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Oxidation of iron by lead oxide - Silica melts Portier, Bernard 1967

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THE OXIDATION OF IRON BY LEAD OXIDE - SILICA MELTS. by BERNARD PORTIER A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE iri the Department of METALLURGY We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of Metallurgy The University of British "Columbia March,I967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r 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 f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x -t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n by the Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n -c i a l g a i n s h a l l no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f M e t a l l u r g y  The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date A p r i l 25, I967 I Resume L'oxydation du fer par des l a i t i e r s constitues de s i l i c e et d'oxydesde plomb a f a i t l ' o bjet d'une etude experimentale pour un large i n t e r v a l l e de composition entre 850 et 1000°C.Les vi t e s s e s de reaction ont ete obtenues par des mesures de resistance electrique.Dans l e domaine de composition massique 80-88 % de PbO, l a v i t e s s e d'oxydation est proportionnelle a l a f r a c t i o n molaire d'oxyde de plomb dans l e bain, c'est-a-dire a l a concen-t r a t i o n en cations Pb^.On suppose done que l a v i t e s s e de reaction est l i m i t e e par l e t r a n s f e r t d'electrons entre les ions me t a l l i q u e s c o n t r a i r e -ment a l a r e a c t i o n d'oxydation du carbone par l e s memes l a i t i e r s dans l a -quelle interviennent les ions oxygene. L'energie apparente d'actiVation est de 50± 7 Kcal/mole. Deux series de d i f f e r e n t e s valeurs d ' a c t i v i t e pour le systeme b i n a i r e Pb0-Si02 ont ete u t i l i s e e s et sont comparees a l a lumiere de l a presente etude. ABSTRACT An i n v e s t i g a t i o n of the oxidation of s o l i d i r o n by lead o x i d e - s i l i c a melts was undertaken between 850°C and 1000°C over a wide range of o x i -d i s i n g p o t e n t i a l s . The experimental reaction rates were measured by a tech-nique of e l e c t r i c a l resistance measurements. In the intermediate range of concentration investigated (80-88 % wgt.PbO) the rate of oxidation was found to be proportional to the mole f r a c t i o n of lead oxide i n the melt, i n other words, to the lead ion concentration. The rate determining step of i r o n oxidation by lead o x i d e - s i l i c a melts i s supposed to involve lead cations i n contrast with the oxidation of carbon where oxygen.ions are involved. The apparent a c t i v a t i o n energy was found to be 50 ± 7 Kcal/mole. Two sets of a c t i v i t y data concerning the lead oxide i n Pb0-Si02 melts were a v a i l a b l e and were compared by processing the present r e s u l t s on i r o n oxidation and previous r e s u l t s on carbon oxidation by s i m i l a r melts. I I ' ACKNOWLEDGEMENT ' The author wishes to express his gratitude for-the valuable assistance rendered by the members of the Department- of Metallurgy through-out this work. Sincere-appreciation is especially extended to Dr.C'.S. Samis who directed .this investigation and to Dr. E.Peters for many useful discus-sions of this work. The author is also particularly indebted to the Canada Council for a Scholarship which made this study possible. I l l TABLE OF CONTENTS Page •INTRODUCTION Kinetics of the gaseous oxidation of metals............ 1 Kinetics of oxidation by oxidising melts. 2 Object and scope of the present investigation..... 3 • EXPERIMENTAL Apparatus . 5 Materials 5 Procedure 8 PRELIMINARY CALCULATIONS Reaction rate . . .... 10 Temperature dependence of the parameters- 11 . "Oxygen potential of Fb'0-Si02 slags ik RESULTS A". Kinetics f o r a given melt at fixed temperature ..... 16 B. Oxidation rates for various melts at different temperatures 16 C . Lead oxide mole fraction dependence 19 D. Oxygen potential dependence .. 21 E. Evaluation of the apparent activation energies ..... 25 IV Page DISCUSSION A. Reproducibility . . » .-. ... . 3U B. Reaction rate for a given melt at fixed temperature . .36 C . Lead oxide mole fraction dependence • 37 D. Oxygen potential dependence- 37 E. Activation energy . . . 38 •P. Zero rate melts . . . Uo CONCLUSIONS kl BIBLIOGRAPHY k2 APPENDICES 1. Error on reaction rates 1J4 Ibis. Relation between weight and mole fraction in Pb0-Si02 U9 2. Richardson's activity data 50 3 . Kozuka-' s activity data ............ < _ = t o ^ k. Jena^s data 59 5. Zero rate melts 66 V LIST OF FIGURES Page 1. PbO-SJ^ phase diagram h 2. Experimental set-up 6 3. A l t e r n a t i v e experimental set-up . 7 4. Temperature dependence of the i r o n conductivity 12 5A. Iron conductivity 13 5B. Temperature dependence of the c o e f f i c i e n t K ••••• 13 2 6. (aPbO) scale from Richardson's data \.... 15 2 7. (aPbO) scale from Kozuka's data 15 8. Example of a t y p i c a l rate curve 17 9. Lead oxide mole f r a c t i o n dependence 20 10. Log Log pl o t s for Richardson's scale 23 11. Log Log plots f or Kozuka's scale 2k 12. Corrected Log Log plots f or Kozuka's scale 26 13. Oxygen p o t e n t i a l dependence (Richardson's a c t i v i t y scale) i . 27 14. Oxygen p o t e n t i a l dependence (Kozuka's scale) 28 15. Arrhenius plot (w.r.t. NPbO ) i n concentration range 80-88%. 31 16. Arrhenius plot (w.r.t. NPbO) i n concentration range 76-80% . 32 17. Arrhenius plots (w.r.t. oxygen p o t e n t i a l dependence) 33 18. Comparative Arrhenius plots 39 19. Relation between weight a n c* m ° l e f r a c t i o n i n Pb0-Si02 b $ 20. Plot of LogT^PbO versus I/T from Richardson's data 51 21. Lead oxide a c t i v i t y i n PbO-SiO„ (Richardson's data) 52 VI Page 22. Temperature dependence of the emf (Kozuka's data) 55 23. Lead oxide a c t i v i t y i n PbO-SiC^ (Kozuka's data) 56 24. Processing of Jena's.data. 6 l 25. PbO a c t i v i t y i n PbO-Si0 2 at 1000°C 62 26. Jena's r e s u l t s at 1000°C 63 27. Processing of Jena's data; corrected Log Log pl o t 5^ 28. Lead oxide mole f r a c t i o n for Jena's data 65 VII LIST OF TABLES Page 1. ll+ 2. Experimental reaction rates 18 3- 22 k. Reaction order from corrected logj-jLog plots 25 5- •Specific rate constants kx ( w.r.t. NPbO)- ................ 29 6. S p e c i f i c rate constants k 2 (w.r.t. NPbO in 76-80$ melts) . 30 7- •Specific rate constants ks (w.r.t. (aPbO) 2 ) 30 8. 'Richardson's a c t i v i t y data f o r FbO i n "Pb0-Si02 . . . • 50 •9. A c i v i t y of FbO i n PbO-SiOp'-w/.r.t. .mole fraction(Richardson) 53 10. A c t i v i t y of'PbO w.r.t. wgt.$ (Richardson.) 53 11. Log aPbO from Kozuka's data 5^  12. A c t i v i t y of PbO ( .'Kozuka's data ..) ......................... 57 13- A c t i v i t y of PbO w.r.t. wgt (Kozuka's - data) 58 14. Jena*s reaction rates .................................... 60 15- ' Thermodynamic data for the oxidation of Pb and Fe ........ 66 16. Fr® energies at 1000°C and 850CC ......................... 66 1 I N T R O D U C T I O N S l a g - m e t a l s y s t e m s a r e o f t e n d e a l t w i t h i n i n d u s t r i a l p r a c t i c e a n d t h e y h a v e b e e n f r e q u e n t l y i n v e s t i g a t e d . M o s t s t u d i e s , h o w e v e r , c o n c e r n l i q u i d s y s t e m s a n d l i t t l e a t t e n t i o n h a s b e e n f o c u s s e d o n h e t e r o g e n e o u s r e a c t i o n s b e t w e e n s o l i d m e t a l a n d l i q u i d p h a s e s . T h e s t u d y o f t h e l a t t e r t y p e o f r e a c t i o n s i s , i n t h e c a s e o f o x i d a t i o n , a r e a s o n a b l e a p p r o a c h t o a b e t t e r u n d e r s t a n d i n g o f t h e m o l t e n s t a t e , s i n c e t h e g a s e o u s o x i d a t i o n o f m e t a l s i s b e t t e r k n o w n t h a n t h e o x i d a t i o n r e a c t i o n s i n m o l t e n s y s t e m s . T h e p r e s e n t w o r k o n t h e o x i d a t i o n o f s o l i d i r o n b y l e a d o x i d e -s i l i c a m e l t s h a s b e e n u n d e r t a k e n i n o r d e r t o s t u d y t h e k i n e t i c s o f t h e r e a c t i o n a n d t o d r a w c o m p a r i s o n s w i t h p r e v i o u s s t u d i e s o n s i m i l a r , 1,2 s y s t e m s I t i s a d v a n t a g e o u s f i r s t t o c o n s i d e r t h e p r e s e n t k n o w l e d g e o n t h e g a s e o u s o x i d a t i o n o f i r o n a n d t h e n t h e a v a i l a b l e r e s u l t s a b o u t o x i d a t i o n b y o x i d i s i n g m e l t s . K i n e t i c s o f t h e G a s e o u s O x i d a t i o n o f M e t a l s T h e k i n e t i c s o f t h e g a s e o u s o x i d a t i o n o f i r o n h a v e b e e n i n v e s t i g a t e d b y v a r i o u s a u t h o r s " ^ ' " ^ ' ^ ' ^ . B o t h t h e c h e m i c a l i n t e r f a c e r e a c t i o n a n d d i f f u s i o n t h r o u g h t h e o x i d e s c a l e c a n b e r a t e d e t e r m i n i n g . 3 4 L i n e a r r e a c t i o n r a t e s c a n b e o b s e r v e d ' a n d t h e c o r r e s p o n d i n g r a t e 4 5 c o n s t a n t s a r e d e p e n d e n t o n t h e p r e s s u r e o f t h e o x i d i s i n g g a s ' ; i n t h e 3 c a s e o f C 0 „ a l i n e a r d e p e n d e n c e h a s b e e n f o u n d - . T h e c o r r e s p o n d i n g 2 a c t i v a t i o n energy was found to be 60 KCal/mole i n the case of carbon 3 5 dioxide and 16 KCal/mole i n the case of oxygen at low pressure . In contrast to t h i s , parabolic reaction rates are generally observed and correspond to a reaction c o n t r o l l e d by the d i f f u s i o n of atoms 3 or point d e f e c t s , i n the external oxide layers . The oxygen pressure dependence varies with the nature of the oxide layer. If magnetite i s 4 6 produced, the oxygen pressure has no e f f e c t on the reaction rate ' • If only wustite i s produced, the oxygen pressure has a- p o s i t i v e e f f e c t 4 5 7 on the reaction rates ' ' . The a c t i v a t i o n energy corresponding to the 3 5 d i f f u s i o n of i r o n i n a wustite layer i s 30 KCal/mole ' . K i n e t i c s of Oxidation by Oxidising Melts As an example of oxidation of s o l i d metals by o x i d i z i n g melts, 9 an i n v e s t i g a t i o n on s o l i d i r o n was made , and an a c t i v a t i o n energy of 72 KCal/mole,was obtained for the reaction: Fe + [Ye^O^] 3[FeO] • j n t h i s connection, the electrochemical studies of o x i d i s i n g melts show that the physico-chemical.properties of slags are c l o s e l y r e l a t e d to the oxygen p o t e n t i a l of the s y s t e m ^ ' . The oxidation of s o l i d carbon by lead o x i d e - s i l i c a melts has 1 2 8 been investigated by several authors ' ' . It was shown that the rate determining species i s oxygen ions, and that the rate of oxidation i s proportional to the geometric surface area of carbon and to the oxygen p o t e n t i a l of the binary melts'*' or to the square of the oxygen ion concentration 2 of the ternary melts . The a c t i v a t i o n energy was found to be i n -2 dependent of the nature of carbon . This suggests that the carbon 3 oxidation i s rate controlled by the melt rather than by the s o l i d phase. Object and Scope of the Present Investigation The object of the present work i s to study the oxidation k i n e t i c s of s o l i d iron i n lead o x i d e - s i l i c a melts. Its main purpose i s to compare the kinetics of two similar systems: s o l i d iron'-molten slag 1 2 and s o l i d carbon-molten slag, the l a t t e r being known,from previous works ' . The experimental technique consists i n measuring the e l e c t r i c a l resistance of an iron wire. A similar technique has been previously described"^. The lead o x i d e - s i l i c a slags are low melting phases (70%-93% Wgt PbO) (Fig. 1), so that a large range of oxidising melts and temperatures i s available experimentally. S i l i c a weight per cent F i g . l ; PbO-SiO g Phase diagram. 5 EXPERIMENTAL Apparatus The experimental set-up i s shown schematically i n F i g . 2. An a l t e r n a t i v e set-up i s shown i n F i g . 3 and o f f e r s two improvements: the p o s s i b i l i t y of e s t a b l i s h i n g a neutral atmosphere.and a better temperature c o n t r o l . The lower part of the i r o n wire S constitutes the sample, de--l i m i t e d by the two points where s t a i n l e s s s t e e l leads used for p o t e n t i a l reading are spot welded. The main e l e c t r i c a l c i r c u i t consisted of a battery, an amperemeter, a v a r i a b l e r e s i s t o r f o r current adjusting and a standard r e s i s t o r with potentiometer reading i n order to co n t r o l p r e c i s e l y the i n t e n s i t y of the current. Materials Lead oxide Mono (General Chemical Division) and s i l i c a powder (Fisher) of reagent grade were used throughout. The i r o n was commercial i r o n wire of the following composition (<$>): C Mn S S i Cr .03 .2 .Ok .1 .1 Fig.2: Experimental set-up. F: Globar Furnace T: Chromel-Alumel thermocouple connected to a Wheelco controller Ct Fireclay crucible D: Four hole porcelaine pipe B: Iron wire connected,to the main circuit P: Stainless steel wire connected to a potentiometer. • Fig.3: -Alternative experimental set-up. F: Electrical, resistor furnace T: Chromel-Alumel thermocouple connected to a Wheelco controller C: Zirconia crucible B:.Iron wire P: Stainless steel leads Ar: Argon flow. D: Four hole porcelaine pipe. 8 Procedure (1) Preparation of the Samples . The slag mixtures were prepared i n 400 gm batches by weighing s u i t a b l e amounts of reagents and mixing them manually. The i r o n wire was cleaned with emery paper over a length of 3, 6, or 12 inches. Two s t a i n l e s s s t e e l leads for p o t e n t i a l measurements were spot welded at the ends of the desired sample, the cleaned part of the ir o n wire was s p i r a l shaped and the four v e r t i c a l leads were protected i n a fo u r hole porcelaine holder. The resistance of the sample was then checked at room temperature. (2) Stages of a Run „ 400 gm of slag mixture were placed i n afire clay c r u c i b l e and heated up i n the Globar furnace as shown i n the following table: Time (hours) heat rate (°C/hour) 1 300-400 2 150 3 100 4-7 0 Af t e r s u f f i c i e n t homogeneisation (2-3 hours) at the desired temperature (850°C-1000°C) the wire at room temperature was plundged into the melt. 9 The p o t e n t i a l at the ends of the sample was measured every minute. At the end of a run the wire was l i f t e d and quenched to room temperature. 10 PRELIMINARY CALCULATIONS R e a c t i o n R a t e The mass o f i r o n u n r e a c t e d c a n be c a l c u l a t e d f r o m t h e measure o f t h e e l e c t r i c a l r e s i s t a n c e o f t h e s a m p l e , a s s u m i n g t h a t t h e a t t a c k o f t h e c y l i n d r i c a l w i r e i s u n i f o r m : R e s i s t a n c e : R = V = (? ^ " mass : I TT r M = TT r 2 I d M = P ( 2 d l 7 = K V V where r = r a d i u s o f t h e sample (cm) $s = l e n g t h (cm) d = d e n s i t y V = p o t e n t i a l a t t h e ends o f t h e sample (v) I = c u r r e n t i n t e n s i t y ( k e p t c o n s t a n t ) (Amp) K = c o n s t a n t f o r g i v e n I and T . The s u r f a c e a r e a A i s p r o p o r t i o n a l t o t h e r a d i u s o f t h e c y l i n d r i c a l w i r e , and t h e mass M to t h e s q u a r e o f t h e r a d i u s ; t h e r e f o r e , t h e r e a c t i o n r a t e e x p r e s s e d i n mass u n i t / s u r f a c e a r e a u n i t x t i m e u n i t i s f u n c t i o n a l l y s i m i l a r t o t h e r a d i u s o f t h e w i r e : r \/B5T a ) V T T V V -rr-Cd A s t u d y o f t h e e r r o r on t h e r e a c t i o n r a t e c a l c u l a t e d by t h i s method i s p r e s e n t e d i n a p p e n d i x 1. The r e a c t i o n r a t e b e i n g measured as t h e d e r i v a t i v e o f t h e r a d i u s ( s l o p e o f t h e c u r v e : r a d i u s v e r s u s t i m e ) , r e l a t i v e a c c u r a c y i s m o r e , i m p o r t a n t t h a n a b s o l u t e a c c u r a c y and t h e v a r i a t i o n s o f t h e p a r a m e t e r s 11 included i n equation (1) w i l l be taken into account i n the range of temperature investigated (850-1000°C). Temperature Dependence of the Parameters 1. Current I The current was kept constant by means of a v a r i a b l e carbon plate r e s i s t o r and was c o n t r o l l e d by p o t e n t i a l reading at the ends of a standard manganin r e s i s t o r . . The most s u i t a b l e current for the present set up was 0.25 Amp. 2. Length of the Sample  The length of the sample i s considered to be constant i n the range of :temperature investigated (850-1000°C), the l i n e a r expansion of i r o n being 0.25% i n t h i s range. 3. E l e c t r i c a l R e s i s t i v i t y The temperature dependence of the r e s i s t i v i t y of the i r o n wire was determined i n an argon atmosphere i n the experimental set-up shown i n F i g . 3. A l i n e a r dependence i s found i n the range of temperature 850-1000°C (Fig. 4 and 5A) and a mean l i n e a r dependence of the c o e f f i c i e n t K i s shown i n F i g . 5B. Table 1 gives the values of K at 850°C for three lengths of l 2 / sample. K defined by r = K x M i s independent of temperature. 12 Voltage(volts x ±Q 0 500°C 1000 - • - - "" "Temperature F i g , k : Temperature dependence of the i r o n conductivity. 13 85r5 §00 950"u Fig. 5A ; Iron wire conductivity (* 0.Q3). - K f 'M = K / V | | = 3 inches ^ d = soAono inch 85I) 900 950J|J Fig.^B : Temperature dependence of the coefficient K . 14 inches K / K 3 0.0278 53 x 10~ 4 : 6 0.0511 26.5 x I O - 4 12 0.02045 13.25 x I O - 4 Table 1: Rate c a l c u l a t i o n c o e f f i c i e n t s (T = 850°C, I = 1/4 Amp.) Oxygen P o t e n t i a l of PbO-Si0 2 Slags In the binary system PbO-Si02 the oxygen pressure i n equilibrium with the lead oxide in,the melt i s d i r e c t l y proportional to the square of 2 the lead oxide a c t i v i t y . Two-sets of a c t i v i t y data are a v a i l a b l e from 14 15 studies by Richardson and Kozuka . By extrapolating t h e i r data as shown 2 . i n appendices 2 and 3, two (aPbO) scales are obtained for each temperature (Fig. 6 and 7). F i g . 7 :.(aPbQ) scale from Kozuka's data 16 RESULTS A . K i n e t i c s f o r a G i v e n M e l t a t F i x e d T e m p e r a t u r e (1) L i n e a r ^ R e a c t i o n R a t e I n g e n e r a l e v e r y : e x p e r i m e n t d i s p l a y s two r e a c t i o n r a t e s t a g e s (Fig^,8): A s h o r t s t a g e o f low r a t e (0-12 m i n u t e s ) , more o r l e s s l i n e a r , and a l o n g e r s t a g e o f l i n e a r r a t e . The l a t t e r s t a g e c o r r e s p o n d s t o a f a i r l y r e g u l a r a t t a c k o f t h e c y l i n d r i c a l w i r e as r e v e a l e d by e x a m i n a t i o n o f t h e s a m p l e . I t s s l o p e (cm/min) i s a measure o f t h e r e a c t i o n r a t e . Some e x p e r i m e n t s a l s o d i s p l a y a f i n a l s t a g e o f f a s t , n o n l i n e a r ' r a t e ( F i g . 8)'C o r r e s p o n d i n g t o an i r r e g u l a r a t t a c k o f t h e v' w i r « e r e s u l t i n g i n a p p a r e n t l y h i g h r a t e s . (2) : -Reproduc i b i l i t y A r e p r o d u c i b i l i t y o f ± 20% i s g e n e r a l l y o b s e r v e d f o r r a t e m e a s u r e m e n t s . (3) D i f f u s i o n R e c i p r o c a t i o n o f t h e sample d i d n o t e x e r t any s i g n i f i c a n t e f f e c t on t h e r e a c t i o n r a t e , and t h i s l e a d s t o t h e c o n c l u s i o n t h a t n e i t h e r t h e d i f f u s i o n o f Pb I o n s n o r t h e d i f f u s i o n o f F e i o n s t h r o u g h a b o u n d a r y l a y e r c a n be r a t e - d e t e r m i n i n g u n d e r t h e s e e x p e r i m e n t a l c o n d i t i o n s , B . O x i d a t i o n R e a c t i o n R a t e s f o r V a r i o u s M e l t s a t D i f f e r e n t T e m p e r a t u r e ^ The e x p e r i m e n t a l r e a c t i o n r a t e s a r e p r e s e n t e d i n T a b l e 2. I a h i g h l e a d o x i d e m e l t s <>86% PbO) t h e e x p e r i m e n t a l s c a t t e r i n c r e a s e d w i t h lC^x radius(cm) F i g . 8 : Example of a t y p i c a l experimental rate curve 18 temperature to such an extent ( + 50 °/o ) that the observed rates were not considered meaningful. i PbO(wgt) 850°C 875 °C 900X 9506C !1000°C 76 0.005+0.001 0.017+0.002 O.O25+O.OOI 0.050 77 0.0258 78 0.0188+0.03 0.05 0.03+0.01 0.07 0.10 79 O.O35 0.05^  80 0.027+0.009 0.07 0.07*0.01 O.I5+O.O3 81 O.O55 0.09 82 O.037+O.OI 0.11 0.126+0.008 0,25 o.ko 83 0.12+0.01 0.13 8k 0.07+0.01 0.10 0.20+0.01 0.39+0. oi+ 0.66+0.1 85 Q.Ik 0.22 86 0.09+0.02 0.25+0.05 0A±0.2 0.99±o.05 87 0A9 90 0.12+0.02 0.35 92 0.12 Table 2. Experimental Reaction Rates (10 cm/min). 19 C. 'Lead Oxide Mole Fraction Dependence The relationship between reaction rates and lead oxide mole fraction i s found to be linear [Fig. 9l a t each temperature investigated and presents two stages corresponding to the concentration ranges 76-80$ wgt. PbO and 80-88$ wgt. PbO [Fig. 9]. A complementary processing of data concerning the oxidation of carbon by similar melts [Appendix k] does not give a comparable linear dependence of the rate on PbO mole fraction. Fig. 9 t Lead oxide mole fraction dependence 2 1 D. Oxygen P o t e n t i a l Dependence In, order to compare the present data with previous r e s u l t s 1 2 concerning the oxidation of carbon by s i m i l a r melts ' a study of the oxygen p o t e n t i a l dependence of the oxidation of i r o n follows. Preliminary considerations on the oxidation of carbon are useful for reducing the inaccuracy due to the present experimental scatter. 1. Carbon Oxidation A processing of carbon oxidation data"'' for the concentration range 7 7 - 8 6 % PbO i s presented i n appendix 4 and points out the following conclusions: (1) A log Log plot of the reaction rate versus the lead oxide a c t i v i t y (Fig. 24) gives an order of reaction r e s p e c t i v e -ly larger ( 2 . 5 0 for Kozuka's a c t i v i t y scale) and smaller ( 1 . 8 5 for Richardson's a c t i v i t y scale) than the t h e o r e t i c a l value (n = 2) adopted by the author. (2) On the same Log Log plot the rates observed i n high s i l i c a melts (77% PbO) are lower than expected from the general dependence (Fig. 2 4 ) . (3) The l i n e a r oxygen p o t e n t i a l dependence (rate 2 versus (aPbO) ) gives two d i f f e r e n t zero rate melts: 0% PbO on Richardson's a c t i v i t y scale and 72% PbO on Kozuka's a c t i v i t y scale (Fig. 2 6 ) . (4) The corrected Log Log.plot for Kozuka's a c t i v i t y scale gives a l i n e a r dependence for a l l reaction rates (Fig. 27) the corresponding slope,being reduced to 1.93. 22 2. Present Results A log log plot of reaction rates versus lead oxide a c t i v i t y (fig.10,11) presents the following features: (1) No general l i n e a r dependence i s observed over the whole range of concentration investigated (76-88%). (2) A l i n e a r approximation over the concentration range 78-86% gives the following slopes (reproducibility±20%): T°C Richardson Kozuka 850 1.67 2.16 875 2.20 2.60 900 1.77 2.50 950 1.52 1.90 1000 1.90 2.45 average 1.81 2.22 . Table 3. Reaction orders from log log plots The mean values are close to the ones found i n the preliminary study on carbon oxidation. (3) The rates observed for high s i l i c a melts ( <C 78% PbO) are lower than expected from the preceeding l i n e a r approximation. Log(aPbO) Log(aPbO) 25 (4) A corrected log log plot for Kozuka's a c t i v i t y scale with a zero rate melt at 72% PbO gives a l i n e a r dependence (Fig. 12) over the concentration range 76-86% PbO. The corresponding slopes increase with temperature as shown i n the following table: °c Kozuka (corrected) 850 2 02 900 2 ;16 950 2 ;48 1000 2-75 Table 4. Reaction, order from corrected log log plots  with Kozuka's scale . 2 The corresponding oxygen p o t e n t i a l dependence (rate versus (aPbO) ) i s shown i n F i g . 13 and 14. A l i n e a r approximation can be found i n the concentration range 78-86% and gives two zero rate melts: re s p e c t i v e l y 0% PbO (pure s i l i c a ) for Richardson's PbO a c t i v i t y scale and 72% PbO for Kozuka's PbO a c t i v i t y scale. E. Evaluation of the Apparent A c t i v a t i o n Energies The a c t i v a t i o n energy of the oxidation of solid i r o n by Pb0-Si02 melts i s calculated from the curves r e l a t i n g the reaction rates to the melt c h a r a c t e r i s t i c s , the slopes of these curves being the s p e c i f i c rate constants at the corresponding temperature. l o g ( a P b O ) Fig, ik : Oxygen potential dependence (Kozuka^s activity scale). CD 29 [l] Pb"1"4- Dependence The Pb + + dependence [lead mole fraction dependence ] gives an activation energy of 50 + 7 KCal/mole [Table 5, Fig. 15], in the concentration range 80-88$ wgt. PbO. In the high s i l i c a concentration range [76-80$ wgt. PbO] the corresponding activation energy is found to be 36 + 7 KCal/mole [Table 6, Fig. 16]. [ 2 ] Oxygen Potential Dependence The oxygen potential dependence[(aPb0)2 dependence] gives, by linear approximation in the intermediary concentration range [78-86$ wgt. PbO], two sets of•specific rate constants corresponding to the two sets of activity data'[Table 7]. The corresponding Arrhenius plots [Fig. 17] give two close lines and the apparent activation energy is found to be 1+0 + 10 KCal/mole. Table 5. Specific rate constant k x (gm/cm2xmin xNPbO) °C origin IO 2 X RATE (NPbO=0.65) k x xlO 2 log k'i 850 0.1+5 0.105 O.525 -2.28 875 0.46 0.20 •1.05 -I.98 900 0.1+75 O.JO 1.72 -1.76 950 • 0.1+75 O.55 5.11+ -1.50 1000 0.50 .1.15 7-7 -1.11 •50 ° c origin lC^x rate (NPbO=0.55) k 2.x 102 log k2\ 850 0A5 0,04 0.4 -3.40 900 Q.kk8 °-l 0.98 -5.01 950 0.445 0.195 1.82 . -2.74 1000 0.455 0.25 2.17 -2.66 Table 6. "Specific rate constant kp (in high s i l i c a melts) R ichardson- s scale Kozuka's scale T°C origin 102'rate (aPb0) 2 = .025) k 3 x l 0 2 log k 3 origin lC^rate k 3 x l 0 2 i°g fes 85O 0 O.O67 2.68 -1.572 0.009 0'. 064 1.25 -1.905 875 0 0.159 5-6 -1.265 0.0095 0.155 2.70 -1.574 900 0 O.I.55 6.2 -1.208 0.010 O.I78 5.56 -1.45 950 0 O..285 11.4 -0.944 0.011 0,55 l . l k -1 .46 1000 ' 0 0 .42 " 16.8 -0.775 0.012 0.53 11.0 -O.96 Table 7. Specific rate constant-kg (gm/cnr^ x min x (aPbQ)g ). DISCUSSION A. Re p r o d u c i b i l i t y I. Observations The basic assumption of the present experimental technique i s a uniform,attack of the c y l i n d r i c a l sample. Observations show that t h i s i s not always true: (1) Samples observed i n the course of the main l i n e a r stage present generally a uniformly reduced shape. The dispersion measured by means of a micrometer i s ±5%. (2) Samples observed i n the' f i n a l , non l i n e a r stage show a p r e f e r e n t i a l attack i n d i f f e r e n t points o r . i n one point, a l l of them located i n the lower parts of the sample. A study of the error introduced i n c a l c u l a t i n g reaction rates on the basis of a regular attack i s presented i n appendix 1 and shows that the error remains smaller than +8%. I I . Parameters The poor r e p r o d u c i b i l i t y (±20%), confirmed by the above ob-servations, i s a t t r i b u t e d to the following f a c t o r s : temperature c o n t r o l , concentration gradient, electrochemical e f f e c t and c r u c i b l e corrosion. (1) Temperature Control In a l l runs the temperature control was not better than +5 °C and -30°C. Temperature co n t r o l of the furnace does not r e s u l t i n an accurate temperature control of the bath. The temperature measured i n the 35 melt was generally lower than the temperature of the furnace by 10-30°C. Direct temperature control of the melt was inaccurate for two reasons: f i r s t a v a r i a b l e temperature gradient (5-30°G) and convection currents e x i s t i n the melt; secondly the i n e r t i a of the Wheelco temperature c o n t r o l l e r r e s u l t s i n a gradual s h i f t i n g of the co n t r o l l e d temperature a f t e r any readjustement. Nevertheless, i n the l a t t e r case of temperature control of the melt the temperature i s more,accurately known than i n the f i r s t case of temperature control of the furnace. (2) Concentration Gradient The accummulation of reaction products r e s u l t s i n an i r o n oxide concentration gradient. A v e r t i c a l section of a v i t r i f i e d slag shows that the slag consists of a dark brown,upper part and a clear lower part corresponding to the o r i g i n a l slag. The t o t a l concentration of i r o n oxide remains low ( 1 % ) but l o c a l accummulation i n the v i c i n i t y of the sample slows down the oxidation reaction. Reciprocation of the sample did not bring meaningful im-provements but too high a number of wire c o i l s i n a small space resulted i n markedly lower rates. (3) Local Electrochemical E f f e c t s The i r r e g u l a r attack, more pronounced i n the lower parts of the sample, i s at t r i b u t e d to an electrochemical e f f e c t enhanced by gravity: lead droplets drip down along the sample and accummulate i n the lower part of t h e . c o i l s , forming a l o c a l electrochemical c e l l . 36 (4) Crucible Corrosion High lead oxide melts corrode f i r c l a y c r u c i b l e s and pierce them e a s i l y . Z i r c o n i a c r u c i b l e s were t r i e d but were given up because of s u s c e p t i b i l i t y to thermal.shocks. B. Reaction Rate for a Given Melt at Fixed Temperature Each s i n g l e . r e a c t i o n rate curve presented two consecutive stages (Fig. 8). (1) I n i t i a l Stage The i n i t i a l stage of low rate observed in.most reaction rate curves corresponds p a r t i a l l y to a thermal homogeneisation of the.system. As could be expected from the d r i v i n g force of the,system, the more o x i d i s i n g the melt, the smaller the length of t h i s stage. (2) Linear Stage In a l l cases the reaction rate i s proportional to the geometric surface area. Although t h i s was. true for the oxidation of carbon (1, 2), the actual experimental l i n e a r rates reported do not e x p l i c i t l y take into account the changing surface area of the sample, the o v e r a l l l i n e a r e f f e c t being explained by means of counter-balancing fa c t o r s . In the present . case, the progressive decrease i n the o x i d i s i n g power of the melt and the production of an i r o n oxide gradient.and an i r r e g u l a r attack can account for the observed l i n e a r rates which are then considered to r e f l e c t the 37 i n i t i a l properties of the melt. C. Lead Oxide Mole Frac t i o n Dependence The l i n e a r r e l a t i o n s h i p between reaction rates and lead oxide mole f r a c t i o n means that the rates are d i r e c t l y proportional to the concentration of lead cations i n the melt. This implies an. electrochemical step corresponding to the following reactions: Pb4"*" + 2e" ——e> Pb Fe Fe 4 4" + 2e~ [ | The reaction between Pb and the m e t a l l i c phase may be con-sidered to take place by c o l l i s i o n s of the reactants at the same s i t e or a l t e r n a t i v e l y by consecutive electrochemical p a r t i a l reactions, the s i t e s of which need not coincide, since electrons may flow through the .metal 21 ++ from the anodic to the cathodic s i t e s . For high Pb melts C>90%) the reaction i s supposed to become con t r o l l e d by the d i f f u s i o n a l transport of cations i n the melt. S i m i l a r l y the slow rates observed i n the con-centration range 76-80% PbO where the slags are more viscous are a t t r i b u t e d to d i f f u s i o n c o n t r o l . D. Oxygen P o t e n t i a l Dependence In the intermediary range of concentration (78-86%) the experimental reaction rates are proportional to the oxygen p o t e n t i a l of the binary lead s i l i c a t e system. Such a dependence was found by previous studies (1, 2) on the oxidation of s o l i d carbon. Furthermore s i m i l a r r e s u l t s are obtained i n both systems by using two sets of a c t i v i t y data 38 and by extrapolating the oxygen p o t e n t i a l dependence to zero rate melts. As i t appears that the present system i s very l i k e l y c o n t r o l l e d I | by an electrochemical oxidation process involving lead cations (Pb dependence), the comparison between the a c t i v a t i o n energies of the oxidation of i r o n and carbon i s useful for d i f f e r e n t i a t i n g between the two systems.. It would require ternary systems to d i s t i n g u i s h between, a lead ion dependence and an oxygen p o t e n t i a l dependence. E. A c t i v a t i o n Energy A comparison of the a c t i v a t i o n energies calculated by means of a rate law based on oxygen p o t e n t i a l dependence.for the oxidation of carbon and i r o n (Fig. 18) presents the following features: (1) The a c t i v a t i o n energies are s i g n i f i c a n t l y d i f f e r e n t (22 KCal/mole and.40 KCal/mole). (2) The values of the Arrhenius constants A are d i f f e r e n t by four orders of magnitude. This means that there i s a large d i f f e r e n c e i n a c t i v a t i o n entropies for the two oxidation reactions; i n other words, the rate determining steps are d i f f e r e n t . This i s consistent with the model of an electrochemical process inv o l v i n g lead cations for the oxidation of i r o n i n contrast to a process inv o l v i n g oxygen ions i n the oxidation of carbon. In the l a t t e r case the.oxygen ions must be involved for producing the,gaseous oxidation product (C + 20 —^CO^ + 4e.) whereas i n the case of i r o n oxidation a transfer of: electrons between the two m e t a l l i c species i s s u f f i c i e n t : ko Pb + + + 2e~ '. Pb ' ' ^ . " + + '.. •.'"v'/'-\ • Fe . . . . Fe . .+.,:2e" When a rate law involving only Pb is used , the activation energy of the reaction is found to be p0:+ 1 Kcal/mole, •F. Zero-rate Melts. -A complementary study of high s i l i c a melts ( 7C?fo and 73 ».5$ w g t . PbO) shows that a reaction rate can be measured .in a 73-75$ PbO melt , •whereas an equilibrium is rapidly reached.in 70$.PbO. melts. A consistent zero rate melt has a .composition between 70$ and .73•75$.PbO, as confirmed by a thermodynamical treatment of the system( appendix.5 ).. "In this con-nection, the processing of data relative to the oxidation of carbon and .based on a oxygen potential, rate law( appendix•k ').resulted :in.two different zero rate melts-; 0$ PbO (pure silica) for Richard son >-s PbO activity scale and 72$ PbO for Kozuka's scale. In view of this and in view.of the fact'that-Kozuka's activity scale resulted in a better f i t t i n g for the-oxygen potential dependence of the oxidation of carbon, .the..data ,of Kozuka is more consistent with the investigated kinetics than the data of Richardson e t a l . 41 CONCLUSIONS A study of the oxidation of s o l i d i r o n by lead o x i d e - s i l i c a melts was undertaken at d i f f e r e n t temperatures. The experimental technique consisted i n measuring the e l e c t r i c a l resistance of the sample. (1) Experimental r e s u l t s showed.that the amount of i r o n oxidised per time unit was proportional.to the geometric surface area of the sample. (2) The rate of oxidation was found to.be proportional to the mole f r a c t i o n of lead oxide in.the melt, i n the concentration range 80-88% wgt. PbO. (3) The experimental a c t i v a t i o n energy was found to be 50 ± 7 KCal/. mole. (4) By comparing the a c t i v a t i o n energy of the oxidation of i r o n and carbon by molten s l a g s . i t i s suggested that the .present system i s c o n t r o l l e d i n an electrochemical process by cation movements whereas the carbon system involves oxygen.anions i n the rate determining step. (5) Two sets of a c t i v i t y data concerning the a c t i v i t y of lead oxide i n the binary system Pb0-Si02 are a v a i l a b l e . A complementary processing of data concerning the oxidation of carbon shows that the a c t i v i t y data of Kozuka are more,consistent with k i n e t i c data. \2 BIBLIOGRAPHY 1. Jena, P.K., M.A.Sc. Thesis, Jan. 1959, Department of Metallurgy, University of B r i t i s h Columbia. 2. J o s h i , A.P., M.A.Sc. Thesis, Dec. 1960, Department of Metallurgy, University of B r i t i s h Columbia. 3. Smeltzer, W.W., Trans. Can. Inst. Min. Met. 64, 445-50 (1961). 4. Rahmel, A. and Engell, H.J., Arch, fur Eisenhuttenwesen, 30, 1459, 743-6. 5. B e l i n , P., Corrosion et, Anticorrosion, 1960, 8_, 140-56. 6. Engel, H.J., Acta Metallurgy, New York, 6. (1958), 439-45. 7. Hauffe, K. and P f e i f f e r , H., Z e i t . Metallde, 44 (1953) 27-28. 8. Turnbull, J.D.S., M.A.Sc. Thesis, A p r i l 1958, Department of Metallurgy, U.B.C. 9. Grigoryan, V.A., Mikhalik, E. and Ch'Ih Yung Han, Akademia,Nauk SSSR, Izv. Otd. Tekhnich. Nauk Metal, i i o p l . , ' 6_, (1962), 27-31. 10. Littlewood, R., Trans. AIME, 233, (1965), 772-779. 11. Ponomarenko, A. G., Teor. Prakt. Met. (Chelyabinsk) No. 7, pp. 200-9, 1964. 12. Vaisburd, S.E., and K e i f e r s , V.L., Izv. Vys. Ucheb. Zaved., Tsvet. Metal, (1959), 2, 6, pp. 76-84. 13. Vorontsov, E.S., and Ermakov, A.V., Izv. Vys. Ucheb. Zaved., Tsvet. Metal,, 1964, _7, 4, pp. 53-9. 14. Richardson, F.D., and Webb, L.E., Trans. Inst. Mining and Met., 64, 529 (1955). 15. Kozuka, Z., and Samis, C.S., unpublished report. 16. Darken, L.S., and Gurry, R.W., Physical Chemistry of Metals, 1963, McGraw-Hill, p. 268. 17. E l l i o t t , and G l e i s e r , Thermochemistry- for Steelmaking. 18. E l e c t r i c Furnace steelmaking , vol. ll}-p.2kQ, I96J),Wiley. 19. Toop, G.W., M.A.Sc. Thesis, Sept. 1960, Department of Metallurgy. UBC. 20. Richardson, F.D., The Physical Chemistry of Steelmaking, Techn. Press of the M.I.T., 1956, p. 55. 21. King, T.B., and Ramachandran, S. The Physical Chemistry of Steelmaking, Techn. Press of the M.I.T., 1956, p. 121. Appendix No. 1 Error on Reaction Rates The hypothesis of a regular attack of the sample r e s u l t s an approximate calculated reaction rate. I. D e f i n i t i o n s M : Actual mass of unoxidised i r o n 2 r .: Actual equivalent radius (M = 7V JC d) Mo: Calculated mass (assumption of a regular attack (Mo = P t d I ) 2 V ro: Calculated radius (Mo = 7f r Q Jl, d) (X^: Relative mass error (M = Mo(l r^ : Smaller radius R : Larger radius <^: Irregular attack portion length L : Specimen length X = L - y . 4 L E = rA-ro rA radius error (E = 1 - 1 ) Vi -w The following table gives the va r i a t i o n s of E with oi 0.1 0.2 0.-3 0 4 0.5 E 0.05 0.08 0.12 0.15 0.18 Table 1,1. I I . Experimental Observations "regular" attack' ( l i n e a r rates) : 0 <^ x ^ 0.8 " i r r e g u l a r " attack (non l i n e a r rates: 0.8 <^ x <C 2 (the l a t t e r cases were not taken into account i n reaction rate c a l c u l a t i o n s ) . I I I . C y l i n d r i c a l Attack i _ J £ . -L Resistance R., = (p 1 R2 -rr r 1 z -TTR2 Total resistance = L [ 1 + ^  . (R^ -1) ] = P L "T R 2 ~ r x 2 T T r o 2 .*. R 2 = r o 2 [1 + y (1 - 1)] Actual m*ss M = 7VR (L-i^d + TV r ^ 2 , d M = 7TR 2 L d [ l + y ( 1 2 - 1)] X 2 •M = Mo [1 + y ( l - y ) ( x Z + 1^ - 2)] . ' • 0( = y ( l - y ) ( x 2 + 1 2 - 1) X Variations of y X 0.1 0.2 0.3 0.5 0.9 0.004 0.007 0.009- 0.011 0.83 0.012 0.021 0.028 0.033 0.66 0.091 0,163 0.21 0.25 0.5 0.20 0.35 0.46 0.55 Table 1, 2 Conclusions i n a l l cases of "regular" attack ( l i n e a r r a t e s ) : x <C 0.8 , y ^. 0.2 E < 8% IV Conic Attack * 4 7 Resistance R l 0 ( 1 d £- _ I) fts 1 d ^ T \ I T TrTrTTn2 = ( ^ 2 « j V ^ n 2 R l r l R R 9 = fV1) i Total resistance = (\ [1 + ^ ( R - 1) ] R2 I - T-L . * . R 2 = r o 2 [1 + y (1 - 1) ] X" Actual Mass M =TX R 2 ( L - ^ ) d + 2 V(^_) d (vcfi) = volume of the h a l f cone) ~2 " 4 2 ^ 1 6 2 2 2 3 1 M = -trdLro (1 + .y (1^1) ] [1-y + l y (1 + x + x ) ] x 2 2 l x l x _ lyx 1 _ _2 y_ 3 3 3 x 3 x Variations of Attack i n one,single point: x ^ 0 . 5 y = 0.1 ^ = 0 .05 5% general attack with c o n s t r i c t i o n i n one point: x _^ 0.5 y = 1 0<f = 1 (-2 + x + 1) = 0.16 3 x E<8% VI Conclusions In a l l cases the error on the experimental reaction rate i s i n f e r i o r to 8%. APPENDIX 1 b i s F i g . 19 : Relation between weight and mole f r a c t i o n i n PbO-SiOp. NPbO _^ _ _ g_ wgt io PbO 50 Appendix No. 2 Richardson's Activity data Richardson shows that the molten si l i c a t e Pb0-Si02 can be consi-dered as a regular solution in the investigated concentration range ( 70-95 io wgt. PbO ).This is confirmed by Kozuka 1 5. Therefore Richardson's data are extrapolated to lower temperatures ( 85O, 900,950°C ) by plotting logTfPbO versus reciprocal temperature, since in a regular solution RTln^ remains constant for a given mole f r a c t i o n 1 6 . aPbO (ref . 14) 2fFbO - log^PbO NPbO 1000°C 1100°C 1194°C 1000°C 1100°C li94°c 1000°C 1100°C 1194°C 0.95 O.93 0.93 0.93 0.978 0.978 0.978 0.0083 0.0083 O.OO83 0:90 O.85 O.85 O.85 0.943 0.943 0.943 0.0259 0.0259 0.0259 0.85 O.76 O.76 • O.76 0.893 0.893 0.893 0.0495 0.0495 0.0495 0.80 0.66 0.66 0.66 0.825 0.825 0.825 0.0839 0.0839 0.0839 0.75 0.52 0.54 0.56 0.694 0.720 0.746 0.159 0.142 O.127 0.70 o.4o 0.43 0 A 5 0.572 o.6i4 0.656 0.243 0.212 O.183 0.65 0.30 0.33 0.36 0.462 0.507 0.538 0.336 0.295 0.269 0.60 0.22 0.24 0.27 0.367 o.4oo 0.450 0.435. 0.398 0.347 0.55 0.15 0.17 0.20 0.273 0.309 0,345 0.564 0.510 0.462 0.50 0.11 0.12 o.i4 0.220 0.240 0.280 0.657 0.620 0.553 0.45 0.077 0.091 0.10 0.171 0.202 0.222 0.767 0.694 0.653 o.4o 0.058 0.069 0.079 0.145 0.172 0.200 0.838 0.764 0.699 Table 8. Richardson's activity data for PbO in PbP-SiOP. F i g . '20 : P lot , o f Log if FbO v e r s u s l /T ( f r o m R i c h a r d s o n ) . aPbO 53 - l o g Tf ^ P b O aPbO e x t r a p o l a t i o n ref.14 NPbO 850°c 900°C 950°c 850°C 9000 C 950°C 850°C 900°C 950°c 1000°C O.70 0.305 0.281 0.261 O.496 0.524 0.549 0.347 0,367 0.384 0.40 O.65 0.408 0.380 0.357 0.391 0.417 o.44o O..254 0,271 0,286 O . 3 O 0.60 0.528 0.496 0.467 O.287 0.319 0..341 0,172 0.191 O.205 0.22 0.55 0.670 0.630 0.595 0..214 0.234-. 0.254 0,118 0.1285 0.1395 0.15 O.5O 0.778 0.737 0.700 0.167 0.1835 0.200 0.0835 0.0917 0.100 0:11 0.1+5 0.885 o.84o 0.800 0.1305 0.145' 0.159 O.O587 0.0652 0.0715 O.O77 o.4o 0.993 0.935 0.885 0.1018 O.1152 0.1305 0.0407 o.o46i 0.052 O.O58 T a b l e 9 . A c t i v i t y o f PbO i n PbO-SiOc, w . r . t . mole f r a c t i o n . 850°C 900°C 950°C 1000°C aPbO (aPbO) 2 ' SPbO (aPbO)? ( a P b O ) ' $Pb0 aPbO aPbO (aPbO) -. 0.04 0.0016 0.046 0.0021 °-'052 0.0027 O.O57 0.0032 71 0.043 0.0018 0.05c 0.0025 O.O55 0.0030 0.060 O . O O 3 6 72 0.047 0.0022 0.054 0.0029 O.O59 O .OO35 o.o64 o.oo4i 73 0.052 0.0027 0.058 0.0033 0.064 0.0041 0.070 0.0049 74 O.O59 0.0032 0.064 0.0041 0.068 o.oo48 0.076 O .OO58 75 0.063 o.oo4o 0.070 0.0049 O.O77 0.0059 o.o84 0.0070 76 0.070 0.0049 0.076 O .OO58 0.084 0.0070 0.092 O.OO85 77 O.O76 O . O O 5 8 o.o84 0.0070 0.092 0.0085 0,102 0.0104 78 O.O85 0.0072 0.093 0.0086 0.103 0.0106 0.112 0.0125 79 0.094 O .OO87 0.103 0.0106 0,112 0.0125 0.123 0.0151 80 0.105 0.0110 0.115 0.0132 O.I25 0.0156 0.136 O . O I 8 5 81 0.119 0.0142 0.131 0.0172 0.142 0.0201 0.153 0.0234 82 0.134 O.OI79 0.149 0.0221 0.161 0.0259 0.175 0.0306 83 0.155 0.0240 0.170 0.0289 O.I85 0.0342 0.-200 o.o4oo 84 0.179 0.0320 0.195 O .O38O 0.211 0.0445 0.226 0.0510 85 0.209 0.0436 0,225 O .O5O8 0.240 0,0575 0.256 0.0655 86 0.242 O.O585 0,260 0.0675 0.273 0.0745 0.290 o.o84o 87 T a b l e 1 0 . A c t i v i t y o f PbO i n P b 0 - S i 0 2 w . r . t . wgt.j> PbO. Appendix No 3 K o z u k a ' s A c t i v i t y d a t a 1 5 , Kozuka's data are extrapolated to lower temperatures (850°C) by using the l i n e a r dependence between temperature and electromotive force nEF= -RTLnaPbO n = 2 F = 96k9k c. • R = I.9872 cal/mole: x degree = B.Jlkk joules/mole x degree. E x 1+6121 = -I+.57U x T x log aPbO - T °C log aPbO 1273 -7.90 E 1223 -8.22 E 1173 -8.59 E 1123 -8.96 E Table 11 . log aPbO from the emf (Kozuka's data). 55 E ( v o l t s ) NPbO 0.30 0.25 -o o-0.20 0.15 -c c-0.10 -c o —o ©- 0.05 960 lcJoo" Temperature °C 1 5 Fig.22 : Temperature dependence of the emf (Kozuka s data ) K o z u k a ' s d a t a E x t r a p o l a t e d d a t a #PbO E logaPbO aPbO E logaPbO .aPbO 1000°C 950°C 5 10 15 20 25 50 0.0167 0.04ll O.O687 O .O93O 0.111 0.127 -0.1322 -0,324 -0.544 -0.735 -O.877 -1.005 0.737 O.475 0.286 0.184 0.132 0.099 0.0157 0.0595 O.0668 O.091 O . IO85 0.124 -0.1295 -O.3245 -O.549 -O.747 -O.892 -1.018 O.741 0.474 0.2825 0.179' 0.1282 O.096 900°C 850°c 5 10 15 20 25 30 0.015 O.O38 O.O65 O.O89 0.106 0.121 -0.129 -O.326 -O.558 -0.764 -0.910 -l.o4o 0.743 0.472 0.276 0.172 0.123 0.091 o.oi4 0.0365 0.063 0.087 0.1037 0.1182 -0.1255 -O.327 -O.565 -O.78 -0.93 -1.06 O.749 0.471 0.272 0.166 0.115 O.O87 T a b l e 12 . L e a d o x i d e a c t i v i t y d a t a f r o m K o z u k a . 58 i 850°C 900°c 950°c 1000°C PbO 2 aPbO ( a P b O ) 2 aPbO ( a P b O ) 2 aPbO (aPbO) aPbO (aPbO) 70 O.087 O . O O 7 6 0.091 O.OO85 O.O96 O.OO92 O.O99 0.0099 71 O.O89 O.OO79 0.095 0.0086 0.099 O .OO98 0.105 0.0110 72 O.O95 0,0086 O.O99 O.OO98 0.105 0.0110 0.110 0.0121 73 O.O99 O .OO98 0.106 0.0912 0.112 0,0125 0,117 O.OI57 7^  0.106 0.0112 0.112 0.0125 0.118 0.0159 0,124 O.OI54 75 0.114 0.0150 0,120 0.0144 0.126 O.OI58 0.0184 0.152 0.0174 76 0.122 0.0148 0.129 0.0166 0.156 0.l4l O.OI99 77 0.151 0.0172 O.I58 0.0190 0.145 0.0210 0.151 0.0221 78 0.l4l O.OI98 0.148 0.0219 0.155 0.0240 0.161 0.0260 79 O.I55 0.0240 0.161 0.0260 0.167 0.0279 0.175 0.0500 80 0.166 0.0275 0.175 0.0500 0.179 0.0520 0.184 0.0559 81 O.I85 0.0555 O.I89 O.0556 0.195 O.O58O 0.201 O.O575 82 0.202 0.0407 0.208 0.0452 0.214 0.0456 0.220 0.0482 85 0.225 0.0496 0.229 O.O525 0.255 O .O55O 0.240 O.O575 84 0.246 0.0605 0,252 0.0655 0.258 O.O665 0,265 O.O69O 85 0.272 0.0740 0,277 O.O77O 0,282 0.0795 0.286 O.O87O 86 0,508 0.0950 0,512 O.O97O 0,516 0,100 0.520 0.102 87 0,346 0.120 O.55O 0.125 0,553 0.125 0.556 0.126 88 0.575 o.i4i O.58O o.i44 0.585 o.i48 o.4o 0.160 89 0.420 0.176 - — - — — — 90 0.470 0.221 0.470 0.221 0.470 0.221 0.47 0.221 91 0.525 0.275 — — — — — — 92 0.580 0,556 — — — — — 95 0.65 0,425 — — — — T a b l e 15. A c t i v i t y o f PbO i n P b O - S i O g w . r . t . w g t . $ ( K o z u k a ' s d a t a ) 59 Appendix No k. Oxidation of carbon : Jena's data . I,. Oxygen potential. A processing of Jena's data with the help of Richardson's and Kozuka's activity scales are presented in table ik and f i g . 2k (log log plot). The following observations can be made: (1) The log log plot shows a linear dependence for both sets of data. (2) The slopes are reproduced in each series of experiments. (5) -The values of the slopes are respectively larger. ( 2.50 for Kozuka's scale) and smaller ( I.85 for Richardson's scale) than the theoretical value adopted by the author (• n = 2 •), -(k) The common point between each couple of lines corresponds to the common point of the two lead oxide activity scales at that tempera-ture (1000°C). This point is estimated between 92 and 93 $ PbO and this is confirmed in f i g . 25 showing the two activity curves obtained from Richard-son's and Kozuka's data. (5) The rates observed at high s i l i c a contents ( 77 $ RbO ) are somehow lower than expected from the general linear dependendence. The f i r s t three observations confirm the validity of Jena's conclusions concerning the oxygen potential dependence. 60 #PbO 10 4rate( gm/cm2xmin) 10 4rate graphite carbon 77 1.00 0.79 78.8 1.63 1,17 81 2.45 1.84 82 3.13 2.24 83 3-67 2.90 84 4.80 3.68 85 6.00 4.76 86 7.90 5.85 Table l4. Jena's reaction rates The corresponding l i n e a r oxygen p o t e n t i a l dependence 2 (rate versus (aPbO) i s shown i n fig.26 and present a s i g n i f i c a n t d i s c r e -pancy with respect to the zero rate melts: Richardson's scale gives a zero rate melt at 0 $ PbO (pure s i l i c a ) whereas Kozuka's scale indicates 12 $ PbO. Since Kozuka's scale does not give a straight l i n e passing through the o r i g i n a correction i s necessary f o r the log log plot.The corrected p l o t ( f i g . 27) gives a l i n e a r dependence f o r a l l React ion rates.The corresponding slopes are reduced to I.96 and I.89. II.Lead mole f r a c t i o n dependence. The corresponding pl o t s are shown i n f i g . 28. 61 I T •1-82 2 -50 Log(aPbO) V s <P*ou (KozukaVscale) -I aPbO 1 1 1 1 I 70 75 80 85 90 w g t $ P b O 10 x r a t e ( c m / m i n ) 6k Appendix No 5 . Zero rate melts I.Thermodynamic data For the reactions of i n t e r e s t : Pb + £ o 2 --4> PbO (1) (1) (1) Fe + £ 0 2 t> FeO (2) ( 8 ) (B) 2Fe + | o 2 -—t> F e 2 0 3 (3) (s) 2 ( 8 ) the following free energies are a v a i l a b l e 2 7 : T t ' A * i c a l A F 2 A F 3 1100 -264-50 -46050 -128100 1159 -25150 1184 -44700 -123200 1200 • -24450 -44450 -122200 1300 -.22800 -42900 -116400 •Table 15 . Thermodynamic data f o r the oxidation  of lead and i r o n . By l i n e a r extrapolation'. A P i c a l A F 2 A. F 3 1123 1273 -25750 -23250 -45650 •-43300 -126700 -118000 Table l6.Free energies at 1000*0 and 850°C f o r the oxidation of Fe and Pb. 67 I I . Oxygen Potential. From equation (1) we can estimate the oxygen potential for a 72 $ PbO melt: aPbO aPb f P 0 2 ) 2 log K = 5 .with aPb - 1 and aPbO = 0.086 (Kozuka): 1123 ' .13 po.= 1°-Similarly: logK = h . with aPbO = 0.11(Kozuka) ' t 1273 > - 1 0 P 0 2 = 1 0 I I I . Zero rate point The equilibrium between ferrous and ferric oxides 2 FeO + PbO Fe 20 3 + Pb (k) gives the following equilibrium constant: ^F, = -I965O cal aFe a0 3 log K 4 = 3-8 .% K 4 = 6 x IO 3 = — 1123 (aFeO) aPbO From the value of the oxygen potential in the system one estimate approxi-mately the ratio between the two iron oxides from a ternary diagram Si0 2-FeO-Fe 20 3 2 8 : aFe 20 3 1 aFeO 1 0 _4 hence aFeO i 2 x 10 1123 Similarly ; A p 4 - = -8I5O cal 1273 log K 4 = l . k K 4 = 25 aFeO ~ k x 10 1273 ; !273 Conclusion: The iron oxide activies are very low in a 72$ PbO melt.Therefore an equilibrium must be rapidly reached. .2 

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