Davidson, J. F., paper presented at Joint A.1.Ch.E.-C.S.Ch.E. Conference, Vancouver, Sept 1973. De Acetis. J., Thodos. G.. Ind. Eng. Chem., 52, 1003 (1960). Eichhorn, J., White, R. R:, Chem. Eng. Progr. Symp. Ser.. 48, 11 (1952). Ferron. J. R.. Watson, C. C., Chem. Eng. Progr. Symp. Ser., 58, 79 (1962). Frantz, J. F.,Chem. Eng. Progr., 57, 35 (1961). Grace, J. R., private communication, McGill University, Montreal. Que., 1974. Juveland. A. C., Deinken, H. P., Dougherty, J. E ., lnd. Eng. Chem., Fundam., 3, 329 (1964). Kettenring, K. N., Manderfield, E. L., Smith, J. M., Chem. Eng. Progr., 46, 139 (1950). Levenspiel, O., Walton, J. S. Chem. Eng. Progr. Symp. Ser. , 50, 1 (1954).
Lindauer,G.C.A./.Ch.E. J., 13, 1181 (1967). Lovell, C. L.. Karnofsky, G., Ind. Eng. Chem., 35, 391 (1943). McConnachie, J. T. L., Thodos, G., A./.Ch.E. J., 9, 60 (1963). Rozentai, A. L., lnf. Chem. Eng., 2, 425 (1962). Sen Gupta, A., Thodos, G., A./.Ch.E. J., 9, 751 (1963). Walton. J. S..Olson. R . L., Levenspiel, O., Ind. Eng. Chem., 44, 1474 (1952). Wamsley, W. W.. Johanson, L. N.. Chem. Eng. Progr., 5 0 , 3 4 7 (1954). Wen, C. Y . , Chang, T. M., Chem. Eng. Progr. Symp. Ser., 62, 491 (1966). Werther, J., paper presented at A.1.Ch.E. Meeting, Detroit, Mich., June 1973.
Received for review August 3, 1973 Accepted April 4,1974
Kinetics of the Oxidation of Carbon Monoxide and the Decomposition of Carbon Dioxide in a Radiofrequency Electric Discharge. I, Experimental Results Lloyd C. Brown’ and Alexis T. Bell* Department of Chemical Engineering, University of California, Berkeley, California 94720
Experimental results are presented for the simultaneous oxidation of carbon monoxide and the decomposition of carbon dioxide in the 13.56-MHz radiofrequency electric discharge. The feed for the reaction The ranges of the operating consisted of either pure C 0 2 or a stoichiometric mixture of CO and 02. conditions were as follows: pressure, 2-32 Torr; flow rate, 2-30 pmol/sec; power, 50 to 350 W. The composition of the products is reported as a , the fraction of the carbon-containing products present as COz. investigations of the effect of power o n cy performed at constant pressure and flow rate show that the values of cy for the oxidation and decomposition reactions approach each other and form two nearly parallel lines at high powers. Failure of the two lines to converge at higher powers is interpreted as an indication of a partial bypassing of unreacted feed. Accounting for the bypassing leads to the conclusion that the composition of the reacted gases is uniquely determined at high powers and does not depend on whether CO2 or CO and 0 2 are fed to the discharge. This composition is ascribed to the presence of a kinetic steady state which is not associated with a state of thermodynamic equilibrium. Studies of the effects of pressure show that the value of a rises with pressure for both the oxidation and the decomposition reactions. Variations in the gas flow rate demonstrated that the product composition during CO2 decomposition is independent of flow rate at low flow rates but shows a consistent trend toward less decomposition as the flow rate is raised above 5 pmol/sec. Data are also presented on the variations of discharge volume and gas temperature as a function of operating conditions. Simple expressions are proposed for the correlation of these two characteristics.
Introduction The development of reactor models which could be used to predict the progress of a reaction in a low-pressure glow discharge has become an increasingly important problem as more and more examples appear illustrating useful applications for plasma chemistry. In two recent pubiications (Bell, 1972; Bell and Kwong, 1973) it has been demonstrated that it is possible to develop models for the description of the dissociation of hydrogen and oxygen starting from the basic physical laws pertaining to electric discharges. The present work was undertaken in an effort to extend these modeling concepts to the interpretation of more complex chemical reactions. The system chosen for this study was the oxidation of carbon monoxide and the decomposition of carbon dioxide in a radiofrequency glow discharge. These reactions were selected because of the small number of products formed, the ease of detecting both the reactants and products, the availability of the basic physical data required to charac-
’
Present address, Gulf Energy and Environmental Systems, Gulf General Atomic, San Diego, Calif. 921 12.
terize the discharge, and the availability of sufficient kinetic data to allow a quantitative model of the reaction kinetics to be established. By working with a high-frequency electrodeless discharge the complicating effects of having electrodes within the discharge were eliminated. Part I of this paper describes the experimentally observed dependence of the extent of reaction upon the reaction conditions. In part 11 a reaction mechanism is proposed and combined with a physical description of the discharge to produce a model of the discharge as a chemical reactor. Calculations based upon this model are then compared against the data and the data are interpreted in the light of the physical phenomena occurring within the discharge.
Previous Work Both the oxidation of carbon monoxide and the decomposition of carbon dioxide have been studied by a large number of investigators using a variety of electric discharges and a broad range of operating conditions (Brown, 1973). This situation makes it difficult to compare the results of different investigators. As a result, the present reInd. Eng. Chem., Fundam., Vol. 13, No. 3, 1974
203
view of the literature is limited to those studies which have employed low-pressure glow discharges since those investigations have the most in common with the work described here. Brewer and Kueck (1931) studied the oxidation of carbon monoxide in the positive column of a dc glow discharge. Their observations of the pressure rise in a closed system showed the oxidation rate to be proportional to the discharge current and for pressures below 10 Torr to be independent of pressure. At higher pressures the rate increased rapidly with pressure. Using an inductively coupled radiofrequency discharge operating between 0.67 and 1.12 MHz, Schumb and Bickford (1936) studied the decomposition of carbon dioxide. The gases in the discharge were recycled by means of a mercury piston pump and the rate of reaction was determined by measuring the rate of pressure increase. Since no meaningful electrical parameter was measured or maintained constant as the pressure and frequency were varied, most of the trends in the data cannot be interpreted. Nevertheless, it was observed that as much as 33% of the carbon dioxide was decomposed at 1 Torr and 46% a t 0.05 Torr. As a part of their investigation of carbon oxidation by atomic oxygen, Blackwood and McTaggart (1959) examined the effects of passing an equimolar mixture of carbon monoxide and oxygen through an inductively coupled radiofrequency discharge (30 MHz). Operating at 0.1 Torr and an unspecified power it was found that the stream leaving the discharge contained 5% carbon dioxide. An interesting aspect of this work is that a similar run was made in which some platinum black was located 20 cm downstream from the coil. In this case the concentration of carbon dioxide rose to 12%, indicating that surface reactions can play an important part in the oxidation of carbon monoxide by atomic oxygen. Ogryzlo and Schiff (1960) studied the amount of atomic oxygen formed by the dissociation of carbon dioxide in a microwave discharge. It was found that the decrease in atomic oxygen concentration with distance from the discharge exit could be described by a first-order recombination reaction taking place on the discharge tube wall. An extrapolation of the atomic oxygen concentration to the outlet of the discharge showed it to be 5%. Unfortunately, no indication was given of the pressure or the discharge power. The only investigators who report producing measurable quantities of ozone in a low-pressure electric discharge sustained in carbon dioxide are Nikitin and Eremin (1962). Employing a dc glow discharge operating at 1 Torr they observed that ozone was formed by passing the gases from the discharge directed into a liquid nitrogen cooled trap. By this means almost 5% of the carbon dioxide was converted to ozone. The total conversion of carbon dioxide was approximately 50%. Barton, et al. (1967), attempted to determine the effect of the surface area to volume ratio on the rate of decomposition of carbon dioxide in a low-pressure electrodeless discharge operating a t 10 kHz. The pressure was varied between 0.03 and 0.04 Torr and the power between 2 and 15 W. The initial rate of reaction was determined by measuring the change in pressure within the discharge tube. Based on these measurements it was found that the rate was proportional to the power and had both zero- and first-order pressure-dependent terms. The zero-order term increased linearly with the ratio of volume to surface area for a ratio less than 2 cm, but the first-order term could not be correlated in terms of the volume to surface area 204
Ind. Eng. Chem., Fundam., Vol. 13, No. 3, 1974
ratio. Upon closer examination of these results it seems possible that the zero-order effect might be due to thermal heating of the gas by the electric discharge and not due to dissociation of carbon dioxide. As a result these data cannot be viewed as conclusive. A more careful study of the initial rate of carbon dioxide dissociation in a closed system has been reported by Corvin and Corrigan (1969). These experiments were performed in a dc discharge equipped with a movable anode. Pure carbon dioxide was discharged for a short time (1-12 sec) at a constant current of 0.6 mA. During this period the discharge voltage was measured as well. The amount of carbon dioxide dissociated was determined by freezing out the carbon dioxide and measuring the residual pressure due to carbon monoxide and oxygen. By making runs with different interelectrode distances it was possible to subtract off the electrode effects and to determine the dissociation rate in the positive column of the glow discharge, The measured dissociation rates were represented as a Townsend coefficient or the number of dissociations occurring per electron per centimeter of electron drift and were correlated with the ratio of electric field strength to pressure. This ratio was also correlated with the product of the pressure and the discharge tube radius. From their experiments Corvin and Corrigan were able to demonstrate that the primary dissociation mechanism is by electron bombardment dissociation of carbon dioxide into carbon monoxide and atomic oxygen. Barton and Von Engel (1970) have confirmed Corvin and Corrigan’s conclusions regaring the mechanism for carbon dioxide dissociation but their own work is not reported in any detail. Finally, Buser and Sullivan (1970) studied the initial dissociation rates of COZ in COZ dc glow discharges for pressures near 1 Torr. Their results indicated that both dissociative electron attachment and molecular collisional dissociation contributed to the loss of COz in an initially pure CO2 discharge. After several minutes the gas composition was observed to come to a steady state which seemed to be dictated by the vibrational temperature of the CO2-CO-02 mixture. It was found that the steadystate mixture defined an effective equilibrium constant which was independent of pressure above 0.5 Torr. Furthermore, it was observed that the steady-state mixture composition obeyed Le Chatelier’s principle.
Experimental Section A schematic of the experimental apparatus is shown in Figure 1. The central component of this apparatus is the discharge reactor, which consists of a 1-cm i.d. quartz tube. Two cylindrical copper electrodes were placed on the outside of the tube in order to couple the radiofrequency power to the discharge. These sleeves were each 2 cm long and were spaced 3 cm apart. The quartz tube and electrodes were enclosed by a Pyrex jacket through which an air stream was passed to cool the discharge. In addition to the straight quartz tube which was used for the reaction studies a special tube was constructed so that the gas temperature within the discharge could be measured. This tube had a side arm through which a glass-sheathed platinum-platinum-rhodium thermocouple could be inserted as shown in Figure 2. To avoid the transmission of rf currents to the potentiometer used to detect the thermocouple output, rf chokes and capacitors were inserted between the thermocouple and the potentiometer. Power for the discharge was supplied by a Tracerlabs Model 600 radiofrequency generator operating at 13.56 MHz and capable of delivering up to 350 W. The genera-
To Vacuum PumD n
t'A
.From I Helium Supply
Gas Chromatograph
Figure 2. Placement of temperature probe
Reactor Rotameter Matching
Manometer
El
-+-
4-wayValve
+ f f" o2
I
2
+4- Needle Valve
3
+
4
-&- Back-Pressure
5
co
c02
Helium for sample compression Flow restrictor Porapak-Q column Molecular sieve 5 A column Thermal conductivity detector
Regulator
Figure 1. Schematic of experimental apparatus.
tor was connected to the discharge through a matching network which balanced the impedance of the discharge with that of the generator. The power supplied by the generator to the matching network as well as that reflected from it could be read on a power meter incorporated into the generator. The net power to the discharge could thus be determined by obtaining an optimum match and then reading the difference between the forward and reflected power. Reactants were fed to the discharge from a gas manifold. The flow of each gas was controlled by a Nupro fine metering valve and the flow rate was measured with a Brooks rotameter. The pressure in the manifold was maintained at 40 Torr above 1 atm by a pressure regulator and was monitored by a mercury manometer. A Nupro fine-metering valve located at the outlet of the manifold reduced the pressure to vacuum. The pressure within the reactor was maintained by a mechanical vacuum pump and was measured using a Wallace and Tiernan Model FA141 pressure gauge located upstream of the reactor. A needle valve placed before the pump was used to control the pressure within the reactor. The concentrations of oxygen, carbon monoxide, and carbon dioxide in the product stream from the reactor were determined by gas chromatography. Since the separation of all three gases could not be achieved with a single column, the chromatograph (Varian Aerograph Model A-90-P3) was modified to permit the use of two columns. Each of the columns was made of a 10 ft long l/s-in. diameter stainless steel tube. The first column was packed with Porapack Q and the second with molecular sieve 5A. Both columns were operated at 40°C. The sampling and valving arrangements for the gas chromatograph are shown in Figure 1. Analysis of a Sample was initiated by turning the first of the two four-way stopcocks. The isolated sample was then partially pressurized with helium before turning the second four-way valve which injected the sample into the helium carrier gas stream. Passage of the sample through the Porapak column separated it into an oxygen-carbon monoxide peak
and a carbon dioxide peak. The first peak was then further separated into an oxygen peak and a carbon monoxide peak in the second column. In order to record all three of the chromatographic peaks with a single detector and recorder it was necessary to use both sides of the detector in the following manner. Six minutes after a sample was first injected the oxygen peak passed through both columns and was detected on the sample side of the thermal conductivity detector. At this point the switching valve was turned, routing the carbon dioxide peak through a restriction and into the reference side of the detector. After the carbon dioxide peak had been eluted, the carbon monoxide peak came out of the second column and was detected on the sample side of the detector. Using this technique a sample could be analyzed in 15 min. The output from the gas chromatograph was recorded on a Sargent Model SR recorder equipped with a disk integrator. Since the carbon dioxide peak passed through the reference side of the detector, its signal was negative. A polarity inverting switch was installed at the input to the recorder so that the carbon dioxide peak could be displayed in a positive manner and integrated by the mechanical integrator.
Results In order to characterize the effectiveness of the discharge for promoting the reversible reaction
co +
'/?O*
= eo:,
the composition of the products leaving the reactor were measured as a function of power, pressure, and gas flow rate. For the study of the forward reaction a stoichiometric mixture of CO and 0 2 was used while the reverse reaction was studied using pure C02. In addition to measuring the conversion accomplished in the discharge, the discharge volume and temperature were measured as well. These measurements were performed using a feed of COn alone. The gas chromatograms of the products leaving the discharge showed only three peaks corresponding to 0 2 , CO, and COz. Consequently, it was possible to characterize the effluent gas composition by the mole fractions of the three components. In order to represent the results for both the forward and the reverse reactions on a common scale, the measured mole fractions were converted into other parameters: cy, the mole fraction of carbon in the form of carbon dioxide, and /3, the ratio or carbon to oxygen. These two parameters are related to the mole fractions, x L ,of each component by the equations
Ind. Eng. Chem., Fundam., Vol. 13, No.
3,1974 205
0'
p = 4 torr
0.4-
-
FZ = 14.5pmole/sec
-
N
0
+
0.3-
0
-, B 0.2Feed
D
0.1
0
200
P (watts)
I
I p
2
0
IO
300
Figure 3. Gas composition as a function of power; p = 4 Torr and Fco = 14.5pmol/sec. I .o
20
30
p (torr)
Figure 5 . Gas composition was a function of pressure; P = 300 W and F[.O = 14.5pmol/sec.
I
8 torr
i
F; = 14 5 pmole/sec
o.2 -
0
100
200 P (WOttS)
300
t
00
1 IO
20
30
FtO2(pmole/sec)
Figure 4. Gas composition as a function of power; p = 8 Torr and Fco = 14.5pmol/sec.
Figure 6. Gas composition as a function of flow rate; p = 4 Torr a n d P = 100W.
Since the value of p is fixed by the inlet gas composition its value remains constant and the reactor performance can be described in terms of a alone. In the present experiments the value of @ was held at 0.5. For this particular value the fractional conversion can be conveniently expressed in terms of a . The fractional conversion is equal to a for a stoichiometric feed mixture of CO and 0 2 and equal to 1 - a for a feed of pure C 0 2 . Figures 3 and 4 illustrate the influence of discharge power on the value of a when the reactions are run at a constant pressure of 4 and 8 Torr. For all of the data shown in these figures the flow rates of reactants were adjusted to give an equivalent flow rate of carbon Fro of 14.5 bmol/sec. As may be seen, increasing the power causes the value of a for the forward reaction to increase and then pass through a broad maximum. The value of a for the reverse reaction decreases continually with increasing power. An interesting feature of the data is that for powers greater than about 200 W the curves for forward and reverse reactions became essentially parallel. The influence of pressure on the product composition is shown in Figure 5 for a constant power of 300 W. Here again the equivalent flow rate of carbon was maintained at 14.5 fimol/sec. The data for both the forward and re-
verse reactions show a linear increase in a with increasing pressure. At higher pressures both sets of data approach a common value of a . Figure 6 shows the effect of C 0 2 flow rate on the extent of C 0 2 decomposition in a discharge operated at 4 Torr and 100 W. At low flow rates the extent of decomposition is independent of flow rate. As the flow rate is increased above about 5 cLmol/sec a rises, indicating that the extent of C 0 2 decomposition decreases with increasing flow rate. During the course of the experiments it was observed that the volume occupied by the discharge was a strong function of the operating conditions. The glowing region was found to expand as the power was raised or as the pressure was lowered. A determination of the volume was undertaken since this information was needed for the interpretation of the kinetic data. These measurements were performed with a COa discharge. Since the actual shape of the visible glow is quite complicated, as shown in Figure 7, it was decided to effect a simplification by assuming that the glow could be represented by a cylinder with a diameter equivalent to the inside diameter of the discharge tube and a length equivalent to that of the visible glow. In order to make the measurements of the discharge length as objective as possible, these measurements were made by photographing the discharge. The photographs were taken in a dark room a t night using the discharge as the primary light source. A luminescent screen on which were shown the discharge
206
Ind. Eng. Chem., Fundam., Vol. 13, No. 3,1974
Symmetric about Center line
Electrode ~
___-
50 Extent of visible glow .1-_--
~~
_____
Ouorll Tube
30
!Figure7. Schematic of visible glow
100 P
200
300
(WOftS1
Figure 9. Discharge length as a function of power and pressure
Figure 8. Typical photograph used in length measurements.
conditions and a length scale were also recorded in the same photograph. For this work Kodak Tri-X film rated at ASA 400 was used together with an f-stop of 16 and a speed of 5 sec. Figure 8 shows a typical photograph. Since the discharge was symmetric about the electrode region, the measured length was obtained by doubling the length measured on the photograph and adding the overall length of the electrode region. The results of these measurements are shown in Figure 9. The dependence of the leneth on the dischawe Dower P and the uressure u was fouid to be given by th;! empirical equation
L = 4.53(P/P)1'2 The lines shown in Figure 9 are based on this equation. Measurements of the gas temperature in the dischargt were performed using the y-shaped discharge tube showr in Figure 2. The dependence of the temperature indicatec by the thermocouple on the power and pressure is illus trated in Figure 10. The maximum power used in thest experiments was limited to 100 W since it was observec that a t higher powers the thermocouple head began t o ra diate and the probe was destroyed in a very short timt ? thereafter. It is believed that this behavior at higher pow. ers was due to the formation of a pinhole in the glass sheath Once formed the pinhole would allow for direct contact he. tween the thermocouple head and the plasma, The curves shown in Figure 10 must he interpreted witk some care. The increase of the measured temperatun with pressure a t lower pressures is a real effect which car he associated with a change in the properties of the dis. charge. The appearance of a maximum and the subse. quent decrease in the temperature at higher pressures is., however, an artifact caused by the contraction of the glou to a point where it no longer surrounded the probe completely. Discussion Kinetics. Only a qualitative interpretation of the data presented in Figures 3-6 will he offered here. A more de. tailed analysis will he undertaken in part II of this papei once a theoretical framework has been established. The data presented in Figures 3 and 4 indicate thal; above 200 W the composition of the products leaving the!
'loot1 i *
3
c
0
o
10
20
u
D (lW.1
Figure 10. Gas temperature as a function of power and pressure reactor approach a common level from both the forward and reverse directions. The curves of a for the forward and reverse reactions do not converge, however, hut instead become nearly parallel to each other. The presence of an almost constant difference between the two curves suggests that this behavior may be due to a partial bypassing of reactants around the discharge zone. A further examination of this interpretation is warranted in view of the shape of the discharge zone shown in Figures 7 and 8. We may begin by dividing the cylindrical volume occupied by the discharge into two parts, a central cylindrical volume V, in which reaction does occur surrounded by a thin annular volume V, in which no reaction occurs. Therelationshiu of these volumes to the total discharee zone volume Vis given by ~
V , = 6V V,
=
(1
(4 \
- 0)V
Under the added assumption of plug flow through the disL . . . . -
---- ... car, --- exp'eJs ^
C I l U g e ZULIB, we
IL.
L'lC
L-L-1
WLkaLI
n L. lllvlar U " W raw _^I..
T1
-c
I- VI
any component as
F
= F,
+ F=
(5)
where
F , = 6F Fa = (1
- b)F
(6)
For the C / O ratio used in these experiments (k, p = 0.51, (1 - a) is equal to the conversion for the forward
reaction and CY is equal to the conversion for the reverse reaction. Consequently, the flow rate of CO leaving the Ind. Eng. Chem., Fundam.. VoI. 13, No. 3.1974
207
discharge zone can be expressed as
Table I. Computed Equilibrium Temperatures p, w
for the forward reaction. In eq 7 Froo is the inlet flow rate of CO and (1 - af’)is the conversion of CO occurring in V,. The quantity af‘ can be related to af,the value of a measured experimentally, by
F,,/FcOo = (1 - a f ) = 6 ( 1 -
cyf’)
+
(1 - 6 ) (8)
Solving for af’,we obtain
(9 1
= au,/6
CYf’
A similar series of expressions can be developed for the reverse reaction. Thus, the flow rate of COz leaving the reactor can be written as
where Fc0zo is the inlet flow rate of COZ and a,’ is the conversion of COz occurring in V,. Here again, a,’ can be related to values of a measured experimentally by Fcoz/Fc4
0
= err =
KCL,’
+
(1 - 6 )
(11)
Solving for a,’ we obtain
a,’ = 1
-
(1 - cr,)/F
(12)
If a steady-state composition is achieved within V,, then af’will equal a,’. Under this condition eq 9 and 12 can be combined to give cy,
-
(xi
= 1 - 6
(13)
From eq 13 we can conclude that as long as the steadystate condition and the assumptions of the bypass model are maintained, the difference between the experimentally measured values of af and a , will be a constant. These results may now be applied to the interpretation of Figures 3 and 4. In these figures (af - a,) is almost constant for powers above 250 W. Using the value of (af - a,) at 350 W we may determine from eq 13 that 6 = 0.90 for p = 4 Torr and 6 = 0.92 for p = 8 Torr. These figures suggest that 90% of the total discharge volume is active and that the remaining 10% acts as a bypass for the reactants. As a further application of the bypass model we have used eq 9 and 12 to complete a,’ and af’as a function of power. These results are illustrated by the dashed curves in Figures 3 and 4. Notice that the computed product compositions approach a common value for powers above 250 W. Whereas the displacement of the curves for cyf and a , in Figures 3 and 4 can be interpreted satisfactorily by assuming a partial bypassing of reactants, the physical basis for this assumption must be examined further. As stated, the bypass interpretation requires that the reactants passing through the annular region not mix with those passing through the central region where reaction occurs. The extent to which this description is correct depends upon the Peclet number. An estimate of the Peclet number shows it to be about 1, which means that in fact a significant amount of radial diffusion will occur. This conclusion, however, does not totally rule out the possibility of bypassing since it is still possible that due to the highly nonuniform radial distribution of the glow intensity (which is a rough measure of the intensity of reaction within the glow) and incomplete radial diffusion an effective appearance of bypassing is achieved. The existence of a steady-state product composition is further supported by the data shown in Figure 6. There it 208
Ind. Eng. Chem.,Fundam., Vol. 13, No. 3, 1974
p , Torr
300 300 300 300
5
10 20 30
a
Teq,
0.26 0.28 0.32 0.36
O K
2431 2492 2496 2496
is observed that below a flow rate of 5 pmol/sec the value of a becomes independent of the gas flow rate. This characteristic can be interpreted by saying that at low flow rates the space time is sufficiently long for the steadystate product composition to be achieved. The influence of pressure on the product composition is shown in Figure 5. As the pressure increases the values of a for both the forward and the reverse reaction increase and approach each other more closely. An important question raised by the observation of a steady-state product composition is whether or not this composition corresponds to thermodynamic equilibrium. To answer this question equilibrium temperatures were calculated for values of a lying midway between those for the forward and reverse reactions shown in Figure 5. These temperatures are listed in Table I. As may be seen, all of the equilibrium temperatures are above 2400°K. While no direct measurements of gas temperature were performed for the conditions shown in Table I, estimates made on the basis of measurements performed at lower powers suggest that the gas temperatures are considerably lower than 2400°K. Based on these considerations we can conclude that the steady-state values of a listed in Table I are not the result of thermodynamic equilibrium but, rather, correspond to the establishment of a kinetic steady-state condition in which the rates of the forward and reverse reactions are just balanced. The occurrence of such a condition has been observed previously by Andreev (1964a,b) and Semiokhin (1964, 1965, 1966) and their coworkers during their study of the oxidation of carbon monoxide and the decomposition of carbon dioxide in a silent discharge and by Buser and Sullivan (1970) as a part of their study of carbon dioxide decomposition in a dc glow discharge. A further discussion of the means by which the steady state is maintained will be presented in part II of this series. Temperature Measurements. The temperatures shown in Figure 10 are those measured by the thermocouple probe inserted into the glow of the discharge. An important question to be raised is to what extent these measurements are a true representation of the gas temperature within the discharge. To ascertain this a heat balance may be written around the probe as follows
A,-
k
LP
( T , - T,)
+ Ap
