984
RICHARD A. FASS
Reaction of Hot and Thermal Hydrogen Atoms with Hydrogen Bromide and Bromine' by Richard A. Fass2 Department of Chemistry, University o j Wisconsin, Madison, Wisconsin (Received September 4, 1969)
+
+
+
+
(2) (3) The ratios of the rates of the reactions €1 HBr --t Hz Brand H Brz -+ HBr Br have been determined for both thermal and unmoderated H atoms in the gas phase at temperatures from 300 to 523"K, using H atoms produced by the photolysis of HBr in the presence of Rrz at 1850 and 2480 A. In the absence of inert gas moderators, the ratio ka*/kz* for the reactions of hot H atoms = 5.3 0.4 at each wavelength,independent of the temperature. The independence of wavelength and temperature suggests that most of the hydrogen atoms react with HBr or Brz before being thermalized. He is much more efficient than COZfor thermalizing the 2.9-eV H atoms from 1850-d photolysis. The data for thermal H atoms in the range 300 to 523'K, coupled with earlier data between 900 and 1400°K,give ks/kz = 6.8 exp(800/RT). The ratio of preexponentialfactors for the thermal reactions is approximately the same as the ratio of the reaction probabilities for hot hydogen atoms in the same system.
Introduction Photodissociation of HBr by 1850 A and 2480radiation produces H atoms with 2.9 and 1.2 eV of translational energy, respectively. 3 , 4 These may react while retaining energy in excess of average thermal energies (H*), or after moderation (H), by the following steps
d
+ Br(2P1/,) H* + HBr +Hz + Br H* f Brz +HBr + Br H* + 34-H H + HBr Hz- + Br H + Br2 +HBr + Br 2Br + M -+ Br2 + R/I HBr -+ H*
-+
(1) (2*) (3 *I
(4) (2) (3) (5)
In pure HBr, all the H atoms must form Hz by reaction 2" and/or 2, leading to a quantum yield of 2.0 for HBr consumption. As the Brz concentration grows [reaCtiOnS 2* and 2 followed by 51, the quantum yield falls due to reactions 3" and 3. Because (1) HBr is useful an actinometer for ultraviolet radiation;4 (2) there are discrepancies in the literature concerning the reactions of thermal H atoms in the HBr-Brz System; and (3) the system is of intrinsic interest for the study of hot reactions, we have investigated the relative probabilities per collision of reactions 2* and 3* and the relative rate constants of reactions 2 and 3. The ratio ks*/lcz* from the 2537-A photolysis of HBr has been reported as 0.66,6but parallel results on the HI-I2 system using the same apparatus have been shown to be in error.6,6 Previous measurements of ka/k2in studies of the thermal reaction of Br2 with HZ The Journal of Physical Chemistry
from 228 to 302°,7 the photochemical Br2-H2 reaction from 160 to 218O,*and the Br2-H2reaction in flames and shock tubes from 327 to 1427'9 give values between 8.2 and 10.1, temperature independent within the detection limits of the experiments. Bodenstein and J ~ n g ' ~ reported k3/kZ = 8.6 from a photochemical experiment a t 25", but Sullivanlo has shown that a t this temperature the photochemical Br2-Hz reac$ion is dominated by a mechanism different than the chain assumed. There is, therefore, no reliable measurement of k3/k2 below 160°, and a small temperature coefficient might not have been detected a t the higher temperatures. By analogy with the HCl-Cl2 system" and the HI-I2 system,I2 it might be expected that the activation energy for reaction 2 would be about 1 kcal mol-' higher than that for reaction 3.
(1) This work has been supported in part by the U. S.Atomic Energy Commission under Contract AT (1 1-1)-17 15. (2) Department of Chemistry, Pomona College, Claremoiit, Calif
I
91711.
(3) R. M. Martin and J. E. Willard, J . Chem. Phys., 40, 3007 (1964). (4) (a) R. A. Fass and J. E. Willard, ibid., in press; (b) R . M. Martin, Ph.D. Thesis, University of Wisconsin, Madison, Wis. 1964. (5) H. A. Schwarz, R. R . Williams, Jr., and W. H . Hamill, J . Amer. Chem. sot,.. 74,. 6o07 (1952), (6) J. L. Holmes and P. Rodgers, Trans. Faradau SOC.,64, 2348 (1968). (7) (a) M . Bodenstein and S. C. Lind, Z . Phys. Chem., 57, 168 (1906); (b) M . Bodenstein and G. Jung, {bid., 121, 127 (1926). (8) M. Bodenstein and H. Lutkemeyer, ibid., 114, 208 (1924). (9) (a) A. Levy, J . Phys. Chem., 62, 570 (1958): (b) S. D . Co,Dley and R. C. Anderson, Ind. Eng. Chem., 44, 1402 (1952); (c) D. Britton and R. M . Cole, J . Phys. Chem., 65, 1302 (1961). (10) J. H. Sullivan, J . Chem. Phys., 49, 1155 (1968). (11) F . S.Klein and M.. Wolfsberg, ibid., 34, 1494 (1961). (12) R. D. Penzhorn and B. de B. Darwent, J . Phys. Chem., 1639 (1968).
REACTION OF HOTAND THERMAL HYDROGEN ATOMSWITH HBr AND Bra Experimental Section Matheson HBr (99.8% minimum purity) was degassed and distilled under vacuum a t -78”. Air Reduction Co. research grade COz and Hz and Matheson ultrahigh-purity grade He were used without further purification. The quantum yield of decomposition of pure HBr did not vary from the expected value of 2 even when an excess of C02, H2,or He was added, thus verifying the adequacy of the purity of these additives. Cylindrical quartz cells with 2.5-cm diameter Suprasil end windows and 10-cm path lengths were used for all photolyses. They were fitted with graded seals and greaseless stopcocks which did not react with HBr or Br2. A ground-glass joint attached to the stopcock allowed attachment of the cell to the mercuryfree vacuum line which was used for cell filling. The stopcocks on the vacuum line were lubricated with Kel-F 90 grease. HBr was metered into the cells by means of a click which permitted measurements reproducible to 0.5 Torr. After removal of the cell from the line the HBr pressure was measured on a Cary 14 spectrophotometer, using a molar extinction coefficient of 155 1. mol-’ cm-’ a t 2100 A.13 COZ,He, and Hz pressures were measured on a mercury manometer isolated from the mercury-free manifold by a U-tube trap cooled to -78”. An Osram HBO-200W “super-pressure” mercury arc coupled with a Bausch and Lomb uv-visible grathg monochromator was used for photolyses a t 2480 A, with a 250-A bandpass. This arrangement permitted about 10l6 photons sec-I to be delivered to a cell. Two Hanovia SC 2537 low-pressure mercury lamps with Suprasil windows, one directed a t each end of the reaction cell, were used for 1850-A photolyses, providing about 2 X 101j photons sec-l. For rapid photolyses designed to build up the Brz/HBr ratio to a desired level for quantum yield measurements, a low-pr%ssure spiral mercury lamp which provided an 1850-A intensity of about 10” photons sec-’ in the 10-cm cylindrical cells was used. This lamp was constructed by L. C. Glasgow of our laboratory. Actinometry was done by measuring the rate of Br2 production from the photolysis of 15 Torr HBr a t Br2/HBr ratios less than 0.01, where reactions 3* and 3 are negligible. The Brz concentration was determined on the Cary spzctrophotometer using E = 170 1. mol-’ cm-I at 4160 A.14 The decrease in HBr concentration measured a t 2100 A was always greater than the increase of Brz by a factor of 2.00 0.02, as predicted by the mechanism. All experiments were done a t HBr pressures in the from 15 to 7 Torr (optical densities at 1850 A from ca. 4 to 2) so that even at the highest per cent decompositions studied there was essentially complete absorption of the 1850-A incident radiation. In the 1850-A photolyses, approximately 15% of the absorbed light in a 15 Torr HBr sample was
*
985
a t the 2537-A mercury line. At this pressure of HBr the 2537-A optical density is ca. 0.02, so at this wavelength the absorbed light intensity is directly proportional to HBr pressure. Utilizing these facts the total absorbed light intensity was calculated as a function of HBr pressure for the quantum yield measurements. Similar calculations weze made for the quantum yield measurements a t 2480 A. In experiments where the ratio of the rates of reaction 2” to reaction 3* was to be studied using Brz/HBr ratios produced by prior photolysis of HBr, the Hz formed in the photolysis was first pumped out to avoid any moderating effect. Likewise, in experiments above room temperature the Hz concentration was never allowed to reach more than 2% of the HBr concentration. This precluded interference by the inhibiting chain reaction of Br atoms with H2, represented by the reverse of reaction 2 followed by reaction 3. Calculations using rate constants given by SullivanlO indicate that this chain reaction should not contribute significantly a t low Hz pressures, and this was verified in several experiments which showed k3/k2 ratios to be independent of Hz concentration up to at least 3% of the HBr concentration. Results Determination of k3/k2 and k3*/kz*. The rate of formation of Brz by reactions 1-5 derived from steadystate considerations and applicable to both hot and thermal reactions is given by
I , is the rate of light absorption (einsteins 1.-l sec-I), [Brz]is in units of mol l.-’, and the “constants” k3’ and k2’may be either k3* and kz* applicable to the distribution of H atoms present during unmoderated HBr photolyses, or k3 and k2 applicable to thermal H atoms. If photolysis is done under conditions such that I , is constant and [Br2]/[HBr] is nearly constant (an average value over the time of photolysis can be used if the ratio does not vary substantially), then (I) can be rearranged, giving 1 - Jc3’ [Bra] -__ _ +1
@
~
r
kz’ ~ [HBrl
(11)
where @ B is ~ ~(d[Brz]/dt)/l,. I n Figure 1, plots of l / @vs.~[Br2]/[HBr] ~ ~ for the photolysis of HBr with and without the 600 Torr of He moderator required to thermalize the H atoms (see below) give straight lines with slopes of k 3 / k ~= 22.7 and lc3*/k2* = 5.3, respectively. (13) B . J. Huebert and R . M. Martin, J. Phys. Chern., 72, 3046 (1968). (14) A . A . Passohier, J. D. Christian, and N.W. Gregory, ibid., 71, 937 (1967).
Volume 74, Number 6 March 6,19YO
986
RICHARD A. FASS
r-
25-
12
10
. 8
-la$
';*
6
'5
O
r
4 MODLMiOR
(torr x
10-2)
Figure 2. Effect of inert moderators on k s ' / k ~ ' . Photolyses a t 1850 A, 27". HBr pressures, 7-15 Torr: 0, He; A, COS;,. Ha.
2
.1
I
I
I
I
I
.2
.3
A
.5
.6
t Br, 1 / t HBrl
Figure 1. Reciprocal Bra quantum yield us. [Brz]/[HBr] for moderated and unmoderated systems at 27". Initial HBr pressure, 15 Torr. [Bm]/[HBr] varied by successive photolyses of the same mixture. 0, 600 Torr He a t 1850 if; B, unrnoderated a t 1850 if; A, unmoderated at 2480 if.
For experiments in which pure HBr ( [Brz]/[HBr] = 0) is photolyzed until a significant amount of Brz is accumulated, (I) can be integrated to give
- --
I d - [Brzlt
k3'
1~2'
[HBr]i
4
[HBrJi ln---[HBrlt
[Brzlt 2
(111)
where [HBrli and [HBr]t are the initial and final HBr concentrations respectively, [BrzIt is the final Brz concentration, and t is the photolysis time. The conditions of eq I11 were used in one experiment, with an excess of inert moderator. The value of k3/kZ = 25 a t 27" obtained is in good agreement with k3/kz = 23 a t 27" obtained in separate experiments using eq 11, and serves as a check on the validity of the assumed mechanism. Effect of Moderators on Reaction Probabilities. In order to determine the pressure of inert gas required to eliminate reactions of hot hydrogen atoms the ratios of specific reaction rates ka'/kz' were determined as 5 function of pressure of He and of COZ for 1850-A photolysis. These data, including one point for Hz as moderator, are given in Figure 2. The point for Ht moderator indicates that HZis more efficient than He or COZ as would be expected. If it is asgumed that the one point for H2and the point a t 1400 Torr He represent mixtures in which virtually all of the H atoms are thermalized before reaction with HBr or Br8, then it can be estimated that in the mixtures The Journal of Phgsical Chemiatry
containing 600 Torr He, ca. 85% of the H atoms are thermalized while the remaining 15% react as hot atoms with k3'/kz' = k3*/kz* = 5.3. I n mixtures containing 600 Torr COz (COZ/HRr = 40: 1) only ca. 60% of the H atoms are thermalized, as shown in Figure 2. Similar COz mooderator curves have been obtained in the 2400-2800-A photolysis of HI-IZ mixtures12a t d in HzS-CzH4mixtures photolyzed a t 2138 and 2490 AI5 (both systems producing 1-2 eV H atoms). Reasoning from the apparent plateau in these curves, these authors12J6concluded that all of the H* atoms are thermalized before reaction a t a C02/HI or COZ/HZSratio of 40:1. Our data for 2.9 eV H atoms indicate that this ratio does not completely thermalize all H atoms in the C09-HBr-Br2 system even though the COz curve (Figure 2) appears to be nearly horizontal. The very slow approach to complete thermalization indicated by these moderation curves is probably a result of the lower energy loss per collision a t energies near the threshold for reactions 2* and 3*. Considering the scatter of the data of Figure 2 and ref 12 and 15, this suggests that the appearance of a plateau is not sufficient evidence for complete thermalization. Temperature Coepcient of k3/k2. Data obtained in this work over the temperature range from 27 to 250" are shown in Figure 3 on an Arrhenius plot which includes data from other sources taken a t much higher temperatures. The straight line corresponds to an activation energy difference E z - E3 = 0.8 f 0.3 kea1 mol-1, where the indicated error limits include the limits placed by the lines of extreme maximum and minimum slopes which could reasonably be drawn through the points and the error introduced by the probability that ca. 15% of the H atoms were not (16) G. R.Woolley and R.J. Cvetanovic, J . Chem. Phys., 50, 4697 (1969).
987
REACTION OF HOTAND THERMAL HYDROGEN ATOMSWITH HBr AND Br2
Table I : Rate Parameters for Reactions of Hydrogen Atoms (2) + HX + Hz + X (3) H + Xz *H X + X
H
-
I
9
\
4
1
X
C1"
Br' I"
E2 - Ea, koa1 mol-'
1.5 0.8 0.6
Aa/Aa
ks*/k2*d
6.9 6.8 5.0
5.3 4.2
a Reference 11. 'This work, Reference 12. This is the ratio of reaction probabilities for hot H atoms. See text.
-k
X
101
Figure 3. Temperature dependence of Ics/kz. A, ref 9a; A, ref 9b; ., ref 9c; V, ref 7b.
0, this
work;
moderated by the 600 Torr of He, as discussed above. The ratio of preexponential factors derived from the data of Figure 3 is 6.8 f 2.
Discussion Fraction of H Atoms Which Reacts before Moderation. The data of Figure 2 show that the ratio of reaction of H atoms with Br2 to their reaction with HBr in the absence of inert gas moderator is the same (5.3) re; gardless of whether activation is with 1850- or 2480-A radiation. Since the analogous ratio for reaction of thermalized atoms is much different (lc3/kz = 23), it may be concluded that in the unmoderated system most of the H atoms produced a t each wavelength react before thermalization. This implies that the reaction H* 4 13 BrH* as a process for producing HBr thermal H atoms is improbable relative to reaction 2*. k3*/kz* CornpaTed to A3/A2. The ratio of preexponential factors A3/A2 of 6.8 f 2 obtained from Figure 3 is, within experimental error, the same as the ratio of the corresponding reaction probabilities for hot H atoms, k3*/k2* = 5.3 f 0.4. A similar relationship (see Table I) has been found for the reaction of hydro-
+
+
gen atoms with H I and 12.12This is consistent with the collision theory interpretation of the Arrhenius preexponential factor as being directly proportional to the probability that a collision at an energy above the reacton threshold will result in chemical reaction. Comparison with Literatuye Values. The data of Figure 3 clearly indicate that reactions 2 and 3 have an activation energy difference. This difference is small enough to have been missed in the high-temperature work using shock tube and flame techniques.O Consequently the value of Ez - E3has frequently been quoted as zero. The available data on the analogous reactions in the HC1-C12 and HI-I2 systems are included in Table I. The parameters for the HBr-Brz system found in this work fit into a consistent trend in this series. The activation energy of reaction 2 has been independently reported t o have values of 0.9 to 3.7 kcal mol-l.16 If these values bracket the correct value, E3 must lie in the range of 0 to 3.2 kcal mol-'.
Acknowledgment. The author wishes to thank Professor John E. Willard for his helpful suggestions and encouragement during the course of this work. (16) A. F. Trotman-Dickenson and G. S. Milne, "Tables of Bimolecular Gas Reactions," National Bureau of Standards, NSRDSNBS9 (1967).
Volume 74- Number 6 March 6, 1970
