the process variables 126 and 42-46. These curves are shown i n Figure 23. For the sets: 23-28, 65-77 and 42-46, the maximum steady-state concentration of sodium d i t h i o n i t e i n the product stream i s 0.385%, 0.89% and 2.3% at the CHGF values of 0.0303%, 0.064% and 0.1439% re s p e c t i v e l y . For the following presentation, the concentration of sodium i n fresh amalgam at which the maximum steady-state concentration of sodium d i t h i o n i t e was produced for a set of experimental runs, i s c a l l e d CHGF_ . Therefore, the CHGF ... , for the sets: 23-28, 65-77 and 42-46 are 0.0303%, 0.064% and 0.1439% r e s p e c t i v e l y . The CHGF ... i i s found to be l i n e a r l y r e l a t e d to c r i t i c a l 2 the molarity of s u l f u r dioxide i n the aqueous feed as shown i n Figure 24. The c o r r e l a t i o n shown i n Figure 24 could be very useful from the p r a c t i c a l point of view. If the con- centration of s u l f u r dioxide i n the aqueous feed solution i s known, the concentration of sodium i n the fresh amalgam at which the maximum concentration of sodium d i t h i o n i t e would be obtained, can be determined. (b) The v a r i a t i o n of steady-state values of Y g 0 , v N a / CONNA and X N a with change i n the concentration of sulfu r dioxide i n the aqueous feed s o l u t i o n The trend of the steady-state Y _ versus Na/S0 o, Y N a versus Na/S0 2, CONNA versus Na/S02 and X N a versus Na/S0 2 curves for the sets: 23-28 and 4 2-46 i s the same as that of the corresponding curves for the set: 65-77. These 127 1 1 1 1 S T S 0 2 O - 1.30 M O L A R I I I I I I •05 -10 -15 -20 CHGF (gmNa/100gm Amalgam) Figure 2 3 Steady-state sodium d i t h i o n i t e concentrations versus concentrations of sodium i n amalgam entering the CFSTR at d i f f e r e n t concentrations of s u l f u r dioxide i n the aqueous feed. See Tables 6 , 1 1 and 12 for the l e v e l s of the process variables 128 E cc co £ < £ o o CO £ D) CO (J CD X o •3 -6 -9 1-2 CONC.OF S0 2 (gmmole/liter) Figure 24 C r i t i c a l concentrations of sodium i n amalgam entering the CFSTR versus molarity of su l f u r dioxide i n the aqueous solutions entering the CFSTR. See Tables 6, 11 and 12 for the l e v e l s of the process variables 129 31 27 23 STS02 O - L 3 0 MOLAR A -0.65 " • -0-40 -3 -4 Na/S0 2 Figure 25 Steady-state y i e l d s of sodium d i t h i o n i t e on su l f u r dioxide i n the aqueous feed versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t concen- tr a t i o n s of su l f u r dioxide i n the aqueous feed. See Tables 6, 11 and 12 for the le v e l s of the process variables 1 3 0 •2 -3 -4 -5 Na/S0 2 Figure 26 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of su l f u r dioxide i n the aqueous feed. See Tables 6, 11 and 12 for the l e v e l s of the process variables 131 Na/S0 2 Figure 27 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/SC>2 ra t i o s entering the CFSTR at d i f f e r e n t concen- tr a t i o n s of su l f u r dioxide i n the aqueous feed. See Tables 6, 11 and 12 for the l e v e l s of the process variables 132 X 70 6 0 5 0 40 1 STS0 2 O - 1.30 MOLAR A - 0.65 " • — 0-40 // 1 •3 -4 Na/S0 2 Figure 28 Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t concentrations of s u l f u r dioxide i n the aqueous feed. See Tables 6, 11 and 12 for the le v e l s of the process variables 133 curves for the sets under consideration are shown i n Figures 25 to 28 re s p e c t i v e l y . Figures 25 to 27 show that at a fixed Na/SC^ r a t i o entering the reactor, when a l l of the other process variables are kept constant, an increase i n the concentration of s u l f u r dioxide i n the feed solution increased the steady-state y i e l d of sodium d i t h i o n i t e on t o t a l s u l f u r dioxide entering the reactor ( v s 0 )/ the steady-state y i e l d of sodium d i t h i o n i t e 2 on sodium entering the reactor with fresh amalgam ( Y N a) a n ^ the steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (CONNA). Figure 28 shows that at r e l a t i v e l y low values of Na/S02 r a t i o entering the reactor, an increase i n the concen- t r a t i o n of s u l f u r dioxide i n the feed s o l u t i o n does not a f f e c t the steady-state conversion of sodium to d i f f e r e n t products i n the reactor, X N a, appreciably (considering the 95% error l i m i t s ) . However, at r e l a t i v e l y high values of Na/S02 r a t i o entering the reactor, an increase i n the concen- t r a t i o n of s u l f u r dioxide i n the feed s o l u t i o n increases the steady-state values of X N a s i g n i f i c a n t l y . 3. A g i t a t i o n i n the aqueous phase Before describing the experimental work i n d e t a i l i t should be pointed out that there were some d i f f i c u l t i e s which influenced the choice of lower and upper l i m i t s on 134 degree of a g i t a t i o n i n the aqueous phase. Below a s t i r r e r Reynolds No.= 1 0 , 0 0 0 (corresponding to the pr o p e l l e r rpm of 376),the r e s u l t s obtained from the laboratory i n v e s t i g a t i o n could not be used i n making estimations using scale-up methods (84-88, 1 0 3 ) . On the other hand when the rpm of the propeller was well above 7 0 0 , a substantial a g i t a t i o n was imparted to the amalgam phase causing r i p p l e s . Some preliminary experiments were performed to assess the e f f e c t s of a g i t a t i o n but they d i d not y i e l d any useful information. A short account of these experiments follows. The reactor was f i l l e d up to the lower end of the b a f f l e s with an amalgam of a known sodium concentration. Then, known volumes of a s u l f u r dioxide sol u t i o n of a known concentration and a Rubine-R so l u t i o n of a known normality were added to the reactor and the a g i t a t i o n i n the aqueous phase was started. The rpm of the propeller was varied through the range of 110 to 7 00 for the d i f f e r e n t experi- ments and the times taken for the Rubine-R colour to disappear were compared. These experiments did not provide very useful data, since even for large volumes of Rubine-R (the dye solution available was very d i l u t e ) , the colour disappeared almost immediately. Informative r e s u l t s were obtained when the e f f e c t of a g i t a t i o n i n the aqueous phase of the CFSTR, on the steady- state C G n , Y n , Y , CONNA and X. was investigated. During the sets: 65-77 and 47-57, the rpm of the propeller i n the aqueous phase was kept fixed at 673. The l e v e l s of the other process va r i a b l e s , under steady-state conditions, are presented i n Tables 6 and 5 respectively and the steady- state C_ ~ versus Na/S0 o, Y c r i versus Na/SO~, Y T versus ^2 4 2 wa Na/SC^/ CONNA versus Na/S02 and X N a versus Na/S02 curves are shown i n Figure 7. The experimental sets: 66-76, 62-63 and 87-91 were performed at an rpm of 225 and the steady-state C c _ versus Na/SO», Ycr. versus Na/S0 o, Y versus "2 4 2 Na/S0 2f CONNA versus Na/S0 2 and X N a versus Na/S0 2 curves are shown i n Figure 8. For these sets, the l e v e l s of a l l of the other process variables were the same as for the sets: 65-77 and 45-57 as shown i n Table 7 to 9. S i m i l a r l y , the experimental set: 86-90 (expts. 86, 88 and 90) was performed at an rpm of 110. The steady-state C_ , Y o r i , Y„. , CONNA •̂2 4 2 i^a and X„ were calculated at the three Na/SO,, r a t i o s and the Na ' 2 r e s u l t s are shown i n Figure 29. As there were only three points for each calculated quantity, only broken l i n e curves are drawn. The l e v e l s of the process v a r i a b l e s , under the steady-state conditions for the set: 8 6-9 0 are presented i n Table 13. Pr i o r to presenting the r e s u l t s , i t should be mentioned that a few experiments were c a r r i e d out i n the experimental TABLE 13 LEVELS OF THE PROCESS VARIABLES IN SET: 86-90 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF STS0 2 . ( R P M>Aq FLS0 2 FLHG ( W ) A q TEMP PH .0372 - .0986 .655 -.658 110 .096 47.5 .0784 17 5.35 - 5.8 TABLE 14 LEVELS OF THE PROCESS VARIABLES IN SET: 94-104 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF STS0 2 (RPM) A g FLSO 2 FLHG ( A / v ) A q TEMP pH .0280 - .0912 .652 -.660 673 .066 47.5 .0784 17 5.75 - 6.1 LO 137 I 1 I I I I I L_ •2 -3 -4 -5 Na/S0 2 Figure 29 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SG^ r a t i o s entering the CFSTR for the experimental set: 8 6- 90. See Table 13 for the l e v e l s of the process variables 138 reactor to ensure that the conditions of perfect mixing existed at the d i f f e r e n t l e v e l s of a g i t a t i o n . Johnson (41) ca r r i e d out tracer studies i n the experimental reactor under the conditions used i n the present i n v e s t i g a t i o n . Using the Cholette and C l o u t i e r model (15) f o r the CFSTR h i s r e s u l t s showed that, under the s p e c i f i e d experimental conditions, perfect mixing occurred i n the reactor. The curves obtained by p l o t t i n g the steady-state Cg Q versus Na/S0 2, Y g 0 versus Na/S0 2, Y^ v e r s u s Na/S02,CONNA versus Na/S0 2 and X^versus Na/S0 2 at three d i f f e r e n t l e v e l s of ag i t a t i o n i n the aqueous phase are shown Figures 30 to 34 res p e c t i v e l y . Figures 30 to 33 show that at a fix e d Na/S0 2 r a t i o entering the reactor, when the l e v e l of a g i t a t i o n i n the aqueous phase was increased, the steady-state concentration of sodium d i t h i o n i t e i n the product stream (C_ n ), the y i e l d b2 u4 of sodium d i t h i o n i t e on t o t a l s u l f u r dioxide entering the reactor (Y c_ ), the y i e l d of sodium d i t h i o n i t e on sodium entering the reactor with the fresh amalgam ( Y N a) a n d t n e y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (CONNA) also increased. However, the percentage increase i n the steady-state C c _ , Ycr. , Y M and CONNA at values of 2 4 2 Na/S0 2 r a t i o below the steady-state Na 2S 20 4 concentration maximum ( i . e . at the Na/S0 2 r a t i o s <0.29) i s les s than the percentage increase i n these values at Na/S0 2 r a t i o above the steady-state sodium d i t h i o n i t e concentration maximum ( i . e . , at the Na/S0 2 r a t i o s >0.29). Figure 34 shows that at 139 ^ 2-4 E o ? 2-0 c? 1-6 CvJ CO E C? CN CO O 1-2 •8 R P M ) Aq • • - 673 - 2 2 5 - 110 1 1 •3 -4 Na/S02 Figure 30 Steady-state sodium d i t h i o n i t e concentrations versus Na/SC^ r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed. See Tables 5-9 and 13 for the l e v e l s of the process variables 140 2 7 - 2 3 CN o 19 15 11 ( R P M ) A q • • • - 673 - 225 - 1 1 0 1 1 •3 -4 Na/S0 2 Figure 31 Steady-state y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed versus Na/SO- r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed. See Tables 5-9 and 13 for the l e v e l s of the process variables 141 J I I L •2 -3 -4 -5 Na/S0 2 Figure 32 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed. See Tables 5-9 and 13 for the l e v e l s of the process variables 142 •2 -3 -4 -5 Na/S0 2 Figure 33 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed. See Tables 5-9 and 13 for the l e v e l s of the process variables 143 co X Figure 34 Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/SC>2 r a t i o s entering the CFSTR at d i f f e r e n t l e v e l s of a g i t a t i o n i n the aqueous feed. See Tables 5-9 and 13 for the l e v e l s of the process variables 144 Na/S0 2ratios <0.29, the steady-state conversion of sodium to d i f f e r e n t products i n the reactor ( x N a) does not change appreciably, however, at Na/S0 2 r a t i o s >0.29, the steady- state X N a values increase s i g n i f i c a n t l y with increase i n the l e v e l of a g i t a t i o n . 4. Flow rate of aqueous s u l f u r dioxide s o l u t i o n , i . e . residence time i n the aqueous phase The e f f e c t of v a r i a t i o n i n the flow rate of the aqueous s u l f u r dioxide s o l u t i o n on the steady-state C n , Y_rt , 2 4 b 2 YNa' C 0 N N A a n c ^ XNa' a t v a r ^ - o u s Na/S0 2 r a t i o s entering the reactor, was investigated i n the experimental sets: 94-104 (expts. 94, 96, 98, 100, 102 and 104), 65-77 and 95-105. The flow rates of the aqueous s o l u t i o n i n these sets were 66 ml/min, 96 ml/min and 198 ml/min r e s p e c t i v e l y . The l e v e l s of the other process v a r i a b l e s , under the steady-state conditions, have been reported i n Tables 14, 6 and 10 res p e c t i v e l y . The steady-state C_ _ , Ye_ , Y M , CONNA and &2^4 2 ™a X N a, for the sets: 94-104, 65-77 and 95-105, are plotted against the Na/S02 r a t i o s entering the reactor i n Figures 35, 9 and 36 re s p e c t i v e l y . The curves obtained by p l o t t i n g the steady-state Cg 0 versus Na/S0 2, Y g 0 versus Na/S0 2, Y^ a versus Na/S0 2, CONNA versus Na/S0 2 and X N a versus Na/S0 2 at the three d i f f e r e n t flow rates of the aqueous s u l f u r dioxide s o l u t i o n are shown i n Figures 37 to 41 re s p e c t i v e l y . 145 90h 3 -4 Na/S0 2 Figure 35 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SC>2 r a t i o s entering the CFSTR for the experimental set: 94- 104. See Table 14 for the l e v e l s of the process variables 14 6 2 -3 Na/S02 Figure 36 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SC>2 r a t i o s entering the CFSTR for the experimental set: 95- 105. See Table 10 for the l e v e l s of the process variables 147 Figure 37 Steady-state sodium d i t h i o n i t e concentrations versus Na/SC>2 r a t i o s entering the CFSTR at d i f f e r e n t flow rates of the aqueous feed. See Tables 6, 10 and 14 for the l e v e l s of the process variables 148 i ~ i 1 1 r FLSG-2 A / _ J I I I I L •1 -2 -3 -4 -5 -6 Na/S02 F i g u r e 38 S t e a d y - s t a t e y i e l d s o f sodium d i t h i o n i t e on s u l f u r d i o x i d e i n the aqueous feed v e r s u s Na/SC»2 r a t i o s e n t e r i n g the CFSTR a t d i f f e r e n t flow r a t e s of the aqueous f e e d . See T a b l e s 6, 10 and 14 f o r the l e v e l s o f the p r o c e s s v a r i a b l e s 149 co 70 60 50 40 30 20 F L S O 2 • - . 0 6 6 LIT / M I N O — . 0 9 6 1* A - . 1 9 8 // •3 -4 Na/S0 2 Figure 39 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t flow rates of the aqueous feed. See Tables 6, 10 and 14 for the l e v e l s of the process variables 150 •3 -4 Na/S0 2 Figure 40 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t flow rates of the aqueous feed. See Tables 6, 10 and 14 for the l e v e l s of the process variables 151 § 7 0 X 6 0 5 0 FLS0 2 • - .066 LIT/MIN O - .096 • - .198 1 1 1 •3 - 4 - 5 Na/S0 2 Figure 41 Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t flow rates of the aqueous feed. See Tables 6, 10 and 14 for the l e v e l s of the process variables 152 Figure 37 shows that at a l l of the values of Na/S0 2 r a t i o considered, the steady-state concentration of sodium d i t h i o n i t e i n the product stream, C c n , increases when the h2u4 flow rate of the aqueous su l f u r dioxide s o l u t i o n i s decreased ( i . e . , when the residence time i n the aqueous phase i s increased). Similar behaviour i s observed when the steady- state values of Y g 0 (yields of sodium d i t h i o n i t e on t o t a l 2 su l f u r dioxide entering the reactor) are plotted against the Na/SC^ r a t i o s entering the reactor at the three l e v e l s of the flow rate (Figure 38). Figure 39 shows that at low as well as high Na/S0 2 r a t i o s , the percentage of sodium that i s converted to sodium d i t h i o n i t e under steady-state conditions, CONNA, increases when the flow rate of the aqueous feed s o l u t i o n i s decreased. The trend of the curves obtained by p l o t t i n g the steady-state y i e l d s of sodium d i t h i o n i t e on sodium entering the reactor (Y N a) against the Na/S0 2 r a t i o s at the three l e v e l s of the flow rate was s i m i l a r . Figure 41 shows that at values of the Na/S0 2 r a t i o below the steady-state sodium d i t h i o n i t e concentration maximum ( i . e . , at the Na/S0 2 r a t i o s <0.29), the steady-state conversion of sodium to d i f f e r e n t products i n the reactor (X N a) decreased when the flow rate of the aqueous s u l f u r dioxide feed was reduced. But at Na/S0 2 r a t i o s >0.29 the steady-state values of X^ a did not change appreciably with change i n flow r a t e . 153 The geometry of the reactor was such t h a t the aqueous su l f u r dioxide s o l u t i o n entered the reactor through a 1/4 inch s t a i n l e s s - s t e e l tube, the mouth of which was situated approximately 2 inches above the amalgam surface. Therefore, i t was suspected that an increase i n the flow rate of the aqueous solut i o n would impart greater turbulence to the amalgam phase. To investigate t h i s a colour tracer was introduced i n the i n l e t aqueous s o l u t i o n . Despite the f a c t that the propeller was placed d i r e c t l y below the mouth of the tube which brought the aqueous so l u t i o n to the reactor, i t was observed that, at the rpm under consideration, the stream of the i n l e t aqueous so l u t i o n did not break completely by the mixer and i t impinged on the amalgam surface. 5. Interfacial-area/aqueous-volume r a t i o To investigate t h i s process v a r i a b l e , the volume of the aqueous phase was not changed from 980 ml. The i n t e r - f a c i a l area was changed, as mentioned i n Section IV.B.l, by opening the bottom flange of the reactor and introducing t h i n s t a i n l e s s - s t e e l discs with variable diameter annular holes. In the experimental sets: 65-77, 122-134 (expts. 122, 125,128,131 and 134) and 123-135 (expts. 123,129,132 and 2 2 135) the area of the i n t e r f a c e was 76.8 cm , 24.2 cm and 2 9.35 cm r e s p e c t i v e l y . These areas corresponded to i n t e r - 154 2 3 facial-area/aqueous-volume r a t i o s of .0784 cm /cm , •0247 2 3 2 3 cm /cm and .0095 cm /cm r e s p e c t i v e l y . The l e v e l s of the other process v a r i a b l e s , under the steady-state conditions are presented i n Tables 6, 15 and 16 . The steady-state C o n ' Ycr> ' Y M ' CONNA and X._ , f o r the sets: 65-7 7, 122- 2 4 2 134 and 123-135, are plotted against the Na/S02 r a t i o s entering the reactor i n Figures 9, 4 2 and 43 r e s p e c t i v e l y . The curves obtained by p l o t t i n g the steady-state C g Q versus Na / S 0 2 , Y versus Na / S 0 2 , Y N a versus Na / S 0 2 , 2 4 2 CONNA versus Na / S 0 2 and X N a versus Na / S 0 2 at the three interfacial-area/aqueous-volume r a t i o s are shown i n Figures 44 to 48 r e s p e c t i v e l y . Figures 44 to 4 8 show that, at a fix e d Na / S 0 2 r a t i o entering the reactor, when the interfacial-area/aqueous- volume r a t i o increases, the values of steady-state C n , fa2u4 Y„_ , Y.T , CONNA and X X T also increase. S 0 2 Na Na Figure 49 shows that when the values of steady-state concentration of sodium d i t h i o n i t e i n the product stream (C n ) or the y i e l d of sodium d i t h i o n i t e on s u l f u r dioxide S 2 ° 4 entering the reactor ( v s 0 ) are plotted against the i n t e r - 2 facial-area/aqueous-volume r a t i o s , at d i f f e r e n t Na / S 0 2 r a t i o s , s t r a i g h t l i n e r e l a t i o n s h i p s are not obtained. One of the major problems i n in v e s t i g a t i n g the process variable under consideration was the following. Every time a s t a i n l e s s - s t e e l d i s c was forced into p o s i t i o n to change the interfacial-area/aqueous-volume r a t i o , i t TABLE 15 LEVELS OF THE PROCESS VARIABLES IN SET: 122-134 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF STS0 2 (RPM) A q FLS0 2 FLHG (A/V) A q TEMP pH .0488 - .1238 .658 -.664 673 .096 47.5 .0247 17 5.7 - 5.95 TABLE"16 LEVELS OF THE PROCESS VARIABLES IN SET: 123-135 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF STS0 2 (RPM) A q FLS0 2 FLHG < W ) A q TEMP pH .0488 - .0879 .658 -.664 673 .096 47.5 .0095 17 5.65 - 5.8 156 •2 - 3 - 4 - 5 N a / S 6 2 Figure 42 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SC>2 r a t i o s entering the CFSTR for the experimental set: 122- 134. See Table 15 for the l e v e l s of the process variables 157 9 0 8 0 70 * 6 0 5 0 4 0 3 0 2 0 10 — m l)  — /i nn  / lU U  cf C\J CO fN o £ <3 CM CO o - 19 - 15 - 1-2 — - 11 - -8 — 7 - -4 — •3 -4 Na/S0 2 Figure 43 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and various y i e l d s versus Na/SC-2 r a t i o s entering the CFSTR for the experimental set: 12 3- 135. See Table 16 for the l e v e l s of the process variables 158 2-1 £ o o 1-8 o 1-5 CM CO CM Na  1-2 E •9 o CM CO •6 o — i 1 l A / V l A q • - .0784 CM2/CM3 O - .0247 // A - .0095 ** 1 1 3 -4 -5 Na/S0 2 Figure 44 Steady-state sodium d i t h i o n i t e concentrations versus Na/SO- r a t i o s entering the CFSTR at d i f f e r e n t values of interfacial-area/aqueous- volume r a t i o . See Tables 6, 15 and 16 for the le v e l s of the process variables 159 I 1 1 1 — 2 7 h ( A / v ) A q • - .0784 CM2/CM3 O - .0247 " 23| A — .0095 » V P 19 Figure 45 Steady-state y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t values or i n t e r - facial-area/aqueous-volume r a t i o . See Tables 6, 15 and 16 for the l e v e l s of the process variables 160 T V P 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 I , A / v ) A q • - .0784 CM2/CM3 O- .0247 » A — .0095 » \ I I 3 - 4 Na/S0 2 Figure 46 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium i n the amalgam entering the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t values of interfacial-area/aqueous-volume r a t i o . See Tables 6, 15 and 16 for the l e v e l s of the process variables 161 • - .0784 CM 2/CM 3 O - .0247 " I 1 I I I I •2 - 3 - 4 ' 5 N a / S 0 2 Figure 47 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/SC>2 ra t i o s entering the CFSTR at d i f f e r e n t values of interfacial-area/aqueous-volume r a t i o . See Tables 6, 15 and 16 for the l e v e l s of the process variables 162 9 0 8 0 < 3 * 7 0 2 6 0 X 5 0 4 0 3 0 o • U/v)Aq - -0784 C M 2 / C M 3 - .0247 - .0095 » 1 3 - 4 N a / S 0 2 Figure 48 Steady-state conversions of sodium to d i f f e r e n t products i n the CFSTR versus Na/S0 2 r a t i o s entering the CFSTR at d i f f e r e n t values of inter- facial-area/aqueous-volume r a t i o . See Tables 6, 15 and 16 for the l e v e l s of the process variables 163 (A/V) 'Aq Figure 49 Steady-state values of sodium d i t h i o n i t e concen- t r a t i o n and y i e l d of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed versus i n t e r f a c i a l - area/aqueous-volume r a t i o s at d i f f e r e n t Na/S02 r a t i o s entering the CFSTR. See Tables 6, 15 and 16 for the l e v e l s of the process variables 164 was found d i f f i c u l t to p o s i t i o n i t exactly h o r i z o n t a l . In other words, the interfacial-area/aqueous-volume r a t i o reported may have been le s s than the actual i n t e r f a c i a l - a r e a / aqueous-volume r a t i o . This problem could be avoided by using separate reactors with d i f f e r e n t i n t e r f a c i a l - a r e a / aqueous-volume r a t i o s . However, t h i s was not done i n the present i n v e s t i g a t i o n . 6. Temperature of the aqueous phase The experimental sets: 106-118 (expts. 106, 109, 112, 115 and 118), 65-77 and 110-113 (expts. 110 and 113) were performed to investigate the e f f e c t of v a r i a t i o n i n the temperature of the aqueous phase on the steady-state y i e l d s of sodium d i t h i o n i t e based on the s u l f u r dioxide entering the reactor (Yg 0 ) and on the sodium consumed i n the reactor (CONNA). The steady-state temperature of the aqueous phase i n the reactor, for the sets: 106-118, 65-77 and 110-113, was 13°C, 17°C and 27°C r e s p e c t i v e l y . Lower temperatures could not be obtained due to the exothermic nature of the reactions. The l e v e l s of the process v a r i a b l e s , under the steady-state conditions are presented i n Tables 17, 6 and 18. The steady-state Y and CONNA values are plo t t e d b U 2 against the Na/S02 r a t i o s entering the reactor at the three temperatures of the aqueous phase. These curves are shown TABLE 17 LEVELS OF THE PROCESS VARIABLES IN SET: 106-118 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF STS0 2 (RPM) A q FLS0 2 FLHG < V v ) A q TEMP pH .0372 - .0951 .653 -.660 673 .096 47 .5 .0784 13 5.55 - 6.0 TABLE 18 LEVELS OF THE PROCESS VARIABLES IN SET: 110-113 Range of the Changed Variable VALUES OF THE FIXED VARIABLES CHGF STS0 2 (RPM) A q FLSO 2 FLHG ( V V ) A q TEMP pH .0372 - .0646 .653 . -.654 673 .096 47 .5 .0784 27 5.7 - 5.9 166 2 3 - 19 CM O 15 11 I I I I TEMP — • - 27 ° C — O - 17 »/ A - 13 » —— • 1 • \ ""~A^^O»«, I I I I •2 •3 •4 -5 Na/S02 Figure 50 Steady-state y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t steady-state temperatures of the aqueous phase. See Tables 6, 17 and 18 for the l e v e l s of the process variables 167 80 70 °N°60 < 5 0 z : o O 4 0 30 20 TEMP • - 2 7 ° O - 17 * - 13 1 1 •3 -4 Na/S0 2 Figure 51 Steady-state y i e l d s of sodium d i t h i o n i t e on sodium consumed i n the CFSTR versus Na/S02 r a t i o s entering the CFSTR at d i f f e r e n t steady- state temperatures of the aqueous phase. See Tables 6, 17 and 18 for the l e v e l s of the process variables 168 i n Figures 50 and 51 re s p e c t i v e l y . No curves are drawn f o r the set: 110-113 because there are only two experimental runs i n t h i s set. Figure 50 shows that f o r d i f f e r e n t experimental sets (carried out at d i f f e r e n t temperatures)/ the maximum i n the steady-state Y c n versus Na/S00 curves i s obtained at a Na/SC^ r a t i o of 0.29. This fig u r e also shows that there may be an optimum temperature at every Na/SG^ r a t i o entering the reactor, above which the steady-state Y o n would decrease. & ° 2 7. pH of the aqueous phase For a l l experimental runs discussed i n the previous sections, the steady-state pH of the aqueous phase was i n the recommended range (Section II.B.) of 5 to 6. To i n v e s t i - gate the e f f e c t of a v a r i a t i o n i n the pH, some exploratory experimental runs (expts. 1 to 11) were performed where the pH of the aqueous phase was i n the range 0.8 to 2.0. Various combinations of the other process variables were used i n these experimental runs. In a l l these cases, the y i e l d s of sodium d i t h i o n i t e on sulfu r dioxide entering the reactor were very small. 8. Flow rate of fresh amalgam, i . e . residence time i n the amalgam phase This process variable was not investigated systematically for the reasons outlined i n the Section V.B. 169 However, a few experimental runs (expts. 5 to 11) were performed which gave i n t e r e s t i n g r e s u l t s . When the flow rate of the fresh amalgam was increased such that the Na/SC^ r a t i o entering the reactor was very high (greater than 1), a white p r e c i p i t a t e of s u l f u r was obtained. I t was noted that for none of the experiments was the pH of the aqueous phase l e s s than 0.8. 170 CHAPTER VI DISCUSSION A. Model for the Reacting System i n the Proposed Process 1. Development of the model I t was mentioned i n Chapter III that Ketelaar (44) and Gerritsen (30) proposed models for the reacting system sodium-mercury amalgam and aqueous s u l f u r dioxide. According to Ketelaar's model, the o v e r a l l rate of sodium d i t h i o n i t e formation i s controlled by the rate of sodium mass-transfer to the amalgam-aqueous solut i o n i n t e r f a c e . Gerritsen's model does not take into consideration the heterogeneous decomposition of the d i t h i o n i t e formed at the i n t e r f a c e and assumes a very s i m p l i f i e d expression for the rate of the homogeneous de- composition of d i t h i o n i t e ( i . e . rate i s a function of the concentration of sodium d i t h i o n i t e i n the bulk). Both these models were found inadequate to describe the r e s u l t s presented (Chapter V). A model for the reacting system at a steady-state pH of 5 to 6 i s developed on the basis of the experimental r e s u l t s obtained i n t h i s work and the information a v a i l a b l e i n the l i t e r a t u r e . In the formulation of t h i s model i t was found necessary to consider the mass-transfer of d i f f e r e n t 171 reacting species i n the amalgam and aqueous phases along with the following chemical reactions: - The sodium d i t h i o n i t e formation reaction 2 Na + 2 HSO~ -> 2 Na + + S 20~ + 2 OH." . . . . (16) - The water reaction 2 Na + 2 H 20 -»• 2 NaOH + H 2 . . . . (17) - The heterogeneous decomposition of sodium d i t h i o n i t e Na Na _ Na S2°4 "*" S2°3 S n "* S . . . . (15) - The homogeneous decomposition of sodium d i t h i o n i t e 2 Na 2S 20 4 + H 20 2 NaHS03 + Na 2S 20 3 . . . . (11) Na 2S 20 4 + 2 NaHS03 -»• N a ^ O g + Na 2S0 3 + H 20 . . . . ( 1 2 ) The oxidation of sodium d i t h i o n i t e was eliminated by provid- ing an i n e r t atmosphere of N 2 i n the reactor system. The experimental r e s u l t s indicate that the production of sodium d i t h i o n i t e i n the amalgam process depends pr i m a r i l y upon the Na/S0 2 r a t i o entering the reactor which i s rel a t e d to the Na/S0 2 r a t i o i n the reacting system. The former was controlled i n the present i n v e s t i g a t i o n and w i l l be c a l l e d •Na/SO- r a t i o 1 henceforth. 172 In a l l CFSTR experimental sets, where the concen- t r a t i o n of sulfur dioxide i n the feed s o l u t i o n was about 0.65 molar, the steady-state concentration of sodium d i t h i o n i t e (C c n ), y i e l d of sodium d i t h i o n i t e on s u l f u r b2°4 dioxide entering the reactor (Y c r. ) and conversion of sodium fa°2 to d i f f e r e n t products i n the reactor (X N a) show a maximum at a Na/S0 2 r a t i o of about 0.29. However, thi s r a t i o changes when the concentration of s u l f u r dioxide i n the feed s o l u t i o n changes as shown i n Figures 22, 25 and 28. The s h i f t i n maxima i s probably due to the fac t that these quantities are plotted against the Na/S0 2 r a t i o s entering the reactor and not against the Na/S0 2 r a t i o s i n the bulk of the two phases. In any event, Figure 24 shows that i f the molarity of s u l f u r dioxide i n the aqueous feed s o l u t i o n i s known, the concentration of sodium i n the amalgam entering the reactor (therefore the Na/S0 2 r a t i o entering the reactor) at which maximum steady-state C c n , Y__ and X„ are obtained, 2 4 2 Na can be estimated. Further, the Na/S0 2 r a t i o of about 0.29 i s not a magic number and i t w i l l change, for instance, i f the l e v e l of turbulence i n the amalgam phase i s changed. At values of the Na/S0 2 r a t i o below the steady-state C maximum, for a l l experimental sets, the consumption rate of sodium to produce sodium d i t h i o n i t e and other products i s d i r e c t l y proportional to the Na/S0 2 r a t i o or to the concentration of sodium i n fresh amalgam. For a t y p i c a l set 173 t h i s i s shown i n Figures 11 and 12 r e s p e c t i v e l y . This r e s u l t implies that the o v e r a l l rate of S 2 0 4 formation i s lim i t e d by sodium mass-transfer rate to the in t e r f a c e i n the range vof Na/SC>2 r a t i o s under consideration. At values of the Na/S0 2 r a t i o above the steady-state sodium d i t h i o n i t e concentration maximum, for a l l experimental sets, the rate of sodium consumption i s no longer a l i n e a r function of the Na/S0 2 r a t i o (Figure 11) or concentration of sodium i n amalgam (Figure 12). This observation indicates that the mass-transfer of sodium to the in t e r f a c e i s no longer the l i m i t i n g step i n the d i t h i o n i t e formation process i n t h i s Na/S0 2 r a t i o range. The conclusions reached above are supported by evidence presented below which, i n some cases, also indicates that at values of Na/SO~ r a t i o above the steady-state C n maximum, - * b2 u4 the mass-transfer rate of b i s u l f i t e ions i n the aqueous phase controls the rate of d i t h i o n i t e formation. (a) Figure 34 shows that the steady-state conversion of sodium to d i f f e r e n t products i n the reactor (X N a) above a Na/S0 2 r a t i o of 0.29 i s increased s i g n i f i c a n t l y by i n - creased s t i r r i n g i n the aqueous phase while at Na/S0 2 r a t i o s below 0.29 the change i s i n s i g n i f i c a n t . Figure 30 shows that the rate of d i t h i o n i t e production above a Na/S0 2 r a t i o of 0.29 increased to a greater extent by increased a g i t a t i o n i n the aqueous phase than at values of the Na/SO- r a t i o 174 below 0.29. These r e s u l t s would be expected i f the sodium mass-transfer rate c o n t r o l l e d the d i t h i o n i t e formation at values of Na/SC^ r a t i o below 0.29 and i f mass-transfer rate of b i s u l f i t e ions c o n t r o l l e d at Na/SG^ r a t i o s greater than 0.29. (b) Figures 14 to 17 show that at values of Na/SC^ r a t i o above the steady-state C_ n maxima, the unsteady-state b2 U4 concentration p r o f i l e s of sodium d i t h i o n i t e i n the product stream and sodium i n the outlet-amalgam (spent amalgam) show maxima and minima re s p e c t i v e l y . However such maxima and minima are not observed at Na/SC^ r a t i o s below the steady- state C c n maxima. &2°4 I t was discussed i n Section II.F. that when su l f u r dioxide gas i s dissolved i n water, depending on the pH of the s o l u t i o n , i t can e x i s t i n the form of molecular s u l f u r dioxide, b i s u l f i t e ions or s u l f i t e ions. Assuming u n i t a c t i v i t y c o e f f i c i e n t s for the d i f f e r e n t i o n i c and molecular species that e x i s t when sulfu r dioxide gas i s dissolved i n water, i t was shown that most of the su l f u r dioxide i s availa b l e as b i s u l f i t e ions at a pH of about 4.5. Above thi s pH the concentration of s u l f i t e ions increases and the concentration of b i s u l f i t e ions decreases. S u l f i t e ions, as mentioned i n the previous sections, can not be reduced by sodium dissolved i n mercury to give d i t h i o n i t e . 175 When an experimental run s t a r t s , the rate of sodium d i t h i o n i t e formation increases, thus increasing the con- centration of d i t h i o n i t e i n the product stream. S t a r t i n g with the aqueous feed s o l u t i o n at pH = 3 to 3.5 and the system at unsteady-state the pH of the aqueous phase i n the CFSTR increases and then at t a i n s a steady-state value i n the range 5 to 6. At Na/S02 r a t i o s above the steady-state C c _ maximum, as the pH of the aqueous phase increases b2°4 above 4.5, the bulk concentration of the b i s u l f i t e ions i n the reactor decreases. This decreases the rate of sodium d i t h i o n i t e formation, thus lowering the concentration of sodium d i t h i o n i t e i n the product stream. As the same bulk concentration of the b i s u l f i t e ions i s not avail a b l e for d i t h i o n i t e formation, the concentration of sodium i n the spent amalgam increases and then attains a steady-state value. These maxima and minima are not seen at Na/S0 2 r a t i o s below the steady-state C _ maxima because the rate S2°4 of the sodium d i t h i o n i t e formation i s con t r o l l e d by the rate of mass-transfer of sodium from the bulk of the amalgam to the inte r f a c e and at a l l times there are s u f f i c i e n t b i s u l f i t e ions present at the interface for the re a c t i o n . Further confirmation of the explanation given above i s obtained from Figures 18 and 19. These figures show that for the experimental run 65 a maximum and a minimum are observed i n the curves obtained by p l o t t i n g the concentration 176 of sodium d i t h i o n i t e i n the product stream against time and the concentration of sodium i n spent amalgam against time res p e c t i v e l y . This experiment was done at a Na/SO^ r a t i o above 0.29 and the pH of the aqueous phase increased from 3.53 to 6.0. On the other hand the unsteady-state concen- t r a t i o n p r o f i l e s f o r the experimental runs 71 and 77 do not show any maxima or minima. These experiments were also done at values of Na/S02 r a t i o above 0.29, but the pH of the aqueous phase was fix e d at about 5.9 under the unsteady- state and steady-state conditions. (c) Figure 22 shows that throughout the range of Na/S02 r a t i o s investigated, when the concentration of s u l f u r dioxide i n the feed s o l u t i o n increases at a fixed Na/S02 r a t i o , the rate of sodium d i t h i o n i t e formation increases. Figure 28 shows that i n the range of r e l a t i v e l y low Na/S02 r a t i o s , when the concentration of su l f u r dioxide i s increased at a fix e d Na/S02 r a t i o , the steady-state conversion of sodium to d i f f e r e n t products i n the reactor (X N &) does not change s i g n i f i c a n t l y . However, i n the range of high Na/S02 r a t i o s , the steady-state X N a increases with molarity of su l f u r dioxide at a fix e d Na/S0 2 r a t i o . This indicates that at low Na/S02 r a t i o s although the chemical reaction rates of the sodium consuming reactions may increase, the rate of sodium consumption i s s t i l l l i m i t e d by the rate of mass-transfer of sodium to the i n t e r f a c e . This i s not true at high Na/S05 r a t i o s . (d) Figure 41 shows that the steady-state conversion of sodium to d i f f e r e n t products i n the reactor ( x N a) above a Na/SC>2 r a t i o of 0.29 i s not changed s i g n i f i c a n t l y by increasing the flow rate of the aqueous feed s o l u t i o n (shortening the residence time i n the aqueous phase). Similar behaviour i s expected at Na/SC^ r a t i o s below 0.29 i f the rate of sodium mass-transfer to the in t e r f a c e l i m i t s the rate of sodium consumption. However, Figure 41 shows that the steady-state X N a increases with increase i n the flow rate of the aqueous solu t i o n i n t h i s range of Na/SC^ r a t i o s . This observation i s consistent with the above- mentioned conclusions as explained below. During the experiments outlined i n Section V.E.4., i t was observed that an increase i n the flow rate of the aqueous solution increases the l e v e l of turbulence i n the amalgam phase. At low Na/SO^ r a t i o s , where the rate of sodium consumption i s li m i t e d by the rate of mass-transfer of sodium from the bulk of the amalgam phase to the in t e r f a c e , increased turbulence i n the amalgam phase would increase the rate of mass-transfer of sodium. At a fix e d Na/S02 r a t i o (for values of Na/S0 2 r a t i o below 0.29), t h i s increased sodium mass-transfer increases the steady-state X N a value. At values of Na/SC^ r a t i o s above 0.29, the steady-state conversion of sodium to d i f f e r e n t products i n the reactor (X. ) does not increase because the rate of 178 sodium consumption i s not cont r o l l e d by the rate of mass- transfer of sodium to the i n t e r f a c e . The nature of the response curves obtained during the study and shown i n Chapter V i s not only affected by the sodium mass-transfer and b i s u l f i t e mass-transfer but i s also strongly influenced by the chemical reactions taking place. Some of these reactions are l i s t e d at the s t a r t of this chapter (equations 16, 17, 15, 11 and 12). The r e l a t i v e importance of these reactions at d i f f e r e n t Na/S0 2 r a t i o s i s discussed below. (i) Na/S00 r a t i o s below the steady-state C c _ maximum A b2°4 Figures 12 and 13 show that at very low concentrations of sodium i n mercury (or the Na/SG^ ratios) no sodium i s consumed. However, as the Na/SC^ r a t i o entering the reactor i s increased, the rate of sodium consumption increases l i n e a r l y . This i s understandable because for a l l reactions of sodium-mercury amalgam with aqueous solutions, the oxidation p o t e n t i a l of sodium at the mercury/water i n t e r f a c e determines whether the reaction w i l l take place. At very small concentrations of sodium i n mercury, the oxidation p o t e n t i a l of sodium i s not s u f f i c i e n t to i n i t i a t e a r e a c t i o n . As the Na/SC^ r a t i o i s increased, the concentration of sodium i n amalgam required to i n i t i a t e d i f f e r e n t sodium- consuming reactions i s reached. 179 I t was concluded above that, i n the region under con- si d e r a t i o n , the rate of sodium consumption i s l i m i t e d by the sodium mass-transfer rate to the i n t e r f a c e . I f i t i s assumed that only the sodium d i t h i o n i t e formation reaction takes place i n t h i s region then a l l of the sodium consumed by the aqueous phase would be used to give sodium d i t h i o n i t e . Under those conditions, the rate of sodium d i t h i o n i t e f o r - mation would increase proportionately with an increase i n the rate of sodium consumption (therefore, with an increase i n the Na/S0 2 r a t i o ) . I f the above assumption were true and the values of steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (CONNA) were plotted against the Na/S0 2 r a t i o s , a s t r a i g h t l i n e with zero slope (CONNA = 100) would be expected. However, t h i s i s not the case as shown i n Figure 9. This figure shows the steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed (CONNA) for a t y p i c a l set of experimental runs. I t i s proposed that the steady-state CONNA i s less than 100 per cent due to the homogeneous decomposition of the d i t h i o n i t e i n the bulk of the aqueous phase and the heterogeneous decomposition of the d i t h i o n i t e , produced at the i n t e r f a c e , by the sodium transferred there. The rate of sodium consumption by the water reaction, under steady- state conditions, i s expected to be n e g l i g i b l e i n the range of Na/S0 2 r a t i o s below the steady-state C g Q maximum. The 180 i n f o r m a t i o n a v a i l a b l e i n the l i t e r a t u r e ( S e c t i o n II.G.2.) shows t h a t the water r e a c t i o n takes p l a c e a t the i n t e r f a c e but i t s r a t e , i n the pH range 4 to 10, i s not l i m i t e d by the m a s s - t r a n s f e r r a t e o f sodium to the i n t e r f a c e ; t h i s r a t e i s c o n t r o l l e d by the r a t e o f chemi c a l r e a c t i o n a t the i n t e r f a c e . On the b a s i s o f the ba t c h experiments and the i n f o r - mation a v a i l a b l e i n the l i t e r a t u r e ( S e c t i o n II.G.3.a.) homogeneous decomposition of sodium d i t h i o n i t e takes p l a c e as g i v e n by equations (11) and (12). The e m p i r i c a l e x p r e s s i o n f o r the r a t e of t h i s decomposition has been o u t l i n e d by Spencer (102). rhomo = k c [ S 2 0 = ] 1 t H S O - ] 1 [ S O = ] ° [ H + ] X [ S 2 0 = ] y . . . .(13) From the ex p e r i m e n t a l r e s u l t s i t i s concluded t h a t , i n the range of Na/S0 2 r a t i o s under c o n s i d e r a t i o n , e s s e n t i a l l y a l l o f the sodium t r a n s f e r r e d t o the i n t e r f a c e i s consumed by the sodium d i t h i o n i t e f o r m a t i o n r e a c t i o n and the h e t e r o - geneous decomposition o f d i t h i o n i t e . The r e s u l t s d i s c u s s e d below (a and 8) imply t h a t although the r a t e o f sodium consumption by these two r e a c t i o n s i s l i m i t e d by the sodium m a s s - t r a n s f e r r a t e to the i n t e r f a c e , the p r o d u c t d i s t r i b u t i o n depends on t h e i r r e l a t i v e r e a c t i o n r a t e s . 181 (a) Figures 25 and 27 show that i n the region under considera- t i o n , when the concentration of s u l f u r dioxide i n the aqueous feed solution i s increased at a fixed Na/S0 2 r a t i o , the steady-state y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide (Ycr. ) and on sodium consumed i n the reactor (CONNA) increase, b0 2 but the steady-state conversion of sodium i n the reactor (X N a) does not change s i g n i f i c a n t l y as shown i n Figure 29. These r e s u l t s indicate that at a fixed Na/S0 2 r a t i o , an increase i n the concentration of s u l f u r dioxide i n the aqueous feed causes a greater increase i n the rate of the sodium d i t h i o n i t e formation reaction than i n the rate of the hetero- geneous decomposition of the d i t h i o n i t e . ($) Figures 31 and 33 show that below a Na/S0 2 of about 0.29, the steady-state Y n and CONNA increase at a f i x e d Na/S0 0 r a t i o with an increase i n the l e v e l of a g i t a t i o n i n the aqueous phase. However, the increase i n the steady-state X N a at that Na/S02 r a t i o i s n e g l i g i b l e as shown i n Figure 35. These r e s u l t s indicate that i n the region under consideration, an increase i n the l e v e l of a g i t a t i o n i n the aqueous phase at a fixed Na/S0 2 r a t i o increases the rate of sodium d i t h i o n i t e formation more than the rate of the heterogeneous decomposition of the d i t h i o n i t e . (y) For a t y p i c a l experimental set the rate of the sodium d i t h i o n i t e formation reaction increases with increasing Na/S09 r a t i o s because i n the region under consideration 182 the rate depends on the sodium mass-transfer rate to the in t e r f a c e . The rate of the homogeneous decomposition of d i t h i o n i t e also increases because the concentrations of the $2°^ ions and the S2®~3 x o n s increase. However, i t i s doubt- f u l that the homogeneous decomposition of the d i t h i o n i t e alone would cause such a decrease i n the steady-state CONNA with increasing Na/S02 r a t i o as shown i n Figure 9. ( i i ) Na/SO- r a t i o s above the steady-state C c n maximum * £ >2 U4 I t was concluded e a r l i e r that i n t h i s region, the rate of sodium consumption i s not li m i t e d by the sodium mass-transfer rate to the i n t e r f a c e . Further, i t was con- cluded that the rate of the sodium d i t h i o n i t e formation reaction i s li m i t e d by b i s u l f i t e mass-transfer to the i n t e r - face . In other words, for an experimental set where the concentration of sulfu r dioxide i n the aqueous feed i s f i x e d , the rate of the sodium d i t h i o n i t e formation reaction i n - creases to a maximum value with increasing Na/S02 r a t i o s . An equation for the rate of homogeneous decomposition of the d i t h i o n i t e was given by Spencer (equation 13). This rate probably increases as the Na/S02 r a t i o i s increased above the value corresponding to a maximum steady-state concen- t r a t i o n of sodium d i t h i o n i t e i n the product stream. The increase i n the rate would be due to increase i n the con- centration of S>2®~?, i ° n s which are a product of the homogeneous and heterogeneous decomposition reactions. As the Na/SO~ 183 r a t i o i s further increased the rate of homogeneous decom- po s i t i o n i s expected to a t t a i n i t s maximum value because the concentration of d i t h i o n i t e i n the bulk of the aqueous phase decreases. This i s indicated by the gradual l e v e l l i n g o f f of the steady-state C c _ versus Na/S0o curves at high b2 u4 values of the Na/SO^ r a t i o for a l l of the experimental sets. The occurrence of the heterogeneous decomposition of the d i t h i o n i t e , at l e a s t at very high values of the Na/S0 2 r a t i o , i s indicated by the r e s u l t s presented i n sections V.A.3. and V.E.8. (in conjunction with Section V.A.2.). For none of the experimental runs outlined i n Section V.E.8. was the pH of the aqueous phase less than 0.8, so the s u l f u r could not have formed due to the auto-decomposition of sodium d i t h i o n i t e (see Section V.A.2.). Most probably, the s u l f u r was formed by the oxidation of the s u l f i d e ions by the s u l f u r dioxide present i n the aqueous phase. These s u l f i d e ions were formed by the heterogeneous decomposition of sodium d i t h i o n i t e at the interface (equation 3). In view of the occurrence of t h i s reaction at Na/SG^ r a t i o s below the steady-state C _ maximum and at very high Na/S0 o 2 4 r a t i o s , i t i s l o g i c a l to assume i t s presence i n the intermediate range of Na/SG^ r a t i o s . The experimental r e s u l t s tend to support t h i s . For a t y p i c a l experimental set, Figure 9 shows that the steady-state C decreases b2 U4 sharply when the Na/S02 r a t i o i s increased above 0.29 and then tends to l e v e l o f f . I t i s u n l i k e l y that the sharp f a l l i n the steady-state concentration of sodium d i t h i o n i t e i n the product stream (C ) i s caused by the homogeneous b2 U4 decomposition of the d i t h i o n i t e alone. These r e s u l t s also imply that the rate of heterogeneous decomposition of the d i t h i o n i t e , immediately above Na/S0 2 r a t i o of about 0.29, increases with an increase i n the Na/S0 2 r a t i o . This can happen i f the rate of t h i s reaction i s l i m i t e d by the rate of chemical reaction at the i n t e r f a c e . However, at very high Na/S09 r a t i o s the steady-state C _ versus Na/S0o z s2°4 r a t i o curve tends to l e v e l o f f implying that the rate of the heterogeneous decomposition also attains i t s maximum value. This suggests that the rate of t h i s reaction at very high Na/SC"2 r a t i o s i s con t r o l l e d by the removal rate of the S 2 0 4 ions from the i n t e r f a c e . The following discussion indicates that at values of Na/S09 r a t i o s above the steady-state C c ~ maximum, the z s 2 o 4 i n t e r f a c i a l concentration of sodium i n mercury required to i n i t i a t e the water reaction i s reached. (a) Figure 9 shows that the steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (CONNA) f a l l s very sharply at Na/S0 2 r a t i o s above 0.29; the f a l l i s gradual at very high Na/S0 2 r a t i o s . The sharp f a l l i n the steady-state CONNA i s observed because the rate of the sodium d i t h i o n i t e formation reaction does not change with an increase i n the Na/SO~ r a t i o but the rate of the water 185 reaction and the rates of the heterogeneous and homogeneous decomposition of the d i t h i o n i t e increase. Thus, an increas- ing proportion of the sodium transferred to the inte r f a c e i s used up by the water reaction and the heterogeneous decomposition of the d i t h i o n i t e . The decrease i n the steady- state CONNA i s more gradual at very high Na/S02 r a t i o s because the rates of the heterogeneous and homogeneous decomposition reactions depend upon S2Q~4 concentration and hence do not increase i n d e f i n i t e l y . (3) The curve obtained by p l o t t i n g the rate of sodium con- sumption against the concentration of sodium i n the fresh amalgam (CHGF) for an experimental set shows that at very high values of CHGF (or Na/S0 2 ratio) the rate of sodium consumption increases gradually with an increase i n CHGF. The general nature of th i s curve, i n the region under consideration, i s s i m i l a r to that expected for the water reaction as outlined by Dunning and K i l p a t r i c k (20) [Section II .G. 2 . ] . 2. The model At fixed l e v e l s of a l l the other process v a r i a b l e s , when the concentration of sodium i n the amalgam entering the reactor increases (the Na/S02 r a t^-° increases at a fixed conc.of SO2 i n the feed), the steady-state concentration of sodium d i t h i o n i t e i n the reactor passes through a 186 maximum. The processes occurring i n the reactor, at a steady-state pH of 5 to 6 and i n the i n e r t atmosphere of may be described as follows: Ca) Na/SO- r a t i o s below the steady-state C c _ maximum z fa2 4 At very small concentrations of sodium i n mercury (or low Na/S02 r a t i o s ) , the oxidation p o t e n t i a l of sodium i s not s u f f i c i e n t to i n i t i a t e any reaction. As the Na/SC^ r a t i o entering the reactor i s increased, the threshold concentration of sodium i n mercury required to i n i t i a t e the sodium d i t h i o n i t e formation reaction i s reached. Once the d i t h i o n i t e ions s t a r t forming at the in t e r f a c e , t h e i r heterogeneous and homogeneous decomposition also s t a r t . In the region under consideration the sodium d i t h i o n - i t e formation reaction and the heterogeneous decomposition of the d i t h i o n i t e are the important sodium consuming reactions. The rate of sodium consumption by these reactions i s l i m i t e d by the sodium mass-transfer rate to the in t e r f a c e , however, the product d i s t r i b u t i o n depends on th e i r r e l a t i v e reaction r a t e s . As the Na/S02 r a t i o increases towards the value corresponding to maximum steady-state sodium d i t h i o n i t e concentration (C_ _ ), the rate of mass-transfer of sodium S 2 ° 4 to the inte r f a c e increases which i n turn increases the rates of the sodium d i t h i o n i t e formation reaction and the hetero- 187 geneous decomposition of the d i t h i o n i t e . The r a t e o f homo- geneous decomposition of d i t h i o n i t e a l s o i n c r e a s e s [see eq u a t i o n 13 by Spencer (102)]. However, the i n c r e a s e i n the r a t e o f sodium d i t h i o n i t e f o r m a t i o n i s g r e a t e r than the i n c r e a s e i n the r a t e o f i t s decomposition. (b) Na/S0 o r a t i o s above the s t e a d y - s t a t e C c rt maximum z b 2 u 4 When the Na/SG^ r a t i o i s i n c r e a s e d above the v a l u e c o r r e s p o n d i n g to the s t e a d y - s t a t e C_ n maximum, the con- b 2 ° 4 c e n t r a t i o n o f sodium i n the amalgam i n t e r f a c e i n c r e a s e s and the t h r e s h o l d c o n c e n t r a t i o n o f sodium i n the mercury r e q u i r e d to i n i t i a t e the water r e a c t i o n i s reached. T h e r e f o r e , the sodium t r a n s f e r r e d to the i n t e r f a c e i s consumed by the sodium d i t h i o n i t e f o r m a t i o n r e a c t i o n , the heterogeneous decomposition o f the d i t h i o n i t e and the water r e a c t i o n . However, i n the r e g i o n under c o n s i d e r a t i o n the r a t e of sodium consumption by these r e a c t i o n s i s not l i m i t e d by the sodium m a s s - t r a n s f e r r a t e t o the i n t e r f a c e . The r a t e o f the sodium d i t h i o n i t e f o r m a t i o n r e a c t i o n i s l i m i t e d by the r a t e o f m a s s - t r a n s f e r o f b i s u l f i t e i o n s t o the i n t e r f a c e . T h i s r a t e does not change w i t h i n c r e a s i n g Na/S0 2 r a t i o . The r a t e o f the heterogeneous decomposition o f sodium d i t h i o n i t e i s c o n t r o l l e d by the r a t e o f ch e m i c a l r e a c t i o n a t the i n t e r f a c e and t h i s r a t e i n c r e a s e s w i t h i n c r e a s i n g Na/SO~ r a t i o . A t v e r y h i g h v a l u e s o f Na/SO- r a t i o the r a t e 188 of t h i s reaction becomes controlled by the removal rate of the S20 4 ions from the interface and tends to a t t a i n i t s maximum value. The rate of sodium consumption by the water reaction i s c o ntrolled by the rate of chemical reaction at the i n t e r f a c e . This rate can be given by the empirical expression (equation 10) derived by Dunning and K i l p a t r i c k (20). The rate increases with increasing Na/SO^ r a t i o . The rate of homogeneous decomposition of the d i t h i o n i t e may be given by Spencer's (102) expression shown i n equation 13. This rate increases with increasing Na/SG^ r a t i o . However, at very high values of the Na/SG^ r a t i o the rate of homogeneous decomposition tends to a t t a i n a maximum value. B. Conditions for Improving The Yields of Sodium D i t h i o n i t e In The Proposed Process I t was mentioned i n Chapter I that for the proposed process the steady-state y i e l d s of sodium d i t h i o n i t e on s u l f u r dioxide entering the reactor ( Y c n ) and on sodium consumed i n a single pass (CONNA) must be economical. The experimental r e s u l t s show that the conditions for the highest y i e l d on s u l f u r dioxide are d i f f e r e n t from the 189 conditions for the highest y i e l d on sodium consumed. There- fore, the r e l a t i v e costs of the reacting chemicals must be considered. Figure 10 shows the v a r i a t i o n of steady-state CONNA and Y c~ as a function of the concentration of sodium i n fresh amalgam fo r a t y p i c a l set of experimental runs where a l l the other process variables were kept f i x e d . This figure demonstrates that, for such an experimental set, the highest steady-state CONNA i s obtained at a concentration of sodium i n the amalgam where the steady-state Y c n i s r e l a t i v e l y small. Figures 25 and 27 show that at a fixed Na/S0 2 r a t i o entering the reactor, the steady-state y i e l d s on s u l f u r dioxide i n the feed and on sodium consumed i n a single pass increase with an increase i n the concentration of s u l f u r dioxide i n the feed. At a fixe d Na/S0 2 r a t i o , there may, however, be an optimum concentration of s u l f u r dioxide i n the aqueous feed sol u t i o n above which the steady-state Y e n £>u2 would decrease. There may be such an optimum concentration of s u l f u r dioxide for the steady-state CONNA a l s o . These concentrations could not be determined i n the present i n - v e s t i g a t i o n because an aqueous s u l f u r dioxide s o l u t i o n whose concentration i s su b s t a n t i a l l y greater than 1.30 molar would require p r e s s u r i z a t i o n of the reactor system. Figure 24 shows that when the concentration of su l f u r dioxide i n the aqueous feed i s increased, the concentration 190 of sodium i n the fresh amalgam at which maximum steady-state Y c n i s obtained i n a set of experimental runs ( c r i t i c a l CHGF) also increases. The c r i t i c a l concentration of sodium i n fresh amalgam f o r the experimental set performed at 1.30 molar s u l f u r dioxide i n the feed was about 0.14 39 per cent. The r e s u l t s show that the steady-state Y and CONNA under these conditions are higher than the steady-state values of these quantities, under c r i t i c a l conditions, at 0.65 molar er.0.4 molar s u l f u r dioxide. The c r i t i c a l CHGF would increase with a further increase i n the molarity of s u l f u r dioxide i n the aqueous feed and the steady-state Y and CONNA may also increase. These concentrations of sodium i n fresh amalgam are well outside the l i m i t s recommended for the sodium amalgam: S0 2 - NaHS0 3/Na 2S0 3 buffer process (Section II.B.) by previous i n v e s t i g a t o r s . This i s understandable, because the previous workers were pr i m a r i l y interested i n the y i e l d of sodium d i t h i o n i t e on sodium consumed. Figures 31 and 33 show that an increase i n the l e v e l of a g i t a t i o n i n the aqueous phase increases the desired y i e l d s . The increase i n the steady-state Y was found to b0 2 be greater at values of Na/S0 2 r a t i o above the steady-state Y g 0 maximum. For the reasons given i n Section V.E.3. the e f f e c t of a g i t a t i o n i n the aqueous phase could not be investigated e x c l u s i v e l y at propeller speeds above 700 rpm. 191 F i g u r e s 38 and 40 show the v a r i a t i o n i n the v a l u e s of s t e a d y - s t a t e Y _ and CONNA as a f u n c t i o n o f the flow r a t e s of the aqueous s o l u t i o n . The recommendation by p r e - v i o u s i n v e s t i g a t o r s t h a t the r e s i d e n c e time o f the aqueous s o l u t i o n i n the r e a c t o r should be as s h o r t as p o s s i b l e ( S e c t i o n II.B) d o e s not seem to be c o r r e c t . The model based on the exp e r i m e n t a l r e s u l t s suggests t h a t t h e r e would be an optimum r e s i d e n c e time i n the aqueous phase a t d i f f e r e n t Na/S0 2 r a t i o s below which the s t e a d y - s t a t e Y g 0 and CONNA may d e c r e a s e . F i g u r e s 45 and 4 7 show t h a t a t a f i x e d Na/S0 2 r a t i o e n t e r i n g the r e a c t o r , the s t e a d y - s t a t e y i e l d s o f sodium d i t h i o n i t e on s u l f u r d i o x i d e i n the feed ( Y c n ) and on b U 2 sodium consumed i n the r e a c t o r (CONNA) i n c r e a s e w i t h an i n c r e a s e i n the i n t e r f a c i a l - a r e a / a q u e o u s - v o l u m e r a t i o . F i g u r e 4 9 shows t h a t a t d i f f e r e n t Na/S0 2 r a t i o s i n v e s t i g a t e d t h i s r e l a t i o n s h i p i s n o n l i n e a r . The decrease i n the steady- s t a t e CONNA v a l u e s w i t h a decrease i n the i n t e r f a c i a l - a r e a / aqueous-volume r a t i o , a t a f i x e d Na/S0 2 r a t i o was unexpected. T h i s was probably caused by the manner i n which the e x p e r i - ments were conducted. The d i s c s which were i n t r o d u c e d to decrease the i n t e r f a c i a l - a r e a / a q u e o u s - v o l u m e r a t i o were o f a f i n i t e t h i c k n e s s . When they were i n t r o d u c e d , the l e v e l of t u r b u l e n c e i n the aqueous phase a t the i n t e r f a c e , where the sodium consuming r e a c t i o n s take p l a c e , decreased. That probably decreased the rate of sodium d i t h i o n i t e formation/ rate of the heterogeneous decomposition r a t i o . Figures 50 and 51 shows that at c e r t a i n Na/SOj r a t i o s entering the reactor an increase i n temperature increases the steady-state Y „ and CONNA. The experimental r e s u l t s suggest that there may be optimum temperatures at every Na/S02 r a t i o above which the steady-state Yg Q and CONNA w i l l decrease. For most of the experimental runs done i n t h i s i n - v e s t i g a t i o n , the steady-state pH of the aqueous phase was i n the range 5 to 6. This range has been recommended by previous investigators (Section II.B). Few experimental runs that were done at very low pH values (0.8 to 2.0) gave very poor y e i l d s . When the pH i s lowered, the rates of the homogeneous decomposition of the d i t h i o n i t e and the water reaction increase. The rate of the sodium d i t h i o n i t e formation reaction i s also expected to increase with l i m i t e d pH decrease because the e f f e c t i v e d i f f u s i v i t y of s u l f u r dioxide solutions i n the aqueous phase would increase as would the concentration of b i s u l f i t e ions. The model for the reacting system based on the experimental r e s u l t s suggests that at values of the Na/S02 r a t i o where the rate of sodium consumption i s l i m i t e d by the sodium mass-transfer rate, the steady-state Ycr. and b U 2 CONNA would increase with an increase i n the a g i t a t i o n in the amalgam phase. This information may be of a s p e c i a l 193 i n t e r e s t from the point of view of se l e c t i n g the operating conditions for the proposed process. I t was mentioned e a r l i e r that at r e l a t i v e l y low Na/SC^ r a t i o s , i n the region under consideration, the steady-state CONNA i s high but the steady-state Y c n i s low. Considering the fact that both of these y i e l d s a f f e c t the cost of the product, i t may be advantageous to increase the l e v e l of a g i t a t i o n i n the amalgam phase at r e l a t i v e l y low Na/S02 r a t i o s . At fixed l e v e l s of a l l the other process v a r i a b l e s i f the flow rate of the amalgam i s increased, the e f f e c t on the y i e l d s would be the same as i f the Na/S02 r a t i o and the a g i t a t i o n i n the amalgam phase had been increased. C. Economic F e a s i b i l i t y of the Proposed Process Experimental run 44 was chosen for costing. For th i s run, under the steady-state conditions, the concentra- t i o n of sodium d i t h i o n i t e i n the product stream, C S 2 0 4 =2.3 gms Na 2S 2O 4/100 ml the y i e l d of sodium d i t h i o n i t e on the t o t a l s u l f u r dioxide entering the reactor, Y S 0 2 = 20.4% the y i e l d of sodium d i t h i o n i t e on the sodium consumed i n the reactor, CONNA = 67% the y i e l d of sodium d i t h i o n i t e on sodium entering the reactor with the fresh amalgam YNa = 6 3 % the conversion of sodium from the amalgam to d i f f e r e n t products i n the reactor, X M = 95.1 % Na The l e v e l s of the process variables are presented i n the Table 19. TABLE 19 LEVELS OF THE PROCESS VARIABLES FOR THE RUN 44 CHGF .1439 s t s o 2 moles1 l i t , 1.297 (RPM) jrpmj Aq 673 FLSO. l i t min .096 FLHG ml min, 47.5 cm 3 cm , .0784 TEMP 17 PH 5.75 196 BASIS: 100 lb moles of t o t a l s u l f u r dioxide i n the aqueous feed. The o v e r a l l sodium d i t h i o n i t e formation i s : 2 Na + 2 SO„ + Na oS~0, 2 2 2 4 For every 100 lb moles of the t o t a l s u l f u r dioxide i n the feed, 20.4 lb moles are converted to give sodium d i t h i o n i t e . By stoichiometry, 20.4 lb moles of the su l f u r dioxide give = 1/2 x 20.4 = 10.2 lb moles of Na 2S 20 4. Further 10.2 lb moles of Na 2S 20 4 contains = 2 x 10.2 = 20.4 l b atoms of sodium. The y i e l d of sodium d i t h i o n i t e on sodium consumed = 67 per cent. * • • Tota l sodium consumed to give 10.2 lb moles of sodium 20.4 d i t h i o n i t e = = 30.45 l b atoms. 0.67 I t was shown i n Chapter I that, the cost of sodium i n the amalgam - 5<=/lb, and the cost of S0 2 gas - 1 .5$/lb © • • The chemical cost of sodium d i t h i o n i t e 100 x 64 x 1.5 + 30.45 x 23 x 5 10.2 x 174 = 7.4<:/lb of sodium d i t h i o n i t e The chemical cost of the d i t h i o n i t e ions produced by the 174 proposed process = 7.4 x - 10<r/lb S 2 0 4 197 A small correction could be made for the cost of caustic soda used to adjust the pH of the aqueous s u l f u r dioxide s o l u t i o n . The actual cost of sodium d i t h i o n i t e produced by the proposed process would be higher because i t would also include the c a p i t a l and operating costs. However, t h i s cost can be reduced by increasing the y i e l d s of Na^^O^ on s u l f u r dioxide entering the reactor and on sodium consumed i n the reactor which can be accomplished by changing the l e v e l s of c e r t a i n process variables as discussed i n the l a s t section. By comparison, zinc d i t h i o n i t e produced from zinc dust at 19<:/lb and s u l f u r dioxide at 1.5<r/lb, assuming 100% yi e l d s on both zinc and su l f u r dioxide, gives d i t h i o n i t e at a cost of about l l C / l b of S 2 0 4 ions for chemicals alone. The actual cost of ZnS 20 4 produced i n pulp m i l l s , considering lower y i e l d s , c a p i t a l and operating costs, i s approximately 16<Vlb of S2°4 i o n s ' Thus, i t seems economically f e a s i b l e for a pulp m i l l to change from zinc d i t h i o n i t e produced in s i t u to sodium d i t h i o n i t e produced by the proposed process without involving extra cost. A d d i t i o n a l advantages of the proposed process are that i t can run i n conjunction with Castner-Kellner type c e l l s and does not discharge zinc ions to the e f f l u e n t receiving waters. 198 D. Reactor for the Proposed Process The bench-scale experiments provide information on the type of reactor which would be suitable for the pro- posed process. The chosen reactor should be such that i t would be possible to have large interfacial-area/aqueous- volume r a t i o , high l e v e l of a g i t a t i o n i n the aqueous and amalgam phases and high concentration of s u l f u r dioxide i n the aqueous feed s o l u t i o n . The reactor used i n the present i n v e s t i g a t i o n (CFSTR) has the advantages that i t does not allow much entrainment of mercury i n the product stream and permits f a i r l y good control of the variables such as concentration of sodium i n the feed-amalgam, flow rates of the s u l f u r dioxide s o l u t i o n and the amalgam, temperature and pH. I t can be improved by redesigning i t so that i t has larger i n t e r f a c i a l - a r e a / aqueous-volume r a t i o . The l e v e l of a g i t a t i o n i n the amalgam phase can be increased by providing a s t i r r e r and b a f f l e s i n that phase and the concentration of s u l f u r dioxide i n the aqueous feed can be increased by pressurizing the reactor system. 199 CHAPTER VII CONCLUSIONS 1. I t i s possible to produce sodium d i t h i o n i t e as a r e l - a t i v e l y d i l u t e (approximately 1-2%) water s o l u t i o n from sodium-mercury amalgam and s u l f u r dioxide i n a simple "once-through" reactor [proposed process]. This solu t i o n could be used d i r e c t l y for the brightening of groundwood pulp. 2. The proposed process to produce sodium d i t h i o n i t e can economically compete with the manufacture of zinc d i t h i o n i t e in s i t u . 3. The reactor chosen for the proposed process should be such that i t would be possible to have large i n t e r f a c i a l - area/aqueous-volume r a t i o , high l e v e l of a g i t a t i o n i n the aqueous and amalgam phases and high concentration of s u l f u r dioxide i n the aqueous feed s o l u t i o n . Further, i t should permit good co n t r o l of the variables such as concentration of sodium i n the feed-amalgam, the flow rates of the s u l f u r dioxide s o l u t i o n and the amalgam, temperature and pH. 4. The models suggested by Ketelaar (44) and Gerritsen (30) are inadequate to explain the experimental r e s u l t s 200 obtained i n t h i s i n v e s t i g a t i o n . To formulate a model for the reacting system sodium-mercury amalgam and aqueous s u l f u r dioxide, at a steady-state pH of about 5 to 6 and i n the i n e r t atmosphere of N 2, i t i s necessary to consider mass-transfer of the reacting species i n the amalgam and aqueous phases along with the chemical reactions such as the sodium d i t h i o n i t e formation reaction, the homogeneous and heterogeneous decomposition of the d i t h i o n i t e and the water react i o n . 5. The production of sodium d i t h i o n i t e i n the proposed sodium amalgam process depends pr i m a r i l y upon the Na/S0 2 r a t i o s entering the reactor. At fixed l e v e l s of a l l the other process v a r i a b l e s , when the concentration of sodium i n the amalgam entering the reactor increases (the Na/S0 2 r a t i o entering the reactor increases at a fixed concentration of s u l f u r dioxide i n the aqueous feed s o l u t i o n ) , the steady-state values of the concen- t r a t i o n of sodium d i t h i o n i t e i n the reactor, the y i e l d of sodium d i t h i o n i t e on s u l f u r dioxide i n the aqueous feed and the conversion of sodium to d i f f e r e n t products i n the reactor pass through a maximum. The steady-state values of the y i e l d of sodium d i t h i o n i t e on sodium entering with the mercury and on sodium consumed i n the reactor decrease with increasing Na/SO- r a t i o . 201 6. At Na/SG^ r a t i o s below the steady-state sodium d i t h i o n i t e concentration maximum, the rate of sodium consumption i s l i m i t e d by the sodium mass-transfer rate to the i n t e r - face. At Na/S0 2 r a t i o s above the steady-state sodium d i t h i o n i t e concentration maximum, the rate of sodium consumption i s not li m i t e d by the sodium mass-transfer rate to the i n t e r f a c e . 7. At Na/S0 2 r a t i o s below the steady-state sodium d i t h i o n i t e concentration maximum, the rate of the sodium d i t h i o n i t e formation reaction i s cont r o l l e d by the rate of sodium mass-transfer to the in t e r f a c e , but at Na/S0 2 r a t i o s above the steady-state sodium d i t h i o n i t e concentration maximum, the rate of the sodium d i t h i o n i t e formation reaction i s controlled by the mass-transfer rate of b i - s u l f i t e ions to the i n t e r f a c e . 8. When the steady-state pH of the aqueous phase i n the reactor i s between 5 to 6, the proportion of sodium consumed by the water reaction i s small at Na/S0 2 r a t i o s below the steady-state sodium d i t h i o n i t e concentration maximum. 9. At Na/S0 2 r a t i o s below the steady-state sodium d i t h i o n i t e concentration maximum, the rate of the heterogeneous decomposition of the d i t h i o n i t e i s l i m i t e d by the sodium mass-transfer rate to the i n t e r f a c e . At Na/S00 r a t i o s 202 above the steady-state sodium d i t h i o n i t e concentration maximum, t h i s rate i s controlled by the chemical reaction at the i n t e r f a c e . However, at very high Na/S0 2 r a t i o s the rate of t h i s reaction i s co n t r o l l e d by the removal rate of the d i t h i o n i t e ions from the i n t e r f a c e . The auto-decomposition of the d i t h i o n i t e according to the equation, 2 H 2S 20 4 3 S0 2 + S + 2 H 20 , i n the pH range 0.8 to 6 i s n e g l i g i b l y small under the conditions of the present i n v e s t i g a t i o n . 203 CHAPTER VIII RECOMMENDATIONS FOR FURTHER WORK 1. The reactor used i n the present i n v e s t i g a t i o n (CFSTR) should be redesigned or another type of reactor should be chosen according to the guidelines given i n the discussion (Chapter VI). Then the proposed process should be optimized at a p i l o t - s c a l e . 2. Further studies should be conducted to elucidate the processes i n the reactor at lower values of pH (pH below 4 ) . 3. The mercury content of the product stream should be determined to see i f the product meets the p o l l u t i o n standards. If not, then the process should be modified along the l i n e s suggested i n Chapter 2. 4. I f possible, the k i n e t i c s of the sodium d i t h i o n i t e formation reaction and the heterogeneous decomposition of the d i t h i o n i t e should be investigated separately. 5. The e f f e c t of v a r i a t i o n i n the concentration of el e c t r o l y t e s used i n the proposed process on the rate of the water reaction should be investigated. 204 6. A quantitative expression should be determined for the rate of homogeneous decomposition of the d i t h i o n i t e . I t would be of sp e c i a l i n t e r e s t to know how t h i s rate i s qu a n t i t a t i v e l y affected by change i n the concentration of ̂ 2^3 ions. 7. The mean a c t i v i t y c o e f f i c i e n t s of the i o n i c species and a c t i v i t y c o e f f i c i e n t s of molecular species pre- sent i n the - Ĥ O system should be determined at high concentrations of SO- gas i n water (.5 to 2 molar). 205 CHAPTER IX NOMENCLATURE Symbol Explanation Ty p i c a l Units A (A/V) Aq CHGF CHGS CNa CONNA ' S2°4 D E° E l / 2 ECONNA EX. Na EY Na EY SO, A c t i v i t y of the indicated species i n equations (1)/ (2), and (3) Surface area of int e r f a c e Interfacial-area/aqueous-volume r a t i o Concentration of sodium i n fresh amalgam Concentration of sodium i n spent amalgam Concentration of sodium i n amalgam Y i e l d of sodium d i t h i o n i t e on sodium consumed Concentration of sodium d i t h i o n i t e i n the product stream D i f f u s i o n c o e f f i c i e n t Standard oxidation p o t e n t i a l on hydrogen scale at 25°C Half-wave p o t e n t i a l (reduction potential) The 95 per cent confidence l i m i t s of CONNA The 95 per cent confidence l i m i t s of X M Na The 95 per cent confidence l i m i t s of Y ™ Na The 95 per cent confidence l i m i t s gm mo l e s / l i t e r cm 2 3 cm /cm gm Na 100 gm amalgam gm Na 100 gm amalgam gm moles l i t e r % gm/100 ml cm /sec vo l t s v o l t s 206 Symbol E x p l a n a t i o n T y p i c a l U n i t s FLHG FLSO. AH' A c t i v i t y c o e f f i c i e n t of the i n d i - c a t e d s p e c i e s i n equations (1)/ (2) , and (3) Flow r a t e of sodium-mercury amalgam Flow r a t e of aqueous s u l f u r d i o x i d e s o l u t i o n Heat of f o r m a t i o n o f sodium d i t h i o n i t e a t 25°C R e a c t i o n r a t e c o n s t a n t f o r the o x i d a t i o n of sodium d i t h i o n i t e ml/min l i t e r / m i n Kcal/gm moles ,g moles,-^-(sec)" 1 ( l i t e r > 2 water K, K hs M Na/S0 2 pH P R e a c t i o n r a t e c o n s t a n t f o r the homogeneous decomposition o f sodium d i t h i o n i t e i n e q u a t i o n (13) R e a c t i o n r a t e c o n s t a n t f o r the water r e a c t i o n i n e q u a t i o n (10) Thermodynamic i o n i z a t i o n c o n s t a n t f o r the f i r s t d i s s o c i a t i o n o f SO. •H20 i n e q u a t i o n (2) SO, Thermodynamic i o n i z a t i o n c o n s t a n t f o r the second d i s s o c i a t i o n o f S 0 2 « H 2 0 i n e q u a t i o n (3) Thermodynamic e q u i l i b r i u m c o n s t a n t f o r S0 2*H 20 system i n e q u a t i o n (1) The Na/S0 2 r a t i o f o r a s e t of experimental runs a t which maximum s t e a d y - s t a t e C c _ i s o b t a i n e d b2°4 R a t i o o f sodium to s u l f u r d i o x i d e e n t e r i n g the r e a c t o r pH of the aqueous phase P r e s s u r e of s u l f u r d i o x i d e gas gm moles l i t atm , (gm i o n s o - l Q 9 ^ l i t e r f H +) atm Symbol Explanation 207 T y p i c a l Units homo Rate of homogeneous decompo-s i t i o n of sodium d i t h i o n i t e gm moles 3 . cm mm oxidation (RPM) A g STRUB STS0 2 TEMP V VDITHI Na -Na SO. Rate of oxidation of sodium gm moles d i t h i o n i t e - l i t e r sec Speed of the marine propeller rev/min Weight of sodium d i t h i o n i t e gms which would discolour 5 ml of a standard Rubine-R s o l u t i o n Concentration of t o t a l s u l f u r gm moles dioxide i n the aqueous feed l i t e r s o l u t i o n Temperature of the aqueous °C phase 3 Volume of the aqueous phase cm Volume of the product stream ml required to discolour 5 ml of a standard Rubine-R s o l u t i o n % Variable exponent i n the rate equation (13) Conversion of sodium from the % amalgam to d i f f e r e n t products i n the reactor Exponent i n the rate equation (13) Y i e l d of sodium d i t h i o n i t e on % sodium entering the reactor Y i e l d of sodium d i t h i o n i t e on % sulfur dioxide entering the reactor BIBLIOGRAPHY Anderson, J.S. and Saddington, K., J . Chem. S o c , 381 (1949) . Anon., Chem. Eng., p. 146, Aug. (1952). 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A-1 APPENDIX A EQUIPMENT SPECIFICATION 1. pH measurement The s p e c i f i c a t i o n s of the instruments used f o r contin- uous pH recording were as follows: pH electrode; Sargent-Welch S-30072-15 Thermocompensator; Sargent-Welch S-30115-03 pH meter; Sargent-Welch Model PBL S-30009 pH recorder; Sargent-Welch Model SRG pH recorder chart; Sargent Welch S-72166 2. D i g i t a l temperature recording A l l e l e c t r o n i c instruments used for recording the temperature of the d i f f e r e n t streams were purchased from United Systems Corporation, Dayton, Ohio, U.S.A. Their s p e c i f i c a t i o n s were as follows: D i g i t a l clock - 661 Scanner - 635 D i g i t a l m i l l i v o l t meter - 451 Multiplexer - 64 2 Printer system - 611/620D BCD cable connecting d i g i t a l clock to multiplexer 4378-6 BCD cable connecting scanner to multiplexer 4837-6 A-2 BCD cable connecting d i g i t a l m i l l i v o l t meter to p r i n t e r system 4378-20 BCD cable connecting multiplexer to p r i n t e r system 9054-20. 3. C a l i b r a t i o n curves The c a l i b r a t i o n curves mentioned i n Section IV.C. are shown i n Figures A-I to A-V. A-3 10 20 30 40 SCALE A-I F l o w r a t e o f m e r c u r y p u m p e d b y M o y n o pump v e r s u s m i c r o m e t e r s e t t i n g o n G r a h a m t r a n s m i s s i o n A - I I Flow rate of aqueous s u l f u r dioxide versus reading on the rotameter scale > A-5 S C A L E A - I I I Flow rate of cooling water versus reading on the rotameter scale A - 6 A - I V M i l l i v o l t output of i r o n - c o n s t a n t a n thermocouples versus temperature ° C A-7 1.0 2-0 3-0 SCALE A - V RPM of the pr o p e l l e r versus micrometer s e t t i n g on the thyratron c o n t r o l l e r f o r the v a r i a b l e speed dri v e (Heller motor) B - l APPENDIX B STATISTICAL EVALUATION OF ACCURACY AND PRECISION 1. Error of a measurement process 1 2 3 Eisenhart, Ku and Murphy have described the meaning of c e r t a i n terms such as "precision" and "accuracy" which 3 specify the error of a measurement process. S t r i c t l y speaking, the actual error of a reported value, that i s , the magnitude and sign of i t s deviation from the truth, i s usually not ascertainable. Limits to th i s error, however, can usually be i n f e r r e d , with some r i s k of being i n c o r r e c t , from the p r e c i s i o n of the measurement process by which the reported value was obtained, and from reasonable l i m i t s to the possible bias (or systematic error) of the measurement process. Pr e c i s i o n of a measurement process r e f e r s to the closeness of successive independent measurements of a singl e magnitude. The measurements are generated by repeated applications of the process under s p e c i f i e d conditions. The accuracy i s determined by the closeness to the true value 1. Eisenhart, C, Science, V o l . 160, p. 1201, June (1968). 2. Ku, H.H., Measurements and Data, p. 72, July-August (1968) . 3. Murphy, R.B., Material Research and Standards, p. 264, A p r i l (1961) . B-2 of such measurements. Thus, i f the bias, or systematic error, of a measurement process i s known, i t s accuracy can be s p e c i f i e d . P r e c i s i o n and accuracy are inherent c h a r a c t e r i s t i c s of the measurement process employed and not of the p a r t i c u l a r end r e s u l t obtained. I t i s important to note that a measure- ment process may be extremely precise and at the same time not very accurate. Precision, i n s t a t i s t i c a l language, i s some times c a l l e d "imprecision. 1 1 Since imprecision and systematic error are d i s t i n c t l y d i f f e r e n t components of the uncertainty of a reported value, and are subject to d i f f e r e n t treatments and i n t e r p r e t a t i o n i n usage, two numerics res p e c t i v e l y expressing the imprecision and bounds to the systematic error of the measurement process should be given along with the measured quantity, whenever both of these errors are factors r e q u i r i n g consideration. According to Eisenhart^" four d i s t i n c t cases need to be recognized, v i z . , (a) both systematic error and imprecision n e g l i g i b l e , i n r e l a t i o n to the requirements of the intended and l i k e l y use of r e s u l t s ; (b) systematic error not n e g l i g i b l e , imprecision n e g l i g i b l e ; (c) neither systematic error nor imprecision n e g l i g i b l e ; and B-3 (d) systematic error n e g l i g i b l e , imprecision not n e g l i g i b l e . Eisenhart discussed and outlined the recommended practices on the expression of uncertainties i n the above- mentioned cases. 2. Evaluation of accuracy I t has been mentioned i n the l a s t section that the bias or systematic error of a measurement process i s a measure of i t s accuracy. The systematic error may be due to uncertainty i n constants, uncertainty i n c a l i b r a t e d values or bias i n the method of computation. The following devices may y i e l d some information r e - garding the presence of systematic error i n a measurement process. (a) Measurement of a quantity whose true value i s known. (b) Comparison with other measurement processes. (c) Comparison with modifications of the given measure- ment process. The evaluation of systematic error of a measurement 4 process has been discussed i n great d e t a i l by Youden. In short, (i) Systematic error can be estimated experimentally i f the true value of the measured quantity i s known. 4. Youden, W.J., Material Research and Standards, p. 268, A p r i l (1961) . B - 4 ( i i ) Systematic error can be estimated from experience or by judgment. ( i i i ) Systematic error can be estimated by a number of elemental systematic errors i n the measurement process i f they are known. The mode of specifying l i m i t s of systematic error 2 1 (or accuracy) has been well-described by Ku and Eisenhart. 3 . Evaluation of p r e c i s i o n (or imprecision) In any i n v e s t i g a t i o n , i t i s necessary to know how well the p a r t i c u l a r measured value i s l i k e l y to agree with other values that the same measurement process might have provided i n t h i s instance, or might y i e l d on remeasurement of the same magnitude on another occasion. Such information i s provided by the estimated standard error of the reported value, which measures (or i s an index of) the c h a r a c t e r i s t i c disagreement of repeated determinations of the same quantity by the same method and, thus, serves to indicate the pr e c i s i o n of the reported value (more c o r r e c t l y , p r e c i s i o n of the measurement process i n reporting the measured value). In the following example the p r e c i s i o n of a measure- ment process (or t e s t method) "within a laboratory" has been considered and an expression for i t s s t a t i s t i c a l estimate, standard error, has been derived. B-5 Suppose that a given measurement were repeated 10 times. I t i s c a l l e d set 1, and n^ = 10. From t h i s set of 10 values, the sample mean, x^, and the sample estimate of 2 the population variance, s^, can be calculated by using 5 the following equations n Z x. i = l 3 x = . . . .(B-l) n n 2 I (Xj-X) s 2 = J - Z i — ; . . . .(B-2) n - 1 Therefore, 10 - _ A * 1 * x 2̂  — — —— — — — . . . . (B—• 3 ) 10 10 - v2 1 ( x L i " x l ) 2 i =1 J s^ = -2-^ . . . . (B-4) (10 - 1) These quantities are estimates of the population mean, u, 2 and population variance a . I f a second set of 10 measure- ments of the same quantity were made, the values of x 2 and 5. Mickley, H.S.; Sherwood, T.K. and Reed, C.E., "Applied Mathematics i n Chemical Engineering," 2nd Ed., McGraw-Hill Book Co. Inc. (New York), 1957. B-6 2 s 2 , calculated from the second set of 10 values, would be expected to d i f f e r from the f i r s t set and from the population values. If i t i s supposed that a large number of sets, each of 10 measurements, were obtained, a new set comprising the sample means x^, x 2, x^ could be generated. This set of means would ex h i b i t some very important c h a r a c t e r i s t i c s . If the grand mean, x^, i s calculated k _ x_ = . . . . (B-5) m v (where k represents the number of se t s ) , i t w i l l be found that x m i s a better estimate of the population mean, u, than i n d i v i d u a l x ^ 1 s . Further, on the average, the deviation of x. from x w i l l be less than the deviation of a single term, x m x ^ j , from the mean of the i t h S e t , x^. The sample estimate of the variance of the set of means Z (x.-x ) 2 1 1 m sm = . . . .(B-6) m k-1 w i l l be smaller than the sample estimate of the population 2 variance, s^. I t i s also found that the frequency d i s t r i b u t i o n of the sample means, x^, about the population mean, y, i s e s s e n t i a l l y normal, even though the population frequency d i s t r i b u t i o n may be non-normal 1 When these findings are treated a n a l y t i c a l l y , i t i s found that the sample variance of 2 the mean, s^, may be estimated from the variance calculated from a single set: 2 s 2 2 In equation (B-7), s i s the sample estimate of the population variance calculated from a single set of measurements, n i s 2 the number of measurements i n the single set, and s„ i s the 3 m estimated variance of the set of means. The square root of 2 the estimated variance of the set of means, s , i s c a l l e d ' m' standard deviation of the mean or standard e r r o r . The standard error i s usually denoted by s . u m I t i s desired to determine the l i m i t s within which the true population mean, y, w i l l f a l l 95 times out of 100 termed the "95 per cent confidence l i m i t s on y" ( s u f f i c i e n t for most engineering investigations). Student's ' t ' s t a t i s t i c s could be used for small sample s i z e s . For the case discussed above "n-l,a= .05 _ x-y _ x-y s m s m — /n .(B-8) 95 per cent confidence l i m i t s on y are B-8 x - t , nc- s < u < x + t , n K sm . . . (B-9) n-±,a=.uo m — — n-l,a=.05 m 4. Propagation of random error Most often an investigator comes across a s i t u a t i o n where the precisions (more c o r r e c t l y / precisions i n the measurement processes) of several d i r e c t l y measured quantities are known and i t i s desired to estimate the p r e c i s i o n (pre- c i s i o n i n the measurement process) of any function of these q u a n t i t i e s . To i l l u s t r a t e propagation of random error, i t i s assumed that a quantity z i s calculated from d i r e c t l y measured values of several quantities P^ by means of a mathematical r e l a t i o n which can be represented formally by z = f (P x, P 2/ P 3/ .../ P ±) . . . .(B-10) In a very general case, each measurement P i s made m times under supposedly i d e n t i c a l conditions. The action of random errors r e s u l t s i n a series of values of P 1: P12' P13' **"' P l m w n i c n form the P^ set and a corresponding set forming the P 2 set, etc. I t i s then desired to estimate the best value of z, variance of z and standard error of z (standard deviation of mean of z ) . B-9 If the errors i n the P's are normally d i s t r i b u t e d and the variances of P's are small, then the best value of z 5 6 w i l l be given by the following expression: ' z = f C P ^ P 2, P 3, P ±) . . . .( B - l l ) where P i s the mean of a series of values i n the set P. If the errors i n P's are independent and not too large, 5—8 the variance of z i s given by the following expression: 2 3 2 2 2 8 2 2 2 8 2 2 2 ot = (-=r a* + ( _ )z of + . . . + (—)* a; . .(B-12) 8P-L 1 3P 2 *2 3P ± i 3 z The p a r t i a l d e r i v a t i v e —— i s evaluated numerically at the 3P. mean value of each set: P^, P 2, etc. I t i s important to note that v a l i d i t y of equation (B-12) i s not dependent upon any 6. Parratt, L.G. "Pr o b a b i l i t y and Experimental Errors i n Science," Chapter 3, John Wiley and Sons,N.Y. (1961) . 7. Ratkowsky, D.A. "Notes on S t a t i s t i c a l Techniques," ChE 453/81, October 14 , 1965, Dept. of Chem. Eng., U.B.C, Canada. 8. Bannett, C A . and Franklin, N.L. " S t a t i s t i c a l Analysis i n Chemistry and the Chemical Industry," John Wiley and Sons , N.Y. (1957) . B-10 assumption concerning a normal error frequency d i s t r i b u t i o n . Only two conditions are required. F i r s t , that no c o r r e l a t i o n e x i s t between the AP. terms (P, -P, = AP. P_ -P. = im^ lm^ 1 lm^; 2m2 2 AP 2 m , e t c . ) , an assumption frequently termed "the assumption of s t a t i s t i c a l independence." Secondly, the errors i n the P's must not be too large. On the other hand, the usual methods of r e l a t i n g variance to p r o b a b i l i t y do involve the assumption of a normal frequency d i s t r i b u t i o n . For the mathematical expression (B-10), the standard deviation of mean of z (standard error of z), a , can be z 6 m written as follows: 9 3 2 2 0*1 3 Z 2 ^ 2 3 2 2 ̂ i a 2 = (__)  __L_ + ( _ ) _L_ + ... + ( _ ) m 3P. m, 3P 0 m̂  8P. m. 1 1 2 2 i i . . . . ( B - 1 3 ) Knowing the standard error of z, the 95 per cent confidence l i m i t s of the population mean of z can be estimated by using equation (B-9). One major problem involved i n the use of equation (B-9) i s that * t ' s t a t i s t i c s with known degrees of freedom are used for estimating the confidence l i m i t s . I t may seem d i f f i c u l t to estimate the degrees of freedom of z i n the case i n point. However, i f P^, P 2, P^/ P^ are independent, considering d i f f e r e n t combinations of measurements i n d i f f e r e n t sets, z w i l l have very large B - l l number of degrees of freedom. Under these conditions ' t ' d i s t r i b u t i o n would approach the 'N' (normal) d i s t r i b u t i o n . Hence the 95 per cent confidence l i m i t s on the population mean of z can be estimated by Z - N AC S < Z < Z + N r\ c s , n , .» a=.05 z — — a=.05 z . . . . ( B - 1 4 ) m m where, z = best estimate of population mean, z s = estimated standard deviation of the mean of z z m Na= 05 = [From normal p r o b a b i l i t y t a b l e ] . P r a c t i c a l a p p l i c a t i o n of equation (B-12) and (B-13) for a function l i k e (B-ll) depends upon one's a b i l i t y to 2 2 2 determine a B , a_ , , a D from experimental data, or to *1 *2 F i make an a p r i o r i estimate of them. If i t i s experimentally possible to have estimates (from random samples) of the variances (by equation (B-2)) and variances of the mean (by equation(B-7)) of P^, P 2, P 3, •••,P^ etc., then 95 per cent confidence l i m i t s on the population mean of z can be estimated by equations (B-13) and (B-14) In the absence of an experimental random sample, i t i s possible to get an a p r i o r i estimate of the variance (or i t s square root, the standard deviation) from a con- sid e r a t i o n of the maximum range of random error expected B-12 7 using a p a r t i c u l a r measurement method. I t i s known from elementary s t a t i s t i c s that p r a c t i c a l l y a l l (actually 99.73 per cent) of the area under the curve of the normal d i s t r i b u t i o n i s contained within ±3 standard-deviations of the population mean of a va r i a b l e . Considering ±3a^^ to be synonymous with the range of the var i a b l e P^, then one merely needs to know or to be able to estimate the range to obtain a reasonable estimate of the standard deviation of the variable P. . l Sometimes the value of a p a r t i c u l a r quantity obtained from an instrument or measuring device remains very constant, but the l i m i t i n g factor to p r e c i s i o n of reading i s the smallest scale d i v i s i o n a v a i l a b l e on the instrument. If a temperature measurement made with a thermometer i s considered i n which the smallest d i v i s i o n i s 1°C, then i t seems reasonable to assume that the maximum error range obtainable (due to human reading error alone) i s -about 1°C (or ±.5°C). Thus an a p r i o r i estimate of standard deviation of temperature measure- ment would be 0.5/3 = .167. Of course, the range may be considerably greater than 1°C, due to large f l u c t u a t i o n s or i n s t a b i l i t i e s i n the temperature. In that case, one would once again require experimentation i n order to obtain an estimate of the variance. The above discussion only applies to steady readings where the smallest scale d i v i s i o n imposes a l i m i t i n g factor on the p r e c i s i o n of the reading. Once again B-13 i f one considers the problem where z = f ( P 1 # P 2, P 3 P i) , the standard deviation of z, s z , can be estimated by equation (B-12) using a p r i o r i estimates of a , a • • •, a . Also, the 95 per cent confidence l i m i t s on the population mean of 7 z can be estimated. z " Na=.05 S z 1 z 1 z + Na=.05 S z ' • ' * ( B " 1 5 ) The '95 per cent confidence l i m i t s ' estimated by equation (B-15) are broader than those calculated by equation (B-14). C - l APPENDIX C SODIUM-MERCURY AMALGAM 1. Purity of the chemicals i n preparing amalgam (a) Mercury Technical grade mercury, obtained from various sources, was thoroughly washed and then d i s t i l l e d i n a mercury s t i l l a v a i l a b l e i n the laboratory. I t was assumed that a f t e r d i s t i l l a t i o n the mercury was 100 per cent pure. (b) Sodium metal Reagent grade sodium of the following assay was purchased from Canlab Supplies Ltd. (Toronto). Chloride (Cl) 0.0015% Nitrogen (N) . . . . . . 0.003% Phosphate (P0 4) 0.0005% Sulfate (S0 4) 0.002% Heavy metals ( as Pb) 0.0005% Iron (Fe) 0.001% (c) P a r a f f i n o i l White, heavy (Saybolt v i s c o s i t y 335/350), laboratory grade p a r a f f i n o i l was purchased from Fisher S c i e n t i f i c Co. (Montreal). C-2 2. Problems encountered i n preparation of amalgam (a) Heat of soluti o n When sodium was dissolved i n mercury, a large quantity of heat was l i b e r a t e d . Therefore, small pieces of sodium metal were slowly added to the mercury to promote c o n t r o l l e d amalgamation. (b) Black p r e c i p i t a t e i n amalgam preparation When sodium was dissolved i n mercury (kept under a thin layer of p a r a f f i n o i l ) , a f i n e l y divided black p r e c i p i t a t e was obtained which could be e a s i l y separated from the amalgam by mechanical means. This f i n e l y divided black p r e c i p i t a t e was i d e n t i f i e d as mercury (formed by the reduction of HgO by sodium) which did not dissolve i n the bulk of the amalgam because of a coat- ing of p a r a f f i n o i l on the droplets. Due to t h i s problem i t was d i f f i c u l t to make an amalgam of a known sodium-concentration s t a r t i n g with known quantities of mercury and sodium. (c) Disposal of small pieces of sodium and i t s oxide The layer of oxide, on the surface of sodium metal, was removed by scraping the surface of the metal with a knife under a layer of p a r a f f i n o i l . The most e f f e c t i v e way to dispose of t i n y pieces of sodium and scrapings of the oxide was to dissolve them i n a soluti o n of iso-propanol and benzene (2:3 V/V). C-3 3. Cal c u l a t i o n of sodium content i n an amalgam sample (a) Normality of the standard NaOH solution, N„ _ = 0.1N -1 NaOH (b) Normality of the standard H oS0, sol u t i o n , N„ = 0.1N (c) Weight of the Erlenmeyer + 100 ml d i s t i l l e d water, W1 = 275.3 gms (d) Weight of the Erlenmeyer + 100 ml d i s t i l l e d water + approximately 2.5 ml amalgam sample, W2 = 305.3 gms (e) Weight of the amalgam sample, W^^ = W2~Ŵ  = 30 gms (f) Volume of N„ e_ s u l f u r i c acid added to the Er lenmeyer, H 2 S ° 4 V " H 2 S O 4 = ° ' 0 2 5 L I T E R (g) Volume of N N a Q H sodium hydroxide used to t i t r a t e the excess of s u l f u r i c a cid, V" = 0.020 l i t e r . NaOH Sodium dissolved i n mercury reacts with s u l f u r i c acid according to the following reaction 2 Na + H 2S0 4 -> Na 2S0 4 + H 2 By stoichiometry, the weight per cent of sodium i n the amalgam sample, NAPT, can be given by the following expression. NAPT = lAP-P- (v" N - V" N ) (C-l) WAML H 2 S 0 4 H 2 S 0 4 N a 0 H N a 0 H * * C-4 For the above-mentioned example, NAPT = •2-|°p (0.025 x 0 .1 - 0 .020 x 0 .1) = 0.03 833 gms of sodium/100 gms of the amalgam. 4. Estimation of the p r e c i s i o n of the a n a l y t i c a l procedure The following steps were involved i n the determination of weight per cent of sodium i n amalgam by the proposed ana- l y t i c a l procedure. (a) Standardization of an aqueous sodium hydroxide s o l u t i o n 1 2 by potassium hydrogen phthalate ' V„ ^„liters of N„ sodium hydroxide so l u t i o n was NaOH NaOH J t i t r a t e d with W p H p gms of potassium hydrogen phthalate dissolved i n approximately 200 ml of d i s t i l l e d water. W N = PHP , * * NaOH 204 .22 V rtTT . . . . ̂ - z j NaOH (b) Standardization of a s u l f u r i c acid s o l u t i o n by the standardized sodium hydroxide so l u t i o n 1. Swift, E.H., "A system of chemical analysis ( q u a l i t a t i v e and semiqualitative) for the common element." Prentice- H a l l Inc. , New York, (1946) . 2. Vogel, A.I., "A text-book of q u a l i t a t i v e inorganic a n a l y s i s . " 3rd Ed. John Wiley and Sons, New York, 1961. C-5 V I^SO^ l i t e r s of N H g 0 s u l f u r i c acid was t i t r a t e d 2 4 with v' N aQH l i t e r s °f NNaOH s o < ^ u m hydroxide s o l u t i o n . N = NNaOH V'NaOH _ { Q _ 3 ) z q v' H 2S0 4 (c) Sodium-mercury amalgam sample weighed WAML ^ m s °^ a n a m a - L 9 a m sample was weighed under a layer of d i s t i l l e d water using a Mettler balance. (d) Addition of standard s u l f u r i c acid s o l u t i o n to the amalgam sample V" l i t e r s of the N s u l f u r i c acid was pipetted H 2 b ° 4 2 °4 into the f l a s k containing the amalgam sample. (e) Excess s u l f u r i c acid b a c k - t i t r a t e d with the standard sodium hydroxide s o l u t i o n S u l f u r i c acid s o l u t i o n that d i d not react with sodium i n the amalgam was t i t r a t e d with V" l i t e r s of NXT rt„ sodium ^ NaOH NaOH hydroxide s o l u t i o n . As mentioned i n Appendix C.3, the weight per cent of sodium i n the amalgam can be given by the following expression. NAPT = 2 3 0 0 (V" N - V" N ) WAML H 2 S 0 4 H 2 S ° 4 N a 0 H N a 0 H (C-l) The measured values of the d i f f e r e n t quantities involved i n the above mentioned steps ((a) to (e)) and the range of random errors associated with them have been presented i n Table C-I • Standard deviations (and hence, the variances) of W^^, V" 0 l~ and V" were estimated from the t o t a l range of the 2 4 NaOH 3 random errors i n these quantities by the method outlined i n Appendix B.4. The r e s u l t s are shown i n the Table C-I. Standard deviations (and hence, the variances) of the d i f f e r e n t measured quantities i n the equations (C-2) and (C-3), v i z . WPHP' VNaOH' V ,NaOH a n d V ' H 9 S 0 . w e r e a l s o estimated from the knowledge of the t o t a l range of the random errors i n these quantities (Table C-I). The values and the estimates of variances of N.T _TT and NTT n n . , c ,, NaOH H 2 S 0 4 w e r e c a l c u l a t e d as follows: (i) Value and variance of N„ _„ NaOH Using equation (C-2), M  WPHP 0.6127 n l f t N = ; = =0.10 iNaun 204 .22 V N a Q H 204 .22 x 0.03 Using equation (B-12), 2 _ ( % a O H ) 2 02 + ( 8 NNaOH 2 2 N ' W 3 V V NNaOH d WPHP WPHP ° VNaOH NaOH = 31.229 x 10 TABLE C-I MEASURED VALUES, RANGE OF RANDOM ERRORS AND VARIANCES OF DIFFERENT QUANTITIES Variable Explanation Measured Value Measured To grange a=—3 a 2 W PHP Weight of potassium hydrogen phthalate taken to standardize N NaOH .6127 gm ±.0001 gm 3.3xl0~ 5 1.09xl0~ 9 v NaOH Volume of NXT t i t r a t e d with r. NaOH p.n.p. .030 l i t ±.00005 l i t 1.67xl0~ 5 2.79xl0" 1 0 V NaOH Volume of NXT _„ taken to . , ,. NaOH standardize N„ o r i H 2 s o 4 .025 l i t * ±0 l i t (pipetted) 0 0 V* H 2S0 4 Volume of N„ t i t r a t e d H2S04 W i t h V'NaOH V O l u m e ° f NNaOH .025 l i t ±.00005 l i t 1.67xl0" 5 2.79xl0~ 1 0 W AML Weight of amalgam sample taken for analysis 30 gm ±.05 gm 1.67xl0~ 2 2.79xl0~ 4 V" H 2 S 0 4 Volume of N„ e r. added to the H2 4 amalgam sample .025 l i t - ±0 l i t (pipetted) 0 0 V" NaOH —__________ Volume of N„ used i n back NaOH t i t r a t i o n of the acid Amalgam No I Amalgam No II Amalgam No III .0248 l i t .0200 l i t .005 l i t ±.00005 l i t ±.00005 l i t ±.00005 l i t 1.67x10*";? 1.67x10*";? 1.67x10*° 2.79x10"^ 2.79x10 2.79xlO"-LU o I C-8 ( i i ) Value and variance of N„ H 2 S 0 4 By equation (C-3), NNaOH V'NaOH 0.1 x 0.025 A N q n = = = 0.10 *VU4 V' Q n 0.025 H 2 S ° 4 Using equation (B-12), 2 ,Vy 2 . (9V42 a 2 NH 2S0 4 ~ NaOH NaOH ^ a ^ *aOH H.SO. 2 4 2 9 + ( ) < C , 9 V , H 2 S 0 4 H 2 S 0 4 75.869 x 10' 1 0 Knowing the variances of w , V" H , N , V and 2 4 2 4 NNaOH ^ n e c 3 u a t i ° n ( c ~ l ) i t n e variance of NAPT was estimated by equation (B-12). The 95 per cent confidence l i m i t s on population mean of NAPT were estimated by equation (B-15). Sample c a l c u l a t i o n s have been presented below, where the pr e c i s i o n of the a n a l y t i c a l procedure i n determining the con- centration of sodium i n three d i f f e r e n t amalgams was estimated, Amalgam No. I ( V " N a 0 H = 0.0248 l i t e r ) By equation ( C - l ) , C-9 NAPT = ^|^- (0 .025 x 0.1 - 0.0248 x 0 .1) = 0.00153 Using equation (B-12), 2 _ ,8NAPTv2 .2 , ,3NAPT . 2 2 A , 3NAPT N2 NAPT " (3WTI7) A M T ) °V" o r t + } X ^ 3 V H 2S0 4 H 2 S 0 4 9 N H 2 S 0 4 2 + ( a ^ T _ ) 2 02 + { ^ T _ ) 2 2 H 2 S 0 4 a V" NaOH NaOH 9 ̂ NaOH NaOH = 5.5561 x 10" 8 <W =0-0002357 The 95 per cent confidence l i m i t s on the population mean, of NAPT (By equation (B-15)) = 0.00153 ± 1.96 (0.0002357) = 0.0015 ± 0.0005 • • Percentage p r e c i s i o n - ±33% . Similar c a l c u l a t i o n s were made f o r Amalgam No. II and No. I l l , Amalgam No II ( V " N a 0 H = 0.0200 l i t e r ) NAPT = 0.03833 ° 2NAPT = 5 ' 2 0 6 8 x 1 0 ~ 8 aNAPT = 0.0002282 C-10 The 95 per cent confidence l i m i t s on the population mean of NAPT = 0.03833 ± 1.96 (0.0002282) = 0.0383 ± 0.0005 .*. Percentage p r e c i s i o n - ±1.3% . Amalgam No. I l l (V" N Q H = 0.005 l i t e r ) NAPT = 0.15333 ° 2NAPT = 5 * 2 0 1 8 X 1 0 " 8 °NAPT = ° - 0 0 0 2 2 8 1 The 95 per cent confidence l i m i t s on the population mean of NAPT = 0.15333 ± 1.96 (0.0002281) = 0.1533 ± 0.0005 Percentage p r e c i s i o n * ±0.3 3% D-l APPENDIX D AQUEOUS SOLUTION OF SULFUR DIOXIDE 1. Purity of the chemicals i n preparing aqueous s u l f u r dioxide solution (a) Sulfur dioxide gas A C.I.L. sulfur dioxide tank was used as a source of S0 2 gas. (b) Water Freshly d i s t i l l e d water was used f o r making the aqueous solut i o n of s u l f u r dioxide. (c) Sodium hydroxide Fisher c e r t i f i e d ACS sodium hydroxide p e l l e t s were used for pH adjustment. Their composition was as follows: not l e s s than 97% 0.5% 0.005% 0.001% 0.001% 0.003% 0 .02% 0 .002% Assay (NaOH) Sodium carbonate (Na^O^) Chloride (Cl) Nitrogen compounds (as N) Phosphate (PO^) Sulfate (S0 4) Ammonium hydroxide ppt Heavy metals (as Ag) D-2 Iron (Fe) 0.001% Nickel (Ni) . . . . . . . . . . . . 0.001% Potassium (K) 0.02% Copper (Cu) 0.001% 2. Cal c u l a t i o n of the t o t a l s u l f u r dioxide concentration i n an aqueous so l u t i o n sample (a) Normality of the standard iodine s o l u t i o n , Nj = 0.1N (b) Normality of the standard sodium t h i o s u l f a t e s o l u t i o n , N = 0.1N S 2 U 3 (c) Volume of Nj iodine s o l u t i o n taken i n the Erlenmeyer f l a s k , V x = 0.075 l i t e r (d) Volume of the aqueous s u l f u r dioxide s o l u t i o n sample, injected into the iodine solution, V = 0.005' l i t e r b°2 (e) Volume of the N sodium t h i o s u l f a t e s o l u t i o n S2°3 required to t i t r a t e unreacted iodine i n the E r l e n - meyer f l a s k , V 2 = 0.0095 l i t e r . • • Molarity of t o t a l s u l f u r dioxide i n the aqueous sol u t i o n = — - — (NTV, - N c _ V~) so 2 = - (0 .1 x 0 .075 - 0.1 x 0 .0095) 2x0.005 = 0.655 molar D-3 3. Estimation of the p r e c i s i o n of the a n a l y t i c a l procedure The c a l c u l a t i o n method was s i m i l a r to that used i n estimating the p r e c i s i o n of the a n a l y t i c a l procedure for evaluating the concentration of sodium i n the amalgam. The following steps were involved i n determining the concen- t r a t i o n of t o t a l s u l f u r dioxide i n an aqueous so l u t i o n by iodometric analysis as performed i n our laboratory. (a) Preparation of a standard potassium dichromate solut i o n (primary standard) W. pD(_ gms of pure anhydrous potassium dichromate was dissolved i n V . l i t e r of d i s t i l l e d water, water W Nry. n = — . . . . (D-l) u r 2 u 7 49.035 V . water (b) Standardization of a sodium t h i o s u l f a t e s o l u t i o n by the standard potassium dichromate s o l u t i o n V' _ l i t e r s of a N n sodium t h i o s u l f a t e s o l u t i o n S2°3 S2°3 was t i t r a t e d with V"Cr Q l i t e r s of the N C r Q potassium 2 7 2 7 dichromate s o l u t i o n . N V Cr-,0- C r 9 0 7 N Q n = — — - . . . . (D-2) b 2 U 3 (c) Standardization of an iodine s o l u t i o n with the standard sodium t h i o s u l f a t e s o l u t i o n l i t e r s of iodine solution was t i t r a t e d with V _ l i t e r s of N _ sodium t h i o s u l f a t e s o l u t i o n . S2°3 S2°3 N s 2 ° 3 V s 2 ° 3 • • N = — — — . . . .(D-3) V I (d) Excess of iodine s o l u t i o n taken i n an Erlenmeyer f l a s k l i t e r s of the iodine s o l u t i o n was taken i n an Erlenmeyer f l a s k and was d i l u t e d with d i s t i l l e d water to get a sharp end point. The volume was dependent on the con- centration of s u l f u r dioxide i n the fixed-volume sample to be tested. (e) Injection of the s u l f u r dioxide sample V g 0 l i t e r s of the s u l f u r dioxide s o l u t i o n was taken by a hypodermic syringe, and was injected into the contents i n the Erlenmeyer. (f) B a c k - t i t r a t i o n of excess iodine The unreacted iodine was t i t r a t e d with l i t e r s of N S2O.J sodium t h i o s u l f a t e s o l u t i o n . On the basis of the steps (a) to ( f ) / the molarity of t o t a l s u l f u r dioxide could be given by the following expression: D-5 Molarity = — - (NTV, - N c V 0) . . . .(D-4) 2 V_ n 1 1 S2°3 2 S2°3 Substituting the values of N and N c _ from the equations i b 2o 3 (D-3) and (D-2) resp e c t i v e l y , M I •* 1 , WPDC V C r 2 0 7 % , V1 VS 2Q3 „ , Molarity = ( ) ( V„) 98.07 V' _ V 0 V . V T S 2 0 3 3 water I . . . . (D-5) Knowing the variances of the d i f f e r e n t quantities i n the equation (D-5), the 95 per cent confidence l i m i t s on the population mean of molarity were estimated. E-1 APPENDIX E SODIUM DITHIONITE IN THE PRODUCT STREAM 1. D e t a i l s of the a n a l y t i c a l procedures and sample c a l c u l a t i o n s (a) The iodine formaldehyde method (i) Detailed d e s c r i p t i o n of the iodine-formaldehyde method Two equal-volume (- 5 ml) samples of the product stream that contained p r i m a r i l y ^2^1' S2°3 a n d H S (^3 w e r e taken using a hypodermic syringe. These samples (Sample I and Sample II) were analysed by the iodine-formaldehyde method i n the following three parts. I t i s obvious that the amount of reagents used i n d i f f e r e n t parts of the a n a l y t i c a l procedure would depend on the concentrations of S2®~4' S2^3 and HSO.J i n the sample. Hence, the values given below are only approximate. Part A - Determination of d i t h i o n i t e + t h i o s u l f a t e + b i s u l f i t e : [a] A known volume (- 50 ml) of a standard (- 0.1N) iodine sol u t i o n was taken i n an Erlenmeyer f l a s k and d i l u t e d to about 200 ml with oxygen-free d i s t i l l e d water. [3] A 5 ml sample (Sample I) of the product stream was i n - jected under the d i l u t e d iodine s o l u t i o n . Iodine oxidizes E-2 S2°4' S2°3 a n d H S 0 3 P r e s e n t i n t n e sample as follows: .(E-l) 2S 20 3 + I 2 S.O, + 21 4 6 . (E-2) HSCU + I 0 + H„0 * HSO. + 2HI .(E-3) [y] Excess iodine was back-titrated with a standard (= 0.1N) solut i o n of sodium t h i o s u l f a t e using starch-solution as an i n d i c a t o r . Part B - Determination of d i t h i o n i t e + t h i o s u l f a t e : [a] Approximately 25 ml of a formaldehyde s o l u t i o n (35 ml of 37 per cent HCHO: 50 ml of H20) at about pH = 9 was taken i n an Erlenmeyer f l a s k . I t was d i l u t e d with oxygen-free d i s t i l l e d water (by bubbling N 2 through f r e s h l y d i s t i l l e d water). A drop of phenolphthalein was added which turned the colour of the solu t i o n pink. [8] A 5 ml sample (Sample II) of the product stream was i n - jected under the d i l u t e d formaldehyde s o l u t i o n . If the pink colour of the s o l u t i o n disappeared, some NaOH sol u t i o n was immediately added. The sulfoxylate formation took place as follows. The amount of iodine consumed by the sample i n Part A gave the amount of (S^"^ + S 20~ + HSO~) i n Sample I. E-3 S 2 0 4 + 2HCH0 + H 20 -»• HCHO'HS03 + HCHO'HS02 . . . . (E-4) Any b i s u l f i t e (or s u l f i t e ) present i n the sample was also t i e d down as formaldehyde b i s u l f i t e . [y] The f l a s k was stoppered and allowed to stand f o r about 20 minutes during which time the reaction (E-4) completed. [<S] The solution was a c i d i f i e d ( t i l l the pink colour disappeared) by 20 per cent acetic acid s o l u t i o n i n water. [e] A known volume of a standard (- 0.1N) iodine solution was added to the contents i n the Erlenmeyer. Provided there was an excess of iodine, formaldehyde sulfoxylate and t h i o s u l f a t e present i n the system were oxidized as follows: HCHO'HS02 + 2 I 2 + 2H20 + S0 4 + HCHO + 4I~ + 5H + . .(E-5) 2 S 2 ° 3 + Z2 * S4°6 + 2 I ~ • • • .(E-6) Both reactions took place i n a c i d i c medium [?] Excess iodine was back-titrated with a standard (- 0.1N) solutio n of th i o s u l f a t e using starch-solution as an i n d i c a t o r . The amount of iodine consumed by E-4 HCHO»HS02 and S 2 0 ~ gave the amount of (S 2 0 ~ + S 2 0 ~ ) i n Sample I I . Part C - Determination of t h i o s u l f a t e : [a] A f t e r the end-point had been reached i n Part A, approxi- mately 30 ml of a 5 per cent sodium s u l f i t e heptahydrate solut i o n was added to the contents of the Erlenmeyer. The following reaction took place. S 4Og + SO3 -> S 3 0 = + S 2 0 = . . . . (E -7) [83 The optimum pH range, within which the reaction was quantitative i n f i v e minutes, was 5.5 to 9.5. So a drop of phenolphthalein was added and a normal solut i o n of sodium hydroxide was added u n t i l the sol u t i o n turned pink. I t was . allowed to stand for f i v e minutes. [y] Approximately 5 ml of the formaldehyde s o l u t i o n was added to bind excess s u l f i t e . [6] The contents i n the f l a s k were a c i d i f i e d with 10 ml of 20 per cent acetic a c i d . [e] Thiosulfate generated due to reaction (E-7) was t i t r a t e d with a standard (- 0.1N) solu t i o n of iodine using a starch- sol u t i o n as an i n d i c a t o r . The iodine consumed i n Part C corresponds to 1/2 (thiosulfate present i n Sample I + t h i o s u l f a t e added i n Part A). E-5 ( i i ) Sample c a l c u l a t i o n s for the iodine-formaldehyde method At steady-state, during experimental run 23, two samples of 5 ml were taken by a hypodermic syringe. Normality of sodium t h i o s u l f a t e s o l u t i o n used for analysis = 0.1N Normality of iodine solu t i o n used for analysis = .099N Data obtained i n Part A: Volume of 0.099N iodine taken =60.0 ml Volume of sample = 5 ml Volume of 0.1N Na 2S20 3 used i n b a c k - t i t r a t i o n = 18.9 ml Data obtained i n Part B: Volume of sample dissolved i n formaldehyde • 5 ml Volume of 0.099N iodine taken = 20.0 ml Volume of 0.1N Na 2S20 3 used i n b a c k - t i t r a t i o n = 16.55 ml Data obtained i n Part C: After adding 30 ml of 5 per cent sodium s u l f i t e hepta- hydrate, Volume of .099N iodine used i n the t i t r a t i o n = 9.75 ml On the basis of the above mentioned data, S~07 + S~oT + S07 consumed (by oxidation i n Part A) = (60.0 - 1 8 , Q X g , 1 ) m l of .099N Iodine = 40.91 ml of .099N Iodine S 2 0 3 i n Sample I + S20_, added i n Part A = 2 x 9.75 = 19.50 ml of .099N Iodine S 2 ° 3 added i n Part A 5 1 8 'ogg'1 = 19.09 ml of .099N Iodine Therefore, S20_, i n a 5 ml sample of product stream = 19.50 - 19.09 = 0.41 ml of .099N Iodine Na 2S 20 3 i n the product stream _ 0.41X.099 _ 0 Q 0 0 4 0 5 9 g m m ° l e S N a 2 S 2 ° 3 1000 -00004059 j - — S2°4 + S2°3 :'"n S a m P l e 1 1 consumed o n 16.55x0.1 " 2 0 ^99^ = 3.283 ml of .099N Iodine t ' t Na 2S 20 4 i n the product stream E-7 (3.283 - 0.41) x .099 _ Q000716 ^ m o l e s N a 2 S 2 ° 4 4 x I O O O " : 5 ml Concentration of N a 2 S 2 0 4 i n the product stream .249 gms N a 2 S 2 0 4 = .0000716 x 174 x 20 = 100 ml NaHSO 2 i n the product stream (40.91 - 2.893 x | - 0.41) .099 2 x 1000 gm moles NaHSO_ = .0017899 5 ml sample 9 • # Total SO2 i n 5 ml of the product stream, S 0 2 from N a 2 S 2 0 4 = 2 x .0000716 = .0001432 gm moles S 0 2 from N a 2 S 2 0 3 = 2 x .00004059 = .0000812 gm moles S 0 2 from N a H S 0 3 = .0017899 = = .0017899 gm moles Tot a l = .0020143 gm moles The concentration of ' t o t a l ' SO2 going into the reactor was checked by iodometry. The concentration of s u l f u r dioxide i n aqueous solu t i o n entering the reactor was .4 00 molar • • 5 ml of the su l f u r dioxide s o l u t i o n entering the reactor contained .002 moles of S0 2 which compares well with the SO i n the product stream. (b) The Rubine-R method (i) Detailed d e s c r i p t i o n of the Rubine-R method A standard solu t i o n of Rubine-R dye for d i t h i o n i t e a n a l y t i c a l purposes was purchased from V i r g i n i a Chemicals/ Portsmouth/ Va., U.S.A. This dye s o l u t i o n was re-standar- dized before use i n the laboratory. Five ml of a standard (N^) s o l u t i o n of Rubine-R was pipetted into an Erlenmeyer f l a s k . The dye s o l u t i o n was d i l u t e d with approximately 1.50 ml of oxygen-free d i s t i l l e d water. The Erlenmeyer f l a s k with i t s contents was flushed with a stream of N 2 gas and then i t was stoppered with a rubber bung. Samples of product stream were drawn int o a burette from the reactor, p e r i o d i c a l l y , during an experi- mental run. These samples were t i t r a t e d with the br i g h t red dye solution, with vigorous a g i t a t i o n , to an amber end- point. Throughout the t i t r a t i o n , the burette and the Erlenmeyer f l a s k were kept under N 2 atmosphere. During the course of experiments, i t was observed that at low pH (about pH = 1.0), the colour changed from bri g h t red to colourless very sharply at the end-point. Hence, approximately 2 ml of concentrated s u l f u r i c acid E-9 was added to the d i l u t e d Rubine-R before t i t r a t i n g i t with d i t h i o n i t e i n the product stream. I t was observed that the addition of s u l f u r i c acid to the Rubine-R solut i o n did not have any s i g n i f i c a n t e f f e c t on the r e s u l t s . If V p l i t e r s of the product stream were t i t r a t e d with V_._. l i t e r s of N..-, Rubine-R s o l u t i o n . # • m the concentration of ^ 2 8 2 0 4 i n the product stream 87 .0526 V R R N R R g m s N a ^ 10 V p 100 ml . . . .(E-8) The use of the Rubine-R method depends on accurate standar- d i z a t i o n of the dye sol u t i o n . Rubine-R s o l u t i o n was standardized with a standard s o l u t i o n of 1 1 2 ( 8 0 4 ) - , . Pre- paration and standardization of T i 2 ( S 0 4 ) _ , s o l u t i o n and standardization of Rubine-R with T i 2 ( S 0 4 ) - , s o l u t i o n have been discussed below. [a] Preparation of T i 2 ( S 0 4 ) - . s o l u t i o n A 20 per cent standardized s o l u t i o n of T i 2 ( S 0 4 ) 3 was purchased from La Motte Chemical Products CO.,Chestertown, Maryland, U.S.A. According to manufacturer's s p e c i f i c a t i o n , the s o l u t i o n was prepared for chemical tests and was free of s u l f i d e s (commercial titanous s u l f a t e s o l u t i o n sometimes contains s u l f i d e s which can be eliminated as hydrogen s u l f i d e on b o i l i n g ) . One hundred ml of the concentrated E-10 soluti o n was d i l u t e d to one l i t e r by oxygen-free d i s t i l l e d water. The soluti o n was kept under an atmosphere of oxygen- free carbon dioxide gas (C0 2 was scrubbed through a so l u t i o n that contained one part of Na 2S 20 4, t W O P a r t s °^ NaHCO^ and 20 parts H 20). [3] Standardization of T i 2 ( S 0 4 ) 3 Solution T i 2 ( S 0 4 ) 3 s o l u t i o n i s unstable at high temperatures, i n presence of oxygen and when exposed to d i r e c t sunlight. The following text-book methods were used to standardize d i l u t e d T i 2 ( S 0 4 ) 3 s o l u t i o n before i t s use i n the laboratory. - The f e r r i c ammonium su l f a t e method"*" - The potassium dichromate method^" 2 - The i r o n content determination method The r e s u l t s obtained by these three methods were comparable and reproducible. Only potassium dichromate method has been described here, b r i e f l y , for i t i s a very accurate and precise method. Information on the other methods can be obtained from the l i t e r a t u r e c i t e d . 1. Vogel, A.I., "A text-book of q u a l i t a t i v e inorganic a n a l y s i s , " 3rd Ed. John Wiley and Sons, New York, 1961. 2. Pierson, R.H. and Gantz, E. St. C l a i r . , A n a l y t i c a l Chemistry, 26, No. 11, 1809 (1954). E - l l The potassium dichromate method: If very accurate r e s u l t s are desired or i f the normality of f e r r i c ammonium su l f a t e s o l u t i o n i s not exactly known, the standardization of Ti^SO^)-, s o l u t i o n can be c a r r i e d out with 0.1N potassium dichromate s o l u t i o n using the approximately 0.1N f e r r i c ammonium s u l f a t e s o l u t i o n as an intermediary. Into a 250 ml f l a s k , 25.0 ml of primary standard 0.1N potassium dichromate and 20 ml of d i l u t e s u l f u r i c acid (2:5 W/W) were placed, oxygen-free carbon dioxide was passed to displace a i r and the stream of gas was maintained during the t i t r a t i o n . Forty ml of the titanous s u l f a t e s o l u t i o n was added to the contents i n the f l a s k . The l i q u i d s were mixed by s w i r l i n g the f l a s k gently and the excess titanous s o l u t i o n was t i t r a t e d with 0.1N f e r r i c ammonium su l f a t e s o l u t i o n . When the dark colour due to the titanous s a l t had nearly disappeared, 10 ml of 10 per cent ammonium thiocyanate s o l u t i o n was added and the addition of f e r r i c ammonium su l f a t e s o l u t i o n was continued u n t i l a red or pink colouration was obtained which was permanent f o r at l e a s t one minute. In the same way 40.0 ml of the titanous s u l f a t e s o l u t i o n was t i t r a t e d with 0.1N f e r r i c ammonium s u l f a t e s o l u t i o n but the addition of 0.1N potassium dichromate sol u t i o n was omitted. From the r e s u l t s obtained, the exact normality of the f e r r i c ammonium su l f a t e s o l u t i o n and the E-12 normality of titanous s u l f a t e solution was ca l c u l a t e d . The method of c a l c u l a t i o n has been described below. If, N T = Normality of T i 2 ( S 0 4 ) 3 s o l u t i o n Np e = Normality of f e r r i c ammonium su l f a t e s o l u t i o n N^ n = Normality of potassium dichromate s o l u t i o n o r 2 u 7 V"T = Volume of T i ^ S O ^ ) ^ s o l u t i o n taken i n the f l a s k during the f i r s t t i t r a t i o n where potassium dichromate solu t i o n was added V_ _ = Volume of potassium dichromate s o l u t i o n taken i n <- r2 u7 the f i r s t t i t r a t i o n V_ = Volume of f e r r i c ammonium su l f a t e s o l u t i o n used Fe i n the f i r s t t i t r a t i o n V.J, = Volume of Ti2(S0 4>2 solut i o n taken i n the f l a s k during the second t i t r a t i o n where no potassium dichromate s o l u t i o n was added V* = Volume of f e r r i c ammonium su l f a t e s o l u t i o n used Fe i n the second t i t r a t i o n during f i r s t t i t r a t i o n , V T N T " V C r 2 0 7 N C r 2 0 7 = V F e N F e ' ' * '< E" 9 ) and during second t i t r a t i o n , E-13 V 1 N = V' N VT T Fe ™ Fe . (E-10) From equations (E-9) and (E-10), N, T . ( E - l l ) [y] Standardization of Rubine-R so l u t i o n by standard T i 2 ( S 0 4 ) 3 solut i o n into a 300 ml Erlenmeyer f l a s k . To t h i s was added, 25 ml of d i s t i l l e d water, 5 ml of 10 per cent Na^O^ s o l u t i o n , 50 ml of methanol and 25 ml of 25 per cent sodium tart a r a t e s o l u t i o n . The contents i n the Erlenmeyer f l a s k were b o i l e d gently for f i v e minutes while sweeping with oxygen-free C0 2 and were t i t r a t e d hot with the standard s o l u t i o n of Ti 2(SG" 4) The colour change at the end-point was from pink to amber and was quite sharp. Twenty f i v e ml of Rubine-R dye solu t i o n was pipetted 3. Wood, P.J./ Am. Dyestuff Reporter, 443, June 17 (1957) . E-14 I f , N-^ = Normality of Rubine-R solut i o n N T = Normality of Ti^SO^)-. s o l u t i o n V-^ = Volume of the Rubine-R solut i o n taken i n the flask V" = Volume of T i - ( S O . ) s o l u t i o n used i n the t i t r a t i o n T 2 4 3 II V T N •'• NRR = ' ' • .(E-12) VRR ( i i ) Sample c a l c u l a t i o n s for the Rubine-R method [a] Standardization of Ti-,(S0 4)2 s o l u t i o n by potassium dichromate s o l u t i o n : The following data was obtained f o r the parameters i n equation ( E - l l ) N p y. = 0.10204 V_ = 0.020 l i t e r V C r 2 0 7 = ° - 0 1 0 l i t e r V__ = 0.0112 l i t e r Fe V,J, = 0.010 l i t e r V' = 0.1055 l i t e r Fe Using equation ( E - l l ) , E - 1 5 N T V N Cr O Cr O ^ r 2 u 7 c r 2 u 7 0.010 x 0.10204 V m- V T V F e 0.020 - 0.010 * 0.0112 T v , 0.01055 Fe = 0.10874N [8] Standardization of the Rubine-R solut i o n by T i 2 ( S 0 4 ) - , s o l u t i o n The following data was obtained for the parameters i n equation (E-12) N_ = 0.10874N = 0.010 l i t e r V j = 0.0106 l i t e r Using equation (V. 12 ) , XT T N T 0.0106 x 0.10874 n 1 1 K o C M N P R = ~v = = 0 - 1 1 5 2 6 N RR 0.010 [y] Concentration of sodium d i t h i o n i t e i n the product stream During the experimental run 23, under steady-state conditions, the values of the parameters i n equation (E-8) were as follows: E-16 V D D = 0.005 l i t e r = 0 .11526N V P = 0.01828 l i t e r • • Using equation (E-8), The concentration of Na 2S 20 4 ^ n t n e product stream 87.0526 V R R N R R 10 V P 87.0526 x 0.005 x 0.11526 10 x 0.01828 gms Na 2S 20 4 = 0.2744 100 ml of the product stream 2. Estimation of the p r e c i s i o n of the Rubine-R method In t h i s section various steps involved i n determining the concentration of Na 2S 20 4 i n a sample, from the product stream of the reactor, by the Rubine-R method have been outlined. The method of error c a l c u l a t i o n was indicated i n connection with the analysis of an amalgam sample (Appendix C). For brevity, the c a l c u l a t i o n s have not been attached. The d i f f e r e n t steps were: E-17 (a) Preparation of a standard s o l u t i o n of iodine. (b) Standardization of a sodium t h i o s u l f a t e s o l u t i o n by the standard iodine s o l u t i o n . (c) Standardization of a potassium dichromate s o l u t i o n by the standard s o l u t i o n of sodium t h i o s u l f a t e . (d) Standardization of a titanous s u l f a t e s o l u t i o n by the standard solu t i o n of the potassium dichromate. (e) Standardization of a Rubine-R solut i o n by the standard s o l u t i o n of titanous s u l f a t e . (f) T i t r a t i o n of a product stream sample, containing sodium d i t h i o n i t e , with a known volume of the standard solu t i o n of Rubine-R. F - l APPENDIX F DATA PROCESSING 1. Mathematical expressions for c a l c u l a t i n g C Q n , Y 2 Y N a, CONNA, X N a, Na/SO^y rate of sodium consumption, and sample c a l c u l a t i o n s . (a) Mathematical expressions Mathematical expressions to c a l c u l a t e these quantities were derived from t h e i r d e f i n i t i o n s and the r e s u l t s have been included. The symbols used i n these expressions have been explained i n Chapter IX. I t was assumed that the density of an amalgam d i d not change s i g n i f i c a n t l y i n the range of temperatures used f o r the present i n v e s t i - gation. Therefore, the density of amalgam was calculated by the following expression (Section II.E.4): Density of the amalgam (gm/ml) = 13.55 - 0.9986 x (gms of sodium/100 gms of the amalgam) (i) Concentration of sodium d i t h i o n i t e i n the product stream, C (gms of sodium d i t h i o n i t e ) (100 ml of the product stream) 100 x STRUB VDITHI . (F-l) ( i i ) Y i e l d of sodium d i t h i o n i t e on t o t a l s u l f u r dioxide entering the reactor (%), (gm molar cone, of ^ 2 8 2 0 ^ i n product) x 2 x 100 2 (gm molar cone, of t o t a l SC^ i n aqueous feed) 2 x 10 5 x STRUB . . . . (F-2) 174.1052 x STS0 2 x VDITHI ( i i i ) Y i e l d of sodium d i t h i o n i t e on sodium entering the reactor with the fresh amalgam (%) , (gm moles of ^ 2 8 2 0 - 4 i n product/min) x 2 x 100 ^Na ~ (gm moles of Na entering with fresh amalgam/min) 46 x 10 7 x FLSO 2 x STRUB 174.1052 x VDITHIx FLHG x CHGF x (13.55-0.9986 x CHGF) (iv) Y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (%), (gm moles of Na_S 90 4 i n product/min) x 2 x 100 CONNA = * * gm moles of Na entering with fresh amalgam/min\ -gm moles of Na leaving with spent amalgam/min J F-3 46 x 10 5 x FLSO, x STRUB CONNA =1 174.1052 x VDITHI x FLHG x (CHGF-CHGS) x (100 - CHGS) (F-4) (13.55 - 0.9986 x CHGF) (v) Conversion of sodium from the amalgam to d i f f e r e n t products i n the reactor (%), ( gm moles of Na entering with fresh amalgam/min -gm moles of Na leaving with spent amalgam/min x Na Cgm moles of Na entering with fresh amalgam/min) (100/CHGF - 1) = 100 x | 1 J . . . .(F-5) (100/CHGS - 1) (vi) Na/SQ2 r a t i o entering the reactor, (gm moles of Na entering with fresh amalgam/min) -(gm moles of Na leaving with spent amalgam/min) FLHG x CHGF x (13.55 - 0.9986 x CHGF) 2300 x STS0 2 x FLS0 2 . . . . ( F - 6 ) F-4 (vi i ) Rate of sodium consumption i n the reactor, = (gm moles of Na entering with fresh amalgam/min) -(gm moles of Na leaving with spent amalgam/min) FLHG x (13.55 - 0.9986 x CHGF) 2300 x CHGF - (100 - CHGF) (100 - CHGS) x CHGS . .(F-7) (b) Sample Calculations Experimental run 54 was considered for the sample c a l c u l a t i o n s . The process variables were fix e d at the following l e v e l s : CHGF = .04029% STS0 2 = .6425 gm m o l e s / l i t e r (RPM) A g = 673 rpm FLSO-, = .0955 l i t e r s / m i n FLHG = 47.5 ml/min ( A A ) A „ = .0784 cm2/cm3 TEMP = 17°C pH = 5 . 6 F-5 Under the steady state conditions, CHGS = .00407% VDITHI = 7.40 ml STRUB = .049397 gms of Na 2S 20 4 (i) Steady-state concentration of sodium d i t h i o n i t e i n the product stream Using equation (F-l) , 100 x STRUB 100 x .049397 gms C_ = = = .66753 &2 U4 VDITHI 7.40 100 ml ( i i ) Steady-state y i e l d of sodium d i t h i o n i t e on t o t a l s u l f u r dioxide entering the reactor (%) Using equation (F-2), 2 x 10 x .049397 SO- = = 11.935% ^ 174.1052 x .6425 x 7.40 ( i i i ) Steady-state y i e l d of sodium d i t h i o n i t e on sodium entering the reactor with fresh amalgam (%) F-6 Using equation (F-3), 46 x 10' x .0955 x .049397 "Na 174.1052 x 7.40 x 47.5 x .04029 x (13.55-0.9986x.04029) = 65.145% (iv) Steady-state y i e l d of sodium d i t h i o n i t e on sodium consumed i n the reactor (%) Using the equation (F-4) , CONNA 46 x 10 J x .0955 x .049397 ^ 174 .1052 x 7 .40 x 47 .5 x (.04029-.00407)/ x (100 - .00407) (13.55 - 0.9986 x .04029) = 72.462% (v) Steady-state conversion of sodium from the amalgam to d i f f e r e n t products i n the reactor (%) Using equation (F-5), x N a - 100 *|1 - (100/.04029) - 1) (100/.00407) - 1) = 89.902% F-7 (vi) Na/S02 r a t i o entering the reactor Using equation (F-6), Na/S0 2 = 47.5 x .04029 x (13.55 - 0.9986 x .04029) 2300 x .6425 x .0955 = .18320 (vi i ) Rate of sodium consumption Using equation (F-7), Rate = 47.5 x (13.55 - 0.9986 x .04029) 2300 .04029 - (100 - .04029) (100 - .00407) x .00407 = .010106 gm moles/min 2. The 95 per cent confidence l i m i t s of the steady-state CS 0 ' YSO ' YNa' C 0 N N A ' XNa' N a / S 0 2 a n d r a t e o f sodium 2 4 2 consumption for an experimental run. To estimate the 95 per cent confidence l i m i t s of the steady-state C , Y , Y , CONNA and X M for an experim _>2̂ ^ 2 Wcl Ala run, i t was necessary to know the values and the variances of the parameters used i n equations (F-l) to (F-7). The data taken during experimental run 54 was used for the sample c a l c u l a t i o n s . (a) Value and variance of STRUB The normality of the Rubine-R solut i o n used for the analysis of sodium d i t h i o n i t e i n the product stream was determined by the method outlined i n the Section E . l . b . The normality of the Rubine-R so l u t i o n used i n the experimental run 54 was, N R R = .1134885N. The variance of the normality of the Rubine-R s o l u t i o n was estimated by the method of propagation of random er r o r . The steps involved have been outlined i n the Appendix E (steps a to e Section E.2). The variance of the normality of the Rubine-R solut i o n was estimated to be, a = .856884 -7 . R R x 10 (• • 95 per cent confidence l i m i t s of N__, = ± .0006). STRUB = gms of Na 2S 20 4 which would discolour 5 ml of .1134885N Rubine-R solut i o n = 87.0526 x .005 x .1134885 = .0493973 gms of Na 2S 20 4 Neglecting any error involved i n p i p e t t i n g the 5 ml of Rubine-R so l u t i o n , the variance of STRUB was estimated to 2 7 * be, a S T R U B = .16236 x 10 (• • 95 per cent confidence l i m i t s of STRUB = ± .0003) . (b) Value and variance of VDITHI Volume of the product stream, at steady-state, required to discolour 5 ml of 0.1134885N Rubine-R s o l u t i o n , VDITHI, was 7.40 ml. The variance of VDITHI was estimated by knowing the maximum range of random error expected i n using a 50 ml burette. aVDITHI = <X ) 2= 2 , 7 8 8 9 X 10"4 • (• • 95 per cent confidence l i m i t s of VDITHI = ±.03) (c) Value and variance of STS0 2 2 The method to calc u l a t e STS0 2 and °g TgQ has been out l i n e d i n Appendix D. Knowing the values and the variances of the parameters i n equation (D-5), the value and the variance of STS0 2 were calc u l a t e d . STS0 2 = 0.6425 molar a2 -5 STS0 2 = .327441 x 10 (• • 95 per cent confidence l i m i t s of STS0 2 = ±.004). (d) Value and Variance of FLS0 2 The flow rate of the aqueous s u l f u r dioxide s o l u t i o n , FLS0 2, was determined by measuring the volume of the aqueous solution that flowed into a graduated cylinder i n a fi x e d length of time. This procedure was repeated several times and the mean flow rate, FLS0 2, was found to be .0955 l i t e r s / 2 mm. The variance of FLSO-, c?„T , was estimated by £ r L o ( J 2 equation (B-2). O F L S 0 2 " - 1 1 7 5 8 * 1 0 " 5 (• v 95 per cent confidence l i m i t s of FLS0 2 = ±.002). (e) Value and variance of FLHG The flow rate of pure mercury, FLHG, was determined by measuring the volume of the mercury that c o l l e c t e d i n a graduated cylinder i n a fixed length of time. This pro- cedure was repeated several times and the following r e s u l t s were obtained. FLHG = 47.5 ml/min 2 FLHG = .188695 (• • 95 per cent confidence l i m i t s of FLHG = ± 0.8). F - l l (f) Values and variances of CHGF and CHGS The values of CHGF and CHGS were calculated by the method indicated i n Appendix C. Knowing the variances of d i f f e r e n t measured quantities i n the mathematical expression to c a l c u l a t e CHGF or CHGS (equation C - l / Appendix C), the variances of CHGF and CHGS were calculated by the method of propagation of random error. The following r e s u l t s were obtained CHGF = .04029% aCHGF = ' 6 3 4 2 6 X 1 0 ~ 7 (• • 95 per cent confidence l i m i t s of CHGF = ± .0005) . CHGS = .00407% r r 2 7 °CHGS = .82510 x 10 (• • 95 per cent confidence l i m i t s of CHGS = ± .0005). Knowing the values and the variances of the parameters mentioned above, the variances of C c n , Y _ , Y , CONNA, X. , Na/S02 and rate of sodium consumption were estimated by the method of propagation of random e r r o r . The 95 per cent confidence l i m i t s of these quantities were estimated by using equation (B-15) (Appendix B). The r e s u l t s were as follows: F-12 C c ._ = .668 ± .005 (• • Percentage error - .75%) b2°4 Y c n = 11.9 ± .1 (• • Percentage error - .84%) b U 2 Y N a = 65 ± 2 (• • Percentage error = 3.1%) CONNA = 72 ± 3 (• • Percentage error = 4.2%) X N a = 90 ± 1 (• • Percentage error = 1.1%) Na/S02= .183 ± .006 (•"• Percentage error = 3.3%) Rate of sodium consumption = .0101 ± .0003 (•*• Percentage error = 3%) I t i s i n t e r e s t i n g to note that despite a large error i n determining CHGS (- 12%) , the error i n CONNA and X N a i s r e l a t i v e l y small. 3. Experimental data and r e s u l t s Tables F-I to F-XIV show the steady-state values of the process variables and other quantities which were used to c a l c u l a t e the steady-state values of Na/S0 2, rate of sodium consumption, C , Y _ , Y , CONNA and X M . The 2 4 2 re s u l t s and the 95 per cent confidence l i m i t s of Y„^ , Y„ S0 2 Na CONNA and are also presented. F-13 Tables F-XV to F-XXXII show the unsteady-state r e s u l t s for runs i n the experimental sets: 42-46, 23-28 and 65-77. TABLE F-I STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 47-57 (Expts. 47, 50, 52, 53, 54, 55 and 57) (RPM) = 673; FLSOj = .0955; FLHG = 47.5; (A/V) = .0784; TEMP = 17; STRUB = .049397 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 cs 2o 4 Yso 2 ± E Y s o 2 ± E Y N a CONNA ±ECONNA XNa ± E X N a 47 .09322 .01347 .65500 5.75 7.700 .414 .642 11.3 27.2 32 85.6 ±.1 ±.8 ±1 ±.5 50 .04573 .00383 .64500 5.80 6.650 .207 .743 13.2 64 70 92 ±.1 ±2 ±2 ±1 52 .04257 .00384 .63950 5.60 7.520 .194 .657 11.8 61 67 91 + .1 ±2 ±2 ±1 53 .07735 .00762 .64775 6.0 7.158 .348 .690 12.2 35 39 90.2 ±.1 ±1 ±1 ±.7 54 .04029 .00407 .64250 5.60 7.400 .183 .668 11.9 65 72 90 ±.1 ±2 ±3 ±1 55 .05776 .00399 .63900 5.80 5.770 .264 .856 15.4 58 63 93.1 . ±.1 ±2 ±2 ±.9 57 .06854 .00391 .65625 5.95 5.60 .304 .882 15.4 51 54 94.3 ±.1 ±2 ±2 ±.7 TABLE F-II STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 65-77 (Expts. 65, 67, 69, 71, 73, 75 and 77) (RPM) A g = 673; FLSO, > = .0955 ; FLHG = 47.5; ( A / V ) A g . = .0784; TEMP - 17; STRUB = .049397 RUN CHGF . CHGS STS0 2 pH VDITHI RATE OF Na CONSUMPTION* Na/S0 2 C s 2 ° 4 Y s o 2 ±EY YNa ± E Y N a CONNA +ECONNA XNa ± E X N a 65 .10104 .01932 .65125 6.00 8.250 .0227 .451 .599 10.56 ±.09 23.4 ±.7 28.9 ±.9 80.9 ±.5 67 .06626 .00387 . .65000 5.95 5.600 .0174 .297 .882 15.6 ±.1 52 ±2 56 ±2 94.2 ±.8 69 .04677 .00374 .65050 5.65 6.733 .0120 .210 .734 13.0 ±.1 62 ±2 67 ±2 92 ±1 71 .07542 .00609 .65800 5.95 6.717 .0193 .334 .735 12.8 ±.1 38 ±1 42 ±1 91.9 + .5 73 .05914 .00414 .65300 5.80 5.700 .0153 .264 .867 15.2 ±.1 58 ±2 62 ±2 93.0 ±.9 75 .03921 .00391 .65075 5.40 7.795 .0098 .176 .634 11.2 ±•1 64 ±2 71 ±3 90 ±1 77 .08920 .01104 .65550 5.70 7.770 .0217 .396 .636 11.1 ±.1 28.1 ±.8 32 ±1 87.6 ±.6 * gm moles/min TABLE F - I I I STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 66-76 (Expts. 66, 68, 70, 72, 74 and 76) (RPM) = 225; FLSO, = .0955; FLHG => 47.5; (A/V) = .0784; TEMP = 17; STRUB = .049397 RUN CHGF CHGS STSO- pH VDITHI Na/S0 2 C s 2 ° 4 Y so 2 ± E Y s o 2 YNa ± E Y N a CONNA ±ECONNA XNa ± E X N a 66 .06626 .00421 .6500 5.95 6.120 .297 .807 14.3 48 51 93.7 ±.1 ±1 ±2 ±.7 68 .04677 .00415 .65050 5.65 7.237 .210 .683 12.1 57 63 91 ±.1 ±2 ±2 ±1 70 .07542 .00703 .65800 5.90 7.450 .334 .663 11.6 35 38 90.7 ±.1 ±1 ±1 ±.5 72 .05914 .00471 .65300 5.75 6.237 .264 .792 13.9 53 57 92.0 ±.1 ±2 ±2 ±.9 74 .03921 .00361 .65075 5.35 8.400 .176 .588 10.38 59 65 91 ±.09 ±2 ±2 ±1 76 .08920 .01437 .65550 5.75 9.330 .396 .529 9.28 23.4 27.9 83.9 ±.08 ±.7 ±.8 ±.5 TABLE F-IV STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 62-63 (Expts. 62 and 63) (RPM) - 225; FLSOj = .0955; FLHG - 47.5; (A/V) = .0784; TEMP = 17; STRUB - .049397 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 C s 2 ° 4 Y so 2 ± E Y s o 2 YNa ± E Y N a CONNA ±ECONNA XNa ± E X N a . 62 .10116 .02563 .64550 6.15 9.750 .456 .507 9.02 19.8 26.5 74.7 ±.07 ±.6 ±.8 ±.5 63 .06352 .00413 .6390 5.70 6.210 .290 .795 14.3 49 53 93.5 ±.1 ±1 ±2 ±.7 TABLE F-V STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 87-91 (Expts. 87, 89 and 91) (RPM) = 225; FLS0 2 = .0955; FLHG = 47.5; (A/V) A = .0784; TEMP =17; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 c s 2 o 4 Y so 2 ± E Y s o 2 YNa ± E Y N a CONNA +ECONNA XNa ± E X N a 87 .05605 .00472 .65800 5.75 6.172 .249 .770 13.4 54 59 92 ±.1 ±2 ±2 ±1 89 .09863 .02162 .65450 5.85 9.064 .438 .524 9.2 21.0 26.9 78.1 ±.1 ±.6 ±.8 ±.5 91 .03723 .00360 .65800 5.35 8.38 .165 .567 9.9 60 66 90 ±.1 ±2 ±2 ±1 TABLE F-VI STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 95-105 (Expts. 95, 97, 99, 103 and 105) (RPM) = 673; FLS0 2 = .198; FLHG = 47.5; (A/V) A = .0784; TEMP = 17; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI RATE OF Na CONSUMPTION* Na/S0 2 c s 2 o 4 Y - 2 ± E Y so 2 YNa ± E Y N a CONNA ±ECONNA XNa ± E X N a 95 .04387 .00533 .65700 5.20 14.040 .0108 .094 .338 5.92 63 72 88 ±.06 . ±2 ±2 ±1 97 .09119 .00487 .65800 5.65 8.010 .0240 .195 .593 10.4 53 56 94.7 ±.1 ±1 ±1 ±.6 99 .08184 .00467 .65700 5.60 8.450 .0215 .175 .562 9.8 56 ' 60 94.3 ±.1 ±1 ±1 ±.6 103 .05460 .00455 .66000 5.40 11.267 .0140 .116 .422 7.34 63 69 92 ±.08 ±1 ±2 ±1 105 .07107 .00487 .65300 5.65 9.017 .0184 .153 .527 9.3 61 65 93.2 ±.1 ±1 ±2 ±.8 TABLE F-VII STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 23-28 (Expts. 23, 24, 25, 26, 27 and 28) (RPM)- = 673; FLSC 2 = .0955; FLHG = 47.5; (A/V) A = .0784; TEMP = 17; STRUB = .050169 RUN CHGF CHGS STS0 2 pH VDITHI RATE OF Na CONSUMPTION* Na/S0 2 cs 2o 4 Yso 2 ± E Y s o 2 YNa ± E Y N a CONNA ±ECONNA XNa ± E X N a 23 .01725 .00176 .39996 5.20 18.283 .0043 .126 .274 7.88 62 70 90 ±.08 ±3 ±4 ±4 24 .03765 .00376 .40300 5.70 14.200 .0095 .273 .353 10.1 36.9 41 90 ±.1 ±1 ±1 ±1 25 .05444 .01243 .39898 5.90 19.100 .0117 .398 .263 7.56 19.0 24 .6 77 ±.08 ±.6 ±.9 ±1 26 .04712 .00688 .39924 5.70 17.000 .0112 .345 .295 8.49 24.6 29 85 ±.09 ±.8 ±1 ±1 27 .03027 .00268 .39700 5.40 13.100 .0077 .223 .383 11.1 50 55 91 ±.1 ±2 ±2 ±2 28 .02428 .00239 .39949 5.30 14.850 .0061 .178 .338 9.7 55 61 90 ±.1 ±2 ±3 ±2 gm nles/min TABLE F-VIII STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 42-46 (Expts. 42, 43, 44, 45 and 46) (RPM) = 673; FLS0 2 = .0955; FLHG = 47.5; (A/V) = .0784; TEMP = 17; STRUB = .098795 RUN CHGF CHGS STS0 2 pH VDITHI RATE OF Na CONSUMPTION* Na/S0 2 C s 2 ° 4 Yso 2 ± E Y s o 2 YNa ± E Y N a CONNA ±ECONNA XNa ± E X N a 42 .06561 .00542 1.3100 5.00 7.119 .0168 .146 1.39 12.2 83 91 91.7 ±.1 ±2 ±3 ±.7 43 .10344 .00678 1.3000 5.50 5.217 .0268 .231 1.89 16.7 72 77 93.5 ±.2 ±2 ±2 .±•5 44 .14386 .00708 1.2970 5.75 4.300 .0379 .322 2.30 20.4 63 67 95.1 ±.2 ±2 ±2 ±.3 45 .21265 .03749 1.2875 5.00 6.400 .0483 .476 1.54 13.8 28.9 35 82.4 ±.1 ±.9 ±1 ±.2 46 .18438 .01515 1.2638 5.70 5.600 .0467 .422 1.76 16.0 38 41 91.8 ±.2 ±1 ±1 ±.2 gm moles/min TABLE F-IX STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 86-90 (Expts. 86, 88 and 90) ( R P M ) A q = 1 1 0 ; F L S 0 2 " - 0 9 5 5 ; FLHG - 47.5; (A/V) = .0784; TEMP = 17; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 % o 4 YSO- ± E Y s o 2 YNa ± E Y N a CONNA ±ECONNA XNa ± E X N a 86 .05605 .00494 .65800 5.75 6.394 .249 .743 13.0 52 57 91 ±.1 ±2 ±2 ±1 88 .09863 .02232 .65450 5.80 9.467 .438 .502 8.81 20.1 26.0 77.4 ±.09 ±.6 ±.8 ±.5 90 .03723 .00353 .65800 5.35 8.590 .165 .553 9.7 58 64 91 ±.1 ±2 ±2 ±1 TABLE F-X STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 94-104 (Expts. 94, 96, 100, 102 and 104) (RPM) = 673; FLS0 2 = .0656; FLHG = 47.5; (A/V) = .0784; TEMP = 17; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 ° S2°4 Y s o 2 YNa CONNA Na i E Y s o 2 ± E Y N a ±ECONNA ±EX„ Na 94 .04387 .00351 .65700 5.95 4.580 .284 1.037 18.1 64 69 92 ±.2 ±2 ±2 ±1 96 .09119 .03275 .65800 6.10 7.850 .587 .605 10.6 18.0 28.1 64 ±.1 ±.5 ±.9 ±.5 98 .08184 .02440 .65700 6.10 7.502 .528 .633 11.1 21.0 29.9 70.2 ±.1 ±.6 ±.9 ±.6 100 .02801 .00324 .65150 5.75 6.945 .183 .684 12.1 66 74 88 ±.1 ±2 ±3 ±2 102 .05460 .00449 .66000 6.10 5.420 .351 .876 15.3 43 47 92 ±.2 ±1 ±2 ±1 104 .07107 .01469 .65300 6.10 7.270 .462 .653 11.5 24.9 31 79.3 ±.1 ±.7 ±1 ±.8 TABLE F-XI STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 122-134 (Expts. 122, 125, 128, 131 and 134) (RPM)^ = 673; FLSO,, = .0955; FLHG = 47.5; (A/V)- = .0247; TEMP = 17; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 C s 2 ° 4 * so 2 ± E Y s o 2 YNa ± E*Na CONNA ± ECONNA XNa ± E X N a 122 .06283 .00629 .66000 5.70 8.930 .278 .532 9.3 33 37 90 . ±.1 ±1 ±1 ±1 125 .12382 .05016 .66064 5.90 12.793 .544 .371 6.46 11.9 19.9 59.5 ±.07 ±.4 ±.6 ±.4 128 .04884 .00527 .65802 5.70 10.038 .217 .473 8.26 38 43 89 ±.09 ±1 ±1 ±1 131 .07673 .00942 .65628 5.95 9.900 .341 .480 8.40 24 .7 28.1 87.7 ±.09 ±.8 ±.9 ±.7 134 .08789 .01267 .66400 5.80 10.160 .385 .467 8.09 21.0 24.5 85.6 ±.08 ±.6 ±.7 ±.6 TABLE F-XII STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 123-135 (Expts. 123, 129, 132 and 135) (RPM) = 673; FLS0 2 = .0955; FLHG = 47.5; (A/V). = .0095; TEMP = 17; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 cs 2o 4 Yso 2 +EY xso 2 YNa ± E Y N a CONNA ±ECONNA Na ±EX„ Na 123 .06283 .01603 .66000 5.65 15.897 .278 .299 5.20 18.8 25.2 74.5 ±.04 ±.4 ±.7 ±.9 129 .04884 .01494 .65802 5.65 19.350 .217 .245 4.29 19.8 28' 69 ±.04 ±.6 ±1 ±1 132 .07673 .02303 .65628 5.80 17.275 .341 .275 4.81 14.1 20.2 70.0 ±.05 ±.4 ±.7 ±.7 135 .08789 .03064 .66400 5.65 17.100 .385 .278 4.81 12.5 19.1 65.2 ±.05 ±.4 ±.6 ±.6 t TABLE F-XIII STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 106-118 (Expts. 106, 109, 112, 115 and 118) (RPM) = 673; FLSOj = .0955; FLHG = 47.5; (A/V). = .0784; TEMP = 13; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 C s 2 ° 4 v s o 2 ± E * s o 2 CONNA ±ECONNA 106 .08996 .00742 .65300 6.00 7.740 .401 .614 10.8 29.3 ±.1 ±.9 109 .06455 .00421 .65350 5.80 5.198 .288 .803 14. T 52 ±.2 ± 2 112 .03715 .00344 .65250 5.55 7.947 .166 .598 10.5 70 ±.1 ± 3 115 .05455 .00431 .65950 5.80 6.073 .241 .782 13.6 61 ±.2 ± 2 118 .09505 .00875 .65471 6.00 7.932 .422 .599 10.5 27.4 ±.1 ±.9 TABLE F-XIV STEADY-STATE DATA AND RESULTS FOR EXPERIMENTAL SET 110-113 (Expts. 110 and 113) (RPM) = 673; FLS0 2 = .0955; FLHG = 47.5; (A/V) A = .0784; TEMP = 27; STRUB = .047495 RUN CHGF CHGS STS0 2 pH VDITHI Na/S0 2 Cs 2o 4 Yso 2 ± E Y s o 2 CONNA +ECONNA 110 .06455 .00354 .65350 5.90 5.037 .288 .943 16.6 61 ±.2 ±2 113 .03715 .00357 .65250 5.70 7.850 .166 .605 10.7 71 ±.1 ±3 TABLE XV UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 4 2 I n i t i a l pH = 3.4; F i n a l pH = 5.0; CHGF » .06561 TIME (min) Cs 2o 4 10.4 .915 14.3 1.040 17.5 1.116 21.5 1.198 24.4 1.235 30.0 1.283 35.0 1.291 39.5 1.300 44.0 1.309 51.6 1.392 54.0 1.372 57.5 1.411 61.1 1.392 63.8 1.382 66.6 1.392 69.6 71.4 1.353 1.372 73.8 1.392 TIME 4.5 7.5 12.0 19.0 29.0 34.0 41.0 68.0 73.0 (nin) CHGS .00560 .00593 .00524 .00545 .00503 .00550 .00558 .00506 .00449 TABLE XVI UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 43 I n i t i a l pH - 3.3; F i n a l pH = 5.5; CHGF = .10344 TIME (min) 9.7 13.7 16.9 21.3 27.2 30.8 34.7 37.3 41.8 44.8 49.4 52.0 56.0 58.4 cs 2o 4 1.176 1.432 1.544 1.689 1.780 1.830 1.864 1.864 1.882 1.918 1.900 1.900 1.882 1.882 TIME (min) 3.1 8.5 11.5 18.5 23.0 29.0 33.0 46.5 54.0 59.5 CHGS .00888 .00649 .00630 .00673 .00685 .00634 .00697 .00666 .00702 .00688 I ro co TABLE XVII UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 44 i n i t i a l pH •= 3.3; F i n a l pH = 5.75; CHGF = .14386 TIME (min) 6.5 9.8 14.3 16.6 22.0 25.0 28.8 32.8 37.5 41.4 65.2 67.6 74.5 % o 4 1.326 1.620 1.976 2.058 2.171 2.195 2.245 2.271 2.271 2.298 2.298 2.298 2.298 TIME (nin) 4.5 7.8 11.3 18.0 27.0 52.0 57.0 63.0 71.0 CHGS .00754 .00712 .00707 .00705 .00717 .00720 .00697 .00715 .00689 TABLE XVIII UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 45 I n i t i a l pH = 3.15; F i n a l pH = 5.0; CHGF = .21265 TIME (min) 8.4 11.6 14.9 20.4 23.3 27.9 31.5 35.4 40.9 45.5 49.5 51.9 55.5 C s 2 o 4 1.718 1.918 2.016 1.882 1.813 1.689 1.633 1.620 1.556 1.556 1.544 1.544 1.544 TIKE (min) 2.5 7.0 10.5 16.3 22.0 25.3 29.5 33.3 37.5 47.0 61.5 CHGS .04245 .00802 .00777 .01504 .02939 .03519 .03608 .03698 .03735 .03850 .03664 I ro io TABLE XIX UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 46 I n i t i a l pH «= 3.0; F i n a l pH = 5.7; CHGF - .18438 T I"E (r.in) 6.2 10.8 15.8 18.3 21.8 25.2 28.7 32.3 36.8 40.1 43.1 46.4 48.9 51.6 54.8 57.3 60.0 62.5 65.3 67.8 70.3 1.259 1.900 2.148 2.195 2.245 2.171 2.102 1.976 1.956 1.882 1.882 1.830 1.830 1.813 1.749 1.7 96 1.780 1.780 1.749 1.764 1.764 TIKE (r.in) 3.0 8.S 14.3 20.2 24.0 27.0 33.8 39.0 4S.0 53.0 63.5 CHGS .02508 .00776 .00717 .00915 .01070 .01166 .01348 .01384 .01468 .01616 .01462 TABLE XX UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 23 I n i t i a l pH - 4.0 F i n a l pH 5.2; CHGF - .01725 TIMS (.-in) 4.S 7.4 13.2 23.6 27.2 30.6 32.7 34.5 41.7 46.6 52.5 54.7 57,1 60.9 65.5 68.9 .148 .181 .216 .255 .263 .265 .267 .273 .268 .274 .276 .271 .278 .271 .276 .274 (.-in) 3.8 13.8 30.0 45.0 50.0 73.0 74.0 CHGS .00174 .00176 .00178 .00170 .00200 .00206 .00150 f I co o TABLE XXI UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 24 I n i t i a l pH = 4.2; F i n a l pH •» 5.7; CHGF «• .03765 TIME 7.7 11.5 15.7 19.8 32.9 39.5 52.8 57.5 61.1 63.9 66.7 68.4 (min) Cc n .261 .320 .364 .369 .364 .366 .356 .353 .353 .353 .344 .353 b2°4 TIME 10.0 15.4 24.8 35.0 41.0 49.3 60.9 (min) CHGS .00220 .00300 .00370 .00370 .00400 .00400 .00376 TABLE XXII UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 25 I n i t i a l pH = 4.1; F i n a l pH - 5.9; CHGF - .05444 TIKE 6.8 10.3 14.2 18.9 22.3 29.0 37.0 72.4 77.0 80.0 84.0 (min) C, n .215 .261 .282 .282 .280 .267 .263 .261 .263 .263 .263 i> 2°4 TIME 8.4 11.8 20.2 26.8 59.5 70.2 78.0 84.0 (min) CHGS .00487 .00618 .01081 .01157 .01243 .01306 .01243 .01243 TABLE XXIII UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 26 I n i t i a l pH - 4.1; F i n a l pH » 5.7; CHGF •» .04712 TIME ( min) 9.7 12.7 16.6 19.9 23.3 28.3 35.0 39.3 42.5 47.9 53.0 55.9 60.5 c s 2 o 4 .282 .326 .330 .330 .328 .318 .302 .299 .295 .297 .293 .295 .295 TIME (min) 6.5 16.0 23.0 37.0 45.0 50.0 58.0 63.0 64.0 CHGS .00334 .00400 .00601 .00718 .00737 .00672 .00668 .00677 .00657 TABLE XXIV UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 27 I n i t i a l pH = 4.0; F i n a l pH - 5.4; CHGF = .03027 T I ME (min) 8.0 12.9 16.9 19.8 26.0 29.0 33.2 37.3 41.6 46.9 50.6 55.5 C s 2 o 4 .237 .295 .337 .344 .366 .380 .383 .380 .382 .386 .382 .386 TIME (min) 5.1 10.8 22.0 N 35.1 48.4 52.0 56.8 CHGS .00325 .00185 .00234 .00232 .00292 .00298 .00283 TABLE XXV UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 28 I n i t i a l pH = 3.9; F i n a l pH = 5.3; CHGF - .02428 TIKE (nir.) 9.7 13.7 16.9 21.7 24.9 33.8 40.6 45.2 47.9 51.3 54.3 61.1 64.7 67.5 S°4 .227 .270 .287 .304 .312 .322 .326 .330 .330 .333 .335 .339 .337 .338 TIME (min) 7.3 19.0 35.5 49.5 55.8 62.9 66.6 CHGS .00248 .00281 .00187 .00248 .00232 .00239 .00238 TABLE XXVI UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 65 I n i t i a l pH » 3.53; F i n a l pH - 6.0; CHGF - .10104 TIKE ( min) 9.8 14.0 20.0 27.5 34.7 44.7 54.7 61.3 65.0 68.0 71.0 C S 2 ° 4 .602 .650 .642 .602 .599 .595 .606 .606 .599 .599 .595 TIME (min) 6.6 11.6 18.0 33.1 47.0 56.4 68.0 CHGS .00869 .00769 .01456 .01945 .01903 .01922 .01960 TABLE XXVII UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 67 I n i t i a l pH = 3.38; F i n a l pH = 5.95; CHGF - .06626 TIME 8.3 13.5 19.8 26.3 32.2 41.7 46.7 51.7 55.3 / (m in) C. n .561 .721 .817 .867 .882 .882 .882 .882 .882 s2°4 TIME 6.3 11.8 17.8 24.0 29.0 40.0 44.0 50.2 53.8 (rr. in) CHGS .00436 .00386 .00358 .00343 .00361 .00377 .00393 .00405 .00374 TABLE XXVIII UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 69 I n i t i a l pH «• 3.35; F i n a l pH = 5.65; CHGF - .04677 TIME 8.6 13.7 20.9 27.1 33.1 39.4 45.3 48.5 52.0 57.3 60.8 63.5 66.3 (min) C_ n .447 .567 .643 .696 .707 .716 .716 .726 .726 .734 .732 .737 .732 t ,2 u4 TIME 6.7 12.1 18.9 25.1 31.5 36.7 43.3 50.2 55.7 68.4 (min) CHGS .00421 .00383 .00348 .00388 .00388 .00399 .00368 .00358 .00373 .00364 TABLE XXIX UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 71 I n i t i a l pH • 5.88; F i n a l pH = 5.95; CHGF = .07542 TIKE (min) 5.3 8.3 14.0 19.3 25.3 31.8 34.6 38.4 46.0 49.8 53.6 S*4 .706 .721 .726 .721 .726 .737 .732 .737 .737 .732 .737 TIME (min) 3.7 10.3 17.1 23.5 30.2 36.8 44.1 51.8 ChGS .00554 .00615 .00614 .00599 .00615 .00610 .00605 .00610 TABLE XXX UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 73 I n i t i a l pH = 5.75; F i n a l pH = 5.8; CHGF = .05914 TIME (min) 9.1 15.3 21.3 30.0 35.4 41.0 45.5 53.0 58.5 C s 2 o 4 .844 .849 .867 .867 .867 .867 .867 .867 .867 TIME (min) 5.3 11.9 18.2 23.8 32.3 37.8 42.3 CHGS .00429 .00454 .00464 .00414 .00422 .00408 .00412 I. co TABLE XXXI UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 75 I n i t i a l pH » 5.35; F i n a l pH » 5.4; CHGF - .03921 TIME (min) 4.5 10.3 14.6 20.2 24.7 32.5 37.6 44.0 49.2 51.6 C s 2 ° 4 .587 .613 .618 .625 .633 .633 .632 .633 .637 .633 TIME (ain) 7.8 12.9 17.3 27.1 35.2 40.8 CHGS .00391 .00399 .00394 .00387 .00392 .00386 TABLE XXXII UNSTEADY-STATE RESULTS FOR EXPERIMENTAL RUN 77 I n i t i a l pH = 5.76; F i n a l pH - 5.7; CHGF - .08920 TIHE (min) 8.5 14.3 19.7 24.8 32.8 40.8 44.9 52.3 55.0 C S 2 ° 4 .608 .629 .633 .629 .625 .633 .635 .642 .633 TIME (min) 11.1 17.7 22.1 30.7 39.0 43.1 48.8 55.0 CHGS .00976 .01074 .01094 .01167 .01113 .01094 .01121 .01087 I GO cn

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