570
ARTHURLEVY
Vol. 62
THE HIGH TEMPERATURE KINETICS OF THE HYDROGEN-BROMINE REACTION1 BY ARTHURLEVY Battelle Memorial Institute, Columbus, Ohio Received November 19, 1967
The steady-state reaction of HZand Brz has been studied in a flow system between 600 and 1470°K. The low temperature mechanism of Christiansen, Herzfeld and Polanyi, and therefore the equations of Bodenstein and Lind’s original studies, are shown to be valid at temperatures approaching flame temperature. The equations for k,,, and k z obtained from this study are k e x p = 6.52 X l O I 4 e-40800/RTand kz = 2.04 X 10l2T’h e-17z80’RT cc./mole second.
Introduction Bodenstein and Lind’s study of the kinetics of combination of H2 and Br2 in the range 200-300” and the ensuing explanation of the kinetics2-4 have become a classic example of a system whose rate and mechanism are firmly es$,ablished by experiment and theory. This reaction has taken on more importance in recent years with the improved developments in flame propagation theory. The H2-Br2 flame reaction is the flame system most applicable to the various flame theories because it is basically simpler than any other two-component flame system. The reaction has a low heat of formation for HBr, 8.7 kcal./mole, and therefore has a low flame temperature; the theoretical maximum for a stoichiometric mixture is 1660°K. Added to this, the kinetics of this system are well known a t low temperatures and are less complicated than other flame systems because only straight chains are involved. For these reasons, there has been great interest recently in the H2-Br2 flame reaction. Mathematical models of the H2-Br2 flame are being investigated by Hirschfelder and ~o-workers,~ von KBrmBn, Penner and co-workers,O Gilbert and. Altman,? and Eyring and eo-workers.* Experimental investigations of the H2-Br2 flame have been conducted by Cooley and A n d e r ~ o n . ~Britton and DavidsoiilO and Plooster and Gamin1’ have investigated the autoignition of H2-Br2 mixtures in a shock tube. In general, the Christiansen, Herzfeld and Polanyi (CHP) mechanism for this reaction is ex(1) This research was supported by the United States Air Force under Contract Nos. A F 33(038)-12656 and AF 33(616)3359, monitored by Aeronautical Research Laboratory WCRRC, Wright Air Development Center. Presented in part a t the 132nd National Meeting of the American Chemical Society, New York City, September, 1957. (2) J. A. Christiansen, Kg1. Dansk. Videnskab. Selsk., Math.-fys. Medd, 1, 14 (1919). (3) K. F. Herzfeld, A n n . Physik, 66, 635 (1919). (4) M. Polanyi, Z. Elektrochem., 2 6 , 50 (1920). (5) J. 0. Hirschfelder and C. F. Curtiss, J . Chem. Phya., 17, 1077 (1949); THIS JOURNAL, 66, 774 (1951); J. 0. Hirschfelder, C. F. Curtiss, R. B. Bird and E. L. Spots, “The Kinetic Theory of Gases and Liquids,” John Wiley and Sons, Inc., New York, N. Y., 1954; E. S. Campbell and J. 0. Hirschfelder, Univ. of Wisconsin Naval Research Laboratory Report CF-2108, NORD 9938, Nov. 1953 (AD 24327). (6) T. von K&rm&n,9. S.Penner and G. M i l l h , Calif. Inst. Technology Technical Report No. 16, August, 1956. (7) M. Gilbert and D. Altman. Sixth Intern. Symposium on Combustion, Reinhold Publishing Corp., New York, N. Y., 1957, p. 222. (8) H. Eyring, J. C Giddings and L. G. Tensmeyer, J . Chem. Phya., 24, 857 (1956). (9) 9. D. Cooley and R. C . Anderson, I n d . Eng. Chem., 4 4 , 1402 (1952). ( I O ) D. Britton and N. Davidson, J. Chem. Phya., 23, 2461 (1955). (11) M. N. Plooster and D. Garvin, J . A n . Chem. Soc., 7 8 , 6003 (1958).
”
pected to remain unchanged a t high temperatures, but the attainment of steady-state concentrations in the flame is not expected. For this reason several studies are reported in the literature related to the time necessary to achieve steady-state equilibrium in the dissociation of bromine.12-16 The purpose of the present study has been to investigate the reaction under steady-state conditions a t as high a temperature as possible. The rate of combination of H2 and Brphas been investigated in a flow system between 600 and 1470°K. The results indicate that the CHP mechanism is unchanged between these temperatures. The Low Temperature Reaction.-Bodenstein and Lindl6 investigated the reaction H2 Br2 3 2HBr to 575°K. in a static system. Their results showed that the rate of consumption of the reactants, dx/dt, in forming HBr followed the equation
+
dx
= kex,
(a
- x)(b - 2 ) ’ h m+
&
(1)
where a and b are initial H2 and Br2 concentrations in moles/cc., respectively, x is the reactant consumed in moles/cc. (232 is the HBr formed), and m is a constant. This equation satisfied the experimental data extremely well, and the equation was shown to hold up t o 90% reaction. Bach, Bonhoeff er and Moel~yn-Hughes’~ extended the Bodenstein and Lind results to 612°K.; also using a static system, but following the consumption of Br2 spectroscopically, rather than by chemical analysis. About 13 years after the work of Bodenstein and Lind, the experimentally deduced eq. 1 was finally explained adequately. The mechanism of the reaction was developed independently and almost simultaneously by Christiansen12 Herzfeld3 and PolanyL4 An excellent summary of the Bodenstein and Lind study and the steady-state development of the rate equation is t o be found in Pease’s text.18 Using the five basic equations of the CHP mechanism in the numerical order set down in Pease’s summary, the rate equation becomes identical with eq. 1, and (12) D. Britton and N. Davidson, J. Chem. Phys., 26, 810 (1956). (13) F. A. Matsen and J. L. Franklin, J . A m . Chem. S o c . , 72, 3337 (1950). (14) S. W. Benson, J . Chem. P h y s . , 20, 1605 (1952). (15) H. B. Palmer and D. F. Hornig, ibzd., 26, 98 (1957). (16) M. Bodenstein and S. C. Lind, Z . physzk. Chem., 67, 168 (1907). (17) F. Bacb, K. 9. Bonhoeffer and E. A. Rfoelwyn-Hughes, 2. phyaik. Chem., 27B,71 (1934). (18) R. N. Pease, ”Equilibrium and Kinetics of Gas Reactions,” Princeton Univ. Press, 1942, pp. 112-121.
May, 1058
HIGHTEMPERATURE KINETICSOF
THE
HYDROGEN-BROMINE REACTION
57 1
and k3 % = rn
= 4.2
Bodenstein and Lind originally assigned a value of 5 to m, but a more precise check indicated that 4.2 was a better value, and that m was constant, a t least over the temperature range of 0 to 300°.19 Application to High Temperature Kinetics.Assuming that the low temperature mechanism is unchanged a t high temperatures, some changes must be made in the low temperature rate equation to take into account the high degree of dissociation of bromine. As ordinarily shown in the discussion of this mechanism, the bromine atom . concentration is expressed in the form Br = K’h (BrZ)’/z= K’/z (b
- %)‘/a
(44
At high temperatures the high dissociation of bromine must be accounted for in the dissociation equation so that
Accounting for the high dissociation of bromine at elevated temperatures, the rate equation becomes
dt
k3
X
%+b--2 (5)
.
The integrated forms of this equation are shown in Appendix I. The equation used for the equilibrium constant for the dissociation of bromine is derived from the National Bureau of Standards’ measurements.2o Expressing concentrations in moIes/cc. K = 2.808 e-46210/RT (6) Over the temperature range of these studies, this is a variation in K by a factor of almost lo9moles/cc., K = 9.437 X 1O-I’ moles/cc. a t 600°K. and 2.445 X lo-’ moles/cc. a t 1400°K. Experimental Apparatus.-An all-glass flow system was constructed for this study in the manner outlined in Fig. 1. The system is divided into three sections, the mixing section, the reaction section and the analysis section. The mixing section is made up of four separate lines, labeled by the flowmeters associated with each line as F l , F2, F3 and F4. Lines F l and F2 are referred to as the Brp lines, and F3 and F4 as the Hp lines. The flowmeters were all-glass, Emil Greiner Predictability Flowmeters. The furnace was a firebrick-enclosed volume, heated by four silicon-carbide Globar units, connected in series with a 200-volt variable transformer. Temperatures were maintained constant to 1 4 ’ with a Leeds and Northrup model C potentiometer-controller. Temperatures were measured with chromel-alumel and platinum-lO% rhodium/platinum thermocouples. Enclosed in the furnace volume were two glass coils for preheating the gas mixtures from the bromine and hydrogen lines, a “jet mixer,” and the reactor. Pyrex was used for studies below 850”K., and Vycor for studies above this temperature. The “jet mixer” was designed according to the recommendations of Johnston and Yost.21 The reactor (19) M. Bodenstein and G . Jung, 2. p h y s i k . Chem., 121, 127 (1926). (20) National Bureau of Standards. “Calculated Values of Chemical Thermodynamic Properties,” Series 111, Vol. I, March 31, 1947, to June 30, 1949. (21) H. 8. Johnston and D. M. Yost, J . Chem. Phys., 17, 386 (1949).
U
Fig. 1.-Flow system for studying the H?-Br2 reaction at elevated temperatures: F, flowmeters; 111, manometers; B.G., Bourdon gage; B, bromine saturator; T, traps. volume was calibrated to include the mixer volume. Two reaction volumes were used. The Pyrex reactor was a length of 4 mm. i.d. tubing with a total volume of 31.3 cc. The Vycor reactor was 3.1 mm. i.d. tubing, 4.96 cc. volume. The reactor was made as a tube of uniform diameter to assure continuous passage and removal of reaction gases without stagnation or recirculation. The exit gases were immediately cooled by striking against the wall of a water-cooled “cold-finger” assembly in the wall of the furnace. It is quite obvious that the reaction volume calculation is dependent upon complete and fast mixing of the gases entering into the jet miser and fast cooling of the gases leaving the reaction space. The analysis section was also used to collect the reaction products (HBr, Brz), and was a conventional high-vacuum system. Pyrex wool, packed in the U-traps, prevented frozen crystals of Brp and HBr from being transported out of the cold traps by the high flow of nitrogen.22 Reagents.-Nitrogen and hydrogen (Matheson, Coleman and Bell) were prepurified grades. Nitrogen was passed over heated copper turnings and silica gel, and hydrogen was passed through a Deoxo purifier and silica gel before use. To aid in diluting the hydrogen mixtures, premised cylinders of Hp-Np mixtures (Matheson, Coleman and Bell) were also used. These mixtures were analyzed by the supplier; a check on one cylinder, made by complete reaction of some of the gas with excess bromine, agreed with the suppliek’s analysis. Bromine (Mallinckrodt, A.R. grade) was distilled through CaHp directly into the bromine saturator. Procedure.-Bromine was picked up and passed into the gas stream by passing nitrogen (viaF2) over the bromine and mixing it with additional nitrogen (viaF1) in the mixing bulb. Hydrogen was introduced via F4 and mixed with nitrogen via F3. The bromine-nitrogen and hydrogen-nitrogen mixtures were preheated separately in the furnace, then mixed in the jet mixer, and passed through the reactor. The reaction products were immediately chilled on their way out of the reactor and then passed through the upper manifold for about 15 minutes to await complete equilibration in the bromine pick-up system. When conditions were stabilized, the gases leaving the reactor were passed through the lower manifold and the period of collection timed. Pressure in the system during the runs was usually 15 to 20 mm. above atmospheric. The bromine and hydrogen bromide were separated by standard vacuum, fractional condensation techniques, and quantities of each gas were measured as gas volumes. Pressures were read on a glass Bourdon gauge. The bromine concentration was determined from the sum of the unreacted bromine plus one-half the hydrogen bromide formed. The bromine flow rate waR partially controlled by the flow of NZin F2 and by fixing the saturator temperature. The residence time was calculated from the total flow rate at furnace temperature, divided by the reaction volume.
Experimental Results Table I is a partial tabulation of the experimental data arranged in order of increasing reaction temperature. The data have been chosen to show representative concentrations, residence times and rate constants obtained in these studies. The integrated form of eq. 5 with its two solutions for (22) M . Shaphered, 8. M. Rock, R. Howard and J. Stormes, Anal. Chem., 23, 1431 (1951).
ARTHURLEVY
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Vol. 62
TABLEI REPRESENTATIVE TABULATION OF EXPERIMENTAL DATA Temp., OK.
603 640
a
Concn.,a moles/cc. Brz
HZ
l/z-HBr
3.04(4.50(3.88(6.97(1.15(5.77(1.29(1.31(-
6) 6) 7) 7) 7) 8) 7) 9) 1.18(- 9) 6.22(- 9) 5.37(-10) 5.16(-10) 4.47(-10) 4.87(- 10) 6.15(-10) 9.13(-10) 3.55(-10) 3.34(-10) 3.15(-10) 4.28(- 10)
1.48(- 7) 2.27(- 9) 4.16(- 8) 2.50(- 9) 700 6.38(- 8) 3.92(- 9) 749 4.60(- 8) 2.92(- 8) 790 1.46(- 7) 1.30(- 8) 838 5.62(- 9) 1.81(- 9) 8G9 4.52(- 9) 2.37(- 9) 901 3.83(- 9) 2.14(-10) 950 2.86(- 9) 4.21(-10) 1003 8.03(- 9) 4.49(- 9) 1049 1.79(- 9) 3.78(- 10) 1100 8.59(- 10) 3.38(- 10) 1150 1.13(- 9) 4.22( -10) 1201 8.97(-10) 1.28(-10) 1250 8.42(-10) 3.45(- 10) 1299 3.65(- 10) 1.60(- 10) 1352 8.29(- 10) 8.75(-11) 1404 7.03(-10) 6.87(-11) 1453 1.09(- 9) 8.27(-11) 1477 5.94(- 10) 1.25(- 10) Numbers in parentheses refer to power of ten, Le., (-6) = 10-8.
the non-stoichiometric condition, a # b, (Appendix I) was programmed on to an IBM 650 digital computer and the rate constants, kexp and kz, were calculated from these equations. Fig. 2 is an Arrhenius plot of log kexp against reciprocal temperature of the experimental data. The line through the data was determined from a least-squares analysis of the data. At the lower right-hand portion of the figure are included the low temperature data of Bodenstein and Lind, and Bach, Bonhoeffer and Moelwyn-Hughes (these data are taken from Table XV of Pease's text18). For clarity, not all the data a t T = 1250°K. were plotted, but all are included in the least-squares analysis of the data. Discussion The equation for the line through the data of Fig. 2 is k,,, = 6.52 x 1014 e-40600*16OO/RT The equation for k2, based on a temperature-independent ratio of k 3 / h = 8.4 and on eq. 6, is derived from the kexpequation and is k , = 2.04 x
1012
T V e--172801~~ ~
The data are presented in terms of kexp in order t o compare the low temperature results with the results of the present study. The integrated forms of eq. 5 (Appendix I) do not give kexp directly, as when eq. 1 is integrated, but give k2 directly. Values of k2.-Table I1 compares rate equations for kz,arrived at by various investigators from the low temperature kinetic data and thermodynamic data. Values of kz, calculated for T = 500 and 14OOoK., are also shown in the table to aid in comparing the various equations. The agreement between the equations arrived a t from this study and those from the low-temperature studies is good. It is concluded on this basis that the steady state mechanism for this reaction is unchanged a t high temperatures.
Residence time, t , sec.
ka
11.2 2.45 1.21 1.42 0.351 .234 .0456 ,152 .117 .0901 .0727 .0448 .0517 ,0250 .0360 .0449 .0387 .0371 .0530 ,0475
4.54(4) 1.56(5) 2.46(6) 8.57(6) 2.52(7) 4.35(7) 1.42(8) 2.82(8) 9.79(8) 2.13(9) 5.92(9) 2.80(10) 3.79(10) 7.56(9) 1.97(10) 8.49(9) 4.75(9) 4.72(9) 2.78(9) 7.15(9) ..
Rate constants kex.
0.734(-1) 4 82(0) 1.45(2) 8 85(2) 3.99(3) l.lO(4) 4.72(4) 1.23(5) 6.20(5) 2.02(6) 7.64(6) 4.97(10) 9.01(7) 2.37(7) 7.93(7) 4 30(7) 3.05(7) 3.76(7) 2.68(7) 7.56(7)
TABLE I1
COMPARISON OF kp EQUATIONS Investigators and equation Cooley and Anderson* kz = 8.05 X 1010 T e-177mlRT Pease18 kz = 4.56 X 1012 T1/z e-le7s'3lRT Campbell and Hirschfelder6 k2 = 3.45 X 1010 T e-16640IRT Author kz = 2.04 X 10'1 T1/S e-17mo/RT
Value of kz, cc./mole sec. T = T = 500'K. 14OO0K. 7 . 3 3 X 106
1 . 9 5 X lOlr
6 . 8 0 X 105
1 . 9 8 X 1011
9 . 2 7 X 108
1 . 2 2 X 10"
1 2 . 6 X 106
1 . 5 4 X 1010
The Ratio k3/k4.--Within the accuracy of these data it is also concluded that k3/Ic4 is temperature independent between 600 and 1400°K. Using only the low temperature data (x's on Fig. 2) reported in Pease's text,'s the activation energy for kexp is 40,200 cal. per mole. The average energy calculated from this study is 40,600 cal. per mole, approximately 400 cal. per mole greater than the low temperature value. A small, positive value of AEd - AE3 is not improbable; therefore this difference, although within the probable error of these data, may be real. Other Reaction Steps.-Table I11 summarizes rate equations for all possible reaction steps in this reaction. The equations are taken from the calculations of Cooley and Anderson.9 TABLE I11 RATEEQUATIONSs (for units of moles/cc. and sec.) kl = 7.18 x 1012 T e-k61ao/RT Brl X - 2Br X kz = 8.05 X 1010 T e-177wIRT Hz HBr H Br ka = 2.59 X 1011 T e - l I W I R T Brz HBr Br 3. H HBr HZ Br kr = 3.08 X 1010 T e-llm'RT 4. H 5 . 2Br X -c Brz X k6 = 5.7 X 1015 HBr Brz H k6 = 9.31 X 1010 T e-417mlRT 6 . Br 7. H z + X - 2 H + X k7 = 2.00 X 1018 T e-1024m/RT 8. 2 H + X + H z + X ks = 1.1 X 1016 X -c H Br -I- X kr = 5.95 X 1012 T e-moIRT 9. HBr Br X + HBr X klo = 9 X 1016 10. H 1. 2.
+ + + + + +
+
+
---
+
+ + + + + +
+
+
.
HIGHTEMPERATURE KINETICS OF
May, 1958
0.60
0.70
0.80
0.90
1.0
1.1
1.2
THE
HYDROGEN-BROMINE REACTION
1.4
1.3
1.5
1.6
1.7
1.8
1.9
2.0
573
2.1
T
Fig. 2.-The
temperature dependence for the rate of combination of hydrogen and bromine.
Reactions 6-10 are of interest here in attempting to predict whether any new steps can become important at high temperatures. None of the specific rate constants of these reactions would be expected to reach significant values at 1400°K. If any competition were t o occur between any of the last five reactions (6-10) and the first five reactions (1-5) it would be expected from reactions 6 and 10, where . a competition for Br atoms would exist between reactions 2 and 6, and/or 2 and 10. This competition would be greater a t high temperatures due to the temperature dependency of these reactions and the increased Br-atom concentration. Since some reactions went to almost 90% completion, the increased HBr concentration would also favor reaction 6. At 1400"I
