- Email: [email protected]
The rate of decomposition of nitrosyl chloride in shock waves
DECOMPOSITION OF NITROSYL CHLORIDE IN SHOCK WAVES
139
5. ADAMS, G. K., PARKER, W. (J., AND WOLFHARD,
all faster than the NO decomposition. We rather believe that really dry mixtures would react no faster than pure NO, i.e., that the NO--CO reaction does not occur at all, but is really the NO decomposition followed by the CO--O2 reaction. To attempt to describe the course of the H2(or H20) catalyzed reaction in detail through calculations does not seem to us to be worth while
H. G.: Discussions Faraday Soc., 14, 97 (1953). 6. ROZLOVSKII, A, I,: Zhur. Fiz. Khiln., 30, 912 (1956). 7. HINSHELWOOD, C. N., AND GREEN, T. E.: J.
Chem. Soc., 730 (1926). 8. HINSHELWOOD, C. N., AND MITCHELL, J. W.:
J. Chem. Soc., 378 (1936).
now.
9. KASSEL, L. S. : The Kinetics of Homogeneous
REFERENCES
Gas Reactions, A.C.S. Monograph Series, p. 175. New York, 1932.
1. ASHMORE, P. G., LEVITT, B. P., AND THRUSH,
B. A.: Trans. Faraday Soc., 52, 830, 835 (1956).
10. GLASSTONE, S., LAIDLER, K. J., AND EYRING,
H.: The Theory of Rate Processes, p. 281. McGraw-Hill Book Company, Inc., New York, 1941. 11. FENIMORE, C. P., AND JONrES, G. W.: J. Phys. Chem., 62, 178 (1958). 12. FENIMORE, C. P.: Private communication. 13. FENIMORE, C. P.: J. Am. Chem. Soc., 69, 3143 (1947).
2. ASHMORE, P. G., AND LEVITT, B. P.: Trans.
Faraday Soc., 53, 945 (1957). 3. ASHMORE, P. G., AND LEVITT, B. P. : Seventh
Symposium (International) on Combustion, p. 45. Butterworth & Company, Ltd., London, 1958. 4. GRAVEN, W. M.: J. Am. Chem. Soc., 79, 3697 (1957).
7 THE RATE OF DECOMPOSITION OF NITROSYL CHLORIDE IN SHOCK WAVES By B E R N H A R D DEKLAU AND HOWARD B. PALMER Introduction Measurements are reported here of the rate of decomposition of nitrosyl chloride, ONC1, over the temperature range from 880 to 1350°K. The method has involved what are by now rather standard measurements of the rate of change of light absorption behind primary shock waves produced in a laboratory shock tube. Rate data were obtained in pure ONC1 and in a series of Ar-ONC1 mixtures ranging up to 1:20 ONCI-Ar. The study was undertaken for three principal reasons: (a) The low-temperature published data1,2 on the reaction rate constant in pure ONC1 (up to 573°K) show a curvature in the plot of log10 k versus ( l / T ) that has been postulated a to be caused by the onset of a unimoleeular decomposition mechanism in paralleI with the bimolecular mechanism that dominates at lower temperatures. Hence investigation at temperatures well above 573°K was of interest. (b) The rate is amenable to shock-tube measure-
ment in a temperature region low enough that a good test was expected to be possible of the consistency of shock tube data with kinetic data gathered by other methods. And (c) if the shock tube results were clearly dominated by a unimolecular decomposition, some useful information should then be obtainable concerning energy transfer during the dissociation process. Recently an interesting paper by Ashmore and Spencer4 has appeared in which a reinvestigation of the low-temperature decomposition is reported, including some measurements at 523°K and 573°K of the unimolecular, second-order decomposition rate. In the analysis of the present shock tube results we shall rely heavily on these new low-temperature data.
Apparatus and Procedure The shock tube was constructed from commerciaI seamless mechanical steel tubing with a 2 by 4 in. rectangular cross section. Inside sur-
140
CHEMICAL KINETICS
faces were polished with various grades of emery cloth and steel wool. The driver section and the expansion chamber were 4 ft and 8 ft in length, respectively. Dow Chemical Company "Ethocell" plastic sheet was used for diaphragms. The end of the expansion chamber was closed off by a thin plastic diaphragm held between flanges. This diaphragm separated the nmin chamber from a 6-in. section of the tube which was connected to an exhaust duct by ~--in. copper tubing. The thin diaphragm was ruptured by the impinging shock wave and the reaction products were purged rapidly out of the system by the driver gas. The corrosion of steel by ONC1 and its reaction products did not present any serious problems. Five pairs of circular quartz windows 1 in. in diameter and ~ - i n . in thickness were mounted flush with the inside walls of the narrow sides to give a light path of 9.1 cm through the tube. General Electric No. 1184 tungsten filament bulbs, operated from batteries, served as light sources. A system of slits and one lens with a focal length of 44 mm confined the light beam through the tube to a width of approximately 0.75 mm. Because the temperature dependence of extinction coefficients varies with wavelength, and because Beer's law cannot be expected to apply over a wide band of the continuum under these conditions, interference filters with peak transmissions at 3850 A, 4360 A and 5460 ~- and half-band widths of about 100 A were inserted into the light path. For determination of the ONC1 concentration change as a function of time the output from an RCA 931-A photomultiplier under the third window was photographed with a Dumont type 296 oscillograph-record camera on a HewlettPackard 150A oscilloscope. For shock velocity measurements the outputs from stations 2, 4 and 5 were recorded by means of a Dumont type 327 oscilloscope. Time markers were obtained from a General Radio unit-time/frequency calibrator, type 1213-C. A Kepco Labs Model 1220B regulated power supply provided the high voltage for photomultiplier tubes. Nitrosyl chloride from the Matheson Company, which was contaminated with a substantial amount of nitrogen dioxide or nitrogen tetroxide, was purified by repeated distillation from a trap at about - 5 0 ° C into a trap approximately 5 ° colder until it was found to contain less than 0.1 mole per cent of nitrogen dioxide. NO2 was deternfined by measuring the absorption peak
at 6.15 t~ with a Perkin-Ehner Model 21 doublebeam recording spectrophotometer. Mixtures were prepared by first introducing nitrosyl chloride into evacuated storage bulbs and then adding argon to give the desired pressure ratio. Pressures were measured with a mercury manometer, an oil manometer and a Wallace and Tiernan differential pressure gauge with a range of 50 mm of Hg. The shock tube was evacuated to about 10 g. With the pump turned off the rate of pressure increase in the tube was about 2 tt per nfin. For adequate light absorption about 10 to 30 mm of nitrosyl chloride had to be introduced into the shock tube. In runs in which nitrosyl chloride was diluted with argon 2-, 5-, 10- and 20-fold, the initial pressures in the shock tube ranged from 50 to 200 mm of mercury. Most of the runs were made with helium as driver gas; nitrogen was used in a few cases. In the driver section, gauge pressures of 40 to 200 psi were reached before spontaneous or needle-induced rupture of the diaphragm. Nitrosyl chloride remained in the tube for about 5 min before the shock was passed through. In several separate tests no decrease in light intensity and only very slight decrease in pressure were noted over a period of 20 min. Before each run a sweep with time markers was photographed and also one with a signal from mechanical chopping of the light beam for total intensity calibration. Sweep times of 10 and 5 ~sec per cm were commonly used for the trace from which the change of concentration with time was determined. For shock-velocity measurements sweep times of about 100 ~sec per cm had to be used. Distance measurements on films were made with a Gaertner Scientific Corporation M-301 micrometer slide comparator. Trace slopes for the kinetic data were measured with a simple protractor which could be read to =t=l degree. Velocity measurements were accurate to about :t=1 per cent, the limitation being imposed by trace thickness. M e a s u r e m e n t s and C a l c u l a t i o n s In order to evaluate nitrosyl chloride dissociation rate constants as a function of temperature, it was necessary to determine the temperature of gas, the disappearance rate of nitrosyl chloride as a function of time and the concentrations of gases present. Concentrations of gases at room temperature were calculated from pressure measurements
DECOMPOSITION OF NITROSYL CHLORIDE IN SHOCK WAVES
with the ideal gas law and the equilibrium constant for the reaction 2 0 N C 1 = 2 NO + C12, Kp = 7.5 × 10-8 in atmos. 5 The degree of dissociation is pressure-dependent and increases at room temperature from about 0.5 per cent at 1 atmos to about 1.8 per cent at a pressure of 20 mm of mercury. Deviations from ideal gaslaw behavior were neglected because the value of the second virial coefficient of ONC1 at 25°C is given as B = - 307 cm~/mole. 5This amounts to a correction of about 0.1 per cent or less at pressures used in dissociation experiments. Separate measurements of room temperature extinction coefficients for the 3850 ~_, 4360 -~ and 5460 A interference filters were made with greater ONC1 pressures than in kinetic runs in order to reduce uncertainties. The values found were slightly higher than those measured spectrographically by Goodeve and Katz. 8 The reproducibility of room temperature extinction coefficients was about 4-5 per cent. Values for chlorine extinction coefficients at all temperatures and wavelengths were taken from the work of Sulzer and WielandY Expression (I) was used for calculation of extinction coefficients. e~
=
[1/lct]
log~0
(Io/I)
--
c~ ~2/c,
(I)
where el = extinction coefficient of ONC1, l = length of light path through tube (9.1 era), c~ = concentration of ONC1 in moles per liter, I0 = light intensity for empty shock tube, I = light intensity for shock tube filled with ONC1, c2 = concentration of chlorine and e2 = extinction coefficient of chlorine. Temperatures and concentrations of gases behind the shock front were calculated from the Rankine-Hugoniot relations (see for example, reference 8) with the acid of measured shock velocities, the ideal gas law and heat capacities. C~ for ONC1 was computed with the use of equilibrium statistical thermodynamics and published data on the molecular properties of ONCI2 To obtain high-temperature ONC1 equilibrium extinction coefficients, the experimental traces were extrapolated back to the initial rise point, i.e., to the shock front. In this way the effects of slit transit time, sehlieren effects and vibrational relaxation were minimized. Nevertheless, uncertainties resulted from these factors as well as from the effects of noise, rounding of the front and rapid dissociation immediately behind the front. For these reasons some records that were usable for kinetic measurements further
I41
behind the front could not be used to obtain extinction coefficients. It appears from the scatter that the high-temperature e values are uncertain by about 4.10 per cent. For kinetic data, the change of light intensity with time, (dI/dt), was obtained directly from the measured slope and time scale on the film. Measurable steady slopes of traces were usually established in 1 to 2 #sec film time. These times must be multiplied by a factor ranging between about 3 and 8, depending upon the Ar dilution, in order to obtain the equivalent gas residence times. Only at shock temperatures below 1150°K was the extent of reaction in these times so small that the cooling of gas caused by the endothermic reaction could be neglected and the concentrations be equated to those at the shock front. At higher temperatures it was possible to compute true temperature and gas concentrations at the point of measurement with approximately calculated rate constants plus known heats of reactions and heat capacities. In most such runs the temperature correction applied to the shock front temperature did not exceed 50°K and the uncertainty introduced was not serious. It is estimated that the temperature error may be about 4-20°K near the lower end and about 4-40°K near the upper end of the range covered. The final expression used for computing the rate of dissociation, (I1), is similar to ones used in previous studies of this type. 1° It is more complicated, however, because of the presence of C12, because ONC1 was appreciably decomposed at the point of measurement and because the reaction was ahnost, but not quite, in a steady-state (see later comments) when the measurement was made. Only at 5460 A could the absorption by C12 be neglected. A detailed discussion of the derivation of Expression II, and especially the computation of the correction factor, (F), may be found in reference 11. The expression is
-d[ONC1]/dt = ~l(dI/dt) [exp (a, oi
(H)
+ ~ o~)](F)u/M~Uc~llo where 2~ is the fraction of ONC1 undecomposed; 01 and p2 are densities of ONC1 and CI~; a~ and az are defined by a i --- 2.303 e~ 1/M~, where 311 is the molecular weight of species i; u is the linear gas-flow velocity behind the front, relative to the front; U is the gas-flow velocity ahead of the shock, relative to the front; and (F) is the correction factor. (F) corrects for the
142
CHEMICAL KINETICS
fact that the rate of the endothermic reaction produces a cooling rate in the gas. This results in a rate of alteration of gas density and extinction coefficients, and all of these factors affect the apparent dissociation rate. Typical values for (F) ranged between 1.3 and 5, depending upon front temperature, Ar-dilution and wavelength. Discussion EXTINCTION COEFFICIENTS
As stated earlier, the extinction coefficient results from ONC1 at room temperature are in reasonable agreement with the data of Goodeve and Katz. 6 The variation of e with temperature shows considerable scatter but its behavior at the three wavelengths is in general accord with expectations on the basis of the room temperature results. Wavelength 3850 A lies near a maximum in the absorption continuum, indicating that the lower state at this wavelength is one of the fairly low-lying vibrational levels of the electronic ground state. One would then expect a rise in e as T rises, followed by a continuous decline, as observed. Wavelength 4360 .~ corresponds to transitions from higher vibrational states, and the rising e region would be expected to extend over a longer T interval. The behavior at 4360 ,~ is complicated by the probability that transitions to at least two excited states contribute in this region, over the temperature range used. A sinfilar complication apparently exists at 5460 A. Reference may be made to the attempt by Goodeve and Katz to analyze the entire absorption spectrum in the visible and near ultraviolet in terms of a number of possible excited states. In their treatment, they assmned that ONC1 could he regarded as diatomic, only the N-C1 stretching vibration being of importance in the ground state. Thus they constructed a potential diagram using as abscissa the N-C1 distance. The implication of such a treatment is that the theoretical work of Sulzer and Wieland 7 on the visible-ultraviolet absorption spectrum of diatomic molecules, extended by Sulzer 1~ to more complicated molecules where they could be treated as pseudo-diatomic, should apply to ONC1. A prediction of the T-dependence of e of this basis led to serious disagreement with the experimental data. Therefore the curves shown in Figure 1 were drawn by eye as well as possible.
Since the T-behavior of e enters into the correction factors applied to the rate data, care was taken to exclude from calculation those cases in which the uncertainty in the e data would have been critical. THERMAL QUANTITIES
For purposes of calculation, particularly for the correction factors, it was necessary to have good thermochemical data for ONC1. Several conflicting numbers appear in the literature. Burns and Bernstein 9 computed (F ° - H ~ ) / T and S ° for ONC1, with carefully substantiated data for the vibration frequencies and moments of inertia. We recalculated these quantities, as well as heat capacities, and agree with their results. Use of accurate K~ data 5 then permitted computation of AH o for 2 ONC1 ~ 2 NO + C12, viz., AH~ = +17.25 kcal. From this is obtained AH~o = +12.86 kcal for ONC1. This contrasts with the figure, +13.25 kcal, quoted by Rossini et aU 3 Likewise one computes AH~298 = +12.36 kcal, to be compared to Rossini's +12.57 kcal. The 0°K bond energy of the C1-NO bond may then be calculated to be +37.16 kcal, and the bond energy at 298°K is +38.24 kcal defined o as AH298 for ONC1 ~ NO + C1. KINETIC
DATA
There is, as mentioned earlier, evidence in the literature that ONCI decomposes by at least two parallel mechanisms, the bimolecular path being kl
2ONC1
,
k~
~ 2NO
q- C12
(1,2)
and the unimolecular one being k~
ONC1 ~- M ,
) N O -F C1 +
M
(3, 4)
Cl2
(5, 6)
k,
followed by
Cl +
ONCI
~-%* NO
+
k6
Ashmore and Spencer 4 have also discussed a heterogeneous route for decomposition which has played a role in vessel experiments but which is unlikely to contribute in shock tube studies. Burns and Dainton TM have determined k5 at low temperatures to be ks = 1053'5 exp ( - 1.060 × I03/RT). An examination of the time for es-
DECOMPOSITION OF NITROSYLCHLORIDEIN SHOCK WAVES 28, 24
I
'
I
'
I
'
I
'
I
143
'
I
i
I i
3850A
-
~
~
-
-
~
l
~
~
=
•
20 16 12 _
ET
~A
•
--
8 4 2.6
•
-~&
•
-._
.-2"
2D 5460A 1.5 1.0
I 300
,
I 500
i
I , I , I 700 900 I100 TEMPERATURE , OK
,
I 1300
,
I 1500
FIG. 1. T e m p e r a t u r e dependence of the extinction coefficients of ONC1 at three wavelengths. • is defined by I/Io = 10-~z~ with l in cm and c in moles/liter. t a b l i s h m e n t of the pseudo s t e a d y - s t a t e in competitive, consecutive gas reactions of t h e t y p e found in the unimoleeular m e c h a n i s m here has been made. ~ I t shows t h a t u n d e r the conditions used in t h e present work, reaction (5) is fast enough to produce a n effective unimolecular rate which is within a few per cent of equaling twice t h e rate of reaction (3), in a time less t h a n " Note s u b m i t t e d by Howard B. P a h n e r : I t may be observed t h a t in the low pressure unimolecular region, the Hinshelwood and the Riee-Ramsperger-Kassel expressions for the rate c o n s t a n t have the same form. The ONC] results thus yield, in terms of R R K theory, s = 4.43 for ONC1 decomposing in Ar and s = 8.01 for pure ONC1. s is supposed to be the n u m b e r of effective oscillators in the decomposing molecule and should not depend upon the n a t u r e of the second body. R R K theory hence appears i n a d e q u a t e to describe the low-pressure unimolecular region for ONC1. The Hinshelwood approach is not quite realistic either, b u t at least it has the v i r t u e of t a k i n g b o t h colliding molecules into consideration. Perhaps a still b e t t e r result would be obtained by applying the theory of Nikitin cited by Professor B o u d a r t in his review.
10 -6 sec in all cases. Since the earliest measurem e n t s were m a d e a t a gas time of a b o u t 2 × 10 -8 sec, a negligible error is m a d e in setting t h e unimolecular c o n t r i b u t i o n equal to twice the rate of reaction (3). As is well known, (for a discussion, see reference 15) the order of reactions of t h e t y p e (3) varies with the pressure. Gas pressures in t h e shock wave were of the order of 1 to 2 a t m o s in t h e present study. O t h e r t r i a t o m i c molecules v 16 such as N()2 , F2() '7 a n d N20) is exhibit approxim a t e l y second-order b e h a v i o r i n this general pressure range, so it was expected t h a t ()NC1 would also. I n t h e second-order region, the rate of unimolecular decomposition depends u p o n the n a t u r e of t h e species M. I n particular, when M is a noble gas the rate c o n s t a n t is i n v a r i a b l y lower t h a n when M is t h e decomposing molecule itself, a t least a t m o d e r a t e temperatures. Relatively little i n f o r m a t i o n exists on t h e v a r i a t i o n with t e m p e r a t u r e of such relative rates. Studies of iodine '9 a n d b r o m i n e ~° a t o m r e c o m b i n a t i o n a n d of dissociation of i~ 1 a n d Br~ ° h a v e shown t h a t t h e rate c o n s t a n t s for M = Ar a n d the diatomie halogens tend to equality a t high
144
CHEMICAL KINETICS
I IO'O~
~
I
.~L
I
I
I
~
- d d-~
I
I
I
i
= 2 k3oPP[ONCI'] [M']
-
-
,oLLOglo2k~ pp
, 0.7
. 0.8
,
,
,
0.9 IO00/T,
.', 1.0
I.I
1.2
T in°K ~.pp
FIG. 2. Arrhenius plot of the apparent second-order unimolecular rate constants, 2 k3.M , for pure ONC1 and ONCI-Ar mixtures. A, pure ONC1; 0 , 1:10 and 1:20 ONCI-Ar; ~ , 1:50NC1-Ar; O, 1:2 ONCI-Ar. Solid and dashed lines are drawn for examining precision of the data, as discussed in the text. temperature. From the temperature dependence of the rate constants in such studies one predicts that at high enough temperatures the rate constant for M = Ar will, in fact, exceed that of the diatomics. The present rate data were examined first with respect to scatter and probable accuracy. For this purpose, "apparent" second-order unimolecular rate constants, 2 k~pp, were com~i+pp puted from 2 + {-d[ONC1]/dt} + [0NC1][M]. The results are shown in Figure 2. The range of rate constants is approximately l0 s, a typical coverage for shock-tube kinetic studies. The high-temperature limitation lies in time resolution and a low-temperature limitation results from the restricted total time available for dissociation before arrival of the contact surface, plus uncertainties about boundary layer effects. Unfortunately, these limitations mean that with scatter such as is present here in the rate constants, no accurate equation for the rate constants can be deduced from the hightemperature data alone. The constants for pure ONC1, indicated by triangles, all fall within a factor of 2.5 of the solid line, and those for the Ar dilution runs all fall within a factor of 3 of the dashed line. The pure ONCI data as a whole lie below the Ar dilution data, indicated by circles, a typical difference in the middle of the T range being about a factor of 3. Beyond this
there is no obvious trend with dilution among the Ar-dilution data, any possible trend being obscured by scatter. Our own a priori estimates of the uncertainty in rate measurements, taking into account in particular the correction factors, extinction coefficients and measured rates of change of absorption, yielded a probable maximum of perhaps a factor of 2. This was too optimistic but does support a conclusion that the scatter in the data is representative of the probable error, to which we would now assign a conservative maximum of a factor of 4, or about 0.6 on the log10 scale, for any one measurement. It is this requirement which will be placed on any final treatment of the data. One must of course admit always the possibility of a systematic error somewhere in the rather complex computations used in obtaining the results. This likelihood is minimized by the use of different dilutions with Ar and three different wavelengths for absorption. The correction factors and extinction coefficient behavior differed so markedly for these variations in conditions that the general agreement of the results strongly supports the correctness of calculations. THE RATE CONSTANTS
The general expression for the rate of homogeneous decomposition of ONC1 according
DECOMPOSITION OF NITROSYL CHLORIDE IN SHOCK WAVES '
I
I
I
I
I
145
'
I
'
I1.0 d [ONCl] = dt
k?pp ~)NCI-lZ
so~
oO '
Loom k~ pp
0
9.0-
•• • t
0
e
o 'b
8.0--
ZO O.7
0.8
0.9 IO00/T,
1.0
I.I
Tin °K
F~a. 3. Arrhenius plot of the apparent bimoleeul~r r~te constants, k~p~', for pure ONC1 and ONCI-Ar mixtures. A, pure ONC1; O, 1:10 and 1:20 ONC1-Ar; ~ , 1:50NC1-Ar; C), 1:20NC1-Ar. to the above mechanism is
2 k~pp = kl [ONC1] + 2 ks, oNcl -[ONCI] [M] [M]
-d[ONC1]/dt = k~[ONCI] ~ + 2
k~, o~o~[ONC]]~
-t- 2 k~, Ar[ONCI][Ar] -~- 2 k3,[ONC1] where k3, is the rate constant of reaction (3) when it is in the first-order pressure region. It should be mentioned at this point that the probable contributions of back reactions were computed for critical runs, namely, those in which measurements were made after 20 or 25 per cent decomposition, and were found to be negligible. The reason is that for such runs the equilibrium decomposition was typically some 90 per cent. The computation of apparent rate constants, defined as 2 k~'" = Rate/[ONC1][M]; k~'" = Rate/[ONC1]~; and 2 kS""8' = Ratc/[ONC1], permitted some determination of the relative importance of the reactions. An aid here was the difference in [M], depending principally upon the dilution used in the runs, and the difference in [ONC1]. [M] was larger for the shocks in diluted cases and [ONC1] was smaller. Consider the results for 2 k ~''" 3 •
[ir]
+ 2 k3, ~r [~]] + 2 k3,/[M]. For pure ONC1, this gives 2 k~pp = kl -~- 2 ks. one1 -~- 2
k3,/[ONC1]
For 1 : 10 ONCI-Ar, we have 2 k~'" = 0.09 (kl + 2 ks. ONCl) -~ 0.91 X 2 ]c~, Ar -~ 2
k3,/[M].
It is observed (Fig. 2) that 2 ks""3 for the 1:10 case is greater than that for pure ONC1, roughly by a factor of 2 or 3. Since [M]1:10 > [M],ure in the runs, 2 k~, cannot be making an important contribution, and is, therefore, ignored. I t also appears here that 2 ka, Ar must be 2 or 3 times (kl + 2 ks, ONC]). NO new information actually is gained from the other k~P"s, shown in Figures 3 and 4, but in Figure 3 especially, emphasis is given to the fact that the unimolecular secondorder route in ONC1-Ar mixtures is dominant. If it were not, the values of k~'" would not depend upon dilution.
146
CHEMICAL KINETICS
' 5.0
I
i
I
I
I
i
I
-
d [ONCI] = 2kooPr-.,..,C nT aLul~ =-I
4.0
'.,
LOglo ,~ ~ kapp 3'
: o.}:
:5.0
2D
z 0.7
I 0.8
I 0.9 IO00/T,
I
I 1.0
I
I I. I
I
T in °K
FIG. 4. Arrhenius plot of the apparent first-order unimolecular rate constants, 2 k~;p, for pure ONCI and ONC1-Ar mixtures. A, pure ONC1; O, 1:10 and 1:20 ONCI-Ar; ~ 1:50NCI-Ar; O, 1:20NC1-Ar. An examination of the relative contributions of kl and 2 k3, ONCl depends principally upon the use of low-temperature data in conjunction with the shock tube data. Any attempt to write an equation for rate constants depends also upon this, whether for pure ONC1 or the Ar-diluted cases.
The most recent study of the low-temperature decomposition of pure ONC1 is that of Ashmore and Spencer. 4 Previously, extensive work was done by Waddington and Tolman1 and Welinsky and Taylor,~ with results in substantial agreement. Ashmore and Spencer have found a heterogeneous contribution to the mechanism that should contribute most readily to the rate at the lowest temperatures. Waddington and Tolman's work, covering the range, 423 to 523°K, was free from heterogeneous effects; but their rate constants were influenced by the unimolecular mechanism, which they did not consider in computing apparent kl values. Ashmore and Spencer have corrected Waddington and Tolman's data on the basis of their results, to give values for kl. An Arrhenius fit then yields k~ = 101~5 exp ( - 2 3 . 4 kcal/RT) cc/mole sec. This is shown by the dotted lines in Figures 5, 6 and 7. Ashmore and Spencer report 2 ks.oNcl values equal to 220 =i:40 at 523°K, 6400 d=600 at 573°K. Although it appears to us that their estimated uncertainties are too small, the hum-
bers must be accepted as certainly within a factor of 1.5 of the correct values. They use these two numbers to give an Arrhenius equation for ka. o.~c], choosing as the most reasonable result, ka, oNcl = 1017'9 exp (--38 kcal/RT) co/mole sec. For k3.co= they obtain k3,co2 = 1017a exp ( - 3 7 kcal/RT) cc/mole sec. If the rate constant for M = Ar is about half as large as for COs around 500°K as was observed by Volpe and Johnston=2 in the unimolecular decomposition of 02 NC1 (to which Ashmore and Spencer find parallels in ONC1 decomposition), one would predict k3.Ar = 10I7° exp (--37 kcal/RT). These equations for M = ONC1 and M = Ar are plotted (as 2 k3.M) by the dashed lines in Figures 5, 6 and 7. It is clear in both cases that an Arrhenius expression is inadequate to predict high-temperature unimolecular constants from the low-temperature work. The theories of Rice, Ramsperger and Kassel,2a of Slater 15 and of Hinshelwood24 have been used with fair success in the past to account for unimolecular decomposition rates and should be appropriate here. Uncertainties in the available low- and high-temperature data in the present instance do not justify the determination of more than two parameters, so we choose the Hinshelwood theory, in which the critical energy is arbitrarily taken to be the bond dissociation energy, 37.16 kcal. The theory takes the form,
k = Z[Eo/RT]'~/2[1/(n/2) '] exp ( - - E o / R T )
DECOMPOSITIONOF NITROSYLCHLORIDEIN SHOCK WAVES I1.0
I
I
'
~ I
'
I
147
i
I
i
IO.O
L°g'°k°"ct
_
-
""""
\\\.
--......
kTOTA L : k I + 2ks,oN©=
.
I 0.8
I 0.9
7.0 0.7
,
,
I000/T,
"""'"-......
I
I 1.0
~
-7"--
I I.I
,~
1.2
T in OK
F~(~. 5. Arrhenius plot of the experimental values for kl + 2 k3, ONC1 Solid line is the Hinshelwood theory expression discussed in the text. The dotted line is the Ashmore and Spencer ~ revision of kl and the dashed line is the Arrhenius expression for 2 k3, OSCl given by Ashmore and Spencer. •
II.0
LO,ok,,,,8.°
'
~I
'
"'""'"'-._
0.7
0.8
l
l
I
J
I
0 0
0.9 1.0 I O 0 0 / T , T in OK
I
-
I.I
1.2
FIG. 6. Arrhenius plot of the experimental values for 2 k3, Ar Solid line is the Hinshelwood theory expression discussed in the text. The dashed line is the Arrhenius expression estimated from the Ashmore and Spencer 4 results for 2 k~, cos • The dotted line is the Ashmore and Spencer revision of k1 . •
CHEMICALKINETICS
148
6ok it
I0.0
9.0
8.0
-I.0
Z0
3.0
6.0
3.0
5.0
-4.0
Logm k
,ot 0.5
I 1.0
1.5
1.5
2.0
IO00/T,
2.5
2.5
3.0
3.5
T in °K
FIG. 7. Low T-high TArrhenius plot of decomposition rate constants for pure ONC1. 0 , experimental values of the total rate constant, k, = k~ -F 2 ks, ONCl,from the present work and from the literature.I. 2.4 The solid line is the sum of the Ashmore and Spencer revision4of kl and the Hinshelwood theory expression for 2 k3, oict from the present paper. The dotted line is k~ and the dashed line is the Arrhenius expression for 2 ks. ONClgiven by Ashmore and Spencer. 4 where Z is the apparent collision number, n is the number of classical square terms from which stored internal energy is transferred to the dissociating bond during collision and E0 is the 0°K bond energy. The expression might conveniently be improved for semiempirical purposes by including a term representing a possible change with temperature of the energy transfer efficiency. Because this would introduce a third parameter, it is not included for the present. A 2-point fit for pure ONCI is performed with the 2k3,ONC1values, 220 at 523°K and 10s67 at 1177°K. The latter point is chosen at the approximate midpoint of the high-temperature range and has been corrected for a slight con-
tribution from kl at this temperature, with the use of the Ashmore and Spencer Arrhenius equation for kl. The result is 2k3, oNcl = 2 X 109°~Tt/2[Eo/RT]7"°t
• [1/F (8.01)] exp( -- E o / R T). o
For an assumed collision diameter of 3.5 A, this corresponds to a low collision efficiency, 0.018 per cent. The maximum possible value of n for two colliding ONC1 molecules would be the contributions from 6 vibrations and 6 rotations, subtracting 3 rotations for angular momentum conservation.~4 This yields 15 square terms, or [n/2]m~ = 7.5. Thus n / 2 - 7.0 is perhaps
DECOMPOSITION OF NITROSYL CHLORIDE iN SHOCK WAVES
feasible, but the very low collision efficiency is hard to believe, and there is the added problem that the predicted value of 2ka,oNm at 573°K is 2700, less than half the Ashmore and Spencer value. The sum of the ttinshelwood fit to 2lea,oNe1 plus the Ashmore and Spencer revision of kt is shown in the high-temperature region in Figure 5. in Figure 7 is shown this result over the approximate temperature range, 290 to 2000°K. The Ar dilution result is more reasonable. Our estimates of 2ka,Ar from the ka,co2 data of Ashmore and Spencer are 40 at 523°K and 800 at 573°K. With the 523°K value and the shock tube data at 1137°K, for which 2/ca,A~ 109% the equation 2lt:a. Ar ~- 2 X IOna~T~/2[Eo/RT] ~4~ • [ 1 / r (4.43)] e x p ( - E o / R T) is obtained. This is shown by the solid line in Figure 6. With theoaSSumption of a collision diameter of about 3 A, this gives a collision efficiency of 2.9 per cent. The [n/2] . . . . should be 3. On this basis, 3.43 is too large. However, it is very sensitive to the choice of the low-temperature point. If 2]Ca,A~ at 523°K were 20 instead of 40, one would obtain n/2 - 2.5. The predicted value of 2ka,Ar at 573°K is 680, in decent agreement with the estimate. Although the Ar dilution ka's are rather adequately accounted for by the simple theory, it seems to us that a more sophisticated approach than we can supply probably is necessary to explain the pure ONC1 results. In this regard, the following points may be of significance: (1) There is a parallel between the present results and studies of Br2 dissociation. A recompuration of the low T-high T Hinshelwood fit with the use of shock tube data ~9 and the most recent results of Givens and Willard~° at lowtemperatures yields, for pure Br~, n/2 = 3.89 and an apparent collision efficiency (for ¢ = 3.5) A of 0.91 per cent; for Br~ in Ar the results are n/2 = 1.58 and a collision efficiency (for ¢ = 3 ~_) of 12.3 per cent. Thus with Br2 as with ONC1, the n/2 values tend to be improbably large but close enough to the (n/2)m~ values to be encouraging; the Ar-dilution apparent collision efficiencies are reasonable; and the pure-gas apparent collision efficiencies are surprisingly small. It is, however, interesting to observe that there is a rough correlation between the apparent collision efficiencies required
149
in the Hinshelwood expressions and the complexity of the molecules involved in collisions, i.e., the efficiencies for Br~-Ar, ONCI=Ar, Br2-Br~ and ONCI-ONC1 are (in per cent) 12.3, 2.9, 0.91 and 0.018. If the apparent collision efficiency is viewed as the product of two terms, one being the probability that the available energy will be transferred and the other being the probability that transferred energy will accumulate in the critical bond, one might expect a lower efficiency when more bonds are available, as in ONCIONC1, than in a collision such as Br2-Ar. (2) Interpretation of the pure ONC1 data in terms of complex formation between ONC1 and C1 or NO, in a way analogous to that applied successfully by Bunker and Davidson 25 to halogen atom recombination (or molecular dissociation), would require the existence of a quite stable complex and would probably predict an ONC1 efficiency relative to Ar many times larger than we estimate to be the case at low temperature. Such an approach also would produce a weaker T dependence at low temperatures than does the Hinshelwood fit and hence the discrepancy at 573°K would become still worse. (3) The results could be interpreted even by simple collision theory if one introduced a strongly T-dependent collision efficiency. This possibility has been suggested by others with regard to halogen atom association,~8 but so far as we are aware, no quantitative expression for this effect is available. (4) Our observations are of the rates at which molecules leave rather low energy states in the electronic ground state. Reasonable agreement in rates is obtained for three different mean wavelengths, corresponding to three different groups of low-lying states. The measured rates should equal the rates at which molecules are actually dissociating even when the dissociation rate is limited by the rate at which molecules are supplied to the critically high levels from which they presumably decompose. The reason is that in this case a steady-state should be established very rapidly in which the concentrations of molecules in high states are below the equilibrium (Boltzmann distribution) values but bear fixed numerical relations to the concentrations in the low states. Thus even in this ease one should be observing a representative sample of the molecules by observing those in the low states. If the deviations from a Boltzmann distribution are slight in the lower states, then the
150
CHEMICAL KINETICS
use of equilibrium (Boltzmann) extinction coefficients to measure concentrations should be sufficiently accurate. The rate of dissociation will, in this excitation rate-limited case, be less than it would be if the vibrational relaxation were much faster than dissociation. Thus this effect could account for a dropping off in rate constants at high temperatures. Unfortunately we do not know how rapid the relaxation is in 0NC1. If perhaps 103 collisions are required for relaxation, then it occurs in a time of the order of l0 -1 ttsec. At the highest temperatures in t~e present work, the initial rate of disappearance of ONC1 behind the front approached 10 per cent of the ONC1 per ~sec, or 1 per cent in the estimated relaxation time. Thus relaxation should not have been seriously limiting the rate.
Acknowledgments We wish to express our thanks to Mr. B. E. Knox for performing a number of calculations. This work was sponsored by Project SQUID, which is supported by the Office of Naval Research, Department of the Navy, under Contract Nonr 1858(25) NR-098-038. Reproduction in full or in part is permitted for any use of the United States Government. REFERENCES 1. WADDINGTON,G., AND TOLMAN, R. C.: J. Am. Chem. Soc., 57, 689 (1935). 2. WELINSKY, I., AND TAYLOR, H. A.: J. Chem. Phys., 6, 466 (1938). 3. ASHMORE, P. C., AND CHANMUGAM,J.: Trans. Faraday Soc., 49, 265 (1953). 4. ASHMORE, P. G., AND SPENCER, M. S. : Trans. Faraday Soc., 55, 1868 (1959). 5. BEESON, C. M., AND YOST, D. M.: J. Chem. Phys., 7, 44 (1939). 6. GOODEVE, C. F., AND KATZ, S.: Proc. Roy. Soc. (London), A172, 432 (1939). 7. SULZER, P., AND WIELAND, K.: Helv. Phys. Acta, 25, 653 (1952).
8. HIRSCHFELDER, J. O., CURTISS, C. F., AND BIRD, R. B.: Molecular Theory of Gases and Liquids, p. 785. John Wiley and Sons, Inc., New York, 1954. 9. BURNS, W. G., AND BERNSTEIN, H. J.: J. Chem. Phys., 18, 1669 (1950). 10. PALMER, H. B., AND HORNIG, D. F.: J. Chem. Phys., 26, 98 (1957). 11. DEKLAU, B. : Ph.D. Dissertation, The Pennsylvania State University, 1960. 12. SULZER, P.: Dissertation, E.T.H., Zurich, 1952. 13. RossINI, F. D., WAGMAN, D. D., EVANS, W. H., LEVINE, L., AND JAFFE, S.: Circular 500, National Bureau of Standards, U.S. Govt. Printing Office, 1952. 14. BURNS, W. G., AND DAINTON, F. S.: Trans. Faraday Soc., $8, 52 (1952). 15. TROTMAN-DICKENSON, A. F.: Gas Kinetics, pp. 45-82. Butterworth & Company, Ltd., London, 1955. 16. HUFFMAN, R. E., ANn DAVIDSON, N. : J. Am. Chem. Soc., 81, 2311 (1959). 17. KOBLITZ, W., AND SCHUMACHER, H. J.: Z. physik. Chem., 25B, 283 (1934). 18. JOHNSTON, H. S.: J. Chem. Phys., 19, 663 (1951). 19. BUNKER, D. L., AND DAVIDSON, N.: J. Am. Chem. Soc., 80, 5085 (1958). 20. GIVENS, W. G., JR., AND WILLARD, J. E.: J. Am. Chem. Soc., 81, 4773 (1959). 21. BRITTON, D., DAVIDSON, N., GEHMAN, W., &ND SCHOTT, G.: J. Chem. Phys., 25, 804 (1956). 22. VOLPE, M., AND JOHNSTON, H. S.: Z. Am. Chem. Soc., 78, 3903 (1956). 23. KASSEL, L. S.: Kinetics of Homogeneous Gas Reactions, Chap. V. Chemical Catalog Company 1932. 24. FOWLER, R. H., ANn GUGGENHEIM, E. A.: Statistical Thermodynamics, pp. 489-530. Cambridge University Press, 1952. 25. BUNKER, D. L., AND DAVIDSON, N.: J. Am. Chem. Soc., 80, 5091 (1958). 26. RICE, O. K. : Ninth International Astronautical Conference, Amsterdam, 1958; pp. 9-19. Wien Springer Verlag, 1959.
139
5. ADAMS, G. K., PARKER, W. (J., AND WOLFHARD,
all faster than the NO decomposition. We rather believe that really dry mixtures would react no faster than pure NO, i.e., that the NO--CO reaction does not occur at all, but is really the NO decomposition followed by the CO--O2 reaction. To attempt to describe the course of the H2(or H20) catalyzed reaction in detail through calculations does not seem to us to be worth while
H. G.: Discussions Faraday Soc., 14, 97 (1953). 6. ROZLOVSKII, A, I,: Zhur. Fiz. Khiln., 30, 912 (1956). 7. HINSHELWOOD, C. N., AND GREEN, T. E.: J.
Chem. Soc., 730 (1926). 8. HINSHELWOOD, C. N., AND MITCHELL, J. W.:
J. Chem. Soc., 378 (1936).
now.
9. KASSEL, L. S. : The Kinetics of Homogeneous
REFERENCES
Gas Reactions, A.C.S. Monograph Series, p. 175. New York, 1932.
1. ASHMORE, P. G., LEVITT, B. P., AND THRUSH,
B. A.: Trans. Faraday Soc., 52, 830, 835 (1956).
10. GLASSTONE, S., LAIDLER, K. J., AND EYRING,
H.: The Theory of Rate Processes, p. 281. McGraw-Hill Book Company, Inc., New York, 1941. 11. FENIMORE, C. P., AND JONrES, G. W.: J. Phys. Chem., 62, 178 (1958). 12. FENIMORE, C. P.: Private communication. 13. FENIMORE, C. P.: J. Am. Chem. Soc., 69, 3143 (1947).
2. ASHMORE, P. G., AND LEVITT, B. P.: Trans.
Faraday Soc., 53, 945 (1957). 3. ASHMORE, P. G., AND LEVITT, B. P. : Seventh
Symposium (International) on Combustion, p. 45. Butterworth & Company, Ltd., London, 1958. 4. GRAVEN, W. M.: J. Am. Chem. Soc., 79, 3697 (1957).
7 THE RATE OF DECOMPOSITION OF NITROSYL CHLORIDE IN SHOCK WAVES By B E R N H A R D DEKLAU AND HOWARD B. PALMER Introduction Measurements are reported here of the rate of decomposition of nitrosyl chloride, ONC1, over the temperature range from 880 to 1350°K. The method has involved what are by now rather standard measurements of the rate of change of light absorption behind primary shock waves produced in a laboratory shock tube. Rate data were obtained in pure ONC1 and in a series of Ar-ONC1 mixtures ranging up to 1:20 ONCI-Ar. The study was undertaken for three principal reasons: (a) The low-temperature published data1,2 on the reaction rate constant in pure ONC1 (up to 573°K) show a curvature in the plot of log10 k versus ( l / T ) that has been postulated a to be caused by the onset of a unimoleeular decomposition mechanism in paralleI with the bimolecular mechanism that dominates at lower temperatures. Hence investigation at temperatures well above 573°K was of interest. (b) The rate is amenable to shock-tube measure-
ment in a temperature region low enough that a good test was expected to be possible of the consistency of shock tube data with kinetic data gathered by other methods. And (c) if the shock tube results were clearly dominated by a unimolecular decomposition, some useful information should then be obtainable concerning energy transfer during the dissociation process. Recently an interesting paper by Ashmore and Spencer4 has appeared in which a reinvestigation of the low-temperature decomposition is reported, including some measurements at 523°K and 573°K of the unimolecular, second-order decomposition rate. In the analysis of the present shock tube results we shall rely heavily on these new low-temperature data.
Apparatus and Procedure The shock tube was constructed from commerciaI seamless mechanical steel tubing with a 2 by 4 in. rectangular cross section. Inside sur-
140
CHEMICAL KINETICS
faces were polished with various grades of emery cloth and steel wool. The driver section and the expansion chamber were 4 ft and 8 ft in length, respectively. Dow Chemical Company "Ethocell" plastic sheet was used for diaphragms. The end of the expansion chamber was closed off by a thin plastic diaphragm held between flanges. This diaphragm separated the nmin chamber from a 6-in. section of the tube which was connected to an exhaust duct by ~--in. copper tubing. The thin diaphragm was ruptured by the impinging shock wave and the reaction products were purged rapidly out of the system by the driver gas. The corrosion of steel by ONC1 and its reaction products did not present any serious problems. Five pairs of circular quartz windows 1 in. in diameter and ~ - i n . in thickness were mounted flush with the inside walls of the narrow sides to give a light path of 9.1 cm through the tube. General Electric No. 1184 tungsten filament bulbs, operated from batteries, served as light sources. A system of slits and one lens with a focal length of 44 mm confined the light beam through the tube to a width of approximately 0.75 mm. Because the temperature dependence of extinction coefficients varies with wavelength, and because Beer's law cannot be expected to apply over a wide band of the continuum under these conditions, interference filters with peak transmissions at 3850 A, 4360 A and 5460 ~- and half-band widths of about 100 A were inserted into the light path. For determination of the ONC1 concentration change as a function of time the output from an RCA 931-A photomultiplier under the third window was photographed with a Dumont type 296 oscillograph-record camera on a HewlettPackard 150A oscilloscope. For shock velocity measurements the outputs from stations 2, 4 and 5 were recorded by means of a Dumont type 327 oscilloscope. Time markers were obtained from a General Radio unit-time/frequency calibrator, type 1213-C. A Kepco Labs Model 1220B regulated power supply provided the high voltage for photomultiplier tubes. Nitrosyl chloride from the Matheson Company, which was contaminated with a substantial amount of nitrogen dioxide or nitrogen tetroxide, was purified by repeated distillation from a trap at about - 5 0 ° C into a trap approximately 5 ° colder until it was found to contain less than 0.1 mole per cent of nitrogen dioxide. NO2 was deternfined by measuring the absorption peak
at 6.15 t~ with a Perkin-Ehner Model 21 doublebeam recording spectrophotometer. Mixtures were prepared by first introducing nitrosyl chloride into evacuated storage bulbs and then adding argon to give the desired pressure ratio. Pressures were measured with a mercury manometer, an oil manometer and a Wallace and Tiernan differential pressure gauge with a range of 50 mm of Hg. The shock tube was evacuated to about 10 g. With the pump turned off the rate of pressure increase in the tube was about 2 tt per nfin. For adequate light absorption about 10 to 30 mm of nitrosyl chloride had to be introduced into the shock tube. In runs in which nitrosyl chloride was diluted with argon 2-, 5-, 10- and 20-fold, the initial pressures in the shock tube ranged from 50 to 200 mm of mercury. Most of the runs were made with helium as driver gas; nitrogen was used in a few cases. In the driver section, gauge pressures of 40 to 200 psi were reached before spontaneous or needle-induced rupture of the diaphragm. Nitrosyl chloride remained in the tube for about 5 min before the shock was passed through. In several separate tests no decrease in light intensity and only very slight decrease in pressure were noted over a period of 20 min. Before each run a sweep with time markers was photographed and also one with a signal from mechanical chopping of the light beam for total intensity calibration. Sweep times of 10 and 5 ~sec per cm were commonly used for the trace from which the change of concentration with time was determined. For shock-velocity measurements sweep times of about 100 ~sec per cm had to be used. Distance measurements on films were made with a Gaertner Scientific Corporation M-301 micrometer slide comparator. Trace slopes for the kinetic data were measured with a simple protractor which could be read to =t=l degree. Velocity measurements were accurate to about :t=1 per cent, the limitation being imposed by trace thickness. M e a s u r e m e n t s and C a l c u l a t i o n s In order to evaluate nitrosyl chloride dissociation rate constants as a function of temperature, it was necessary to determine the temperature of gas, the disappearance rate of nitrosyl chloride as a function of time and the concentrations of gases present. Concentrations of gases at room temperature were calculated from pressure measurements
DECOMPOSITION OF NITROSYL CHLORIDE IN SHOCK WAVES
with the ideal gas law and the equilibrium constant for the reaction 2 0 N C 1 = 2 NO + C12, Kp = 7.5 × 10-8 in atmos. 5 The degree of dissociation is pressure-dependent and increases at room temperature from about 0.5 per cent at 1 atmos to about 1.8 per cent at a pressure of 20 mm of mercury. Deviations from ideal gaslaw behavior were neglected because the value of the second virial coefficient of ONC1 at 25°C is given as B = - 307 cm~/mole. 5This amounts to a correction of about 0.1 per cent or less at pressures used in dissociation experiments. Separate measurements of room temperature extinction coefficients for the 3850 ~_, 4360 -~ and 5460 A interference filters were made with greater ONC1 pressures than in kinetic runs in order to reduce uncertainties. The values found were slightly higher than those measured spectrographically by Goodeve and Katz. 8 The reproducibility of room temperature extinction coefficients was about 4-5 per cent. Values for chlorine extinction coefficients at all temperatures and wavelengths were taken from the work of Sulzer and WielandY Expression (I) was used for calculation of extinction coefficients. e~
=
[1/lct]
log~0
(Io/I)
--
c~ ~2/c,
(I)
where el = extinction coefficient of ONC1, l = length of light path through tube (9.1 era), c~ = concentration of ONC1 in moles per liter, I0 = light intensity for empty shock tube, I = light intensity for shock tube filled with ONC1, c2 = concentration of chlorine and e2 = extinction coefficient of chlorine. Temperatures and concentrations of gases behind the shock front were calculated from the Rankine-Hugoniot relations (see for example, reference 8) with the acid of measured shock velocities, the ideal gas law and heat capacities. C~ for ONC1 was computed with the use of equilibrium statistical thermodynamics and published data on the molecular properties of ONCI2 To obtain high-temperature ONC1 equilibrium extinction coefficients, the experimental traces were extrapolated back to the initial rise point, i.e., to the shock front. In this way the effects of slit transit time, sehlieren effects and vibrational relaxation were minimized. Nevertheless, uncertainties resulted from these factors as well as from the effects of noise, rounding of the front and rapid dissociation immediately behind the front. For these reasons some records that were usable for kinetic measurements further
I41
behind the front could not be used to obtain extinction coefficients. It appears from the scatter that the high-temperature e values are uncertain by about 4.10 per cent. For kinetic data, the change of light intensity with time, (dI/dt), was obtained directly from the measured slope and time scale on the film. Measurable steady slopes of traces were usually established in 1 to 2 #sec film time. These times must be multiplied by a factor ranging between about 3 and 8, depending upon the Ar dilution, in order to obtain the equivalent gas residence times. Only at shock temperatures below 1150°K was the extent of reaction in these times so small that the cooling of gas caused by the endothermic reaction could be neglected and the concentrations be equated to those at the shock front. At higher temperatures it was possible to compute true temperature and gas concentrations at the point of measurement with approximately calculated rate constants plus known heats of reactions and heat capacities. In most such runs the temperature correction applied to the shock front temperature did not exceed 50°K and the uncertainty introduced was not serious. It is estimated that the temperature error may be about 4-20°K near the lower end and about 4-40°K near the upper end of the range covered. The final expression used for computing the rate of dissociation, (I1), is similar to ones used in previous studies of this type. 1° It is more complicated, however, because of the presence of C12, because ONC1 was appreciably decomposed at the point of measurement and because the reaction was ahnost, but not quite, in a steady-state (see later comments) when the measurement was made. Only at 5460 A could the absorption by C12 be neglected. A detailed discussion of the derivation of Expression II, and especially the computation of the correction factor, (F), may be found in reference 11. The expression is
-d[ONC1]/dt = ~l(dI/dt) [exp (a, oi
(H)
+ ~ o~)](F)u/M~Uc~llo where 2~ is the fraction of ONC1 undecomposed; 01 and p2 are densities of ONC1 and CI~; a~ and az are defined by a i --- 2.303 e~ 1/M~, where 311 is the molecular weight of species i; u is the linear gas-flow velocity behind the front, relative to the front; U is the gas-flow velocity ahead of the shock, relative to the front; and (F) is the correction factor. (F) corrects for the
142
CHEMICAL KINETICS
fact that the rate of the endothermic reaction produces a cooling rate in the gas. This results in a rate of alteration of gas density and extinction coefficients, and all of these factors affect the apparent dissociation rate. Typical values for (F) ranged between 1.3 and 5, depending upon front temperature, Ar-dilution and wavelength. Discussion EXTINCTION COEFFICIENTS
As stated earlier, the extinction coefficient results from ONC1 at room temperature are in reasonable agreement with the data of Goodeve and Katz. 6 The variation of e with temperature shows considerable scatter but its behavior at the three wavelengths is in general accord with expectations on the basis of the room temperature results. Wavelength 3850 A lies near a maximum in the absorption continuum, indicating that the lower state at this wavelength is one of the fairly low-lying vibrational levels of the electronic ground state. One would then expect a rise in e as T rises, followed by a continuous decline, as observed. Wavelength 4360 .~ corresponds to transitions from higher vibrational states, and the rising e region would be expected to extend over a longer T interval. The behavior at 4360 ,~ is complicated by the probability that transitions to at least two excited states contribute in this region, over the temperature range used. A sinfilar complication apparently exists at 5460 A. Reference may be made to the attempt by Goodeve and Katz to analyze the entire absorption spectrum in the visible and near ultraviolet in terms of a number of possible excited states. In their treatment, they assmned that ONC1 could he regarded as diatomic, only the N-C1 stretching vibration being of importance in the ground state. Thus they constructed a potential diagram using as abscissa the N-C1 distance. The implication of such a treatment is that the theoretical work of Sulzer and Wieland 7 on the visible-ultraviolet absorption spectrum of diatomic molecules, extended by Sulzer 1~ to more complicated molecules where they could be treated as pseudo-diatomic, should apply to ONC1. A prediction of the T-dependence of e of this basis led to serious disagreement with the experimental data. Therefore the curves shown in Figure 1 were drawn by eye as well as possible.
Since the T-behavior of e enters into the correction factors applied to the rate data, care was taken to exclude from calculation those cases in which the uncertainty in the e data would have been critical. THERMAL QUANTITIES
For purposes of calculation, particularly for the correction factors, it was necessary to have good thermochemical data for ONC1. Several conflicting numbers appear in the literature. Burns and Bernstein 9 computed (F ° - H ~ ) / T and S ° for ONC1, with carefully substantiated data for the vibration frequencies and moments of inertia. We recalculated these quantities, as well as heat capacities, and agree with their results. Use of accurate K~ data 5 then permitted computation of AH o for 2 ONC1 ~ 2 NO + C12, viz., AH~ = +17.25 kcal. From this is obtained AH~o = +12.86 kcal for ONC1. This contrasts with the figure, +13.25 kcal, quoted by Rossini et aU 3 Likewise one computes AH~298 = +12.36 kcal, to be compared to Rossini's +12.57 kcal. The 0°K bond energy of the C1-NO bond may then be calculated to be +37.16 kcal, and the bond energy at 298°K is +38.24 kcal defined o as AH298 for ONC1 ~ NO + C1. KINETIC
DATA
There is, as mentioned earlier, evidence in the literature that ONCI decomposes by at least two parallel mechanisms, the bimolecular path being kl
2ONC1
,
k~
~ 2NO
q- C12
(1,2)
and the unimolecular one being k~
ONC1 ~- M ,
) N O -F C1 +
M
(3, 4)
Cl2
(5, 6)
k,
followed by
Cl +
ONCI
~-%* NO
+
k6
Ashmore and Spencer 4 have also discussed a heterogeneous route for decomposition which has played a role in vessel experiments but which is unlikely to contribute in shock tube studies. Burns and Dainton TM have determined k5 at low temperatures to be ks = 1053'5 exp ( - 1.060 × I03/RT). An examination of the time for es-
DECOMPOSITION OF NITROSYLCHLORIDEIN SHOCK WAVES 28, 24
I
'
I
'
I
'
I
'
I
143
'
I
i
I i
3850A
-
~
~
-
-
~
l
~
~
=
•
20 16 12 _
ET
~A
•
--
8 4 2.6
•
-~&
•
-._
.-2"
2D 5460A 1.5 1.0
I 300
,
I 500
i
I , I , I 700 900 I100 TEMPERATURE , OK
,
I 1300
,
I 1500
FIG. 1. T e m p e r a t u r e dependence of the extinction coefficients of ONC1 at three wavelengths. • is defined by I/Io = 10-~z~ with l in cm and c in moles/liter. t a b l i s h m e n t of the pseudo s t e a d y - s t a t e in competitive, consecutive gas reactions of t h e t y p e found in the unimoleeular m e c h a n i s m here has been made. ~ I t shows t h a t u n d e r the conditions used in t h e present work, reaction (5) is fast enough to produce a n effective unimolecular rate which is within a few per cent of equaling twice t h e rate of reaction (3), in a time less t h a n " Note s u b m i t t e d by Howard B. P a h n e r : I t may be observed t h a t in the low pressure unimolecular region, the Hinshelwood and the Riee-Ramsperger-Kassel expressions for the rate c o n s t a n t have the same form. The ONC] results thus yield, in terms of R R K theory, s = 4.43 for ONC1 decomposing in Ar and s = 8.01 for pure ONC1. s is supposed to be the n u m b e r of effective oscillators in the decomposing molecule and should not depend upon the n a t u r e of the second body. R R K theory hence appears i n a d e q u a t e to describe the low-pressure unimolecular region for ONC1. The Hinshelwood approach is not quite realistic either, b u t at least it has the v i r t u e of t a k i n g b o t h colliding molecules into consideration. Perhaps a still b e t t e r result would be obtained by applying the theory of Nikitin cited by Professor B o u d a r t in his review.
10 -6 sec in all cases. Since the earliest measurem e n t s were m a d e a t a gas time of a b o u t 2 × 10 -8 sec, a negligible error is m a d e in setting t h e unimolecular c o n t r i b u t i o n equal to twice the rate of reaction (3). As is well known, (for a discussion, see reference 15) the order of reactions of t h e t y p e (3) varies with the pressure. Gas pressures in t h e shock wave were of the order of 1 to 2 a t m o s in t h e present study. O t h e r t r i a t o m i c molecules v 16 such as N()2 , F2() '7 a n d N20) is exhibit approxim a t e l y second-order b e h a v i o r i n this general pressure range, so it was expected t h a t ()NC1 would also. I n t h e second-order region, the rate of unimolecular decomposition depends u p o n the n a t u r e of t h e species M. I n particular, when M is a noble gas the rate c o n s t a n t is i n v a r i a b l y lower t h a n when M is t h e decomposing molecule itself, a t least a t m o d e r a t e temperatures. Relatively little i n f o r m a t i o n exists on t h e v a r i a t i o n with t e m p e r a t u r e of such relative rates. Studies of iodine '9 a n d b r o m i n e ~° a t o m r e c o m b i n a t i o n a n d of dissociation of i~ 1 a n d Br~ ° h a v e shown t h a t t h e rate c o n s t a n t s for M = Ar a n d the diatomie halogens tend to equality a t high
144
CHEMICAL KINETICS
I IO'O~
~
I
.~L
I
I
I
~
- d d-~
I
I
I
i
= 2 k3oPP[ONCI'] [M']
-
-
,oLLOglo2k~ pp
, 0.7
. 0.8
,
,
,
0.9 IO00/T,
.', 1.0
I.I
1.2
T in°K ~.pp
FIG. 2. Arrhenius plot of the apparent second-order unimolecular rate constants, 2 k3.M , for pure ONC1 and ONCI-Ar mixtures. A, pure ONC1; 0 , 1:10 and 1:20 ONCI-Ar; ~ , 1:50NC1-Ar; O, 1:2 ONCI-Ar. Solid and dashed lines are drawn for examining precision of the data, as discussed in the text. temperature. From the temperature dependence of the rate constants in such studies one predicts that at high enough temperatures the rate constant for M = Ar will, in fact, exceed that of the diatomics. The present rate data were examined first with respect to scatter and probable accuracy. For this purpose, "apparent" second-order unimolecular rate constants, 2 k~pp, were com~i+pp puted from 2 + {-d[ONC1]/dt} + [0NC1][M]. The results are shown in Figure 2. The range of rate constants is approximately l0 s, a typical coverage for shock-tube kinetic studies. The high-temperature limitation lies in time resolution and a low-temperature limitation results from the restricted total time available for dissociation before arrival of the contact surface, plus uncertainties about boundary layer effects. Unfortunately, these limitations mean that with scatter such as is present here in the rate constants, no accurate equation for the rate constants can be deduced from the hightemperature data alone. The constants for pure ONC1, indicated by triangles, all fall within a factor of 2.5 of the solid line, and those for the Ar dilution runs all fall within a factor of 3 of the dashed line. The pure ONCI data as a whole lie below the Ar dilution data, indicated by circles, a typical difference in the middle of the T range being about a factor of 3. Beyond this
there is no obvious trend with dilution among the Ar-dilution data, any possible trend being obscured by scatter. Our own a priori estimates of the uncertainty in rate measurements, taking into account in particular the correction factors, extinction coefficients and measured rates of change of absorption, yielded a probable maximum of perhaps a factor of 2. This was too optimistic but does support a conclusion that the scatter in the data is representative of the probable error, to which we would now assign a conservative maximum of a factor of 4, or about 0.6 on the log10 scale, for any one measurement. It is this requirement which will be placed on any final treatment of the data. One must of course admit always the possibility of a systematic error somewhere in the rather complex computations used in obtaining the results. This likelihood is minimized by the use of different dilutions with Ar and three different wavelengths for absorption. The correction factors and extinction coefficient behavior differed so markedly for these variations in conditions that the general agreement of the results strongly supports the correctness of calculations. THE RATE CONSTANTS
The general expression for the rate of homogeneous decomposition of ONC1 according
DECOMPOSITION OF NITROSYL CHLORIDE IN SHOCK WAVES '
I
I
I
I
I
145
'
I
'
I1.0 d [ONCl] = dt
k?pp ~)NCI-lZ
so~
oO '
Loom k~ pp
0
9.0-
•• • t
0
e
o 'b
8.0--
ZO O.7
0.8
0.9 IO00/T,
1.0
I.I
Tin °K
F~a. 3. Arrhenius plot of the apparent bimoleeul~r r~te constants, k~p~', for pure ONC1 and ONCI-Ar mixtures. A, pure ONC1; O, 1:10 and 1:20 ONC1-Ar; ~ , 1:50NC1-Ar; C), 1:20NC1-Ar. to the above mechanism is
2 k~pp = kl [ONC1] + 2 ks, oNcl -[ONCI] [M] [M]
-d[ONC1]/dt = k~[ONCI] ~ + 2
k~, o~o~[ONC]]~
-t- 2 k~, Ar[ONCI][Ar] -~- 2 k3,[ONC1] where k3, is the rate constant of reaction (3) when it is in the first-order pressure region. It should be mentioned at this point that the probable contributions of back reactions were computed for critical runs, namely, those in which measurements were made after 20 or 25 per cent decomposition, and were found to be negligible. The reason is that for such runs the equilibrium decomposition was typically some 90 per cent. The computation of apparent rate constants, defined as 2 k~'" = Rate/[ONC1][M]; k~'" = Rate/[ONC1]~; and 2 kS""8' = Ratc/[ONC1], permitted some determination of the relative importance of the reactions. An aid here was the difference in [M], depending principally upon the dilution used in the runs, and the difference in [ONC1]. [M] was larger for the shocks in diluted cases and [ONC1] was smaller. Consider the results for 2 k ~''" 3 •
[ir]
+ 2 k3, ~r [~]] + 2 k3,/[M]. For pure ONC1, this gives 2 k~pp = kl -~- 2 ks. one1 -~- 2
k3,/[ONC1]
For 1 : 10 ONCI-Ar, we have 2 k~'" = 0.09 (kl + 2 ks. ONCl) -~ 0.91 X 2 ]c~, Ar -~ 2
k3,/[M].
It is observed (Fig. 2) that 2 ks""3 for the 1:10 case is greater than that for pure ONC1, roughly by a factor of 2 or 3. Since [M]1:10 > [M],ure in the runs, 2 k~, cannot be making an important contribution, and is, therefore, ignored. I t also appears here that 2 ka, Ar must be 2 or 3 times (kl + 2 ks, ONC]). NO new information actually is gained from the other k~P"s, shown in Figures 3 and 4, but in Figure 3 especially, emphasis is given to the fact that the unimolecular secondorder route in ONC1-Ar mixtures is dominant. If it were not, the values of k~'" would not depend upon dilution.
146
CHEMICAL KINETICS
' 5.0
I
i
I
I
I
i
I
-
d [ONCI] = 2kooPr-.,..,C nT aLul~ =-I
4.0
'.,
LOglo ,~ ~ kapp 3'
: o.}:
:5.0
2D
z 0.7
I 0.8
I 0.9 IO00/T,
I
I 1.0
I
I I. I
I
T in °K
FIG. 4. Arrhenius plot of the apparent first-order unimolecular rate constants, 2 k~;p, for pure ONCI and ONC1-Ar mixtures. A, pure ONC1; O, 1:10 and 1:20 ONCI-Ar; ~ 1:50NCI-Ar; O, 1:20NC1-Ar. An examination of the relative contributions of kl and 2 k3, ONCl depends principally upon the use of low-temperature data in conjunction with the shock tube data. Any attempt to write an equation for rate constants depends also upon this, whether for pure ONC1 or the Ar-diluted cases.
The most recent study of the low-temperature decomposition of pure ONC1 is that of Ashmore and Spencer. 4 Previously, extensive work was done by Waddington and Tolman1 and Welinsky and Taylor,~ with results in substantial agreement. Ashmore and Spencer have found a heterogeneous contribution to the mechanism that should contribute most readily to the rate at the lowest temperatures. Waddington and Tolman's work, covering the range, 423 to 523°K, was free from heterogeneous effects; but their rate constants were influenced by the unimolecular mechanism, which they did not consider in computing apparent kl values. Ashmore and Spencer have corrected Waddington and Tolman's data on the basis of their results, to give values for kl. An Arrhenius fit then yields k~ = 101~5 exp ( - 2 3 . 4 kcal/RT) cc/mole sec. This is shown by the dotted lines in Figures 5, 6 and 7. Ashmore and Spencer report 2 ks.oNcl values equal to 220 =i:40 at 523°K, 6400 d=600 at 573°K. Although it appears to us that their estimated uncertainties are too small, the hum-
bers must be accepted as certainly within a factor of 1.5 of the correct values. They use these two numbers to give an Arrhenius equation for ka. o.~c], choosing as the most reasonable result, ka, oNcl = 1017'9 exp (--38 kcal/RT) co/mole sec. For k3.co= they obtain k3,co2 = 1017a exp ( - 3 7 kcal/RT) cc/mole sec. If the rate constant for M = Ar is about half as large as for COs around 500°K as was observed by Volpe and Johnston=2 in the unimolecular decomposition of 02 NC1 (to which Ashmore and Spencer find parallels in ONC1 decomposition), one would predict k3.Ar = 10I7° exp (--37 kcal/RT). These equations for M = ONC1 and M = Ar are plotted (as 2 k3.M) by the dashed lines in Figures 5, 6 and 7. It is clear in both cases that an Arrhenius expression is inadequate to predict high-temperature unimolecular constants from the low-temperature work. The theories of Rice, Ramsperger and Kassel,2a of Slater 15 and of Hinshelwood24 have been used with fair success in the past to account for unimolecular decomposition rates and should be appropriate here. Uncertainties in the available low- and high-temperature data in the present instance do not justify the determination of more than two parameters, so we choose the Hinshelwood theory, in which the critical energy is arbitrarily taken to be the bond dissociation energy, 37.16 kcal. The theory takes the form,
k = Z[Eo/RT]'~/2[1/(n/2) '] exp ( - - E o / R T )
DECOMPOSITIONOF NITROSYLCHLORIDEIN SHOCK WAVES I1.0
I
I
'
~ I
'
I
147
i
I
i
IO.O
L°g'°k°"ct
_
-
""""
\\\.
--......
kTOTA L : k I + 2ks,oN©=
.
I 0.8
I 0.9
7.0 0.7
,
,
I000/T,
"""'"-......
I
I 1.0
~
-7"--
I I.I
,~
1.2
T in OK
F~(~. 5. Arrhenius plot of the experimental values for kl + 2 k3, ONC1 Solid line is the Hinshelwood theory expression discussed in the text. The dotted line is the Ashmore and Spencer ~ revision of kl and the dashed line is the Arrhenius expression for 2 k3, OSCl given by Ashmore and Spencer. •
II.0
LO,ok,,,,8.°
'
~I
'
"'""'"'-._
0.7
0.8
l
l
I
J
I
0 0
0.9 1.0 I O 0 0 / T , T in OK
I
-
I.I
1.2
FIG. 6. Arrhenius plot of the experimental values for 2 k3, Ar Solid line is the Hinshelwood theory expression discussed in the text. The dashed line is the Arrhenius expression estimated from the Ashmore and Spencer 4 results for 2 k~, cos • The dotted line is the Ashmore and Spencer revision of k1 . •
CHEMICALKINETICS
148
6ok it
I0.0
9.0
8.0
-I.0
Z0
3.0
6.0
3.0
5.0
-4.0
Logm k
,ot 0.5
I 1.0
1.5
1.5
2.0
IO00/T,
2.5
2.5
3.0
3.5
T in °K
FIG. 7. Low T-high TArrhenius plot of decomposition rate constants for pure ONC1. 0 , experimental values of the total rate constant, k, = k~ -F 2 ks, ONCl,from the present work and from the literature.I. 2.4 The solid line is the sum of the Ashmore and Spencer revision4of kl and the Hinshelwood theory expression for 2 k3, oict from the present paper. The dotted line is k~ and the dashed line is the Arrhenius expression for 2 ks. ONClgiven by Ashmore and Spencer. 4 where Z is the apparent collision number, n is the number of classical square terms from which stored internal energy is transferred to the dissociating bond during collision and E0 is the 0°K bond energy. The expression might conveniently be improved for semiempirical purposes by including a term representing a possible change with temperature of the energy transfer efficiency. Because this would introduce a third parameter, it is not included for the present. A 2-point fit for pure ONCI is performed with the 2k3,ONC1values, 220 at 523°K and 10s67 at 1177°K. The latter point is chosen at the approximate midpoint of the high-temperature range and has been corrected for a slight con-
tribution from kl at this temperature, with the use of the Ashmore and Spencer Arrhenius equation for kl. The result is 2k3, oNcl = 2 X 109°~Tt/2[Eo/RT]7"°t
• [1/F (8.01)] exp( -- E o / R T). o
For an assumed collision diameter of 3.5 A, this corresponds to a low collision efficiency, 0.018 per cent. The maximum possible value of n for two colliding ONC1 molecules would be the contributions from 6 vibrations and 6 rotations, subtracting 3 rotations for angular momentum conservation.~4 This yields 15 square terms, or [n/2]m~ = 7.5. Thus n / 2 - 7.0 is perhaps
DECOMPOSITION OF NITROSYL CHLORIDE iN SHOCK WAVES
feasible, but the very low collision efficiency is hard to believe, and there is the added problem that the predicted value of 2ka,oNm at 573°K is 2700, less than half the Ashmore and Spencer value. The sum of the ttinshelwood fit to 2lea,oNe1 plus the Ashmore and Spencer revision of kt is shown in the high-temperature region in Figure 5. in Figure 7 is shown this result over the approximate temperature range, 290 to 2000°K. The Ar dilution result is more reasonable. Our estimates of 2ka,Ar from the ka,co2 data of Ashmore and Spencer are 40 at 523°K and 800 at 573°K. With the 523°K value and the shock tube data at 1137°K, for which 2/ca,A~ 109% the equation 2lt:a. Ar ~- 2 X IOna~T~/2[Eo/RT] ~4~ • [ 1 / r (4.43)] e x p ( - E o / R T) is obtained. This is shown by the solid line in Figure 6. With theoaSSumption of a collision diameter of about 3 A, this gives a collision efficiency of 2.9 per cent. The [n/2] . . . . should be 3. On this basis, 3.43 is too large. However, it is very sensitive to the choice of the low-temperature point. If 2]Ca,A~ at 523°K were 20 instead of 40, one would obtain n/2 - 2.5. The predicted value of 2ka,Ar at 573°K is 680, in decent agreement with the estimate. Although the Ar dilution ka's are rather adequately accounted for by the simple theory, it seems to us that a more sophisticated approach than we can supply probably is necessary to explain the pure ONC1 results. In this regard, the following points may be of significance: (1) There is a parallel between the present results and studies of Br2 dissociation. A recompuration of the low T-high T Hinshelwood fit with the use of shock tube data ~9 and the most recent results of Givens and Willard~° at lowtemperatures yields, for pure Br~, n/2 = 3.89 and an apparent collision efficiency (for ¢ = 3.5) A of 0.91 per cent; for Br~ in Ar the results are n/2 = 1.58 and a collision efficiency (for ¢ = 3 ~_) of 12.3 per cent. Thus with Br2 as with ONC1, the n/2 values tend to be improbably large but close enough to the (n/2)m~ values to be encouraging; the Ar-dilution apparent collision efficiencies are reasonable; and the pure-gas apparent collision efficiencies are surprisingly small. It is, however, interesting to observe that there is a rough correlation between the apparent collision efficiencies required
149
in the Hinshelwood expressions and the complexity of the molecules involved in collisions, i.e., the efficiencies for Br~-Ar, ONCI=Ar, Br2-Br~ and ONCI-ONC1 are (in per cent) 12.3, 2.9, 0.91 and 0.018. If the apparent collision efficiency is viewed as the product of two terms, one being the probability that the available energy will be transferred and the other being the probability that transferred energy will accumulate in the critical bond, one might expect a lower efficiency when more bonds are available, as in ONCIONC1, than in a collision such as Br2-Ar. (2) Interpretation of the pure ONC1 data in terms of complex formation between ONC1 and C1 or NO, in a way analogous to that applied successfully by Bunker and Davidson 25 to halogen atom recombination (or molecular dissociation), would require the existence of a quite stable complex and would probably predict an ONC1 efficiency relative to Ar many times larger than we estimate to be the case at low temperature. Such an approach also would produce a weaker T dependence at low temperatures than does the Hinshelwood fit and hence the discrepancy at 573°K would become still worse. (3) The results could be interpreted even by simple collision theory if one introduced a strongly T-dependent collision efficiency. This possibility has been suggested by others with regard to halogen atom association,~8 but so far as we are aware, no quantitative expression for this effect is available. (4) Our observations are of the rates at which molecules leave rather low energy states in the electronic ground state. Reasonable agreement in rates is obtained for three different mean wavelengths, corresponding to three different groups of low-lying states. The measured rates should equal the rates at which molecules are actually dissociating even when the dissociation rate is limited by the rate at which molecules are supplied to the critically high levels from which they presumably decompose. The reason is that in this case a steady-state should be established very rapidly in which the concentrations of molecules in high states are below the equilibrium (Boltzmann distribution) values but bear fixed numerical relations to the concentrations in the low states. Thus even in this ease one should be observing a representative sample of the molecules by observing those in the low states. If the deviations from a Boltzmann distribution are slight in the lower states, then the
150
CHEMICAL KINETICS
use of equilibrium (Boltzmann) extinction coefficients to measure concentrations should be sufficiently accurate. The rate of dissociation will, in this excitation rate-limited case, be less than it would be if the vibrational relaxation were much faster than dissociation. Thus this effect could account for a dropping off in rate constants at high temperatures. Unfortunately we do not know how rapid the relaxation is in 0NC1. If perhaps 103 collisions are required for relaxation, then it occurs in a time of the order of l0 -1 ttsec. At the highest temperatures in t~e present work, the initial rate of disappearance of ONC1 behind the front approached 10 per cent of the ONC1 per ~sec, or 1 per cent in the estimated relaxation time. Thus relaxation should not have been seriously limiting the rate.
Acknowledgments We wish to express our thanks to Mr. B. E. Knox for performing a number of calculations. This work was sponsored by Project SQUID, which is supported by the Office of Naval Research, Department of the Navy, under Contract Nonr 1858(25) NR-098-038. Reproduction in full or in part is permitted for any use of the United States Government. REFERENCES 1. WADDINGTON,G., AND TOLMAN, R. C.: J. Am. Chem. Soc., 57, 689 (1935). 2. WELINSKY, I., AND TAYLOR, H. A.: J. Chem. Phys., 6, 466 (1938). 3. ASHMORE, P. C., AND CHANMUGAM,J.: Trans. Faraday Soc., 49, 265 (1953). 4. ASHMORE, P. G., AND SPENCER, M. S. : Trans. Faraday Soc., 55, 1868 (1959). 5. BEESON, C. M., AND YOST, D. M.: J. Chem. Phys., 7, 44 (1939). 6. GOODEVE, C. F., AND KATZ, S.: Proc. Roy. Soc. (London), A172, 432 (1939). 7. SULZER, P., AND WIELAND, K.: Helv. Phys. Acta, 25, 653 (1952).
8. HIRSCHFELDER, J. O., CURTISS, C. F., AND BIRD, R. B.: Molecular Theory of Gases and Liquids, p. 785. John Wiley and Sons, Inc., New York, 1954. 9. BURNS, W. G., AND BERNSTEIN, H. J.: J. Chem. Phys., 18, 1669 (1950). 10. PALMER, H. B., AND HORNIG, D. F.: J. Chem. Phys., 26, 98 (1957). 11. DEKLAU, B. : Ph.D. Dissertation, The Pennsylvania State University, 1960. 12. SULZER, P.: Dissertation, E.T.H., Zurich, 1952. 13. RossINI, F. D., WAGMAN, D. D., EVANS, W. H., LEVINE, L., AND JAFFE, S.: Circular 500, National Bureau of Standards, U.S. Govt. Printing Office, 1952. 14. BURNS, W. G., AND DAINTON, F. S.: Trans. Faraday Soc., $8, 52 (1952). 15. TROTMAN-DICKENSON, A. F.: Gas Kinetics, pp. 45-82. Butterworth & Company, Ltd., London, 1955. 16. HUFFMAN, R. E., ANn DAVIDSON, N. : J. Am. Chem. Soc., 81, 2311 (1959). 17. KOBLITZ, W., AND SCHUMACHER, H. J.: Z. physik. Chem., 25B, 283 (1934). 18. JOHNSTON, H. S.: J. Chem. Phys., 19, 663 (1951). 19. BUNKER, D. L., AND DAVIDSON, N.: J. Am. Chem. Soc., 80, 5085 (1958). 20. GIVENS, W. G., JR., AND WILLARD, J. E.: J. Am. Chem. Soc., 81, 4773 (1959). 21. BRITTON, D., DAVIDSON, N., GEHMAN, W., &ND SCHOTT, G.: J. Chem. Phys., 25, 804 (1956). 22. VOLPE, M., AND JOHNSTON, H. S.: Z. Am. Chem. Soc., 78, 3903 (1956). 23. KASSEL, L. S.: Kinetics of Homogeneous Gas Reactions, Chap. V. Chemical Catalog Company 1932. 24. FOWLER, R. H., ANn GUGGENHEIM, E. A.: Statistical Thermodynamics, pp. 489-530. Cambridge University Press, 1952. 25. BUNKER, D. L., AND DAVIDSON, N.: J. Am. Chem. Soc., 80, 5091 (1958). 26. RICE, O. K. : Ninth International Astronautical Conference, Amsterdam, 1958; pp. 9-19. Wien Springer Verlag, 1959.