1060
G. A. Takacs and G. P. Glass
tween z 2 and a - a' is not followed since z 2 is slightly positive a t 2" for low t-BuOH molalites, but LZis smaller at 2"than a t 60". The usual interpretation of a positive value for t 2 is entirely different. The overlap of the more hydrogen-bonded water sphere arounld a structure-forming solute as its concentration is increased is interpreted as producing a positive contribution to z2.14 Since all other effects on r";z are neglected, a positive E 2 is taken as evidence for water structure promotion, by BurNBr by instance. In our opinion too much importance is given to this particular contribution caused by the overlap of the hydration spheres. For instance, O( -. a' a t 4" for aqueous t-BuOH solutions may be equated to - - a ~ i n+ a2m2 where --aim may be interpreted as showing the solute influence on the expansion coefficient if no other interaction as solute-solute interaction, overlap of hydlration sphere . . . is present. The term a2m2 incorporates all these effects. Then the contribution of the overlap to 122 should be a t most proportional to a2m2, provided that other effects are absent. Although this contribution to E2 for a water structure former is certainly positive, it cannot be assumed in our opinion that a positive L z is evidence for water structure promotion in view of all the other effects which may exist. In any case such an interpretation would lead to the conclusion that a t low molalities t-BuOH is a strong structure former a t Go", a weak one a t 2" and possib_ly a structure breaker at lower temperatures if a negative LZ is found as the extrapolation of data a1 i! and 60" suggests. This concluslon is difficult to accept. An interesting consequence of the variation of A H ilHo with the temperature is that the partial molal heat capacity of t.BuOI-I around 300 should a t first increase with its molality and then should decrease when the molality is further increased.
Figure 7 shows the plots of +cP2 - epwo against the alcohol mole fraction in the aqueous solution at various temperatures for some alcohols, where +cp2 is the alcohol apparent molar heat capacity and cpwo the pure water heat capacity. These plots are drawn from cp data in the 1 i t e r a t ~ r e .The l ~ values of cPzo - cpWohave been computed from Hill's datas6 and the liquid alcohols heat capacities.17 For all alcohols except MeQH and EtQH these plots show a similar behavior for the variation of 4cp2 with the concentration and support our findings for the variation of the t-BuQH partial molar heat capacity. We do not interpret high solute heat capacity as evidence for water structure promotion by this solute, but rather as showing that the solute structural influence changes much with the temperature.I8 Then an increasing cPz is in our opinion related to a change of the solution structure with the temperature more important than the pure water structural changes, since the solute is assumed to be a structure former a t low temperature and a structure breaker at high temperature, a t moderate concentration. A possibly similar idea is expressed by Frank: " . . . An appropriate heat capacity contribution must also be expected, arising from the transformation, with rising temperature, of bonded to non bonded species."lg
(14) R . H . Wood, H. L. Anderson, J. D. Beck. J. R. France, W. E. de Vry, and L. J. Soltzberg, J. Phys. Chem, 71, 2149 (1967). (15) W. S. Knight, doctoral dissertation, Princeton, 1962. (16) D. M. Alexander and D. J. T.Hili, Ausi. J. Chem., 22, 347 (1969). (17) (a) Landolt-Bornstein, "Physikalische-chemische Tabellen," Voi. 2. Part 4, Julius Springer, Berlin, 1960. ( b ) F. L. Oetting, J , Phys. Chem., 67, 2757 (1963). (18) M. Lucas and A. de Trobriand, C. R. Acad. Sci., Ser C, 274, 1361 (1972). (19) H. S. Frank in "Water a Comprehensive Treatise," Vol, 1, F, Franks, Ed., Plenum Press, New York, N. Y . , 1972, p 543.
Reactions of Hydrogen Atoms and Hydroxyl Radicals with Hydrogen Bromide C. A. Takacs and G . P. Glass* Department of Chemistry, Rice University, Houston, Teras 77001 (Received October 10, 1972) Pb'blkation costs assisted by The Petroleum Research Fund
A fast discharge-flow system was used to study reactions of hydrogen atoms and hydroxyl radicals with hydrogen bromide a t 295 K. The reactions were followed by monitoring the epr spectra of H(2S1,2), Br(2P3,~),and OH(2n3,2) a t a number of different reaction times. A fluorinated halocarbon coating, applied to the flow tube, was found to be extremely effective in eliminating wall recombination of Br(2P3/2). Rate constants of (3.4 & 0.8) x 10-12 and (5.1 & 1.0) x 10-12 cm3 molecule'l see-I were obHz + Br and OH HBr H20 + Br, respectively. An unsuccesstained for the reactions H + HBr ful search was made for Br(2PI,z).
-
Introduction Hydrogen bromide is known to inhibit combustion of hydrogen and hydrocarbon fuels. Numerous studies have demonstrated its effect on flame propagation, flamability, and explosion lirnits~~-7 It i s generally accepted that the The Journal of Physicai Chemistry, Vo/. 77, No. 8, 1973
+
-
inhibition results from reactions of HBr with chain centers which are important for flame propagation; for example, with H and OH. However, absolute rate constants for D . R. Clark, R , F . Simmons, and 66, 1423 (1970).
D.A .
Smith, Trans. Faraday SOC.,
Reactions of H and OH with Hydrogen bromide
1061
TABLE I: Reaction of Atomic Hydrogen with Hydrogen Bromide (HBr)o, X I O i 4 molecule C M - ~
3.88 2.75
2.21 1.78
2.21 .21 I .7a 2.21 1.:E
7.84
( H ) o , X 1014 molecule em-
Method of data reductionb
(HBr)/(H)a
First-order H decay First-order H decay First-order H decay First-order H decay First-order H decay Second-order from H decay Second-order f r o m H decay Second-order from H decay Second-order from Br growth From l / ( M ) - l / ( H ) o
62
k , , cm3
20
11 6 10
Av =
sec-
l
X
2.94 3.03 3.39 3.98 3.20 3.43 4.08 3.08 3.57 3.33 3.4 f 0.4 X 10--'*
cm3 molecule- 1 seca
Ratio measured 3.3 c m downstream of HBr inlet at the first measuring point.
these reactions are not well established. In this study we have measured them (directly in a fast discharge-flow apparatus using epr detection.
Experimental Sectio The construcl ion and operation of the discharge-flow apparatus used in these experiments has been described in detail previously.8*sp The 20-mm i.d. flow tube was operated a t pressures from 0.5 to 1.5 Torr, and linear flow speeds were maintained in the range 1300-1900 cm/sec. Atomic hydrogen was produced by microwave discharge of a dilute mixture of HZ in Ar, and OH was generated from it by reaction with NO2.8 A moveable inlet system consisting of two concentric tubes, with the inner tube of 3 mm o.d. extending ii.25 cm beyond the end of the 6 mm 0.d. outer tube, allowed the HBr to be added 2.25 cm downstream from the point of production of OH. HBr (Matheson 99.8%) was used without further purification. A liquid nitrogen trap was placed immediately upstream of the pump in order to collect Brz and unreacted HBr. The epr signals were recorded with a Varian V4502 spectrometer. Absolu1,e concentrations were determined from the integrated e pr spectra.8 Transition probabilities for all the observed free radicals have been reported.lOJl Results The effect of the wall treatment of the flow tube on the rate of Br(2P3/:l) atom recombination was studied first. Oxy acids, such as irulfuric and phosphoric acid, have been reported to be effective wall poisons.lZ However, other workers claim that measurable bromine atom recombination takes place on both Teflon and phosphoric acid wall coatings.13 In our studies bromine atoms were duced by the reaction of atomic hydrogen with excess r. High reactant concentrations were used to ensure complete production of Br within 1 msec (typically (H)o = 6 X 1014 and (HBr)o = 2 X 1015 molecules ~ m - thus ~ , reactioin is 99% compiete in less than 1 msec). Bromine atom recombination was studied over a reaction time of 20-25 m e c . Using a clean quartz flow tube, first-order decay of Br('P312) was observed, and a rate constant of 465 see-1 was measured. This corresponds to a surface recombination cciefficient for Br(2P3p) of y = 1.12 x When the flow tube was coated internally with ortho boric acid, y was measured in two different experiments as 5.76 X
'IO'*
1
Explained fully in text.
and 5.28 x Three experiments using phosphoric acid as the wall coating gave values of y = 2.0 x 10-3, 2.3 X and 1.0 X Measurable surface recombination was completely eliminated, however, when the flow tube was coated with a fluorinated halocarbon wax,14 and all further experiments reported in this paper were per. formed using a flow tube treated in this manner. Reuction of H with HBr. Ten experiments were performed to determine the ratio of the concentration of Br(2P3,2) formed to the concentration of atomic hydrogen removed by reaction 1. These experiments were performed
-
H + WBr H2 -t- Br (1) at reaction times varying from 1.9 to 15.4 msec, and on a variety of different reaction mixtures. The ratio was measured as 0.91 f 0.11. The dynamics of the reaction were studied using the seven reaction mixtures listed in Table I. In order to obtain adequate spacial resolution for the fast reaction of H HBr, the mixtures were chosen to have relatively low reactant concentrations. Unfortunately, thib fact limited the range of mixture stoichiometries that could be investigated a t adequate epr signal to noise ratios. Experimental data were treated in three different ways. (a) When HBr was present in a large excess, the reaction was assumed to be first order, and the integrated rate expression 2.303 log (H) = -h,(HBr)t
+
was used. (HBr) was taken as the average HBr concentra-
C. Powall and R. F. Simmons, Symp. Combust. 13th, 585 (1971). M. J. Day, D. V. Stamp, K. Thompson, and G. Dixon-Lewis, Symp. Combust. 73th 705 (1971). R. N. Butlin and R. F. Simmons, Combust. Flame, 12,447 (1968). W. E. Wilson, Jr., J. T. O'Donovan, and R. M. Fristrom, Symp. Combust. 72th, 929 (1969). D. R. Rlackmore, G. O'Donneil, and R. F. Simmons, Symp. Combust. 70V, 303 (1965). W. A. Rosser, H. Wise, and J. Miller, Symp. Combust. 7fh, 1'75
(1959). J. E. Breen and G. P. Glass, J . Chem. Phys., 52, 1082 (1970). J. E. Breen and G. P. Glass, inf. J. Chem. Kin., 3, 145 (1970). A. A. Westenberg and N. deHaas, J . Chem. Phys., 40, 3087
(1964). A. A. Westenberg, J . Chem. Phys.. 43, 1544 (1965). N. Vandarkool, Jr., and J. S. MacKenzie. Advan. Chem. Ser., No.
36.98 (1962). P. B. Davies, 8. A. Thrush, and F. Tuck, Trans. Faraday SOC., 66, 686 (1970). MarChem Inc., Houston, Texas 77005. The Journalof Physical Chemistry, Vo!. 77,No. 8, 7973
6.A. Takacs and G . P. Glass
I
2
I
I
I
3
4
5
6
TIME
MSEC
Figure 2. Plot of log (OH) vs. time in reaction of OH with HBr: 0 represents ( H B r ) == 1.35 X 10l4 molecule/sec (in reaction zone; a represents ( H B r ) = 2.51 X 10l4 molecule/sec, flow speed = 1362 cm/sec. ?lME
MSEC
Figure 1 , (a) Plot of log ( H ) vs. time for reaction of H I- .HBr. (b) Plot of log [(MBr)o ( H ) / ( H ) o - ( H ) ] ks. time: 0 represents ( H B r ) o = 1.78 X ( H ) o = 6.7 X 1013 molecule/cm3, flow speed = 1322 cm/sec; E l represents (HBr),, = 2.21 X (H)" = 7.0 .X I O i 3 molecule/cm3, flow speed 1270 cm/ I -
see.
tion over the regnori in which the reaction was followed, and the reaction time, t, was calculated from the linear flow speed, and the distance from the HBr inlet to the center of the modulating coils of the epr cavity. Log (H) was plotted against t as shown in Figure l a , and k l was calculated from tire slope of the plot. (b) The second-order integrated rate equation
Reaction of OH with HBr. This reaction was studied by adding HBr to the flow tube 2.25 cm downstream of the point at which OH was generated by reaction of atomic hydrogen with NO2. The reaction was followed by monitoring the OH and Br(2P3,a) concentrations as a function of distance downstream from the HBr inlet. Initial measurements were made at a point 2.5 cm (corresponding to a reaction time of 3.3 msec) downstream of the HBr inlet. At this point, the ratio of the conqeattration of unreacted HBr (given as (HBr)o - (Br)) to the measured OH concentration, varied from 34 to 183 in the seven mixtures studied. Thus, all measurements were made in the presence of a large excess of HBr. The experimental results were analyzed in terms of the following mechanism OH f HBr
was used to reduce data from several experiments. Here, x represents the conccmtration reacted a t time t x was computed from entheir I3 decay or the Br(2P3,2) growth measurements, and plots of log [(HBr)o - x/(H)o - x] us. t were made as shown in Figure Ib. (e) When (H)o and (HBr)o are nearly (equal, method a cannot be used and method b is inappropriate since any small errors in the measurement of (HI0 and (HBr)o are greatly magnifred in their difference term. Under these conditions the expression ~
- (H),-l] = k t was used. The expression was derived by integrating the rate equation after setting (HBr) equal to (H). This procedure is strictly justified if (H)o = (HBr)o, because the reaction stoichiometry is such that equal amounts of H and l-1Br react together. Values of k b are listed in Table I. The reactant concentrations and the methods of data treatment for each mixture are also given. The Journal of Physical Chemistry, Vol. 77, No. 8, 1973
H 2 0 4- Br
(2)
OH -* HzO + 0 (3) OHi-03- 0 2 (4) OH wall (5) If reaction 2 is fast and HBr is present in large excess, OH is largely consumed by reaction 2, and, to a first approximation, the removal of OH is described by the equation - d(QH)/dt = h,(HBr)(OH) which integrates to In (OH)ll(OH) = h,(H where ( 0 H ) l is the OH concentration at some arbitrary point chosen to represent t = 0. In our experiments, HBr was present in large excess and this expression was used to determine approximate values for k2. Log (OH) was plotted against t, and k2 was caiculated from the gradient. Figure 2 clearly shows that such plots remain linear for a variation in OH concentration of a factor of 20-30.
OH
+
-
4
Reactions of H and OH with Hydrogen Bromide TABLE II: Rate ~ o r m s for ~ athe ~ Reaction ~ ~ H 4- HBr
k , cm3 rnolecule-' sec-
'
-
1063 HZ 4- Br
k a t 295 K, cm3 molecule-' sec-'
2.3 X 10- 10exp(--3100/RT)a 1.8 x I O - ~ ~ ~ X ~ ( - W O O / R T ) ~ ~ 2.1 X IO-" exp(-900/RT) 1.0 x l O - ' O exp(--2200/RT) 2.5 X ~!xp(--900/RT)C 4.0 X 10-lo exp(-2900/RT)C 8.7 x i o - " E ~ x P ~ - ~ ~ o o / R T ) ~
1.06 x 3.24 x 4.50 X 2.40 X 5.58 X 7.43 x 6.20 x 3.40 X
10-13 10-13 10- l2
lo-" 10- l 2 10-13 10-13 10-l2
Method of study
Temperature of study, K
HZ-HBr photolysisd
300-523 973-1673 821-984 1150-1284
Flame propagati0nd.e HBr--H2thermal reactionf H2-02 ignitiong H 2 - B r 2 photolysish Critical review6 Critical review/ This s t u d y
500-1 700 295
+
+ *
a Calculated from a ratio of rate constants, using the value of ref 20 for the reaction H Br2 HBr H. Estimated by ref 20 from the kinetic data of ref 17. Calculated from values for the reverse reaction together with the equilibrium constant. Reference 16. e Reference 17. f Reference 18. g Reference 19.h An interpretation by B. A. Thrush, Progr. React. Kinet., 3, 88 (19651, of data reported by M. Bodenslein and W. Muller, Z.Electrochem., 30,416 ('1924); W. Jost, Z. Phys. Chem., 83,95 (1929). I Reference 20. Reference 21.
A more sophisticated analysis was made using the computer program described in detail in an earlier paper.9 This program fits the experimental data to data generated from a reaction schame involving reactions 2-5. Known values of the rate constants h3 and 1125 were introduced into the program, and t,he value of hz that gave the best fit between the experimental data and the predictions of the reaction scheme Waf; computed. In order to determine h5> which has not been measured in a fluorinated halocarbon coated tube, several measurements were made of the rate of OH decay in the absence of HBr.. These were analyzed in a manner identical with that described giving 1123 as (1.50 f 0.40) x 10--I2 c:m3 molecule-i sec-I, and hg as (62 f 17) sec-1. Using these rate constants 1122 was comput,ed as (5.1 f 1.0) x cmJ molecule-1 sec--1. In ail of the above calculations, the HBr concentration was computed as (PIBr)o - (Er). This assumes the stoichiometry of reaction 2 tzobe as written. The following experiment was -made to confirm this fact. Excess HBr was added to atomic hydrogen, and the Br(2P31z) signal was recorded 15 cm downstream. Then, NO2 was added to the system a t the HBr inlet. Br(2P3/2) was again recorded, and its concentration compared to that produced in the absence of NOz. Five experiments were performed and the ratio of Br(2P3,2) formed from reactions of OH, to that formed in reaction 1, was measured as 0.90 zt: 0.14. In these experiments, sufficient NO2 was added to ensure that between 76 and 90% of the atomic hydrogen was converted to OH before reaction with HBr.Ib Corrections were made for that atomic hydrogen that reacted with HBr even in the presence of NO2, and to account for the small amount of OH (less than 10%)that reacted viet reactions 3-5. An unsuccessful search was made for Br(2P1/2) in both reactions 1 and 2 . The sensitivity of the apparatus was such that its presence would have been detected if its concentration had been greater than 4-5% of that of
W2~3/d. Discussion In this study, the rate constant for the reaction of atomic hydrogen wit,h hydrogen bromide has been estimated from measurementi; of hydrogen atom decay, and from measurements of bromide atom growth. Three methods of data reduction have been used. Since the values of hl obtained from first-order H decay do not depend on concentrations determined using integrated epr signals, and
+
since values obtained from plots of 1/(H) - l(H)o against reaction time depend solely on absolute epr measurements, the constancy of the various estimates allows some confidence to be placed in the measured value of 3.4 f 0.4 x 10-12 cm3 molecule-1 sec-I. The value of the standard deviation is, however, smaller than the estimated calibration uncertainties. These arise mainly from an oversimplified view of the gas flow, and from uncertainties in flowrate measurements, and amount to f25%. There have been a number of previous attempts to determine the rate constant for the reaction of hydrogen atoms with HBr.16-21 All of these determinations have either inferred the rate of reaction 1 from measurements on the reverse reaction, or have estimated hl relative to some other reaction rate (usually H -t r2 HBr Br). No direct measurements have been made. Values of hl that have been reported are listed in Table 11, and, a t 295 K, range from 1.06 X to 4.50 X cm3 molecule-1 see-I. At this temperature our measurements are in best agreement with those of Steiner18 or Steiner and Ringrose,lg but if our data are combined with previous hightemperature measurements,16-20 an activation energy of 1.2-2.0 kcal/mol is obtained. The production of Br(2PI,2) in the reaction of atomic hydrogen with HBr was first observed by Polanyi and coworker^^^^^^ in 1966, and a very recent measurement indicates that its formation rate is 8% of that of Br(ZP3/2).24 In this study, nearly quantitative conversion (91 f 11%) of H to Br(2P3/z) was observed, and no Br(2P112) was detected. However, these observations do not preclude its formation, since physical quenching of Br(2P1/2) could have preceded our measurements. Rate constants for quenching of Br(2P~/2)by Ar, MBr, and Mz are known,25 and are too small to produce effective quenching of Br(2P1/2) in our system. However, quenching by atomic
-
(15) The rate constant for H iNO2
+
-
OH i- i\lO was taken as 4.3 X cm3 molecule-' sec-' as measured by L. F. Phillips and H. I. Schiff, J. Chem. Phys., 37,1233 (1962). (16) R. A. Fass,J. Phys. Chem., 74,984 (1970). (17) S.D. Cooley and R. C. Anderson, lnd. Eng. Chem., 44, 1402 (1952). (18) H. Steiner. Proc. Roy. SOC..Ser. A , 173, 531 (1939). (19) G.8.Steiner and G. H. Ringrose, J. Chem. Phys., 43, 4129 (1965). (20) A. F. Trotman-Dickenson and G. S. Milne, "Tabies of Bimolecular Gas Reactions," NSRDS-NBS 9, U. S. Government Printing Office, Washington, D. C.. 1967. (21) A. A. Westenberg and R . M. Fristrom, "Flame Structure," McGrawHill, New York. N. Y.,1965,p 358. (22)J. R. Airey, P. D. Pacey. and J. C. Polanyi, Symp. Combust. I f t h ,
lo-"
85 (1967). (23)J. C. Polanyi, Chem. Brit., 15 (1966). (24) P. B. Davies, 8 . A. Thrush, A. J. Stone, and F. D. Wayne, Chem. Phys. Left., submitted for publication. The Journal of Physical Chemistry, Vol. 77, No. 8,1973
1064
G. A. Takacs and G. P. Glass
TABLE Ill: Reaction of OH with Hydrogen Bromide ( A r ) o , I O i 4 ( H ~ ) oIO1* , ( N O z ) ~1014(HBr)o, , IOi4 ( H ) o ,1014 r n o I ~ ! c ~ I e smoIecuies ct11-~
cm-? ~..__ ~~
2.36 2.23 2.62 U,42 0.42 0.74 0.72
236 223 231 271
2 71 254 247
~~~~
molecules
molecules
CIT-~
c w 3
molecules cm - 3
3.22 2.96 3.98 3.42 3.01 2.47 3.14
4.28 4.65 4.98 1.05 0.99 1.31 1.31
% H removed by No7
IOl3
molecuies ~ 1 7 1 1 ~
(Br)l,a 1013 molecules cm
i plot
~
~
~ From ~ computer
~
~~~
4.81 8.90 5.80 2.90 4.14 1.98 1.92
74
Excess NO2 92
Excess N O 2 Excess NO2 96 95
18.7 11.3 18.4 3.54 4.24 6.35 6.16
2.82 3.71 3.68 I .48 1.43 2.68 2.52 Av
a
k2b
~
Measured 3 3 cm downstream from HBr inlet at the first measuring point.
hydxogen or wall quenching could have taken place. Atomic hydrogen is known to quench C1(2P1,2) with unit collisional efficiency,25 and I(2P1,2) is effectively removed a t thlil walls.26 A rate constant of (5.1 f 1.0) x cm3 molecule-I sec-l was obtained for reaction 2 from computer analysis of the reaction of hydroxyl radicals with HBr. This number is similar to the average value (5.7 X obtained from plots of log (OlH) us. reaction time. Since this latter procedure neglected any contribution from reaction5 2-5, the closeness of the two values indicates that these reactions are not very important in determining the rate of rernovad of OH. This conclusion can be confirmed using known values for ka and kg27,25and data from Table 111, since it can be estimated that, under the conditions of this study, reaction 2 is always 20 times faster than reaction 5, and I00 times faster than reaction 3. Thus, the present disagreement concerning k$,27-28 does not influence the value measured for kz. Only one previous measurement bas been made of the rate of reaction 2 . From a study of flame inhibition by have estimated k z as halogen compounds, Wilson, et 2.65 x 10-11 cmg molecule sec-l a t 1875-1975 K. Combining this rate constant with our value a t 295 K, k z can exp(-(1.15 f 0.14)/ be estimated as (3.7 $. 0.7) x RTJ cm3 molecule-' sec-l, where the activation energy is expressed in kcal/mole. Good agreement was obtained between the measured stoichiometry and that predicted for reaction 2. In this system all atomic bromine is expected to be present as Br('P3,2), since any Br(2P1,2) formed would be rapidly quenched to Br(zP3,~)by collision with NO,25 which is produced in the initial reaction generating OH, namely, H I- NC12 OH -I.NO The value measured for k3 is higher than that previously rcported from this laboratory,8 although the error bounds placed on the two measuremLents almost overlap. -+
The Journal of Physical Chemistry, Vol. 77, No. 8, 7973
Units of 10-
l2
value of It2
cm3 molecule-
7.2 6.9 6.0 4.4 4.6 5.6 5.6 (5.7 A 0.9)
6.9 6.0 5.2 3.8 4.1 5.1 (5.1 4.8 r f 7.0)
sec-I.
The reason for this discrepancy is not clear. The present measurement was made using an entirely new apparatus, and a different wall coating, but the experimental procedure used was identical with that described previously. The only significant difference between the measurements was that in the present study OH was followed over a reaction time of 18 msec, while in the previous study, it was followed for only 6-7 msec. At this point, it is worth noting that only a small change in the experimental data is needed to produce a sizeable simultaneous change in kS and kg, since the effects of an increase in ka can be largely offset by a decrease in kg. The new value agrees closely with that measured by K a ~ f m a n . ~ ~ The work presented in this paper was greatly facilitated by the use of the fluorinated halocarbon wall coating. The inertness of this coating to halogen atom recombination allowed reaction stoichiometries to be measured, rate constants to be estimated from measurements of bromine atom concentrations, and the HBr concentration to be calculated a t any reaction time using the expression (HBr) = (HBr)o - (Br). Acknowledgments. Acknowledgment is made to the Donors of The Petroleum Research Fund, administered by the American Chemical Society, for the support of this research. The authors would like to thank the Robert A. Welch Foundation of -Houston, Texas, for the use of the epr spectrometer, and thank Dr. E,. T. Cupitt for assisting in the early work with wall coatings. (25) R. J. Donovan and D. Husain, Chem. Rev.. 90,509 (1970). (26) D. Husain and J. R. Wiensenfeid, Trans. Faraday Soc., 63, 1349 (1967). (27) F. Kaufman, Ann. Geophys.. 20, 106 (1964). (28) (a) A. A . Westenberg and N . deHaas, J. Chem. Phys., 43, 1550 (1965); (b) G. Dixon-Lewis, W. E. Wilson, and A. A. Westenberg, ibid., 44, 2877 ( 1 966) (29) W. E. Wilson, Jr., J. T. O'Donovan. and R , M. Fristrom, Symp. Combust. 12th, 929 (1969).
d
~
~
