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The oxidation of carbon by lead oxide-silica melts Jena, Prafulla Kumar 1959

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THE OXIDATION OF CARBON BY LEAD OXIDE-SILICA MELTS • • by FRAFULLA KUMAR JENA A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of MINING AND METALLURGY We accept this thesis as conforming to the standard required from'candidates for the degree of MASTER OF SCIENCE Members of the Department of Mining and Metallurgy. THE UNIVERSITY OF BRITISH COLUMBIA January, 1959-i ABSTRACT An investigation of the oxidation of carbon by lead oxide-silica melts was undertaken. The carbon specimens utilised in this investigation were spectroscopic graphite,, petroleum coke (baked at 900°C) and spectro scopic carbon0 The kinetics of the reactions were studied for different geometric surface areas over a wide range of concentrations of lead oxide and at different temperatures. In a l l cases the rate of oxidation was found to be directly proportional to the geometric surface area of the carbon sample used. The rate was also proportional to the square of the activity of lead oxide or equilibrium pressure of 0 2 obtained from the dissociation of PbO in the melt. The experimental rate constant k values were calculated,, The values of k for the oxidation of graphite, petroleum coke and carbon at 1000°C were found to be 1.35 x IO"2, 1.31 x 10~2 and 0,97 x 10"2 gm.C/cm2/mino respectively. The values of the experimental activation energies of the oxidation of graphite, petroleum coke and carbon were found to be 33* 28 and 22 kilo- calories per mole respectively. In a l l cases carbon dioxide was the product gas. The results obtained in the present investigation indicated that the stoichiometry of the reaction is two molecules of lead oxide and an atom of carbon to produce metallic lead and carbon dioxide,, In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Mining and Metallurgy The University of British Columbia, Vancouver &, Canada. Date January 27th,,1959.  i i ACKNOWLEDGEMENT The author is grateful to. the members of the Department of Mining and Metallurgy for their valuable assistance throughout this work and is especially grateful to Dr. CS 0 Samis who directed this investigation« The author is also indebted to the National Research Council for the financial assistance necessary to carry out this project. i i i TABLE OF CONTENTS Page INTRODUCTION O o o » o o o o o o o o o o « o . o . o o o o o o o o o 1 (A) Oxidation or: Adsorption Process . . . . 0 0 0 . 0 0 0 0 0 0 1 (B) Combustion or Desorption Process „ „ o o o . . 0 0 0 0 0 0 4 Object and Scope of the Present Investigation 0 0 0 0 0 0 0 0 0 5 EXPERIMENTAL . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Apparatus ... . 0 0 0 . . o . o . . . . . . . . . . 9 Materials' 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 Procedure o o o . o o o o o o o . . o . o o « « » o o o o o o 11 Reproducibility o o o . . o o o o o o . . » o o o o o o o o o o 12 Dxffusion 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 RESULTS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (A) Oxidation of Graphite . . . . . . . . . . . . . o . . . ' . 13 (B) Oxidat ion of Carbon 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22 (C) Oxidation of Petroleum Coke 0 o . . . 0 . . « . . o . o . 30 DISCUSSION o ' " o o o o 0 0 0 0 0 0 0 0 . o o o o o o o o 0 0 0 o 0 0 43 CONCLUSIONS o o . o o o o . o o o o o o o o o o o o o o o o o o o o I4.S RECOMMENDATIONS . . . . . . . . . . . . . . . . . . . . . . . . . o . 47 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 APPENDIX o o . . . . 0 . 0 0 0 0 0 0 . o o o o o . o o o o . 0 0 51 LIST OF FIGURES P a £ e 1. PbO-Si02 phase diagram . . . . . . . . . . . . . . . . . . . . . . 7 2„ Activity-mol fraction relation of lead oxide . < , . . . „ » . < > 8 3« Apparatus for study of chemical oxidation . . . . . . . . . 10 4. Rate curves for the oxidation of graphite having different geometric surface areas . . . . . . . . . . . . . . . . ° 14 5» Dependence of the reaction rate on the geometric surface area of graphite . . . . . . . . . . . o 16 6. Rate curves for the oxidation of graphite by Fb0-Si0 2 melts of different compositions . . . . . . . . . . . . . . . . . . . . 1 8 7. Dependence of the rate of oxidation of graphite on the activ i t y of lead oxide 0 . . . . . . . . . . . . . . . • 19 8. Dependence of the rate of oxidation of graphite on the square of the activity of lead oxide „ „ . . . . . . . . 20 9. Rate curves for the oxidation of graphite at different experimental temperatures . . . . . . . . . . . . . . . . 23 10. Log-.Qk vs 1 for the oxidation of graphite . . . . . . . . o 24 T°K 11. Rate curves for the oxidation of carbon having different geometric surface areas . . . . . . . . . . . > . . . . . 25 12. Dependence of the reaction rate on the geometric surface area of carbon . . . . . . . . . . . . . . . . . . . . 26 13. Rate curves for the oxidation of carbon by Pb0-Si02 melts of different compositions . . . . . . . . . . . . . . . . 28 14. Dependence of the rate of the oxidation of carbon on the square of the activity of lead oxide i n the melt , . . „ . 29 V List of Figures (cont'd.) P a £ e 15. Rate curves for the oxidation of carbon at different experimental temperatures 0 31 16. Log^ Qk vs 1 for the oxidation of carbon 32 T ° K 17i Rate curves for the oxidation of petroleum coke having different geometric surface areas , 34 IS. Dependence of the reaction rate on the geometric surface area of petroleum coke 35 19. Rate curves for the oxidation of petroleum coke by PbO-Si02 melts of different compositions . . . . . . . . . . . . . 37 20. Dependence of the rate of oxidation of petroleum coke on the square of the activity of lead oxide in the melt ......... _ 38 21. Rate curves for the oxidation of petroleum coke at different experimental temperatures . . . . . . 40 22. Log1nk vs 1 for the oxidation of petroleum coke „ 41 vx LIST OF TABLES Page I, E f f e c t of geometric surface area of graphite on the r a t e of OXlCLci/b XOIl 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 l i e E f f e c t of a c t i v i t y of lead oxide i n the melt on the rate of „ » oxidation of graphite o o o o o o o o o o o ° o o o o o 21 I I I 0 E f f e c t of temperature on the rate of oxidation of graphite 0 <> 22 IV, E f f e c t of geometric surface area of carbon on the rate of o c^icLcLiji ion 0 0 6 0 0 0 0 0 0 0 D 0 0 0 0 0 0 0 0 0 0 0 2*7 V„ E f f e c t of a c t i v i t y of lead oxide i n the melt on the r a t e of oxidation of carbon » „ „ <. » . . » ° . « » , « « 0 o » 30 V I o E f f e c t of temperature on the r a t e of oxidation of carbon „ „ » 33 V I I , E f f e c t of geometric surface area of petroleum coke on the rate of oxidation 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 36 VIIIo E f f e c t of a c t i v i t y of lead oxide i n the melt on the r a t e of oxidation of petroleum coke 0 0 0 0 0 0 0 0 0 0 0 0 0 0 39 IX 0 E f f e c t of temperature on the rate of oxidation of petroleum coles 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X0 Summary of the r e s u l t s 0 » » » .„ . » ° » » « . » » - » 0 » o 0 4 4 THE OXIDATION OF CARBON BY LEAD OXIDE-SILICA MELTS INTRODUCTION The reactions between carbon and oxygen, and carbon and various metallic oxides are of considerable theoretical and industrial interest. For example j, the reactions between metallic oxides and carbon are important In' the case of blast furnace operation and in the anodic reaction occurring in the aluminium-reduction c e l l 0 In the past two or three decades much work has been done on the gaseous oxidation o f carbon and much valuable information has been obtained concerning the nature and mechanism of these reactions„ Howeverj very l i t t l e is known about the kinetics of the reaction of carbon with metallic oxides either in the solid or molten states. In view of this,, the present work on the oxidation of carbon by lead oxide-silica melts has been undertaken. The kinetics of the reactions of carbon with oxidizing gases such as oxygen, carbon dioxide have been studied by Langmuir, Hinshelwood, Sykes, Gulbransen and others .l**^,3,4,5 The entire reaction process can be divided into two main stages. (A) the oxidation or adsorption process and (B) the combustion or desorption process, (A) The Oxidation or Adsorption Process The work of Gulbransen and coworkers^*^ on the kinetics of the oxidation of graphite with gaseous oxygen provides some concept on the oxida tion process. In their study, the effect of pressure of oxygen on the i n i t i a l rate of reaction 8K° was found to follow the equation K = A + Bp, where A and B are constants and p is the pressure of oxygen, A first order reaction was found for pressures of 10 cm. of mercury of oxygen or higher j, while a zero or*der reaction was found at low pressures„ The experimental activation energy for this oxidation reaction was found to be 36»7 kilo calories per mole„ A comparison of the experimental rate with those calculated from the absolute reaction rate theory, developed by Eyring,^ has shown that either (i) mobile adsorption or (ii) immobile adsorption with ^dissociation is a possible rate-controlling step 0 (i) In the case of mobile adsorption, the activated complex-formed is mobile on the carbon surface with vibrational and rotational degrees of freedom similar to the reactant gas molecules. However, the activated complex has only two degrees of translational freedom over the surface. This is in contrast to three such degrees of freedom in the gaseous state. Where Fg and F* are the partition functions for a cm-^  of gas and per cm2 of activated complex respectively 9 the ratio^ F^/Fg reduces to 1/f^ where f-j. is the contribution of one translational degree of freedom. The value of f^ . is (27T mkT)"1^2, where k is Boltzmann0s constant, h is Planek°s constant, T is h the temperature, m is the mass of the molecule, Eyring's equation applicable to mobile adsorption as the rate controlling step is as follows; 2 x * - E / R T Rate (atoms , C/cm /sec) = Cg0kT.FJ,e h Fg -E/RT = CgnkT0 h ce h (2TmkT)i/2 (1) where Cg represents the concentration of oxygen gas in molecules per c c , R is the gas constant and E is the energy of activation. The rate of oxidation of graphite for an oxygen pressure of 7-6 cm of mercury at 500°C calculated from Equation (l) was 7.3 x 10 atoms.C/cm /sec compared to the experimental 11 2 value of 7.2 x 10 atoms/C/cm /sec under the same conditions<, (ii) In the case of immobile adsorption with dissociation, the gas adsorbed on the surface forms an immobile layer. This means that the atoms obtained from the dissociation of reacting molecules are assumed to be attached to the sites until they are desorbed. Hence, their translational and rotational contributions to the partition function of the activated complex are unity. In this case the ratio of the partition functions of the (activated complex and the reacting gas molecules F v F _ reduces to 1 where f-, is the contribution f? . f2, * of one rotational degree of freedom,, Eyring's equation applicable to immobile adsorption with dissociation reduces to: Rate (atoms.C/cm2/sec) = C C g okT . h 5 g-E/RT ( 2) h (2irmkT)^(8Tr 2IkT) where Cs represents the number of sites per square centimeter and I is the moment of inertia and other terms have the same meaning as before. The rate of oxidation of graphite for an oxygen pressure of 7.6 cm 12 of mercury at 500°G calculated from the above equation was found to be 2„1 x 10 2 11 atoms.C/cm /sec. whereas the rate va^ lue obtained experimentally was 7.2 x 10 atomsoC/cm^/sec. Like gaseous oxygen pure molten metallic oxides or their mixtures are also able to oxidise carbon. One might speculate on the fundamental difference between the oxidation of carbon by gaseous oxygen and that by molten oxides. In the gaseous oxidation of carbon, the oxygen goes from the state of a gaseous molecule to an activated complex. On the other hand in the oxidation of carbon by molten metal oxides, the i n i t i a l reactant goes from the liquid state to atti activated complex state on the carbon surface. It is not very likely that the - 4 - corresponding partition functions of the activated complex and the reactants in both the cases will be the same in magnitude. Therefore, by taking absolute reaction rate theory in to consideration, i t appears that the rates of oxidation for both cases w i l l also be quite different under similar experimental conditions 0 (B) The Combustion or Desorption Process. A large number of investigations in the field of carbon combustion has been carried out by Rhead, Sykes, Arthur, Gilliland, Bowring and 7 « o in i i 1 ? T J others,, '* s 7 s * 3 * J These investigations indicate the following points with respect to the CO and C 0 2 ratio desorbed from the carbon surface under conditions of gaseous oxidation of carbon with oxygens ( 1 ) CO and C 0 2 are simultaneously produced by the desorption of the surface oxide of carbon, ( 2 ) The observed ratio of CO to C 0 2 desorbed covers a wide range-of values and is dependent upon numerous factors such as (a) temperature, (b) pressure, (c) presence of halogens in the gas phase, (d) presence of hydrogen atoms on the carbon surface, (e) presence of transition metal atoms in the carbono Some valuable work on the reaction of carbon dioxide with carbon has also been done. Comments of R.F. Strickland-Constable1^ on the work of Key,1-* indicate that carbon dioxide reacts with coke by a two stage mechanism: in the first stage, a surface oxide is formed and in the second stage, the surface oxide decomposes to give C 0 „ This reaction is retarded by C 0 „ This is attributed to the reversal of stage 1 , in that the CO is assumed to react with the surface oxide to reform C 0 2 . The studies of Bonner,1^ Broom1? and Gadsby1^ on the reaction of carbon dioxide with carbon and recently the work - 5 - of Gulbransen and Andrew-^ on the reaction of carbon dioxide with a r t i f i c i a l graphite, suggest the probability of a secondary reaction at the carbon surfaces C + C0 2 ^ 2 CO. Recently J.D.S. Turnbull^ has studied the oxidation of commercial graphite by a lead-borosilicate melt with and without the application of an electrical potential. His work was mainly focussed on the combustion products of carbon and the effect of temperature and current density on them, A rough value of 2 x 1Q^ atoms of oxygen per cm2 per sec. at 1000°C, was found for the rate of the oxidation of commercial graphite in the above melt. In his work, there may be an error due to the secondary reaction of the exposed graphite surface with the product gas inside the apparatus, Ob.ject and Scope of the Present Investigation. The object of the present investigation has been to study the kinetics of the oxidation of (i) spectroscopic graphite, (ii) spectroscopic carbon and ( i i i ) a petroleum coke mixture (National Carbon Company graphitizing stock, baked at 900°C) by lead oxide-silica melts at different temperatures. Three different types of carbon and graphite were investigated because of the fact that they show a range of properties.21,22,23 p o r instance, with increase in temperature of heat treatment the nature of the carbonaceous material changes from a molecular solid through an aggregate of "turbostratic 9 micro- crystallites to polycrystalline graphite. This polycrystalline graphite is obtained at temperatures greater than 2500°C„ It has been observed2^ that as the heat treatment .temperature is increased, the reactivity of carbon in the oxidation process progressively decreases. Thus the activation energy for the oxidation of carbon should increase with the increase in heat treatment temperature, Sebastian and Mayers^ -6 - investigated the gaseous oxidation of a series of cokes having calcination temperatures from 400°C to 1000°C with varying rates of calcination. The activa tion energy of the oxidation varied directly with the calcination temperature and inversely with the rate of heating to temperature. Above 1000°C, the rate of calcination appeared to have no effect on the activation energy of the oxidation process, Gilliland and coworkers1^ found that the activation energies of the oxidation of Ceylon graphite, metallurgical coke and hardwood charcoal in oxygen gas were 49* 29 and 16 kilocalories per mole respectively. In view of the above results, in the present study the magnitudes of the experimental activation energy 'E° for the oxidation of graphite^petroleum coke and carbon should be in the order of E g r a p h i t e ^ ^petroleum coke / ^carbon. In the present study, lead oxide in s i l i c a melts was selected as the oxidizing agent for the oxidation of carbon for the following reasons? (1) In the oxidation of carbon in oxygen gas a relation between the reaction rate and the pressure of the reacting oxygen has been found. In order to establish a relation between the oxygen pressure of the oxidizing melt and the rate of oxidation of carbon in the present study, i t was necessary to investigate the rates of oxidation in different lead oxide-silica melts since these melts have variable oxygen .pressure.* An examination of the phase diagram of the lead oxide-silica system25 (Fig, 1) shows that a large number of low melting melts of lead oxide and silica can be obtained, (2) The activities of lead oxide (Fig, 2) over a wide range of compositions of the lead oxide-silica system have been determined accurately by 26 Richardson, The oxygen pressure in equilibrium with lead oxide in the melt is directly proportional to the square of the activity of lead oxide in the melt. - 7 - SILICA 16-4 29-2 M O L E S PER CENT. 39-6 48-3 55-3 61- 66-6 160 40 20 100 L J SiO a' S1O2 . • 1 l4PM.|i02 • 1 0 5 10 85 P b O . S i O z + Quartz 30 35 SILICA WEIGHT PER CENT Fig. 1. PbC-Si0 2 Phase Diagram. - 8 -_ 9 - (3) It was also found that the rate of oxidation of carbon in most of these melts was measurable at the present experimental temperatures0 EXPERIMENTAL Apparatus. A diagram of the apparatus in which the chemical oxidation of carbon by' lead oxide-silica melts has been performed, is given in Fig, 3° In that sketch, A = Globar furnace B = Chromel-Alumel Thermocouple to control the temperature of the furnace (±2 to 3°C). through a Leeds and Northrup Micromax controller,, C = a fireclay crucible containing the lead oxide-silica melt„ D = a funnel. The stem of the funnel was a high temperature porcelain protection tube (supplied by McDanel Refractory Porcelain Co., Pennsylvania) and the cone portion was made of fired 'synthetic lava 0. The cone was machined from a grade 'A9 synthetic lava block (supplied by American Lava Corporation, Tennessee) and then fired slowly up to approximately 1150°Co The cone and the stem portions were joined by "Sersit' cement. The cone portion of the funnel was then coated completely with lead oxide and silica paste (containing approximately 78.8% of PbO by weight) and then fired slowly nearly up to 1050°C . in order to coat the funnel uniformly. It was found from preliminary experiments that when the portion of the funnel was dipped into the reacting melt (nearly 200 grams), the thin coat on the funnel did not cause a measurable change in the composition of the reacting melt. The purpose of the coating on the funnel was to avoid any diffusion of the product gas through its wall during the reaction of carbon with the lead oxide-silica melt. Synthetic lava, fireclay, vitreosil and inconel were tried as funnel materials and the fired synthetic - 10 - Fig„ 3 Apparatus for study of chemical oxidation. - 11 - lava was found to be~ the most suitable material,, E = a thin chromel rod holding in a loop a piece of carbon sample "F", G = a glass tube0 This was joined to the stem of the funnel,, This glass tube had a side tube which was joined to the gas collecting cylinders °H' which were themselves joined in series, I = a stopcock. Materials, Special spectroscopic carbon and graphite electrodes were supplied by National Carbon Company in the form of rods of different diameters. Petroleum coke mixture (the sample from the 500 ampere cell carbon) was National Carbon Company graphitising stock, baked at 900°C and supplied in blocks, from which rods of different diameters were machined. The materials for the melt were reagent grade lead oxide (mono) (Baker arid Adam£on) and pure silica powder (supplied by Cave and Company Limited), Procedure, Weighed amounts of lead oxide and silica were placed in crucible 'C'„ This crucible and the funnel 'D' (without the chromel rod holding the carbon) were then assembled in the electric furnace. The funnel was not dipped into the melt until the experiment was started. The furnace was maintained at the desired experimental temperature by a controller. After half an hour at temperature, the cleaned chromel rod 'E' holding a piece of carbon (whose geometric surface area was measured previously by a micrometer) was rapidly introduced into the funnel. The funnel was then dipped into the molten lead oxide-silica so that the carbon piece was completely immersed in the melt and - 12 - the o x idation process began,, Aft e r t h i s the side tube of the glass tube "G5 i n F i g . 3 was joined to the burettes «H'„ Then the pinch cock ' 1 ° was closed. This time was considered as the zero time. The i n t e r v a l from the immersion of the carbon to c l o s i n g of the pinch cock was of the order of one minute. Time was read by means of a stopwatch. The gases evolved f o r d i f f e r e n t r e a c t i o n times were c o l l e c t e d by displacement of acidulated water ( 5 - 6 volume percent of concentrated sulphuric a c i d i n d i s t i l l e d water) i n gas c o l l e c t i n g graduated burettes "H* under atmospheric pressure and the gas volumes were simultaneously measured. After the experiment, the c o l l e c t e d gases were analysed i n an Orsat apparatus f o r carbon dioxide, oxygen and carbon monoxide. The absorbants f o r these gases were r e s p e c t i v e l y potassium hydroxide s o l u t i o n , a l k a l i n e p y r o g a l l o l and Frantz reagent. Potassium hydroxide s o l u t i o n contained 5 0 0 grams of pure potassium hydroxide per l i t r e . A l k a l i n e p y r o g a l l o l was a mixture of one volume of a s o l u t i o n containing 3 0 0 grams of pure p y r o g a l l i c a c i d per l i t r e of s o l u t i o n with 4 to 6 volumes of the above potassium hydroxide s o l u t i o n . One gall o n of Frantz reagent s o l u t i o n contained 9 1 0 grams of cuprous chloride, 1 7 0 0 cc. of monoethanolamine, 6 0 grams of ammonium chloride and water. Analysis by t h i s method i n a l l cases showed the product gas to consist of carbon dioxide and 0 . 0 to 0 . 5 percent of carbon monoxide. It was l i k e l y that some of the carbon dioxide would d i s s o l v e i n the acidulated water during c o l l e c t i o n and hence there might be some error i n the measurement of the volumes fo r d i f f e r e n t reaction times. Thus, i n some separate experiments, pure carbon dioxide was c o l l e c t e d i n the usual way and i t was found that less than 1 . 5 percent of t o t a l carbon dioxide went into s o l u t i o n over a time period of an experimental run. R e p r o d u c i b i l i t y For a p a r t i c u l a r set of experimental conditions the amount of carbon - 13 oxidized was found to bear a linear relationship with the reaction time0 The rate of oxidation was obtained from the slope of the above curve0 The reproducibility of the experimental technique was checked by a series of experiments under identical conditions„ It was found that the rates were reproducible to within ±4 to 5%0 Diffusion In three experiments under otherwise identical conditions the melts were stirred with the chromel rod 'E' in an electric stirrer at the rate of l s 2 and 3 revolutions per second respectively. The rate of oxidation was found to be independent of the stirring rates. This indicated that under the present experimental conditions, diffusion of the reactants to the carbon surface was not rate controlling,, RESULTS (A) Oxidation of Graphite. (1) Oxidation rate as a function of geometric surface area (G.S.A,') Special graphite spectroscopic electrodes of different diameters were machined to different sizes. The G.S.A. of each graphite piece, which varied 2 2 from 5.1 cm to 12,7 cm , was measured with a micrometer. Separate experiments were carried out with these at 1000°C in lead oxide-silica melt (containing 78.8$ of lead oxide by weight). For each piece of graphite the amount of carbon oxidized per unit time was determined (given in Fig. 4 and Table I). A plot of these values (gm. of C oxidized per piece of graphite per minute) against their respective G.S.A. values (in cm2) is given in Fig. 5. It was found that the rate of oxidation of graphite was directly proportional to the G.S.A. of graphite. The rate of oxidation of graphite by a lead oxide-silica melt, Time i n minutes F i g . Ue Rate curves f o r oxidation of graphite having d i f f e r e n t geometric surface areas„ TABLE I E f f e c t of geometric surface area of graphite on the rate of oxi d a t i o n . Experimental temperature = 1000°C. Percentage of PbO by weight i n the melt = 78.8 Geometric surface area of graphite i n cm. (Gram of C oxidized per piece of graphite per min.) x 10^ Rate of oxid a t i o n (R) x 1Q4 ( i n gm.C/cm2/min.) 5.1 0.84 1.64 7.5 1.14 1.63 8.9 1.29 1.45 9.9 1.45 1.47 12.7 1.78 1.40 - 17 - containing 78.8% of lead oxide by weight was found to be 1„63 x 10~^ gm.C/an2/mini. at 1000°C. (2) Effect of the composition of the lead oxide-silica melt on the rate  of oxidation. The rates of oxidation of graphite at 1000°C were determined in different compositions of lead oxide-silica melts (varying from 77 to 86 percent of lead oxide by weight) using graphite specimens of 7.5 cm of G.S.A. It was found that the rate of oxidation of"graphite in lead oxide-silica melts was proportional to the square of the activity of lead oxide, ^ p^ Q (given in Fig. 8). A plot of the rate against ap-^ g resulted in the parabolic curve (given in Fig.7). The apkg values corresponding to the different melt compositions were obtained from Fig. 2 (Richardson's data). The results are summarized in Figs. 6, 7 and 8 and in Table II. From the above relation the rate equation can be expressed as R = k a 2 b Q (3) where k is the experimental rate constant. (3) Determination of the experimental activation energy of the oxidation  of graphite. The rates of oxidationbf graphite in lead oxide-silica melt (contain ing 78.8% of PbO by weight) were measured for different experimental temperatures varying from 96l°C to 1060°C using graphite specimens of 7.0 cm of G.S.A. From the values of the rate of oxidation, the corresponding experimental rate constants «k' were calculated from equation 3, rate = ka^Q. The effect of temperature on the activity of lead oxide in a lead oxide-silica melt (78.8% 26 of PbO by weight) was obtained from Richardson's data. The activities of lead oxide in the above melt at 1000°C and 1100°C were found to be 0.11 and 0.12 respectively, indicating that the effect of temperature on the activity of PbO 18 - Time in minutes Fig. 60 Rate curves for oxidation of graphite by Fb0-Si02 melts of different compositions. - 20 - Fig, 8. Dependence of the r a t e of oxidation of graphite on the 'square of the. a c t i v i t y of lead oxide. - 21 - TABLE II Effect of activity of lead oxide in the melt  on the rate of oxidation of graphite. Experimental temperature ~. 10.00°G„ 2 G.S.A. of graphite used in each experiment = 7.5 em. •Percentage Rate (R) x 10 4 by wt. of PbO N P b 0 a P b 0 a P b 0 (gmoC/cm /min0) in the melt. 77.0 0 .474 0„095 0o0090 l o 0 0 78 ,8 0.499 0.110 0,0121 1 063 81„0 0.535 0 o 1 4 0 0„0196 2„45 82,0 O 0551 0.155 0 O 0240 3ol3 8 3 . 0 . 0.567 0.170 0.0289 3»67 8 4 . 0 O0586 0„200 0o0400 4»80 8 5 . 0 0 .603 0.225 0„0506 60OO 8 6 . 0 0 .624 0 o 2 5 5 0„0650 7.90 is very small 0 However, assuming a linear relationship between the activity of PbO and temperature, the temperature coefficient of activity was obtained directly from the above two values. The corresponding activities for different experimental temperatures (varying from 96l°C to 1060°C) were obtained by interpolation (given in column 4* Table III), Knowing the experimental reaction rates and the activities, the values of k for different experimental temperatures were calculated from equation (3)o The value of the experimental activation energy was calculated by plotting the values of log q nk against the reciprocal of absolute temperature - 22 - TABLE III Effect of temperature on the rate of  oxidation of graphite, 2 .'G.'S.'A, of graphite used in each experiment -"7,0 cm Percentage of PbO by weight in melt =» 78,8, Experimental temperature in K° (T) 1 x 10 3 T°K Rate (R) x 10^ (gm, C/cm2/min„) a Pb0 Experimental rate constant k x 1CT (gm, G/ em^ / min) -log 1 0k 1234 0,810 0,95 0,106 0,85 2,070 1255 0,797 1,27 0,108 1,09 1.963 1273 0,785 1,63 0,110 1,35 • 1,870 1316 0,760 2,48 0,114 1,91 1.719 1333 0,750 2,90 0,116 2.16 1,666 .. .. _ (l/T°K) and was found to be 33 * 2 kilocalories per mole. The results are summarised in.Figs, 9 and 10 and Table III, (B) Oxidation of Carbon (l) Oxidation rate as a function of G,S,A, of .carbon. Special carbon spectroscopic electrodes were machined to different 2 sizes whose G.S„A„ varied from 5.1 to 12,7 cm , Utilising these carbon specimens, the amounts of carbon oxidized per minute by a lead oxide-silica melt (containing 78,8% of PbO by weight) at 1000°C were determined and found to be directly proportional to the"G.S,A. of carbon. The results are given in Figso-11 and 12 and Table IV, The rate of oxidation of carbon in the above melt at 1000°C was found to be 1,17 x 10"^ gm.C/cm /min., Time i n minutes F i g . 9. Rate curves f o r oxidation of graphite at d i f f e r e n t experimental temperatures. - 2 5 0 5 10 15 20 25 30 3 5 40 45 50 Time in minutes Fig» H p Rate curves for oxidation of carbon having different geometric surface areas„ 1 - 27 - TABLE IV Effect of geometric surface area of  carbon on the rate of .oxidation,, "Experimental temperature = 1000°C Percentage of PbO by weight in the melt = 78„8 GoSoAo of carbon in cm (gram of C oxidized per piece per minute) x 10-3 Rate of oxidation (R) x 104 (gm. C/cm^ /min „•) 5.1 0o60 1.17 7.5 0.82 1.10 0.95 1.07 9.9 1.18 1.19 12,7 1.36 1.07 J (2) Effect of composition of lead oxide-silica melt on the rate of  oxidation. The rates of oxidation of carbon (using specimens of 7<>0 cm2 of G . S . A . ) at 1000°C were determined for lead oxide-silica melts of different compositions. The composition of lead oxide in the melt varied from 77 to 86 percent by weight.. The results of these experiments showed that the rate of oxidation was proportional to the square of the activity of lead oxide in the melt. The experimental results are summarised in Figs. 13 and 14 and Table V. (3) Determination of the experimental activation energy of the' oxidation  of carbon. The study of the oxidation of carbon in lead oxide-silica melt (containing 78.8% of PbO by weight).at different experimental temperatures 28 Time in minutes Fig. 13, Rate curves of oxidation of carbon by Fb0-Si0 2 melts of different compositions„ - 29 - 30 - - . - TABLE V Effect, of activity of lead oxide in the melt on the rate of.oxidation of carbon, Experimental" temperature = 1000°C „..""' G.S.A. of carbon used for each experiment = 7<>0 cm' Percentage of PbO (by weight) in the melt NPb0 aPb0 aPb0 Rate of oxidation (R) x 10^ (gm„C/cm2/min.) 77.0 0.474 0.095 0.0090 0.79 78.8 0 . 4 9 9 0.110 0.0121 1.17 81.0 0.535 0 . 1 4 0 0.0196 1.84 82 00 0.551 0.155 0.0240 83.0 0 . 5 6 7 0 . 1 7 0 0.0289 2 . 9 0 84.0 0.586 0'„200 0 . 0 4 0 0 3.68 85.0 0.603 0.225 0.0506 4 . 7 6 86,0 0 . 6 2 4 0 . 2 5 5 0.0650 5.85 (varying from 958°C to 1063°C) by using carbon specimens of 7.0 cm of G„S 0A., was undertaken. From the reaction rate values of experimental rate constants 8k' were calculated as mentioned i n the case of graphite. Then by plotting l o g i o k against 1/T°K, the experimental activation energy was determined as 22 ~ 2 kilocalories per mole. The experimental results are summarised i n Figs. 15 and 16 and Table VI, (C) Oxidation of Petroleum Coke Mixture (Baked at 900°C) Unlike the oxidation of graphite and carbon, the rate of oxidation of petroleum coke showed a gradual departure from the linear relationship with the reaction time after a few minutes. For example, the amount of carbon oxidized after 22 minutes of reaction from a piece of petroleum coke of 7,5 cm" of G.S.A, by a melt (containing 78.8% of PbO by weight) at 1000°C was - 31 - 0- 5 10 15 20 25 30 35 40 45 50 Time i n minutes F i g . 15. Rate curves f o r the oxidation of carbon at d i f f e r e n t experimental temperatures. - 32 -- 33 - TABLE VI Effect of temperature on the rate of oxidation of carbon G.S.A. of carbon used for. each experiment'-^ 7,0 cm2. Percentage of PbO by weight in the melt = 78.8 Expt51 temp0 in K° • (T) 3 1 x 10 T°K Rate of reaction (R) x 1Q4 (gm.C/cm^ /min,) aPb0 Experimental rate constant (k) x 102 (gm„ C/cm^ /min,) -log 1 0k 1231 0.813 0.79 0,106 o„7l 2.152 1253 0.798 1.01 0,108 0,87 2,061 1271 0,787 1.17 0.110 0.97 2.014 1293 0,773 1.39 0,112 1.11 1.955 1315 0,760 1,63 0,114 1,25 1.903 1336 0.748 1.97 0,116 1.47 1.833 28.0 x 10°^ instead of 26.5 x.10"-^ gram of carbon. This might be due to an increase in roughness of petroleum coke during the oxidation process. In order to avoid this error in the calculation of the. rate of oxidation, only a few i n i t i a l readings in an experimental run were considered, (1) Relation of G.S.A. of petroleum coke with the rate of oxidation. Samples of petroleum coke were machined to different diameters and different sizes,. Each piece had a uniform diameter within ±0,004°c. The G.S.A, of specimens used in the experiments varied from 5.9 cnr to 12.7 cm . The oxidation of these specimens by a lead oxide-silica melt (containing 78.8% of PbO by weight) at 1000°C showed that the amount of carbon oxidized per unit time was directly proportional to the geometric surface area. The results are summarised in Figs, 17 and 18 and in Table VII. The rate of oxidation at the above temperature and slag composition was found to be 1,6 x 10"^ gm'.G/cm /min... '>.: , - 34 - Time in minutes Fig. 17. Rate curves for oxidation of petroleum coke having different geometric surface areas. - 36 - TABLE VII Effect of geometric surface area of petroleum  coke on the rate of oxldatiorio Experimen1»£temperature = 1000°C„ Percentage of PbO by weight in the melt = 78„8 G.S.A. of petroleum coke mixture (baked at 900°C) (in cm2) 9o9 7.5 5.9 (gram of C oxidized per piece per min. ) x 103 0o86 I.46 1.19 Rate of oxidation (R) x 10^ (gm0C/cm2/min„) 1.59 1.46 1.49 12.7 I.65 1.30 (2) Effect of the composition of lead oxide-silica melt on the rate of oxidation. The study of the oxidation of petroleum coke at 1000°C using 2 specimens of 7.5 cm of G.S.A. by lead oxide-silica melts whose composition varied from 78.8 to 85.0% of PbO by weight, was undertaken. The experimental results showed that the rate of reaction was proportional to the square of the activity of lead oxide in the melt. The results are given in Figs. 19 and 20 and Table VIII. (3) Determination of experimental activation energy of the oxidation  of petroleum coke. The rates of oxidation of petroleum coke by lead oxide-silica melt (containing 78.8% of PbO by weight) using specimens of 7.5 cm of G<,SoA00 were measured"for a number of temperatures varying from 980°C to 1065°C0 The experimental rate constant «k°(gm.C/cm2/min.) at different experimental temperatures were calculated as before. Then by plotting log-j^k against 1/T°K - 37 - 5 10 15 20 25 Time in minutes Fig. 19, Rate curves for oxidation pf petroleum coke by PbO-Si02 melts of different compositions. 38 Fig, 2 0 , Dependence of the rate of oxidation of petroleum coke on the square of the activity of lead oxide ih the melt. TABLE VIII Effect of activity of lead oxide in the melt on the  rate of oxidation of petroleum coke. Experimental temperature = 1000°C G.S.A. of petroleum coke used in each experiment = 7.5 cm" Percentage of PbO by weight in the melt. %b0 aPb0 2 aPb0 -Ratenof .oxidation""• (R) x 10^ (gm„G/cm2/min.) 78.8 0.499 0.110 0.0121 1.59 81.0 0.535 0.140 0.0196 2.36 82.0 0.551 0.155 0.0240 2.91 83.0 0.567 0.170 0.0289 3.50 84.0 0.586 0.200 0.0400 4.45 85.0 0.603 0.225 0.0506 5.98 the value of experimental activation energy was determined and was found to be 28 ± 2 kilocalories per mole. _ The experimental results are summarised in Figs 0 21 and 22 and Table IX. O' 5 .10 15 20 25 30 Time in minutes Figo 210 Rate curves for the oxidation of petroleum coke at different experimental temperatures,, 0.74 0.76 0.78 0.80 0.82 1 x 10 3 T°K F i g . 22. Logigk vs 1 f o r the oxidation of T°K petroleum coke. TABLE IX Effect of temperature on the rate of oxidation of petroleum coke. G.S.A. of petroleum coke used in each experiment ~ 7.5 cm' Percentage of PbO by weight in the melt = 78.8. Experimental temperature in K° (T) 1 xlO 3 T°K Reaction rate (R) x 104 (gm. C/ cm2/ min) Activity of lead oxide (aPbo) Experimental rate constant: k x 10 2 (gm.C/cm2/min) -log 1 0k 1253 0.798 1.22 0.108 1.04 1.983 1273 0.785 1.59 0.110 1.31 1.883 1295 0.772 2.01 0.112 1.61 1.793 1314 0.761 2.40 0.114 1.85 1.733 1338 0.747 3.00 0.117 2.19 1.660 - 43 - DISCUSSION From the study of the kinetics of the oxidation of graphite, carbon and petroleum coke by lead oxide-silica melts, i t was found that the amount of carbon oxidized per unit time was proportional to the geometric surface area of the carbon sample and the rate of oxidation of lead oxide in the melt. The pressure of oxygen in the melt obtained from the dissociation of lead oxide was proportional to the square of the activity of lead oxide in the melt. Therefore, in every case the rate of oxidation was directly proportional to the oxygen pressure of the melt. The rate equation for a l l cases investigated can be expressed by a general equation: R(gm.C/cm^ /min) = k.a^^ .(3) where ap^ Q. I s the activity of lead oxide in the melt and k is the experimental rate constant. The values of k(gm.C/cm /min) for graphite, petroleum coke and carbon at 1000°C were found to be 1.35 x IO*"2, .1.31 x 10"2 and 0.97 x 10~2 respecitvely (given in column 5, Table X). The experimental activation energy (E) values are given in column 6, Table X. This shows a range of values from graphite (33 * 2 kilocalories per mole), petroleum coke (28 ± 2 kilocalories per mole) and carbon (22 ± 2 kilo- calories per mole). As anticipated in the introduction, this characteristic gradation in the magnitude of E was expected because of the different -heat I treatment temperatures applied at the time of their manufacture. From the above experimental rate constant values 'k*, i t is observed TABLE X Summary of the "results» (Results at 1 0 0 0 °C) Percentage Type of Reaction Activity Experimental of PbO by carbon rate of PbO rate constant: weight in used for ^ (R) x 1 0 J in the k x If}2 the melt. oxidation (gm0C/cm /min) melt, (gm.C/cm /min) After intro ducing S.R. factor.j Experimental Reaction activation rate (/t) energy x 1017 (kilocalories (atoms . . the value of per mole) C/cm /sec) /% x 10^5 (atoms C/cm2/sec) 7 8 . 8 7 8 . 8 graphite petroleum coke mix (baked at . 900°C) 1.63 1 .59 0 .110 0 .110 1.35 1 .31 33 ± 2 28 ± 2 1 . 4 1 .3 1 .4 7 8 . 8 Carbon 1 . 1 7 0 . 1 1 0 0 . 9 7 22 ± 2 1 .0 1 I - 45 - that the magnitude of k for graphite is nearly equal to that of petroleum -2 coke and is higher by 0.4 x 10 than that of carbon,, However, the experi mental activation energy of the oxidation of graphite is greater than those of the other two. This might be due to one or both of the following factors; (i) the surface roughness factor (i.e., the ratio of the real surface area to the geometric surface area) was not the same in a l l three types of carbon; (ii) the activation entropy change involved in the oxidation process was not identical in a l l three cases, 27 Gulbransen and Andrew determined the surface roughness of graphite using the adsorption of krypton vapour at liquid nitrogen temperature following the modified B,E«T, method. They found the surface roughness factor 2 for graphite was of the order of 10 . In the present study the reactant is in the liquid state and because of the surface tension effects, the effective surface will probably be less than one hundred times the geometric surface area. Thus the true rate could be slower than the experimental value by less 2 than 10 o From the experimental results obtained in a l l cases, i t appears that the reactant species in the melt contains oxygen atoms associated with two molecules of lead oxide. This may be inferred from the observation that in a l l cases the rate of oxidation was proportional to the square of the activity of lead oxide in the melt, i.e., was directly proportional to the equilibrium pressure of oxygen in the melt. In addition to this, i t was also found that in a l l cases the product gas was carbon dioxide. Therefore the stoichiometry of the reaction for the oxidation of carbon in lead oxide- silica melt can be written as 2 PbO + C — 2 Pb + C02. -•  46 If i t was assumed that oxidation of graphite by the oxygen obtained from the dissociation of lead oxide in the melt and that by gaseous oxygen were identical, the mobile adsorption of the activated complex should be a possible rate determining step as observed by Gulbransen.-' In Pb0-Si02 melt (containing 78.8 percent of PbO by weight) the reacting .oxygen/expressedd.. as oxygen pressure was calculated from the dissociation of lead oxide (given in Appendix » Expressing this pressure in terms of concentration of oxygen, the value was found to be 5,4 x 10^ molecules per cm3. Utilising this oxygen concentration and Gulbransen"s experimental activation energy (E - 36.7 kilo- calories per mole as compared to the value of 33 * 2 obtained from the present study) ..for the oxidation of graphite in gaseous oxygen, the reaction rate was calculated in the same way as done by the above author. The rate value was • found to be of the order of 10 atoms,C/cm /sec at 1000°C where as the experimental rate in the above melt at 1000°C was found to be of the order of 17 2 10 atomSoC/cm /sec (given in column 7, Table X). Taking the highest surface 27 2 roughness factor value (10 ) possible for this case, the experimental value reduced to the order of 10^ atoms.C/cm^/sec. Therefore the mechanism for the oxidation of graphite in Pb0-Si02 melt was not similar to that in the case of gaseous oxidation. The high difference in rate values of the oxidation of graphite in gaseous oxygen and in Pb0-Si02 melt might be due to the difference in character of the reactants as well as the activated complexes in the above two mediums, CONCLUSIONS 1 0 A study of the oxidation of graphite petroleum coke mixture (baked at 900°C) and carbon :by lead oxide-silica melts was undertaken at different temperatures. Experimental results showed that the amount of carbon - 47 - oxidized per unit time was proportional to the geometric surface area of the graphite, carbon or petroleum coke investigated. The rate of oxidation was found to be proportional to the square of the activity of lead oxide in the melt, or in other words, the rate was directly proportional to the equilibrium pressure of oxygen obtained from the dissociation of PbO in the melt. The. general rate equation can be expressed as R (gmoC/cm'ymin) = 2 k 0a where a_,, rt is the activity of lead oxide in the melt and k is the PbO PbO J experimental rate constant. The value of k is constant for a particular carbon. The values of k at 1000°C for graphite, petroleum coke and carbon were respectively 1.35 x 10 - 2, 1*31 xl©~ 2 and 0,97 x 10 - 2 gm.C/cnrVmin. ' 2. From the study of the rates of oxidation at different temperatures, i t was found that the experimental activation energy of the oxidation process was in the order of ^graphite^ ^petroleum coke^ ^carbon The activation energy values for graphite^ petroleum coke and carbon were respectively 33 * 2, 28 - 2 and 22 i 2 kilocalories per mole, 3o In a l l cases the product gas was carbon dioxide, 4o From the experimental results i t appears that the stoichiometry of the reaction of oxidation of carbon by lead oxide-silica melts can be written as 2 PbO + C -+ 2 Pb + C02, RECOMMENDATIONS 1. In order to determine the true values of the rate of oxidation of different types of carbon, i t is necessary to correct the rate values expressed in terms of geometric surface area for the surface roughness of the respective carbon0 As mentioned before the effective surface roughness factors of different types of carbon in lead oxide-silica melt are not known0 Thus methods for the measurement of the surface roughness factors of different types of carbon should be investigated, 2 0 From the present investigation i t was found that the rate of oxidation was proportional to the square of the activity of lead oxide (or directly proportional to the pressure of oxygen obtained from the dissociation of lead oxide) in the melt. It would be very interesting to study the oxidation of carbon by mixtures of different metal oxides in sil i c a melts. From this study i t could be determined whether the reaction rate is proportional to the sum of the pressures of oxygen obtained from the dissociation of different oxides in the melt. This work may give an idea about the oxidizing power of an unknown melt from the magnitude of the rate of oxidation of carbon in that melt0 - 49 - BIBLIOGRAPHY 1. Gadsby, J„, Hinshelwood, CN, and Sykes, K.W., Proc, Roy, Soc,, 187A«_ 129 (1946). 2. Langmuir, I,, J. Amer, Chem. Soc. 37, 1154 (1915). 3. Long, F.J, and Sykes, K.W., Proc. Roy. Soc. 193A, 337 (1948). 4« Gulbransen, E.A. and Andrews, K.F., J. Ind. Eng. Chem, 44> 1034 (1952). 5. Gulbransen, E.A., J. Ind. Eng. Chem. 4Jt, 1045 (1952). 6... Eyring, H., J, Chem. Physics, _3, 107 (1935); Chem. Rev., 17, 65 (1935); Trans. Faraday Soc, 34., 41,(1938). 7. Rhead, T.F.E. and Wheeler, R.V., J. Chem. Soc, 103. 461 (1913). 8. Arthur, J.R,, Trans. Farad. Soc, 4 7 , 164^(1951). 9. Arthur, J.R., Nature, 157, 732 (1946). 10. G i l l i l a n d , E.R., Lewis, W.K, and Paxton, R.R,, J. Ind. Eng. Chem., 46, No. 6, 1327 (1954). 11. Mertens, E., J. Chim. Pbys. 4 7 _ , 353 (1950), 12. Arthur,. J.R. and BpwringV J.R,,; J«. Chim. Phys. ^ , . 5 4 0 (1950). 13. Meyer, L. s .J. Chim. Phys. 328. (1950),, 14. Strickland-Constables, R.F., J. Chim. Phys. 4J7, 356 (1950). 15. Key - Publication G.R.B. 40 of the Gas Research Board, 1 Grosvenor Place, London, S.W, 1. This work was carried out in 1939-40. 16. Bonner, F0/ and Turkevich, J„, J. Amer. Chem. Soc 73, 561 (1951). 17. Broom, W.E.J., and Travers, M.W., Proc. Roy. Soc, 135A, 512 (1932). 18. Gadsby, J,, Long, F.J., Sleightholm, P. and Sykes, K.W,, Proc Roy, Soc., 193A, 357 (1948), 19. Gulbransen, E.A. and Andrew, K,F„, J, Ind, Eng. Chem. 4Jj., No.5, 1048 (1952) 20. Turnbull, J.D.S., M.A.Sc. thesis, submitted April 1958, Department of Mining and Metallurgy, University of British Columbia, 21. Riley, H,L,, J. Chim, Phys, /£, 565 (1950), 22. Schaeffer, W.D., Smith, W.R, and Polley, M„H„, J. Ind. Eng, Chem, _4j>, 1721 (1953), - 50 - Bibliography (cont'd.) 23. Proceedings of the First and Second Conferences on Carbon, University of Buffalo, (1953-55). 24. Sebastian, J.J.S. and Mayers, M.A., J. Ind. Eng. Chem, 29, No. 10, 1118 (1937). 25. Geller, R.F„, Creamer, A.S. and Bunting, E.N., F„ Res. Nat. Bur:„ Stand., 22J 237 (1934). 26. Richardson, F.D. and Webb, L,E., Trans. Inst. Mining and Met. 6L±9 529 (1955). 27. Gulbransen, E.A. and Andrew, K.F., J. Ind. Eng. Chem, 44, 1°39 (1952). 28. Thompson, deKay Maurice, "The Total and Free Energies of Formation of the Oxides of Thirty-two Metals.!' Published by The Electrochemical Society, Inc., New York, 1942. APPENDIX Calculation of Oxygen Pressure of Lead Oxide-Silica Melt, 28 The standard free energy ^>F° of the reaction Fb(£) + 1/2 0 2 s=i PbO(£) is -22,900 calories at 1000°C„ The equilibrium constant °K' of this reaction is K = a F b 0 = apbQ apb x p 1/ 2 p 1/ 2 ° 2 0 2 as the activity of lead is equal to 1„ The value of K obtained from the value of is 1015 x KA. or K2 « (1.15 x 104) 2 = a p b o The activity of lead oxide in a lead oxide-silica melt (containing 78.8% of lead oxide by weight) is 0.110 at 1000°C. p Substituting the value of a^^ ^ n ^he above equation, the value of p was found to be 9.3 x 10~-L1atmosphere at 1000°C. Converting this oxygen pressure to concentration units at this temperature, the concentration of oxygen (Cg) was found to be 8 5.4 x 10 molecules/cc. 

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