Oscillatory and Explosive Oxidation of Carbon Monoxide BY CHINGH. YANG Department of Mechanics State University of New York at Stony Brook Stony Brook New York 11794 U.S.A. Received 30th July 1974 The glow and explosion limits of the CO and O2system are calculated in wide ranges of composi- tion water content surface efficiency temperature and pressure. The boundary of the oscillatory region in the P-Tplane is theoretically predicted. Results are compared with the existing experimental data. The well-known experimental observation that traces of water sensitively affect the oxidation process of carbon monoxide is quantitatively examined and verified. The kinetic oscillation in the low temperature oxidation of carbon monoxide reported by Dickens Dove Harold and Linnett is perhaps one of the most striking observations in gas kinetics.Obviously the autocatalytic chain mechanism in its classical form does not explain this intriguing phenomenon. In an attempt to construct the kinetic oscillation mechanism mathematically a scheme which focused on the interaction between an autocatalytic chain carrier (0atoms) and an inhibitive intermediate (CO molecules) was postulated.2 A binary non-linear model was derived from the scheme. Analysis of this simple model not only yielded solutions for sustained oscillation it also predicted the glow and explosion phenomena that are associated with the oxidation of CO. In order to examine the detailed kinetic mechanism with realistic rate constants a general model which conserves all reactants catalytic impurities (H,O) and ntermediate species was formulated to contain all proposed reactions without invoking the assumption of steady states.Machine-integrated solutions again predicted the various phenomena. Particular effort was directed to the study of the characteristics of kinetic oscillation. The wealth of experimental data on CO oxidation on the other hand is con- centrated on the measurements of glow and explosion limits. It is evident that an extensive calculation programme is needed to map out the limits and oscillatory regions in the P-T plane so that the theory can be quantitatively tested and compared with experimental measurements. This is the primary objective of our present work. The kinetic scheme previously proposed is slightly modified.The glow and explosion limits are calculated with composition of the mixture and wall efficiencies of the vessel varied. The boundaries of the oscillatory regions in the P-T plane are delineated. Computed limits with water content pressure and temperature varied in wide ranges ([H,O] -0.001 -10% P -1-400 Torr and T -400-1 1OOOC) are compared with the existing data. The well-known observation that explosion limits are sensitively affected by traces of water 194-6 is theoretically verified. Wide agreement between the data 7-9 and the theoretical predictions argues convincingly for the validity of the currently proposed kinetic mechanism for the low temperature oxidation of carbon monoxide. 114 C. H. YANG 115 KINETIC MECHANISM AND MATHEMATICAL MODEL The kinetic scheme contains all reactions proposed previously with the addition of only one new reaction (reaction (18)) kl c02+ 02 + c02+ 0 (1) k2 CO+O+M 3CO,"(CO,)+M (2) k3 co:+o 3CO+O (3) k4 CO:+M -+ C02+M (4) ks CO+OH 4CO,+H (5) k7 O+H20 -+20H (7) k8 H -+ wall destruction k9 0 + wall destruction kio HO + wall destruction ki1 H+02+M -+ HO2+M kl2 H02+ HO2 + H202 + 02 k13 H2023-M + 20H+M k14 H02 -+ destruction on wall k15 H2023destruction on wall kl6 H+HzOz 4 H2O+OH k17 O+OH -+ 02+H k18 H+HO + 20H 116 OSCILLATORY AND EXPLOSlVE OXIDATION OF CARBON MONOXIDE y9 = Yg”+!f(Yl-Y8 -Y; f y7-YZ -Y4) -Y5 -Y6* (27) [CO] represents the sum of the concentrations’ of both ground state CO and excited CO; molecules produced in reaction (2) and yo2 represents the initial concentration of the species yi.All chain termination reactions are assumed in the kinetic region. The third body efficiencies for all species are assumed to be unity with only one exception; a value of 2.3 is selected for C02 molecules. Other details of the calculation method are reported in ref. (3). Selected values of the rate constants for all gas phase reactions are listed in table 1. No systematic attempts had been made to iterate the numerical values of rate constants to achieve the optimum fitting of the data. TABLE 1 reaction activation energy/kcal mol-1 Arrhenius factor */cm3 mol-1 s-1 remarks (1) co+o2 (2) CO+O+M (3) co;+o (4) CO;+M’ (5) CO+OH (6) H+02 (7) 0+H20(11) H+02+M (12) HO2+HO2 (13) H202+M (16) H202+H (18) H+HOz (17) OH40 -60 0 0 0 1.08 16.8 19.5 13 0 45 0 9 0 2.25 x loll LOX 1014 5.0~1O1O 1.25 x 105 4.2~10l1 2.24~1014 4.2~1014 5.o~1015 3.18~1014 1.3 x 1013 3.o~1013 1.8 x 10l2 1.17~1O1O ref.(3) ref. (10) ref. (3) ref. (3) ref. (10) ref. (10) ref. (10) ref. (10) ref. (10) ref. (10) ref. (10) ref. (10) (4 * Arrhenius factor for terniolecular reactions has the dimensions of cm‘ mol-2 S-’. (a)A value smaller by a factor of two than the one suggested in ref. (11) is selected. COMPUTATION RESULTS The definitions of the various phenomena such as glow oscillation etc. are generally vague. In the laboratory they are used to differentiate the different characteristics displayed by the bluish light emission from the reacting gases.In general if the pulse of emission is visible for an extended period of time a few seconds or more it is taken to be a glow. The temperature and the pressure of the mixture is then called the “glow limit”. When the emission is intense and brief lasting no longer C. H. YANG 117 than a split second it is identified as an explosion and the corresponding temperature and pressure is denoted as the “explosion limit”. Oscillations are usually referred to a series of glows that appear periodically. The limits of oscillation however had not been systematically measured in previous work. Before the presentation of our results it is desirable to define these terms a little more precisely.Glow-a single stroke of visible emission that lasts a few seconds. After the passage of a glow only a small portion of the reactants in the mixture is consumed. Invisible reactivities are supported for a long time after the glow. In the P-T plane the point where the glow occurs is marked with the sign “2’as the glow limit in our Presentation of data that follows. Sustained glow-an extended stroke of emission which lasts from a second to several minutes. All reactants are consumed after the passage of a sustained glow. The sustained glow limit is marked with “x”. Oscillation-periodic glows with virtually undamped amplitudes. The pressure and temperature at which this occurs is marked with the sign “0”in the P-T plane. After glow-a sustained glow which is preceded by a glow or several cycles of oscillation.It will be shown that there is no real difference between the solutions of sustained glow and explosion. The criterion to differentiate them by the length of their derivation is arbitrarily chosen. It will also be demonstrated that glows and oscilla- tions are all represented by periodic solutions. For a glow the oscillatory solution is sharply damped with only the first one of its emission peaks visible. In all cases calculated trajectories for all reactants and all intermediate species are obtained. As expected the concentration of reactants decays with time. The trajectory of either O2 or CO can be conveniently used to indicate the degree of completion of the reaction at any point in time.0 atom concentration is always the highest among all radicals. The implication is that 0 atoms are involved in the slowest reaction path in the oxidation process. Water concentration is always 180” out of phase with 0 concentration. Hydrogen containing radicals or intermediates are assumed to form water molecules in the gas phase as soon as they are terminated on the walls. According to a bimolecular association theory (CO + 0 + CO +hv) proposed by Broida and Gaydon l4 the emission intensity from the reacting gas is proportional to the concentrations of CO and 0. A threshold intensity must exist below which the emissions become undetectable. An 0 atom concentration of 1O-I’ mol ~m-~ selected previously 2*3 to be the threshold value and it has been was retained in the present work.Since the visible emission always coincides with the 0 atom concentration peaks the presentation of the 0 atom concentration trajectory usually is sufficient to convey the complete kinetic behaviour of the system. The wall efficierxies are assumed to have the values listed in table 2. The first set of limits is calculated with CO +202 mixtures ; results are plotted in fig. 1. Curves A B C D and E correspond to mixtures with water contents of 10 I 0.1 0.01 and 0.001 % by volume respectively. The computing procedure follows the same sequence of steps used in the heating method for determining limits in the laboratory. Trajectories of eqn (19)-(27) are integrated for mixtures with fixed water content composition and pressure.Bath temperatures are raised with increments of 1 or 2 K each time until the desired limits are reached. In fig. 1 solid curves join the points of the lowest temperature at which either a sustained glow or an explosion is calculated. On many occasions these calculated limits are preceded by glows oscillations or both at slightly lower bath temperatures. The boundary of the oscillation region in the P-T plane is drawn with a closed curve of broken lines. 118 OSCILLATORY AND EXPLOSIVE OXIDATION OF CARBON MONOXIDE No oscillation has been obtained for mixtures containing 10 % water or above the pressure of 120Torr. It is interesting to note that the highest pressure at which Dove l2 observed oscillation is 110 Torr. TABLE 2.-wALL EFFICIENCIES reaction wall efficiency (8) H 10-4 (9)0 10-4 (10) OH 10-4 (14) HOz 10-3 (15) Hz0* 10-3 Fig.1. shows that the largest pressure range (40-1 10 Torr) within which oscilla- tions are calculated is for mixtures with 1 % water content. This does not mean however that oscillations are more likely to be found in wetter mixtures experimen- tally. It may be that the reverse is true. Thus for a wet mixture with the pressure fixed the bath temperature range within which oscillation can be calculated is extremely narrow often no more than 1 or 2 K. Unless the heating rate is very slow the heated mixture passes this range and reaches sustained glow or explosion T/"C FIG. 1.-Explosion limits and oscillation region of CO + 202 mixtures.Calculated curves A Water content = 10 % B Water content = 1 % C Water content = 0.1 % D Water content = 0.01 % E Water content = 0.001 %. Experimental results :G Hadman Thompson and Hinshel- woody7Q Gordon and Knipey6 L Lewis von Elbe and Roth,8 NDickens. temperatures before oscillations are fully developed. In contrast with the drier mixtures that contain water from 0.1 to 0.01 % the oscillatory bath temperature range extends up to 20 K in span. To observe oscillations experimentally in these mixtures will probably not be difficult even with an average heating rate. Dove's l2 discovery of oscillations in the CO system is thus probably linked with his use of very dry mixtures at low pressures. Measured axplosion limits by several authors 6-9 are C.H. YANG 119 replotted in dotted lines though the exact water content for the experimental data is unknown. Dickens apparently used the driest mixtures. His data fall in between the calculated limits with water contents of 0.01 and 0.1 %. This seems to be high for his supposedly well dried mixtures. Gordon and Knipe’s data match the limits calculated for mixtures containing 0.1 % water which is one or two orders of magnitude higher than their estimate; one is dubious about the meaning of these discrepancies when the water content in the mixture has not been determined accurately. It should be noted that the experimental limits are merely straight lines drawn through sets of scattered data points. There is no reason to expect the actual limits being straight lilies in the P-T plane.The slopes of the limits are generally steeper for the wetter mixtures. Figures around the points where oscillations are calculated indicate the period of oscillation in seconds. Dove l2 observed no clear dependence of period of oscillation on composition pressure and temperature in his experiments. Our results in fig. 1 show the same random character. EXPLOSION AND SUSTAINED GLOW LIMITS In experimental studies explosion and glow limits are obtained by heating the mixture to a critical temperature. Below this temperature the reactivity of the system is usually unmeasurable. We found this to be the case in our calculations with very wet mixtures or at very high pressures. Two trajectories are plotted in fig.2. They 6 7Q-4-:-j-7794~ r Curve A 1 timeis FIG.2.-Trajectories of explosion and sustained glow. Water content = 10 % composition = COf 20,. Calculated trajectories :A temperature = 441°Cand pressure = 10 Torr B temperature = 400°C and pressure = 3 Torr. are calculated with C0+20 mixtures containing 10 % water. The pressure for trajectory A is 10Torr and the temperature is 441°C. The concentration of 0 atoms rises to exceed the threshold after an induction time of 73 s. Within a period of 0.3 s CO concentration is reduced to 10 % of its initial value. The trajectory describes an explosion according to our definition. If the calculation is repeated with the bath temperature one degree lower than the preceding case the calculated 0 atom con- centration remains indefinitely many orders of magnitude below the threshold.120 OSCILLATORY AND EXPLOSIVE OXIDATION OF CARBON MONOXIDE No reactivity will be detectable in correspondence with this trajectory. The explosion and non-explosion regions in the P-T plane are thus sharply divided by the limit. Trajectory B is calculated at a pressure of 3 Torr and a temperature of 400°C. The 0 atom concentration exceeds the threshold after an induction period of 516 s. It is reduced to 5 % of its initial value in 10 s. The visible emission will probably last 5 to 6 s. It is a sustained glow limit. Again results show the reactivity of the system to be unmeasurable at a temperature one degree lower than the limit. GLOW AND SUSTAINED GLOW TRANSITION The glow and sustained glow phenomena cannot be differentiated in experiments if the reactant consumption is not measured.Hoare and Walsh reported that if stationary conditions of pressure and temperature were used a glow would appear and then slowly fade away in time ; but on reducing the pressure slightly the glow would brighten again. Obviously this could not have happened at a sustained glow limit where the reactants would be exhausted in one stroke. In calculated trajectories glow and sustained glow are clearly different. The trajectory for a glow is an oscillatory solution and the trajectory for a sustained glow is not. A series of trajectories that maps the transition from glow to sustained glow is presented in fig. 3. Mixtures of time/s FIG.3.-Glow and sustained glow transition.Composition = CO+2O2 water content = 0.1 % pressure = 20 Torr. Calculated trajectories A temperature = 575"C B temperature = 577"C C temperature = 580"C D temperature = 581°C. CO +20 with 0.1 % of water are used and the pressure is fixed at 20 Torr. Trajec-tories A B C and D correspond to bath temperatures of 575 577 580 and 581"C respectively. The 0atom concentration represented by trajectory A never exceeded the threshold. It is therefore undetectable. The first peak of trajectory B and the first and second peaks of trajectory C are above the threshold level. Visible glows C. H. YANG will accompany these peaks. The results also show that after the passage of the first peak of trajectory B only 0.4 % of CO concentration is consumed and after the passage of the first and second peak of trajectory C the CO consumption is increased to 3 %.When the bath temperature is raised only one degree to 58 1"C,a sustained glow trajectory D is attained. CO concentration is consumed to 8 % of its initial value in 20 s. The visible glow will last 15 to 20 s and then fade away as reactants are completely exhausted. GLOW OSCILLATION SUSTAINED GLOW AND EXPLOSION TRANSITION Calculations show that as the mixtures become drier the temperature interval in which the transitions take place (glow 3 oscillation -+sustained glow -+ explosion) becomes wider. A series of trajectories is calculated and presented to show such transitions in fig. 4. CO+2O2 mixtures containing 0.1 % of water are used and the tinie/s FIG.4.-Glow oscillation sustained glow and explosion transitions.Composition = CO + 202 water content = 0.1 % pressure = 60 Torr. Calculated trajectories A temperature = 646°C B temperature = 648°C. C temperature = 657°C D temperature = 662°C E temperature = 682°C. pressure is fixed at 60Torr. Trajectories A B C D and E correspond to bath temperatures of 646 648 657 662 and 682"C respectively. Trajectory A is presumably undetectable and a glow must accompany the first peak of trajectory €3. Within the temperature range from 649 to 658°C all solutions are oscillatory and trajectory C (T = 675°C) represents a typical example. The period of oscillation decreases from 18 to 10 s as the bath temperature is raised from one end to the other.Oscillations of this type may continue for many cycles without appreciable change in their period and amplitude. In ref. (3) one hundred cycIes were calculated for one 122 OSCILLATORY AND EXPLOSIVE OXIDATION OF CARBON MONOXIDE case and McCaffrey and Berlad observed over two hundred cycles of oscillation in their experiments with the CO system. In a binary system this type of behaviour is generally associated with oscillations about a limit cycle. Trajectory C represents a sustained glow the visible emission in this case will last about 20 s. The surging second peak of 0 atom concentration is reminiscent of the " pic d'arret " l5 phenomenon in hydrocarbon oxidation. The kinetic mechanism for " pic d'arret "is still unclear but the surge of 0 atom concentration in the final phase of CO oxidation such as shown here may be attributed to the depletion of CO concentration in the mixture.Reactions (2) and (3) are the basic inhibitive steps in the kinetic scheme. The depletion of CO weakens both reactions and chain carriers are no longer pre- vented from a temporary divergence which is finally checked by complete fuel exhaustion. The duration of the sustained glow becomes shorter as the temperature is raised higher above 662°C. At T = 682°C the sustained glow is compressed into a flash or an explosion. AFTER GLOW Linnett et all6 reported the observation of after glows which followed explosions and lasted as long as 20 s. Trajectory A in fig. 5 is computed with a C0+20 mixture containing 1 % water.The pressure is 80Torr and the temperature is 605°C. The flash of emission that coincides with the first peak of 0 concentration is a glow by definition. Seven seconds later the 0 concentration rises again and exceeds the threshold for 10 s. An event like this is naturally identified as an after 20 time/s Fro. 5.-Trajectories of after glow A water content = 1 % pressure = 80Torr temperature = 605"C composition = C0+2OZ. B water content = 1 % pressure = 30 Torr temperature = 525"C composition = CO+502. C. H. YANG 123 glow in the laboratory. The first peak will probably be identified as an explosion due to its brief duration (4s). After glows may also follow many cycles of oscillation. A typical example is calculated with a CO+ 502 mixture containing 1 % water and plotted in fig.5 (trajectory B). The bath temperature and pressure are 525°C and 30 Torr respectively. The glow will last over 20 s. Like the second peak of trajectory C in fig. 4 after glows are caused by the depletion of CO concentration in the final phase of oxidation. EFFECTS OF PRESSURE Egerton and Warren l7 reported that using a withdrawal method a blue glow appeared as the explosion limit of their moist CO and O2mixtures was approached? that on crossing the explosion limit at a fast rate the glow suddenly increased to a brilliant flash ;but that with sufficiently slow evacuation no such transition from glow to flash occurred? the glow rising to a constant intensity throughout the explosion region.Their experiment evidently dealt with the transition between a sustained glow and an explosion. Three trajectories are calculated to show the transitions timeis FIG.6.-Transition among oscillation sustained glow and explosion with pressure varied. Compos-tion = CO+2O2 water content = 0.1 % temperature = 652°C. Calculated trajectories A(A’) pressure = 45 Torr B(B’) pressure = 50 Torr C(C‘ and D) pressure = 45 Torr. among oscillation sustained glow and explosion by varying the pressure. The composition of the mixture is CO +20 and its water content is 0.1 %. The tempera- ture is fixed at 652°C. In fig. 6 trajectory A B and C are calculated at pressures 45 50 and 55 Torr respectively. The fuel consumption rate in terms of CO concentration over its initial value [CO]/[CO],,is also presented for all three cases (curves A B’ and C’).Under 45 Torr pressure trajectory A represents a marginal explosion with a 124 OSCILLATORY AND EXPLOSIVE OXIDATION OF CARBON MONOXIDE duration of about one second. The corresponding fuel consumption curve A’ shows that the fuel concentration falls rapidly one second after the reaction started. Trajectory B (P= 50Torr) represents a typical sustained glow which probably would be visible for about 8 or 9 s. Under the pressure of 55 Torr trajectory C is an oscillatory solution. The corresponding fuel concentration curve C’ shows the steps of falling off that coincide with the peaks of 0 atom trajectory. Water concen- tration over its initial value for the case P = 55 Torr is represented by curve D in fig.6. It shows that 8-12 % of the total water molecules are dissociated at the peaks of 0 atom concentration. Linnett et a1.16 defined a quasi limit according to the time required for the visible emission to build up to the peak intensity. If the required time is equal to or less than 0.15 s then the system is said to be on or to have surpassed the quasi explosion limit. A series of trajectories is calculated with pressures across the entire explosion peninsula B in fig. 1. The composition for the mixture is CO +20 and the water content is 1 %. The bath temperature is fixed at 624°C which was also the value used in the experiments of Linnett ef al. TrajectoriesA B C D E F and G corresponding to pressures of 10 15,20,40 80,90 and 110 Torr respectively are presented in fig.7. Trajectory A (P= 10 Torr) appears to satisfy the criterion for the “ quasi limit ” but the measured limit for the same mixture by Linnett et al. was 20Torr. The dis-crepancy may be attributed to many factors the uncertainties involved with surface efficiencies the numerical values adopted for the rate constants etc. The sustained glow limit for this mixture under 10Torr pressure is 480°C (curve B in fig. 1). Between the temperatures of 480 and 624°C (with pressure fixed at 10Torr) the timels FIG.7.-Trajectories across explosion peninsula. Composition = CO+ 202 water content = 1 % temperature = 624°C. Calculated trajectories A pressure = 10 Torr B pressure = 15 Torr C pressure = 20Torr D pressure = MTorr E pressure = 80Torr F pressure = 90 Torr G pressure = 110 Torr.calculated 0 atom trajectory starts as a sustained glow and accelerates gradually to become a “ quasi explosion ” at 624°C. The transition is always smooth without sudden disruption at any point when the temperature is raised. This is consistent with their conclusion that a lower explosion limit does not exist inside the glow limit. C. H. YANG 125 The mixture is most reactive at the pressure of 40Torr (trajectory D). The ffash of emission in this case lasts no longer than 0.04 s. Curve B in fig. 1 shows that the upper Iimit for the mixture at the temperature of 624°C is 120 Torr. The rate of reaction is gradually decreasing as the pressures are raised to approach the upper limit as shown in fig.7 (trajectories E F and G). EFFECTS OF COMPOSITION Experimental results l2 showed that the reaction rates of lean CO mixtures are usually greater than that of the stoichiometric mixture. Limits for stoichiometric mixtures are calculated and presented in fig. 8. No oscillations can be obtained for T]"C FIG. S.-Explosion limits and oscillation region of stoichiometric mixtures. Calculated curves A water content = 10 % B water content = 1 % C water content = 0.1 % D water content = 0.01 % E water content = 0.001 %. Experimental results from Hoare and Walsh :A' water content = 5 % B' dry. such mixtures with water content in excess of 0.5 %. Hoare and Walsh's data for mixtures of the same composition are replotted as dotted lines (curves A' and B').Their curve A' (5 % water content) appears to fall on the calculated curve A with a water content of 10 %. Results for their dry mixtures (curve B') fit the calculated curve B (1 % water) quite well. It is noteworthy that the peculiar curvature of the measured upper limit at low pressures is closely matched by the calculated one. The shape of the peninsula tip calculated with different water contents does not change appreciably. Hoare and Walsh4 noted that upper limits for the dry and wet mixtures merge together and become one at very low pressures. Our calculated results show that the effect of water on the temperature part of the limit is still distinct only the pressure scale between the different limit curves is compressed at low pressures.It must be pointed out that the glow limits reported by Hoare and Walsh are probably a combina-tion of gtow and sustained glow limits as the two are indistinguishable as long as fuel consumptions are not measured. Limits for very lean and rich mixtures are plotted in fig. 9. Curves A B and C 126 OSCILLATORY AND EXPLOSIVE OXIDATION OF CARBON MONOXIDE are calculated with mixtures containing 1 % water while curves D E and F are for drier mixtures with only 0.01 % of water. The experimental results of Dickens et a2.l are reproduced in dotted lilies A’ B’ and C’. Theoretical results are at least consistent with the experimental measurements in predicting higher reaction rate for the leaner mixtures. The glow and oscillation limits for curves B and E are not shown in fig.9 to avoid crowding. It can be concluded from the results that oscillations are less likely for rich mixtures and the period of oscillation is shorter for leaner mixtures. T/”C FIG.9.-The effects of composition on explosion limits. Calculated curves A 3 C water content = 1 % D E F water content = 0.01 % A D composition = CO+5O2 B E composition = CO+2O2 C F composition = 4CO+O2. Experimental results from Dickens et a/.’ A’composi-tion = C0+902 B’ composition = CO+2O2,C composition = 2CO+O2. EFFECTS OF WALL EFFICIENCIES It is assumed that the kinetic role of the walls is limited to the destruction of chain carriers and intermediates in this work. Wall efficiencies (listed in table 2) which have been used for all calculations so far are intended for mildly reflective vessel surfaces.Limit curves B and D of fig. 1 are replotted in fig. 10 with the labelling retained for comparison with limits curves A and C. Curves A and C are calculated exactly as for curves B and D respectively except all the wall efficiencies are one order of magnitude greater. These higher efficiencies are selected to simulate efkctive vessel surfaces. Curves A and C show the hits shifted to higher temperatures at low pressures where heterogeneous termination is most effective. One surprise result is that the difference between the limits for reflective and effective surfaces are greater at higher pressures than at intermediate pressures. Curves A‘ and C’ represent data from Dickens et aZ.l for CO+202 mixtures in two different vessels (vessel No.1 and 3). Qualitative features of the experimental ~neasurements im clearly followed by the calculated ones. One intriguing question remains namely why the C. H. YANG 127 wall efficiencies for the two vessels which were made of same materials (quartz) and had been treated the same way before tested are so different. The calculated period of oscillation is generally shorter for effective surfaces. The pumping mechanisms due to wall site saturation proposed previously 2* are not invoked in all the calculations presented here. Our other calculations show that the oscillatory region in the P-T plane is enlarged towards the higher and lower pressures if the wall site saturation mechanism is imposed on the scheme.At the present time this region in the P-T plane has not been mapped out by measurements. It is probably premature to either accept or reject this pumping mechanism. T/"C FIG. 10.-The effects of surface on explosion limits. Calculated curves B D reflective surface (wall efficiencies listed in table 2) A C effective surface (lox wall eficiencies listed in table 2). Experimental results from Dickens :A' vessel No. 1 C' vessel No,3. DISCUSSION It was suggested ' that the explosive reaction of CO oxidation is retarded by some product formed in the reaction. Earlier Jon0 found that the reaction rate of a CO and O2mixture fell off sharply after a fast initial start. This was confirmed later by Knipe and Gordon.20 Minkoff and Tipper proposed that in the early phase of oxidation carbon suboxides such as C20and C302may have been produced which inhibit the reaction by removing the chain carrier 0 atoms from the system.Using C20 as an intermediate Gray 21 constructed a theory quite similar in mathematical structure to that of ref. (2) to explain the oscillations and glow limits in CO oxidation. The calculated trajectories for the cases of explosion and sustained glow in fig. 2 3 4 and 7 clearly confirm this observation. The reaction rate which is proportional to 0 atom concentration decreases by as much as several orders soon after the reaction starts. Excited CO; molecules are clearly the inhibitors. Reaction (3) the rate retardation step becomes effective once sukient CO; concentration is accumul- ated shortly after commencement of the reaction.The oscillation phenomenon is of course another product of this autocatalytic and inhibitive reaction tncchanism. 128 OSCILLATORY AND EXPLOSIVE OXIbATION OF CARBON MONOXIDE Dove l2 raised the question :is the supposed effect of water merely to depress an explosion which already exists at high temperature or is the limit entirely dependent on the presence of water? Our answer is affirmative to the second part. It was shown in ref. (2) that water plays a key role in the autocatalytic chain. In the absence of the autocatalytic reaction both the oscillation and explosion phenomena disappear. Our calculations for a mixture with 0.0003 % water have yielded only glow with long lasting slow reaction or extended sustained glow at very high temperature.Dove l2 made similar observations in his experiments with extremely dry mixtures. Dove l2 also reported that intensive use of one vessel caused the limits to become very indistinct or to be replaced by a relatively slow reaction accompanied sometimes by a glow occurring at temperatures above the limit. A possible explanation for his observation may be proposed as follows if we assume that water molecules can cling on the vessel walls so tightly as to defy the drying process they may become active and play a significant role when explosion limits for extremely dry mixtures are measured. After each experiment the wall may readsorb the water from the product gases and the dry mixtures are continually made to appear slightly wetter than they really are.Only after intensive use of the vessel do water molecules manage to escape and when they do the kinetic behaviour of the extremely dry mixture becomes evident as described by Dove. The calculated explosion limits appear to be consistently higher than the experi- 41 mental measurements.” 6* l6 This may mean that either the rate constants selected for the autocatalytic chain reactions are too low or the termination reaction rate constants are too high. One can probably achieve a better fit between the calculated results and data by using a smaller activation energy for reaction (2) or a smaller numerical value for the rate constant k2. Actually a more comprehensive calculation program is needed to optimize the numerical values of all key rate con- stants (such as k3,kq,etc.) in the CO system.P. G. Dickens J. E. Dove J. E. Harold and J. W. Linnett Trans. Faraduy Soc. 1964,60 539. C. H. Yang Comb. Flame 1974 23 97. C. H. Yang and A. L. Berlad J.C.S. Faraday 1 1974 70 1661. D. E. Hoare and A. D. Walsh Trans. Faraday SOC.,1954,50 37. A. S. Gordon J. Chem. Phys. 1952,20 340. A. S. Gordon and R. H. Knipe J. Phys. Chem. 1955,59 1160. ’G. Hadman H. W. Thompson and C. N. Hinshelwood Proc. Roy. SOC.A 1932 137 87; 1932 138,297. B. Lewis G. von Elbe and W. Roth 5th Zrrt. Symp. Combustion (Thc Combustion Institute Pittsburgh Pennsylvania 1955) p. 610. P. G. Dickens Dissertation (Oxford 1956). ’*D. L. Baulch D. D. Drysdale D. G. Hoare and A. C. Lloyd High Temperature Reaction Rute Data (Leeds University 1968) No.1 and 2. ’I R. R. Baldwin L. Mayer and P. Dorao Trans. Faraduy Soc. 1967 63 1665. ’’ J. E. Dove Dissertation (Oxford 1956). B. McCaffrey personal communication. l4H. P. Broida and A. G. Gaydon Trans. Fnruday Soc. 1953 49 1120. Is M. Lucquin J. Chim. Phys. 1968 55 827. l6 J. W. Linnett B. G. Reuben and T. F. Wheatley Comb. Flame 1968 12 325. A. C. Egerton and D. R. Warren Nature 1952 170,420. I8 G. J. Minkoff and C F. H. Tippcr Chemistry of Contbustioii Reactions (Butterworth London 1962). W. Jono Rev. Phys. Chem. Japan 1941 15 17. 2o R. H. Knipe and A. S. Gordon J. Chern. Phys. 1957 27 1418. 21 B. F. Gray Trans. Faraday Soc. 1970 63 1 118.