WESLEYM.
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JONES AND
NORMAN DAVIDSON
VOl. s4
[CONTRIBUTION FROM THE GATESAND CRELLIN THE
LABORATORIES OF CHEMISTRY, CALIFORNIA ISSTITUTE O F TECHSOLOGY, AND Los XLAMOSSCIENTIFIC LABORATORY, UNIVERSITYO P CALIFOXSIA, Lo3 I L ~ Xx EW JMEXICO] ~,
The Thermal Decomposition of Ozone in a Shock Tube' BY
WESLEYAT. J O N E S ~AND
T\TORh1.4N
DAVIDSON
RECEIVEDA-OVEMBER20, 1961 The thermal decomposition of ozone in argon and nitrogen inert gases has been studied in a shock tube. The important reactions are R 1 and R3. R1, R2 M 0,j.% M -/0 2 0 R3 0 0 3 --+ 0 2 0 2 I n the concentration and temperature range studied-argon 0.00334 to 0.0264 mole/l., 769 to 910°K.; nitrogen 0,00902 to 0.01286 mole/l., 689 to 863"K-Rl is a unimolecular reaction a t its low pressure second order limit with k l N t / k l A = kaNr/ kz.4 = 1.64 & 0.1'7. Combining the shock tube data for M = NZwith data in the range 303 t o 383'K.. due to Glissman and Schumacher and reinterpreted by Benson and Axworthy, gives k1y2 = (5.8 f 0.6) X 10" exp( -23,150 Z!C 300/RT)(mole/ L)-l sec.-l and k2x2 = (9.4 i 1 ) X lofiexp(f1700 =I=300/RT) = 2.0 X lo7 (1000/T)1~66(mole/l.)-2 sec.-l. T h e kl d a t a are discussed in terms of the Slater and Hinshelwood-Rice-Ramsperger-Kassel ( H R R K ) theories. Interpretation of the data by the classical H R R K theory gives 2.83 =k 0.2 effective oscillators and a collision efficiency of 0.039. The values of k3 obtained are consistent with a n extrapolation of previous low temperature data. Vibrationally excited oxygen molecules with from 10 t o 17 vibrational quanta, produced by the strongly exothermic R3 involving O( 3P)atoms, were detected by flash absorption spectra.
+
+
Introduction Several investigations have been made of the thermal decomposition of ozone, from slightly above room temperature to 5GS'K. Without attempting a discussion of all this work3 and of the evolution of thought regarding the mechanism, we follow Benson and Axworthy4 in accepting reactions R1, R2 and R3 as providing a satisfactory explanation of the homogeneous thermal decomposition. Reaction R4 is included, although it is unimportant in all previous work and in the present work. R1, R2 0 3 M 0 2 0 M AEo0 = 34.35 kcal. R3 R4
+ 0 +
0 3
+0
2
+ + + 0 2
AEoa = -93.6 kcal.
O+O+M+Oz+M
With the steady state assumption for 0 atoms, eqs. R1, R2 and R3 yield the rate law E l
An important contribution has been made by BA in reviewing earlier work, in studying the thermal decomposition of ozone a t 99.8' and particularly in reanalyzing the extensive data of Glissman and Schumacher5 in the range 70 to 110' on the decomposition of ozone and on the effect of inert gases. Under the conditions of that ~ o r k , extending up to pressures of almost one atmosphere, BL4have concluded that R1 is a unimolecular reaction a t its low pressure limit. The data give k1 and klk3/k2. Equilibrium data give k l / k 2 , so that all three rate constants are determined. BA fitted kl,ka and k3 to Arrhenius equations and gave the efficiencies of 0 2 , N?, COn and He relative to 0 3 for reactions R1 and R2. Some recent data6 (1) This paper was presented a t t h e 135th National Meeting of the American Chemical Society, Boston, Mass., April, 1959. (2) Los Alamos Scientific Laboratory, Los Alarnos, New Mexico. Research Fellow, California Institute of Technology. 1957-1958. ( 3 ) For earlier work on dilute solutions of ozone in oxygen see (a) S. Jahn, Z . a m t g . Chetn.. 48, 260 (1906), and (b) R. C. T o l m a n and 0 . R. Wulf, J . A m . Chem. Soc.. 49, 1650 (1927). (4) S . 1%'. Benson and A. E. Axworthy, Jr., J . Chem. Piiys., 26, 1718 (1957). Hereafter referred t o as B.4. ( 5 ) A . Glissrnan a n d H. J. Schumacher, Z.p h r s i k . Chrm., 2 l B , 323 ( 1 933).
+
+
on rZ.1 for pure ozone are in general agreement with the conclusions of BA. Garvin7 studied the decomposition of ozone in excess nitrogen from 430 to 5G.j°K. using a flow technique. His measurements yield values of kik:j/ka. I t was of interest for several reasons to extend information on this system to the temperatures available with the shock tube. R1 is interesting as a unimolecular reaction involving a polyatomic molecule with a minimum number of vibrational degrees of freedom. The magnitude and temperature coefficients of rate constants of recombination reactions such as R2 have been of considerable recent interest. Moreover, renewed interest attaches to R3 as a result of the important work of McGrath and r';orrish8-10 (hereafter referred to as MN). They have observed oxygen molecules with from 12 to 17 vibrational quanta in the flash photolysis of ozone in ozone-nitrogen mixtures a t room temperature. These molecules are presumably the products of the strongly exothermic R3. Since some 'D oxygen atoms were almost certainly present in their ~ y s t e m ,it~ ,was ~ ~ desirable t o search for such excited molecules in a system where the 0 atoms, produced by R1, would be in their 3P ground state. RIN have again raised the question ~as. t~o whether excited products of R3 might destroy further ozone, perhaps through short energy chains. This possibility has previously been considered in the thermal5 and especially in the photochemical decomposition of ozone.11 The relationship among R1, R2 and R3 in the shock tube work is somewhat different from that in previous work. The oxygen atom concentration in the previous work is determined by a steady state involving R1 and, in general, both R2 and R3. (6) J. A. Zaslowsky, H. B. Urbach, F. Leighton, R. J. Wnuk and J. Wojtowicz, J . A m . Chem. SOC.,82, 2082 (1900). (7) D. Garvin, ibid., 76, 162.3 (1954). ( 8 ) W. D. McGrath and R. G. 1%'. Norrish, P r o c . R o y . SOC.(London), 242A, 265 (1937). (9) W. D. McGrath and R. G. W. Norrish. . V a l u e , 182, 233 (1938). (10) W. D. McGrath and R. G . 1%'. Sorrish, Proc. R o y . SOC.(LUIIdon), 264A, 235 (1960). (11) W. A. Soyes, Jr., and P. A . Leighton, "The Photochemistry of Gases,'' Reinhold Publishing Corp., S e w I'ork, X. Y . , 1OL1.
Aug. 5, 1962
THERMAL DECOMPOSITION OF OZONE
This gives rise t o the rate law El. In the shock tube work R1 and R3 are the most important reactions in the experimentally available time. The atom concentration is not in a steady state, so that E l is not applicable, and one can observe as a function of time the transition from a situation in which essentially only R l is occurring t o one in which R1 and R3 are proceeding a t approximately equal rates. Experimental
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PYREX PIPE. 15cm I D FUSE0 SILICA TUBE. 7 5 c m I O TUNGSTEN LAMPS Hg ARC MONOCHROMATOR Pe PHOTOMULTIPLIERS
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General.-General characteristics of the shock wave method of studying reactions have been described else7, where.l2~l3 Dilute mixtures of ozone in argon or nitrogen were shocked to the desired temperature using Hg or H e Fig. 1.-Measurement end of shock tube; the fused silica driver gases. The initial ozone mole fraction in shocks tube intercepts the shock wave coming from the left. evaluated for kinetic data varied from 4.83 X lo-‘ to 1.87 X 10-2 for ozone-argon and from 1.38 X 10-3 to 1.93 X 10-3 chromator with a 600 grooves per mm. grating and 33 A. for ozone-nitrogen. Total concentrations of shocked gas per mm. dispersion. Light v, hich could not enter the monovaried from 3.34 X to 2.64 X lo-* moles liter-’ chromator was excluded from the shock tube as much for ozone-argon and from 9.08 X to 1.285 X as po5sible. For most runs the monochromator was set at moles liter-’ for ozone-nitrogen. Temperatures of shocked gas varied from 769 to 910°K. for ozone-argon and from 2485 A., corresponding to a maximum output of the HBOti89 to 863°K. for ozone-nitrogen. Ozone concentration 200-photomultiplier combination %nd close to the ozone was observed spectrophotometrically as a function of time. absorption maximum around 2550 A. I n measurements at The temperature and density of the shocked but unreacted %nd above 0.4y0 ozone the monochromator was set at 2975 gas were calculated from the measured shock velocity and A. The transmittedJight had a triangular profile with a the known state of the gas before arrival of the shock wave. base of 66 A. at 2975 A. and a trapezoidal profile with bases This calculation was facilitated by tables obtained with an IBM-704 computing code made available to us by Dr. R . E. of 66 and 132 A. at 2485 A. Calculations based on the room temperature absorption spectrum indicated negligible error in Duff of Los Alamos. Correction was made for departure of the rate constants due to the finite spectral width. The the initial temperature of the gas from t h a t on which the tables were based. Thermodynamic data were taken from signal from a 1P28 photomultiplier at the output of the monochromator went to the Tektronix 531 and 512 oscillothe XBS tables,14 but corrections were made for the new scopes operated in parallel. The output load resistor of dissociation energy of oxygen.16 The Xg was taken to be the photomultiplier was 5 K and the R C time of the signal vibrationally unrelaxed. The vibrationai relaxation of input circuit was about 0.6 p s . In many shocks measurepure nitrogen16 is long compared to the reaction time. Instrumentation.-The 6” i.d. driver section was 9 feet ments of light emission from a defined section of the shock tube were made with a 1P28 photomultiplier and 513 long and was separated by a cellulose acetate membrane from a 10 foot long, 6 ” i.d. low pressure section ofaluminum oscilloscope. I n the flash absorption spectrograms of decomposing pipe and Pyrex pipe. The Pyrex was joined by a n O-ring seal to a section of 3 ” i . d . fused quartz (Fig. l ) ,which permit- ozone the light of a n Edgerton, Germeshausen, and Grier FX-3 flash lamp passed through a defined section of the ted the measurement of ozone concentration by ultraviolet spectrophotometry. The various distances in Fig. 1 quartz shock tube and was focussed with a quartz lens on the slit of a Bausch and Lomb medium quartz spectrogave adequate time for observation of the once-shocked gas. graph. A 1/2 Ffd. condenser charged to 12 kv. was disDural collars a t the center and right hand end of the quartz charged through the lamp. T h e spread of the light beam piece fitted closely, were stabilized symmetrically with shim stock, and then cemented to the quartz with Epibond 1-0.corresponded to 3 p s laboratory time or 9 p s molecule time. 208 resin (Furane Plastics, Los Angeles 39, Calif.). The Eastman 111-0 plates were used. The relative unfiltered quartz wall thickness was about 2 mm. For aerodynamic light intensity of the FX-3 was measured with a 1P28 purposes a taper was ground onto the outside of the wall of photomultiplier and 531 oscilloscope (with appropriately triggered and delayed sweep) and was known as a function the quartz tube where it intercepted the shock wave. The slit system has been previously described.’? One of time following passage of the shock r\ave past the position of spectroscopic observation. The lamp intensity mm. slits were used. The measured shock velocity was the average value over a 40 cm. interval. Schlieren optics and robe to a maximum in about one microsecond. The main portion of the light decayed approximately exponentially a trigger circuit were used to start and stop the 1.6 megacycle Potter time intervalometer and to start the delaying sweep with a 4 p s half life. There may be a long duration tail with a n intensity about 1% of the maximum intensity. of a 531 Tektronix oscilloscope. After a suitable delay the Reagents.-Ozone was prepared from Matheson research inain sweep of the 531 started, and the associated plus gate signal was used to start the sweep of a Tektronix 512 oscillo- grade oxygen (stated maximum impurity limits: COZ scope on which a parallel spectrophotometric record was 0.17’, CO O.Ol?c, il O.O1?o, N2 0.017,, H PO.Olyo)in a high vacuum system from which mercury vapor was excluded with taken. In order to estimate attenuation, the shock velocity was also determined for the first 20 cm. of the 40 cm. a liquid nitrogen trap. The oxygen was passed through Ascarite and P205, condensed in liquid nitrogen and then interval by utilizing the known delay and the duration of vaporized into the ozonizer system. Stopcocks were kept t o the 531 trace before arrival of the shock wave. a minimum and greased with Kel-F No. 90 with no evidence The light source for ozone spectrophotometry was an of reaction. Convective circulation in the ozonizer was Osram HBO-200 high pressure D C mercury arc, operated maintained by passing one limb of the circulation loop from batteries. Light passed through the shock tube into a 500 mrn. focal length Bausch and Lomb grating mono- through a Styrofoam dewar containing liquid nitrogen. The circulation greatly increased the rate of ozone formation. Ozone was condensed a t the exit of the ozonizer with liquid (12) T . Carrington and N. Davidson, J . Phys. C h e m . , S T , 418 nitrogen. Oxygen was thoroughly pumped off and the (1953). ozone stored at liquid nitrogen temperature. S o explo(13) D.Britton, N. Davidson and G. Schott, D i s c i r s s i o ~ sFavaday sions occurred. Sac., 17, 58 (19.54). (14) “Selected Values of Chemical Thermodynamic Properties,” Linde argon (stated to be 99.99% pure, 20 4.p.m. 0 2 , 20 p.p.m. H2, principal impurity X g ) and Linde high purity h-ational Bureau of Standards, Washington, D . C . , Series I11 (1954). (15) P. Brix and G . Herzberg, J. Chem. Phys., 21, 2240 (1933); dry nitrogen (0.01% 0 2 , traces of rare gases and COz) were used. Can. J . Phys., 32, 110 (19.54). (16) V. Blackman, J . Fluid Mechanics, 1, 61 (19%). Os-A and 03-hTzmixtures were prepared and stored in a 22-liter Pyrex bulb which was protected from light by a black (17) D . Britton, N. Davidson, W. Cehman and G. Schott, J. Chein. Phyr., 26, 810 (1958). cloth. Mixtures i t ere prepared as follows. Ozone was
WESLEYA I .
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NORMAN DAVIDSON
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Fig. 2.-Oscilloscope trace of shock 15; writing rate 20 ps./ cm. Downward deflection means increasing light intensity. vaporized into a one-liter bulb. The pressure was measured on a sulfuric acid manometer. I t was usually 100 to 400 mm. of acid. T h e stopcock to the one-liter bulb was then closed, the ozone was condensed with liquid nitrogen in a side a r m of the bulb and the small line volume evacuated. A residual pressure in the 1-liter bulb, usually about 0.3 mm. of sulfuric acid, was then measured, and this gas was pumped off. The ozone was then condensed into a side arm on the 22-liter bulb. The inert gas was then bled into the 22-liter bulb, after slow passage through Ascarite, PaOs, and two Dry Ice-trichloroethylene traps. The liquid nitrogen was removed from the side arm and the ozone and inert gas were allowed to mix. The final total pressure, usually 130 cm., was measured on a mercury manometer. A cardboard cylinder was then placed on top of the bulb and Dry Ice added to i t in order t o promote convective mixing. One to two hr. were sufficient. Samples were withdrawn and analyzed for ozone on a Carp spectrophotometer a t 2500 A. Procedure.-The shock tube was pumped down to a pressure of about 0.3 micron. Ozone-inert gas mixture was admitted to the shock tube, the pressure and the temperature were measured, H2 or H e was added to the driver section, and the stressed membrane was pierced t o initiate the shock. T h e contact time of the ozone with the shock tube was about four minutes. The ozone mixture was analyzed on a Cary spectrophotometer shortly before a shock was to be run. This measurement, with the known pressure, the length of light path in the shock tube and the oscilloscope trace deflection before arrival of the shock wave, allowed prediction of IO,the oscilloscope deflection after complete decomposition of the shocked ozone. Agreement was within experimental error. In a few cases where complete decomposition was not observed the calculated 10was used in data evaluation.
Results Evaluation of k, in Dilute Mixtures.-Figure 2 shows an oscilloscope record of transmitted light intensity versus time. The usual procedure was t o draw a smooth curve through a large scale plot of the record, evaluate d log ( O D ) / d t s c o p e as a function of time and extrapolate this quantity t o t = 0, which was taken to be the midpoint of the sharp rise in the trace which indicates arrival of the shock front. The quantity OD is the optical density, log (10;I). At ozone concentrations of 0.27, and less, E2 was then used to obtain kl.
For such mixtures corrections do not have to be made for changes in temperature, extinction coefficient and density, due to reaction. Strictly, the ozone concentration rather than the optical density should be used in E2, but there is no distinction if the extinction coefficient is constant. The total concentration before shock arrival is COand
100
I50
tmol, miCrOSeCOnd6
Fig. S.-Data from shock 15. OD is the optical density. The intercept at zero time is k , . The meaning of the three curves is discussed in the text.
A is the density compression ratio across the shock front. The time on the scope trace since the shock wave passed the observation slit is tscope. Because the shocked gas is flowing, the gas being observed a t time tscope has been in the shocked state for a longer time, which we call molecule time, tmol and which is equal to A.tscOpe. Especially in the fastest reactions, a rounding of the trace in the immediate neighborhood of the shock front prevented utilization of this data. The rounding is due to some combination of electronics rise time, bow and tilt of the shock front, and vibrational relaxation. There is no evidence for a systematic difference between values of kl obtained from fast and slow reactions. No correction was made for scattered light (0.6% of 10at 2485 A,),which had less than lgib effect on kl. Right behind the shock front ozone disappears only by R1. As the oxygen atom concentration rises, R 3 sets in. If R1 and R3 are the only reactions, the atom concentration reaches an approximate steady state determined by them, and the fractional rate of disappearance of ozone, a = d ln(Os) Idt, approaches approximately twice the initial value. This situation is illustrated in Fig. 3, based on the trace of Fig. 2 (Shock 15). -1fter practically all of the ozone has decomposed, first R4 and then R2 compete with R3 for 0 atoms. R2 and R4 are of negligible importance in our work. Fig. 3 contains three calculated curves. The lowest curve was calculated (with the aid of a computing codeI8 made available to us by Dr. R . E. Duff, Los Xlamos) for an ideal non-attenuating shock wave for the k1 obtained by extrapolation and k., obtained as discussed later. R2, R4 and R5 (discussed later) were included in the calculation, but they are not important. For this curve, the ratio of a to its initial value was calculated (see next section) to approach 1.7 rather than 2 . The departure from 2 is almost entirely due to the inapplicability of the steady state approximation. At the end of the experimental period in Fig. 3, the calculated oxygen atom concentration is ap(18) R.E. Duff, J . Chem. P h y s . , '28, 1193 (1958). T h e Duff code, For use with a n I B M 704 computer, integrates the differential equations of chemical kinetics subject t o the conditions of a steady state shock wave. Concentrations of all species, temperature, density, etc. are calculated as a function of time when rate constants, initial conditions a t the shock front, and shock velocity are specified.
Aug. 5, 1963
THERMAL DECOMPOSITION OF OZONE
2S7 1
preciable and amounts to about one-fifth of the initial ozone concentration in the shocked gas. The middle curve in Fig. 3 is corrected for the effect on kl of the progressive increase in temperature of gas behind the shock front in an attenuating shock.lg The top curve contains an additional and more uncertain correction to kl for a calculated temperature rise due to boundary layer intera c t i ~ n . l ~I ~n *Fig. ~ 3 the attenuation was taken to be 0.34Ye decrease in shock velocity per 10 cm. length of 3” i.d. shock tube, corresponding to the average for argon shocks with 0.2% 0 3 or less. (This estimate of attenuation is reasonable, but it has an uncertainty almost equal t o itself.) The attenuation averaged 1.OYofor nitrogen shocks, and l.77e for the E-series argon shocks. Considering the uncertainties in the experimental points in Fig. 3, especially a t longer times, and the effects of shock wave non-ideality, there seems to be no reason to doubt that R1 and R3 are the principal reactions removing ozone. The values of k 1 in the dilute runs and of ka are not corrected for the nonideal effects. The resultilig error in kl is negligible, and the error in kn is probably not large compared to other sources. Evaluation of kl above 0.2 Mole Per Cent. Ozone.-With argon as the inert gas several shocks were made with ozone mole fractions of 0.004 or greater (the E-series of Table I). At these higher ozone mole fractions the above extrapolation procedure becomes increasingly uncertain since the rate of R3 approaches that of R1 too rapidly. Although the steady state approximation for R1 and R3 becomes better, k l cannot be obtained in a simple way. Corrections must be made for changes in temperature and density and for vibrational relaxation, as discussed below. As will be discussed later, i t is likely that one of the 02 products of R3 has high vibrational excitation, so that R3 can be written as R3’. The relaxation of o?*to oxygen with an equilibrium vibrational distribution is written as R5. It is assumed
depending on the experiment, in order to obtain the fractional rate of disappearance of O3 a t the shock front; kl was then calculated by E2. In the calculation o f f a sufficiently accurate value of kl was known from the shocks on dilute mixtures; k3 was known as discussed later; and k d , to which the calculation of ,f is insensitive, was taken t o be 2 X IO9 (mole/’l.)-2sec.W1.?l I n RS it was sufficiently accurate to consider 0 2 * to have 16 vibrational quanta. If the vibrationally excited species relax stepwise such that kv+.--l = vklo, then the internal energy relaxes in a simple exponential way with a time constant 7, even for an arbitrary initial distribution of 02* among vibrational states.22 Reaction 5 was used to simulate this relaxation of vibrational energy, and ks was derived from T in a simple way. The values of T for relaxation of oxygen by argon were taken to be one-thirdZ3of those for pure oxygen.I6 There is a t present no experimental information on the deactivation rate of the high vibrational states. The indications are that anharmonicity would appreciably increase the rate.24 The factor f was calculated for k g corresponding to 7 and to 7/10. The average f was used. Assuming that this procedure brackets the effect of the actual relaxation on the temperature, an average maximum uncertainty of 3y0 is introduced into the values of k1 in the E-series. If the extreme assumption of instantaneous relaxation were made, the greatest resulting change would be for shock E-8, whose kl would become about two-thirds of that listed in Table I. A further correction, averaging about lo%, was made to f and thus to k 1 for the combined effects of attenuation and boundary layer interaction on the temperature of the gas. The values of k l A in the E-seIies are in satisfactory agreement with the other values of kl-4, but they have a greater uncertainty. Comparison with Other kl Data. Relative Efficiencies of Argon and Nitrogen.-Figure 5 gives plots of the shock tube and lower temperature data for Nz, according to E3 and E12. The low R3’ 0 0 3 = O?* + 0 2 temperature values of KIN, were obtained by multiR5 02* M = 0 2 +M plying the values of k 1 for M = 0 3 in BA’s Fig. 4 that the energy release of R3’ which is not contained by 0.41, the relative efficiency of N2 compared to O3 in 02*is immediately utilized in raising the tem- which was obtained by BA from their reanalysis perature of the gas, ;.e. the second oxygen molecule of Glissman and Schumacher’s data. The relative efficiency is believed by BA t o be correct to product in R3‘ is effectively equilibrium oxygen. The Duff codeI8 was used to obtain k 1 in the E- There are no published lower temperature data for series from data a t appropriate times behind the ozone-argon. The Iine through the Nz data in Fig. shock front, as described below. Reactions R1, 4 corresponds t o E12. In general the quality of the nitrogen shocks was R3’, R4,R5 and their reverses were considered in the code. a was obtained from the data a t times poorer than for the argon shocks, so that Figs. 4 sufficiently long that R1 and R3 were almost a t a and 5 may give a misleading impression as to the steady state, so that a was essentially independent precision of k ~ s , . The fact that cy increased from of k3. The times were not so long, however, that its value a t the shock front t o roughly three times too great uncertainty was introduced, especially this value by the end of the reaction, rather than in the temperature, by the vibrational relaxation by the expected factor of about two, as in argon, and by attenuation and boundary layer effects. is further evidence for greater non-ideality of condiIt was found from the computing code that the ob- tions well behind the shock front in nitrogen mix(21) A . Vaughan and M. Camac, B d I . A m . Phys. Soc., Series 11, served a’s a t the above times should be divided (1959). by a factor f of approximately 2, the exact value VOl.(22)I V E, 290 . W. hlontroll and K. E. Shuler, J. Chein. Phys., 26, 454
+ +
(19) 31. Camac and A. Vaughan, Avco Research Report 84, December 1959, Avco Research Corporation, Everett, Mass. (20) N. R o t t and R . Hartunian, “On the Heat Transfer t o the Walls of a Shock Tube,” Cornell University Report, Sovember, 1955.
(1957). ( 2 3 ) S. R . Byron, ibid., 30, 1380 (1969). (21) (a) S . W. Bazley, E . W . Mostroll R . J. Rubin and K. E. Shuler, ibid., 28, 700 (1958); (b) 29, 1185 (1958).
2572
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1.2
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1.3
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NORMAN DAVIDSON
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1.5
I O ~ / T ,*K-I
Fig. 4.-Plot of kl shock tube data. The line through t h e nitrogen points corresponds t o E12. The line through the :trgon points is drawn parallel t o the nitrogen line and is (lis])laced from i t by log 1.54 = 0.188; 0, in ozone--nrgori; O , i i i iizone-iiitrogen.
A
o, In,,
Fig. G.-Plot
,
( 0 0 ~-~
11,
150
m1cro115O"d'
of 10g 0, YS. t for various ks in shock 15
(ES) k,v, = ( 5 . 8 =t0.6) (mole/l.)-1 sec. -1
x
1011 exp( -23,150 I-t 300,/K7')
+ 300:Kll') 2.0 X IOi( 1000/T)1.6' (mole/l.)-2 sec.-1 (E5) kixvl/ki.k = k m s / k i A 1.54 i 0.17 (IN)k?hP = (9.4 i 1) X IO6 esp(+1700
7 6\
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20
35
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Vig. 5.-Shock tube and lower temperature4J data on klu,. The upper line atid left hand ordinate correspond t o liX. The lower line and right hand ordinate correspond t o 1312.
tures. However, the calculated effects of attenuation and boundary layer interaction are also larger :tnd account, within the uncertainties, for the larger factor by which CY increases in nitrogen shocks. Each experimental value of K I A was compared with k l N l calculated at the same temperature from E12 below. The average of the twenty values of klStlklA is 1.54 f 0.17 (standard deviation of an individual value). The ratio of the relative velocities of approach is calculated from the masses to be 1.11. The experimental ratio may be coni1)ared with the value 1.49 f 0.07 found by Volpe and Johnstonz5for the unimolecular decomposition of NOaCl at its low pressure limit a t 203O, and the value 1.73 given by Johnston26for the decomposition of N?Oba t its low pressure limit a t 50.5O. The combined shock tube and lower temperature data are represented by E3, E4 and E5. ( 2 5 ) M. l'olpe and H.
S.J o h n s t o n , J . A m . Chein.
( 1 9%).
(20) 11, S. Johnston, ibid., 75, 1567 (19X).
S o c . , 78, 39fl';
=
Other representations will be considered later. is negative as is The temperature coefficient of k31\~~ well established for the recombination of atoms. The shock tube values of knx, would have to be increased by a factor of more than three in order to eliminate a negative temperature coefficient, E4 was obtained from E3 and the dissociation constants for the equilibrium K1,K2, corrected for the new dissociation energy of oxygen.15 The uncertainty in the energy in the exponential term in E4 does not include an uncertainty of perhaps 250 calories in the heat of formation of ozone. Uncertainties in E3 and E4 include the effects of a 10% uncertainty in the relative efficiencies of nitrogen and ozone in R1 and R2.4 Determination of &.-Roughly speaking, k3 determines the time dependence with which the rates of R1 and R3 tend to equality. Values of k s were determined by a curve fitting procedure. Using k,, determined for a given run as described, the Duff code was used t o compute (0:Jas a function of time for various values of ka. That kj was chosen which fit the experimental data best on a plot of log(03) veysiis time. This is illustrated in Fig. 0. R1,K3', R-l, R5 and their reverses were included in this calculation. R4 and R5 are unimportant, since the ozone mole fraction was always less than 0.002. The values of k s given in Table I were obtained from seven argon and four nitrogen shocks, selected for the quality of their oscilloscope traces. I n the case of nitrogen k:1 was based on data pertaining to conditions closer to the shock front that1 in argon, because of the greater non-ideality of the nitrogen shocks. The equation for ka given by BA4,after correctiori for the new dissociation energy of oxygen,l3 is (EF) kl
=
(2.96 & 0.2) X sec. -l
( tnole/l, )
-'
exp(-55000 i 5 0 0 / K T )
The activation energy cannot be deterniincd Eronl oiir data. Taking the activation energy to ])e
in Garvin's experiments averaged only about half the equilibrium value for R1, R2, so that Garvin's KATE CONSTATTS FOR M O3 M O2 0 AND experiments are consistent with E6. The activation energy of k3 0 b t a i n e d ~ ~ from 9 ' ~ Garvin's data ks is 5600 1300cal. 0f0 3 0 2 f0 2 c.- .. x ~. in2 The data on k3 from the thermal decomposition Nos X 103 total concn. thus seem to be in general agreement. AxworthyZ9 Temp., ozone mole shocked gas, log k i h log k ? Shock fraction M liter mole-' set.-' has also shown that k z / k 3 from the photolysis of 0.721 2 779 1.14 5.13 ozone in red light a t 17' (see ref. 40 below) is lower 1.230 5.48 3 841 1.58 than calculated from the equations of BA by a 1.237 5.33 5 825 1.49 factor of 2.2. This may represent agreement within 1.227 G 840 1.42 5.51 the uncertainties. 1.235 5.42 8 828 1 84 A preliminary account has been given30of a de5.42 8.89 0.778 10 827 2.06 termination of k3 from low pressure flow experiments 2.145
