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The electrochemical oxidation and combustion of carbon. Turnbull, John Douglas Shand 1957

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THE ELECTROCHEMICAL OXIDATION AND COMBUSTION OF CARBON by JOHN DOUGLAS SHAND TURNBULL A THESIS SUBMITTED IN PARTIAL FULFILMENT QF THE REQUIREMENTS FOR THE DEGREE OF MASTER QF APPLIED SCIENCE i n the Department of Mining and Metal lurgy We accept t h i s thes i s as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of Mining and Meta l lurgy . THE UNIVERSITY OF BRITISH. COLUMBIA October, 1 ° 5 7 i i ABSTRACT The o x i d a t i o n and combustion of g r a p h i t e i n a l e a d -b o r o s i l i c a t e s l a g of t h e c o m p o s i t i o n PbO„Si02.0.1Na2B407 were s t u d i e d w i t h and w i t h o u t an a p p l i e d p o t e n t i a l . The r e a c t i o n was f o l l o w e d by t h e a n a l y s i s o f t h e desorbed anode gas. The CO/CO2 r a t i o o f t h e anode gas i n any one experiment was found t o i n c r e a s e l i n e a r l y w i t h t i m e i n a l l c a s e s . T h i s i n c r e a s e was thought t o be r e l a t e d t o the d e c r e a s i n g o x y g e n - i o n c o n c e n t r a t i o n . The CO/CO2 r a t i o was found t o i n c r e a s e w i t h t e m p e r a t u r e and t o d e c r e a s e w i t h i n c r e a s i n g c u r r e n t d e n s i t y . The a p p a r e n t d i f f e r e n c e i n a c t i v a t i o n e n e r g i e s f o r t h e d e s o r p t i o n o f CO and CO2 w i t h o u t an a p p l i e d p o t e n t i a l was found t o be 32 ± 6 k i l o c a l o r i e s . T h i s i s c o n s i d e r a b l y h i g h e r t h a n t h e v a l u e s (8 t o 17 k i l o c a l o r i e s ) r e p o r t e d f o r t h e gaseous r e a c t i o n , A t h e o r e t i c a l e x p l a n a t i o n f o r the i n c r e a s e d p r o d u c t i o n o f C 0 2 i n c h e m i c a l and e l e c t r o c h e m i c a l c o m b u s t i o n o v e r t h a t o b s e r v e d i n gaseous co m b u s t i o n was advanced. T h i s e x p l a n a t i o n extended t h e d e s o r p t i o n model o f Long and Sykes t o t h e s l a g -g r a p h i t e r e a c t i o n . T h i s extended model e x p l a i n s why t h e CO/CO2 r a t i o i n c r e a s e s w i t h time i n c h e m i c a l c o m b u s t i o n , but does not p r e d i c t t h i s o b s e r v e d e f f e c t f o r t h e e l e c t r o c h e m i c a l r e a c t i o n . The r a t e o f oxygen removal f r o m t h e s l a g d u r i n g t h e c h e m i c a l r e a c t i o n was c a l c u l a t e d f r o m t h e r a t e of e v o l u t i o n and the c o m p o s i t i o n of t h e desorbed gas. The a c t i v a t i o n energy i s 2 6 - 5 k i l o c a l o r i e s . Absolute reac t ion rate ca l cu l a t ions were made for r a t e - c o n t r o l l i n g steps of immobile adsorpt ion , mobile adsorpt ion, chemical reac t ion , and desorpt ion. The c a l -culated rates were at leas t a factor of 10 d i f f e rent from the observed ra te . In presenting t h i s thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representative. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of »»j 9- Mc-fa //<-•/-The University of B r i t i s h Columbia, Vancouver 8, Canada. Date /"7c*.y /S A  ACKNOWLEDGEMENT The a u t h o r would l i k e t o acknowledge the a d v i c e , a s s i s t a n c e , and encouragement f r e e l y g i v e n by t h e members of the s t a f f o f the Department of M i n i n g and M e t a l l u r g y , , e s p e c i a l l y t h a t of Dr. C.S„ Samis,. who d i r e c t e d t h i s i n v e s t i g a t i o n . The a u t h o r i s a l s o i n d e b t e d t o the N a t i o n a l R e s e a r c h C o u n c i l and the Defense R e s e a r c h Board f o r the f i n a n c i a l a s s i s t a n c e n e c e s s a r y t o c a r r y out t h i s p r o j e c t . V TABLE OP CONTENTS Page INTRODUCTION 1. GASIFICATION OF CARBON . . . 1 O x i d a t i o n P r o c e s s . . . . 2 Combustion P r o c e s s . 3 IONIC OXIDATION AND COMBUSTION OF CARBON 7 E n t r o p y Change 11 OBJECT AND SCOPE OF THE PRESENT INVESTIGATION . . . . Hj. EXPERIMENTAL PROCEDURE , . . l£ OVERVOLTAGE MEASUREMENTS IN FAYALITE SLAGS . . . . . . 1$ REACTION OF GRAPHITE IN LEAD-SILICATE SLAGS . . . . . 16 M a t e r i a l s . 16 A p p a r a t u s . . 16 S l a g C o m p o s i t i o n . „ . 1 9 S l a g P r e p a r a t i o n . . ... 20 P r o c e d u r e , 20 C u r r e n t D e n s i t y Measurement . . 21 Gas A n a l y s i s .. 22 RESULTS . . . . . . . . . . . . . . . . 2$ CHEMICAL OXIDATION . 2$ ABSOLUTE REACTION RATE CALCULATIONS . . . . . . . . . 2$ CHEMICAL COMBUSTION 27 ELECTROCHEMICAL COMBUSTION 32 DISCUSSION . ' lj.2 DESORPTION MECHANISM h,2 v i Page Properties of Graphite and Carbon . . . . . . . . . . i}3 1. Formation . l\.3 2 . Structure . . . . . . . . . . . . . . . . . . . IL$ .Slag-Graphite Interface . . . . . . . . . . . . . . . l\S 1. Semi-Conductor Band Theory . . . . . . . . . . . l±9 2 . Slag-Graphite Interface . . . . . $2 Mechanism f o r the Combustion of Graphite . . . . . . . 60 COMPARISON OF EXPERIMENTAL RESULTS WITH THEORY . . . 6£ CONCLUSIONS . . . . . . . . . . . . . . . . 67 RECOMMENDATIONS FOR FURTHER WORK . . . . . . . . . . . . 68 BIBLIOGRAPHY . . . . . . . . . . . 69 APPENDIX A 72 APPENDIX B . . . . . . . . . . . . . . . . 79 v i i LIST OF FIGURES Figure No. Page 1 . Apparent A c t i v a t i o n Energy Difference i n Gaseous Combustion . . . . . . . . . . . . . . . . . . 5 2 . P o t e n t i a l Energy Diagram . . . . . . . . . . . . 9 3 . Experimental Apparatus f o r F a y a l i t e Slags . . . . 16 4 . Experimental Apparatus for P b O . S i 0 2 . l Na2 B 4°7 5 . Photograph of E lec t rochemica l ly Oxidized Anodes . 23 6 . Arrhenius P lo t fo r Chemical. Oxidat ion . . . . . . 26 7 . V a r i a t i o n of CO/C0 2 Ratio with Time for Chemical Combustion . . . . . . . . . . . . . 29 8 . A c t i v i t y of PbO i n PbO-Si0 2 Melts . . . . . . . . 31 9 . Apparent A c t i v a t i o n Energy Difference for Chemical Combustion . . . . . . . . . . . . . 33 1 0 . V a r i a t i o n of CQ/C0 2 Ratio with Time at 9 0 0 ° C . . 35 1 1 . V a r i a t i o n of CQ/C0 2 Ratio with Time at Q25 °C . . 36 1 2 . V a r i a t i o n of C0/C0 2 Ratio with Time at 9 5 0 ° C . . 37 1 3 . V a r i a t i o n of CQ/C0 2 Ratio with Current Density . 38 14. Apparent A c t i v a t i o n Energy Differences for Electrochemical Combustion . . . . . . . . . 40 1 5 . V a r i a t i o n of Apparent A c t i v a t i o n Energy Difference with Current Density . . . . . . . 41 1 6 . Aromatic Hydrocarbon Ser ies . . . . . . . . . 44 1 7 . TT - E l e c t r o n Molecular O r b i t a l s i n Benzene . . . . 4 7 1 8 . E l e c t r o n D i s t r i b u t i o n i n Graphite . . . . . . . . 47 1 9 . E l e c t r o n Band Structure of Carbon . . . . . . . . 48 v i i i Figure No. Page 20. V a r i a t i o n of Energy Gap with Heat Treatment Temperature 50.. 21. H a l l Coef f i c ient as a Function of Temperature of Heat Treatment 53 22. Band Structure of Slag-Graphite Contact 55 23. Postulated Structure of Slag-Graphite Boundary Layer 57 24. Influence of Appl ied P o t e n t i a l on Slag--Graphite Band Structure 59 25. Oxygen Bonding on Graphite 6 l 26. tT-Bond Orders i n Phenpxyl Radica l . . . . . . . . 6 l 27. TP-Bond Orders f or oC-Naphthoxyl and A-Naphthoxyl Radicals 63 28. Ketene Structure . . 63 THE ELECTROCHEMICAL OXIDATION AND COMBUSTION OF CARBON INTRODUCTION One of the chemical react ions most useful to mankind has been the reac t ion of carbon-containing mater ia l s with oxygen. This heterogeneous reac t ion i s of considerable t h e o r e t i c a l and i n d u s t r i a l in teres t and has been the subject of extensive research for some years. However, a modi f i ca t ion of t h i s process i n v o l v i n g the reac t ion of carbon with the oxygen ions i n a melt , as t y p i f i e d by the anodic reac t ion occurr ing i n the alumina-reduction c e l l , has recent ly been accorded much i n t e r e s t . This i n v e s t i g a t i o n i s concerned with the consumption of carbon using a molten l e a d - b o r o s i l i c a t e s lag as a source of i on ic oxygen. Before d i scuss ing the procedure and re su l t s of t h i s study, i t i s advantageous f i r s t to consider the present knowledge of the gaseous consumption of carbon. Using these data as a basis of comparison, the changes involved i n u t i l i z i n g oxygen ions i n place of molecular oxygen w i l l be discussed. GASIFICATION OF CARBON The consumption of carbon may be considered to consist of two general stages: an oxidat ion step invo lv ing adsorption and chemical r eac t ion , and a combustion step cons i s t ing of the desorption of carbon oxides. The oxidat ion stage normally contro l s - • 2 -the r a t e o f r e a c t i o n , and the combust ion s tage de termines th e a c t u a l amount o f ca rbon consumed p e r molecu le of oxygen s i n c e both CO and CO2 a re desorbed s i m u l t a n e o u s l y . O x i d a t i o n P r o c e s s The o x i d a t i o n o f carbon w i t h oxygen gas has been s t u d i e d e x t e n s i v e l y (1) , (2 ) , ( J ) , (4 ) . There i s g e n e r a l a g r e e -ment t h a t the r e a c t i o n i s f i r s t o r d e r w i t h r e s p e c t t o 02, and thus the r a t e - c o n t r o l l i n g s tep p r o b a b l y i n v o l v e s an oxygen m o l e c u l e . F u r t h e r m o r e , the c o n c e n t r a t i o n o f s i t e s remains cons t an t and does not i n f l u e n c e the r e a c t i o n o r d e r . The a c t i v a -t i o n e n e r g i e s have been found t o l i e between 20 and 50 k i l o -c a l o r i e s per gram mole (5)» (6)> (7)> (8(• However, i n s p i t e o f numerous comprehensive k i n e t i c s t u d i e s , the mechanism o f ca rbon o x i d a t i o n has not been d e f i n i t e l y e s t a b l i s h e d . Gu lbransen ( Q ) , by u s i n g the a b s o l u t e r e a c t i o n r a t e t h e o r y , has c a l c u l a t e d t h a t e i t h e r immobi le a d s o r p t i o n w i t h d i s s o c i a t i o n o r m o b i l e a d s o r p t i o n i s the r a t e -d e t e r m i n i n g s t e p . However, these c a l c u l a t i o n s are o n l y approximate and t h e r e i s no e x p e r i m e n t a l v e r i f i c a t i o n o f e i t h e r mechanism. T h e r e f o r e , i t may be conc luded t h a t : 1. The o x i d a t i o n o f ca rbon i s a f i r s t - o r d e r r e a c t i o n w i t h r e s p e c t to m o l e c u l a r oxygen. 2. The r a t e i s not i n f l u e n c e d by the c o n c e n t r a t i o n o f s i t e s . - 3 -3. The ca l cu la t ions of Gulbransen ind ica te that e i ther adsorption with d i s s o c i a t i o n or mobile adsorption may be the r a t e - c o n t r o l l i n g step. Combustion Process One of the most s i g n i f i c a n t experimental studies on ' the combustion of carbon i s that of G i l l i l a n d et a l ( 1 0 ) . They reacted charcoa l , coke, and graphite with a i r i n a f lu id i zed-bed reactor . Upon rep lac ing the nitrogen c a r r i e r gas with C0 2 > .no change was found i n the resul tant C 0 / C 0 2 r a t i o over and above that of pure d i l u t i o n . This would indicate that the CO2 in- the g a s did not back-react with the carbon to form CO under these condi t ions . I t may be concluded from t h i s work, therefore , that the CO and CO2 desorbed from a carbon surface are primary products of combustion. Much work has been done on the CO/CO2 r a t i o i n the desorbed gas. Arthur ( 1 1 ) , who studied the desorption of CO and o C02 i n the temperature range from 470 to 900 C . , found that the CO/CO2 r a t i o was uniquely determined by the temperature according to the equation ., „ , _ _ 3 .4 -12 ,400 C 0 / C 0 2 = 1 0 e R T Long and Sykes (4) have measured the a c t i v a t i o n energy fo r the desorption^ of CO as 53 k i l o c a l o r i e s per gram mole with an entropy term of 1 0 1 1 . Their.measured value for the a c t i v a t i o n energy fo r the desorption of CO2 i s 38 k i l o c a l o r i e s with an entropy term of 1 0 7 , Thus - k-the C O / C O 2 r a t i o from t h e i r data Is g i v e n by the equation This i s In good agreement with that of Arthur. From the equations of Arthur, and Long and Sykes, i t i s seen that t h e i r a c t i v a t i o n energy differences for the desorption of 0 0 and C O 2 are 12. IL k i l o c a l o r i e s and 17 k i l o c a l o r i e s respectively. Rhead and Wheeler ( 1 2 ) Combusted carbon at temperatures from l j . 0 0 to 6 f ? 0°C. by both a s t a t i c and a dynamic method. The r e s u l t i n g CO/COg r a t i o s are shown In Figure 1 with the data of Long and Sykes, and Arthur. This figure i s a graph of log C O / C O 2 " r a t i o against the r e c i p r o c a l of the absolute temperature. The slope of this l i n e gives an "apparent" difference i n the a c t i v a t i o n energies f o r the desorption of CO and of C 0 2 . This energy difference i s only apparent because the C O / C O 2 rat;Lo i s not the r a t i o of the s p e c i f i c reaction rates. The data of Rhead and Wheeler y i e l d s an apparent a c t i v a t i o n energy difference of 8 k i l o -c a l o r i e s per gram mole, as compared with the values of 1 2 .i| and 17 k i l o c a l o r i e s found by Arthur, and Long and Sykes, respectively. The c a t a l y t i c effects of various substances on the desorpti on of C O 2 have been studied by Arthur ( 1 3 ) , Bridger ( 1 1 1 ) , and Mertsns (if?). Hydrogen i n any form seems to accelerate the reaction, while P 0 C 1 2 , F C l ^ CCl^, NO, halogens, and F e ( C 0 ) £ a l l i n h i b i t the production of C Q 2 . - £ -F i g u r e 1, Apparent A c t i v a t i o n Energy D i f f e r e n c e s f o r the D e s o r p t i o n o f CO and CO2 i n Gaseous Combustion - 6 -The e f f e c t o f t h e i n h i b i t o r s can be d e s t r o y e d by the a d d i t i o n o f l a r g e amounts of Hg o r HgO. Long and Sykes (16) have found t h a t t r a n s i t i o n meta l s i n the g r a p h i t e l a t t i c e i n c r e a s e the r a t e o f the CO d e s o r p t i o n r e a c t i o n . They p o s t u l a t e t h a t t h i s r e s u l t i s e f f e c t e d by t h e t r a n s i t i o n m e t a l atoms a b s o r b i n g TT - e l e c t r o n s from the g r a p h i t e and chang ing t h e TT-bond o r d e r s i n such a way t h a t CO i s p r e f e r e n t i a l l y d e s o r b e d . o o A t temperatures between 900 C and 1200 C , t h e r e a r e -many c o n f l i c t i n g da t a i n the l i t e r a t u r e . S t r i c k l a n d - C o n s t a b l e (17) found I n t h e combust ion o f g r a p h i t e t h a t o n l y CO was p r o d u c e d . On the o t h e r hand, Meyer (18) observed a CO/COg r a t i o o f about one , independent o f temperature and p r e s s u r e . The o n l y c o n c l u s i o n t h a t may be drawn from these da t a i s , t h a t the desorbed gas w i l l p r o b a b l y be r i c h i n CO. From the f o r e g o i n g d i s c u s s i o n , i t may be conc luded t h a t : 1. CO and C 0 2 a re p r imary p r o d u c t s o f the combust ion o f c a r b o n . 2. At r e l a t i v e l y low t e m p e r a t u r e s , the C0/C02 r a t i o i s u n i q u e l y de termined by t h e . t e m p e r a t u r e . 3. At h i g h t e m p e r a t u r e s , the desorbed gas i s p r e d o m i n a n t l y CO. 4. The apparent a c t i v a t i o n energy d i f f e r e n c e s f o r the d e s o r p t i o n o f CO and C 0 2 a re between 8 and 17 k i l o -c a l o r i e s . - 7 -5„ Adsorbed hydrogen o r w a t e r vapour a c c e l e r a t e the C0 2 d e s o r p t i o n r e a c t i o n , w h i l e P0C1 2, P C I 3 , C C l ^ , NO, h a l o g e n s , and Fe(CO)^ I n h i b i t i t . 6. T r a n s i t i o n m e t a l s i n the l a t t i c e promote' the d e s o r p t i o n o r CO. IONIC OXIDATION AND COMBUSTION OF CARBON I n a het e r g e n e o u s r e a c t i o n , any one of a number o f p r o c e s s e s may be r a t e c o n t r o l l i n g . Three s t e p s w i l l be c o n s i d e r e d h e r e ; namely, 1. A d s o r p t i o n 2 . C h e m i c a l R e a c t i o n 3- D e s o r p t i o n I n the i o n i c o x i d a t i o n o f ca r b o n , the a d s o r p t i o n p r o c e s s c o n s i s t s p r i m a r i l y o f t h e d i s c h a r g e of oxygen i o n s onto the c a r b o n s u r f a c e . The e x t r a e l e c t r o n s i n the v a l e n c e s h e l l o f the oxygen i o n w i l l flow, i n t o the conductance band o f t h e carbon a t the a d s o r p t i o n s i t e s . The oxygen atoms c r e a t e d i n t h i s manner w i l l f o r m c h e m i s o r p t i v e bonds w i t h the c a r b o n s u r f a c e i n a l o o s e l y - h e l d CxOy a c t i v a t e d complex. T h i s complex, as p o s t u l a t e d by S i h v o n e n ( 1 9 ) , w i l l be f r e e t o move about the Carbon s u r f a c e . He s t a t e s : "Oxygen atoms w h i c h a r e combined w e a k l y ... move a l o n g the s u r f a c e toward the boundary carbon atom c h a i n s . They may t h e n a t t a c h t h e m s e l v e s t o f r e e boundary atoms a t the r u p t u r e p o i n t s . " T h i s complex g r a d u a l l y forms a d e f i n i t e bond w i t h the p e r i p h e r a l c a r b o n i n t h e r e a c t i o n s t a g e . S u b s e q u e n t l y , - 8 -the carton-carbon bond i s ruptured and CO or CO2 i s desorbed. Str ickland-Constable ( 2 0 ) describes t h i s desorption step as fo l lows : wAs the carbon molecule i s progress ive ly eaten away the process must involve the cont inual breaking of the hexagon r i n g s . The approaching oxygen atoms w i l l meet with carbon i n d i f fe rent and various states of chemical combination and i t i s poss ible that whether CO or C 0 2 i s desorbed w i l l depend p r e c i s e l y on what t h i s state i s . However, the progressive demolit ion of the hexagon r ings can be assumed to take place i n a f a i r l y regular manner as a c e r t a i n f ixed proport ion of the carbon w i l l react to form CO and the remain-ing proport ion w i l l form C 0 2 . " It is advantageous to construct a schematic diagram showing the change i n free energy of the oxygen as i t goes from the ion ic state i n the bath, through the "discharge" proces's, and i s f i n a l l y desorbed as CO or C O 2 . This diagram, shown i n Figure 2 , i s patterned a f ter that of Gulbransen ( 9 ) . The ordinate represents the free energy of the oxygen as i t passes from one step to the next. The abscissa represents distance i n Xngstrom uni t s as the oxygen t r a v e l s from the bath onto the in ter f ace , and thence i s desorbed. For true represen-t a t i o n , a three-dimensional model shoud be used. However, for convenience the distance has been represented schematical ly on a plane as going from bath to discharge on chemisorption s i t e s , from the chemisorption s i t e s through a ser ies of states intermediate between - 9 -C-Sur face I A d s o r p t i o n 1 I Desorbed I CO I O x i d a t i o n Stage i Combust ion Stage D i s t a n c e ^ I ^ D i s t a n c e F i g u r e 2« F r e e Energy Diagram - 10 -c h e m i s o r p t i o n and chemical combination to s t a t e s of pure chemical bonding and thence to the gas phase„ There are f o u r s t a t e s of minimum f r e e energy on the diagram i n which oxygen may be found, namely, . 1. As oxygen ions i n the bath, 2. As chemisorbed CxOy complexes on the anode s u r f a c e . 3. As c h e m i c a l l y bonded r e a c t i o n products of CO and CO2 4. As desorbed CO and CO2. The o x i d a t i o n process as d e f i n e d f o r the gaseous r e a c t i o n i n c l u d e s the two h i g h e r minimum-energy s t a t e s on t h i s diagram; the combustion r e a c t i o n , the two lower s t a t e s . The f r e e energy r e q u i r e d to a c t i v a t e the oxygen from the bath t o the chemisorbed complex i s Fi^, from the chemisorbed complex to bonded CO i s F 2 , a n d from bonded CO t o desorbed CO gas i s F^„ I f COg i s produced, the r e a c t i o n curve w i l l be s i m i l a r t o the dotted U l i n e i n F i g u r e 1, w i t h the c o r r e s p o n d i n g a c t i v a t i o n f r e e energy F ^ T . T h i s diagram i s q u a l i t a t i v e only because the e n e r g i e s are not known. The r a t e - c o n t r o l l i n g step w i l l have the h i g h e s t a c t i v a t i o n f r e e energy. However, s i n c e i t i s not known which step i s l i m i t i n g the r e a c t i o n , a l l three a c t i v a t i o n b a r r i e r s have been drawn equal. The necessary a c t i v a t i o n f r e e . e n e r g y to overcome the p o t e n t i a l b a r r i e r comes from the thermal energy of the bath. I n the case of g r a p h i t e i n a l e a d - b o r o s i l i c a t e s l a g , as found i n t h i s study, the f r e e energy change f o r the o v e r a l l process i s n e g a t i v e , but there i s not enough thermal energy present to overcome the p o t e n t i a l - 11 -b a r r i e r u n t i l the temperature i s over 950 0 C 0 i f an e l e c t r i c a l p o t e n t i a l i s a p p l i e d a c r o s s the b a t h , the p o t e n t i a l energy of the oxygen i o n i s i n c r e a s e d and the energy d iagram i s t i p p e d so t h a t the a c t i v a t i o n energy i s l o w e r e d . S i n c e the b a r r i e r i s l o w e r e d , the r e a c t i o n of g r a p h i t e i n l e a d - b o r o s i l i c a t e w i l l proceed at a measurable r a t e at 850°G i f a p o t e n t i a l i s a p p l i e d . The d e c o m p o s i t i o n v o l t a g e i s the d i f f e r e n c e between t h e p o t e n t i a l energy o f the oxygen i n the s l a g and t h a t o f the oxygen i n the desorbed gas . The anod ic o v e r v o l t a g e c r e a t e d when a p o t e n -t i a l i s a p p l i e d i s the v o l t a g e excess needed to h e l p th e oxygen surmount the r a t e - c o n t r o l l i n g energy b a r r i e r . Thus the o v e r v o l t a g e i s a measure of the f r e e energy of a c t i v a t i o n f o r the r a t e - d e t e r m i n i n g s t e p . I f the ent ropy of; a c t i v a t i o n i s r e l a t i v e l y s m a l l , t h i s f r e e energy o f a c t i v a t i o n w i l l have n e a r l y the same v a l u e as the heat of a c t i v a t i o n , and the e x p e r i m e n t a l a c t i v a t i o n energy . I f , however , the ent ropy change i s l a r g e , these e n e r g i e s w i l l be s i g n i f i c a n t l y d i f f e r e n t . E n t r o p y Change P r o b a b l y the most; s i g n i f i c a n t d i f f e r e n c e between, the consumption o f ca rbon by oxygen gas and by oxygen i o n s i s t h e d i f f e r e n c e i n the ent ropy change f o r the o v e r a l l r e a c t i o n . The r a t e o f r e a c t i o n , as d e s c r i b e d by the t r a n s i t i o n - s t a t e t h e o r y , i s r a t e = J^T e Where ^ , S + and are the ent ropy and e n t h a l p y , r e s p e c t i v e l y , o f the a c t i v a t e d complex . Thus any change i n th e e n t r o p y of a c t i v a t i o n w i l l g r e a t l y a f f e c t t h e rate„ The e n t r o p y term e ' ^ 'can c o n v e n i e n t l y be r e p r e s e n t e d as t h e change i n t h e p a r t i t i o n f u n c t i o n s o f t h e r e a c t i n g s p e c i e s d u r i n g r e a c t i o n . The p a r t i t i o n f u n c t i o n i s made up of t h r e e t e r m s : t h e t r a n s i t i o n a l , r o t a t i o n a l , and v i b r a t i o n a l p a r t i t i o n f u n c t i o n s . Each t e r m i s c a l c u l a t e d f o r t h e change i n t h e number of degrees of freedom o f t h a t t ype ( i . e . t r a n s l a t i o n a l , r o t a t i o n a l , o r v i b r a t i o n a l ) w h i c h o c c u r s i n t h e r e a c t i o n . I n t h e gaseous r e a c t i o n t h e r e a c t a n t oxygen m o l e c u l e has t h r e e t r a n s l a t i o n a l , two r o t a t i o n a l , and one v i b r a t i o n a l degree o f freedom. The p r o d u c t m o l e c u l e CO^ has t h e same number of t r a n s -l a t i o n a l and r o t a t i o n a l degrees of freedom and t h r e e a d d i t i o n a l degrees o f v i b r a t i o n a l freedom. However, the change i n t h e p a r t i t i o n f u n c t i o n , and t h u s t h e r a t e , caused by t h e i n c r e a s e o f t h r e e v i b r a t i o n a l degrees o f freedom i s v e r y s m a l l , p o s s i b l y no more t h a n 10. The e n t r o p y change i n t h e o x i d a t i o n of c a r b o n by oxygen i o n s i s r a d i c a l l y d i f f e r e n t . P a r t i t i o n f u n c t i o n s f o r l i q u i d s , a l t h o u g h not a c c u r a t e l y known, a r e much l e s s t h a n t h o s e f o r gases because o f the r e s t r i c t i o n o f movement i n l i q u i d s . The t r a n s -l a t i o n a l p a r t i t i o n f u n c t i o n f o r t h e oxygen i o n s i n t h e s l a g used may be i n t h e neighborhood o f 10 t o 1000, w h i c h may be a r t i f i c i a l l y r e p r e s e n t e d as l e s s t h a n one degree o f t r a n s l a t i o n a l freedom. The pr o d u c t gas, on t h e o t h e r hand, has t h r e e degrees o f t r a n s l a t i o n a l freedom. Thus, p e r m o l e c u l e o f oxygen, t h e change i n t h e t r a n s -l a t i o n a l degrees of freedom d u r i n g r e a c t i o n i s from l e s s t h a n one - 13 -t o t h r e e o r s i x , d e p e n d i n g u p o n w h e t h e r C O 2 o r CO i s d e s o r b e d . F o r t h e p r o d u c t i o n o f COg a t one a t m o s p h e r e p r e s s u r e and 1000°C, •50 t h i s c h a n g e may he a b o u t 10y . A s s u m i n g s m a l l r o t a t i o n a l a n d v i b r a t i o n a l c h a n g e s , t h e o v e r a l l p a r t i t i o n f u n c t i o n c h a n g e ( w h i c h i s i n t u r n r e l a t e d t o t h e e n t r o p y c h a n g e and t h e r a t e by t h e t e r m e — ) c o u l d be a b o u t i0^° t o 1 0 ^ 2 . H o w e v e r , t h i s d o e s n o t mean t h a t t h e r a t e w i l l be i n c r e a s e d b y t h i s amount. I t w i l l be f i x e d by t h e s l o w e s t r e a c t i o n s t e p and t h e c h a n g e i n e n t r o p y f o r t h i s s t e p w i l l a f f e c t t h e r a t e . I t i s p r o b a b l e , t h e r e f o r e , t h a t t h e a c t u a l e l e c t r o -c h e m i c a l o x i d a t i o n r a t e w i l l be g r e a t e r t h a n t h e g a s e o u s r a t e by a f a c t o r c o n s i d e r a b l y s m a l l e r t h a n 1 0 - ^ . I f i t i s a s sumed t h a t t h e m o b i l e a d s o r p t i o n o f o x y g e n m o l e c u l e s i s e l e c t r o c h e m i c a l l y r a t e - c o n t r o l l i n g , a s s u g g e s t e d by G u l b r a n s e n (9) f o r t h e g a s e o u s o x i d a t i o n o f g r a p h i t e , a n d a s s u m i n g a n o x y g e n i o n p r e s s u r e o f -6 13 10 a t m o s p h e r e s , t h e e l e c t r o c h e m i c a l r a t e w i l l be a b o u t 10 t i m e s . a s f a s t a s t h e g a s e o u s r e a c t i o n . The a s s u m p t i o n . t h a t t h e m o b i l e a d s o r p t i o n s t e p i s r a t e - c o n t r o l l i n g i s n o t n e c e s s a r i l y j u s t i f i e d f o r t h e e l e c t r o c h e m i c a l r e a c t i o n . - 14 -OBJECT AND SCOPE OF THE PRESENT INVESTIGATION The o b j e c t o f t h i s i n v e s t i g a t i o n has been t o s tudy the e l e c t r o c h e m i c a l consumpt ion o f g r a p h i t e by oxygen i o n s i n s l a g s . P r e l i m i n a r y t e s t s were conducted u s i n g f a y a l i t e s l a g s i n i r o n c r u c i b l e s . However, the h i g h temperatures r e q u i r e d t o me l t the s l a g made i t i m p o s s i b l e t o c o n s t r u c t a g a s - t i g h t appara tus and c o l l e c t samples of the desorbed ca rbon o x i d e s . A l e a d - b o r o s i l i c a t e s l a g was t h e n c o n s i d e r e d . I t was thought t h a t the r a t e o f r e a c t i o n would be so r a p i d t h a t t h e g r a p h i t e would immedia te ly reduce the l e a d from the s l a g . I t was f o u n d , however, t h a t t h i s r e a c t i o n proceeds a t a measurable r a t e o n l y above 950°C. A l e a d - b o r o s i l i c a t e s l a g was t h e r e f o r e used f o r a l l the subsequent exper iment s . U t i l i z i n g a s l a g o f the c o m p o s i t i o n P b O . S i 0 2 . 0 . lNa2B40r / , the i n f l u e n c e o f t e m p e r a t u r e , c u r r e n t d e n s i t y and t ime on the r a t i o o f CO and COg i n the anode gas was i n v e s t i g a t e d . I n a d d i t i o n , crude k i n e t i c da ta were o b t a i n e d f o r the r a t e o f p r o -d u c t i o n o f anode gas w i t h o u t the a p p l i c a t i o n o f a p o t e n t i a l . - 15 -EXPERIMENTAL PROCEDURE OVERVOLTAGE MEASUREMENT IN FAYALITE SLAGS. An attempt was made t o s i m u l t a n e o u s l y o b t a i n o v e r -v o l t a g e measurements and CO/CO2 gas r a t i o s u s i n g a f a y a l i t e s l a g of the c o m p o s i t i o n : FeO 48% S i 0 2 33% CaO 17% F e S 2 2% T h i s s l a g has t h e lowest m e l t i n g p o i n t on the CaO-FeO-S i 0 2 phase d iagram. The F e S 2 was added to lower the m e l t i n g p o i n t f u r t h e r . The o v e r v o l t a g e s genera ted w i t h v a r i o u s c u r r e n t d e n s i t i e s on a g r a p h i t e anode r e l a t i v e t o a p l a t i n u m r e f e r e n c e e l e c t r o d e were measured on a Beckman model H-2 pH meter u s i n g the apparatus shown i n F i g u r e 3. A l t h o u g h the a n o d e - p l a t i n u m e l e c t r o d e d i s t a n c e was o n l y 0.1 i n c h e s , a s i g n i f i c a n t v o l t a g e drop c r e a t e d by the r e s i s t a n c e of the s l a g was noted i n the o v e r v o l t a g e s measured. I t was not p o s s i b l e t o o b t a i n gas samples c o i n c i d e n t w i t h these o v e r v o l t a g e measurements because the h i g h tempera tures i n v o l v e d p r o h i b i t e d the c o n s t r u c t i o n o f a l e a k - p r o o f gas c o l l e c t i o n sys tem. I t Was t h e r e f o r e d e c i d e d t o i n v e s t i g a t e s l a g s w i t h lower m e l t i n g p o i n t s . - 1 6 -F i g u r e 3 . E x p e r i m e n t a l A p p a r a t u s f o r F a y a l i t e S l a g s - 17 -REACTION OF GRAPHITE IN LEAD-BOROSILICATE SLAGS. The major p o r t i o n o f t h i s i n v e s t i g a t i o n has been concerned w i t h l e a d - b o r o s i l i c a t e s l a g s . P r e l i m i n a r y e x a m i n a t i o n showed t h a t g r a p h i t e c h e m i c a l l y reduced the l e a d i n the s l a g o n l y above 9 5 0 ° C . I t was a l s o found t h a t the l a r g e e l e c t r i c a l r e s i s t -ance o f the s l a g c r e a t e d a c o n s i d e r a b l e IR v o l t a g e drop from the anode to t h e p l a t i n u m r e f e r e n c e e l e c t r o d e . Thus i t was not p o s s i b l e t o o b t a i n u s e f u l o v e r v o l t a g e measurements. M a t e r i a l s The anodes were commerc ia l e l e c t r o d e g r a p h i t e s u p p l i e d by t h e N a t i o n a l Carbon Company. The l i t h a r g e and t e s t l e a d were assay g r a d e . The borax and s i l i c a f l o u r were t e c h n i c a l - g r a d e r e a g e n t s . Appara tus The e x p e r i m e n t a l a p p a r a t u s , as shown i n F i g u r e 4 , c o n s i s t e d b a s i c a l l y o f a 30-gram f i r e c l a y c r u c i b l e h e l d by a plumbago pot and a g r a p h i t e anode w i t h a g a s - c o l l e c t i n g cup and t u b e . The s l a g - c o n t a i n i n g f i r e c l a y c r u c i b l e , w i t h a h o l e d r i l l e d i n the bottom, and t h e chromel c a t h o d e - l e a d w i r e were p l a c e d i n the plumbago pot which h e l d 1320 grams o f m o l t e n l e a d . The c r u c i b l e was h e l d i n p l a c e by a chromel c lamp. The o n e - i n c h d iameter g r a p h i t e e l e c t r o d e was turned down to f i t a 3 / 4 - i n c h h o l e i n a 15-gram f i r e c l a y c r u c i b l e . - 1 8 -« To Gas An a l y z e r Graphite Anod e S l a g Molten Lead Cathode V i t r e o s i l G a s - C o l l e c t i n g Tube F i r e c l a y C r u c i b l e s Chrome1 Cathode Lead-Wire Plumbago C r u c i b l e F i g u r e I4... Experimental Apparatus f o r PbO'SiO p S l a g s - 19 -which had the top cut off two inches from the base. This cup also had a separate •f-.inch hole for the gas-collecting tube. V i t r e o s i l tubing of ^-inch inside diameter was used to con-vey the anode gas outside the furnace. The whole anode assembly was cemented with a mixture of s i l i c a and water glass. After curing at about 120°C, t h i s cement was very sa t i s f a c t o r y up to about 1 0 f ) 0°Cthe highest temperature used i n this study. The anode gas was transported to the gas-analysis apparatus by f?/l6-inch tygon tubing. The v i t r e o s i l - t y g o n j o i n t on top of the furnace was cooled by a small fan. The furnace used was equipped with s i x hori z o n t a l jg~inch-diameter globars arranged i n two p a r a l l e l sets of three. The temperature was measured by a chrome1-alumel + thermocouple, and controlled to within -^.Centigrade degrees at the thermocouple t i p by a Leeds & Northrup Micromax model ttCn c o n t r o l l e r with ah M.E.C. automatic proportioning control unit. The e l e c t r o l y z i n g d i r e c t current was supplied by an u n f i l t e r e d full-wave copper-oxide transformer-rectifier. Slag Composition The slag used was of the composition: FbO 72% S i 0 2 20.3$ Na 2B^0 7 7-7$ - 20 -T h i s c o r r e s p o n d s t o an a p p r o x i m a t e m o l a r c o m p o s i t i o n of PbO . S i Q 2 . O o l N a 2 B 4 . O 7 . The b o r a x was added t o i n c r e a s e t h e f l u i d i t y of the s l a g . T h i s p a r t i c u l a r . c o m p o s i t i o n was s e l e c t e d a r b i t r a r i l y a t t h e b e g i n n i n g o f t h e i n v e s t i g a t i o n o n l y because of i t s r e l a t i v e l y low m e l t i n g p o i n t ( l e s s t h a n 770°C„) and i n t e r m e d i a t e l e a d - o x i d e c o n t e n t . Subsequent work has shown t h a t a p p a r e n t l y t h e s l a g c o m p o s i t i o n has a d e f i n i t e e f f e c t on t h e c o m p o s i t i o n o f the d e s o r b e d gas. A l s o c o n d u c t i v i t y d a t a (21) show a d i s c o n t i n u i t y i n t h i s r e g i o n . Had t h i s been known at t h e o u t s e t , a d i f f e r e n t s l a g c o m p o s i t i o n would have been s e l e c t e d . S l a g P r e p a r a t i o n Four hundred grams o f t h e s l a g components were f u s e d i n a f i r e c l a y c r u c i b l e and h e l d a t 950°G f o r two h o u r s . Then 100 grams o f t e s t l e a d were added and t h e s l a g a l l o w e d t o r e a c h e q u i l i b r i u m w i t h t h e l e a d . The c r u c i b l e and s l a g were t h e n c o o l e d and u t i l i z e d i n t h e a p p a r a t u s d e s c r i b e d . P r o c e d u r e The a p p a r a t u s , w i t h o u t t h e anode, was h e a t e d up t o t h e d e s i r e d t e m p e r a t u r e and h e l d f o r a t l e a s t o n e - h a l f hour t o a t t a i n a s t e a d y t e m p e r a t u r e . Then t h e anode, w i t h an a p p l i e d o p e n - c i r c u i t p o t e n t i a l of a p p r o x i m a t e l y 10 v o l t s , was p l a c e d i n t h e s l a g and th> g a s - s a m p l i n g tube a t t a c h e d . A f t e r about t e n m i n u t e s , t h e s l a g was a g a i n up t o t e m p e r a t u r e and gas s a m p l i n g begun. The t i m e s r e q u i r e d - 21 -c o l l e c t the 100-cubic centimeter gas samples were recorded. Each sample was analyzed as soon as i t had been c o l l e c t e d and the anode gas produced i n the meantime was vented to the atmosphere. • ' In any one run, the t o t a l current f l o w i n g was held constant. As each run progressed, the r e s i s t a n c e of the s l a g increased. Thus i t was necessary to increase g r a d u a l l y the applied p o t e n t i a l i n order to keep the current constant. The runs were of v a r y i n g length depending upon the temperature, rate of oxygen removal from the s l a g , and how w e l l the apparatus was constructed. The experiments were u s u a l l y halted e i t h e r by anode f a i l u r e due to gaseous o x i d a t i o n of the p o r t i o n exposed i n the furnace or by the s l a g foaming up i n t o the g a s - c o l l e c t i n g tube, thus c u t t i n g o f f the gas flow. As any one run progressed, the i n c r e a s -ing s i l i c a content of the s l a g caused i t to become more viscous and, t h e r e f o r e , more prone to foam. Current Density Measurements During p r e l i m i n a r y t e s t s , i t was found t h a t the", anode surface was o x i d i z e d very unevenly. Since i t was thought that changes i n both the temperature and the amperage would a l t e r the o x i d i z e d surface area, a l l sub-sequent runs were c a r r i e d out at a constant amperage and temperature. The current d e n s i t y was then c a l c u l a t e d by using the measured o x i d i z e d area of the anode. Since t h i s s e l e c t i v e o x i d a t i o n made the measurement of the - 22-e f f e c t i v e anode areas very d i f f i c u l t , the calculated current densities may be i n considerable error. I t i s d i f f i c u l t to assess the probable error but i t may be as high as 50 percent. There was no way of predicting the area of the anode that would be attacked under any one set of conditions. This i s c l e a r l y shown i n Figure 5« Anodes A and B were oxidized under i d e n t i c a l conditions of amperage, temperature and i n i t i a l composition. However, i t i s apparent from the picture that the areas eff e c t i v e i n reaction are very different f o r the two anodes. By measure-^ ment, anode A has four times the e f f e c t i v e area of anode B, and, thus, one-quarter the current density of that on anode B. Anode C, oxidized i n a lead-borate slag, desorbed CO/CO2 r a t i o s very similar to those obtained with l e a d - s i l i c a t e slags. This surface i s much more evenly oxidized than those of anodes A and Bo This slag may give more r e l i a b l e current-density results than those obtained i n lead-borosilicate slags. However, because some of the anode carbon dropped into the bath during t h i s p a r t i c u l a r run and was not electrochemically consumed, the oxida-t i o n may be p r e f e r e n t i a l . Gas Analysis A l l the gas samples were analyzed i n a Hays orsat appara-tus. Carbon dioxide was absorbed i n a potassium hydroxide solution, oxygen i n Hays-brand "Seez C>2W and carbon monoxide i n ammoniacal cuprous. - 2 3 -F i g u r e Photograph of E l e c t r o c h e m i c a l l y O x i d i z e d Anodes - 2k -c h l o r i d e . P o r most of the runs the a p p a r a t u s was m o d i f i e d by the a d d i t i o n of a second carbon monoxide p i p e t t e t o a c c e l e r a t e a n a l y s i s . The measuring f l u i d was a f i v e p e r c e n t s o l u t i o n o f s u l p h u r i c a c i d w i t h about t e n p e r c e n t sodium s u l p h a t e added. The 100 c c . gas samples were c o l l e c t e d i n the a n a l y z e r under p r e s s u r e ; t h a t I s , the anode gas d i s p l a c e d the w ater i n the b u r e t t e by i t s own p r e s s u r e . The p r e s s u r e i n s i d e the b u r e t t e was n e v e r a l l o w e d t o b u i l d up more th a n about 1 mm. Hg g r e a t e r than a t m o s p h e r i c p r e s s u r e . The t o t a l volume of gas a n a l y z e d was always l e s s than 100 p e r c e n t , r a n g i n g f r o m 80 t o 93> p e r c e n t . The l o n g e r a sample t o o k t o c o l l e c t , the l o w e r the f i n a l volume of a n a l y z e d gases. T h i s would suggest t h a t some i n e r t gas was b e i n g d r i v e n o f f from the anode. However, a s e r i e s of anodes w h i c h was heated t o 1000°F. f o r t e n hours showed no a p p r e c i a b l e d e c r e a s e i n the "dead" gas volume. The f a c t t h a t the samples were c o l l e c t e d by p r e s s u r e d i s p l a c e m e n t would seem to i n d i c a t e t h a t no c o n t a m i n a t i o n o f the sample by a i r o c c u r r e d . T h i s b e l i e f i s f u r t h e r s u p p l a n t e d by the f a c t t h a t no gas samples c o n t a i n e d any oxygen a f t e r the f i r s t h a l f h o u r , a l t h o u g h i t i s p o s s i b l e t h a t the oxygen would be consumed by the r e a c t i o n CO + Co* w h i c h i s f a v o u r a b l e t h e r m o d y n a m i c a l l y a t the t e m p e r a t u r e s used. - 2 £ -RESULTS Throughout t h i s paper the terms " c h e m i c a l o x i d a t i o n " and " c h e m i c a l combustion" w i l l r e f e r t o the o x i d a t i o n and combustion o f g r a p h i t e by oxygen i o n s i n the s l a g w i t h o u t the a p p l i c a t i o n o f an e l e c t r i c a l p o t e n t i a l . T h i s i s con-t r a s t e d w i t h the e l e c t r o c h e m i c a l r e a c t i o n s i n wh i c h a p o t e n t t i a l i s a p p l i e d . CHEMICAL OXIDATION The i n i t i a l r a t e s of oxygen re m o v a l f r o m the s l a g were c a l c u l a t e d by u s i n g the r a t e of e v o l u t i o n and the c o m p o s i t i o n of the desorbed gas. These r a t e s , w h i c h may be i n e r r o r because the ap p a r a t u s was not always g a s - t i g h t , are shown i n an A r r h e n i u s p l o t i n F i g u r e 6. The s l o p e of t h i s l i n e c o r r e s p o n d s t o an a c t i v a t i o n energy o f 26 ^ 5 k i l o c a l o r i e s p e r gram mole. ABSOLUTE REACTION RATE CALCULATIONS By use o f the determined r a t e s and a c t i v a t i o n energy, i t i s p o s s i b l e t o c a l c u l a t e t h e o r e t i c a l r a t e s o f r e a c t i o n f o r v a r i o u s r a t e - d e t e r m i n i n g s t e p s by a p p l y i n g the e q u a t i o n s o f G l a s s t o n e , L a i d l e r , and E y r i n g (22) . The rate^-l i m i t i n g s t e p s w h i c h t h e y c o n s i d e r e d a r e : 1. Immobile A d s o r p t i o n 2. M o b i l e A d s o r p t i o n 3. C h e m i c a l R e a c t i o n a. F i r s t - o r d e r K i n e t i c s b. Z e r o - o r d e r K i n e t i c s - 26 -o X •H CD bO 3 RECIPROCAL TEMPERATURE x 10 6 . Arrhenius Plot for Chemical Oxidation 4„ D e s o r p t i o n A l t h o u g h they have a l s o d e r i v e d ah e q u a t i o n f o r d i f f u s i o n r a t e - c o n t r o l l i n g , the q u a n t i t i e s i n v o l v e d i n the e x p r e s s i o n cannot be e v a l u a t e d o r even e s t i m a t e d w i t h our p r e s e n t knowledge. The o t h e r s t e p s have been examined and t h e r a t e s c a l c u l a t e d i n Appendix A. At 1000°C, t h e e x p e r i m e n t a l l y o b s e r v e d r a t e i s 2 x 1 0 ^ ^ atoms o f oxygen r e a c t i n g per square c e n t i m e t e r e v e r y second. T h i s r a t e i s compared w i t h t h e c a l c u l a t e d v a l u e s i n T a b l e 1. A l l t h e c a l c u l a t e d r a t e s a r e v e r y d i f f e r e n t f r om t h a t e x p e r i m e n t a l l y o b s e r v e d . The r a t e s assuming immobile a d s o r p t i o n and f i r s t - o r d e r \\ 7 k i n e t i c s r a t e - c o n t r o l l i n g a r e a f a c t o r o f 5 x 10 f a s t e r . The m o b i l e a d s o r p t i o n , z e r o - o r d e r k i n e t i c s , and d e s o r p t i o n v a l u e s a r e i n e r r o r by about 105. Thus, the r a t e s c a l c u l a t e d , assuming t h e s e s t e p s r a t e - c o n t r o l l i n g , a r e a t l e a s t 100,000 t i m e s f a s t e r o r s l o w e r t h a n t h a t o b s e r v e d . I f t h e v a r i o u s assumptions i n v o l v e d i n t h e s e c a l c u l a t i o n s a r e c o r r e c t , none o f t h e p r o c e s s e s c o n s i d e r e d d e t e r -mines t h e o v e r a l l r a t e . T h i s f a c t makes the p o s t u l a t i o n t h a t d i f f u s i o n i s ' r a t e - c o n t r o l l i n g appear a t t r a c t i v e , but t h e r e i s no e x p e r i m e n t a l e v i d e n c e t o i n d i c a t e t h a t t h i s i s so. CHEMICAL COMBUSTION The v a r i a t i o n o f t h e desorbed C 0 / C 0 ^ r a t i o w i t h tempera-t u r e and t i m e i s shown i n F i g u r e 7. T h i s f i g u r e shows t h a t t h e C O / C O 2 r a t i o s i n c r e a s e w i t h t e m p e r a t u r e , as found i n gaseous co m b u s t i o n of TABLE I Immobile Adsorption Rate Equation • Rate Theory Observed Discrepancy (0=) + [C] iio.gr G r Co] f. Z e. Mobile Adsorption C o l Desorption Cc - o]=3 t ° F i r s t -Order K ine t i c s Zero Order K ine t i c s h 1 1x10 26 2x10 18 2 x l 0 1 3 ,2x10 18 l x l O 2 4 2xlO l 8 l x l O 2 6 2xlO l 8 Ix 1 0 2 4 2x10 18 5x10 10' 5x10-5x10 5x10^ - 29 -TIME IN MINUTES Figure 7. V a r i a t i o n of C 0 / C 0 2 Ratio with Time for Chemical Combustion - 30 -carbon, and, unexpectedly, increases with time. This inve s t i ga -t i o n was begun assuming that there should be no v a r i a t i o n i n the gas composition with time of combustion at any one temperature. I t i s very surpr i s ing to f i n d that , i n these experiments', the CO/CO2 r a t i o d e f i n i t e l y increases with time. The only s i t u a t i o n reported at a l l s i m i l a r to t h i s i s the slow increase i n the CO/CO2 r a t i o noted i n alumina-reduction c e l l s as the alumina concentrat ion decreases. '. In these runs, without an appl ied p o t e n t i a l , the lead oxide composition of the s lag decreased as much as 17 percent; that i s , from 72 percent to 55 percent. The v a r i a t i o n of the oxygen a c t i v i t y i n a l e a d - s i l i c a t e s lag with composition has been ca lcula ted i n Appendix B. The re su l t s of t h i s c a l c u l a t i o n are shown i n F igure 8. This graph shows that the a c t i v i t y of the oxygen i s changing r e l a t i v e l y slowly i n the composition range of t h i s study. For example, at 1000 °C the a c t i v i t y decreases from 9 x 10" to 5 .5 x -10" atmospheres. However, Sche l l inger and Olsen (21) found a d i s c o n t i n u i t y i n the conduct iv i ty of s i m i l a r l e a d - s i l i c a t e slags In th i s composition range. This may indicate that there i s a s t ruc tura l rearrangement occurr ing i n 4_ t h i s area. The normal s i l i c a t e structure i n a s lag i s a SiO^ tetrahedron. With the i n i t i a l composition used i n th i s study, 2-there i s only enough oxygen to form SiO^ groups, or , preserving the te t rahedra l character of the s i l i c o n bonds, Si^O-^g^ - ions . As the oxygen ion concentrat ion decreases, these Si40;L2^~ : MOLE FRACTION PbO F i g u r e 8 . A c t i v i t y of PbO i n P b O - S i O p M e l t s - 32 -u n i t s w i l l b e g i n a s s o c i a t i n g w i t h one a n o t h e r and t h e m o b i l i t y o f the oxygen i s decreased.- T h i s d e c r e a s e i n m o b i l i t y might . p o s s i b l y a f f e c t t h e desorbed gas r a t i o . I t i s apparent from t h e change i n t h e CO/CO2 r a t i o w i t h t i m e t h a t t h e s e r a t i o s can o n l y be compared a t t h e same oxygen c o n c e n t r a t i o n of t h e s l a g . U s i n g t h e r a t e s o f oxygen remo v a l , i t has been p o s s i b l e t o e v a l u a t e t h e CO/CO2 r a t i o s f o r d i f f e r e n t t e m p e r a t u r e s a t t h e same s l a g c o m p o s i t i o n . These v a l u e s , p l o t t e d l o g a r i t h m i c a l l y a g a i n s t t h e r e c i p r o c a l tempera-t u r e i n F i g u r e 9> g i v e an apparent a c t i v a t i o n energy d i f f e r e n c e f o r t h e d e s o r p t i o n of CO and CO2 o f 3216 k i l o c a l o r i e s p e r gram mole. W i t h i n the e x p e r i m e n t a l e r r o r , t h i s a p p a r e n t energy d i f f e r e n c e appears t o be c o n s t a n t w i t h v a r y i n g c o m p o s i t i o n . T h i s v a l u e i s somewhat h i g h e r t h a n t h o s e (8 t o 17 k i l o c a l o r i e s ) found i n t h e gaseous r e a c t i o n . ELECTROCHEMICAL COMBUSTION E x p e r i m e n t s w i t h v a r y i n g c u r r e n t d e n s i t i e s were done a t 900°C, 925°C, and 950°C. The t e m p e r a t u r e range was l i m i t e d s i n c e below 900°C t h e s l a g foamed i n t o the g a s - c o l l e c t i n g t u b e because o f i t s i n c r e a s i n g v i s c o s i t y , and above 950°C t h e r a t e . o f t h e c h e m i c a l r e a c t i o n . w a s s u f f i c i e n t t o m a t e r i a l l y a f f e c t t h e CO/COg r a t i o . S e v e r a l runs were c a r r i e d out a t 975°C. Because of the c h e m i c a l o x i d a t i o n , however, no u s e f u l d a t a were o b t a i n e d . - 33 -1.5 0.1+1 0 . 3 U i ,Y r • • , ,- ;< i i i _ 7.5 . 7 - 6 ' 7 - 7 7 . 8 7 - 9 ' 8 . 0 RECIPROCAL TEMPERATURE x 1 0 ^ Figure 9 - Apparent A c t i v a t i o n Energy Difference fo r Chemical Combustion - 34 -The v a r i a t i o n of the CO/CO 2 r a t i o with time and current density at each temperature studied i s shown i n Figures 10, 11, and 12. These graphs show that the CO/COg r a t i o increases l i n e a r l y with time as found i n chemical combustion, but the rate of increase of th i s r a t i o genera l ly decreases with increas ing current dens i ty . A l s o , increas ing the current densi ty decreases the CO/COg r a " t i ° a t any one time. The logarithmic v a r i a t i o n of the CO/COg r a t i o with the log of the current density i s shown i n Figure 13 fo r the three temperatures inves t iga ted . These data were obtained from Figures 10, 11, and 12 at a concentrat ion of 4.77 percent of the oxygen associated with the PbO i n the s lag , a change of 0.3 percent from the i n i t i a l concentrat ion. This change i s equivalent to e l e c t r o -l y s i s at one ampere for 30 minutes. For longer times of r e a c t i o n , the log- log r e l a t i o n s h i p i s not l i n e a r . Figure 13 shows that genera l ly the CO/COg r a t i o decreases with increas ing current dens i ty . The temperature v a r i a t i o n of t h i s r a t i o , however, i s not cons i s tent , with the runs at 9 5 0 ° C not fo l lowing the trend of the other two se r i e s . In. the 9J>0°C ser ies the evolut ion of gas from the anode other than CO and COg was much greater than usua l . This abnormality may have affected the CO/CO2 r a t i o of the desorbed gas. The d i f f i c u l t i e s i n measuring the current dens i t i e s also may have some bearing on t h i s discrepancy. - 3 £ -TIME IN MINUTES F i g u r e 10. V a r i a t i o n of C0/C02 R a t i o w i t h Time at 900°C. - 3 6 -0.2k I I ' ' 1 I I 1 —I L- , — » i ' J — • 0 1 0 3 0 50 7 0 9 0 110 TIME IN MINUTES F i g u r e 11. V a r i a t i o n o f CO/COg R a t i o w i t h Time at 92J?°C. - 3 7 -- 38 -i5 L F i g u r e 13. V a r i a t i o n of C 0 / C 0 2 R a t i o w i t h Current D e n s i t y - 39 -The data of Figure 13 are shown i n an Arrhenius plot i n Figure 14. As expected, the re su l t s at 9 5 0 ° C are not consistent with the other two se r ie s , with a s t ra ight l i n e occurr ing only at a current density of f i ve amperes per square i n c h . Considering the two ser ies at Q 0 0 ° C and 9 2 5 ° C , i t i s seen that the apparent d i f ference i n the a c t i v a t i o n energies for the desorption of CO and COg (that i s , the slope of the l i n e ) decreases with increas ing current dens i ty . This graph in fer s that the a c t i v a t i o n energy for the production of COg i s increas ing r e l a t i v e to that for CO with increas ing current dens i ty . This does not seem reasonable because the rate of production of CO2 increases r e l a t i v e to that for CO with increas ing current dens i ty . Fur ther , an extrapolat ion of t h i s curve to zero current density gives an apparent a c t i v a t i o n energy di f ference of about 100 k i l o c a l o r i e s , as contrasted with the value of 32 k i l o c a l o r i e s found for chemical combustion. Since such high apparent a c t i v a t i o n energy di f ferences are obtained, i n electrochemical combustion no importance can be attached to the energy di f ferences obtained from an Arrhenius plot of the CO/CO2 r a t i o . - kO -0.2, 0.l£. 8..1 ' '8.2 8.3 8.k 8.5 8.6 RECIPROCAL TEMPERATURE x 10^ " F i g u r e l k . Apparent A c t i v a t i o n Energy D i f f e r e n c e s f o r E l e c t r o c h e m i c a l Combustion Figure 15>. Variation of Apparent Activation Energy Difference with Current Density - 42 -DISCUSSION In the combustion of graphite , the re su l t s of t h i s i n v e s t i g a t i o n show that the desorbed gas i s r i c h e r i n C0 2 when a l i q u i d oxidant i s used i n place of oxygen gas as a reactant . The a p p l i c a t i o n of a po tent i a l causes the COg content of the gas produced to increase fur ther . This i s shown c l e a r l y i n Figure 7. Increasing the current density also increases the r e l a t i v e amount of COg produced. Further , i t has been demonstra-ted that the CO/COg r a t i o i n the desorbed gas . increases with time of reac t ion both with and wittiout an appl ied p o t e n t i a l . A tentat ive mechanism to expla in at leas t p a r t i a l l y these re su l t s i s given next. By cons ider ing the inf luence of the s lag-graphite contact on the band structure of the graphi te , i t has been poss ib le to determine the effect of using oxygen ions on the desorption react ions as described by the mechanism of Long and Sykes. (16) DESORPTION MECHANISM To promote a better understanding of the, proposed mechanism, the relevant propert ies of carbon and graphite are discussed i n some d e t a i l . The band theory of semi-conductors i s described and appl ied to the s lag-graphite i n t e r f a c e . The e lec t ron ic s tructure of the inter face thus deduced i s used to expla in , through the mechanism of Long and Sykes, some of the experimental r e s u l t s . - k3 -P r o p e r t i e s of G r a p h i t e and Carbon 1. F o r m a t i o n G r a p h i t e i s the u l t i m a t e p r o d u c t of the t h e r m a l d e c o m p o s i t i o n of a l l o r g a n i c s u b s t a n c e s and can l o g i c a l l y be c o n s i d e r e d the l i m i t i n g member of a s e r i e s of a r o m a t i c h y d r o c a r b o n s as shown i n F i g u r e 16 (23). Carbons a r e the i n t e r m e d i a t e s u b s t a n c e s formed by l e s s severe heat t r e a t m e n t t h a n t h a t r e q u i r e d t o f o r m g r a p h i t e . T h i s h e a t t r e a t m e n t c o n s i s t s m e r e l y o f h e a t i n g the o r i g i n a l o r g a n i c m a t e r i a l i n the absence o f a i r or I n a r e d u c i n g atmosphere. As the t e m p e r a t u r e i s i n c r e a s e d , p o l y m e r i z a t i o n o c c u r s and, r e g a r d -l e s s whether the o r i g i n a l o r g a n i c was a r o m a t i c or n o t , the r e s u l t I s a system o f c r o s s - l i n k e d p l a n a r c o n d e n s e d - r i n g m o l e c u l e s . A t the s e t t i n g t e m p e r a t u r e , a s o l i d i s formed i n w h i c h the c o n d e n s e d - r i n g p l a n e s are s t a c k e d p a r a l l e l i n g r o u p s . These r i n g systems grow g r a d u a l l y i n the t e m p e r a t u r e range kOO t o 7 0 0 ° C , b u t they r e t a i n most of t h e i r p e r i p h e r a l hydrogen or h y d r o c a r b o n groups. From 700 t o 8 0 0 ° C , much of the p e r i p h e r a l hydrogen i s d r i v e n o f f , l e a v i n g s m a l l c r y s t a l l i t e s of 20 t o 30 £ d i a m e t e r w h i c h B i s c o e and Warren (2k) have c a l l e d " t u r b o s t r a t i c c r y s t a l l i t e s . " The word " t u r b o s t r a t i c " r e f e r s to t h o s e mesomorphous c r y s t a l l i t e s w h i c h are made up of p a r a l l e l and e q u i - s p a c e d p l a n e s b e a r i n g no d i r e c t i o n a l r e l a t i o n s h i p t o one a n o t h e r . As the heat o t r e a t m e n t temperature i s i n c r e a s e d up t o 3000 C , the c r y s t a l l i t e s grow g r a d u a l l y and, when t h e i r d i a m e t e r exceeds 100A (23), t h e y r o t a t e i n t o the r e g u l a r g r a p h i t i c s t r u c t u r e . _ 44 -Compound C 6 H 6 c i o H 8 C14 H10 c i 6 H i o C n H o Structure 0 CO $9 graphite Entropy i n E.U. Per Carbon Atom at 298°K 5.48 3.61 3.21 1.36 Figure 1 6 . Aromatic Hydrocarbon Series - K$ -2. S t r u c t u r e The graphite l a t t i c e as proposed by B e r n a l (26) c o n s i s t s of carbon atoms arranged i n hexagonal r i n g s i n e q u i d i s t a n t l a y e r s stacked i n t h i s manner: one-half the atoms i n one l a y e r l i e normally above h a l f the atoms i n the l a y e r beneath, while the other h a l f are normally above the centres of the hexagons beneath. Thus the s t r u c t u r e repeats i t s e l f i n the sequence abab. However, t h i s s t r u c t u r e does not account f o r c e r t a i n f a i n t l i n e s i n the x-ray powder photographs of many gr a p h i t e s . Lipson and Stokes (27) have proposed an a l t e r n a t i v e s t r u c t u r e made up of about 80 percent of the B e r n a l s t r u c t u r e , 6 percent of a d i s -ordered s t r u c t u r e ( t u r b o s t r a t i c ) and l k percent of the o r i g i n a l s t r u c t u r e proposed by Debye and Scherrer (28), w i t h a l a y e r sequence abcabc. The s t r u c t u r e of the s o - c a l l e d amorphous carbons i s s t i l l a c o n t r o v e r s i a l s u b j e c t . However, i t appears that i n g e n e r a l , these carbons contain some very small turbo-s t r a t i c c r y s t a l l i t e s and a disordered t h r e e - d i m e n t i o n a l l y c r o s s - l i n k e d s t r u c t u r e i n which c e r t a i n of the hexagons have been rotated 60 degrees about t h e i r axes. Wo matter what i t s thermal h i s t o r y , every carbon or graphite contains many l a y e r s of condensed r i n g s . In t h i s arrangement, each carbon atom has f o u r valence e l e c t r o n s : three tT-type e l e c t r o n s which form chemical bonds symmetrical about each carbon atom i n the plane of the r i n g , and one TT-type mobile e l e c t r o n which i s at r i g h t angles t o t h e g r a p h i t e p l a t e . T h i s T T - e l e c t r o n d i s t r i b u t i o n f o r a s i n g l e r i n g (benzene) i s shown i n F i g u r e 1 7 . These 7T-e l e c t r o n s g i v e c a r b o n and g r a p h i t e t h e i r m e t a l l i c c h a r a c t e r . . C.A. C o u l s o n ( 2 9 ) has c a l c u l a t e d t h a t f o r an i n f i n i t e g r a p h i t i c l a t t i c e t he W (E) a g a i n s t E c u r v e i s as shown i n F i g u r e 1 8 . However, t h i s c u r v e i s not c o n s i s t e n t w i t h d e n s i t y - r e s i s t i v i t y c u r v e as i n t e r p r e t e d by S. Mrozowski ( 3 0 ) , By an a n a l y s i s o f t h i s c u r v e f o r d i f f e r e n t c a r b o n s , he has come t o t h e c o n c l u s i o n t h a t t h e r e must be a f i n i t e energy gap >^JE between the f i l l e d e l e c t r o n energy bands and the conductance band. T h i s energy gap ,.^ >.E, w h i c h t e n d s t o ze r o i n g r a p h i t e , means t h a t c a r b o n and g r a p h i t e w i l l be i n t r i n s i c s e m i - c o n d u c t o r s The g e n e r a l l e v e l s o f energy d i s t r i b u t i o n f o r c a r b o n ar e shown i n F i g u r e 1 9 . There a r e t h r e e main e l e c t r o n bands i n the g r a p h i t e s t r u c t u r e : t h e tS o r l o w e r - l e v e l band w h i c h has a mean energy l e v e l o f a p p r o x i m a t e l y 12 e l e c t r o n v o l t s from the escape b a r r i e r , the TT -band w h i c h has a mean energy l e v e l o f about f i v e e l e c t r o n v o l t s above t h e 6 " -band and a work f u n c t i o n of about 4 . 3 e l e c t r o n v o l t s , ,and t h e conductance band a d i s t a n c e ^ E above t h e t o p o f t h e fT -band. T h i s energy gap, w h i c h approaches zero f o r i n f i n i t e g r a p h i t e p l a n e s , i s a f u n c t i o n o f the h e a t - t r e a t m e n t and i s p l o t t e d a g a i n s t c a l c i n a t i o n tempera-t u r e i n F i g u r e 2 0 . The p e r i p h e r a l atoms i n baked carbons and g r a p h i t e s h o u l d be e x t r e m e l y r e a c t i v e because t h e y have one f r e e v a l e n c e e l e c t r o n . However, t h i s has p r o v e n t o be. - 4 7 -F i g u r e 1 7 . T T - E l e c t r o n M o l e c u l a r O r b i t a l s i n Benzene, F i g u r e 1 8 , E l e c t r o n D i s t r i b u t i o n i n Graphiteo - lid -F i g u r e 19. E l e c t r o n i c Band S t r u c t u r e of Carbon - 49 -i n c o r r e c t . I t i s p r o b a b l e , on e n e r g e t i c grounds, t h a t t h i s f r e e < 5 * -electron and a 77°-electron w i l l form a s p i n p a i r i n some s t a t e of h y b r i d i z a t i o n . Thus each p e r i p h e r a l atom w i l l have e f f e c t i v e l y f o u r < 5 *-electrons and l e a v e a m o b i l e vacancy i n the TT -band. Slag-G-raphite I n t e r f a c e 1. Semi-Conductor Band Theory I n t r i n s i c s e m i - c o n d u c t o r s such as g r a p h i t e and carbon have a r e l a t i v e l y s m a l l energy gap between the h i g h -e s t f i l l e d band and the empty c o n d u c t i o n band. A l t h o u g h the m a t e r i a l i s an i n s u l a t o r a t a b s o l u t e z e r o , a t f i n i t e temper-a t u r e s enough e l e c t r o n s a re t h e r m a l l y e x c i t e d f r o m the f i l l e d t o the empty band t o produce a l i m i t e d amount of c o n d u c t i o n . T h i s c o n d u c t i o n i s produced n o t o n l y by the e x c i t e d e l e c t r o n s b u t a l s o by the h o l e s c r e a t e d i n the n e a r l y f i l l e d band. I n the case o f a few e l e c t r o n s i n the n o r m a l l y empty band,, t h e s e e l e c t r o n s a c t as a f r e e c l a s s i c a l assembly. T h e i r v e l o c i t y i s z e r o at the bo t t o m of the band and i n c r e a s e s p r o p o r t i o n a l l y t o the square r o o t of t h e i r energy measured f r o m the botto m of the band. T h e i r e f f e c t i v e mass, however, may be l a r g e r than t h a t o f a f r e e e l e c t r o n . S i n c e t h e y are few i n number, t h e y do not form a deg e n e r a t e F e r m i - D i r a c gas as do the e l e c t r o n s i n a m e t a l , but obey the c l a s s i c a l Maxwell-BoItzmann s t a t i s t i c s . The e l e c t r o n s of a n e a r l y f i l l e d band, however, behave, i n a v e r y d i f f e r e n t manner. S i n c e almost a l l t he a v a i l a b l e energy l e v e l s are f i l l e d , t he e l e c t r o n gas I s - $0 -TEMPERATURE OP HEAT TREATMENT F i g u r e 20. V a r i a t i o n o f Energy Gap w i t h Heat-Treatment Temperature - 51 -highly degenerate. The group v e l o c i t y i s zero at the top of the band and increases with decreasing energy i n the band. This anomaly i s related to the fact that the e f f e c t i v e mass of an electron near the top of the band i s negative. For these reasons, i t i s more convenient to consider the action of the holes i n the nearly f i l l e d band rather than the electrons. These holes, few i n number, move about the l a t t i c e as the electrons f i l l them and leave new holes behind. It has been shown (31) that, generally, the holes act p r e c i s e l y as though they were positively-charged electrons with p o s i t i v e mass. It i s possible, i n f a c t , . t o ignore the electrons e n t i r e l y ; that i s , to assume the band i s completely f u l l and treat the holes as a free c l a s s i c a l non-degenerate assembly of p o s i t i v e electrons obeying the Maxwell-Boltzmann d i s t r i b u t i o n . . Thus the nearly f u l l band i s s i m i l a r to a nearly empty band with the difference that, i n the nearly f u l l band, the current" c a r r i e r s are positively-charged holes with energy increasing from the top to the bottom of the band. Wilson (32) has derived a formula f o r the equilibrium number of electrons i n the conduction band by considering the reaction as a d i s s o c i a t i v e equilibrium. Using his formula and assuming no energy gap, f o r graphite at 1000°C, the number of 14 electrons i n the conduction band i s 7 x 10 electrons per cubic centimeter. This figure i s much less than the number of "free 1* electrons i n a metal which i s of the order of 1 0 1 ? per cubic centimeter. - ^2 -The predominant type of e l e c t r i c a l conduction i n a semi-conductor may be determined by measuring the H a l l c o e f f i c i e n t of the m a t e r i a l which i s d e f i n e d as R = t where n = e l e c t r o n or hole d e n s i t y e = absolute value of the e l e c t r o n i c charge R = H a l l c o e f f i c i e n t . When R i s p o s i t i v e , conduction i s mainly by h o l e s ; when R i s n e g a t i v e , conduction i s by e l e c t r o n s . F i g u r e 2 1 , taken from S e l d i n ( 3 3 ) , shows the H a l l c o e f f i c i e n t as a f u n c t i o n of heat-treatment f o r carbon. T h i s graph shows that the con-d u c t i o n c h a r a c t e r of carbon changes c o n s i d e r a b l y w i t h heat-treatment. Graphite shows a predominance of conduction by e l e c t r o n s because i t s energy gap i s v i r t u a l l y zero, or n e g a t i v e ( o v e r l a p ) . 2 . S l a g - G r a p h i t e I n t e r f a c e In order to f u l l y understand the p o p u l a t i o n changes i n the e l e c t r o n i c bands of g r a p h i t e d u r i n g r e a c t i o n , i t i s necessary to c o n s i d e r the m o d i f i c a t i o n i n the band s t r u c t u r e caused by the slag-semi-conductor c o n t a c t . The s l a g may be considered s i m i l a r to a metal; t h a t i s , a con-v e n i e n t source of r e l a t i v e l y f r e e e l e c t r o n s . The work f u n c t i o n s f o r the s l a g and g r a p h i t e w i l l determine the p o t e n t i a l d i f f e r e n c e at the s l a g - g r a p h i t e c o n t a c t . As s t a t e d e a r l i e r , the work f u n c t i o n f o r g r a p h i t e i s i | . 3 e l e c t r o n v o l t s . A l though i t i s d i f f i c u l t to estimate the work f u n c t i o n of the s l a g , i t may be assumed that i t i s - S3 -F i g u r e 21. H a l l C o e f f i c i e n t as a F u n c t i o n o f T e m p e r a t u r e o f H e a t T r e a t m e n t - $k -l e s s t h a n t h a t of g r a p h i t e b e cause, above 9 5 » 0°C, t h e r e i s c h e m i c a l r e a c t i o n and thus a t r a n s f e r of e l e c t r o n s f r o m the s l a g t o the g r a p h i t e . The changes t h a t t a k e p l a c e on c o n t a c t are shown i n F i g u r e 22. B e f o r e c o n t a c t , the F e r m i l e v e l i n the s l a g i s h i g h e r than t h a t o f the g r a p h i t e . On c o n t a c t , t h e r e i s a t r a n s f e r o f e l e c t r o n s f r o m the s l a g t o the g r a p h i t e anode. S i n c e the F e r m i energy of a substance i s e q u a l t o i t s c h e m i c a l p o t e n t i a l {3k-), a t e q u i l i b r i u m the F e r m i l e v e l s must be the same. However, the F e r m i l e v e l s w i l l r e a c h e q u i l i b r i u m i n t h i s system o n l y when the g r a p h i t e F e r m i l e v e l i s f i l l e d up t o t h a t of the s l a g by a d s o r p t i o n o f e l e c t r o n s f r o m the oxygen i o n s a t the s u r f a c e . I n r e a l i t y , e q u i l i b r i u m i s n e v e r a t t a i n e d because the l e a d reduced i n the p r o c e s s w i l l absorb t h e s e e l e c t r o n s . The t r a n s f e r o f e l e c t r o n s f r o m the s l a g t o the g r a p h i t e i n v o l v e s the movement of oxygen i o n s t o the s u r f a c e and t h e i r subsequent o x i d a t i o n and a d s o r p t i o n as oxygen atoms. These i o n s are p r o b a b l y s u p p l i e d by the d i s s o c i a -t i o n o f the S i ^ O - ^ complex. T h i s p r o c e s s w i l l c r e a t e 'a boundary l a y e r between the s l a g and the g r a p h i t e . The t h i c k -ness of t h i s l a y e r may be e s t i m a t e d by assuming th e n o r m a l p a r a l l e l - p l a t e c a p a c i t a n c e e q u a t i o n t o a p p l y t o t h i s l a y e r (35)J t h a t i s C c A £ a ) Before Contact b) Just a f t e r c) During R e a c t i o n Contact F i g u r e 22. Band S t r u c t u r e of Slag-Graphite Contact - 56 -where C = c a p a c i t a n c e i n e l e c t r o s t a t i c u n i t s E = d i e l e c t r i c c o n s t a n t A = a r e a o f p l a t e s d = s e p a r a t i o n o f p l a t e s . Rempel and Khodak (36) have found the c a p a c i t a n c e of the c r y o l i t e - c a r b o n c o n t a c t l a y e r t o be about 20 m i c r o f a r a d s p e r square c e n t i m e t e r . U s i n g t h i s v a l u e and a d i e l e c t r i c c o n s t a n t f o r g r a p h i t e o f 10, the b a r r i e r l a y e r t h i c k n e s s may be c a l c u l a t e d t o be i ° - , — - - A <- z o The carbon-oxygen s e p a r a t i o n i n carbon/ionoxide i s about 1 A, o and one g r a p h i t e hexagon i s about 3 A a c r o s s the p o i n t s . T h e r e f o r e , a b a r r i e r l a y e r o f a CxOy complex, composed o f about one oxygen atom and one g r a p h i t e hexagon, i s a p p r o x i -m a t e l y the same t h i c k n e s s as t h a t c a l c u l a t e d above. T h i s l a y e r i s shown s c h e m a t i c a l l y i n F i g u r e 2 3 . The t r a n s f e r o f e l e c t r o n s f r om th e s l a g t o the g r a p h i t e t h r o u g h the b a r r i e r l a y e r w i l l cause the F e r m i l e v e l i n t h i s l a y e r t o be r a i s e d . T h i s w i l l i n t u r n cause the number of h o l e s i n the 77*"-band t o d e c r e a s e . By a con-s i d e r a t i o n o f the d i s s o c i a t i v e e q u i l i b r i u m b elow, t h i s phenomenon may be e x p l a i n e d . bound e l e c t r o n ^= h o l e + f r e e e l e c t r o n K number of f r e e e l e c t r o n s x number o f h o l e s number of bound e l e c t r o n s where b o t h the h o l e and t h e bound e l e c t r o n s are i n the 77" -band. By i n c r e a s i n g the, number o f f r e e e l e c t r o n s , a Bound ary Layer *-  0 VjT. F i g u r e 23. P o s t u l a t e d S t r u c t u r e o f S l a g - G r a p h i t e Boundary L a y e r - 58 -r e a d j u s t m e n t i n the number o f h o l e s and bound e l e c t r o n s i s . caused i n o r d e r t o keep the e q u i l i b r i u m c o n s t a n t t h e same. C o n s e q u e n t l y , the number o f e l e c t r o n s i n the 77"-band i s i n c r e a s e d when the g r a p h i t e comes i n c o n t a c t w i t h the s l a g . S i n c e the r a t e d e c r e a s e s as the c h e m i c a l r e a c t i o n p r o g r e s s e s , t h e r e i s a d e c r e a s e i n t h e number o f e l e c t r o n s p o s s e s s i n g energy above t h a t of the F e r m i l e v e l of the g r a p h i t e . T h e r e f o r e , as the r e a c t i o n p r o c e e d s , the a c t u a l number of e l e c t r o n s i n the b a r r i e r l a y e r at any one i n s t a n t i s d e c r e a s i n g and the g r a p h i t e p l a n e s o f the b a r r i e r l a y e r are becoming l e s s n e g a t i v e . When the s l a g i s made n e g a t i v e w i t h r e s p e c t t o the g r a p h i t e by the a p p l i c a t i o n o f a p o t e n t i a l , the F e r m i l e v e l o f the s l a g i s r a i s e d so t h a t the e l e c t r o n f l o w f rom the s l a g to the g r a p h i t e : i s i n c r e a s e d . F i g u r e 2li shows t h i s change i n F e r m i l e v e l s . I n o r d e r t o keep a c o n t i n u o u s F e r m i l e v e l t h r o u g h o u t , the number of e l e c t r o n s i n the b a r r i e r l a y e r i s i n c r e a s e d a p r o p o r t i o n a t e amount. As a r e s u l t , the p o p u l a t i o n of the 77"-band w i l l i n c r e a s e a s i m i l a r amount. Assuming 100 p e r c e n t c u r r e n t e f f i c i e n c y d u r i n g e l e c t r o l y s i s , a l l the e l e c t r o n s t r a n s f e r r e d are the r e s u l t o f o x i d a t i o n . S i n c e the number of e l e c t r o n s w i t h e n e r g i e s above the F e r m i l e v e l of the g r a p h i t e d e c r e a s e s as the r e a c t i o n p r o g r e s s e s , the e x t e r n a l p o t e n t i a l o f the c i r c u i t must be i n c r e a s e d i f the c u r r e n t d e n s i t y i s t o be kept c o n s t a n t . T h i s w i l l r a i s e the energy l e v e l s o f the s l a g so t h a t the e l e c t r o n f l o w i s c o n s t a n t . C o r r e s p o n d i n g l y , the F i g u r e Zli. I n f l u e n c e o f A p p l i e d P o t e n t i a l on S l a g - G r a p h i t S t r u c t u r e - 6 0 -e l e c t r o n d e n s i t y of the 77*-band w i l l be c o n s t a n t . I n summary, when the s l a g and g r a p h i t e come i n c o n t a c t , the number o f e l e c t r o n s i n the g r a p h i t e 77*-band i n c r e a s e s over t h a t o f the i s o l a t e d g r a p h i t e . As the r a t e of c h e m i c a l o x i d a t i o n d e c r e a s e s , the p o p u l a t i o n o f the vT"-rband w i l l c o r r e s p o n d i n g l y d e c r e a s e . However, when the s l a g i s made n e g a t i v e r e l a t i v e t o the g r a p h i t e , the F e r m i l e v e l s r e a d j u s t i n such a manner t h a t the e l e c t r o n d e n s i t y of the 77" -band w i l l i n c r e a s e . F u r t h e r m o r e , e l e c t r o l y s i s a t a c o n s t a n t c u r r e n t d e n s i t y w i l l keep the 77"-band p o p u l -a t i o n c o n s t a n t . Mechanism f o r the Combustion o f G r a p h i t e I t has been shown i n the p r e v i o u s s e c t i o n t h a t the c o n t a c t between the g r a p h i t e and the s l a g i n c r e a s e s the p o p u l a t i o n of the g r a p h i t e 77*-band. The e f f e c t o f changing t h i s 77"-band p o p u l a t i o n on the d e s o r p t i o n r a t e s of CO and C O 2 has been shown by Long and Sykes ( 1 6 ) i n a t r e a t m e n t o f the e f f e c t o f t r a n s i t i o n m e t a l s i n the g r a p h i t e l a t t i c e on the d e s o r p t i o n mechanism. They have advanced t h e t h e o r y t h a t the a c t i v e s i t e s f o r d e s o r p t i o n are the l e s s - f i r m l y bound p e r i p h e r a l c a r b o n atoms at the edges of the g r a p h i t e p l a n e s . When an oxygen atom i s adsorbed on such a p e r i p h e r a l carbon s i t e , the e l e c t r o n d i s t r i b u t i o n may be of two types as shown i n F i g u r e 25>. Type (a) i s a s t r u c t u r e i n w h i c h o n l y one o f the oxygen e l e c t r o n s i s p a i r e d w i t h a carbon e l e c t r o n . Type ( b ) , - 61 -a) b) Figure 2 5 . Oxygen Bonding i n Graphite 0 . 7 3 2 0 . 3 8 2 0 . 3 8 2 0.71+8 0 . 8 7 2 0 . 2 3 2 / x o . 232 0 . 7 4 8 0 > 8 o b b .802 0 . 6 9 5 J o . 5 9 k 0 . 5 3 X \ 0 . 5 3 3 0 . 6 9 5 a) Neutral b) Pos i t ive c) Negative Figure 26. -rBond Orders i n Phenoxyl Rad ica l - 62 -i n w h i c h a s t a b l e double bond i s formed between the p e r i p h e r a l carbon and the oxygen, i s more f a v o u r a b l e f o r the e v o l u t i o n of CO because the c a r b o n - c a r b o n bonds are weaker and the carbon-oxygen bond more c l o s e l y a p p r o x i m a t e s the CO bond. However, t h i s t r e a t m e n t i s not c o n s i s t e n t w i t h the now accepted p r o c e d u r e s o f m o l e c u l a r o r b i t a l s . T h i s concept assumes t h a t each carbon atom forms t h r e e h y b r i d i z e d <5"-type bonds w i t h i t s n e i g h b o u r s and f o u r t h 77"-type bond i s d e l o c a l i z e d o v er the whole s t r u c t u r e as shown p r e v i o u s l y i n F i g u r e 17• Thus, these d e l o c a l i z e d T T - e l e c t r o n s can be i n f l u e n c e d by i m p u r i t y c a t a l y s t s a t random p o i n t s i n the carbon l a t t i c e . Long and Sykes have c a l c u l a t e d the e f f e c t on 7T-bond o r d e r s of c r e a t i n g a p o s i t i v e o r n e g a t i v e carbon hexagon by the p r o c e s s o f e l e c t r o n t r a n s f e r f r o m c a t a l y s t t o carbon or v i c e v e r s a f o r the p h e n o x y l r a d i c a l . The r e s u l t s of t h i s c a l c u l a t i o n a re shown i n F i g u r e 26. I t i s e v i d e n t from t h i s f i g u r e t h a t the c r e a t i o n of a p o s i t i v e i o n w i l l f a v o u r c o n s i d e r a b l e e v o l u t i o n o f CO s i n c e the carbon-oxygen bond i s s t r e n g t h -ened and the c o r r e s p o n d i n g c a r b o n - c a r b o n bonds a r e weakened. C o n v e r s e l y the a d d i t i o n of e l e c t r o n s w i l l r educe the CO d e s o r p t i o n r a t e . S i m i l a r c a l c u l a t i o n s f o r «< - and /3 - n a p h t h o x y l r a d i c a l s made by the same w r i t e r s are shown i n F i g u r e 27. T h i s c a l c u l a t i o n shows the same e f f e c t as t h a t found f o r the p h e n o x y l r a d i c a l . Thus the c o n c l u s i o n s o b t a i n e d f r o m the p h e n o x y l group are q u i t e g e n e r a l ; namely, i f by some p r o c e s s - 63 -N e u t r a l P o s i t i v e N e g a t i v e - 0 .427 - 0 . 3 7 3 0 . 6 0 6 k 0.477 7f -Bond Orders f o r <* - N a p h t h o x y l and ^ - N a p h t h o x y l R a d i c a l s C =— 0 —*r 0 — C—O F i g u r e 2 8 . Ketene S t r u c t u r e - 6k -a 7 7 * - e l e c t r o n i s removed from the carbon l a t t i c e , an i n c r e a s e d r a t e o f e v o l u t i o n of CO w i l l r e s u l t from the weakening o f the c a rbon-carbon bonds and t h e s t r e n g t h e n i n g o f the carbon-oxygen bonds. C o n v e r s e l y , the a d d i t i o n of e l e c t r o n s w i l l h i n d e r the p r o d u c t i o n o f CO. I f the r a t e o f t r a n s f e r o f oxygen i s c o n s t a n t ( f o r example, i f the d e s o r p t i o n s t e p i s not r a t e c o n t r o l l i n g ) , t h i s e xcess o f e l e c t r o n s w i l l i n c r e a s e the r a t e of d e s o r p t i o n o f CO2. The s t r u c t u r e proposed by S i h v o n e n (20) t o f a v o u r the e v o l u t i o n of C 0 2 i s of a ketene form such as shown i n F i g u r e 28. D u r i n g the p r o g r e s s i v e consumption o f the carbon r i n g s , t h i s s t r u c t u r e w i l l be produced by the l o s s of e v e r y second carbon atom i f the s u r f a c e i s c o m p l e t e l y r e g u l a r . An excess o f 77?-electrons would s t r e n g t h e n the s i n g l e c a r b o n - c a r b o n bond and tend t o p r e v e n t the e v o l u t i o n o f CO. However, s i n c e t h i s i s s t i l l t he weakest p o i n t i n the p a r t i -c u l a r s t r u c t u r e , i t i s p o s s i b l e t h a t a m o b i l e oxygen atom c o u l d b r e a k t h i s bond and form C 0 2 as shown i n t h i s f i g u r e . I f the mechanism o f Long and Sykes i s c o r r e c t , t h e n , an e x c e s s o f e l e c t r o n s i n the g r a p h i t e 77"-band w i l l f a v o u r the d e s o r p t i o n o f CO^ and a d e f i c i e n c y o f 7 T - e l e c t r o n s w i l l f a v o u r the p r o d u c t i o n of CO. Summary of D e s o r p t i o n Mechanism D i s c u s s i o n From the band t h e o r y d i s c u s s i o n and the mechanism of Long and S y k e s , i t may be c o n c l u d e d t h a t : 1. The combustion of g r a p h i t e by i o n i c oxygen s h o u l d produce a gas r i c h e r i n C 0 2 than t h a t desorbed i n - 65 -The gaseous r e a c t i o n because t h e "TP-band e l e c t r o n d e n s i t y of t h e g r a p h i t e i s i n c r e a s e d upon c o n t a c t w i t h the s l a g . 2. As t h e r a t e of c h e m i c a l r e a c t i o n w i t h t h e s l a g d e c r e a s e s , t h e desorbed gas s h o u l d become r i c h e r i n CO because t h e TP-electron p o p u l a -t i o n i s d e c r e a s i n g p r o p o r t i o n a l l y w i t h t h e r e a c t i o n r a t e . 3. The a p p l i c a t i o n o f a p o t e n t i a l t o the s l a g s h o u l d cause t h e gas t o become r i c h e r i n CO2 because t h i s p o t e n t i a l r a i s e s t h e energy l e v e l s o f t h e s l a g and t h u s i n c r e a s e s t h e TT-band p o p u l a t i o n . T h e r e f o r e t h e p e r c e n t CO2 desorbed s h o u l d i n c r e a s e w i t h i n c r e a s i n g c u r r e n t d e n s i t y . I f t h e c u r r e n t d e n s i t y i s c o n s t a n t , t h e CO/CO2 r a t i o s h o u l d remain c o n s t a n t . COMPARISON OF EXPERIMENTAL RESULTS WITH-THEORY The o b s e r v e d f a c t t h a t t h e desorbed gas i s r i c h e r i n . CO2 when oxygen i o n s a r e used i n p l a c e o f oxygen m o l e c u l e s i s i n agreement w i t h the d e s o r p t i o n mechanism d e v e l o p e d . The f a c t t h a t t h e a p p l i c a t i o n of a p o t e n t i a l causes a f u r t h e r i n c r e a s e i n t h e CO^ c o n t e n t o f t h e gas i s c o n s i s t e n t w i t h t h e mechanism. The t h e o r y a l s o p r e d i c t s a n i n c r e a s e i n t h e CO/CO2 r a t i o w i t h t i m e i n the c h e m i c a l r e a c t i o n . T h i s s u r p r i s i n g p r e d i c t i o n i s v e r i f i e d - 66 -by the experimental data. However, t h i s increase i n the C O / C O g r a t i o with time i s also noted during the e l e c t r o l y t i c reaction, while the mechanism requires that the r a t i o remain constant. There appears to be no immediate explanation f o r t h i s discrepancy. - 67 -CONCLUSIONS I t has been shown t h a t a COg r i c h gas i s produced i n t h e c h e m i c a l and e l e c t r o c h e m i c a l combust ion of g r a p h i t e by a l e a d - b o r o s i l i c a t e s l a g . T h i s f a c t has been e x p l a i n e d by a mechanism i n v o l v i n g t h e e l e c t r o n p o p u l a t i o n o f the g r a p h i t e TT-band. The agreement between the p r e d i c t i o n s o f t h i s mechanism and most o f the e x p e r i m e n t a l r e s u l t s i n d i c a t e s t h a t i t i s p o s s i b l e t h a t t h i s mechanism d e s c r i b e s the a c t u a l combust ion p r o c e s s . I f the a s sumpt ion used i n t h e r a t e c a l c u l a t i o n s a r e c o r r e c t , i t may be conc luded t h a t the proce s se s^ immobi l e a d s o r p t i o n , mobile a d s o r p t i o n , f i r s t - o r d e r k i n e t i c s , z e r o - o r d e r k i n e t i c s , and d e s o r p t i o n do not c o n t r o l the c h e m i c a l r e a c t i o n o f ca rbon w i t h oxygen i o n s . i - 68 -RECOMMENDATIONS FOR FURTHER WORK 1. Because i t has been found t h a t the CO/CO2 r a t i o v a r i e s c o n s i d e r a b l y w i t h t i m e , e x p e r i m e n t s should be done i n w h i c h t h i s i s d e f i n i t e l y shown t o be a f u n c t i o n of some parameter; f o r example, whether o r not i t i s governed by the o xygen-ion c o n c e n t r a t i o n of t h e s l a g . T h i s c o u l d be done by u s i n g a l a r g e s l a g b a t h and v a r y i n g i n i t i a l con-c e n t r a t i o n s . 2. T h i s i n v e s t i g a t i o n has a l s o p o i n t e d up the s e l e c t i v e o x i d i z i n g n a t u r e of l e a d - s i l i c a t e s l a g s . The l e a d - b o r a t e s l a g suggested should be i n v e s t i g a t e d more f u l l y because i t appears to o x i d i z e the g r a p h i t e i n a much more r e g u l a r manner. 3. The r a t e s of r e a c t i o n w i t h o u t an a p p l i e d p o t e n -t i a l s h o u l d be measured by a more s u i t a b l e method i n o r d e r t o d etermine more a c c u r a t e l y the a c t i v a t i o n energy f o r o x i d a t i o n . It. The p o s s i b i l i t y t h a t d i f f u s i o n of the oxygen t o the s l a g - g r a p h i t e i n t e r f a c e i s r a t e - c o n t r o l l i n g s h o u l d be i n v e s t i g a t e d . T h i s may be d e termined by s t i r r i n g the s l a g . 5. The gas s a m p l i n g arrangement should be changed t o f a c i l i t a t e more r a p i d a n a l y s i s . A c o n t i n u o u s setup might prove u s e f u l . 6 . V a r i o u s carbons s i m i l a r t o t h o s e used i n the aluminum i n d u s t r y s h o u l d be i n v e s t i g a t e d and the r e s u l t s i n t e r p r e t e d i n the l i g h t of the e l e c t r o n i c d i f f e r e n c e s between carbon and g r a p h i t e . - 69 -• B I B L I O G R A P H Y 1. Gadsby, J.,. Hinshelwood, C.N., and Sykes, K.W., P r o c . Roy. S o c , 187A, 129 (1946) . 2 . G o r i n g , G.E., C u r r a n , G . P . , Tarbox, R.P., and G o r i n , E., Ind . Eng. Chem., kjj., 1057 (1952). 3. Langmuir, I . , J . Amer. Chem. S o c , J2» ( I 91 f> ) . k. Long, P . J . , and Sykes, K.W., P r o c Roy. S o c , 1 9 3 A , 337 (19k8). ' 5. A r t h u r , J.R., and Bo w r i n g , J.R., J . Chim, Phys. k7. 136 (1935)• 6. 'Tsukhanova, Chem. A b s t r . IL2, 3982g (191+8) . 7. L e t o r t , Mr and Magrone, R., J . Chim. Phys. k 2 , 576 (1950) . 8. G u l b r a n s e n , E.A., and Andrews, K.F., J . I n d . Eng. 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S o c , 61+A, 815 ( 1 9 5 2 ) . 3 0 . M r o z o w s k i , S., Phys. Rev., 85^1+. 609 ( 1 9 5 2 ) . 3 1 . S e i t z , - P . , "The Modern Theory of S o l i d s , " M c G r a w - H i l l , New Y o r k , 191+0, pp. 3L+ - 3 1 9 . 3 2 . W i l s o n , A.H., P r o c Roy. S o c , 1 3 3 A . 1+58 ( 1 9 3 2 ) , and 131+ 277 (1932) . ' 3 3 - S e l d i n , E . J . , " P r o c e e d i n g s of the F i r s t and Second Con-f e r e n c e s on Carbon," U n i v e r s i t y of B u f f a l o , B u f f a l o , 1956, p. 118. 3l+. K i t t e l , C , " I n t r o d u c t i o n t o S o l i d S t a t e P h y s i c s , " W i l e y , New Y o r k , 1953-3 5 . T o r r e y , H.C., and Whitmer, C.A., " C r y s t a l R e c t i f i e r s , " M c G r a w - H i l l , 191+8, pp. 75~76. 3 6 . Rempel, S . I . , and Khodak, L.P., J . A p p l . Chem., U.S.S.R., 2 6 , 857 ( 1 9 5 3 ) . 37- R i c h a r d s o n , F.D., and Webb, E., Tra n s . I n s t . M i n i n g and Met., 6 4 , 529-561+ (1955) • - 71 -C o u g h l i n , J.P., B u l l e t i n £1+2, U.S. Bureau o f Mines, p. 27. Kubaschewski, 0., and Evans, E.L., " M e t a l l u r g i c a l Thermo-c h e m i s t r y , " Pergamen P r e s s , London, 195>3>, p. 298. R o s s i n i , , F.D., Wagman, D.D., Evans, W.H., L e v i n , S., and J a f f e , I . , C i r c u l a r £00, Nat. B u r . S t d s . , 19^2. - 7 2 -APPENDIX A ABSOLUTE REACTION RATE CALCULATIONS - 73 -Immobile A d s o r p t i o n Immobile a d s o r p t i o n may be c o n s i d e r e d a b i m o l e c u l a r r e a c t i o n i n v o l v i n g an oxygen i o n f r o m the s l a g and an a c t i v e c e n t e r i n a f i x e d p o s i t i o n on the g r a p h i t e s u r f a c e . An a c t i v a t e d complex i s assumed t o f o r m between t h e i o n and the a c t i v e s i t e . The r a t e o f a d s o r p t i o n i s g i v e n by the r a t e o f passage o f t h i s complex o v e r the p o t e n t i a l energy b a r r i e r . A c c o r d i n g t o the p o s t u l a t e s o f the a b s o l u t e r e a c t i o n r a t e t h e o r y , e q u i l i b r i u m e x i s t s between the oxygen i o n s , the a c t i v e c e n t e r s , and the a c t i v a t e d complexes. Thus-whereC += c o n c e n t r a t i o n o f a c t i v a t e d complexes C . = c o n c e n t r a t i o n of oxygen i o n s C s = c o n c e n t r a t i o n o f s i t e s . The -f terms are t h e complete p a r t i t i o n f u n c t i o n s f o r the i n d i c a t e d s p e c i e s . T h e r e f o r e , a c c o r d i n g t o the t h e o r y , the a d s o r p t i o n of i o n s onto s i t e s o f the ( i ) t h k i n d p e r square c e n t i m e t e r i s g i v e n by vt • ca, £_ h L t. where ^ d i f f e r s f r o m by the r e m o v a l o f one t r a n s l a t i o n a l degree of freedom i n the d i r e c t i o n of the r e a c t i o n c o o r d i n a t e . E x t r a c t i o n o f the z e r o - p o i n t energy g i v e s V " C-^i e. * • A c t u a l l y the t e r m £ f h f» V U r e p r e s e n t s the e n t r o p y change e R • The e q u a t i o n f o r - 74 -t h i s reac t ion may be wr i t ten *[c s] —> [o] + z e where 0 = oxygen ion i n the s lag [CJ]= ac t ive center on the graphite surface. [ . 0 ] = oxygen atom adsorbed onto the f i x e d s i t e . Since the structure of a l i q u i d i s c lo ser to that of a s o l i d than a gas, we can assume that the t r a n s l a t i o n a l p a r t i t i o n funct ion of the oxygen ion i s very s i m i l a r to that of the adsorbed atom. Also the r o t a t i o n a l and v i b r a t i o n a l p a r t i t i o n functions w i l l change very l i t t l e i n t h i s process.. Thus we may assume that the entropy change i s n e g l i g i b l e . To change the standard state of the p a r t i t i o n . funct ion, however, we must include the entropy of d i l u t i o n -"Kl^C. which i s 3 .7 x 1 0 ~ 2 0 . The various values to be subst i tuted i n the rate equation are as fo l lows : V = rate = 2 x 10^8 atoms of oxygen reac t ing per square centimeter every second at 1 0 0 ° C . r 21 C*0= 2.5 x 10 ions per cubic centimeter, assuming the oxygen complexed as S i40 i2^ _ r e c i p r o c a l seconds. E = approximately 26,000 c a l o r i e s per gram mole e^j-= 4 x 10-^' C^= 10-*-^  s i t e s , assuming a l l the per iphera l carbon atoms are a c t i v e . V= 2.7 x 10 4^ x 3.7 x 10~ 2 0= 1 x 10 2 6atoms oxygen crn^ sec. - 13 - , This value i s much d i f f e rent from that observed. Thus i t appears that immobile adsorption i s not the r a t e -c o n t r o l l i n g step. Mobile Adsorpt ion The formation of an adsorbed mobile l ayer involves an entropy change very d i f f e rent from that i n immobile adsorpt ion. Because the layer i s mobile, the concentrat ion of ac t ive centers does not appear i n the rate equation. The over-a l l equation fo r th i s process i s where£0]= oxygen atom at the anode surface which has been neutra l i sed by -the release of e lectrons to the graphi te . (oJ= the mobile adsorbed l a y e r , which may be regarded as a two-dimensional gas. Energet ics favour the formation of a molecular rather than an atomic gas. The oxygen atom has e f f e c t i v e l y no t r a n s l a t i o n a l degrees of freedom, while the adsorbed gas has two t r a n s l a t i o n a l degrees of freedom. Also the adsorbed molecule w i l l have one degree of r o t a t i o n a l freedom which the oxygen atom did not have. Thus the t o t a l entropy term w i l l be c ' L h - * Using the arguments put forward i n the development of the rate equation for immobile adsorption, we get fo r mobile - 76 -adsorption that - AS where tf entropy term, which may be replaced by L ° ] = c o n c e n t r a t l ° n o r " oxygen atoms at the anode surface. = 1,2 x IO-1-4 atoms oxygen per square centimeter Using the same condit ions as before the rate may be ca lcu la ted t 0 b e v = 1.2 x 10 1 4 .2.65 x 10^.5 x 1 0 1 0 . 4 x 10"* = 6 x IO- 5 2 x 3.7 x I O " 2 0 = 2 x l O 1 ^ atoms oxygen 2 cm sec, A comparison of t h i s to the experimental value of 18 2 x 10 would inc idate that the formation of a two-dimensional oxygen gas i s not rate c o n t r o l l i n g . Chemical Reaction The reac t ion i s assumed to involve one atom of oxygen and one act ive s i t e on which reac t ion occurs . The ac t iva ted complex consis t s of an adsorbed molecule which has acquired the approximate amount of energy and the. proper conf igura t ion . The reac t ion may be p ic tured as £QJ Q ^ (0 " ' C ) ^ ^ £ Q where C = react ive carbon at the s i t e . Thus the rate equation i s v - C C J C C J ^ TCeo rs i ) F i r s t - O r d e r K i n e t i c s . I f the surface i s sparsely covered with adsorbed oxygen atoms, the concentrat ion of s i t e s , C$, i s near ly constant and v i r t u a l l y i d e n t i c a l with the number of s i tes for a bare surface. - 77 -Under these c o n d i t i o n s , the r a t e i s p r o p o r t i o n a l to the c o n c e n t r a -t i o n o f atoms on the anode s u r f a c e and the r e a c t i o n i s f i r s t o r d e r . The r a t e e q u a t i o n i s V = *~£0j ^s.~^~' ~f~ T h i s assumes t h a t the ent ropy change d u r i n g r e a c t i o n i s n e g l i g i b l e . U s i n g the v a l u e s p r e v i o u s l y d e t e r m i n e d , th e c a l e u l a -t e d r a t e i s 1 x 10 atoms oxygen. I t s h o u l d be noted t h a t t h i s cm^ sec. i s the same r e s u l t as that- o b t a i n e d f o r immobi le a d s o r p t i o n , i i ) Z e r o - O r d e r K i n e t i c s . I t i s assumed t h a t t h e s u r f a c e i s covered by adsorbed oxygen atoms t o an a p p r e c i a b l e e x t e n t . I f the s u r f a c e i s n e a r l y c o m p l e t e l y covered w i t h atoms, ^-QJJ i - s v i r t u a l l y cons t an t and t h e r e a c t i o n i s independent o f C 5 . Thus the r a t e e q u a t i o n i s Co] h e * r T h i s e q u a t i o n y i e l d s a c a l c u l a t e d r e s u l t o f 1 x l O ^ 4 - atoms oxygen 2 cm s e c . D e s o r p t i o n D e s o r p t i o n from an immobile l a y e r may be regarded as i n v o l v i n g an a c t i v a t e d s t a t e i n which a m o l e c u l e a t t a c h e d t o an a c t i v e s i t e a c q u i r e s the n e c e s s a r y c o n f i g u r a t i o n and a c t i v a t i o n •^energy t o permit i t to escape from the anode s u r f a c e . A p p l y i n g the t h e o r y o f a b s o l u t e r e a c t i o n r a t e s , the f o l l o w i n g r a t e e q u a t i o n may be d e r i v e d : - 7 8 -V s C J«J ll e ^ T where C = c o n c e n t r a t i o n p e r square c..0 c e n t i m e t e r o f the adsorbed CO and C0 2 f * = p a r t i t i o n f u n c t i o n f o r the a c t i v a t e d complex (not CxOy) £ o= p a r t i t i o n f u n c t i o n f o r adsorbed p r o d u c t s The r e a c t i o n may be g i v e n as ' ° J —=» co, I t thus i n v o l v e s the d e s o r p t i o n of b o t h CO and C02. I f b o t h the adsorbed m o l e c u l e s and a c t i v a t e d complex are c o n s i d e r e d , i m m o b i l e , the r a t i o of the p a r t i t i o n f u n c t i o n s i s a p p r o x i m a t e l y u n i t y . I t s h o u l d be n o t e d t h a t t h e d e s o r p t i o n p r o c e s s as d e f i n e d i s almost i d e n t i c a l t o t h a t o f zero-rorder k i n e t i c s . T h e r e f o r e , the r a t e e q u a t i o n s f o r b o t h p r o c e s s e s are s i m i l a r . Assuming the v a l u e quoted by G l a s s t o n e , L a i d l e r , and E y r i n g (22) of 10^ atoms p e r square c e n t i m e t e r f o r a n e a r l y covered s u r f a c e as t h e c o n c e n t r a t i o n of the adsorbed CO and COo,. the r a t e i s 1 * l O * * < * * ° > ~ * T h l s v a l u e i s the same as t h a t o b t a i n e d f o r z e r o - o r d e r k i n e t i c s . - 7 9 -APPENDIX B ACTIVITY OP OXYGEN IN LEAD-SILICATE SLAGS - 80 -R e c e n t l y , R i c h a r d s o n and Webb (37) have s t u d i e d the a c t i v i t y of PbO I n l e a d s i l i c a t e s l a g s by means of the e q u i l i b r i u m PbO —>- Pb + [O] where PbO i s l e a d o x i d e , e i t h e r pure o r d i s s o l v e d i n the s i l i c a t e ; Pb i s m o l t e n lead;- and (0] i s oxygen d i s s o l v e d i n the m o l t e n l e a d . E q u i l i b r i u m was a t t a i n e d by vapor phase c o n t a c t between the m o l t e n PbO o r s i l i c a t e s l a g s and t h e m o l t e n l e a d i n s e p a r a t e c r u c i b l e s . Two s m a l l c r u c i b l e s f o r l e a d and a s m a l l c r u c i b l e f o r s l a g were h e l d i n s i d e a l a r g e r i r i d i u m c r u c i b l e covered w i t h double l i d s t o p r e v e n t the escape o f PbO vapor. T h i s assembly was he a t e d up t o the r e a c t i o n t e mperature and a l l o w e d t o come t o the e q u i l i b r i u m . At e q u i l i b r i u m , the p a r t i a l p r e s s u r e o f the oxygen over the s l a g must be e q u a l t o t h a t over t h e m e t a l . A l s o the a c t i v -i t y o f the PbO i n b o t h phases must be e q u a l . Assuming t h a t : and t h a t S i e v e r t ' s law ( i . e . N[o-j <* ^ Po^ ) a p p l i e s t o the s o l u b i l i t y o f oxygen i n m o l t e n l e a d up t o s a t u r a t i o n , R i c h a r d s o n and Webb c a l c u l a t e d the a c t i v i t y of PbO f r o m the r e l a t i o n c x P b o = k • ^ • A ' t ' l . C o l . By u s i n g t h e i r d a t a f o r the s o l u b i l i t y o f oxygen i n m o l t e n l e a d , i t i s p o s s i b l e t o c a l c u l a t e the a c t i v i t y o f oxygen i n the s l a g i f the f r e e e n e r g i e s o f f o r m a t i o n of the l i q u i d are known. T h i s has been e s t i m a t e d by C o u g h l i n (38). These d a t a , c o r r e c t e d f o r the h e a t o f f u s i o n of l e a d o x i d e as g i v e n by Kubaschewski and Evans (39) t o be - 81 -6 , 3 0 0 c a l o r i e s p e r gram mole, are shown i n Table 1 . I n h i s c a l c u l a t i o n s , C o u g h l i n used the v a l u e o f 2,800 c a l o r i e s p e r gram mole as g i v e n b y R o s s i n i (kO). T h i s v a l u e has been shown t o be i n e r r o r by the work o f R i c h a r d s o n and Webb. The p a r t i a l p r e s s u r e of oxygen may be c a l c u l a t e d by the e q u a t i o n o f f o r m a t i o n P L + ' — P ^ O , and the r e l a t i o n „ . . where ^ T h i s c a l c u l a t i o n i s shown i n Table 1. S i e v e r t ' s law may be assumed t o a p p l y here ( i . e . N t ^ i?( \ ) where ^ to ] =- a c t i v i t y o f oxygen d i s s o l v e d i n m o l t e n l e a d ^AtWefo] = atomic p e r c e n t oxygen d i s s o l v e d I n the m o l t e n l e a d . However, when the s l a g and m e t a l a r e i n vapor-phase e q u i -l i b r i u m where o.(^ i s the a c t i v i t y o f oxygen i n the g l a g Thus, o,,„v = fe' A t c / 6 C o 3 Co) When pure PbO i s i n e q u i l i b r i u m w i t h t h e metal,, the a c t i v -i t y of the oxygen i n the pure PbO and i n the m e t a l i s e q u a l t o the p a r t i a l p r e s s u r e o f the oxygen. T h i s i s c a l c u l a t e d i n T a ble 1 w i t h a s t a n d a r d s t a t e o f one atmosphere pf oxygen TABLE 1 . OXYGEN PARTIAL PRESSURE CALCULATED PROM EQUATION Pb § 0 2 —* PbO T°K K c a l . Log K K I = 1 K po 2 1173 -21+.91 1+.61+ 4 .37 X 10^ 2 . 2 9 X 5 . 2 5 X 10" •10 1198 -21).. [+7 h-kl 2 . 9 5 X 3 .39 X i . i 5 X 10" •9 1223 -21+. 0^ 1.995 X 5 . 0 2 X 1 0 " S 2 . 5 2 X 10" •9 121+8 - 2 3 - 5 8 1+.13 1.35 X 10^ 7-1+1 X 5 . 5 X 10" :9 1273 - 2 3 . 1 5 3 .97 9 . 3 3 X 103 1.07 X 1 0 ^ i . i 5 X 10" •8 1298 - 2 2 . 7 3 . 8 2 6 . 6 1 X i o 3 1.51 X lO" 1* 2 . 2 8 X 10" •8 1323 - 2 2 . 2 7 3 .68 1+.79 X i o 3 2 . 0 9 X l o "^ 1+.37 X 10" •8 1373 - 2 1 . 3 9 3.1+0 2 . 5 1 X 1 0 3 3 .98 X 1 0 ^ 1.58 X 10" •7 - 8 3 -gas. Thus , _ _ I yfS^ R i c h a r d s o n ' s d a t a f o r the s o l u b i l i t y of oxygen i n l e a d , as shown i n T a b l e 2 , were p l o t t e d l o g a r i t h m i c a l l y a g a i n s t the r e c i p r o c a l t e m p e r a t u r e i n F i g u r e 1 . The s o l u b i l i t i e s o f oxygen i n l i q u i d l e a d a t v a r i o u s t e m p e r a t u r e s were t a k e n f r o m t h i s g r a p h and the a c t i v i t i e s of oxygen c a l -c u l a t e d as shown I n T a b l e 3 . These d a t a are p l o t t e d as a f u n c t i o n o f c o n c e n t r a t i o n o f PbO i n F i g u r e 2 , w h i c h i s F i g u r e 8 i n the t e x t . TABLE 2. SOLUBILITY OP OXYGEN IN MOLTEN LEAD IN VAPOR-PHASE EQUILIBRIUM WITH VARIOUS LEAD-•SILICATE SLAGS 1000°C. 1100°C. 119ko C Mole % PbO i n S l a g A t % CO] i n l e a d Mole % PbO At % Lol Mole % PbO At % [ol IOO 1.76 100 2.81 100 k.09 89.8 1.52 90 2.k5 90 3 4 9 85 1.36 85 2.18 85 3.11 83 1.25 83 2.07 83 2.95 80 1.16 80 1.87 80 2.71 75 0.93 75 1.5k 75 2.25 65 0.532 65 0.02 65 147 50 0.188 5o 0.347 -5o 0.579 kO 0.105 » ko. 0.193 ko 0.325 S i 0 2 s a t ' d . 0.09k S i 0 2 s a t ' d . 0.16k S i 0 2 sat»d. 0.266 C O 4=-TABLE 3. OXYGEN ACTIVITIES 900UC • k900 Mole ! % At % PbO 0 100 1.03 90 0.9 85 0.78 83 0.735 80 0.66 75 0.518 65 0.283 5o 0.091 1+0 0.05l .29xl0"^ = 2.22x10"^ 1.03 a ( o ) -5 2.29 x 10 2 x lO" ? . 1.735 x 10-5 1.635 x 10-5 1.1+7 x 10-5 1.152 x 10-5 0.629 x 10-5 0.202 x 10-5 0.113 x 10-5 950°C.k' nJ'62x10-^ f 6 6 x l Q - 5 950 1 > 3 7 £ oMole % At % PbO 0 a (0) 100 90 85 83 80 75 65 5o l+o 1..37 1.18 1.03-0.98 0.88 0.7 0.393 0.132 0.07I+ 5.02 x 10"^ 4.33 x 10-5 3.77 3.59 3.22 2.56 x X X X X 10-5 i o -5 io-5 io-5 l . l+k x io -5 0.1+81+ x 10-5 0.271 x 10-5 1000 ° - K i o o o ~ -Mole % At % PbO 0 100 1.76 89. 9 1.52 85 1.36 83 1.25 80 1.16 75 0.93 65 0.0532 5o 0.188 1+0 0.105 i o 5 o ° c . • 25x10-5 i i o o o c . k » 100=^ 4§g2l^ =i• 4i7xio-^ Mole % At % PbO 100 90 85 83 80 75 65 5o 1+0 0 2 . 26 1.97 1.74 1.63 1.1+9 1.21 0.715 0.26 0.H+5 2 . 2 6 a ( 0 ) 20.9x10 18.2 x 16.1 x _ 15.1 x 10-5 13.8 x 10-5 11.2 x 10-5 6.61 x 10"5 2.1+ x 10-5 1.31+ x 10-5 Mole % At 5 a i o - 5 PbO 0 100 2.81 90 2.1+5 85 2.18 83 2.07 80 1.87' 75 1.51+ 65 0.92 5o 0.347 1+0 0.193 (0) 39 . 8 x 10"5 31+. 7 x 10-5 30.9 x 10-5 29.3 x 10-5 26.5 x 10-5 21.8 x i o"5 13.01+ x i o~5 I+.81+ x 10-5 2.73 x 10"5 0 7 x i o - 4 = 6 - 0 f l y 1 0 1776 a (0) - 5 10.7 x 10 J 9.25 x 10-5 8.27 x i o-5 7.6 x 10-5 7.06 x i o-5 5 . 6 6 x 10-5 3.21+ x 10-5 1.1I+ x 10-5 0.61+ x 10-5 - 8 6 -10 F i g u r e 1 . S o l u b i l i t y of Oxygen i n Lead v s . R e c i p r o c a l Temperature ' - 37-MOLE FRACTION PbO 

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