T H E
J O U R N A L
OF
PHYSICAL CHEMISTRY Registered in U.S. Patent Office 0 Copyright, 1976, by the American Chemical Society
VOLUME 80, NUMBER 14 JULY 1, 1976
Reactions of Atomic Hydrogen and Deuterium with HBr and DBr H. Endo and 0. P. Glass* Department of Chemistry, William hkrsh Rice Unlversity, Houston, Texas 7700 1 (Received August 29, 1975; Revised Manuscript Received February 5, 1976) Publication costs assisted by the Petroleum Research Fund
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The reactions H HBr, D HBr, H DBr, and D DBr have been studied directly over the temperature range 230-318 K using a discharge flow apparatus equipped for EPR detection of atoms. Absolute rate conexp(-(2130 f 80)/RT],(1.09 f exp(-(2570 f 11O)/RT],(6.40 f 0.57) X stants of (2.77 f 0.32) X exp(-(1690 f 130)/RT] cm3 molecule-l s-l 0.08) X exp(-(2190 f 11O)RT],and (2.27 f 0.21) X were obtained for the reactions H HBr, D HBr, H DBr, and D DBr, respectively. At 295 K, rate conD HBr and D HBr H DBr were measured as S3.9 X stants for the exchange reactions H DBr cm3 m o l e c u l e - l ~ - ~respectively. , and 1.3 f 0.4 X
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Introduction Hydrogen bromide is an effective flame inhibitor. It reduces the rate of flame propagation, decreases flammability, and raises explosion 1irnits.l-7 It is widely accepted that inhibition results from reactions of HBr with reactive chain centers such as H and OH. The reaction of atomic hydrogen with HBr has also been a useful testing ground for theories of chemical reaction rates. In 1931, Eyring and Polanyis calculated the HzBr potential energy surface in their historic paper on the LEP (LondonEying-Polanyi) method. Since that time many semiempirical surfaces have been constructed, and many transition state calculations have been performed using them.9-12 Recently, extensive classical trajectory calculations have been made by White,13 and by White and Thompson14 using a surface developed following a formalism employed by Raff et al.15 From these calculations, reactive cross sections and thermal rate constants for the abstraction reaction H
+ HBr
-
H2
+ Br
(la)
and for the atom exchange reaction
H’
+ BrH
H’Br
+H
(lb)
have been computed, and the dependence of these parameters on the initial reactant vibrational and rotational states has been determined. The product state distributions and the branching ratios (kla/klb) estimated by White13 have been used by Levine and Bernstein16 in a test of their information theoretic approach to chemical rate theory.
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In this study we have used a discharge flow apparatus equipped for EPR detection to measure directly the absolute rate constants for the reactions of H HBr, H DBr, D HBr, and D DBr a t temperatures between 230 and 318 K. Also, branching ratios have been measured a t 295 K for the reactions H DBr and D HBr. Prior to this investigation, the reaction between atomic hydrogen and HBr had been studied directly only a t room temperature.17 At 300 K two m e a s ~ r e m e n t sof~ ~the ~~~ branching ratio for H DBr have been made. These gave values for kla/hlb of 13.3 and 170, respectively. These numbers are much higher than that computed by White13 (0.2-1.0). However, White’s computations are supported by measurements made using translationally hot hydrogen atoms,20and by the results of a recent molecular beam investigation.21 Therefore, a reinvestigation of the room temperature measurements seemed particularly appropriate.
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Experimental Section The discharge flow/EPR apparatus was similar to that described in detail previ0us1y.l~For this study two modifications were made. The flow tube was redesigned as shown in Figure 1, and a new improved EPR spectrometer was used. The changes in the flow tube design allowed a constant temperature bath to be installed immediately upstream of the E P R cavity. Slush baths were used to attain temperatures below 295 K. An ice-water mixture was used a t 273 K, a dry ice-carbon tetrachloride slush a t 252 K, and a dry ice-diethyl ketone slush a t 230 K. Temperatures above 295 K were obtained by electrical heating of a well-stirred water bath. A 1519
1520
H. Endo and G. P. Glass
TEMPERATURE BATH EPR CAVITY
PROBE-
30cm
1
PUMPS
L
4cm
Figure 1. Diagram of apparatus.
strong current of air, directed at the section of the flow tube between the temperature bath and the EPR cavity, ensured that the latter remained at room temperature. The flow tube was split into two sections in the discharge region in order to reduce free-radical impurities. Only 5% of the carrier gas (Ar or He) passed through the discharge itself, Clyne and Cruse22have shown that small atom concentrations are better controlled, and impurity levels much reduced when this arrangement is used. In this study, the bypass was particularly effective in reducing the hydrogen atom concentrations to less than 2% of the D atom concentration. Deuterium bromide (99%) was obtained from Stohler Isotope Chemicals. It was transferred to a storage bulb using a moderately high vacuum system Torr), and its isotopic purity periodically checked by running infrared spectra on samples withdrawn from the bulb. Its isotopic purity remained greater than 95% throughout the experiments. EPR signals were recorded with a Varian E12 spectrometer equipped with an E-235 large access cavity. Relative concentrations of H and D were determined from EPR peak heights. Absolute concentrations were determined by double integration of the spectrometer output, using known pressures of 0 2 as calibration standards. Transition probabilities for all of these species are known.23The improved sensitivity of the new spectrometer allowed H to be detected at concentrations molecule/cm3. of 5 x In order to prevent atom recombination, the flow tube walls were coated with fluorinated halocarbon wax.17 Flow tubes were used for experiments only when a direct test, described in detail previously,17 showed them to be inert to bromine atom recombination.
Results The overall chemistry of the reaction between atomic hydrogen and HBr has been studied previou~1y.l~ In the absence of wall recombination of H and Br, the stoichiometry is particularly simple, and rate constants can be estimated from measurements of the H(D) concentration. In the present study, the detector sensitivity toward H(D) was high, and rate constants were measured by monitoring H(D) atom decay in mixtures containing an excess of HBr(DBr). In a typical experiment the 20 mm i.d. flow tube was operated at pressures of 1.25 Torr and a t linear flow speeds of 1600-2100 cm/s. The initial concentration of HBr(DBr) was 5 to 1 2 times greater than that of the atoms, and the concentration of the latter was followed for 5-10 ms (10-20 cm). Under these conditions the atom decay was pseudo-first order, and rate constants were estimated from the slopes of plots of log (H) vs. reaction time. WestenbergZ4 has shown that the pseudo-first-order rate constant characteristic of the region within the temperature bath can be determined from such plots even when the atom concentrations are measured at a fixed point outside of this region. In a few experiments bromine atom production was moniThe Journal of Physical Chemistry, Vol. 80, No. 14, 1976
tored, and the rate constant for abstraction estimated from plots of In [(HBr)o - (Br)] vs. reaction time. The results of all of our rate measurements are tabulated in Table I. The experimental conditions pertaining during the study are also listed. At each temperature studied, five to ten rate measurements were usually made. Rate constants obtained from these measurements were corrected for the effects of axial diffusion of atomic hydrogen (deuterium) using the procedure employed by Dickens et al.25 Binary diffusion coefficients for atomic hydrogen dilute in argon and helium were taken from the work of Khouw, Morgan, and Schiff,26 while those for atomic deuterium were calculated assuming an inverse square root dependence on reduced mass.26Viscous pressure drop along the flow tube amounted to less than 2%/10 cm, and its effects were neglected. Arrhenius plots for the various reactions are shown in Figure 2. From these, rate constants for the reactions, H HBr, H DBr, D HBr, and D DBr were estimated as (2.77 f 0.32) X exp(-(2570 f 11O)/RT], (1.09 f 0.08) X exp(-(2190 f 11O)/RT}, (6.40 f 0.57) X expl-(2130 f 80)/RT},and (2.27 f 0.21) X exp(-(1690 X 130)lRT)cm3 molecule-l s-l, respectively. At 295 K, branching ratios were measured for the following pairs of reactions H
+ DBr
H and
+
+
+
+
---
+ DBr
+ HBr D + HBr
+ Br
(abstraction)
(2a)
+ HBr
(exchange)
(2b)
HD D
+ Br (abstraction) (34 H + DBr (exchange) (3b) The branching ratio for H + DBr was estimated from meaD
HD
surements of the concentrations of atomic hydrogen and deuterium using the mechanism:
+ DBr H D + Br H + DBr - + D + HBr D + DBr - + D 2 + Br H + HBr -., H2 + Br D + HBr -+DH + Br D + HBr +DBr + H
H
(2a) (2b)
(4) (1)
(3b)
When the branching ratio (hzb/kZa) is very small (an assumption justified a posteriori), reactions 1,3a, and 3b can be neglected and the mechanism simplified to include only reactions 2a, 2b, and 4. Then d(D)/d(H) = [h4(D)/(H)- h2b]/(hZa
+ h2b)
(5)
This equation can be integrated to give
where a = (kza
KZb
- k4)/(k,a + k2b)
b = kzb/(kza
+ kZb - k4)
and (H)o and (D)o are the initial concentrations of H and D, respectively. Since (kza kzb) and k4 are known, h2b can be evaluated from eq 6 and the measured concentrations of H and D.
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1521
Reactions of Atomic H and D with HBr and DBr
TABLE I: Summary of Measurements of the Rate Constants ka H HBr
+
x 10-13
k X 10l2
Carrier
P, Torr
V ,cmls
Ar Ar Ar Ar Ar
1.28 1.28 1.28 1.36
2110 2110 2110 2110 2010
9.03 9.59 9.74 9.34 7.97
1.19 1.80 1.96 1.48 1.26
295
Ar Ar Ar Ar Ar Ar Ar Ar Ar
1.42 1.42 1.42 1.37 1.36 1.36 1.36 1.36 1.36
1770 1770 1770 1830 1840 1840 1840 1840 1840
9.65 10.7 9.56 10.6 11.2 13.2 13.2 11.8 12.4
1.49 1.23 1.83 1.23 2.63 2.21 1.52 1.64 1.83
273
Ar Ar Ar Ar Ar Ar Ar Ar Ar Ar Ar
1.42 1.42 1.45 1.45 1.44 1.44 1.44 1.44 1.44 1.44 1.44
1630 1630 1600 1600 1610 1610 1610 1610 1610 1610 1610
8.56 8.56 7.36 9.02 10.7 10.7 9.81 8.57 8.94 8.63 8.21
0.68 0.84 1.22 1.26 2.18 1.20 1.25 2.36 2.41 2.38 2.06
252
Ar Ar Ar Ar Ar Ar Ar
1.44 1.44 1.44 1.43 1.44 1.44 1.44
1490 1490 1490 1490 1490 1490 1490
7.69 7.69 7.69 14.9 9.96 9.96 9.85
1.60 0.72 2.60 2.24 2.20 2.86
Ar Ar Ar Ar Ar
1.22 1.22 1.25 1.25 1.25
1560 1560 1530 1530 1530
13.1 13.1 10.3 11.8 11.3
0.709 1.22 1.26 1.28 1.28
318
230
1.28
1.18
4.33 5.11 4.79 4.83 5.00 4.81 f 0.30 3.62 3.85 3.77 3.89 3.81 3.80 3.61 3.50 3.57 3.71 f 0.14 1.93 1.99 2.40 2.09 2.03 2.53 2.50 2.32 2.41 2.66 2.11 2.27 f 0.25 1.71 1.29 1.59 1.45 1.65 1.31 1.35 1.48 f 0.17 1.14 1.15 1.22 1.14 1.05
1.14 & 0.06
D
+ HBr x 10-13
T,K
Carrier
P, Torr
V, cmls
318
He He He He He He
1.25 1.25 1.25 1.20 1.20 1.20
2040 2040 2040 2110 2110 2110
11.6 11.6
0.596
10.5
9.80 9.80 10.9
1.24 1.22 1.08 0.840
He He He He He He
1.25 1.25
2050 2050
1.15 1.15
1840 1840
1.15 1.15
1840 1840
13.7 13.7 13.5 13.5 12.8 12.6
1.76 1.31 1.68 2.05 2.04 2.09
295
k 1.21
X
10l2
2.07 2.19 2.03 2.14 2.11 1.92 2.08 f 0.09 1.61 1.81
1.84 1.90 1.74 1.79 1.78 f 0.10
The Journal of Physical Chemistry, Vol. 80, No. 14, 1976
1522
H. Endo and G. P. Glass
Table I (Continued): D
T,K
+ Hbr x 10-13
P , Torr
V, cmls
Ar Ar Ar Ar Ar
0.96 0.95 0.98 0.98 0.96
2037 2058 1995 2058 2037
29fib
Ar Ar Ar Ar Ar
0.96 0.93 0.96 0.96 0.96
2030 2095 2030 2142 2142
273
He He He He He He
1.18 1.18 1.18 1.18
1760 1760 1760 1760 1820 1820
12.6 12.8
He He He He He He
1.08 1.08 1.08 1.12 1.12 1.12
1740 1740 1740 1780 1780 1780
13.7 13.9 13.4 12.8 12.8 12.1
2.46 0.988 1.09 1.24
He He He He He
1.05 1.05 1.31 1.31 1.31
1820 1820 1390 1390 1390
14.9 14.9 18.4 18.4 18.0
0.821 0.764 1.24 1.09 1.13
295
Carrier
19.0
k X 10l2
2.92 2.12 2.40 2.63 2.53
12.8
17.2 21.8 16.2
2.06 1.81
1.64 1.82 1.73 1.82 rt 0.16
252
230
1.15 1.15
2.23 1.98 2.04 2.19 2.04
1.12 1.22 2.53
1.69 1.86 1.65 1.76 1.51 1.69 f 0.13 1.21 1.32 1.23
1.86
1.25
1.19 2.06
1.39 1.42 1.30 f 0.09 0.950 0.738
14.3 14.3 16.2 12.4 20.2
12.8
11.6 18.7 18.7
1.12 2.58
1.05
0.920 0.912 0.727 0.883 f 0.126 0.642 0.664 0.559 0.552 0.603 0.604 f 0.049
H + DBr
T ,K
Carrier
P , Torr
V, cm/s
318
He He
1.32
2020 2080
He He He
1.28 1.15
He He He He He
1.28
He He He He He
1.32 1.32
He He He He He
295
273
252
1.28
1.15
2080 1680 1680
x 10.1
9.82 9.82 9.07 9.25
k X 10l2
10-13
0.763 1.24
3.12 3.53
1.13
3.36 3.37 3.40 3.36 f 0.15 2.65 2.73 2.85 2.74 2.49 2.69 rt 0.13 1.74
1.88
0.974
2040 2040 2040 2040 2040
10.7 10.4 10.4
1.13
10.8
10.8
1.43 1.27
1.28
2020 2020 2020 2020 2020
13.7 13.5 13.9 13.5 12.8
1.52 1.68 1.59 1.46 1.63
1.25 1.25 1.25 1.25 1.25
1680 1680 1680 1680 1680
13.0 13.0 12.6 12.6 10.7
1.79
1.28
1.28 1.28
1.28
1.28
1.28
The Journal of Physical Chemistry, Vol. 80, No. 14, 1976
1.05 1.05
1.82
1.65 1.69 1.20
1.88 1.95 1.88
1.99 1.89 f 0.10 1.69 1.34 1.22 1.31 1.37 1.39 rt 0.18
1523
Reactions of Atomic H and D with HBr and DBr
Table I (Continued): D
+ DBr (DBr)o (D)o
x 10-13
T ,K
Carrier
P , Torr
V, cm/s
318
He He He He He
1.25 1.25 1.25 1.25 1.25
2100 2100 2100 2100 2100
10.2 10.2 11.4 8.87 8.87
1.45 1.63 1.58 1.34 1.24
295
He He He He He
1.30 1.30 1.31 1.31 1.31
1920 1900 1900 1900 1900
10.1
1.42
12.0 10.1 10.1 9.62
1.01 1.11
He He He He He
1.23 1.23 1.23 1.23 1.23
1820 1820 1820 1820 1820
11.6 11.6 12.0 11.9
1.77 1.94 1.63 1.29 1.53
He He He He He He
1.15 1.15 1.15 1.15 1.15
1680 1680 1680 1680 1680 1680
12.1 12.1 12.9 13.4 15.4 15.4
273
252
1.15
k X 10l2
10.1
1.63 1.58 1.52 1.54 1.63 1.58 0.05 1.51
*
1.18
1.21
1.19 1.16
1.01
1.18
*
1.88
1.64 1.53 1.62 1.86 1.37
All concentrations in units of molecules cmF3. Rate constants in units of cm3 molecule-' s-l. bromine atom growth measurements.
*
1.24 0.15 0.876 0.956 1.04 1.04 1.12 1.01 0.09 0.841 0.624 0.821 0.723 0.805 0.873 0.781 0.092 Rate constants measured from
The uncertainty in these rate constants arises mainly as a result of uncertainty in the measured concentration of the exchange product. The noise level on the EPR signal for atomic hydrogen was equivalent to a concentration of 5 X 10l1 cmW3,while that for atomic deuterium was equivalent to a concentration of 1.2 x 10l2~ m - Thus, ~ . in the reaction D HBr, (H) was measured with an uncertainty of between 25 and 50%, while in the reaction H DBr, the concentration of deuterium was such that only an upper limit for it could be given. In comparison with these uncertainties, those introduced due to our lack of knowledge of the true rate constants and due to uncertainties in reactant atom concentrations are of minor importance. For example, the standard deviations for (k2a h2b) and for k4, listed in Table I, introduce an uncertainty into h2b of only 5%. The error in (H)o/(H)amounts to f 2 % , and this introduces an uncertainty of only f 3 % into h2b. From the measured rate constants, the branching ratios can be estimated as
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I
I
35
40
L,
30
I000/T
1
(KI
+
+
Figure 2. Arrhenius plots (In k v s . ?-I) for H HBr (0),H DBr (O), D HBr (e),and D 4- DBr (W). The lines marked (a),(b), (c), (d) are BEB0I0 estimates for H HBr, H DBr, D 4-HBr, and D 4-DBr, respectively.
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Measurements of (H) and of (D) made while studying the reactions D + HBr and H DBr are listed in Table 11. From these measurements kzb was estimated, a t 295 K, as
+
k2b Q 3.9 X
IO-l4
cm3 molecule-1 s-1
(7)
and ksb estimated as k3b
= (1.3 k 0.4) X
cm3 molecule-l s-l
(8)
kza/k2b > 69
(9)
and k3a/k3b
= 137(-32
+ 60)
It is clear that abstraction is overwhelmingly dominant at room temperature. Discussion A comparison of the rate constants for the reaction, H HBr H2 + Br, obtained in this study with those obtained in several of the more recent indirect investigations, is shown
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The Journal of Physical Chemistry, Vol. SO, No. 14, 1976
1524
H. Endo and G.P. Glass
TABLE 11: Measurements of the Exchange Rate Constants D t HBr (HBr)o
(D)o
(Wo
(D)t
iO14 molecule/cm3
2.19 2.19 1.05 1.05 1.05 1.93 1.66 1.66 1.66
1012molecule/cm3
2.13 2.13 2.18 2.18 2.18 1.34 2.89 2.89 2.89
t , ms
1.13
2.40 1.66 5.40 1.50 1.44 2.90 1.45 1.31 2.90 1.54 1.26 2.90 1.27 0.62 3.06 0.83 1.38 6.05 1.94 1.17 6.05 1.55 0.94 6.05 1.08 k3b = (1.31 f 0.38) x 10-14 cm3 molecule-l s-1
1.94
0.80 k2b
+
in Figure 3. All of the previous estimates were made either from measurements on the back reaction, or from measurements of the ratio of k l to the rate constant for the reaction, H Brz HBr Br. The expression k = 2.77 X exp(-2570/RT) cm3 molecule-l s-1, determined from this study, fits all of the data within a factor of 2 over the entire temperature range 230-1673 K. The only previous measurement of kinetic isotope effects in the HzBr system was made by Timmons and Westonll who studied the reactions Br Hz, Br HD, Br Dz, and Br HT. Over the temperature range 438-623 K, the ratios of the second-order rate constants were estimated by them as k(Br
+
-
+
+
+
The Journal of Physical Chemistry, Vol. 80, No. 14, 1976
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