CHARLES D. JOHNSON AND DOYLEBRITTON
3032
Shock Waves in Chemical Kinetics: The Rate of Dissociation of Fluorine'"
by Charles D. Johnson and Doyle Britton School of Chemistry, University of Minnesota, Minneapolis 14, Minnesota
(Received J u n e 6 , 1954)
The rate of dissociation of molecular fluorine has been determined in the presence of argon in the temperature range 1300-1600 OK. by observing spectrophotometrically the disappearance of molecular fluorine behind shock waves in a shock tube. Dissociation rate F F, were determined in 5 , 10, and 2070 Fz constants for the reaction, ;I1 Fz-+ AI in Ar mixtures. In the 5 7 , mixtures the results may be summarized by log kD (mole-' 1. sec.-l) = 9.85 - 65201 T , which corresponds to an apparent activation energy of 30 f 4 kcal., mole. The measurements mere made behind incident shock waves; for reasons not clearly understood, the results of observations behind reflected shock waves were inconsistent with these and much more highly scattered. The recombination rate constant calculated from the above values is only about one-tenth as large as the corresponding constants for Iz,Brz, Clz, and Hz, all of which are roughly equal. Fluorine may be somewhat more effective than argon as a third body.
+ +
+
Introduction All concentrations are in moles/liter and all times in the rate expressions in seconds. The rates of dissociation of most of the halogens have been measured at high temperatures behind shock Experimental waves in the last few years. Iodine,2 b r ~ m i n c , ~ - ~ Apparatus. The experimental setup was essentially chlorine,' lo and hydrogen11-15 have been studied in that customarily used in this laboratory.5'8 The some detail, but for fluorine there is no information shock tube had a 1O-cm. i d . , a 240-cin. drive section, beyond a determination of the dissociation energy and a 480-cni. downstream section. The final 240 from shock velocity measurements in F2-Ar We report here a shock tube measurement of the rate of dissociation of molecular fluorine in the presence of a (1) Presented at the C . 8. Army Research Office, Durham, Symposium on Chemical Reactions in Shock Tubes, Durham, N. C., large excess of argon. With one exception,* all of the April, 1964. studies mentioned above were made in incident shock (2) (a) D. Britton, N. Davidson, and G. Bchott, Discussions Faraday waves. As the extinction coefficient for Fz is much Soc., 17, 58 (1954); (b) D. Britton, N. Davidson, W. Gehman, and G. Schott, J . Chem. Phys., 25, 804 (1956). lower than that for the other halogens, it was originally (3) D . Britton and N. Davidson, ibid., 25, 810 (1956). felt that it would be impossible to study fluorine dis(4) H. B. Palmer and D. F. E-Iornig, ibid., 26, 98 (1957). sociation behind incident shock waves in our ap(5) D. Britton, J . Phys. Cham., 64, 742 (1960). paratus. However, as will be described, the results (6) G. Burns and D. F. Hornig, Can. J . Chem., 38, 1702 (1960). behind the reflected shock waves in Fz-Ar mixtures were (7) H. Hiraoka and R. Hardwick, J . Chem. Phys., 36, 1715 (1962). inexplicably erratic, and another set of experiments, (8) C . D. Johnson and D. Britton, ibid., 38, 1455 (1963). which appear more acceptable, were run behind inci(9) T. A. Jacobs and R. R. Giedt, ibid., 39, 749 (1963). dent shock waves. (10) D. Britton and M . van Thiel, Intern. Congr. Pure A p p l . Chem., 28th, Montreal, 6 (1961). The rate constants mentioned above are indicated (11) W ,C. Gardiner, Jr., and G. B. Kistiakowsky, J . Chem. Phys., more explicitly by 3 5 , 1766 (1961).
xz + RI
kD
kR
T h e Journal o,f Phyaical Chemistry
x + x + I1
(12) (13) (14) (15) (16)
J. P. Rink, ibid., 36, 262 (1962). J. P.Rink, ibid., 36, 1398 (1962). R. IT. Patch, ibid., 36, 1919 (1962). E. A. Sutton, ibid., 36, 2923 (1962). K. L. Wray and D. F. Hornig, ibid., 24, 1271 (1956).
SHOCK WAVESIN CH~EMICAL KISETICS
3033
cni. of the downstream section, hitherto Pyrex pipe, was replaced by a section of 10-cni. i.d. aluminum tubing with 2.5-cm. 1,hick walls in which ports for miiidows were machined. Circular blocks of quartz or sapphire, 19 mm. in diameter, were cemented1' on1,o blanks 25 mm. in diameter and the larger blank seated against a shoulder in a port machined so that the 1'3mm. disk fit snugly and joined as sinoothly as possible on the inside of the tube. A vacuuni seal was made with a Teflon O-ring against the bmk of the window. A flat 19-mm. window in a round 10-cni. diameter tube leads to an irregularity of 0.46 inin. Experiments with artificial irregularities in shock waves in Brz-Pir mixtures in a glass tube led us to the opinion that this irregularity was tolerable and would not lead to any observable effects, hut that this was about the niaximum acceptable size for an abrupt disturbance at the walls. Larger steps a t the walls led to anomalous oscilloscope traces. There were two triggering stations 50 cm. apart and an observation station 10 cm. after the second triggerh g station. To minimize any possible effects of shock wave attenuation, it would have been desirable to have the observation station between the velocity measurement stations, so that the rate measurements might be made a t a point where the true velocity of the shock wave was closer to the observed (average) velocity. I n earlier work,j however, observations made 10 cni. after the first windo a. had been indistinguishable frorn observations made 10 cm. after the second window, so that we think any possible attenuation effects may be ignored. For reflected shock waves an insert brought a smooth surface for the reflection to 1.0 cm. past the observation station. A vacuum line in which the gas mixtures were prepared was attached to the shock tube. The modifications to the previously described system5 were t h e addition of a Pyrex spiral manometer1Yand a fluorine handling system. The spiral manometer was used as a null indicator to avoid hysteresis problems; it had a sensitivity of about 0.3 mm. The fluorine inlet system consisted of the fluorine tank, a I\latheson l5F-670 reducing valve, and a trap to remove hydrogen fluoride; the exhaust system was a sodiuni chloride trap, a soda lime trtbp, and a vacuum pump. All of these items were contained in a hood and were connected to a nitrogen flushing system and also to the regular vacuuin line. Gas mixtures were made as described previously, but the filling of the tube was done in a different way l,o minimize the contact lime of the fluorine mixture with the windows, diaphragms, etc., in the shock tube itself. A bulb of known volume mas filled with enough 1
mixture at a known high pressure to fill the bulb and the shock tube, whose volume was also known, a t the desired lower pressure. The bulb was filled accurately, with no need for haste, in the all-glass system; the previously exhausted shock tube was filled by opening it to the bulb and allo-vving the pressure to equilibrate, which took about 0.5 niin. This meant that shocks could be, and usually were, run within 0.5 min. of filling the alurninuni tube with the mixture. However, there was no observable loss of fluorine, nor change in the shock behavior, whether the delay period was 0.5 or 5 min. (See further comments in the section on Extinction Coefficients.) It was feared that the cellulose acetate diaphragms used in previous work in the shock tube would be rapidly attacked by the fluorine. I n order to protect against this, a layer of 1-mil aluminum foil was placed in front of the 3 to 10-mil cellulose acetate diaphragm. This aluminum foil tended to wrinkle and leak, and caused considerable extra work thereby. I n desperation, some shocks were tried without the aluminum foil, and it was found that in the time of the experiment no measurable decrease in the fluorine concentration nor any noticeable weakening of the cellulose acetate diaphragm took place. Therefore, in the later experiments the aluminum foil was omitted. In the hottest shocks there was trouble with the fragments of the burst diaphragm charring in the hot fluorine mixture after the shock. This did not affect the measurements in any way, but it made cleaning the tube quite difficult. To avoid this, Mylar was used in place of cellulose acetate in the strongest shocks even though it does not break as reproducibility as the cellulose acetate. The drive gas mas helium rather than hydrogen, which had been used in all the earlier work. The triggering system used previously,j which depended on a change in optical density a t the shock front, was not possible here since only one ultraviolet light source was available, and fluorine does not absorb in the visible range. Therefore, a schlieren arrangement with visible light was used. When the schlieren system was carefully adjusted, shocks in which the initial pressure of argon was 0.1 atni. and in which the density doubled at the shock front could be consistently detected. ~~
(17) The most successful cementing arrangement was to grease the windows lightly with Kel-F grease from the Kellog Mfg. Co. and press them together. This produced a transparent and completely adequate mount. Later samples of Kel-F grease from another manufacturer were not of the same quality and contained t o o large a fraction of volat,ile components t o be suitable. Canada Balsam was reluctantly used as a substitute. It did not appear to be attacked by the fluorine in the experimental conditions used. (18) J. D. Ray. Rec. Sci. Instr., 32, 600 (1961); 'we wish t o thank Professor Ray for his gift of this manometer.
Volume 68, IYurnber 10
October, 1964
3034
For the observation of the disappearance of Fz a PEK-109 mercury arc lamp was used as light source.lg This was mounted about 200 cni. from the windows and focused (through a quartz lens of 50-cni. focal length) at the center of the shock tube. This gave a beam t'hat was small enough to be passed through the bottoiii half of one 19-nim. window, reflected from the back silvered lower half of the opposite window, reflected from the silvered top half of the first window, and passed out the top half of the opposite window without losing much of the beam and without having part of the light go directly through the unsilvered windows. The light source and lens had to be mounted separately from the table on which the shock tube was mounted in order to avoid vibrations which led to erroneous oscillograms. Since the laboratory was not large enough to mount the light 200 cm. to one side of the shock tube, it was suspended from the ceiling about 150 cm. down the axis of the tube and reflected a t 90" into the shock tube ports. After passing through the shock tube and through I-nim. collirnating slits on both sides of the tube, the light went through a Bausch and Loinb 33-86-40 monochromator and into a 1P28 photomultiplier. The rest of the detection system has been described previously.5 The lighting alignment was fairly critical, but within experimental error of about 1YGall the light entering the nionochroniator had passed through 30 cni. of gas, and none through only 10 cm. For a fely of the shocks, used only for the measurement of extinction coeficients at lower temperatures, a single pass (10 mi.) of light was used rather than a triple pass; the results agreed with those from triple pass measurements. Chemicals. Fluorine from the General Chemical Division of Allied Chemical Corp. was purified by passing it through a sodium fluoride trap to remove HF. A sample of gas that was allowed to react with niercuiy showed, within an experimental error of 0.2%, no unreacted gas after 3 days. This same method of purification was used by Shields,?O who then fractionally distilled the fluorine and could detect no difference in vibrational relaxation times in the first and last fractions. Since it seems likely that any impurity that would have a large effect on the dissociation rate would also have an effect on the vibrational relaxation rate, LTe believe the method of purification to be adequate. I n particular, we believe that the amount of HF present is coiiipletely negligible. ;\latheson Co. argon was used without further purification. Oxygen from the Air Reduction CO. was further purified by a bulb-to-bulb distillation at liquid nitrogen temperature on the vacuum line, with the middle fraction being used. Carbon dioxide from T h e Jovrnal of Physical Chemistry
CHARLES D. JOHNSON h i i D DOYLEBRITTON
the Ohio Chemical and Manufacturing Co. was purified by repeated partial condensation in the vacuuni line. Calculations. The methods of calculation for incident and reflected shock parameters as well as for high temperature extinction coefficients and rate constants have all been described previously.6 * The thermodynaniic data were taken from the JASAF tablesz1 and need no comment, x i t h the exception of the heat of dissociation of Fz. This heat, which was long thought to be 60-70 kcal.iniole of Fn, has recently been reconsidered and remeasured. The pertinent literature references are given in the JAKAF tables, and we have used their value of 36.7 kcal. 'mole at OOK. If this were in error by lo%, it would lead to a 5% error in the measured value of the rate constants in incident shocks in 570Fz-95Y0 h r mixtures. For our purposes, therefore, any remaining uncertainty in this value can be ignored. Those calculations which were too tedious to do by hand, mainly the calculation of shock wave parameters, were made using FORTRAN programs on the control data 1604 computer of the Numerical Analysis Center of the University of Minnesota.
Results Introductzon.
Two kinds of experimental measurements were made. First we studied the disappearance of F? behind reflected shock waves in 5% FT95% Ar, 5% Fz-l% COn-947, h r , and 5% Fz-2.5% O2-92.5% Ar mixtures. Second, we studied the disappearance of Fz behind incident shock waves in Fz-Ar mixtures with 5, 10, and 20% Fz. Originally we had thought that the limitations of the apparatus would preclude the use of incident shocks-that the highest pressure of Fz-hr niixturc that could be used safely in the existing shock tube would not be concentrated enough to allow us to incasure the changes in Fz concentration with reasonable accuracy nor to cause large enough schlieren signals for triggering. I n view of this we studied8 the measurenient of rate constants behind reflected shock waves in a known system, BrZ. and then proceeded to the study of Fz. As will be seen below, the results did not seem reliable, although we cannot offer a good explanation for thcir invalidity. Therefore, (19) The PEK-109 power supply gave d c current with a c ripple sufficient to cause 10% ripple in the light intenslty This was reduced to 1% by the addition of two more LC sections, each wlth L = 0 02 h and C = 500 pFf The power supply had adequate reserves so that, even with this addltional filterlng, the lamp could be run a t the rated power (20) F D Shields, J Acoust Soc A m , 34, 271 (1962) (21) 'JAXAF Thermochemical Tables," The Daw Chemical CO Xidland, Mich , June, 1960
3
SHOCKWAVESIN CBEMICAL KIXETICS
it was decided to make observations behind incident shock waves, starting a t the lowest pressures that allowed triggering and observation of the F B concentration, and a t a rather low temperature in the incident shock wave, and to increase the temperature, i.e. the drive gas pressure, as long as the apparatus held together. To our surprise we finished all the experiments that seemed necessary without any mishap; no windows broke nor even leaked. The results behind the incident shock waves showed no anomalies, and me believe they are reliable. The details of both sets of experiments follow. Extinction CoefJicients. The extinction coefficient of F2 has been measunld a t room teniperature as a funotion of wave length by three g r o ~ p s . ~ These ~ - ~ ~are in general agreement; the most recent24seemed to us the most reliable, and we have used their values a,t room temperature. The observations in the shock tube were all made a t 313 mp. Except that the extinction coefficient, e , is lower, which is somewhat critical in our experiments, this is a better wave length for observations than the maximum because the change in E with temperature is less. The spectrum of Fz at room temperature has been analyzed in detail,25 and it is clear that the simple theory of Sulzer and Wieland,z6which wa,3 useful in predicting the tempera,ture dependence of the extinction coefficients of Brz and Clz, should not work here. Severtheless, it should give a rough idea of the temperature dependence t o be expected, and, accordingly, we have fit the experimental curve to a single peak, gaussian with respect to wave number, and from this peak calculated E us. T a t 313 mp. High temperature extinction coefficients were measured in the various shock waves, each incident shock wave experiment giving one point on each oscillogram, and each reflected slhock wave experiment giving onle point in the incident wave and another higher temperature value in the reflected wave. The results for all the incident shock waves are given in Fig. 1, and for all the reflected shock waves in Fig. 2. The high temperature values for the incident shocks were fit to a straight line by a least-squares calculation, and this line wai3 used to calculate d In E/dT, which is needed in the rate constant calculations. It can be seen that the results in reflected shock waves in F2-Ar are consistently lower and slightly more scattered than in the incident shock waves. The results in the FZ-O2-Ar and Fz-C02-kr mixtures show that something anomalous is happening in these mixtures. We regard only the incident shock wave measurements as reliable. The agreement, (see Fig. 1) between the extinction coefficients measured in shock waves and those measured in a static experi-
3035
400
1200
800 T
1600
OK
Figure 1. Extinction coefficient for Fz os. temperature a t 313 mp (incident shock waves): cross, room temperature value (ref. 24); aquares, 5% Fz in Ar; circles, 10% FP in Ar; triangles, 20% FZin Ar; heavy line, least squares fit to E = 5.20 - 0.00118T; dotted line, prediction from the approximate theory of Sulzer and Wieland.
6
i
5 E
C)
A
4
OB
3
-
0
000
°
I
4-
0
1
I 1200 T
I 1400
i
I
J
1600
OK
Figure 2. Extinction coefficient for Fz us. temperature a t 313 mp (reflected shock waves): heavy line, heavy ' line from Fig. 1; circles, 5% F%in Ar; triangles, 5% F2-2.5% 0 2 in Ar; squares, 5% Fz-l% COz in Ar.
ment at room temperaturez4indicates that no significant amount of F2 has disappeared in the period between making up the mixture and running the shock. As mentioned previously, there was no slow disappearance after putting the mixture in the shock tube. The extinction coefficient measurements indicate that there was no unobservably rapid disappearance when the ~~
(22) H. von Wartenburg, G. Sprenger, and J. Taylor, 2. p h y s i k . Chem., Bodenstein Festband, 61 (1931). (23) &I. Bodenstein and H. Jockusch, 2. anorg. allgem. Chem., 231, 24 (1937). (24) R. Stuenberg and R. Vogel, J . Am. Chem. Soc., 78, 901 (1966). (25) A. L. G. Rees, J . Chem. Phys., 26, 1567 (1957). (26) P. Sulzer and K. Wieland, Helv. Phys. Acta, 2 5 , 653 (1952).
Volume 68, ATumbes 10 October, 1964
3036
CHARLES D. JOHNSON AND DOYLE BRITTON
tube was first filled. The reaction of a few per cent of the total F, would not have been detected in either case. Emission. In the Brz and Clz work4s5lo emission from two-body recombination of Br and C1 atoms was appreciable at the higher temperatures. Two experiments were run in 5yoFz-9570 Ar incident shocks with initial temperatures near 1650OK., with the light source turned off. In neither case could any emission be detected. Since this was hotter than any of the experiments where the rate constants were measured, it was assumed that no emission correction was necessary. Vibrational Relaxation. Shieldsz0has measured the vibrational relaxation times for Fz a t 28 and 102'. If these results are extrapolated to high temperatures by the method of Millikan and White127they indicate that vibrational relaxation would require only a few microseconds under the conditions of our experiments, so that we can assume the Fzalways to be vibrationally relaxed. This assuniption is borne out by the extinction coefficient values that are measured a t the shock front; these values fall off Kith temperature in the fashion that would be expected for vibrationally equilibrated F B . ReJected Shock Waves in Fz-Ar Mixtures. A series of 11 reflected shock waves was run in 5To Fz-9570 Ar a t temperatures between 1000 and 16OOOK. The dissociation rate constants measured in these shocks are shown in Fig. 3. These rate constants were calculated assuming that the degree of dissociation a t the end plate was zero. This introduces a small error into the calculated temperature and density, but it would not significantly alter the temperature dependence. These experiments give the untenable result that there is no activation energy for the dissociation reaction. Primarily for this reason it was decided to run a series of experiments in incident shock waves if possible.
j': 5
1 110
I
8
9
io4/ T Figure 3. Log k~ YS. 1/T (reflected shock Kaves): line, incident shock wave result: see Fig. 4; circles, 59; FQin h r ; triangles, 574 F2-2.5% 0 2 in A r ; squares, 5% F2-170 COa in .4r.
The Journal of Physical Chemistry
I
7
Rej?ected Shock Waves in Fz-Ar Mixtures with Added 0% or CO,. In order to test whether small amounts of air as an impurity could lead to serious errors in measured rate constants some experiments with added Oz or COZwere run in reflected shock waves before it was realized that the reflected shock wave results were unsatisfactory. , Four shock waves were run with a 5yo Fz-lY0 co2-94yo Ar mixture with temperatures between 1100 and 12OOOK. with the results shown in Fig. 3. The apparent rate of dissociation is about ten times greater than in the absence of COz for all the points. An inspection of Fig. 2 indicates that these shocks are suspect, and in any event we would not attribute the increased rate of dissociation simply to a greater efficiency for CO, as a third body. Clearly some reaction between COz and F B is occurring. However, it is also reasonably clear that traces of COP due to air leaks would not lead to serious errors in the dissociation rate nieasurenients in the presence of argon. If air leaked in to the unlikely extent that 1% of a niixture were air, only approximately 0.01% of the total would be COz. This could lead to a 10% error in the rate constants if the reaction were a chain reaction and proceeding as in these mixtures. If the reaction were a simple nonchain reaction, leading perhaps to stable products such as fluorophosgene, then the error would be even less. Four experiments in 570 F2-2,57G0 ~ - 9 2 . 5 7Ar ~ niixtures at temperatures between 1200 and 135OOK. led to the apparent dissociation rate constants shown in Fig. 3. The rate constants are about three to four tinies larger than the corresponding values in argon. Again in a 1% air leak the Ozconcentration would be about 0.2%, and this would lead to at most a 5% error in the rate constant. It is apparent that both 0 2 and COz are acting as more than simple third bodies, and it would be of interest to determine the actual reactions and rate constants, For the purpose of this study it was sufficient to know that these conceivable impurities would not lead to a significant error in the rate constants being studied. It was not felt necessary to test the effect of added Kz. In spite of the uncertainties in the reflected shock wave results, we did not feel it was necessary to repeat these tests with added COz and O2 in incident shock experiments. Incident Shock Waves in Fz-Ar Mixtures. A series of six incident shock waves was run in 5% Fr95% Ar, a series of nine in 10% Fz, and a series of five in 20% Fz. The high drive pressure required (up to 200 p.s.i.) (27) R. C. 3'Iillikan and D. R. White, J . Chem. Phys., 39, 3209 (1963).
SHOCKWAVESIN CHEMICAL KINETICB
3037
limited the range of initial low pressures to 0.070.2 atm., but otherwi,se the series covered a reasonable range of experimental conditions. The results of the experiments are shown in Fig. 4. Lines fit to the equaB / T by least squares give for the tion log k D = A three series
+
5% Fz log k~
=
9.85 - 6520/T
10% Fz log k~
=
8.54 - 4520/T
20% Fz log k~
=
6.61 - 2410/T
The slopes correspond to activation energies of 29.9 =t 3.7, 20.7 f 5.6, and 11.0 f 7.6 kcal./mole of Fa, respectively. We regard the 5% Fz results as most reliable for two reasons: first, the scatter is less; second, the correction for changing density and temperature behind the shock front is smallest here, and so subject to the least uncertainty. This correction term, (1
6D
Y
-B 5-
II.
4c
/ '
II -I
Figure 4. Log kn us. 1/T (incident shock waves): line, leastsquares fit to the 5 % data; squares, 570 Fz in Ar; circles, 10% FZin Ar; triangles, 20% Fz in fir.
most we could say is that Fz is between 1 and 20 times as effective as Ar. Equilibrium Constants. As a check on the validity of our experiments the equilibrium constant for the reaction Fz = 2F was calculated in many of those experiments where the observation time was sufficiently long that equilibrium was reached. Since the density and temperature can be calculated as a function of the degree of dissociation behind a shock wave, it is possible to construct a plot of light intensity us. degree of dissociation with no approximations and, by measuring the equilibrium light intensity, to calculate the equilibrium degree of dissociation. From the known initial concentration and a knowledge of the density as a function of the degree of dissociation for the particular shock, it is then possible to calculate the equilibrium constant. The calculated equilibrium constants agreed with the JASAF valuesz1within a factor of 2, and for the' 10% and 20% were scattered around them. The values of the constants from the 5% experiments were all low, but still within the experimental scatter of the 10 and 20% points. As these measurements are made 200-500 psec. behind the shock front, and as the scatter was large, this is not strong evidence,'but, such as it is, it suggests that these shocks are normal.
Discussion Comparison with Other Halogens. With this study dissociation rates for all the halogens, including hydrogen, have been determined a t high temperatures behind shock waves in the presence of argon as a third body. If one assumes that k~ = A exp( - H / R T ) with no temperature dependence in the pre-exponential Table I: Apparent Activation Energies for the Reaction Ar Xz = Ar 2X
+
+
- d In e/da - d In A/da)-l, has an average value of 1.26, 5.0, and -2.0 for the 5, 10, and 20% series, respectively, and in the last two cases changes appreci-. ably with the shock temperature. A.n error of 10% in d In E/dT would cause errors of 1, 10, and 8%, respectively, in the correction terms of the 5, 10, and 20% shocks. Also it should be recognized that the measurement of the initial slope is more uncertain in the mixtures with the larger percentages of Fz, either because the slope is smaller than in the more dilute mixture, or because it is changing more rapidly with the degree of the reaction, and it is, in fact, a slope near the shock front, rather than the slope a t the shock front, that is measured. As can be seen from Fig. 4 the data are not good enough to draw significant conclusions about the relative effectiveness of Fz and Ar as third bodies. The
xz
AH*,t"
Ref!
I2 Brz
30.8 i 0 . 3 43.8 f 3 . 7 38.2 39.0 f 0 . 8 37.7 i 1 . 0 5 1 . 3 =!= 1 1 . 7 48.5 f 2 . 9 47.2 f 2 . 2 2 9 . 9 i. 3 . 7 95-97*
2 3
Clz
Fz Hz
Do0
35.4 45.4
4 5
8 7 9 10 This work 12, 14, 15
57.1
36 7 103.6
Difference
4.6 1.6 7.2 6.4 7.7 5.8 8.6 9 9 6 8 7-9
a The measured rate constants were fit to an equation kn = A exp( - A H / R T ) . The HZresults in these references have been reported in the form k~ = AT-' exp( -Doo/RT). If these had been fit t o the form ICU = A exp( - A H / R l ' ) , then AH would have been lower by about RT = 7-9 kcal./mole. An RT correction will not account for the discrepancy in any of the other halogens, however.
Volume 68, Number 10 October, 1964
3038
CHaRLES D. JOHNSOB A N D DOYLE BRITTON
term, then in every case the apparent activation energy for dissociation is less than the dissociation energy of the halogen. These activation energies are summarized in Table I. The hydrogen results can be accounted for by using Do@in the exponential term and including a pre-exponential temperature dependence of T-l. For all of the others the power of the temperature in the pre-exponential term would have to be considerably greater than this. Since the dissociation energies are quite different for the several halogens a more meaningful coniparison of the differences among thein can be made by comparing recombination rate constants, k~ = kD/K,, . The high temperature results converted to this form are shown in Fig. 5 along with the low temperature
10
7 1
i
et 3
2
OyT
1
1
0
Log k~ us. 1/T for the various halogens: Fz,this research; C1, ref. 9, 10; Brz, ref. 8 , 2 8 ; 1 2 , ref. 2, 2 7 ; H,, ref. 15. Figure 5 .
results for IaZSand Brz.29 It would appear that the shock wave results uniformly show a greater teniperature dependence than the low temperature results. This large temperature dependence is another way of viewing the low activation energy of the dissociation reaction. Three explanations for this temperature dependence come to mind: first, that there is a systematic experimental error in the shock wave work; second, that the shock wave rate constants are measured too far from equilibrium to be converted nieaningfully to recombination rate constants; third, that the effect is real and the temperature dependence of the three body recombination rate constant is highly unusual. The first of these is probably ruled out by the spectrophotometric shock wave studies of the hydrogen-bromine r e a ~ t i o n ,where ~ @ the high temperature results showed the same temperature dependence as the low temperature results. PritchardS132 has given theoretical reasons for preferring the second alternative, reasons that have been disputed by Rice.333 4 In support of the third alternative it should be noted that Phillips and S ~ g d e nhave ~ ~ found similar large negative teinThe Journal of Physical Chemistry
perature dependences for t'he reactions occurring in flames
H
+ X + XI = HX + 3 f *
where X is H, C1, or Br and M is T1 or Pb. It, can be seen in Fig. 5 that' FSdissociates more slowly than might, be expected by comparison with the other halogens. It can also be seen that Iz, Br?, CI2, and H, all show about, the same recombination rate const,ants at high t'emperatures. If species as different as I atoms and H atoms recombine at, roughly the same rate, it is surprising that F atoms should recombine only one-tent,h as fast. This would lead us to suspect the results present'ed here except bhat there is no conceivable way that' the reaction could be slowed down. Any small amount of impurity must either be less efficient^ than a,rgon as a third body, in which case it would have an effect on the observed rate constant only as large as its relative concentrat'ion, or else it must be more efficient than argon, in which case the apparent rate constant is t,oolarge. The Possibility of A r F OT ArFz. It is possible that the observed rate constant,s appear low because anot,her colored species is being formed, and the observed color change is due to more than the disappearance of Fz. It is not to be expected that the F atoms absorb at 313 mh, but the possibility that, argon fluorides, such as ArF or ArF2, are being formed must be considered. The formation of ArF? alone (or any higher fluoride) could not explain any apparent anomaly in the init'ial slopes, since the formation must involve some sort of recombination reaction, although if the species were stable they could affect the apparent equilibrium positions. An effect on the initial rates would have to lie in the formation of ArF according to
+ 5i i r ~+ F ArF + 1% -% Ar + F + &I hr
Since me are considering the init'ial reaction, only the forward ra,tes will be considered. If kt 5 k l , then the change in light intensity int,erpret,ed as d [Fz]/dt eAr~[ArF]/e~,)/dt, mould really be due to d([FzJ
+
(28) D. L. Bunker and N. Davidson, J . A m . C'hem. SOC., 80, 5085 (1958). (29) W. G. Givens, Jr., and J. E. Willard, ibid., 81, 4773 (1959). (30) D. Britton and R. >I. Cole, J . Phys. Chem., 6 5 , 1302 (1961). (31) H. 0. Pritchard, ihid., 6 5 , 504 (1961). (32) H. 0. Pritchard, ibid., 66, 2111 (1962). (33) 0. K. Rice, ibid., 6 5 , 1972 (1961). (34) 0. K. Rice, ibid., 67, 1733 (1963). (36) L. F. Phillips and T. M . Sugden, Intern. Congr. Pure A d . Chem., i8th, Montreal, 35 (1961).
SHOCK WAVESI N CHEMICAL KISETICS
3039
where e refers to the extinction coefficient of the species in question. Since the ArF is formed a t the same rate as the FSdisappears and its rate of disappearance is low, the apparent rate of disappearance of Fz is lower than the actual rate by a factor of (1 - e A r ~ / EF,), and the apparent rate constant is lower than the true one. If the ratio E A ~ F / E F , were independent of temperature, the activation energy measured would be that associated with the first reaction and k,. It is this last factor which tells against this possibility. One would expect 1 he activation energies of both these reactions to be roughly equal to their enthalpy changes, but 1c2 5 kl implies that E2is of the order of E l , which is measured 1,o be 30 kcal.,'iiiole, while E , tEz is known to be 36 kcal./mole. The observed activation energy is that expected for the dissociation of I'z, as was discussed earlier, or a t most it is a few lical /mole lower. A lowering of, say, 5 kcal./mole would imply that the second reaction above had an energy of approximately 5 kcal./mole and an activation energy of the same order or lower. This would mean, however, that the second reaction should be many times faster than the first, in which case no appreciable concentration of h r F could form, and that which did form would be related to the Fz concentration by the steady-state approximation so that [ArF] ( k l / k s )[Fz],and the apparent rate would not be affected, or would be inueased slightly, if anything. This has been discussed at some length because in other experinients in this l a b ~ r a t o r ywe ~ ~have found that when xenon is present in the shock mixture EL definite effect attributable to the formation of a xenon fluoride can be observed. R e recognize that the experiments described here cannot be regarded as conclusively settling this interesting question in Ar-Fs shocks-this would require observations at more than -J
one wave length-but we report our results a t this time because circumstances required the dismantling of the fluoiine handling system, and we do not foresee the possibility of further experimental work in the near future. ReJlected Shock Waves. A comparison of the results of the Fs-Ar experiments in incident and reflected shock waves shoms clearly the anomalously high rate constants in the reflected shock waves at the lower end of the temperature range studied. At about 14OOOK. the two methods give the same results, but a t lower temperatures the reflected shock wave results deviate more and more from what might be considered normal. We cannot explain this result. Our work on the dissociation of Brs in reflected shock wavess gives us a general confidence in reflected shock wave results. The only suggestion we can offer is that some impurity with a remarkably high catalytic effect is produced behind the incident shock wave, and when the reflected shock wave comes back, the composition of the mixture has been subtly changed (no significant amount of Fz has disappeared), and the impurity catalyzes the deconiposition. The effectiveness of any given catalyst would be expected to decrease with increasing temperature so that the decreasing deviation from normal with increasing temperature is an argument for the presence of a catalyst. The presence of this catalyst in the incident shock wave is unlikely, for the rate constants measured behind the incident shock waves seem unusually low. Aclmowledgnaents. We thank the U. S. Army Research Office (Durham) for support of this work. C. D. J. thanks the Shell Oil Company and the Procter and Gamble Company for fellowship support. (36) D. J. Seery and D. Britton, unpublished work.
Volume 68,Sumber 10
October,lQG4
