Applied Science, Faculty of
Materials Engineering, Department of
DSpace
UBCV
Stenhouse, James Fairley
Master of Applied Science - MASc
University of British Columbia
A study of the humid oxidation of pyrite, that is, oxidation of pyrite in aqueous medium under oxygen pressure, was undertaken to learn something of the reaction kinetics and mechanism Involved in the primary humid oxidation reactions. The method of investigation is based on measuring the oxygen consumption by the reaction and using this measurement to determine the reaction rates. Experimentally, this measurement is accomplished by recording the change in pressure in an oxygen storage bottle feeding the reaction. Based on the experimental results of this Investigation, a model for the oxidation process is proposed. During the reaction, a stable oxide layer forms on the surface of the pyrite particle and in the model for the oxidation process, the following steps are proposed: 1. Adsorption of oxygen molecules to the surface of the particle and dissociation of the molecules to atoms on the surface. 2. Transfer of electrons from sulfur atoms, through the oxide layer, to adsorbed oxygen atoms. 3. Interstitial diffusion of sulfur ions through the oxide layer to the surface of the particle. 4. Reaction between sulfur ions and oxygen on the surface and desorption of the products of this reaction into solution. 5. Diffusion of lattice defects created at the pyrite oxide interface by sulfur removal to the surface of the particle and diffusion of oxygen atoms into the oxide layer. The mathematical expressions which are developed for the effect of reaction variables are based on this model and are supported by experimental results.
HUMID OXIDATION OF PYRITE. by JAMES FAIRLEY STENHOUSE A thesis submitted i n p a r t i a l f u l f i l m e n t the requirements f o r the degree of MASTER OF APPLIED SCIENCE i n the Department of Mining and Metallurgy at the University of B r i t i s h Columbia THE UNIVERSITY OF BRITISH COLUMBIA September, 1 9 5 0 . ABSTRACT. A study of the humid oxidation of p y r i t e , that i s , oxidation of p y r i t e i n aqueous medium under oxygen pressure, was undertaken to learn something of the reaction k i n e t i c s and mechanism Involved i n the primary humid oxidation reactions. The method of investigation i s based on measuring the oxygen consumption by the reaction and using t h i s measurement to determine the reaction rates. Experi-mentally, t h i s measurement i s accomplished by recording the change in pressure i n an oxygen storage b o t t l e feeding the reaction. Based on the.experimental r e s u l t s of t h i s Investigation, a model for the oxidation process i s pro-posed. During the reaction, a stable oxide layer forms on the surface of the p y r i t e p a r t i c l e and i n the model for the oxidation process, the following steps are. proposed; 1. Adsorption of oxygen molecules to the surface of the p a r t i c l e and d i s s o c i a t i o n of the molecules to atoms on the surface. 2. Transfer of electrons from sulfur atoms, through the oxide layer, to adsorbed oxygen atoms. 3. I n t e r s t i t i a l d i f f u s i o n of sulfur ions through the oxide layer to the surface of the p a r t i c l e . ^. Reaction between sulfu r ions and oxygen on the surface and desorptlon of the products of t h i s reaction into solution. 5. D i f f u s i o n of l a t t i c e defects created at the p y r i t e oxide interface by sulfur removal to the surface of the p a r t i c l e and d i f f u s i o n of oxygen atoms into the oxide layer. The mathematical expressions which are developed f o r the e f f e c t of reaction variables are based on t h i s model and are supported by experimental r e s u l t s . ACKNOWLEDGEMENT. The author wishes to express h i s appreciation for the f i n a n c i a l assistance received during the summers of 19^ 9 and 1950 from the Canadian L i q u i d A i r Company Limited and for the National Research Council Bursary under whioh the inves t i g a t i o n was ca r r i e d out during the winter of 19^ 9 - 50. He i s g r a t e f u l to Mr. F. A. Forward, Head of the Department of Mining and Metallurgy, and to Associate Professor W. M. Armstrong for t h e i r co-operation and d i r e c t i o n . In addition he wishes to thank Mr. D. Moore and Mr. B. Clement of the Department of E l e c t r i c a l Engineering for t h e i r help i n designing the amplifier described i n t h i s report. T A B L E O F C O N T E N T S . P a g e I I N T R O D U C T I O N 1 I I E X P E R I M E N T A L P R O C E D U R E . . . . . . 2 A. P l a n o f I n v e s t i g a t i o n 2 B . E q u i p m e n t . 4 C . I n s t r u m e n t a t i o n 9 1. W h e a t s t o n e B r i d g e . . . . . . 10 2 . A m p l i f i e r a n d R e c t i f i e r 10 3 . M i c r o m a x R e c o r d e r . . . . . . 13 I I I O P E R A T I O N O F E Q U I P M E N T 13 I V P R O D U C T S O F T H E H U M I D O X I D A T I O N O F P Y R I T E * I N C A U S T I C S O L U T I O N S 16 V E X P E R I M E N T A L R E S U L T S 1 8 A . P r e p a r a t i o n o f P y r i t e 1 8 B . A n a l y s i s o f C u r v e s 19 C . E f f e c t o f I m p u r i t i e s . . . . . . 22 D . E f f e c t o f P o t e n t i a l 23 E . E f f e c t o f P r e s s u r e . . . . . . 23 F . E f f e c t o f T e m p e r a t u r e 28 G . E f f e c t o f P a r t i c l e S i z e 31 H . E f f e c t o f C a u s t i c C o n c e n t r a t i o n 33 V I M O D E L F O R O X I D A T I O N ^0 A. O x i d a t i o n o f a P y r i t e S p h e r e 4-0 B . E f f e c t o f P a r t i c l e S i z e D i s t r i b u t i o n 4 8 Page VII DISCUSSION 52 A. Oxidation of Sulfur 52 1. E f f e c t of Pressure 57 2. E f f e c t of Temperature 58 3. E f f e c t of Caustic Concentration 59 4. E f f e c t of P a r t i c l e Size 60 B. Oxidation of Iron 60 1. E f f e c t of Pressure 61 2. E f f e c t of Temperature 61 3. E f f e c t of Caustic Concentration 61 4. E f f e c t of P a r t i c l e Size 62 C. Ef f e c t of P o t e n t i a l 62 VIII CONCLUSIONS 63 APPENDIX A. Calculation for Logarithmic Replot of Oxygen Consumption Curve 65 APPENDIX B. Logarithmic Replots for E f f e c t of Pressure 67 APPENDIX 0. . . . . . . Logarithmic Replots of E f f e c t of Temperature .'.'..'.. 76 APPENDIX D. Logarithmic Replots for E f f e c t of P a r t i c l e Size ...... 82 APPENDIX E. Derivation of Oxidation Expressions 87 BIBLIOGRAPHY 92 HUMID OXIDATION OF PYRITE. I. INTRODUCTION Humid oxidation of a mineral i s the oxidation of the mineral i n aqueous solutions under oxygen pressure. This method of oxidation has been used i n the treatment of a refr a c t o r y gold ore^ 1^, a cobalt ore^\ and o t h e r s ^ \ The main objective of these investigations has been the recovery of valuables from the ores. The object of t h i s i n v e s t i g a t i o n has been to develop a method f o r studying the rate c o n t r o l l i n g step of the humid oxidation reactions and to apply the method to the study of the humid oxidation of p y r i t e i n caustic solutions. The r e s u l t s from, t h i s study of the humid oxida-t i o n of p y r i t e may be of l i t t l e or no commercial importance (1) Carter, R., The Influence of Roasting Temperature upon Gold Recovery from a Refractory Gold Ore, M.A.Sc. Thesis, The University of B r i t i s h Columbia, 19*1-9. (2) Mcintosh, R.B., Recovery of Cobalt from Taylor Gem Ore by Aqueous Oxidation, M.A.Sc. Thesis, The University of B r i t i s h Columbia, 1950. (3) Congreve, W.K.A., The Use of High-Pressure Oxygen i n Extraction Metallurgy, The University of B r i t i s h Columbia, 19^9. 2. b u t t h e r e s u l t s o f t h e i n v e s t i g a t i o n a r e o f i n t e r e s t b e c a u s e o f t h e t y p e o f r e a c t i o n e n c o u n t e r e d . D u r i n g t h e p r o c e s s o f t h e h u m i d o x i d a t i o n o f p y r i t e i n c a u s t i c s o l u -t i o n s , t h e p h e n o m e n o n o f a g r o w i n g i n t e r m e d i a t e f i l m b e t w e e n t h e r e a c t i n g p h a s e s i s e n c o u n t e r e d . A f i l m o f i r o n o x i d e i s f o r m e d o n t h e s u r f a c e o f t h e p y r i t e p a r t i c l e a n d s e p a r a t e s t h e r e a c t i n g s u l f i d e a n d d i s s o l v e d o x y g e n g a s . T h i s c o n d i t i o n i s o f c o u r s e c o m m o n i n t h e r o a s t i n g o f s u l f i d e s . I n t h i s c a s e , a n o x i d e l a y e r f o r m s o n t h e s u r f a c e o f t h e r o a s t i n g s u l f i d e p a r t i c l e a n d s e p a r a t e s - t h e ( 4 ) s u l f i d e f r o m o x y g e n i n t h e a t m o s p h e r e . T h e r e s u l t s o f t h i s i n v e s t i g a t i o n p r o v i d e i n f o r m a t i o n o n t h e k i n e t i c s a n d m e c h a n i s m o f t h i s i m p o r t a n t t y p e o f p r o c e s s . I I E X P E R I M E N T A L P R O C E D U R E A . P l a n o f I n v e s t i g a t i o n . T h e p l a n o f i n v e s t i g a t i o n f o r t h i s w o r k w a s b a s e d o n d e t e r m i n a t i o n o f c h a n g e s i n t h e r a t e o f t h e h u m i d o x i d a -t i o n r e a c t i o n s w i t h c h a n g e s i n r e a c t i o n v a r i a b l e s . T h e r e a c t i o n v a r i a b l e s I n v e s t i g a t e d i n t h e h u m i d o x i d a t i o n o f p y r i t e i n c a u s t i c s o l u t i o n s w e r e : 1 . A v e r a g e p a r t i c l e s i z e o f c h a r g e , 2 . P a r t i a l p r e s s u r e o f o x y g e n i n r e a c t i o n c h a m b e r , (4) P e r e t t i , E . A . , A N e w M e t h o d f o r S t u d y i n g t h e M e c h a n i s m o f R o a s t i n g R e a c t i o n s , D i s c u s s i o n s o f t h e F a r a d a y S o c i e t y , N o . 4 , 1 9 4 8 . 3» Temperature of oxidation, 4; Caustic concentration of solution. The equipment used i n t h i s i n v e s t i g a t i o n was not suitable for studying the effects of a g i t a t i o n on the reaction. This variable has been held constant throughout the.investigation. The humid oxidation reactions were ca r r i e d out i n a pressure reaction chamber. The mineral charge and the aqueous, solution were placed i n the reaction chamber and the chamber was sealed, heated, and continuously agitated. When the reaction temperature was reached, oxygen was fed into the reaction chamber* A constant p a r t i a l pressure of oxygen was maintained i n the chamber /during the reaction by means of a standard oxygen regulator In the oxygen l i n e feeding the reaction chamber. The rate of oxygen consumption by the reaction was used as a measure of the reaction rate. Oxygen con-sumption was determined by recording the change i n pressure i n the oxygen storage bo t t l e feeding the reaction chamber with time. Since the p a r t i a l molal properties of any pure material i s equal to the molal value of that property, the change i n pressure i n t h i s storage bottle i s d i r e c t l y pro-po r t i o n a l to the amount of oxygen flowing from the b o t t l e . I f the pressure and temperature i n the reaction chamber i s constant," t h i s oxygen flowing from the storage b o t t l e i s equal to the oxygen consumed i n the oxidation of the charge. B. Equipment. The preliminary investigation of the humid oxida-t i o n of p y r i t e was c a r r i e d out i n a small rocking autoclave b u i l t i n the Department of Metallurgy at the University of B r i t i s h Columbia. A photograph of t h i s autoclave i s shown In figure I. The pressure vessel oonsisted e s s e n t i a l l y of a 12 inch length of 3 Inch s t e e l pipe closed' at one end with a cast i r o n cap and at the other with a flange and flange pl a t e . This pressure vessel was mounted on a rocking p l a t -form. I t was heated by a nichrome resistance wire heater, wound around the pipe and insulated e l e c t r i c a l l y from i t by a layer of f i b r e g l a s s tape. Oxygen was fed to the reaction from an oxygen storage tank, through a pressure regulator and on to the reaction chamber through a length of f l e x i b l e rubber hose. Temperature was controlled from a thermocouple i n a well i n the reaction chamber connected to a Wheelco Capacltrol. This method of temperature control allowed considerable f l u c t u a t i o n about the operating temperature. The unit was found to be unsatisfactory f o r two reasons. Variations i n steam pressure caused by f l u c t u -ations i n temperature were large enough to seriously a f f e c t the rate of flow of oxygen from the storage b o t t l e and thus destroy the value of the pressure record. The low maximum working pressure of the unit (200 p.s.i.) l i m i t e d the range Figure I AUTOCLAVE USED IN PRELIMINARY INVESTIGATION OF THE HUMID OXIDATION OF PYRITE. of investigation of the effect of temperature and pressure on the reaction. These d i f f i c u l t i e s were overcome with a pressure unit from the American Instrument Company. This unit consists of a stainless s t e e l pressure vessel, an inner removable stainl e s s s t e e l reaction chamber, and a rocking heating jacket. The assembled unit i s shown i n figures 2 and 3. A more complete d i s c r i p t l o n of the unit i s given i n the company catalogue under Catalogue Numbers 4 0 6 - 2 5 K 3 , 406-32H2, 4 0 6 - 0 1 0 A , 406-25LS, 4 0 6 - 2 5 L P . The only change i n the equipment necessary to adapt i t f o r use i n humid oxidation was the replacement of o i l soaked packing with dry asbestos packing i n a l l valves. The maximum operating pressures of t h i s equipment extended the possible scope of investigation of the e f f e c t of temperature and pressure on the reactions. The operating temperatures and pressures for t h i s equipment are: Temp. °F 100 500 650 800 Pressure, p . s . i . 4600 43OO 4000 38OO Close temperature control was achieved by using a p e n c i l thermocouple placed between the heating Jacket and pressure vessel and connected to a Leeds and Northrup, No. 10769-G- electronic c o n t r o l l e r . Figure 2 . PRESSURE UNIT FROM THE AMERICAN INSTRUMENT CO. 8. COPY OF CATALOGUE SKETCH OF PRESSURE UNIT 9 . C. Instrumentation. The method of inves t i g a t i o n of the humid oxida-t i o n reaction i s based on determination of the reaction rate. The experimental plan for measuring t h i s reaction rate consists of feeding the oxygen to the reaction from a small oxygen b o t t l e and measuring the pressure drop In the b o t t l e with time. The volume of a 1 . 5 l i t r e oxygen b o t t l e was adjusted so that the oxygen consumed i n the oxidation of approximately 5 0 grams of s u l f i d e would pro-duce a 1 0 0 0 p . s . i . drop i n pressure i n the b o t t l e . Several attempts were made to design and b u i l d a s a t i s f a c t o r y instrument to measure t h i s pressure change^! A reasonably s a t i s f a c t o r y pressure recording instrument, based on changes i n resistance with pressure was b u i l t and has been used i n the inves t i g a t i o n of the humid oxidation of p y r i t e . A wheatstone bridge of nichrome resistance wire, powered with a 6 . 3 v o l t transformer, was b u i l t into a bourdon tube gauge. Two legs of the bridge were connected, under tension, between the bourdon tube and the case of the gauge. The bourdon tube was connected to the oxygen supply b o t t l e . Changes i n pressure of oxygen i n the supply b o t t l e resulted i n changes i n the tension i n the nichrome wire. This change i n tension caused a change i n resistance and developed a p o t e n t i a l across the wheatstone bridge. ( 5 ) Stenhouse, J.F., Humid Oxidation of Sulfides, Progress Report No. 1 , The University of B r i t i s h Columbia, 1 9 ^ 9 . 10. The p o t e n t i a l was then fed Into an A.C. ampli-f i e r and r e c t i f i e r . The output voltage from t h i s unit was recorded on a Leeds and Northrup Micromax recorder. .1. Wheatstone Bridge. The wheatstone bridge was b u i l t with O.OO3 inch diameter nichrome wire. The wire was strung i n open c o i l s between Insulators. Two legs of the bridge were connected between the case of the gauge and the end of the bourdon tube. The other two legs were wound about f i x e d Insulators mounted i n the case. A wire wound variable r e s i s t o r was connected i n series with one leg for balancing the bridge. A l l legs of the bridge were made as si m i l a r as possible In.order to balance changes In resistance caused by temper-7 ature f l u c t u a t i o n s . The arrangement of the bridge Is shown i n figures k and 5» With a 6.3 v o l t supply to the bridge, a 2 m i l l i -v o l t p o t e n t i a l was developed across the bridge with each 1000 p . s . i . drop i n pressure i n the oxygen supply b o t t l e . 2. Amplifier and R e c t i f i e r . The bridge response was fed into a constant current A.C. amplifier. This amplifier was designed to produce a stable output of low impedance to drive the balancing mechanism of the Micromax recorder. The output of the amplifier ranges between 0 and 50 m i l l i v o l t s and the amplifier i s l i n e a r above a 5 m i l l i v o l t output. The c i r c u i t diagram for t h i s amplifier and r e c t i f i e r i s shown i n figure 6. 1 1 Figure 4. ARRANGEMENT OF VARIABLE AND FIXED LEGS IN WHEATSTONE BRIDGE. F i g u r e 6. A mp//f/e>r for> Af /crom o x + 30DV //S 6 0^J SV of SY3G S/3G jooo • V N / W V v V R /SO VR 150 + 300 WIRING DIAGRAM FOR A . C . AMPLIFIER. 13. 3. Micromax Recorder. The r e c t i f i e d output from the amplif i e r was fed to a Leeds and Northrup model S, 40,000 series, Micromax recorder. In order to compensate f o r the ef f e c t of fluctuations i n l i n e voltage on the output of the wheat-stone bridge, the comparison voltage f o r the Instrument was supplied from r e c t i f i e d l i n e voltage. With t h i s new source of reference voltage i t was necessary to remove the standard c e l l from the recorder. I I I . OPERATION OF EQUIPMENT I f pressure change i n the oxygen storage b o t t l e i s to be a measure of the reaction rate, the rate of oxygen flow from the bott l e must be equal to the rate of consumption i n the oxidation of the mineral charge. Leaks i n the pressure unit would destroy t h i s basic r e l a -t i o n . The equipment has been designed for use at high pressure but i t i s d i f f i c u l t to eliminate a l l small leaks. The leaks can often be detected only from the pressure record a f t e r the oxidation of the mineral charge i s com-plete. Since the rate of leakage may not be constant throughout the reaction, i t i s impossible to correct the pressure curve for leakage and the res u l t s must be discarded. The t o t a l pressure i n the oxidation chamber i s held constant with an oxygen regulator i n the l i n e between 1 4 . the oxygen storage bottle and the reaction chamber. Any decrease i n the p a r t i a l pressure of steam i n the reaction chamber w i l l r e s u l t i n an increase i n the p a r t i a l pressure of oxygen i n the chamber. The oxygen flow necessary to increase the p a r t i a l pressure of oxygen w i l l cause an error i n the pressure curve. S i m i l a r i l y , an Increase i n steam pressure w i l l reduce the rate of flow of oxygen and the rate of change of pressure, and w i l l therefore cause an apparent decrease i n the reaction rate. Although temperature control of the equipment i s s a t i s f a c t o r y , heat generated i n the oxidation of the charge r e s u l t s i n changes i n steam pressure. To correct for t h i s v a r i a t i o n , reaction chamber temperature Is recorded throughout the reaction from a thermocouple well located near the center of the chamber. The change i n steam pressure caused by the temperature change i s determined and the pressure curves are corrected for the v a r i a t i o n . The oxygen regulator which controls pressure i n the reaction chamber i s affected by the rate of gas flow through i t . As the reaction rate decreases, the p a r t i a l pressure of oxygen In the chamber may increase. I t i s therefore necessary to record reaction chamber pressure throughout the reaction and correct the pressure curve for any variat i o n s i n pressure. During the oxidation of a su l f i d e mineral, s u l f u r i c acid i s formed. This acid w i l l neutralize some 15. of the sodium hydroxide to form sodium su l f a t e . The formation of t h i s new s a l t may have a s l i g h t e f f e c t on the p a r t i a l pressure of saturated steam i n the reaction vessel. The e f f e c t of t h i s change on pressure curves has been neglected. Changes In the contact resistance of the balancing r e s i s t o r of the wheatstone bridge has caused i r r e g u l a r i t i e s i n some oxygen consumption curves. In cases i n which the i r r e g u l a r i t i e s have been serious, the r e s u l t s have been discarded. Reactions i n caustic solutions are c a r r i e d out in a st a i n l e s s s t e e l reaction chamber. A f t e r the vessel has been used a few times, a stable oxide f i l m i s b u i l t up on the walls of the vessel. Runs have been made with-out a mineral charge to determine i f there was any oxygen consumption by the vessel a f t e r the stable f i l m had formed. In these runs i t was found that there was no apparent oxygen consumption. 1 6 . IV PRODUCTS OF THE HUMID OXIDATION OF PYRITE IN CAUSTIC SOLUTIONS. The f i n a l products of the humid oxidation of p y r i t e i n caustic solutions are iron oxides and s u l f a t e . The iron oxides form a stable layer around the s u l f i d e p a r t i c l e . X-ray patterns i d e n t i f i e d F e 9 0 o and Fe.O, i n the ^ 3 3 ^ oxides, The i n t e n s i t y of the l i n e s i n the patterns i n d i -cated that a r e l a t i v e l y large amount of an amorphous material was present, probably limonite. A photograph of an X-ray pattern of the oxides i s shown i n figure ?• The iron to s u l f u r r a t i o of the s u l f i d e remains constant during oxidation. This fact was established by analysis of several small p a r t i a l l y oxidized p y r i t e c r y s t a l s a f t e r the oxide l a y e r had been removed. - The f i n a l product of the oxidation of s u l f u r i s sulfate ion. I t i s u n l i k e l y that t h i s material Is produced i n a single reaction but rather by a series of simpler reactions between sulfur and oxygen. In analysis of solu-tions from the oxidation of su l f i d e minerals c a r r i e d out i n ammoniacal aqueous solutions at lower temperatures, such reduced sulf u r compounds as S0^ =, S 20^ =, and Sn0^!St are found. At the temperatures and pressures at which the oxidation of p y r i t e has been c a r r i e d out, the concentration of these reduced forms of s u l f u r i s very low and i t was impossible to i d e n t i f y any of the compounds. T i t r a t i o n of solutions taken from incompletely oxidized charges with a strong Figure 7. 1 <!££ *1 8 Ox iaat/on /?es/o/c/e 60 gms A/oOH /SOO m/. A/c O i I Average /Ctorhc/e S i z e -/O. TemperaSt/re '/BO °C /''re ss c/s*e '/SOp.s-c Ox/c/of/o/? 77/he - 3 Aws /^e 7-1/6 e 7s*nce Spee</ /S~//7cAes/£r: ^ In 1 5 . - - - ° X-RAY PATTERN OF OXIDE. 18. oxidizing agent (KMnO^) Indicated that a trace of some reducing agent was present, probably reduced forms of sulfur. It appears then that the sulfur i s oxidized to sulfate through a series of simpler reactions. Since the concentration of intermediate products in the series of reactions i s low, the f i r s t reaction in the series must be the rate controlling step. Under these conditions the rate of formation of a l l products of the reactions w i l l be equal to the rate of the f i r s t reaction in the series. The rate of oxygen consumption by the series of reactions w i l l therefore also be equal to the rate of the f i r s t reaction in the series.. This i n i t a l reaction must be a surface reaction between sulfur and oxygen. V EXPERIMENTAL RESULTS A. Preparation of Pyrite. A l l experimental runs were carried out with a pyrite concentrate prepared by flotation of Kenville gold ore. The concentrate assayed: Iron: 50.8 % Sulfur: 48.3 % Insoluble: O.o % The concentrate was ground in a laboratory rod m i l l and screened into sized fractions. A portion of the concen-trate was ground further in a laboratory pebble m i l l . The average particle size of each portion was 1 9 . determined. With the l a r g e r sized f r a c t i o n s the average p a r t i c l e size was determined from photomicrographs of samples from the f r a c t i o n s . The product of the largest and smallest dimension of each p a r t i c l e i n the sample was determined. The arithmetic mean of t h i s quantity f o r a l l p a r t i c l e s i n the sample was calculated. The average p a r t i -c l e size of the charge was taken as the square root of t h i s arithmetic mean. The average p a r t i c l e size of the smaller p a r t i c l e size charges was measured with a photoelectric instrument ( 6 ) . B. Analysis of Curves. From the oxygen consumption curves the difference between the t o t a l oxygen consumption and the oxygen consump-t i o n at d e f i n i t e time i n t e r v a l s was calculated. The logarithm of t h i s difference was pl o t t e d against time. A photograph of an oxygen consumption curve i s shown i n figure 8 . The logarithmic pl o t i s shown i n figure 9 . The c a l c u l a -t ions f o r t h i s curve are given i n appendix A. I t was d i s -covered that many of these curves could be divided into two exponential curves. One curve i s att r i b u t e d to the oxida-t i o n of sulfur, the second to the oxidation of ir o n . The two exponential curves were calculated from the combined curve and replotted. These replots are shown In figure 9 * The calculations for the curves are given i n appendix A. ( 6 ) Charles, R.J.T., Photometric Measurement of P a r t i c l e Size and Relative Surface Area, M.A.Sc. Thesis, The University of B r i t i s h Columbia, 1 9 5 0 . F i g u r e 8 OXYGEN CONSUMPTION CURVE. to O F i g u r e 9. 7 7 / 7 7 e /n M/'/iufes LOGARITHMIC REPLOT OF OXYGEN CONSUMPTION CURVE. Q 0 = TOTAL OXYGEN CONSUMPTION. Q = OXYGEN CONSUMPTION AT TIME t . 22. This procedure was repeated for a l l oxygen consump-t i o n curves and i n most cases, two exponential curves were obtained. I t was found that i n runs c a r r i e d out at low p a r t i a l pressures of oxygen, and at low temperatures, the curves corresponding to the oxidation of s u l f u r were not exponential. Increasing the caustic concentration of solu-tions completely changed the c h a r a c t e r i s t i c of the logarithmic curves. A few runs had been stopped before oxidation was complete and i t was necessary to exterpolate the curves beyond t h i s time. This exterpolation was accomplished by comparing the oxygen consumption curve to curves run under si m i l a r conditions. The f i n a l portion of the exponential curves are very sensitive to small errors i n the oxygen consumption curves. In most cases, the logarithmic p l o t s were stopped when the difference between the f i n a l oxygen consumption and the actual oxygen consumption reached approximately two percent of the t o t a l oxygen consumption. C. E f f e c t of Impurities. Additions of small amounts of s i l i c a to the p y r i t e charge had a pronounced ef f e c t on the rate of both reactions. I t was found to be possible to completely stop the oxidation of p y r i t e i n a one normal solution of caustic soda at 150°C and a p a r t i a l oxygen pressure of 200 p . S i i . by addition of 5° percent s i l i c a to the charge. No attempt 2 3 . has been made to record the e f f e c t of s i l i c a content on the rate of oxygen consumption. Additions of l i n e and barium hydroxide to the charge had similar e f f e c t s . D. Ef f e c t of P o t e n t i a l . An insulated electrode was connected to a single large p y r i t e c r y s t a l . This c r y s t a l was then placed i n the small reaction vessel described i n t h i s report and shown i n figure 1. The electrode was passed through an asbestos packed gland i n the flange plate. A steel s h i e l d had been welded to the cooling c o i l i n the unit and the c r y s t a l was placed i n t h i s s h i e l d . A second pyrite c r y s t a l was wired to the cooling c o l l . A 6 vo l t p o t e n t i a l was applied between the unit and the c r y s t a l with the py r i t e c r y s t a l as the negative electrode and the charge was oxidized i n a one normal solu-t i o n of caustic soda at 130°C and 100 p . s . i . t o t a l pressure f o r four hours. The cathodic p y r i t e c r y s t a l was completely oxidized i n t h i s time.. The. second c r y s t a l showed only s l i g h t surface tarnish. The iro n oxide formed during the reaction was f a i r l y coarse but had been removed from the c r y s t a l during the reaction. An X-ray pattern of t h i s material proved i t to be Fe^O^. A photograph of the pattern i s shown i n figure 10. E. E f f e c t of Pressure. A l l experimental pressure runs were made i n a one Figure 10. X-RAY PATTERN OF OXIDE RESIDUE FROM SINGLE CRYSTAL. 25. normal caustic soda solution at 120°C using p y r i t e prepared i n the laboratory pebble m i l l . The average p a r t i c l e size of t h i s material, as measured by the photoelectric apparatus was found to be 10.9 microns. Pressure was varied between 50 and 800 p . s . i . The charge to the unit was held constant at: 40 grams p y r i t e 60 grams caustic soda 1500 m i l l i l i t r e s water. The rate of oxidation of ir o n obeys Sievert's Law f a i r l y well. The rate of oxidation i s proportional to the square root of the p a r t i a l pressure of oxygen above the charge. The r e s u l t s from the logarithmic curves plotted against the root of pressure are given i n figure 11. The curves at t r i b u t e d to the oxidation of su l f u r were found to be exponential when the p a r t i a l pressure of oxygen exceeded approximately 350 p . s . i . at 120°C. At lower p a r t i a l oxygen pressures, the f i r s t portions of the curves were apparently exponential. The slope of these low pressure curves increased with time. The slope of the i n i t i a l exponential portion of these curves was chosen to represent the rate of oxidation of sulfu r at low pressure. A plot of the rate of oxidation of su l f u r against the p a r t i a l pressure of oxygen i s given i n figure 12. This curve i s a saturation type curve s i m i l a r to a gas adsorption curve. The saturation value i s reached at approximately 500 p . s . i . EFFECT OF PRESSURE ON THE RATE OF OXIDATION OF IRON. Figure 1 2 . EFFECT OF PRESSURE ON THE RATE OF OXIDATION OF SULFUR. 2 8 . C u r v e s u s e d t o p l o t f i g u r e s 11 a n d 12 a r e g i v e n i n a p p e n d i x B . F . E f f e c t o f T e m p e r a t u r e . A l l e x p e r i m e n t a l t e m p e r a t u r e r u n s w e r e made i n a o n e n o r m a l c a u s t i c s o d a s o l u t i o n w i t h a n o x y g e n p a r t i a l p r e s s u r e o f 2 0 0 p . s . i . T h e a v e r a g e p a r t i c l e s i z e o f t h e p y r i t e c h a r g e s was 1 0 . 9 m i c r o n s . T h e c h a r g e t o t h e u n i t was h e l d a t : 4 0 g r a m s p y r i t e 60 g r a m s c a u s t i c s o d a 1500 m i l l i l i t r e s w a t e r . T e m p e r a t u r e w a s v a r i e d f r o m 9 0 ° C t o 1 8 0 ° C . T h e u p p e r t e m p e r a t u r e , was l i m i t e d "by t h e w o r k i n g p r e s s u r e o f t h e o x y g e n r e g u l a t o r . T h e l o w e r l i m i t t o t e m p e r a t u r e was f i x e d b y t i m e r e q u i r e d t o c o m p l e t e o x i d a t i o n . T h e r e s u l t s o f t h e e f f e c t o f t e m p e r a t u r e o n t h e l o g a r i t h m o f t h e r a t e o f t h e o x i d a t i o n o f i r o n i s g i v e n i n f i g u r e 1 3 . T h e a c t i v a t i o n e n e r g y , c a l c u l a t e d f r o m t h e s l o p e o f t h i s c u r v e i s e q u a l t o 1 , 8 4 0 c a l o r i e s . T h e r e s u l t s o f t h e e f f e c t o f t e m p e r a t u r e o n t h e l o g a r i t h m o f t h e r a t e o f o x i d a t i o n o f s u l f u r i e g i v e n i n f i g u r e 1 4 . A t l o w e r t e m p e r a t u r e s , t h e c u r v e s f o r the o x i d a t i o n o f s u l f u r were not e x p o n e n t i a l o v e r t h e e n t i r e l e n g t h . The s l o p e o f . t h e i n i t i a l p o r t i o n o f t h e c u r v e s was chosen t o r e p r e s e n t t h e r a t e o f o x i d a t i o n o f s u l f u r a t l o w t e m p e r a t u r e s . .The a c t i v a t i o n e n e r g y for- t h i s p r o c e s s , c a l c u l a t e d from t h e s l o p e o f t h e c u r v e i n f i g u r e 14 i s EFFECT OF TEMPERATURE ON THE LOGARITHIM OF THE RATE OF OXIDATION OF IRON. F i g u r e 14. EFFECT OF TEMPERATURE ON THE LOGARITHIM OF THE RATE OF OXIDATION OF SULFUR. 31. 4,210 c a l o r i e s . A l l replots of the work on the effect of tempera-ture are given i n appendix 0. G-. Effect of P a r t i c l e Size. Experimental runs were made i n a one normal caustic soda solution at 120°C with an oxygen p a r t i a l pressure of 200 p . s . i . Four ranges of p a r t i c l e size were investigated. The charge to the unit was held constant at; 30 grams pyrite 60 grams caustic soda 1500 m i l l i l i t r e s water. The curves corresponding to the oxidation of s u l f u r were not truly, exponential. The slope of the i n i t i a l portion of these curves was chosen to represent the rate of oxidation of sulfur. The logarithmic replots of the oxygen consumption curves are given In appendix D. The r e s u l t s of the effect of p a r t i c l e size on the rate of the two reactions are given i n figure 15. The rea.ction rate i s plotted, against the Inverse of the square of the average p a r t i c l e size of the charge. The f i r s t three points of each curve l i e on a f a i r l y straight l i n e . The points corresponding to the reaction rates of the charge with an average p a r t i c l e size of 10.9 microns deviate greatly from t h i s l i n e . This deviation Is believed to be caused by increased s i l i c a content of t h i s charge. The assays of each p a r t i c l e size range investigated were: 32. Figure 15. EFFECT OF PARTICLE SIZE ON RATES OF OXIDATION. Average p a r t i c l e size i n microns: 1 0 . 9 2 7 . 7 8 8 . ~ 119 Percent iron: 4 4 . 6 4 7 . <5 4 8 . 2 4 8 . 2 Percent sulfur: 4 7 . 0 5 0 . 4 5 0 . 8 5 1 . 0 Percent i n s o l u b l e s 5 . 0 1.8 0 . 8 1 .0 I t i a doubtful that the rates of oxidation of the p y r i t e with an average p a r t i c l e size o f 1 0 . 9 microns could have reached the t h e o r e t i c a l rates obtained by projection o f the straight l i n e s of figure 15 before the reaction became controlled by solution of oxygen. The fact that higher rates were obtained i n the oxidation of the p y r i t e with an average p a r t i c l e size o f 2 7 « 7 microns proves that the rate of solution o f oxygen i s able to support h i g h e r rates than those obtained i n the oxidation of the f i n e r p y r i t e and that the reduction in the reaction rates of t h i s p y r i t e was not caused by oxygen solution becoming the rate c o n t r o l l i n g step i n the reaction. H. Effect of Caustic Concentration. .Experimental runs on the effect of caustic con-centration on the rates of oxidation were carried out on p y r i t e of 1 0 . 9 m i c r o n average p a r t i c l e size at 1 2 0 ° C and with oxygen p a r t i a l pressure of 200 p . s . i . Five experi-mental runs were ms.de with caustice concentration varied between one and eight normal. In each case, runs were made with 40 grams of p y r i t e and 1500 m i l l i l i t r e s of solution. The logarithmic plots from the oxygen consumption curves for runs made with one and two normal caustic solu-tions separated Into two curves. These curves are given i n figures 16 and 17 . Figure 16 34. 1-4 LOGARITHMIC REPLOT OF OXYGEN CONSUMPTION CURVE. CAUSTIC CONCENTRATION - 1 NORMAL F i g u r e 1 7 . LOGARITHMIC REPLOT OF OXYGEN CONSUMPTION CURVE. CAUSTIC CONCENTRATION = 2 NORMAL. 36. The curves corresponding to the oxidation of sul f u r are not true exponentials. Using the slope of the i n i t i a l portion of these curves to represent the rate of oxidation of sulfur, i t i s found that increasing the caustic concentration, of the solution increased the rate of oxida-t i o n of sulfur. From the slope of the curves corresponding to the oxidation of iron, i t was found that increasing caustic concentration also increases the rate of oxidation of the i r o n . Experimental logarithmic curves f or runs made i n solutions with caustic concentration greater than two normal could not be separated into two curves. Only the l a t t e r portion of these curves were exponential. The curves are given i n figures 18, 19 and 20. The slope of the oxygen consumption curves for these runs was found to be constant for the f i r s t t>art of the reaction. The reaction rate for t h i s portion of the curve i s apparently independent of the amount of sulfide present. During the i n i t i a l stages of the reaction, the reaction must therefore be controlled by solution of oxygen or adsorption of oxygen to the surface of the p a r t i c l e s . During the l a t t e r stage of the reaction, oxygen consumption follows an exponential law. Apparently during t h i s stage 5 the rate of d i f f u s i o n of sulfur and the rate of oxidation of iron f a l l below the rate of solution and adsorption of oxygen and they become the c o n t r o l l i n g step Figure 18. O SO 40 60 80 ,. /OO /So /-ft 7~' /?? e //? A////7C/ Ye s LOGARITHMIC REPLOT OF OXYGEN CONSUMPTION CURVE. CAUSTIC CONCENTRATION = k NORMAL F i g u r e 19 CAUSTIC CONCENTRATION - 6 NORMAL. Figure 20. /•4 7~//T?<P />? /ty//?i//e s LOGARITHMIC REPLOT OF OXYGEN CONSUMPTION CURVE. CAUSTIC CONCENTRATION = 8 NORMAL. 40. In the reaction. The slope of the exponential portion of these curves i s independent of caustic concentration. VI MODEL FOR OXIDATION A. Oxidation of a P y r i t e Sphere. There are two l o g i c a l methods by which the oxida-t i o n reaction could take place. I f the oxide layer which forms on the surface of the s u l f i d e p a r t i c l e i s porous, oxygen could d i f f u s e through pores and defects i n the oxide lay e r to the s u l f i d e oxide interface, and react at t h i s surface. The sulfur-oxygen compound formed would d i f f u s e to the surface of the p a r t i c l e and go into the solution. I f the oxide layer i s compact, d i f f u s i o n of oxygen would be d i f f i c u l t and d i f f u s i o n of sulfur-oxygen compounds would be impossible. In t h i s case, i t seems more l i k e l y that s u l f u r would diffuse i n t e r s t i t l a l l y through the oxide layer to the surface of the p a r t i c l e and react at the surface with oxygen. The l a t t i c e defects created at the s u l f i d e oxide interface through sulfur removal would provide a means for s u b s t i t u t i o n a l d i f f u s i o n of oxygen into the oxide layer. The experimental r e s u l t s are i n agreement with the second mechanism of oxidation. The rate of oxidation of sulfur and the e f f e c t of p o t e n t i a l on t h i s rate indicate that sulfur diffuses.as a p o s i t i v e ion through the oxide layer. Work on the e f f e c t of oxidizing conditions on conductivity of s u l f i d e s also indicates that s u l f u r ions form during oxidation^ 8 K Based on ion i c sulfur d i f f u s i o n through a compact oxide layer, the following steps i n the oxidation process are proposed: 1; Adsorption of oxygen molecules to the surface of the p a r t i c l e and d i s s o c i a t i o n of the molecules to atoms on the surface. : 2. Transfer of electrons from sulf u r atoms, through the oxide layer, to adsorbed oxygen atoms. - 3. I n t e r s t i t i a l d i f f u s i o n of sulfur ions through the oxide layer to the surface of the p a r t i c l e . 4. Reaction between sulfur ions and oxygen-on the surface and desorption of the products of t h i s reaction i n t o solution. 5. D i f f u s i o n of l a t t i c e defects created at the p y r i t e oxide interface by sulf u r removal to the surface of the p a r t i c l e and d i f f u s i o n of oxygen atoms into the oxide layer. . The electron transfer would take place by thermal e x c i t a t i o n of electrons from the pyrite into the conduction band of the oxide. The electrons would move through the oxide and f i l l vacant l e v e l s on the adsorbed oxygen atoms, forming oxygen ions. This process i s shown diagrammatl-c a l l y i n figure 21. (8) Anderson, J.S., The Primary Reaction in Roasting and Reduction Processes Discussions of the Faraday Society, No. k, 1948. Figure 2 1 . T i f Vecanf £/ec/>-e>/7 Su ///</«> When an electron transfer takes place, a potential' would be set up across the oxide. I f the process of electron transfer was rapid, i t would continue u n t i l the po t e n t i a l across the oxide r a i s e d the l e v e l of vacant l e v e l s on the oxygen atoms to the height of the energy l e v e l of electrons in the s u l f i d e . This condition i s shown diagrammatically i n figure 2 2 . In t h i s sketch the effect of the sulfur ions d i f f u s i n g through the oxide layer on the po t e n t i a l across the layer Is neglected. When the electron transfer takes place, a p o s i t i v e s u l f u r ion would form at the pyrite surface. During the oxidation, t h i s ion would pass through the oxide layer.by i n t e r s t i t i a l d i f f u s i o n . Oxygen atoms diffuse into the oxide layer by moving into l a t t i c e defects. The rate of d i f f u s i o n of the oxygen atoms would depend upon the concentration of l a t t i c e defects i n the oxide layer and the concentration of oxygen atoms absorbed to the surface of the p a r t i c l e . I t would be reasonable to expect a concentration gradient f o r oxygen through the oxide layer. X - r a y patterns have i d e n t i f i e d Fe 20^ and Fe^O^ i n the oxide. The Intensity of l i n e s i n the patterns suggest the presence of an amorphous material, probably limonite. The oxide layer i s therefore probably composed of four layers: 1. A region of iron atoms pseudomorphic with the c r y s t a l structure of iron atoms i n pyri t e , containing a 4 4 . Figure 22. Ox,</e 4 5 . low concentration of oxygen atoms. The concentration of oxygen atoms i n t h i s structure would increase with distance from the p y r i t e i n terface. 2 . A layer of Fe„0.. 3 . A layer of Fe 20^. 4 . An outer layer of limonite. There appears to be an equilibrium concentration of Fe^Oj^ and Fe 20^ or FegO^.nHgO i n the f i n a l oxide. Fe^O^ has been i d e n t i f i e d i n X-ray patterns of powders taken from oxidized charges i n which measurable oxygen consumption had ceased. No attempt has been made to determine the amount of Fe^O^ present or the e f f e c t of the conditions of oxida-t i o n on t h i s quantity. Based on t h i s model for oxidation, the possible rate c o n t r o l l i n g steps i n the reaction are; 1. Adsorption of oxygen to the surface of the p a r t i c l e . 2. Reaction between sulfu r ions and oxygen ions on the surface of the p a r t i c l e . 3 . Desorption of the products of the surface reaction between su l f u r and oxygen. 4 . Transfer of electrons from sulf u r to oxygen. 5 . D i f f u s i o n of sulfur ions through the oxide layer. The problem of obtaining a mathematical expression f o r the rates of oxidation based on t h i s model has proven 46* to be too d i f f i c u l t . In a survey of the mathematical l i t e r a t u r e on theories of d i f f u s i o n i t was discovered that (a) no general solution for the problem has been found*- 7 7. The problem Is e s s e n t i a l l y one of d i f f u s i o n from a moving interface. Attempts to solve the problem by assuming expressions f o r the rate of motion of the p y r i t e -oxlde interface were unsuccessful. In order to obtain an expression f o r the rates of oxidation of sulfur and iron, i t has been necessary to neglect the interface reaction and assume that the process i s one«of pure d i f f u s i o n . In the following expression f o r the oxidation of s u l f u r i t i s assumed that sul f u r ions di f f u s e from a sphere.- At zero time, the concentration of s u l f u r ions i s assumed to be constant throughout the sphere. The concentration of sulfur Ions at the surface of the sphere i s assumed to be equal to zero for a l l time. Under these assumptions, the following expression i s obtained: Where: Q 0 = i n i t i a l quantity of sulfur In the sphere. Q' = quantity d i f f u s e d out at time t . C 0 = i n i t i a l concentration of s u l f u r i n the sphere. a' = radius of sphere D = d i f f u s i o n c o e f f i c i e n t t - time. (9) Carslaw, H.S., Introduction to the Mathematical Theory of the Conduction of Heat i n Solids. 2 ed. Dover Publications 1 9 4 5 . 4 ? . The derivation of t h i s expression i s given i n appendix E. The true expression for the rate of oxidation would probably be an expression similar to t h i s , but modified to include the e f f e c t s of the interface reaction. In deriving an expression for the rate of oxida-t i o n of iron i t has been necessary to make s i m i l a r assump-ti o n s . The expression is-based on the assumption that oxygen diff u s e s into a sphere with an i n i t i a l concentration of oxygen equal to zero. The concentration of oxygen on the surface of the p a r t i c l e i s assumed to he constaht. The expression, based on these assumptions i s equal to? 7T Where: 0 ^ = f i n a l quantity of oxygen i n the sphere Q = quantity of oxygen diffused i n at time t Cj_ » concentration of oxygen at the surface. The derivation of t h i s expression i s given i n appendix E. This expression ignores possible e f f e c t s of changes of phase i n the oxide and also the e f f e c t of the concentration of l a t t i c e defects i n the sphere. The actual expression for the rate of d i f f u s i o n of oxygen would be rel a t e d to the rate of formation of l a t t i c e defects at the pyrite-oxlde interface. 48. Bo E f f e c t of P a r t i c l e S i z e D i s t r i b u t i o n . The t r u e e x p r e s s i o n f o r the o x i d a t i o n o f a s i n g l e p y r i t e p a r t i c l e w i l l be some f u n c t i o n of time and o f p a r t i c l e s i z e . L e t t h i s f u n c t i o n be: f ( t , r ). The e x p r e s s i o n f o r the o x i d a t i o n o f n suoh p a r t i c l e s a l l o f the same s i z e w i l l be: n f ( t , r ). I f the p y r i t e charge c o n t a i n s p a r t i c l e s w i t h a p a r t i c l e s i z e d i s t r i b u t i o n g i v e n by some f u n c t i o n of p a r t i c l e s i z e ; i . e . n = g ( r ) the e x p r e s s i o n f o r the o x i d a t i o n o f t h i s charge w i l l be equal t o : / f ( t , r ) g ( r ) d r . As has been shown, wit h c e r t a i n assumptions, the e x p r e s s i o n f o r f ( r , t ) i s of the form: K - t Where: becomes: A r ^ - Br3e r A, B, and K are co n s t a n t s r » the r a d i u s o f the p y r i t e sphere t = time. S u b s t i t u t i n g t h i s e x p r e s s i o n i n the i n t e g r a l , i t - - h A/ r3g(r)dr - B/ r3g(r)e r dr - f e t O o h s i d e r a p l o t o f t h e t e r m e r . T h i s 49. e x p r e s s i o n h a s t h e g e n e r a l f o r m s h o w n i n f i g u r e 23 . T h e s l o p e o f t h i s c u r v e d e p e n d s u p o n t h e v a l u e s o f K a n d t . T h e e x p r e s s i o n f o r t h e c h a n g e o f s l o p e o f t h e c u r v e i s e q u a l t o : e - h t . W h e n K a n d t a r e s m a l l , t h e s l o p e , i s l a r g e . A s K a n d t i n c r e a s e , t h e s l o p e d e c r e a s e s e x p o n e n t i a l l y . T h e s l o p e a l s o d e c r e a s e s r a p i d l y w i t h d e c r e a s i n g r . : C o n s i d e r a p a r t i c l e s i z e d i s t r i b u t i o n t h a t h a s d e f i n i t e l i m i t s , r - ^ a n d v^i i . e . . g ( r ) = 0 r < r ^ : g ( r ) = 0 r > r 2 * L e t r a b e t h e a v e r a g e p a r t i c l e s i z e o f t h i s d i s t r i b u t i o n . I n t h i s r a n g e , c o n s i d e r t h e e x p r e s s i o n r ^ e t o b e a c o n s t a n t e q u a l t o ~ 2 X e • a . T h e e r r o r i n t h i s a s s u m p t i o n w i l l b e s m a l l p r o v i d i n g t h e s l o p e o f t h e c u r v e i s s m a l l i n t h e r a n g e r ^ t o r^. T h e e x p r e s s i o n f o r t h e t o t a l o x y g e n c o n s u m p t i o n t h e n r e d u c e s t o : L + r^i ~ r 2 r ' V A / r 3 g ( r ) d r — Be a / r 3 g ( r ) d r . 50. 51. . CO The expression / r 3 g(r)dr i s equal to the t h i r d moment of o the d i s t r i b u t i o n about the o r i g i n m u l t i p l i e d by the t o t a l number of p a r t i c l e s i n the charge; -V i . e . nAr3 - nBf»3e a . The error i n t h i s expression depends upon the spread of the p a r t i c l e size d i s t r i b u t i o n and upon time. As time increases, the slope of the curve e r 2 decreases and the error i n assuming i t to be a constant equal to K_ t " r 2 e a decreases. It has been assumed In t h i s development that the p a r t i c l e size d i s t r i b u t i o n has d e f i n i t e sharp l i m i t s . This condition may be true i n charges prepared by screening. As has been stated, one portion of the p y r i t e charge was prepared by grinding i n a laboratory pebble m i l l and t h i s material has been used for the majority of the experimental runs. I t would be l o g i c a l to suppose that t h i s material would have a less sharply defined l i m i t to the p a r t i c l e size d i s t r i b u t i o n than the screened fracti o n s and an analysis of the possible effect of t h i s condition would be u s e f u l . 52. The increased spread i n the p a r t i c l e size d i s t r i -bution would tend to increase the error i n the assumption that the expression was constant equal to e a over the t o t a l p a r t i c l e size range. However, the f i n e r p a r t i c l e size produced by fine grinding i n the pebble m i l l would decrease the slope of the curve and tend to compensate for p a r t i c l e size d i s t r i b u t i o n spread. Any e f f e c t s from the d i s t r i b u t i o n spread would be most notlcable at small values of time. In the method of i n v e s t i g a t i o n used, i n t h i s work there was a c e r t a i n time lag between the start of the reaction and the start of oxygen consumption measure-ment. This l a g was usually In the order of f i v e minutes and no p e c u l i a r i t i e s i n the oxygen consumption curves that could be a t t r i b u t e d to size d i s t r i b u t i o n have been observed. VII DISCUSSION A. Oxidation of Sulfur. The expression fo r the oxidation of sulfur Is based on the assumption that the concentration of s u l f u r at the surface of the p a r t i c l e i s zero. This assumption i s Inexact since i n the reaction between s u l f u r and oxygen 53-o n t h e s u r f a c e o f t h e o x i d e l a y e r , t h e r e w i l l b e a n e q u i l i b r i u m c o n c e n t r a t i o n o f s u l f u r w h i c h w i l l d e p e n d u p o n t h e r a t e a t w h i c h s u l f u r a r r i v e s a t t h e s u r f a c e a n d t h e r a t e a t w h i c h i t r e a c t s w i t h o x y g e n . T h e e x p r e s s i o n f o r t h e r a t e a t w h i c h s u l f u r a r r i v e s a t t h e s u r f a c e o f t h e p a r t i c l e a t c o n s t a n t t e m p e r -a t u r e h a s t h e f o r m : A e ~ k t w h e r e A a n d k a r e c o n s t a n t s t = t i m e . T h e e x p r e s s i o n f o r the r a t e o f r e a c t i o n o f s u l f u r a t t h e s u r f a c e o f t h e p a r t i c l e w i l l d e p e n d u p o n t h e c o n -c e n t r a t i o n o f o x y g e n a d s o r p t e d - t o t h e s u r f a c e a n d t h e c o n c e n t r a t i o n o f s u l f u r o n t h e s u r f a c e . T h e e x p r e s s i o n w i l l a l s o d e p e n d u p o n t h e p r o d u c t o f t h l B s u r f a c e r e a c t i o n . F o r s i m p l i c i t y a s s u m e t h a t o n e a t o m o f o x y g e n r e a c t s w i t h o n e a t o m o f s u l f u r . T h e e x p r e s s i o n f o r t h e r a t e o f t h i s s u r f a c e r e a c t i o n a t c o n s t a n t t e m p e r a t u r e , w i l l t h e n h a v e t h e f o r m : w h e r e K = C o " K C 0 G B c o n s t a n t c o n c e n t r a t i o n o f o x y g e n c o n c e n t r a t i o n o f s u l f u r . T h e e x p r e s s i o n f o r t h e c h a n g e o f t h e c o n c e n t r a -t i o n o f s u l f u r o n t h e s u r f a c e a t c o n s t a n t t e m p e r a t u r e i s e q u a l t o : 5 4 . dCfl = Ae~ k t - KC 0O s dt At constant pressure, the concentration of adsorbed oxygen i s assumed constant. Solution of t h i s l i n e a r f i r s t -order d i f f e r e n t i a l equation y i e l d s : c s = A ( e ~ K C o t - e~ k t) KC 0 - k When the concentration of adsorbed oxygen i s large, the expression KC 0 approaches k and the expression reduces to zero, and the assumption made i n the derivation of the expression f o r oxidation of sulfur, i . e . that the concentration of sulfu r at the surface of the p a r t i c l e i s zero, w i l l " n o t be seriously in error. » At low oxygen pressures however, the assumption w i l l be more seriously i n error. The concentration of adsorbed oxygen w i l l be low and the expression for the concentration of s u l f u r on the surface w i l l be equal to: C a = A (e- KCot - e - k t ) KC 0 - k A sketch of t h i s function i s given i n figure 2 4 . The t o t a l change i n concentration of su l f u r on the surface of the p a r t i c l e with time w i l l increase with decreasing pressure. This r e l a t i v e l y high concentration of sul f u r w i l l have an important effect on the rate of oxidation of the su l f u r . E f f e c t i v e l y , an appreciable 55. Figure 24. J5>£&fcA of /A>e (Tt/s^isff Q-- A— (e ~e 5 6 . c o n c e n t r a t i o n o f s u l f u r a t t h e s u r f a c e o f t h e p a r t i c l e w i l l d e c r e a s e t h e c o n c e n t r a t i o n g r a d i e n t o f s u l f u r t h r o u g h t h e o x i d e l a y e r a n d t h u s r e d u c e t h e r a t e o f d i f f u s i o n o f s u l f u r . A t l o w o x y g e n p r e s s u r e s , t h e c o n c e n t r a t i o n o f s u l f u r a t t h e s u r f a c e o f t h e p a r t i c l e w i l l f o l l o w t h e c u r v e s h o w n i n f i g u r e 2 4 . T h e c o n c e n t r a t i o n g r a d i e n t f o r s u l f u r , c o m p a r e d t o t h e g r a d i e n t i n a p a r t i c l e w i t h z e r o c o n c e n t r a t i o n a t t h e s u r f a c e , w i l l d e c r e a s e t o a m i n i m u m a t C m a n d t h e n i n c r e a s e w i t h t i m e . T h e r a t e o f o x i d a t i o n o f s u l f u r s h o u l d t h e r e f o r e a p p r o a c h t h a t o f o x i d a t i o n o f a p a r t i c l e w i t h z e r o c o n c e n t r a t i o n o f s u l f u r a t t h e s u r f a c e . I n t h e r e g i o n o f 0 m ( f i g u r e 2 4 ) t h e c o n c e n t r a t i o n o f s u l f u r a d s o r b e d t o t h e s u r f a c e o f t h e p a r t i c l e w i l l b e s u b s t a n t i a l l y c o n s t a n t . I n t h i s r e g i o n , t h e r a t e o f o x i d a -t i o n o f s u l f u r s h o u l d b e v e r y c l o s e " t o a n e x p o n e n t i a l . A t t h i s c o n c e n t r a t i o n , o f a d s o r b e d s u l f u r , t h e r a t e o f o x i d a t i o n o f s u l f u r w i l l r e a c h a m i n i m u m . T h e e x p e r i m e n t a l r e s u l t s o n t h e e f f e c t o f p r e s s u r e o n t h e o x i d a t i o n o f s u l f u r a r e i n a g r e e m e n t w i t h t h i s p i c t u r e . A t h i g h o x y g e n p a r t i a l p r e s s u r e s , t h e s u l f u r o x i d a t i o n c u r v e s a r e t r u e e x p o n e n t i a l s w h i l e a t l o w o x y g e n p r e s s u r e s , t h e c u r v e s d e v i a t e f r o m e x p o n e n t i a l . T h e m i n i m u m v a l u e f o r t h e o x y g e n p a r t i a l p r e s s u r e a t w h i c h t h e c u r v e b e c o m e s e x p o n e n t i a l a p p e a r s t o b e a p p r o x i m a t e l y 350 p . s . i . a t 1 2 0 ° C . I n a l l l o w p r e s s u r e o x i d a t i o n r u n s , t h e r a t e o f o x i d a t i o n o f s u l f u r i n c r e a s e s w i t h t i m e . 5 7 . Apparently, through the delay i n s t a r t i n g the oxygen consumption record, the part of the curve corresponding to the increase i n the concentration of sulfur on the surface to C m (figure 24) and the corresponding decrease i n the rate of oxidation of s u l f u r has been missed. The experimental values for the rates of oxidation of s u l f u r at low pressures i s believed to be the minimum rate of oxidation corresponding to the rate encountered with a surface concentration of sulfur equal to C m (figure 24). 1. E f f e c t of Pressure* Providing that-the concentration of sulfur on the surface of the p a r t i c l e i s low, the concentration gradient fo r d i f f u s i o n of sulfur i s determined by the difference i n p o t e n t i a l between electrons i n the p y r i t e and vacant l e v e l s on adsorbed oxygen atoms (figure 21) and the thickness of the oxide layer. The rate of d i f f u s i o n of s u l f u r under t h i s condition should be equal to the rate of oxidation of s u l f u r and therefore should be independent of the oxygen p a r t i a l pressure. This condition i s supported experimentally. At low oxygen p a r t i a l pressures, the change i n concentration of sulfur on the surface of the p a r t i c l e w i l l be appreciable but w i l l decrease with time. The rate of oxidation of sulfur should therefore increase with time. This condition i s supported experimentally. 58. T h e v a l u e o f C m ( f i g u r e 2 4 ) w i l l d e c r e a s e w i t h i n c r e a s i n g p r e s s u r e . T h e c o n c e n t r a t i o n g r a d i e n t a t t h i s t i m e w i l l t h e r e f o r e a l s o I n c r e a s e t h e p r e s s u r e t o a m a x i -m u m w h e n C m i s e q u a l t o z e r o . T h e r a t e o f d i f f u s i o n a n d o x i d a t i o n o f s u l f u r a t t h i s p o i n t w i l l t h e r e f o r e a l s o i n c r e a s e t o a m a x i m u m w i t h p r e s s u r e . T h e e x p e r i m e n t a l p l o t o f t h e e f f e c t o f p r e s s u r e o n t h e r a t e o f o x i d a t i o n o f s u l f u r i s i n a g r e e m e n t w i t h t h i s p i c t u r e . 2 . E f f e c t o f T e m p e r a t u r e . T h e e x p r e s s i o n f o r t h e c o n c e n t r a t i o n o f s u l f u r o n t h e s u r f a c e o f a p a r t i c l e a t c o n s t a n t t e m p e r a t u r e i s e q u a l t o : i C 8 -_- A < e- K°o* - e - k t ) K C 0 - k T h e e f f e c t o f t e m p e r a t u r e o n t h i s e x p r e s s i o n w i l l d e p e n d u p o n t h e s e n s i t i v i t y o f K , C Q a n d k t o t e m p e r a t u r e . E x p e r i m e n t a l l y , i t i s f o u n d t h a t t h e o x y g e n c o n s u m p t i o n c u r v e s b e c o m e e x p o n e n t i a l w i t h i n c r e a s i n g t e m p e r a t u r e . T h i s f a c t w o u l d i n d i c a t e t h a t t h e p r o d u c t K C Q i n c r e a s e s m o r e r a p i d l y w i t h t e m p e r a t u r e t h a n d o e s k . T h e e f f e c t o f t e m p e r a t u r e o n t h e r a t e o f o x i d a t i o n o f s u l f u r i s f o u n d t o o b e y t h e A r r h e n l u s e q u a t i o n . T h e e x p e r i m e n t a l a c t i v a t i o n e n e r g y f o r t h e p r o c e s s i s f o u n d t o b e 4 , 2 1 0 c a l o r i e s . T h i s l o w v a l u e f o r t h e d i f f u s i o n p r o c e s s i s b e l i e v e d t o b e c a u s e d b y t h e h i g h s t a t e o f d i s o r d e r a n d h i g h c o n c e n t r a t i o n o f l a t t i c e d e f e c t s t h a t 5 9 . must exis t i n the oxide layer. 3 . Effeot of Caustic Concentration. Increasing the caustic concentration of the solutions from one to two normal increased the rate of oxidation of s u l f u r . The reaction has apparently become contr o l l e d by solution or adsorption of oxygen with caustic concentration above two normal. Based on the model'for oxidation, increasing caustic concentration should have the same ef f e c t on the rate of oxidation of s u l f u r as decreasing pressure since increasing caustic concentration of the solution would cause a decrease i n the s o l u b i l i t y of oxygen^ 1 0K This condition i s supported experimentally i n solutions of high caustic concentration. -In these solutions the s o l u b i l i t y of oxygen i s reduced to the point where the rate of adsorp-t i o n or solution of oxygen becomes the rate c o n t r o l l i n g step i n the reaction. The point at which oxygen solution or adsorption becomes rate c o n t r o l l i n g w i l l depend upon the degree of a g i t a t i o n of the solution. The experimental increase in the-rate of oxidation of sul f u r cannot be explained by the model for the process. I t i s believed that t h i s increase i s caused by i n t e r a c t i o n between the s i l i c a impurities i n the charge and the caustic. (10) Markhan, A., and Kobe, K., The S o l u b i l i t y of Gases i n Liquids, Chemical Reviews, 28, 19^1. 6o. 4 , E f f e c t o f P a r t i c l e S i z e . T h e m a t h e m a t i c a l e x p r e s s i o n f o r t h e o x i d a t i o n o f s u l f u r i s e q u a l t o : Q = Q o - n8C0a3 e ~ a t o ; 7T T h e e x p r e s s i o n f o r t h e r a t e o f o x i d a t i o n i s e q u a l d l n ( Q , 0 - ft) = -d t - 2 a T h e c h a n g e i n r a t e w i t h t h e i n v e r s e o f t h e s q u a r e o f t h e a v e r a g e p a r t i c l e s i z e i s e q u a l t o : d 2 l n ( Q 0 - Q ) - - / l t ' d t d y A t c o n s t a n t t e m p e r a t u r e , D , t h e r a t e o f d i f f u s i o n o f s u l f u r i s c o n s t a n t . B a s e d o n t h e m a t h e m a t i c a l e x p r e s -s i o n f o r o x i d a t i o n o f s u l f u r , t h e r a t e o f o x i d a , t l o n i s f o u n d t o h e i n v e r s e l y p r o p o r t i o n a l t o t h e s q u a r e o f t h e a v e r a g e p a r t i c l e s i z e o f t h e c h a r g e . T h i s c o n d i t i o n i s i n a g r e e m e n t w i t h e x p e r i m e n t a l r e s u l t s . B. O x i d a t i o n o f I r o n . T h e m e t h e m a t i c a l e x p r e s s i o n f o r t h e o x i d a t i o n o f i r o n i s e q u a l t o : - % D t Q = Q l - 8Cja3 e a 61. The quantity - Q, which l a determined experimentally from the oxygen consumption curve should be exponential and t h i s condition i s found to be true experimentally. 1. E f f e c t of Pressure. Solid-gas interactions which involve the process of d i s s o c i a t i o n followed by d i f f u s i o n obey Sieverts law. The rate of such reactions i s proportional to the square root of the p a r t i a l pressure of the gas. In the model fo r the oxidation of iron, these steps are proposed and the experimental r e s u l t s substantiate the hypothesis. 2. Ef f e c t of Temperature. The experimental Increase i n the rate of oxidation of iron with temperature obeys the Arrhenius equation. The experimental a c t i v a t i o n energy for the process Is equal to 1,840 c a l o r i e s . This low value for the s u b s t i -t u t i o n a l d i f f u s i o n process i s believed to be caused by the high degree of disorder i n the oxide layer. A s i m i l a r condition i s encountered i n grain boundary and surface d i f f u s i o n i n metals where a high degree of disorder r e s u l t s i n a low value f o r the a c t i v a t i o n energy. 3 . E f f e c t of Caustic Concentration. Based on the model fo r oxidation, increasing the caustic concentration of the solution should decrease the rate of oxidation of the i r o n by reducing the s o l u b i l i t y of the gas i n solution. Experimentally, increasing the caustic concentration has caused an increase i n the rate 62. of oxidation of the Iron. This experimental r e s u l t may-be caused by i n t e r a c t i o n between impurities and caustic for, based on the e f f e c t of p a r t i c l e size on the rate of the reaction, the t h e o r e t i c a l rate of oxidation of the iro n i n the 10.9 micron average p a r t i c l e size charge should have been much higher than that obtained experimentally. 4 . E f f e c t of P a r t i c l e Size. As i n the case of oxidation of sulfur, the experimental rate of oxidation of i r o n i s i n v e r s l y pro-p o r t i o n a l to the square of the average p a r t i c l e size. This fact i s In agreement with the mathema.tical expression fo r the oxidation of Iron. C. E f f e c t of P o t e n t i a l . I f the process of electron transfer across'the-oxide layer i s assumed to be in equilibrium, the concentra-t i o n gradient across the oxide layer i s determined by the difference i n po t e n t i a l betweenthe po t e n t i a l of electrons i n the pyrite and the p o t e n t i a l of vacant el e c t r o n " s i t e s on the adsorbed oxygen atoms, and the thickness of the oxide layer. I f a p o t e n t i a l i s applied between the p y r i t e p a r t i c l e and the solution with the py r i t e as the negative electrode, the p o t e n t i a l of the vacant electron s i t e s on the adsorbed oxygen atoms w i l l be lowered by an amount equal to the applied p o t e n t i a l . Assuming that the process of electron transfer i s s t i l l able to reach equilibrium, 6 3 . a g r e a t e r number o f e l e c t r o n s w i l l be r e q u i r e d t o f l o w a c r o s s the oxide to r e a c h t h i s s t a t e . The d i f f u s i o n g r a d i e n t f o r s u l f u r a c r o s s the oxide w i l l t h e r e f o r e be g r e a t e r than t h a t encountered w i t h no a p p l i e d p o t e n t i a l and the r a t e of d i f f u s i o n of s u l f u r w i l l a l s o i n c r e a s e . A p p l i c a t i o n o f a p o t e n t i a l to the p y r i t e c r y s t a l w i l l have no d i r e c t e f f e c t on the o x i d a t i o n o f i r o n , but s i n c e the r a t e o f d i f f u s i o n o f oxygen i n t o the oxide l a y e r i s dependent on the r a t e o f d i f f u s i o n of s u l f u r through the r a t e o f formation o f l a t t i c e d e f e c t s a t the p y r i t e oxide i n t e r f a c e , the a p p l i c a t i o n o f a p o t e n t i a l w i l l r e s u l t i n an i n c r e a s e i n the r a t e o f o x i d a t i o n o f i r o n . VIII CONCLUSIONS The u t i l i z a t i o n o f the r a t e o f oxygen consumption as a measure o f r e a c t i o n r a t e a f f o r d s a s a t i s f a c t o r y method f o r st u d y i n g the.humid o x i d a t i o n r e a c t i o n s . Many of the experimental r e s u l t s o b t a i n e d are c o n s i s t a n t with w e l l known p h y s i c a l laws. T h i s f a c t i n d i c a t e s t h a t the method I s b a s i c a l l y soundi The main disadvantage o f the method l i e s i n the d i f f i c u l t y i n m a i n t a i n i n g the u n i t f r e e o f l e a k s at h i g h p r e s s u r e s . A l a r g e number of experimental runs had to be d i s r e g a r d e d because o f l e a k s i n the u n i t . A l i t e r a t u r e survey has not uncovered any work on the mechanism or k i n e t i c s o f o x i d a t i o n o f m i n e r a l s i n 6 4 . aqueous solutions. The model proposed i n t h i s report i s based therefore e n t i r e l y on the experimental r e s u l t s of t h i s investigation. Most of the experimental r e s u l t s are supported by the model. The model i s l i m i t e d i n that i t does not explain the effect of impurities on the reactions. The increase i n rate with increased caustic concentration from one to two normal solutions apparently- disagrees with the model. This behavior i s believed to be- caused by i n t e r a c t i o n between caustic and impurities. Other experimental r e s u l t s are i n agreement with the model. 6 5 . APPENDIX A. Calculations from Oxygen Consumption Curve. From Oxygen Consumption Curve (Figure 8 ) . Q 0 = Total Oxygen .Consumption = 37 Units. Q = Oxygen Consumption at Time t. Time i n Minut e s . % - Q . L o g l Q (Q 0 Q) 0 - 15.5 1.19 5 10.8 I . 0 3 10 8 . 4 0.92 15 6.7 0.83 20 5.5 0.74 25 4 . 6 O.56 30 4 . 2 0.62 ?5 4 . 0 0.60 4o 3.6 O.56 45 3-1 0.49 50 2.8 0.45 55 2.5 0.40 60 2.2 O.34 65 1.8 0.26 100 G.8 - . 1 0 120 0 . 4 - . 4 0 130 0.2 - . 7 0 The oxygen consumption by the i r o n i s obtained by extending the exponential portion of the logarithmic replot (Figure 9 ) . ( Q 1 0 - Q x) 8.7 7.6 6 .9 6 .2 5.5 Q l 0 = Total Oxygen Consumed by Iron. Q,]_ = Oxygen Consumed at Time t. Time i n T n r v ( n n . Minutes Log ( Q l 0 - Q x) 0 0 .94 5 0.88 10 0.84 15 0.78 20 0.74 66. The oxygen consumption by the s u l f u r must equal the d i f f e r e n c e between the t o t a l oxygen consumption and the oxygen consumed i n the o x i d a t i o n of i r o n . M ^ u t e s ( Q 0-Q) - (%0-Qj) Log ( Q Q - Q ^ - ^ - Q J 0 6.8 0,83 5 3-2 0.50 10 1.5 0.18 15 0.5 -0.30 APPENDIX B. LOGARITHMIC REPLOTS FOR EFFECT OF PRESSURE. Charge: 40 grams py r i t e 60 grams caustic soda 1500 m i l l i l i t r e s water. Conditions: Average P a r t i c l e Size of Charge » 10.9 microns Temperature = 120°C. 9o z° 4o 60 so /oo /eo /4< 7 2 . 7~/me /n A4//?u/-es 76. APPENDIX C. LOGARITHMIC REPLOTS FOR EFFECT OF TEMPERATURE. Charge: 40 grams p y r i t e 60 grams caustic soda 1500 m i l l i l i t r e s water. Conditions: Average P a r t i c l e Size of Charge = 10.9 microns Oxygen P a r t i a l Pressure = 200 p . s . i . 93'C • f-4 T/rne /r> /W/nates 79. —1 : : 1 | ' O ZO 40 60 SO /OO /£o T/n->e /n A4//7 u s Mr APPENDIX D. LOGARITHMIC REPLOTS FOR EFFECT OF PARTICLE SIZE. Charge: 30 grama p y r i t e 60 grams caustic soda 1500 m i l l i l l t r e a water. Conditions: Temperature = 120°0 Oxygen P a r t i a l Pressure = 200 p . s . i . 84. . . : ; /? ises>o $ e fvfc/e S/ze of ffar^e ri 1 1—• 1 L _ s I I o £0 40 60 80 /oo " /eo 7~/m e /n M/nc/fes 8 7 . APPENDIX E. DERIVATION OF OXIDATION EXPRESSIONS. Assuming that the py r i t e p a r t i c l e i s i s o t r o p i c , Fick's law for spherical d i f f u s i o n i s equal to: C = concentration i n the sphere, t « time. r = distance from the center of the sphere. D = d i f f u s i o n c o e f f i c i e n t , a = radius of sphere. The concentration i n the sphere i s a function of the distance from the centre of the sphere and time. Expressing concentration as the product of two functions, one a function of time, the other a function of distance; at i . e. C(t,r) - r(t)-R(r) the expression becomes r Separating variables; D T dt R i dr^ r <f/> j Since these two functions are equal, they must be constant. Let. t h i s constant b e- /V. Then: d T . _ * D d t r 88. d A * 2 - dr /? = A Gns/Xr + B s/n/Tr P where A and B are constants. c - r - R To solve for the constants A, B and , the boundary conditions must be considered.. For d i f f u s i o n of sulfur from the sphere the boundary conditions are: (1) C(a,t) = 0 (2) 0(r,o) = constant - C 0. (3) C(o,t) = f i n i t e value. From condition ( 3 ) , A must be equal to zero. Applying the f i r s t condition, the equation becomes: o = ft s , n ^ ° o t o therefore: 5 in /7\ Q * O 2 fl* 2-o where n i s an Integer. From the second condition CQ = 5 SJD. sin JZJf* IT-. /» O This i s a Fourier series. The values for B n are given by 8 9 . the expression: « = f*Co r sin aJT> c/r The expression f o r C i s then equal to: The expression for Q, the quantity of sulfur d i f f u s e d from the sphere as a function of time i s equal to: Q\ 4 XTo'G- 4>T faCr*</r> 3 O • Q.o + 8 Co a f ^ rjJe * v r s i n n T r r / p ^ 3 ^ -lllf^Ot Since the series HE- £ Q^ converges very rapidly, the f i r s t term of the series w i l l be used as an approximation. 90. .For the d i f f u s i o n of oxygen into the sphere, the boundary conditions are: 0(a,t) = a constant = C^. G(r,o) » 0. C(o,t) = f i n i t e value. Consider the concentration C as the difference between two quantities C = ' o x - W. Where: C^ i s the f i n a l concentration of oxygen i n the sphere, W i s a function of r and t. The boundary conditions for W become W(a,t) » 0 W(r,o) = C x W(o,t) = f i n i t e value. These are the same boundary conditions as those fo r the d i f f u s i o n of sulfur. The expression for W i s then equal to = - 2 C a r r r 91. The expression for C, the concentration of oxygen i n the sphere i s then equal to: CCr>t)*C - £ (dT s/n a£t The expression for Q, the quantity of oxygen di f f u s e d into the sphere as a function of time i s equal to: Evaluating t h i s i n t e g r a l y i e l d s : Q - Q, - ®S± > a " a> s~. •<-9 2 , BIBLIOGRAPHY Anderson, J.S., "The Primary Reactions i n Roasting and Reduction Processes", Transactions of the Faraday Society, June 1 9 4 8 . Barrer, R . M . "Diffusion In and Through Solids", The Cambridge Series of Physical Chemistry, Cambridge University Press, 1 9 4 1 . Bognar, A., "Humid Oxidation of Sulphide Ores Under High Pressures", Magyar Mernak Epiteszegylet Kbzhonye, 78 , 2 0 0 - 4 , 1944, Chemical Abstracts, 7 3 4 0 a , 1 9 4 7 . Carslaw, H.S., "Introduction To The Mathematical Theory of the Conduction of Heat In Solids", 2nd ed., Dover Publications, 1 9 4 5 . Evans, U.R., "The Mechanism of the Formation of Films on Metals", Pit t s b u r g International Conference on Surface Reactions, Corrosion Publishing Company, 1 9 4 8 . Glasstone, S., "Thermodynamics f o r Chemists", D. Van Nostrand Company, 1 9 4 7 . ' Glasstone, S., L a l d l e r , K., and Eyrlng, H., "The Theory of Rate Processes", McGraw-Hill Book Company, 1 9 4 1 . ( 8 ) Hickman, J.W., "Investigation of Gas-Metal Reactions by Reflection Electron D i f f r a c t i o n " , Pittsburgh International Conference on Surface Reactions, Corrosion Publishing Company, 1 9 4 8 . ( 9 ) Hoel, P.G., "Introduction to Mathematical S t a t i s t i c s " , John Wiley and Sons Inc., 1 9 4 7 . (10) Hougen, 0 . , and Watson, K., "Chemical Process P r i n c i p l e s " , Part I I I , John Wiley and Sons Inc., 1 9 4 7 . (11) Kendall, M.G., "The Advanced Theory of S t a t i s t i c s " , C. G r i f f i n , 1 9 4 3 - 4 6 . (12) L a i d l e r , K.J., "The Mechanism of Some Elementary Surface Reactions", Pittsburg International Conference on Surface Reactions, Corrosion Publishing Company, 1 9 4 8 . ( 1 3 ) Meljering, J.L., ahd P h i l i p s , N.V., "Some Aspects of Internal Oxidation i n S i l v e r , Copper, Nickel and Iron All o y s " , Pittsburg International Conference on Surface Reactions, Corrosion Publishing Company, 1 9 4 8 . (14) Mott, N. F., "The Theory of the Formation of Protective Oxide Films on Metals", Transactions of the Faraday Society, July 1 9 4 7 . (15) Reddick, H.W., and M i l l e r , F.H., "Advanced Mathematics for Engineers", John Wiley and Sons Inc., 1 9 4 7 . ' (16) Seitz, F., "The Physics of Metals", McGraw-Hill Book Company, 1 9 4 3 .
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Humid oxidation of pyrite
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