L. RHEAUME A N D G. PARRAVAKO
264
Vol. 63
DECORlPOSITION KINETICS OF NITROUS OXIDE O N a-MANGANESE SESQUIOXIDE BY L. RHEAUME AND G. PARRAVANO~ Prick Chemical Laboratory, Princeton University, Princeton, New Jersey Received August 86, 1968
The detailed kinetics of the catalytic decomposition of nitrous oxide on a-MnrOa has been determined in the temperature range 280 to 346". The experimental results are consistent with a reaction mechanism in which the slow, rate determining step is the decomposition of adsorbed NzO molecules. The derived rate equation is eq. 11, where kz is the rate constant for the rnte-determining step, [ S ~ Ois, the total concentration of sites suitable for reaction, and b, and ba, the equilibrium functions for the adsorption of NzO and 02, respectively. This rate equation is capable of expressing the experimental results: ( a ) the reaction rate is less than 1st order with respect to NzO, (b) the reaction rate is not affected by Nz, (e) the reaction rate 18 retarded by oxygen. The rate equation derived only from initial rate data ( 2 4 % reaction) also expresses the "course of reaction" rate. From the temperature dependence of k2,an activation energy of 35.0 kcal./mole is obtained. The temperature dependence of 61 yields, for NzO, an adsorption enthalpy of - 16.9 kcal./mole and an entropy of adsorption of -36.4 cal./mole "C. The temperature dependence of ba yields, for Op, an adsorption enthalpy of -43.2 kcal./mole and an entropy of adsorption of -60.0 cal./mole "C. An idea of the mobility of the adsorbed molecules is given by comparing the experimental with calculated entropy changes, the calculated changes being based on the assumption that the adsorbed molecules have lost certain degrees of freedom. Rate equations derived from kinetic mechanisms involving other ratedetermining steps are shown to be inconsistent with experimental results.
The catalytic decomposition of nitrous oxide has been used repeatedly as a test reaction for a number of concepts which are now prevailing in the field of heterogeneous catalysis. The conclusions reached in these studies are largely based on the validity of a reaction scheme deduced from kinetic investigations of the decomposition reaction. It is, then, fitting to assess critically the soundness of the proposed reaction mechanism with more detailed studies of the rate of the reaction. With this aim in view, and as a continuation of previous work on the catalytic activity of semiconducting materials, s we have endeavored t o gather information on a-manganese sesquioxide, since there are no quantitative recorded data on the catalytic activity of this metal oxide for the decomposition of nitrous oxide. The results of this investigat#ionare collected in the present communication, together with a discussion on the reaction mechanism which can be deduced from a kinetic analysis of the experimental data. Experimental Materials.-a-Manganese sesquioxide was prepared by thermal decomposition of reagent grade manganous carbonate (Baker and Adamson). A paste of manganous carbonate and acetic acid (1:1) was heated slowly in a porcelain crucible u p to 400°,and kept at that temperature for three hours. The resulting oxide was thoroughly ground, mixed in an agate mortar and fired in a stream of air in a porcelain crucible a t 800' for four additional hours. The oxide was then cooled overnight, d y e d again and fired under the same conditions previously. This procedure was repeated six times, giving a total ignition period of 27 hours a t 800 f loo. An X-ray pattern of the resulting black powder produced values of interplanar spacings and line intensities in good agreement with previous work.4 Surface area determinations by means of the B.E.T. method, using nitrogen as (1) This communication is based on a dissertation submitted by L. Rheaume in partial fulfillment of the requirements for t h e degree of Doctor of Philosophy at Princeton University. (2) Department of Chemical and Metallurgical Engineering, University of Michigan, Ann Arbor, h'fich. (3) G. Parravano. J. Am. Chem. Soc., 74, 1194 (1952): 75, 1448, 1452, 5293 (1953); G. Parravano, RI. Bondart, "Advances in Catalysis," Val. V I I , Academic Press, Inc., New York, N. Y.,1955; P. P. Clopp and G. Parravano, THISJOURNAL, 62, 1055 (1958). (4) T. E. Moore. M. Ellis and P. W.Selwood, J . A n . Chem. SOC., 72, 8.56 (1950). Fop detailed X-ray data on the present preparation see: L. Rlieuume, Thesis, Pihceton, 1955.
adsorbate, gave a value of 4.5 m.Z/g. I n most of the temperature range studied, the oxide showed a semi-conducting p-type behavior. This result was obtained by means of measurements of thermoelectric power, which, in the temperature range investigated, was found to decrease with increasing temperature. Nitrous oxide, from a commercial cylinder (Matheson), was purified by passing it through a column of phosphorus pentoxide and solidified by freezing it with liquid nitrogen. The solid was evacuated for a half hour to remove non-condensable gases, the temperature then was raised to -go", and one-third of the nitrous oxide was allowed to distil off. The middle third fraction was collected by distillation into an evacuated container. This fraction was again solidified, pumped off for a half hour, and finally collected into a storage bulb. Oxygen from a commercial tank (Matheson) was purified by passing it through calcium chloride, palladized asbestos, calcium chloride, Ascarite, magnesium perchlorate and, finally, phosphorus pentoxide. Pre-purified nitro en (Matheson) was purified by passin it through calcium ctloride, hot activated copper, calcium &loride, Ascarite and phosphorus pentoxide. Experimental Procedure.-Experimental data were obtained in an all-glass closed system, the gases being circulated by means of a motor driven bellows-type gas pump. Catalytic activity was tested at several circulating speeds in order to make sure that mass transfer effects would not control the rate of the chemical reaction. "he catalyst was placed in a Pyrex reactor (f0.3"),supplied with a preheater. Gold foils were inserted in the gas lines to protect the catalyst from mercury vapor. The pressure increase due to the decomposition reaction was followed on a mercury manometer and manometric readings were taken as an indication of the course of the reaction. A standard pretreatment of the catalyst was used throughout this study. The system was evacuated a half hour a t room temperature; the reactor then was heated a t 200' during a one hour period and maintained a t that temperature for two hours. Nitrous oxide subsequently was introduced and the circulating pump turned on. This completed the pretreatment of the catalyst. For a typical run, the catalyst wa heated to the desired reaction temperature, the circulation pump turned off and the system evacuated for six minutes. The reactant or reactant-products mixture was introduced, the circulation pump turned on and pressure readings were taken with a cathetometer (f0.005 em.). At the end of the run, the circulation pump was turned off, the system evacuated, and a fresh reactant or reactantproducts mixture introduced. Following this procedure, a good reproducibility of the reaction rate and catalytic activity constant with time was obtained. Gas mixtures of the desired compositions were prepared with the use of a Toepler pump, connected with the reaction system.
Results Preliminary d s t n showed that the rate of the reslctioii was returded by oxygen. Therefore, the
Feb., 1959
DECOMPOSITION O F NITROUS
OXIDE ON
kinetics of the reaction was determined by measurements of initial rates. For this purpose, a sufficient number of pressure readings were taken a t short intervals of time and plotted versus time. The best straight lines mere drawn through the points. The prevailing partial pressures a t the midpoint of these lines were those recorded for the given rate. The effect of the partial pressure of nitrous oxide on the rate of the reaction WVRSdetermined by measuring initial rates nt different initial pressures of nitrous oside, ~ O N ~ O These results are presented in Table I.
2 0.1000
.E
I
g 0.0800
v
m
U
E
g 0.0600
.-cl
.e U
H
0.0400
1,
, , , , , , , ,
4 0 8 1.0 (cm.). Fig. 1.-Effect of oxygen on the decomposition of nitrous oxide on e-Mn2O3,temp. = 333', a-RInp03= 1 g., p0N20 = 33.5 em. 0
TABLE I DECOMPOSITION O F N ~ Oo x a-nin203. EFFECT AXD
T
=
POh 2
f c n i .)
4.88 9.68 13.93 18.71 26.15 32.43 32.54 33.12 33.38 33.50 33.65 33.68 33.94 34.13 34.41 35.27 44.25 47.57 56.41
OF P O N ~ O
333O, poo, = 0.22 cin., Mn2Or = 1 g.
TON20
0,0233 .0450 .0558 .Of332 ,0858
14.69 15.02 15.27
.lo4
... ...
... ... ... ... ...
...
...
TABLE I1 EFFECT OF TEMPERATURE ON THE DECOIIPOSITION O F NzO
Initial rate (cin./inin.)
... ... ... ... ... ... ...
ON
.IO0 .lo2 .on09
.lo6 .lo3 .lo7 .lo2 .lo5 .lo6 .lo8 .lo6
,142 .158
The order of the reaction with respect t o nitrous oxide was determined by means of data obtained st constant poop, ON, and temperature. The order was found equal to 0.75. This result was obtained with poo, = 0.13 t o 0.33 cm. The effect of p~~ on the rate was determined by making initial rate measuremen ts on premixed nitrous oside-nitrogen mixtures. Some typical results of these measurements are collected in Table I. An inspection of Table I shows that nitrogen has no effect on the rate of the decomposition reaction. I n a similar fashion, the effect of PO, on the rate of reaction was studied by making rate measurements on premixed nitrous oside-oxygen mixtures. As the data reported in Fig. 1 show, oxygen has a strong inhibiting action on the rate of the reaction. Typical reaction velocity data obtained a t different temperatures are collected in Table 11. These data represent the average values of three to four runs for each set of experimental conditions. Discussion The catalytic decomposition of nitrous oxide may be visualized to occur according to the reaction sequence
+ Jr + +
NzO(g) S NnO-S N20-S +Nz(g) 0-S 2(0-S) _r 2s Odg)
2
POZ
P'NZ
(cm.)
265
a-MANGANESE SESQUIOXIDE
(1)
(2) (3)
Temp. ("C.)
P0N20
286 286 286 286 300 300 300 300 317 317 317 346 3-26 346
33.80 49.84 33.74 34.63 33.47 45.35 33.47 35.74 32.06 49.24 33.58 19.37 32 :82 34.57
a-RlnZOs
(mi.)
)PO? (?Ill.)
Initial rate
0.IG
0.0131 .0166 .00808 .00478 ,0333 ,0411 .0225 ,0151
.18 .81
3.34 0.15 .13 .80 3.40 0.20 .30 .80 .I8 .03 3.43
(cni./niin.)
.0544
. 0676 .0406 .127 ,156 .120
where S is a surface site a t which reaction occurs, and N20-S and 0-S are an adsorbed nitrous oxide molecule and an adsorbed osuygen atom, respectively. The reaction sites S me assumed t o be energetically all of the same kind, or belonging t o a narrow energy range. Reaction 1 represents the chemisorption of nitrous oxide, reaction 2 the decomposition of adsorbed aitroris oxide, a.nd reaction 3 the desorption of oxygen. If it is assumed that reaction 2 is the slowest of the sequence, the rate of the over-all decomposition reaction can be expressed as - - dpNzo =
dt
kz[NzO-S]
(4)
where kz is the rate constant for reaction 2 and [NzO-S] is the concentration of adsorbed nitrous oxide molecules. Furthermore, assuming that equilibrium is established rapidly in procesPes 1 and 3, then
where [SIand [0-SI are the concentrations of bare surface sites and surface sites occupied by chemisorbed oxygen, respectively. Moreover [SI = [SI0 - [NnO-SI - [O-SI (7) where [SIo is the total concentration of available
266
L. RHEAUME AND G. PARRAVANO 26.0 1 24.0
-
be obtained by computing "course of reaction" data. To this end, the constants in equation 11 were determined with the method of least square^.^ The results of such computation are collected in Table 111.
-
20.0 22.0
-
g 18.0 --. fi lG.0 -
h
-3
Vol. 63
TABLE I11 VALUESFOR THE CONSTANTS OF EQUATION 11
2 12.0 10.0 8.0 14.0
8
\ ri
4.0 G.o
L
0.5 1.0 1.5 2.0 2.5 3.0 po2'/2 (cm.l / 2 ) . Fig. 2.-Plot I/rate us. po2'/2 for nitrous oxide decomposition on a-h'h203, temp. = 333", a-iUny03 = 1 g., ~ O N Z O = 33.5 cm. 0
286 300 317 333 346
0.00102 ,00300 ,00482 ,0061G .0107
0.043 ,031 ,023 ,011 ,011
6.21 2.80 2.14 1.07 0.91
0.044 .10 .21 .55 .03
In order to integrate equation 11, let a, a - x, II: and z/2, be the initial concentration of nitrous oxide, the concentration of nitrous oxide remaining at tinie t , the concentration of nitrogen formed at time t, and the concentration of oxygen at time t , respectively. Introducing these symbols into the rate equation 11, me obtain
surface sites for the reaction. Substitution of (7) into ( 5 ) and, upon integration and (7) into (6) gives
Solving (8) for [0-SI, substituting into (9)) one obtains
and combining (10) and (4)
Let US now check the rate expression (11) with the experimental data. The data have shown that (a) the reaction rate is less than 1st order with respect to N20; (b) the reaction rate is not affected by Nz; (e) the reaction rate is retarded by Equation 11 may be rewritten as 02. 1 Rnte-
1
blPNno
+
b3'/2~02'/2
According to this equation, a plot of l/rate versus p0,'/2 should result in a straight line, when using experimental rate data taken at coiistant temperature and ~ N ? o . One such plot is presented in Fig. 2 . A straight line can he drawn fairly well through the experinieiitnl points. Oxygen is considered to be adsorbed with dissociation, and as a result PO, s h o w a t half power in the rate equation 11. If, however, oxygen is assumed to be adsorbed without dissociation, one oxygen molecule per site S, it can he shown easily that po, will appear in the rate equation 11 as an additive term to the first power, and the points of a log l/rate versus pot plot should be fitted into a straight line. When this is done, the experimental data deviate considerably from a straight line. A further test of the derived rate equation may
A run on the decomposition of NzO vas performed up to 53.7% completion a t 333". Using the values of the constants obtained from initial rate data a t 333" (Table 111))pressure-time points mere calculated by means of the integrated rate equ at'ion 12. The calculated and observed data for this run are recorded in Fig. 3, which shows good agreement between calculated and experimental values. From a knowledge of values of kz a t different temperatures (Table 111), the value of the activation energy for reaction 2 was computed by means of the Arrheiiius equation and found to be equal to 35.0 kcal./mole, and the value for the preexponential factor, A [SI0 = 2.09 X 1 0I2. Furthermore, let AFO, AH0 and ASQbe the standard Gibbs free energy, enthalpy and entropy changes associated with reactions 1 and 3, the standard states being one em. of pressure for the gas and one site per for the adsorbed and bare sites. In the present case, due to the forni of the equilibrium functions, AS0 is independent of the standard state for the adsorbed and bare sites. Since the pressures used in the present work are not too high, the equilibrium functions bl and b3 may be used to compute A S and AH under the expenmental conditions. By application of the method of least squares to values of bl and b3 at different temperatures, the values of AH and AX in Table IV were obtained. Utilizing a value of - 19.4 for the enthalpy change for the over-all decomposition reaction,6the energy ( 5 ) J. B. Scarborough, "Numerical Mathematical Analysis," The Johns Hopkins Press, Baltimore, Md., 1930. ( G ) F. D. Rossini, D. D. Wagmitn, W. H. Evans, 8. Levine and I. Jaffe, "Selected Values of Chemical Thermodynamic Properties," Circular National Bureau of Standards 500, U. 6. Government Printing Office, Washington, D. C., 1952.
DECOMPOSITION O F NITROUS
Feb., 1959
OXIDE O S a - n l A N G A N E S E SE8QUIOXII)E
TABLE IV ENTHALPY AH A N D ENTROPY, AS, CHANGES FOR REACTIONS
34
1 AND 3 Temperature range 286 to 346' AH
32 30
AS
Reaction
(kcal./mole)
(cal./inole "C.)
1 3
-16.0
-36.4 -66.0
-43.2
267
. 28
? v
changes derived for the catalytic reaction 011 cymanganese sesquioxide are schematically slimmarized in Fig. 4. The values for A S reported in Table IV can be compared with computkd values for the eiitropy change following adsorption for oxygen and nitrous oxide. Assuming immobile adsorption for the former one, with the loss of two vibrational and three translational degrees of freedom of the oxygen upon adsorption, the equilibrium function, b ~ in , terms of the partition functions is
26
2 24 F4 22 20 18 16
50 100 150 200 350 300 350 400 450 500 Time (min.). Fig, 3.-Experimental (0) and calcnlnted ( 0 ) p ~ 2 0from initial rate data for the decomposition of nitrous oxide on a-Mn203,temp. = 333O, o r - M n ~ 0 3 = 1 g. 0
1 If the partition functions of reaction sites and adsorbed species, toget,her with the vibrational contribution of the gaseous osygen molecule, are assumed t o cancel each other, the equilibrium constant becomes
and since AF = -RT In
L3 and A S
=
-
then Fig. 4.-Enei,gy
where the first term corresponds to the entropy change due to the loss of three translational degrees of freedom and the second term to the loss of two rotational degrees of freedom. With the standnrd state for oxygen being one em. of pressure, mid using a moment of inertia of 19.3 X g. cm.2,it is possible to calculate from equation 13 a value of A S = -GO cal./mole "C. in close agreement with the experimental value of -66.0 cal.,/niole "C. This agreement is taken as supporting evidence for the postulated dissociative adsorption of oxygen. Following a similar procedure for nitrons oxide and assuming that the partition function of reaction sites and of adsorbed species, together with the vibrational and rotational contributioiis of the gaseous nitrous oxide molecule, cancel each other, one obtains an expression of Ah' identical with the first term of the second member of equation 13. This treatment is tantamount to assuniing the loss of three translational degrees of freedom of the nitrous oxide molecule upon adsorption. A calculated value of A S = -49.3 cal./mole "C. results. If, however, we assume the loss of only two translational degrees of freedom upon adsorption, AX = - (2/3) 49.3 = -32.9 cal./mole "C., the
Reaction coordinate. diagram for the decomposit,ion of nitrous oxide on a-RInzOs.
experimental value is - 36.4 cal./niole "C. These comparisons indicate that the adsorbed nitrous oxide molecule has a considerable amount of freedom, and it is probably accommodat)ed 011 the surface by means of the oxygen end of the molecule only. The decomposition of the NzO molecule by rupture of the N-0 bond is similar t o the primary step postulated for the homogeneous decompositioii of N207and more recently for the mercury photosensitized decomposition of N20.* Previous values of the adsorptioii enthalpy of O2 determined caloriinetically on M112O3, treated in high vacuum and 450°, are of the order of 24 kcal./ mole a t 17" and PO, = 5 X and 12.2 kcal./inole for the differential enthalpy oht,ained from adsorption isotherms between 180 and 320". lo The value of 43.2 kcal./inole o1)taiiied in the present work, althougli differing from the two reported values, should be compared with the calorimetric adsorption enthalpies of 55 ltcal./niole for 0 2 on Cu2011and 37 kcal./mole on Cr203.12 (7) H. S. Johnston, J . Chem. Phus., 19, 663 (1951); L. Friedman and J. Bigeleisen, J . A m . Chem. Soc., '75, 2215 (1953). (8) R. J. Cvetanovic, J . Chem. PhUs., 2 3 , 1203 (1953). (9) W. E. Garner and T. Ward, J . Chem. Soc., 837 (1939). (10) H. Saito, J . Chem. Soc., Japan, Pure Chem. Sect., 72, 202
(1951).
L. RHEAUME A N D C. PARRAVASO
268
Trol. 03
The value of the enthalpy of adsorption obtained decomposition on metal oxides, it has been sugfor NzO supports the mechanism of a reversible gested often that p-type semi-conductors are the adsorption-desorption of NzO molecules followed best catalysts for this reaction and that the rateby a slower decomposition of adsorbed nitrous oxide determining step of the reaction sequence on these molecules. The concept of adsorbed NzO molecules materials is not the chemisorption of NzO, but the is further substantiated by photoelectric investi- desorption of O2 from the catalytic gations of a Pt surface in a NzO atm0~phere.l~that is These studies showed that a strong interaction N20(g) 2e J _ N2(g) O-a chem. (17) exists between adsorbed N 2 0 molecules and the NLXg) O-%hern +N k ) Odg) 2e (18) metal surface, under conditions such as to minimize the decomposition of the adsorbed NzO or molecules. 1 O-%hem. + O,(g) 2e (19) Discussion of Other Reaction Mechanisms.Since the decomposition of nitrous oxide has been investigated on several oxide catalysts by different These conclusions were based on measurements of authors, it is fruitful to examine the rate equations electrical conductivity of metal oxides, mainly which are obtained, if a kinetically slow step NiO, in NzO-OZmixtures.15 It is possible that the differing from (2) is considered. Let us discuss discrepancy between the decomposition mechanism first the case resulting from assuming reaction 1 as presently suggested for a-Mnz03and that previously the slow step of the over-all reaction. By means deduced for N O is due to an inherent difference in of a treatment similar to that outlined previously, surface behavior between two chemically dissimilar surfaces. There is also the possibility, however, rate expression (14) is obtained in this case that measurements on changes of electrical con--d p N i O = kl [SIoPNzO ductivity of NiO during the decomposition reaction dt 1 + ba'/zpon'/a + ( b ~ ' / % / / b 2 ) ~ ~ , ~ o(14) *'/~ are influenced by adsorbed nitrous oxide molecules. According to equation 14 the reaction rate should They will, in fact, affect the electrical conductivity be retarded by oxygen or nitrogen and show a first- of the oxide in the same manner as adsorbed order dependence on nitrous oxide. Only the oxygen, Deriving a rate equation from steps 17, first condition is brought out by the experimental 18 and considering step 18 rate determining, the data. Therefore the assumption that step 1 is expression (20) is obtained slow compared to (2) and (3) cannot be justified - -dPNzo = k18[S10P2N~0 (20) in the present case. If steps 1 and 2 are combined dt PNa bl7P~nO into one reaction, that is and from steps 17 and 19, considering 19 to be rate NJXg) S ---f Ndg) 0-S (1') determining and it is further supposed that reaction 1' is slow compared to reaction 3, the rate equation (15) obtains Equations 20 and 21 require that Nz should influence the rate of reaction, while 0 2 should not. Previously, a retardation effect of 02 on the rate of Equation 15 can be derived from (14) when [Nz- decomposition of NzO on NiO and CuzO was re0-SI is very small compared to [0-SI, and the ported. l6 A similar conclusion also was recently term containing bz in the denominator of the rate reached in a more general study of the electrical law may be neglected. According to equation 15 and catalytic effects of adsorption of gases on. semithe rate of reaction should be retarded by oxygen, conducting materia1s.l' A final comment is apunaffected by nitrogen, and show a first-order propriate on the effect of Oz on the rate of reaction. dependence on nitrous oxide pressure. This last In the present work it was shown that the rate condition cannot be confirmed experimentally. equation, derived from initial rate data only (2Let us now consider the case in which reaction 3 6% conversion), is capable of expressing the kiis assumed to be the slow step of the reaction se- netics of the reaction up to about 53% conversion quence 1, 2 and 3, In this instance the rate of the a t least. This result throws some doubt on the over-all reaction becomes suggestion that Oz formed during the decomposition of NzO has a different effect than added OZ.~*
+
+
+
+
+
+
+
+
(14) (a) K. Hauffe, R. Glang and H. J. Engell, 2. phyaik. Chem., 201, 22 (1952); (b) H.J. Engell and K. Hauffe, Z . Elekfrochem., 67, 762 (1953): (0) R. M. Dell, F. 9. Stone and P. F. Tiley, Trans. Faraday Soc., 49, 201 (1953); (d) W. E. Garner (Editor), "Chemistry of the Solid State," Academic Press, Inc., New York, N. Y.,1955, Article by F. 9. Stone; (e) K. Hauffe, Advances i n Catalysis, 7 , 213 (1955); 9; 187 (1957). (15) C. Wagner and K. Hauffe, 2. EEektrochem., 44, 172 (1938). (16) G. M. Schwab and R. Staeger, 2. physik. Chem., 836, 418 ( 1 934). (17) T. Takaishi, 2. Nalurforach., lla, 297 (1956). (18) H. Cassell and E. GIUokauf, 2. physik. Chem., B17, 380 (1932); (11) W. E. Garner, F. S. Stone and P. F. Tiley. Proc. Roy. SOC. 8 9 , 427 (1930): G. M. Schwab and B. Eberle, ibid., Bl9, 102 (1032): (London), A211, 472 (1952). E. W. R. Steacie and J. W. McCubbin, J. Chem. Phys., 2 , 585 (1934); (12) D. A. Dowden and W. E. Garner, J . Chem. Soc., 893 (1939). "Catalysis," Vol. 1 , P. H. Emmett, Editor, Reinhold Publ. Corp., (13) R. Suhrmann and W. Sachtler, Z . Naturforsch., A14,..(1954). New York, N. Y.,1954, D. 146, article by Ii. J. Laidler.
where k3f,k3b refer to the forward and reverse reaction rate constant of step 3 and bz = PNZ. [OS]/ [NzO-S 1. According to equation 16 the reaction rate should be 2nd order with respect to nitrous oxide, and retarded by oxygen and nitrogen. This latter condition is, again, not fulfilled experimentally. In previous studies and discussions of the NZO
