On the kinetics of oxidation of graphite

Carbon

1964, Vol. 2, pp. 281-297,

Pergamon Press Ltd.

Printed in Great Britain

ON THE KINETICS Of; OXIDATION

OF GRAPHITE

J. N. ONG, Jr. Materials Sciences Laboratory,

Lockheed Missiles and Space Company,

Palo Alto, California

(Receioed 5 May 1964) Abstract-The

kinetics of the graphite-oxygen

system have been examined with respect to two primary

reactions, C+ Os(g)=COa(g) and 2Cf Oz(g)=XO(g), and one secondary reaction, C-j- CO&)= 2COcg). Adsorbed molecular oxygen (C . . 02). atomic oxvaen CC.. 0) and carbon dioxide CC.. CO2) ._I

have been assumed as intermediate species from which se;en thermochemically and kinetically con: &tent processes have been proposed. Categorization of the proposed kinetic scheme has been made with respect to simultaneous or consecutive formation of products, successive and competitive processes, open and closed systems, high and low temperatures, reversible and irreversible behavior, reversible behavior of the first and second kinds, mechanism and molecularity. Under the restriction of stationary-state conditions and other limiting conditions, both high- and low-temperature and highand low-pressure experimental results are rationalized with respect to temperature and pressure dependencies on rates, orders of reaction, and the sensitivity of the rates to the flow of gases. 1. INTRODUCTION do not give rise to well-behaved Arrhenius plots.(s~Il*ra) At 10-w pressures, the two-step effect ALTHOUGHan extensive amount of work has been is absent but the rate exhibits a maximum with done on the oxidation of carbon and of graphite in its various forms, a fully comprehensive explanation of the kinetic behavior of the C-02 system TEMPERATURE (OKi has not as yet been proposed. Some of the complications encountered in performing an analysis are noted below. Graphite exists in a variety of forms, whose properties are highly dependent upon methods of preparation. In general, there exist, from one manufacturer and grade to another, differences in microstructure, porosity, pore size, crystallite size, degree of graphitization, orientation, impurity content and surface area.(l) Both COs and CO are simultaneously formed as reaction products. Broadly speaking, the CO/COs ratio is less than unity at high pressures and low tempera~res, (*-@and greater than unity at low pressures and high temperatures.(7-s) Marked differences in kinetic behavior are exhibited at low temperatures, compared with high temperatures, an example of which is shown in Fig. 1. The data of OKA~A and IKEGAWA~~) on “artificial graphite” in air from 923 to 2273°K show a marked nonlinearity of the Arrhsnius plot. Similar results have also been reported by GOLOVINA and &IAuSTOVITCH(~) on “carbon”. SignifiFrc. 1. Arrhenius plot of experimental data of Okada cantly, many of the data reported in this range, and Ikegawa at a pressure of 0.21 atm 0s. Comparison while not exhibiting this effect as dramatically, with calcuiated curves is also shown.

281

282

J. N. ONG,

3000 10-7

2250 1600 1500 2500 , 2000, I 1600,140O I ,

SLOPE

T-’

FIG.

1300 : 1200

1100 j 1000

= 46.500

*K I

X 103(‘K!-’

Arrhenius plot of low pressure (lo+ atm) oxidation rates of carbon, interpolated from data of Duval. 2.

to temperature.(8,g*13-17) The data of DwAL(g) on “graphitized” and “nongraphitized” carbon at a pressure of 10-s atm pressure of oxygen are plotted in Fig. 2. The pressure dependency on the rate observed by DWAL was approximately PI/s at llOO”K, Pl at 1200°K and PWS from 1300 to 2000°K. Carbon monoxide has been reported to be the predominant species at these pressures.(sJ*) The reactions exhibit a marked sensitivity to the flow of gases. KHITRIN”~) and others~s~ss~sl~ss) attribute the change in slopes of the Arrhenius plots to a transition from surface-controlled processes at low temperature to bulk gas diffusion controlled processes at high temperatures. NAGLE and STRICKLAND-CONSTABLE,(12) on the other hand, have shown that, whereas these reactions were flow sensitive, their “reactor grade graphite” reacted nine times faster then their “pyrographite” under comparable temperatures (1973°K) and gas flow rates. The present article represents an attempt to correlate many of the existing data by presenting respect

JR.

a comprehensive characterization of a proposed kinetic scheme. Although the various grades of graphite exhibit many differences, they also exhibit many similarities, and it is precisely these similarities that will be emphasized in this treatment. In particular, the thermochemical properties of the gas given by the chemical potential, and the dissociation energy of the gas molecule, will remain unchanged regardless of the nature of the solid. In addition, the chemical potential and bond energies of graphite will characterize the thermochemical properties of graphite, and differences between grades should be in degree only and are probably most sensitive to impurity content and degree of graphitization. Lastly, the chemical potential of adsorbed species and the energies of adsorption will characterize the thermochemical

properties of adsorbed species. Depending upon impurity content, these also may be expected to exhibit minor differences between grades. In brief, categorization will be made with respect to primary and secondary reactions, the temporal sequence of formation of products (simultaneous and consecutive) the number of intermediate species (adsorbed molecular and atomic oxygen and adsorbed carbon dioxide), the number and type of processes (successive and competitive), the molecularity, the mechanisms, the system (open and closed), the temperature (high and low), the reversibility (irreversible and reversible), and the kinds of reversible behavior (first and second kinds). When the limiting conditions of the scheme are systematically examined, the high-pressure behavior (e.g. OKADAand IKEGAWA),the low-pressure behavior (e.g. DWAL), and the flow-sensitivity effects are adequately accounted for. The model selected entails only one type of surface graphite site and thus differ8 basically from the scheme proposed by BLYHOLDER, BINFORD and EYRING.~~) Since we will be discussing three reactions involving seven processes under three limiting conditions, we have designated the reactions as (A), (B) and (C); the processes as Pl, P2, etc.;

and the equations pertaining cases as a, /I and y.

to the three special

2. ANALYSIS The basic chemistry of the C-OS reaction generally considered to be the following:(ss’

is

ON THE

Primary reactions 2C+O&7)%2CO(g) C+COs(g)%2CO(g)

KINETICS

OF OXIDATION

C+Os(g)~C0s(g) (A) and (B). Secondary reactions (C) and 2CO(g)+Oz(g)%

2COz(g) (D). Reactions (A) and (B) occur simultaneously, while reactions (A) and (C), and (B) and (D) may occur consecutively. From the point of view of carbon consumption, the amount consumed by reaction (C) can never exceed that of reaction (A) and may in fact be considerably less under certain kinetic conditions. To a first approximation then, reaction (C) will be neglected except to recognize that measured rates of consumption of carbon may correspond to consumption of carbon by reaction (A) to within only a factor of + to 1. Also from the point of view of carbon consumption, reaction (D) is uninteresting and will not be considered further. A more complete discussion of the secondary reactions and their influence is deferred to a later section. 2.1 Kinetic scheme To correlate much of the existing experimental information, we propose that the rates of formation of COs and CO involve only one type of site on the carbon surface, according to the following scheme. For CO2 formation, klf P

CfOs(g)

c.

.02

(P-1)

ha

c.

.03

kZf F?

co2(g)+cc

(P-2)

klf P c. .02 klb

(P-1)

km

and for CO formation,

c+os(g)

CfC.

.02

k3f 8 2c.

.o

ksb

(P-3)

k4f

2c.

.o 8 2co(g)+2& k4b

The C’s represent surface carbon and C. .O represent chemisorbed

(P-4) atoms; C. . Cl2 molecular and

OF GRAPHITE

283

atomic oxygen, respectively, and kv and ktb represent the respective forward and backward rate constants for the designated processes. For kinetic consistency, it is necessary in these equations to include Ze, which represents a site on the graphite surface from which a carbon atom has been removed. Table 1 represents a possible kinetic characterization of the scheme presented. A process involves intermediate species (C. . 0s and C. . 0), whereas a reaction involves only reactants and products (02, C, CO2 and CO). The processes are both chemically and thermochemically additive to form reactions; thus, Pl+P2=A, and Pl+P3+P4=B. The terms successive and competitive are used in connection with processes, and the terms simultaneous and consecutive are used in connection with Thus, for example, in Table 1 the reactions. notation “succ/lf” in connection with process 2f is to be read “P2f successive to Plf” and “comp/;?flC. . 0s” for P3f is to be read “P3f competitive with P2f for the species C. .Os”. Likewise, under the heading Reaction Class, “simult/CO/B” is to be read “the formation of COs occurs simultaneously with the formation of CO by reaction B”. Before general rate equations can be formulated the system for which the equations are to pertain must be specified. Two common systems are normally used: open and closed. We will have occasion to consider both. The principal difference between the two is this: when gaseous products are formed in a closed system and the backward rate is greater than the forward rate, consumption of reactant will tend to become depressed, whereas, in an open system, consumption of reactants may still proceed since the gaseous products are being continuously removed by gas transport from the reaction site.(23,24’ Because large entropy changes accompany these processes, both forward and backward rates should initially be considered as kinetic possibilities. In a closed system, the forward and backward rates for each process are as designated in Table 1. In the open system, P2 and P4, both of which form gaseous products, should both proceed in the forward direction only. As we show in the next section, P2 exhibits no thermochemical tendency to proceed in the backward direction, so that the form of the rate equation for vsf is the same for

284

J. N. ONG,

TABLE 1.

PROPOSED

KINETIC

CHARACTJJRIZATION

OF

c-02

MOLLXXLARITY

No.

Reaction or Process reactants-+products

lf

CfOz(g)+C.

lb

c.

2f

c. . Oa+COa(g)+

3f

c. .os+c+2c.

Reaction class and process designation

.o‘a

Primary

comp/lf/C.

.Oa+C+Oa(g) z .o

JR.

SYSTBM AND

WITH

RESPECT

TO

Rate equation

Molecularity

o1a=k1&.

.Oal

succ/lf

tq=ky[C.

.021

succ/l f

7J3f=k3frC.

.021~1Cl

comp/2f/C. .02

::f=k’3,[C. .Oz][C] 4f

2c.

.0+2CO(g)+

2z

succ/3f

4b

ZCO(g)+

A B

C+Oa(g)zCOa(g) 2c+oz(g)?+2co(g)

2L&2C.

.0

comp/4f/C.

zI4fr= 2RmcAK01 .0

~4 b = 2k4 b[CO]

[&I

simult/CO/B simult/COs/A

both the open and the closed system. However, P4 will exhibit a thermochemical tendency to proceed in either direction, depending on the temperature. In the irreversible case (forward tendency) the rate equation for v4f will be the same for both the open and the closed system, while in the reversible case (backward tendency) the rate equation for the open system will be v4f=&A[CO], where K,t is a mass transfer coefficient and A[CO] is the concentration difference between CO existing at the immediate vicinity of the surface and the surroundings (free stream). In general, the basic rates (to be distinguished from the working rates) off and v(b refer to the rates of formation of products as designated in Table 1 for their respective processes and are defined as d(n/A)/dt, where 12 is molecules, A is the true area over which the reaction proceeds (ems), and t is time (set). The surface concentrations [Cl, [C. . Os] and [C. .O] have dimensions sites or molecules per cm2 and the gas concentration, [Os], molecules per cm3. For P3f we have suggested a LangmuirHinshelwood mechanism (termolecular oxygen dissociation); however, a bimolecular oxygen

dissociation

Suggested mechanism

Bimolecular 0s dissociation Activated decomposition Gas phase transport Nonactivated adsorption

w4j<=Zk4f[C. .O]

succ/3f

PR-,

SYSTBM,

Remarks

Nonactivated adsorption Nonactivated adsorption Activated desorption Activated decomposition Termolecular Oa dissociation

olf=k’YrCl[oal or Vlf=Klf[clPos .02

REACTION,

MECHANISM

mechanism

v4fr

applicable for open systems in lieu of v4* for closed systems

may not be excluded as a

possibility at this point. For purposes of determining molecularity, either occupied or unoccupied surface sites are considered to be “molecules”. As will he shown later, the dependence of the concentrations [C. . 021 and [C . . 0] on the oxygen concentration [Os] or oxygen pressure P is not simple and is dependent upon both temperature and the predominant rate-controlling process. For this reason, the concept of order is of limited utility in gas-solid reactions and will not be employed. In fact, the elementary process Plf is the only one which is truly first order with respect to [Os]. All the other processes are kinetically complex. 2.2 Thermochemistry Before pursuing the kinetics in further detail, the use of the terms reversible and high temperature in connection with the thermochemistry of the proposed processes will he discussed. The individual processes must be thermochemically additive and equal to the overall thermochemistry of the reactions. Figures 3 and 4 are plots of the standard chemical potential A$ versus temperature T for

ON THE

KINETICS

OF OXIDATION

the proposed C-02 processes and reactions. Note that Pl+P2=A, and that Pl+P3+P4=B. With regard to the slope of the lines, it is sufficient for the moment to note that they are determined approximately by the negative change in the number of moles of gas (in turn proportional to the entropy change) between reactants and products, An; thus, for P2 and B(An=+l), the slopes are equal and negative; the slope of P4(An=+2) is twice that of P2 and B; the slope of Pl(An=-1) is equal and opposite to that of P2 and B; and the slopes of P3 and A(An=O) are approximately zero.

I .,’ <’

60,000 (Pl)

iz d

c+02

(g) --c

02

40.000

i

5

/

28.5

OF GRAPHITE

“any temperature at which entropy differences play a significant role in determining the reaction equilibria of interest”, we will refer to high temperature as “any temperature above which A$ changes sign”. From Figs. 3 and 4, we see then that Pl is at a high temperature above about 1500°K and P4 is at a high temperature above about 450°K. One immediate consequence of the foregoing is that the rate equation for P4f in the open system case will have the open system form at low temperatures (denoted by 4fr in Table 1) and the closed system form at high temperatures (denoted by 4fi in Table 1). We will refer to the change in rate equation for process 4f, for example, in going from high temperature to low temperature as a change to newersible behavior of the jirst kind. Reversible behavior of the second kind may be said to be exhibited by those processes whose rate equations remain basically unchanged but whose expressions for the concentrations will be different at low temperature compared with high temperature. The precise form of these expressions for concentrations will dU,OOU

1 ,’ (Pll

C102(g)=

c .02

,;

60,000 l/2 (Pl + P3) c t l/2 O*(g)

iz d

/

20,000

\

I

\

i’

--__

/

5

TEMPERATURE, FIG.

T!“K)

3. Plot of standard chemical potentials, Ape vs. T for reaction A and processes 1 and 2.

At a pressure of 1 atm, A$ may be taken as a measure of the direction in which a reaction will tend to proceed. Thus, if it is assumed that P4 is endothermic, as indicated in Fig. 4, the species C 0 will tend to exist as a stable surface oxide at low temperatures (A$>O) and will tend to decompose to CO(g) at higher temperatures. For kinetic purposes, we will refer to processes and reactions having A@ > 0 as reversible and to those having A$ < 0 as irrmersible. In addition, followwho defines high temperature as ing SEARCYcz5’

..

i (

/’

;J’.

-60,000

‘x,,

5

-80.000

7:’

8 3

-100,000

z &

-120,000

5

i:

/’

“1

/ /

______..

!

(P3)C.O2+C=2C -40,000

.I

,’

,v

\

0

,’

,.’

‘\

a-1

& a 2

om-

40,000

5 i 1

t

\ =c

,--(P4)

2c

o---2

0

CO(g)

,*’

-

(E) 2c+o*(g)

=2CO(g)

‘A

-140,000

-160,000--

300

-~ ~~ L. .L_lFo6_1 900 TEMPERATURE,

:_(oo-~--J 2700 T(“K)

FIG. 4. Plot of standard chemical potentials, Ap“, vs. T for reaction B and processes 1, 3 and 4. Also plotted is Ape for C+ $Os = C. .O, denoted J(Pl+P3), used in discussion of case CL

286

J. N. ONG,

depend on further assumptions regarding the bate-control~ng processes, on the nature of the system, and on the temperature. The particular values for the energies and entropies assigned to the standard chemical potentials for the individual processes have been determined from the kinetic analysis to be described in the next section. For the present, it is sufficient to note that Pl and P3 have been found to be exothermic. Pl is less exothermic than the overall reaction A, so that beeause of the requirement that Pl -j-E?= A, P2 will also be exothermic and kinetically irreversible at all temperatures. Thus, a reversible form of rates vQf and VZ~ will not be applicable. Similarly, if Pl is more exothermic than B and since Pl+P3+P4=B, then P4 must be endothermic as originally assumed. This is consistent with the well-known fact that stable surface oxides of carbon are known to exist at low temperatures. MUD) An interesting point to be made in connection with reaction B is that even though this reaction is thermodynamically irreversible under all conditions, P4 will exhibit both irreversible (at high temperatures) and reversible (at low temperatures} kinetic behavior. This discussion is admittedly academic since this rate will be infinitesimally small at around 500°K. However, a similar discussion will be employed in connection with the C--C@, reaction in which a high temperature for one of the processes will be in the vicinity of 1700°K. The use of the terms rmersible, ~~~~~~~~~, Zgh tempevatzlre and low ttmperatzlre in terms of A#’ is strictly accurate only at pressures of 1 atm. At pressures other than atmospheric, the transition from one type of behavior to another will occur at different temperatures. 2.3 Special cases of Kinetic scheme The simultaneous formation of COQ and CO by primary reactions (A) and (B) can occur under several limiting conditions, the three most important of which are considered below. We restrict the formulation of the rate equations to the open-system stationary-state caSe (d[C . ,011 dt=d[C. . 02]/db=0.) (a) Case cx(vlf> u2f and vlf> mf < EJS~). In this case, neither the formation rate of C. . OQ nor C. . 0 is rate controlling so that wcoa and ace, the rates of formation of CUQ and CO, will be given

JR.

by the rates af decomposition species according to

of the adsorbed

and wco=2u4f=2k&

+. 01,X

e-21

The subscript M distinguishes the expressions for the concentrations from those pertaining to the other cases which will, in general, be different. (b) Case /I (zllf> af and uu> z~af< zrqf). In this case, the rate of formation of C ..O, zr3f,will govern ~co so that the rates of COs and CO formation may be represented by

and ele*=2VQf=2k&C.

. o,]z&]@

IS-21

where the subscript p will, as before, distinguish the expressions for the concentrations from other cases. (c) Case y (v~~
and

~cclz=e)lf[~zfi(~2f+2~3~)] ~~0=2vlf[2v3,f{~2~2~3~)]

(Y-1) (Y-2)

If the rate is expressed in terms of oxygen consumption cue%, then the rate equation becomes simply : ~Og=wf

b-3)

Since the mechanism by which CO forms is at best bimolecular, it is likely that under these conditions ersf> oaf, so that in terms of carbon consumption the rate may be expressed by %!=fJlf

(P-4)

The particular forms that the rate equations will take under the conditions of cases ~1, fi and y will depend upon further assumptions regarding the kinetics and thermochemical behavior of the reacting system. Fur purposes of further development, we assume the following: (1) The transition state theory of kineties(QQ~sQ) is applicable, with rate constants being expressible

ON THE TABLB 2. TABLE Chemical Gaseous species fG=Ua, /Lo=@& kTh pc

p~=p”+

kTln

KINETICS

OF

OXIDATION

CO ur CC&)

[GJ

Surface graphite species [ C=C or ZC) ~,Z=@‘+ kT In xx &Y=pZO+ kT In [%I+ RT In [z] = @Y+

kT ln[Z]

Adsorbed species (AZ&. . 02, C . . 0 or C. . CO%) pA=pA*+ kTh xA f.LA =pA* - kT ln[rr& kT ln[A] = p.s”‘+ RT ln[Al Activated species (t) ~t=~~++ kT In x+ ~+=~r~-kTIn[nc]+kTtn~~]=~~~‘+kTInEI]

Standard states

{am+l

Pc=l

(cma~rnole~~le)

PGIkT (moleculesjcms)

dimensionless

xx=1

dimensionless (cm2~mofecule)

&x&=1 XA=l

(crn2/&~)

.a

& .09@2C.

dimensionless (cm2JmolecuIe)

WI

.a

atm

KINETICS Remarks

(a) Pressure f dependence o cl0 and p”‘ for z, R and t assumed negligible. (b) Relationship between atom fractions (xi) and concentrations assumed to be given by the same constant

[ncl; e.g.

XZEncl= rJJ1,

.%A[?&] = [Al and

+[4=C”rl.

KU and

%Z=I

287

IN c-0$j-c02

Diiensions of ew (#WY, or =P (LLr"'lW

in the general form ~~~=~~~~~)~~~=~~~~ exp -_IAg+r/KT>, where K is Boltzmann’s constant, h is Planck’s constant, Abler is the difference in standard chemicaf potential between the activated state and the reactant, and &t is an equilibrium constant. The particular form of &t will depend upon the molecularity, (2) All chemical species including the activated complex undergoing reaction behave ideally. For reference, the appropriate chemical potentials are listed in Table 2. (3) All species in stationary states arc in equilibrium with their reactants, so that kif/flKeb=Ka= exp -~A~~~~~~~, where & is an equilibrium constant and Apt0 is the change in standard chemical potential between the intermediate species and its reactants. We return now to a detaiied analysis of the individual cases. (ta) Case t(. Under the conditions assumed for this case (~rf> z/sfand QZ=- ztdf< ~sf and stationaryboth C. ,Oz and C..O are state conditions), assumed in equilibrium with their reactants. Consequently, we may write the equilibrium expressions from (P-l) and (P-3) and Table 1.

C-+c.

GRAPHlTE

OF CHEMICAL POTENTIALS OF SPECIES ENCOUNTERED

Potential

~z(g)+C~~.

OF


.ur=l x,=1

If (g-3) and (g-4) are subject to the condition that the sum of the concentration of sites with adsorbed moIecular oxygen, adsorbed atomic oxygen, and unoccupied sites is equal to the total concentration of available sites for adsorption, [nc] (sitesjcmZ), then [C. -~23+[C.-q+[q=f4

b-5)

By eliminating [C] and changing &, the concentration-dependent form, to Kl, the pressuredependent form, of the equilibrium constant, it can be shown that@s)

and

where XC. .O and xc. .az are the fractions of sites occupied by C. -0s and C. . 0, respectively. These equations may now be subsituted into (a-1) and (a-2), together with the appropriate unimotecular forms of the rate constants, to give the following rate equations for case CI:

J. N. ONG, JR.

288

w,,=2w+K4f+tc]

(ww>l’2

i l+(&&iP)11s+&P

1

(a-9) The particular forms of the K’s appearing in the above equations will depend upon additional assumptions concerning the details of the processes. From the assumption of ideality we may write (pOOa)total

=

(/foa)t

+

(po&

+

(/Jo&

+

(pode

+

where the subscripts t, r, w, e and o refer, respectively, to the translational, rotational, vibrational, electronic, and degeneracy contributions to For simplicity of notation, a combina(p002)tota1. tion of subscripts will be understood to represent a sum of terms. Thus, for example, ($‘o.&,,= The zero of energy is (~“oa)t+(~oz)r+(~Oa)o. chosen as a molecule at rest and the entropy as zero for a pure crystal at 0°K. We will assume that (1) Differences in chemical potential due to vibration (AB)~ of the surface sites either occupied (C. .Os, C. .O) or unoccupied (C, Z:,) or in activated states (C. . Ost, C. .O+) are negligible. (2) Only differences in electronic chemical potential, (A&, exist between reactant and activated state, so that (po&

changing temperature. The consequence of this will be that the expressions for [C. . 021. and [C. . 01, will assume different limiting forms at different temperatures. Three main regions may be identified: region (l), KlP>(KlK$‘)1/2 (Pl+P3 is at a high temperature relative to Pl); region (2), (KlK#)lI2>KlP (Pl is at a high temperature relative to Pl+P3); and region (3), K1P-c (KlK#)1/2 < 1 (both Pl and Pl+P3 are at a high temperature). The limiting forms for the concentration expressions for each region are given in Table 3. Also shown in the table are the slopes of the In xi vs. T-1 plots for C . . 0s and C. . 0 for each region. The variation of XC. oa and XC. . 0 as a function of temperature at a pressure of 1 atm is shown in Fig. 5. The transitions between regions are of particular interest. It is possible to show, for example, that at Tls, the temperature between regions 1 and 2, d(ln XC. .oz)/d(l/T) and are at a maximum at xc. .oa= d(ln XC. .o)/d(l/T) XC..o z 0.5,and KlP=(KlK3P)1/2. Similarly at T33, the temperature between regions 2 and 3,

TEMPERATURE (“K1

and Ap4ft=p4f’

-$c

. . o=@rft)s-(uc.

.o)e=Aufa+

(3) Upon adsorption, 0s is completely immobilized with respect to translation and rotation and also loses its degeneracy, so that Aur=Aulwhere Au1 is the energy of adsorption ~o&Yu* (4) When adsorbed molecular oxygen dissociates, its vibrational chemical potential is lost, so that for P3, A~s=A~s---(~o~)~ where Aus is the energy of adsorption. The equilibrium constants will now take the specific forms Kzft=exp-(Auzft/kT); Kdft=

exp-(A~~~t/~T);~~=~~p-[(Au~-(~oo~)~~wl~~)l ; K3=exp-[(Au3-(~t&/kT)] which may now be substituted into the rate equations (a-8) and (a-9). Because of the marked temperature dependence of A$1 in comparison with Ap’s (due to the immobilization of the gas in Pl), A$‘1 will change value relative to A$3 and relative to zero with

10-51 i 0.3

0.4

0.5

t 0.6

0.7

0.0

0.9

1.0

T-‘X103F’K)-’ FIG.

5.

Plot of xc. .os and xc. .o vs. l/T at a pressure of 1 atm for case a, using (a-6) and (a-7).

ON THE TABLE 3. LIMITING

KINETICS

OF OXIDATION

289

OF GRAPHITE

FORMS OF [C. .O& AND [C. . Ola FOR CASE a SHOWING THEIR TEMPERATURE AND PRESSURE DEPFNDENClES IN DIFFERENT TIXMPERATURJ!REGIONS

(All slopes were obtained by plots of ln(C. . Or& or ln(C. . O)b vs. T-1.

Values in brackets were obtained by analysis

of kinetic data.) Thermochemical conditions

Temperature Region

rc * . Oal,l -==xc

[%I

1

KlP= (KIKsP)~~~ > 1 KIP<(KIKzP)~I~

T== TIZ Tu.< T-c Taa T=

T23

T>

Tz3

(KlK3P)‘13= 1 KlP<(KlK3P)1f2<

(K1;23)‘I”

rc. .Ola -=xc.

Slope

. .0s

[WI

0

-

(K3/KlP)l12

(AuI- Aua)/2k

0.5 1

Slope

.o

-

(Aua- Au1)/2k r- 17,7OO(“K)l .

0

[+ 17,77O(“K)l K1P/2 1

KIP

(Kl&l~~

- Aur/k

- ( Aurf

[+ 39,50O(“K)l

d(ln XC. .d/d(l/T) is at amaximum

at xc. .ogO.5, and KlKsP= 1. Accordingly, if the two changes in slope of the Arrhenius plot of the graphite oxidation rate of Fig. 1 can be identified with Tl2 and T23 and furthermore if an estimate of A$ for oxygen at these two temperatures for both processes can be made, then the energies of reaction for Pl and P3 can be determined. Using the data of OKADAand IKEGAWA(~~) and GOLOVINA 120,000

-

___.___

__

(P5) C_tCO2(g)-- c .co2---; (Pa c .co2--c.

i

0 +co (g) ‘\

Au3)/2k

[+ 21 ,gOO(“K)l

and I(HAUSTOVITCH(2’ at a pressure of 0.21 atm of oxygen and estimating Tla=1225”K and Tas=1650”K, we calculate for Au1 at 298°K the value-78,410 Cal/mole and for Aua at 298°K the value-7990 Cal/mole. The value of Au3 obtained includes the vibrational energy of 02 and will change slightly with increasing temperature. These are the values that we have used in preparing Figs. 3, 4 and 6. The function -kTln(K~Ks)r/2=(A~“l+A$s)/2 has been included in Fig. 4 for comparison with -kTlnK~=A~~“~. For reference, the energies of reaction at 298”K, AuOass, calculated for each process (including both electronic and vibrational contributions), and the change in standard chemical potential assumed for each process have been tabulated in Table 4. The standard energy change A$aas for reactions (A), (B) and (C) have been taken from PITZER and BREWER.‘31) The standard chemical potential of the gas has been calculated by standard statistical methods from the formula(aa’

II” =-_In kT

II 1 2nmkT h2

313

kT-ln-$+g+ -7

In [l-exp-(Or/T)]--Inwe

:,

where 0,. = 8712IkT/hz and O,=hv/k=characteristic temperature for rotation and vibration, respectively me1 = degeneracy of the electronic ground state 0 = a symmetry number I = moment of inertia m = mass of the molecule = frequency of vibration V

yJ,\,,,,“‘I 300

1500 2100 TGVIPERATLJRE,T(“K)

2700

FK;. 6. Plot of standard chemical potentials, APO, vs. T for reaction C and processes 5, 6 and 7.

290

J. N. ONG,

Tam

4. s’,-mm

ASSUMED

DBTERMINBD

FOR

BY

EACH

KINETIC

PROCESS

AND

A$* Pl

c+ O&f

P2

C..Oa ~Oz(g)+Z;: c+ 02(g) tiCOz(g)+ & c+ 02(g) Hz. .Oa c. .02+c*2c. .o 2c..o ?+2CO(g)-t 2zc 2c+ 02(g) *2co(g)+ 2.G c+ COa(g)*C. . co2 c. .COs *c. .o+ CO(g) c..o rrCO(g)+ zz Cl- COao~2CO(g)+ xc

:* P3 P4 3 P5 P6 P7 c

zc.

.Oa

Am+ (pc. .o~)~-(~)~-(~‘c~)~,~

Auea+ Q.Pco&rpl+ &%&-4~o~)v-(~c)u

AM+

(p’co&v+ (~~,),-(~c),-(r’o~)truw (PC. .os)o-(~c)“-(~~‘os)tra,

ha+

2(@co)tru+

Au~A-I-

Am+

2Cpc. .ob-2(pch-(~odv

2(~&--2(~. .o)v 2(1~Cc)~-2(t~~)y-(~‘0s)trvo Aues+ Qc. .co~)v-(fl~)u-(~_t’cos)tr Auesf t/w. .o)v+ fp”cobw-(pc. .o& AM+ @ohm+ W&-+c. .o)v Auec+2(p0co)tw+ (~~~)"-(~~c)~-(~~co~)trv Az(~B+

2(p"co)tru+

The values used for oxygen are: 0,=2.07”K, Qv=2230*K, cr=2 and wel=3. It is instructive to note in Table 3 that all the high-temperature limiting forms for XC. .us and xo. .o, both with respect to each other and with respect to A$=O, are pressure sensitive, whereas the low-temperature forms are not. We see then that, in general, reversible behavior of the second kind is characterized by pressure sensitivity and by changes in slope of the Arrhenius plot. To this point we have considered only basic expressions for the rate. To convert to a working rate equation which is expressed in measurable quantities, we put A=A,rs and noM/iVO=rnc, where A as previously defined is the true area over which the reaction occurs (ems), A, is the geometric area (ems), Y is a roughness factor, s is an active site factor, no is molecules of carbon, M is molecular weight (gm~gm-moles, me is grams of carbon, and No is Avogadro’s number (molecules/mole). Subsitution of these expressions into the basic rate equation gives for the working rate equation the expression Rate=d(mcfd,)dt=(Mr~~~~)etc

(x-10)

In terms

of the rate of carbon consumption ex P ressed in terms of the working rate equation can be rearranged to give

(w=wo2),

(a-8)

Rate=d(mcjd,)dt=(Mr~~~~)(KT~~) =F

[PZ~]exp-

(A~zft~k~~c, -08 exp-(Ausft/kT)xc. .02 (u-11)

STANDARD

ENERGY

CHANC=

AT

ANALYSIS

Standard chemical potential change

Reaction or process

No.

(Aw)

CHEMXCAL POTENTIALS 298°K

JR.

Electronic energy change A UEZ

-78,410 - 15,600 -94,010 -78,410 - 5760 + 36,970 ~~~~~ + 87:OOO + 18,490 f 46,810

Standard energy change at 298°K

Au’m = Au& (Auvd -78,410 -15,640 -94,050 -78,410 7990 + 32,970 - 53,430 - 58,680 + 82,810 + 16,490 + 40,620

where F, the pre-exponential factor, is (~rsi~~) (kT~k)[~c~ (gm~cm2sec). Similarly, for the rate of carbon consumption by CO formation VC= oco, a comparable expression results: d(mcjA,)/dt=W

exp-(Au4ft[kZ’)xc.

.O (a-12)

The factor F in general will vary widely from one grade to another of commercial graphite, particularly owing to the roughness factor r, so that comparison and correlation of experimental data can be made only on a relative basis. HERZBERG, HERZFELDand TELLER(33’34) have pointed out that in the process of removal of atoms from the edge of a hexagonal graphite lattice, the removal of the first atom requires the breaking of two bonds, the secondatomone bond, the third two, the fourthone, etc. Kinetically this probably means that only the removal of the atom requiring the rupture of two bonds is rate limiting and that the other atom is removed instantly thereafter. The active site factor s is thus -&. The foregoing argument should apply to both COa and CO formation rates. When the experimental values for the activation energy Ausft and pre-exponential factor F are used in connection with derived values, experimental rate curves are adequately reproduced. Figure 1 shows the comparison between the calculated rate and the experimental rate of OKADA and IKEGAWA using the values listed in Table 5. It is interesting to note the change in slope predicted from the derived equations around 2150°K. This effect is

ON THE

KINETICS

OF OXIDATION

probably due to the change in chemical potential of vibration of molecular oxygen, which may be expected to become appreciable in the vicinity of TABLE 5. EXWRIMENTALLY ~~~1~~ ACTIVATION

ENERGIES

AND FOR

A\ut (cd/mole) ~(~~crnssec)

VALUES

PRE-EXPONENTIAL CASE

OF

FACTORS

CL

COs Formation

CO Formation

22,800 2.95 x 10’0

51,400 9.5 x 10s

OF GRAPHITE

of Fig. 6 cf DAY, WAKER and WRIGHT on “petroleum coke”, from which this energy is calculated to be 50,000 Cal/mole in the temperature range 1900 to 2300°K. (e) Case p. Under the conditions assumed for this case (vx~> osf and vrf> vsf< vdf), only C ..02 may be assumed to be in equilibrium with its reactants, so that we may write from Pl and Table 1

KlC 02$-c 4 subject to the condition

0,=223O”K. This decrease in slope has in fact been experimentally observed by NAGLE and STF~CKLAND-CONSTABLE. Although the calculated heats of reaction are only approximate, their reasonableness should be considered. We expect that Aus will be Iess exothermic than AUI, since the process of dissociation of an oxygen molecule will be endothermic to the extent of Aud=122,000 Cal/mole. We may also obtain from the foregoing an estimate of the energy of adsorption of atomic oxygen on graphite, namely, (-Au&Aus)/2= (-122,000-7990)/2= -65,000 Cal/mole 0, which is of the same order as the value for molecular oxygen of -78,410 Cal/mole 0s. The derived values for the energies are also reasonable in that they are consistent with the known thermochemistry of thegraphite-oxygen reaction in which COs formation is favored at low temperatures and CO formation is favored at high temperatures. The derived energies for all processes have also been included in Table 4. Finally, it is worthwhile to note that if Aus had been found to be positive, then the competitive adsorption effect would not have been noticeable and very much less CO would have formed. The CO/COs ratio is often measured in kinetic studies. From Fig. 1 we see that at high temperatures (T> 7’2s) this ratio should be equal to v~o/vco~. Furthermore, this ratio should change with temperature by the relation exp-_([Au,t+(Aus+Aul)/2]lkTZ =exp-([Au4t--Aast+(Aus--A&/2]

/exp-CrA~~~+A~l]~~~~ /kT)

From our values of the energies of activation and adsorption, the quantity in brackets is 69,000 Cal/mole. This may be compared with the data

291

(P-3)

that

[C * *021+ By eliminating before, we get:

c. *02

[Cl= cm21

[C] and changing

Kl,

F. . ozl~=(r~clsc*.*+=rncl($&

(P-4) to Kl as

j

(/3-S)

Equation (8-S) may now be substituted into (p-1) and (p-2) together with the appropriate forms ~unimolecular and termolecular, respectiveIy) of the rate constants. For vcoz we get vcoz=v2f

=h

kTK t[ncl

For z~co the rate equation vcO==

2v3f=h

(P-6)

4

is

2kT %f[“c1($&)~

[Cl (8-7)

which by making use of the relation (p-4) can be rearranged to

oco =

2vs~==--‘“h’Wh13

(wy

(1+&--fy

(P-8)

thefamiliarLangmuir-Hinshelwoodexpression.’sa) Note that at high temperatures the rate decreases with increasing temperature and varies as F’s. If the activation energy of vsf is associated with the energy of dissociation of molecular oxygen (A~~=122,000 Cal/mole 0s) and the energy of adsorption of 0s taken from case CI to be Aul= -78,410 Cal/mole 02, then the apparent activation energy of vsf at high temperature is on the order of 122,000+2( -78,410)= -34,800 Cal/mole. These conclusions may be compared with the experimental findings of DuvAL,‘~) Fig. 2, who obtains an approximate PI.5 dependency on the rate and

292

J. N. ONG,

an apparent activation energy of approximately -20,500 Cal/mole. We may test the Langmuir-Hinshelwood possibility as follows. It can be shown that the maximum in the rate for (b-8) will occur when J&P= exp-(A~“~/kT)=2. Using the value for Au01 from Fig. 3 and selecting a representative pressure in the range of DWAL’S study of 10-s atm pressure of oxygen, we calculate that the maximum should occur at about lOOO”K, whereas the experimentally determined temperature is about 1300°K. A more serious discrepancy arises if a rate calculation is made; using T=1780”K, P=lO-satm, Auaf+= 122,000 Cal/mole, and A$1 as determined from Fig. 3, and assuming [nc]=lOX5 sites/cma, we calculate nco to be on the order of 10s smaller than DWAL’S experimental rate, which cannot be rationalized by a roughness factor. A second possibility of a bimolecular mechanism whose rate equation may readily be shown to take the form

will not produce the observed inversion in rate with increasing temperature, assuming Aua and A~.Qthe same as above, and will give a pressure dependency on the rate of P-1. DUVALhas reported that the products of reaction at low oxygen pressures (10-s atm) are primarily CO. If the third possibility that secondary reaction (C) may occur consecutively to reaction (A) is admitted, then (/I-6) will account for the rate inversion with temperature, provided that the rate of formation of CO by reaction (C) is very rapid under these conditions and that Auaf+ and Au1 are the same as in case a, giving for an apparent activation energy approximately 22,800-78,410= -55,600 calfmole. A pressure dependence of P would be expected by this scheme, however. The fourth possibility is that secondary reaction (C) occurs consecutively to reaction (A) and that one of the processes associated with reaction (C) is rate controlling. We show in the next section that one such process could be the reduction of adsorbed CO2 according to C. . CO&C. .O+ CO(g), which is endothermic by an amount of 82,800 cal/mole, We will defer further discussion of this point to the next section, however, except

JR.

to remark that this appears to us to be the most likely possibility. It is quite likely that the Langmuir-Hinshelwood mechanism may predominate in a pressure range intermediate between 1 and 10-6 atm. The pressure dependency on the rate should vary ,as Pllz to Pz to Pl with decreasing pressure at T > Ta3 and should be readily accessible to experiment. The assumptions made in case a with regard to Apat+ and Apr are considered to be valid in this case also. For Apsf+, both electronic and vibrational differences will probably enter into its value, but for simplicity wewill ~sume~atA~s,+=A~s~+. cf) Case y. The third case is that the primary process Pl, whose rate is vu, controls voa and erc by (y-3) and (y-4). From Table 1 we get

Assuming that the activated state is an immobilized gas molecule just prior to becoming adsorbed,‘aa) t-thenKr~+=exp-(AuV+-($‘oa)tr)/kTwhereA~v ~v+-(~~)v and is assumed negligible. At high temperatures, [C]=[n&Jso that the rate of adsorption is given by:

kT vc=vo~=v~f= -k expi@ “o,)trk*lPtwl

(Y-6)

The function exp (p’&/kT is proportional to T-7/2 so that vlf=f(T-s/a, P). The high temperature limiting rate for vco (case a) by (a-9) is quite insensitive to temperature and resembles(y-6) but with a different pressure dependency (PI/a) which should be experimentally differentiable. The working rate equation is given by

W&Wd~=Fexp

[(,u”oz)tr/kTJP

(Y-7)

where F is defined as in case a. Since (y-7) is assumed to be not activated, its rate will be very much greater than any rate in cases a and /3 at moderate pressures (atmospheric). It is unlikely, therefore, that vlf will become rate controlling except at very low pressures. For convenience, we have tabulated in Table 6 the working rate equations for limiting cases a and /I and the appropriate general form and dimensions for K;+

cn+/site2

d~en&dess 2F ew (atm)-l

(at4 dimensionless

A/w+ = p4+- /cc. .o

Apay+ = p4+- p’co -pox A per+- A/Pa= p’co

+ /PC. .o-$c. A~7f+=~7+-$c. .o

Kvc

kb

kofr(‘)

klf(‘)

(a) osf, and v7f pertain to CO formation only. (a) F’=(Mrs/No)(kmt/kT).

.oa

1+

(KlK3p)l,2+

(KXSPV

cK,Ks$$2

Klp)

+ KIP)

2F exp-(Atw+lkT)

2F’ exp-(Ap”s/kT)(b)

RATE

-

EQUATIONS

l~>~~~o2

Case /3

F exp-(&zr+lkT)($&)

Working rate equations, d(mc/&)/dt

-(Aw+/kT)(

tl+

Case a

F exp - (Apzf+/kT)

A~3f+=~s+‘-_CLO’c-21Lo’c. .oa

/PC. .oa

ksr

(atm)-l dimensionless dimensionless

Apart= pz+-$a-

.os

A/w+ = pl+ - p3c - $02

Al_llb+=~l+--“~.

In Kc+

ha kzr

-kT

klr

Cons:ant

Rate

Dimensions of Kit

POTENTIALS FOR ACTIVATED COMPLEX AND ITS REACTANTS, Api+, DIMENSIONS, AND WORKING FOR LIMITING CASES Q AND p FOR PRIMARY AND SECONDARY REACTIONS

TABLET. TABLE OF STANDARD CHEMICAL

294

J. N. ONG, JR.

2.4 Secondary reactions The prior discussion notwithstanding, it is a well-known fact that the reaction of oxygen with all forms of graphite and carbon is markedly dependent upon the flow of gas around the reacting solid. Opinion is divided on the question of whether the rate of reaction is controlled by diffusion processes in the gas phase@*2@21*s7 or by phase boundary processes. (1~38~391 Those favoring the gas-phase diffusion controlpossibilityciteassupport the flow sensitivity and the marked insensitivity of the rates to temperature at elevated temperatures. We showed in the last section, however, that this insensitivity to temperature can be a characteristic of high-temperature phase boundary controlled processes. We favor the latter view and consider that the flow sensitivity is an effect caused by the porosity of graphite and its concomitant influence upon secondary reactions that may occur within the graphite pores. We remark, first of all, that the volume contained within a pore approximates a closed system more closely than an open system. An immediate effect of this, of course, is that the pore volume, containing reactants originally, say, will soon be filled with products by reactions (A) and (B), thus causing further reaction to be depressed. Further reaction, in fact, may proceed only by diffusion of products out of, or reactants into, the pore across a pore aperture of some efEctive cross-sectional area. Another effect of the closed system is to permit secondary reactions to occur more readily. When CO2 is a predominant product under the conditions given in the last section, reaction C(C+CO+ 320) will become an important consideration. We. assume that reaction (C) takes place by the following sequence of processes :

ka

c.

kfv c.

.CO2 e

.0-/420(g)

km

P-6)

kv

c. .o s

km

CO(g)+Cc

(P-7)

P7 is recognizable as one-half of F4. KHITRXN and GQLOVINA(~~)have observed a maximum in the rate of the C-CO2 reaction at about 1700°K; If this can be interpreted as the approximate temperature at which lpci reaches high temperature (and thereby changes its kinetics fram reversible behavior of the first kind to irreversible behavior), an estimate of Aua= 82,800 caljmob C. LCO2 can be made. From the thermo&hemi~~ additivity of P5+PS+p7=C, we estimate the energy of adsorption Au5 to be -58,680 Cal/mole CO2. Both A,u” and AU for each process for reaction (C) have also been included in Table 4. Figure 6 is a plot of A$ versus T for the C-CO2 reaction. From the figure we see that even though reaction (C) tends to become irreversible above lOOO”K, P6 is reversible to 1700“K. Thus, the secondary reaction itself consists of at least one process (P6) which will be sensitive to gas Aow by an equation of the form utrf=K,tA[CO] below 1700°K. If [CO] in the surroundings is very small, then to a good approximation we can write;

where [CO], is the concentration of CO in the immediate vicinity of the surface and Pco the partial pressure of CO from the equilibrium relationship P6 given by PCo==exp-(A$‘ajkT). This may be substituted into the above equation to give

Since the mass-transfer coefficient does not involve an activation energy, an Arrhenius plot will give the value of due. ROSSBERG~*~) has reported an activation energy for reaction (C) of Ahut=86,000 Cal/mole in very good agreement with our value for ALUSof 82,800 Cal/mole CO. Returning to the discussion of case j3 at low pressures, if 2’6 were the rate-controlling process the rate should exhibit a maximum at the temperature at which P6 became irreversible in a manner similar to the C-CO2 rate data of KHITRIN and GOLO~INA. Using a pressure of 10-6 atm and the appropriate equilibrium relation from 2’6, we calculate that the maximum in the rate will occur at

ON THE KINETICS

OF OXIDATION

llOO”K, which is closer to the experimental value of 1300°K (Fig. 2) than the value of 1000°K calculated in case /?. We thus conclude that it is very likely that in the study made by DWAL the products observed (CO) and the process measured were due to secondary reaction (C) and ratecontrolling process F6. Two measurable quantities that the presence of porosity in graphite might be expected to change are the rate and the CO/CO2 ratio. To a first appro~mation the geometric area A, may be considered to consist of (I) an area Aopen over which reactions are proceeding according to the open-system considerations of the preceding section and (2) an area Aclosed over which reactions are proceeding according to the closed-system considerations outlined. Representing the ratio Aopen/Ao by q and from the relation A,=Aope,+

Aclosed, we get Aopen=qAoandAclosed=(l

-q)Ao.

The basic difli.rsion equation may be related to a working rate equation by

where m, No, A,,, Y and s are defined as in (a-11); kmt=Dld is a mass-transfer coefficient, where D is the diffusion coefficient (cms/sec) and d is the diffusion distance (cm); and A[CO] is the difference in concentration of difiusing gas (CO or CO4 between the surface and the surroundings (molecules/ems). If the total rate is the sum of the two rates, then

or, in terms of a working rate equarion. d(mclAo)ldt=q(MyslN,)v,,,,+ If vopen and Z)croeedare appreciably different from each other, then the variation in rate from one grade of graphite to another under the same experimental conditions will depend upon q. NAGLE and STRICKLAND-CONSTABLE have observed as much as a ninefold difference in rate between grades of graphite under similar experimental conditions.(ls) The value q depends upon porosity but is not necessarily a direct function of it. Porosity will also affect the CO/CO2 ratio, to the degree that a certain portion of the reaction may be considered as taking place under conditions approximating a closed system. DAY, WALKER G

OF GRAPHITE

29.5

and Wnrou~fss) have observed sixfold differences in the CO/CO2 ratio between “anthracite-base carbon” and “graphitized anthracite” under the same experimental conditions of unspecified but presumably different porosities. 3. DISCUSSION AND CONCLUSIONS It has been stated that among the aspects which are disputed concerning the C-02 reactions are the primary product,‘ls~s0~41i4s) the order of rea~ion,(ss,~l) and the activation ener~.(ls,sO?sl~ We have shown in this article that both CO2 and CO are primary products and that one or the other usually predominates at different temperatures and pressures. We have indicated that the concept of the order of a reaction when applied to gas-solid reaction kinetics is of limited utility and that the molecularity is a more meaningfuli concept. In case CI, for example, depending upon the temperature, the order may take the values -4, 0, -+Q and 1 with a different activation energy being associated with each order. This fact, together with the fact that it has not generally been realized that straight-line Arrhenius plots are the exception rather than the rule in gas-solid reactions, has given rise to reported activation energies ranging from 8000 to 60,000 cal/mole.frs.sr) It is a popular aphorism that a kinetic mechanism may be disproved but never proved.@) We have attempted, however, to justify the reasonableness of the proposed kinetic scheme on thermochemical grounds. Furthermore, MILNBR has recently shown(Q) that, for a given reaction, the number of processes that may characterize the kinetics can be no more than one more than the number of intermediate species that are assumed to enter into the rate process. For reaction (A) we have proposed one intermediate species (C. . 0s) and two processes (Pl, P2) ; for (B), two inte~ediate species (C. . 02, C. . 0) and three processes (Pl, P3, P4); and for (C), two intermediate species (C. . CO2, C. .O) and three processes (P5, P6, P7). All are kinetically consistent with MILNER’S theorem. In addition, MILNER has shown that the only differences in kinetic mechanisms for an overall reaction involving intermediates are in the values that may be assigned to the stoichiometric coefficients in each process. The bimolecular and termolecular mechanism, (/l-S) and (8-g), respectively, discussed in case 8, are thus mutually

296

J. N. ONG,

JR.

7. BONNETAIN L. B., DUVAL X. and LBTORT M., Proceedings of the Fifth Conference on Carbon, Vol. 1, p. 107. Pergamon Press, Oxford (1962). 8. STRICKLAND-CONSTABLE R. F., Trans. Faraday Sot. 40, 333 (1944). 9. DWAL X., Ann. Chim. (Paris), Series 12, 10, 903 (1955). 10. OKADAJ. and IKECAWAT., r. Appl. Phys. 24, 1249 (1953). 11. HORTON W. S., Proceedings of the Fifth Conference on Carbon, Vol. 2, p. 233. Pergamon Press, Oxford (1963). 12. NACLE J. and STRICKLAND-CONSTABLE R. F., Proceedings of the Fifth Conference on Carbon, Vol. 1, p. 154. Pergamon Press, Oxford (1962). 13. BLYHOLDER G. D., Kinetics of Graphite Oxidation. University of Utah, Doctoral Dissertation, Pub. No. 18707, University Microfilms, Ann Arbor, Michigan (1956). 14. BLYHOLDER G., BINFORD J. S. Jr. and EYRING H., r. Phys. Chem. 62, 263 (1958). 15. EUKEN, A., Z. Angew. Chem. 43, 986 (1930). 16. MEYER L., Z. Phys. Chem. 17B, 385 (1932). 17. SIHVONEN,V., Z. Electrochem. 36, 806 (1930). 18. BLYHOLDER G. and EYRING H., J. Phys. Chem. 61, 682 (1957). 19. KHITRIN L. N., Sixth Symposium (International) on Combustion. D. 565. Reinhold. New York (1951). 20. WALKER P.‘i. Jr., &~NKO F: Jr. and AU&IN i. G., in Adwunces in Catalysis, Vol. XI, p. 133, Academic Press, New York (1959). 21. SCALA S. M., The Ablation of Graphite in Dissociated Air. -1. Theory, General Electric Missile and Space Division, Report No. R 62 SD 27 Class I (Sept. 1962). 22. GARBER, A. M., NOLAN E. J. and SCALA S. M., Pyrolytic Graphite-A Status Report, General Electric Missile and Space Division, Report No. R 63 Acknowledgements-I acknowledge with thanks the SD 84 (Oct. 1963). assistance, critical comments and helpful discussions 23. YOSIM S. J., MCKISSON R. L., SAUL A. M. and that have been offered by W. G. Bradshaw, Dr R. H. MCKENZIE D. E., Progr. Nucl. Energy, Series IV, Bragg, Dr N. L. Jensen, M. P. Gomez and M. L. 2, 301 (1960). Hammond during the course of this work. The work 24. FA~SELL W. M. Jr., ONG J. N. Jr. and SAUL has been supported in part by the Independent ReA. M., High Pressure Oxidation of Refractory search Program of LMSC and in part under Navy Metals Experimental Methods and Interpretation, Contract NOW-63-0050~. AIME-ASD Joint Conference on Refractory Metal Oxidation, New York (Nov. 1962). REFERENCES 25. SEARCY, A. W., High Temperature Inorganic 1. WALKKR P. L. Jr., Am. Scientist 50, 259 (1962). Chemistry, in Progress in Znoraanic Chemistry,_. p. _ 51 2. GOLOVINAE. S. and KHAUSTOVITCHG. P., Eighth Interscience, New York (1962). SymDosium (International) off Combustion, p. 784. 26. HENNIG. G. R.. Proceedinzs of the Fifth Conference V&ll&ms ani Wilkins, Bahimore (1962). _ on Curb& Vol: 1, p. 143;Peigamonbress, &ford 1. R.. Brit. Coal Utilisation Research Assoc. 3. AR~HIJR (1962). 8, 296 (l&4). 27. SCHMIDT L., BOEHM H. P. and HOPMANNU., Pro4. ARTHUR J. R., Brit. Coal Utiltiation Research Assoc. ceedings of the Third Conference on Carbon, p. 235, 13, 297 (1949). Pergamon Press, Oxford (1959). 28. GLASSTONES., LAIDLER K. J. and EYRING, H., The 5. SNOW C. W., WALLACE D. R., LYON L. L. and CROCKHRG. R., Proceedings of the Third Conference Theory of Rate Processes. McGraw-Hill, New York on Carbon, p. 279. Pergamon Press, Oxford (1959). (1941). 6. GULBRANSENE. A., ANDREW K. F. and BRASSART 29. LAIDLER K. J., in Catalysis, Vol. I, Chaps. 3, 4, 5 F. A., J. Electrochem. Sot. 110, 476 (1963). Reinhold, New York (1954).

exclusive possibilities for the formation rate of CO. The scheme that has been proposed in this article is based on the analysis of only a limited amount of the available published data and may not, upon closer examination, be found to be correct in all details. Nevertheless, the purpose of this article may be considered to have been well served if it has shown that the problem must be stated in terms of reaction, process, mechanism, molecularity, system, temperature, reversibility, and limiting conditions to provide the answer in terms of order, activation energy, and predominant reaction products. The essence of the method used here has been the assumptions made concerning the configurations of the gaseous species for each process and the estimation of the temperatures Tls and T2s. The calculated energies for all the processes have been determined from these assumptions. Different estimates of Y’ls and T2s from Fig. 1, as used in Table 3, will change these values. However, more careful assignments of these temperatures await additional experimental data in the temperature range 1100 to 2500°K. Finally, we wish to stress that much of the information gained from this analysis has been from a detailed knowledge of the gas rather than the solid, and that the changes in kinetic behavior are due solely to the thermochemical properties of the gases.

ON THE KINETICS

OF OXIDATION

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