GEORGE BLYHOLDER AND HENRY EYRING
1004
Vol. 63
TABLE V FORMATION CONSTANTS FOR COMPLEX Author
Rileyao Ledens' King22 Korshunov28 Vasil'ev24 Strocchi26 Golub28 Eri ksson27 Vanderzee28
Method
Potent. titr. Potent. titr. Solubility Polarography
THE
CADMIUM-CHLORIDE SYSTEM
Medium
log ki
log ka
KC1, varying 3 M NaC104 3 M NaC104
2.00
0.60 .66
1.59 1.40
log kr
.81
.43 Polarography 2 M NaNOa .08 $24 Potentiometry 2 . 1 IF KNOI 1.45 .25 Polarography 3 M NaCI04 0.52 .40 Potentiometq 3 M yaC1o4 1.54 .66 .os Extrap. to zero ionic. str. 2.00 .70 .58 1.95 .55 - .15 This work anion exchange LiC1, varying HCl, varying, in addition to above also log 2.18 1.57 1.77 1.54
-
number of authors using various different methods, ionic media and medium concentrations. Comparison is valid only if due cognizance is taken of differences in the activity coefficient functions inv ~ l v e d . ~It . ~may however by pointed out that the parameters obtained by the anion-exchange method are most similar to the thermodynamic complex formation constants reported, those obtained for zero ionic strength. ( 2 0 ) H. C. Riley and V. Gallafent, J . Chem. Soc., 514 (1932). (21) I. Leden, 2. physik. Chem., 188A,160 (1941). (22) E. King, J . A m . Chem. Soc., 71, 319 (1949). (23) I. A. Korshunov, N. I. Malyugina and M. 0. Balabanova, Zhur. Obshchei K h i m . , 21, 620 (1951). (24) A. M. Vasil'ev and V. I. Proukhina, Zhur. Anal. K h i m . , 6 , 218 (1951). (25) P. M. Strocchi and D. N. Hume, Abstracts 123rd Meeting Am. Chem. Soc,, March 1953, p . 4P. The values quoted in Table V are those corrected for nitrate complex formation, c f . Vanderzee and Dawson.20 (26) A. M. Golub, Ukrain. Khim.Zhur., 19, 205 (1953). (27) L. Eriksson, Acta Chem. Scand., 7 , 1146 (1953). (28) C. E. Vanderzee and H. J. Dswson, J . A m . Chem. Soc., 7 6 , 5659 (1953).
log kr
0.30
0.11 .18 .I8 .78
.30
-
.05
-
.70
= -0.15
Further values for comparison are: log kl,by conductometry and extrapolated to zero ionic strength, RighelattoZg and Davies30 2.00, Harneda1 1.95; Briih1,32from considerations of activity coefficients, appr. 2.5, and Turv'an33 2.30. For log PBKnobloch34 found by potentiometry in KC1 solutions 2.93, while K ~ r e n r n a nfound ~ ~ in HC1 solutions 1.7 to 2.5. For log k3k4 ( = log p+') Bourion36found by ebullioscopy a t 100" appr. 0.0. Acknowledgment.-This paper is published by the kind permission of the Director of Research, Israel Atomic Energy Commission, t o whom thanks are due. (29) E. C. Righelatto and W. C. Davies, Trans. Faraday Soc., '26, 592 (1930). (30) W. C.Davies, Endeavour, 4, 114 (1945). (31) H. S. Harned and M . E. Fitzgerald, J . Am. Chem. Soc., 58, 2624 (1936). (32) L. Brahl, Gazz.chim. ital., 64, 615 (1934). (33) Y.I. Tury'an, Zhur. Neorg.. Khim., 1, 2337 (1956). (34) W.Knoblooh, Lotos, 78, 110 (1930). (35) K. M. Korenman, Zhur. Obshchei Khim., 18, 1233 (1948). (36) F. Bourion and E. Rouyer, Ann. Chim., [lo]10, 263 (1928).
KINETICS OF GRAPHITE OXIDATION. I1 BY GEORGE BLYHOLDER' AND HENRY EYRING Department of Chemistry, University of Utah, Salt Lake City, Utah Received September I f , 1068
The kinetics of the oxygen-graphite reaction in the 800 to 1300' temperature range and 1 to 100 fi pressure range are investigated. Above 1000" the true surface reaction is half order with respect to oxygen and the activation energy is smell. The effect of the diffusion of oxy en into the pores of the graphite sample is elucidated. Absolute rate theory together wlth the observed kinetics is used to !evelop a mechanism for the reaction.
Introduction In the previous paper1 the reaction of oxygen with graphite in the 600 to 800' temperature range and one to one hundred p pressure range was presented. Here the data for this reaction from 800 to 1300' are given and discussed. The data for the two temperature ranges were taken concurrently. The division into two temperature ranges is done purely for convenience in discussing the results. I n the 600 to 800' temperature range the observed reaction has a constant activation energy and is one-half order with respect to oxygen. Above 800' the plot of the log of the reaction rate versus the (1) Q. Blyholder and H. Eyring, THIEJOURNAL, 61, 682 (1957).
inverse of the absolute temperature is no longer linear. The observed order of the reaction also changes above 800'. Experimental Since all the data were gathered a t the same time the apparatus is that described in the first publication.' The graphite samples were prepared from the same batch of spectrographic electrodes manufactured by the National Carbon Company that was used for the low temperature data. The details of the sample preparation are as reported in the f i s t paper. The geometric areas and thickness of the samples are given in Table I.
Experimental Results For previously stated reasons the reaction rate changes in a regular manner from one similar
4
KINETICS OF GRAPHITE OXIDATION
June, 1959
1005
TABLE I" Ares (om.9
@ample
Thickness (cm.)
6.94 0.1 2 1.77 .1 4 1.4 .I 9 1.12 .I 10 1.32 .1 11 1.04 .1 14 9.88 2 x 10-4 a Samples which were used in both the high and low temperature range bear the same number in both publications. 1
run to the next. In order to obtain meaningful results, a set of conditions for a run were selected as standard. A standard run is then made between successive runs in which the conditions are varied. The results are then normalized so that all the standard runs are the same. After this adjustment the true relationship among runs a t varying conditions is seen. The temperature dependence of the reaction a t an O2 pressure of 26 p is shown in Fig. 1. Samples numbered 1, 2, 9, 10 and 11 were used to obtain these data. Using samples numbered 2, 9, 10 and 11 the pressure dependence data shown in Fig. 2 were obtained. In order to place all of the pressure dependence data for one-mm. thick samples on the same graph, one rate from the data for each temperature was multiplied by a factor which would place it on the R = kP3I4line in Fig. 2. All of the data for a particular temperature were then multiplied by the same factor. The results of this are the experimental points in Fig. 2. The result of a pressure dependence study on sample number 14, which had a very thin layer of graphite, is shown in Fig. 3. Due to the small amount of graphite in the thin layer of this sample the amount of graphite and consequently the rate of oxidation decreased rapidly from one run to the next on this sample. This particular set of data is therefore probably not as reliable as the rest of the data. The results obtained by making runs with the copper oxide catalyst cold are recorded in Table 11. By comparing the results of these runs with previous runs under the same conditions the amounts of carbon dioxide in the product gases can be determined. The percentage of carbon dioxide in the product gases is given in the last column of this table. These results were obtained using sample number 4.
+
17 63 149 174 344 57
0 2
300 250
s 200
'
150 100 75 50 25 0
0
10 20
30 40 50 60 70 80 90 O2 pressure, p. Fig. 2.-Pressure dependence.
100
200 160
'
a; 120
P
Temp., OC.
% COz
27 27 26 17
804 900 1008 1107 1205 800
3
28
0.6
e
pressure,
16
0.7
350
TABLE I1 RESULTSWITH CATALYST COLD Rate of production of CO CO,,in p / 3 min. into a 0.404 1. system a t 300°K.
1.0 0.9 0.8 1/T x lo+. Fig. 1.-Log of rate vs. 1/T.
1.1
1.2
80
6 11
40
22 39 10
0
Interpretation of Results I n the first paper it was established that, in the 600 to 800' temperature range, carbon monoxide is the primary product of the reaction of graphite with oxygen in the one to one hundred p pressure
0
5
10 15
Fig. 3.-Pressure
range.
20
25
30 35
40 45
50
Oa pressure, p. dependence of thin layer at 900'.
In the temperature range from 800 to
1000°, the results shown in Table I1 indicate that
carbon monoxide is the primary product. At 1100 and 1200O the results show about 20 and 40% COZ,
GEORGE BLYIIOLDER AKD HENRY EYRING
1OOG
respectively, in the product gas. We believe that this increase in the COz percentage is due to the secondary reaction 2co
+ *2 c 0 2
The rate, taking pore diffusion into consideration, is obtained from the following equation given by Wheeler.
0 2
rr2D dx2
The equilibrium constant for this reaction greatly favors the formation of COz. The rate of this reaction is apparently too slow for much COz to be observed at any but the highest temperatures studied. We shall therefore continue with the assumption, which has been demonstrated over 5/7 of the temperature range studied, that CO is the primary reaction product, The role of pore diffusion in the reaction of oxygen with the artificial graphite used in this study was established in the first paper. Pore diffusion enters into the kinetics of a reaction of a gas with a porous solid when the reaction of the gas with the surface is fast enough that the concentration of gas in the pores of the solid is less than the concentration of gas outside the pores. This condition was demonstrated to be true in the 600 to 800' temperature range. Since the surface reaction in the 800 to 1300' temperature range is faster than in the 600 to 800 range, pore diffusion will be a factor in the reaction in the 800 to 1300' range. The model developed by Wheeler2 for the reaction of a gas in the pores of a solid will be used. One of the results of this model is that when pore diffusion affects the reaction, if the true order with respect to the gas of its reaction with the surface is n, the observed order will be (n 1)/2. With samples 2 X 10-4 cm. thick, i t is seen from Fig. 3 that at 900' the true surface reaction is order in the exwith respect to oxygen. Using n = pression (n 1)/2 gives an observed order of 3/4 for reaction plus pore diffusion. From Fig. 2 it is seen that for samples 0.1 cm. thick the observed a t 900'. This order of the reaction is indeed confirms the conclusion that pore diffusion is a factor in the reaction. Another result of Wheeler's model is that the observed activation energy for pore diffusion plus reaction will be one-half of the true activation energy for the surface reaction. This condition has been shown to be true a t 800'. From Fig. 1 it is observed that above 800' the reaction rate no longer increases with the same exponential factor as the temperature is raised that it did from 600 to 800'. I n the temperature range from 1100 to 1300' the activation energy has dropped to 1 kcal. per mole. Figure 2 shows that the observed order with respect to oxygen of the reaction on 0.1-cm. thick samples is 3//4 from 900 to 1300'. Taking pore diffusion into account, this leads to the conclusion that from 900 to 1300' the true surface order with respect to oxygen. reaction is The true surface reaction is given by the expression
+
+
R = KC'h
Vol. 63
(1)
where
2rrR
where
-- pore radius D = diffusion coefficient 2 = coordinate along pore length r
Wheeler did not consider the case where R is given by equation 1. Substituting equation 1 into 2 yields (3)
This is the fundamental differential equation t o be solved. The boundary conditions are C = CO at X = 0 and dc/dz = 0 a t X = L. The latter boundary condition is found because by symmetry there is no net flow through the cross section a t X = L. The reaction rate per half pore is the rate a t which oxygen flows into the pore, which is nr2D times the concentration gradient a t X = 0. This gives (4)
where R p is the rate per half pore. The problem is to evaluate (dc/dz),a from equation 3. Equation 3 may be integrated once to yield '& = 4 2K C% + 2i3)"z
(
(5)
dx
where B is an integration constant. Unfortunately this equation cannot be integrated in closed form. Also the boundary conditions as given are not applicable to equations 5. Considerable simplification results from letting C = CL at X = L, where also dc/dx = 0. With these substitutions equation 5 may be solved for B to yield B
- 413 Ka CL'/*
(6)
Substituting the value for B into equation 5 gives
At x = 0 this yields c
where Co is the oxygen concentration outside the solid. I n the reaction from 600 to 800' it was found that a zero-order surface reaction became an observed half-order reaction when pore diffusion affected the reaction. This means that a t X = L, CL = 0 for the reaction in the 600 to 800' range. Since the surface reaction is even faster in the 800 to 1300' range, i t is valid to replace CL by 0 in equation 7. Substituting dc/dx,-o from equation 7 into equation 4 yields
R = rate per unit area
K = constant
C = gas phase oxygen concn.
(2) A. Wheeler, "Advances in Catalysis," Vol. 111, Academio Press, Ino., New York, N. Y . , 1951, p . 250.
Having a value for the rate per pore the total rate of the reaction may be calculated. RT = n,R, (0)
KINETICS OF GRAPHITE OXIDATION
Julie, 1959
1007
surface, the following expression is obtained
where RT = rate per sq. cm.-sec. n, = no. of pore mouths per unit area
@ dl
According to the model used
=
2(1
- 6)'Pkl - 2
~ ~e he 2
(15)
where e = fraction of sites covered by absorbed oxygen atoms kl = rate constant for formation of surface oxide
8' = 0.4 = porosity of sampleZ
Since the mean free path of the gas is much greater than the pore diameters, the diffusion coefficient is for molecular flow. This is given by 2r D=3
where
k
= rate constant for O2 leaving surface = rate constant for oxygen atoms on the surface re-
P
=
k-1
where
v-
in which rn is the molecular mass of oxygen. Assuming a perfect gas yields 0.65 X 10"
Making the steady-state assumption that dO/dt yields e = (4Pkl
B is the average molecular speed given by
co
acting to produce CO gas phase oxygen pressure
P
T
(13)
where P is in mm. of Hg. At 26 1.1pressure and 900' the use of equations 10, 11, 12 and 13 in equation 9 gives RT = 5.3 X 1 0 l z d z (14) This expression for the rate taking pore diffusion into consideration may be checked by finding the value for K from a measurement of the true surface reaction and placing this value in equation 14 and comparing the result with the measured reaction rate. From Fig. 6 of the paper2 on the results in the low temperature range the rate of the true surface reaction at 900' and 26 1.1 preesure is found to be 2.7 X 1013 molecules of O2 per crn.%ec. Using equation 1 this gives a K value of 2.5 X lo6. From equation 14 the calculated rate is given by
=
0
+ k) - d ( 4 P k l -I- k)z + S.Ph(2k-1 - 2Pk1) -2(2k-1 - 2Ph-I) (16)
In order for 0 to be real and not greater than one it is necessary that the minus sign be chosen in equation 16. I n evaluating the square root, if the first of the two terms under the square root sign is allowed to dominate the second, the result is kinetics which are either zero or first order. This is contrary to experiment. If the second term under the square root sign dominates, the expression for e becomes
If now J C - ~ >> t l P the result is The rate of production of CO is now given by I-
where N is the number of carbon sites per cnx2 This result is in accord with which is 3.5 X the experiniental order of the reaction. The rate constant k will now be considered in some detail. I n order t o obtain the correct pres&(CalCd.) = 8.4 X 1016 molecules per cni.2-sec. sure dependence for R, i t was necessary to assume From Fig. 1 the observed rate is 6.5 X 10'6 mole- that the oxygen atoms on the surface progress from cules per cm.2-sec. which is in good agreement with site to site on the surface rapidly enough that the the calculated rate. distribution of oxygen atoms on sites is random desWe now wish to inquire into the sort of kinetics pite the arrival of the oxygen atoms in pairs. I n necessary t o obtain a half-order surface reaction. the temperature range from 600 to 800' where the A slow step of the gas phase equilibrium dissocia- reaction is zero order, it seems likely that the stable tion of oxygen molecules into atoms followed by a surface oxide is one in which the oxygen atom is fast reaction of the oxygen atoms with the surface attached to the surface by a carbonyl type bond. would produce half-order kinetics. Due to the In the high temperature range it seems not unlikely high heat of dissociation of oxygen molecules, the that the oxygen atoms which are capable of rapid number of oxygen atoms in the gas phase is strongly movement over the surface are less firmly attached temperature dependent. Any process depending to the surface than a carbonyl bond implies. For on this as the slow step would then be strongly example, it may be that an oxygen atom is on the temperature dependent. This is clearly contra- surface as a singly negatively charged ion which is dictory t o the experimental evidence, so this mech- attached to R carbon atom by a single bond. The anism is eliminated. We must then turn to n movement of the oxygen atom over the surface consideration of processes taking place on the could then be accomplished by the ion forming surface. another single bond with an adjacent carbon atom If the adsorbed oxygen is assumed to be immobile and then breaking the bond with the original the kinetic expressions yield only rates which are carbon atom to become an ion on a new site. Using either independent of pressure or are proportional this model an oxygen atom appears first on the to the first power of the pressure. Since this is surface as an oxygen ion which hops around until it contradictory to the experimental results this forms a carbonyl type bond with a carbon atom. mechanism is eliminated. This carbonyl surface oxide then decomposes to If the oxygen atoms are able to migrate on the produce a carbon monoxide molecule. The process
GEORGEBLYHOLDER AND HENRY EYRING
1008
represented by the rate constant k now becomes a two-step process. Step one is the formation of a carbonyl type surface oxide. Step two is the decomposition of this oxide to give GO. If fl is the fraction of the oxygen atoms on the surface which have carbonyl type bonds with the surface, we have
9 = kZ(1 - P ) - k-zP dt
- krB
kz
= k-2 = ka =
= partition function for gas phase oxygen molecule (ftr)3(frot)a = 3.2 X loaaat lGOOaI
