T H E
J O U R N A L
O F
PHYSICAL CHEMISTRY Registered in U . 8. Patent Oflce @ Copyright, 1970, by the American Chemical Society
VOLUME 74, NUMBER 19 SEPTEMBER 17, 1970
Radical Reactions in an Electron Spin Resonance Cavity Homogeneous Reactor
by A. A. Westenberg,* N. deHaas, and J. M. Roscoe Applied Physics Laboratory, The John8 Hopkins Uniwrsity, Si2zer Spring, Maryland 80920
(Received May 7 , 1970)
Experiments are described using a homogeneous reactor entirely contained within the detection cavity of an esr spectrometer. This permits atom and radical concentrations in the homogeneous reaction zone to be directly measured. The effective reactor volume was calibrated using the room temperature 0 C ~ H reZ action as a known “standard” rate constant, and the volume obtained was very close to the geometric volume. Direct measurements on the reaction 0 OH -P O2 H (k4) were then carried out with the reactor operated a t temperatures in the range 228-340’K. The results gave kb = 2.0 f 0.3 X l O l a cma mol-1 see-’ independent of temperature, in good agreement with previously reported values. Attempts to measure OH OH HzO 0 were unsuccessful, for reasons which are discussed.
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Int roduction The idea of a homogeneous (“well-stirred”) reactor was apparently first developed by Denbighl as a means of measuring reaction rates in liquids: and the basic principles were later summarized by Denbigh and Page.2 After a number of engineering applications of this concept to the determination of overall rates in combustion reactions,3 the well-knownwork of Kistiakowsky and Volpi4 appears to be the first use of a homogeneous reactor for the determination of rate coefficients of elementary gas reactions. A few other studies by this technique have been reported subsequently.616 Electron spin resonance (esr) spectroscopy has now been developed into a practical and rather versatile method for the quantitative measurement of gas-phase atom and radical concentrations, and a number of apAll of these plications to kinetics have been studies utilized esr as a detector in a linear (one-dimensional) fast-flow system. The work of Mulcahy, et is the only previous report of the use of esr with a homogeneous reactor, where esr was used to monitor inlet and outlet atom concentrations in a double cavity arrangement. All previous esr work in both linear and
homogeneous reactors has been concerned with measurements of atom-molecule reaction rates, except for the study of OH OH 4HzO 0 in this 1aboratory.l’ It seemed that the use of a homogeneous reactor entirely contained within an esr detection cavity might offer
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* To whom correspondence should be addressed. (1) K. G. Denbigh, Trans. Faraday Soc., 40, 352 (1944). (2) K. G. Denbigh and F. M. Page, Discuss. Faraday Soc., 17, 145 (1954). (3) J. P. Longwell and M. A . Weiss, Ind. Eng. Chem., 47, 1634 (1955). (4) G. B. Kistiakowsky and G. G. Volpi, J . Chem. Phys., 27, 1141 (1957). (5) E. L. Wong and A. E. Potter, ibid., 43, 3371 (1965); Can. J. Chem., 45, 367 (1967). (6) M. F. R. Mulcahy, J. R. Steven, and J. C. Ward, J . Phys. Chem., 71, 2124 (1967). (7) A. A. Westenberg and N. deHaas, J. Chem. Phys., 50, 707 (1969), and preceding papers. (8) J. M. Brown and B. A. Thrush, Trans. Faraday Soc., 63, 630 (1967). (9) K. Hoyermann, H. G. Wagner, and J. Wolfrum, Ber. Bunsenges. Phys. Chem., 71, 599 (1967). (10) M. J. Kurylo and R. B. Timmons, J . Chem. Phys., 50, 5076 (1969). (11) G. Dixon-Lewis, W. E. Wilson, and A. A. Westenberg, ibid., 44, 2877 (1966).
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A. A. WESTENBERC, N. DEHAAS,AND J. 14. ROSCOE
some possibilities in the difficult area of atom-radical and radical-radical rate measurements. The work on the OH OH reaction'l was done in a linear reactor with movement of the entire esr cavity (and associated magnet) to establish the time (spatial) dependence of the OH decay. This was not only tedious and difficult, but would be practically impossible at other than room temperature. Another important consideration when attempting to deal with extremely fast atom-radical reactions ( k > 10la cma mol-' sec-') is the difficulty of separating mixing time from reaction time in a linear flow system before concentrations drop too low for adequate measurement, a particularly vexing problem using esr, where spatial resolution (-2 cm) is not especially good. The present paper outlines the principles for operating an esr cavity as a homogeneous reactor and gives some results with such a system.
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Reactor Theory
(0)o. NO? was then metered into the central injector, and since the rate constant for H NOZis a t least 10 times larger than that for 0 NOz, the former reaction occurred practically to the exclusion of the latter, as was noted earlier. The OH generated in reaction VI then reacted homogeneously with the 0 present by reaction IV (and with itself to a slight extent by reaction V) giving esr readings (0)and (OH). The governing relation for 0 loss in the reactor was then
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Results for Radical-Radical Reactions
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3435
ESRCAVITYHOMOGENEOUS REACTOR
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so that
I n practice the second term above was completely negligible compared to the first, so that kq could be determined by relative measurements of the 0 signal with the NO2 off and on, and an absolute esr measure of (OH) when the NO2 was flowing. (The absolute OH required the NO calibration procedure which has been described,2aand the details for carrying this out a t other than room temperature are given in the Appendix.) Knowledge of k5 was thus not required for (18) A. A. Westenberg and N. deHaas, J. Chem. Phys., 50, 2512 (1969). (19) M.A. A. Clyne, “Ninth Symposium on Combustion,” Academic Press, New York, N. Y., 1963,p 211. (20) F. Kaufman and F. P. Del Greco, ibid., p 659. (21) F. Kaufman, Ann. Geophys., 20, 106 (1964). (22) J. E.Breen and G. P. Glass, J . Chem. Phys., 52, 1082 (1970). (23) A. A. Westenberg, ibid., 43, 1544 (1965). The Journal of Physical Chemistry, Val. 74, No. 19,1970
A. A. WESTENBERG, N. DEHAAS, AND J. M. ROSCOE
3436 Table 11: Summary of Measurements of Helium Carrier. V = 67 cm3 Temp, K-
--------
Pressure, mm
IC4
for 0
+ OH
+
HS
+ H in the Homogeneous Reactor. k4,
Inlet flow rates, om8 atrn sec-1-
H2
0 2
NO2
Total
(O)O/(O)
(OH),
em’ mol-]
mol/cma
5ee-1
x
228 It 2
0.71 0.70 0.70 0.70
O. 080 0.080 0.100 0.100
0.024 0.024 0.034 0.034
0,047 0.062 0.094 0.094
1.41 1.43 2.29 2.29
2.12 9.00 8.26 12.5
0.67 X 5.88 8.88 14.2
2.9 2.4 2.3 2.3
298
0.55 0.56 0.60 0.63 0.63 0.63 0.64 0.64 0.68 0.76 0.88 0.88
0.070 0.070 0.068 0.072 0.072 0.090 0.072 0.072 0.081 0.105 0.069 0.069
0.014 0.021 0.025 0.020 0.020 0,029 0,020 0,020 0.032 0.027 0.027 0.027
0.034 0,043 0.065 0.043 0.046 0.049
0.045 0,055 0,051 0.044
1.27 1.29 1.32 1.88 1.88 1.38 1.37 1.37 1.33 1.43 2.02 2.01
3.30 4.29 4.29 5.42 7.58 2.92 16.9 6.59 2.70 6.95 11.2 3.61
2.85 4.78 4.25 9.63 16.9 3.03 20.7 6.96 2.08 6.01 13.5 3.45
2.3 1.9 2.0 1.7 1.4 1.6 2.0 2.1 1.8 2.1 2.1 2.1
0.40 0.63 0.63 0.70 0.71
0.082 0.082 0.082 0.079 0.079
0.023 0.023 0.023 0.025 0.025
0.016 0,024 0,029 0 038 0.045
1.63 1.64 1.64 0.92 0.93
1.88 2.28 3.72 6.26 10.7
1.90 2.48 4.17 5.68 10.8
2.4 1.7 2.2 1.6 1.6 Av 210& 0.3 x 1013
340 f 4
...
...
I
the measurement of IC4, which is a very desirable feature of this method. A summary of the runs made at three temperatures over a modest range is given in Table 11. The range of flow variables and pressure was rather restricted, mostly because of the necessity of retaining sufficient OH signal for a good integrated intensity measurement. But within the accessible ranges, the results for k4 are rather uniform and show no significant temperature dependence. Averaging the runs at all temperatures together gives IC4 = 2.0 0.3 X 1013,in good agreement with the results of Clynelg and KaufmanZ1discussed earlier. The lack of temperature dependence found by Clyne is also verified over a somewhat larger range. An essentially zero activation energy would be expected for such a fast reaction. The value for IC4 derivedZ4pz5from the extensively studied reverse reaction and the equilibrium constant is 1.3 X 1013with zero activation energy. This is not too significant a comparison, however, since the compilation for k--l itself depends heavily on the data of Clyne and Xaufman for IC4 and the equilibrium constant at the low temperature end. Our present data for kq thus confirm that the H 0 2 composite rate constant k-4 = 2.2 X 1014exp( - 16,80O/RT) derived using this low-temperature k4 anchor is probably valid. Attempts to measure k5 and its temperature dependence were not successful. Two different methods were used which should have worked in principle, but
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The Journal of Physical Chemistry, Vol. 74, No. IO, 1070
1013
there were difficulties which will be noted. With HZ in the discharge with helium, the main inlet flow contained only H in this experiment. NO2 was then metered into the central injector, generating OH by reaction VI, followed by reactions V and IV. Assuming these are the only reactions occurring and that all rates are finite, the homogeneous reactor equation for NO2 is [(NOJo - (NOJ]V =
[ V N O J / V - (NO*)]V = ka(H)(NOz)V (6) where N = P / R T is the total molar concentration. The equation for H atom (with steady-state 0 atom) is [(H)o - (H)]V = [ka(H)(NOz) - k ~ ( 0 H ) ~ l V(7) Since there is no OH in the inlet flow, its equation is -(OH)V = [-kO(H)(NOz)
+ 3ks(OH)2]V
(8)
Method I. Addition of eq 6 and 8 gives
which is the correct form when OH generation by (VI) is assumed to be not infinitely fast. When ks is as(24) R. M. Fristrom and A. A. Westenberg, “Flame Structure,” McGraw-Hill Book Co., New York, N. Y., 1965, p 361. (25) D. L. Baulch, D. D. Drysdale, and A. C. Lloyd, High Temperature Reaction Rate Data Report No. 3, Department of Physical Chemistry, The University of Leeds, England, April 1969.
RADICAL REACTIONS IN
AN
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ESRCAVITYHOMOGENEOUS REACTOR
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Table I11 : Summary of L'leasurements of k6 for OH OH + HzO in the Homogeneous Reactor. Helium Carrier. V = 67 em8
+ 0 at Room Temperature
Method I k6,
Pressure, mm
7 -
Ha
Inlet flow rates, am8 atm sec-'NO1
Total
sea -1
52 x 59 37 56 115 63 106 93 59 78 118 100 66 107 107
0.61 1.47 0.61 1.72 1.20 0.68 1.88 1.11 0.84 0.86 2.27 1.23 1.08 2.00 2.75
0.021 0.039 0.026 0,034 0.078 0.061 0 * 091 0.099 0,053 0.076 0.098 0,094 0.065 0.088 0.090
0.09 0.06 0.09 0.08 0.09 0.07 0.07 0.07 0.09 0.09 0.09 0.09 0.07 0.07 0.07
0.26 0.30 0.30 0.34 0.39 0.56 0.58 0.58 0.63 0.67 0.68 0.70 0.73 0.75 0.75
cma mol-'
(OH), mol/cma
1.5 X 10l2 2.1 3.9 2.0 1.2 3.3 1.6 2.4 2.4 2.1 1.4 2.0 3.2 1.6 1.6
Method I1 Pressure, mm
0.41 0.41 0.43 0.55 0.55 0.66 0.67 0.67 0.88
--Inlet H9
0.12 0.12 0.10 0.10 0.10 0.11 0.11 0.11 0.11
flow rates, om8 atm
(OH),
(Hh,
880-1-
NOa
Total
0,048 0,063 0,037 0.065 0.065 0,048 0.047 0.068 0.037
1.22 1.23 1.22 1.23 1.23 1.56 1.55 1.58 1.13
mol/cma
10 17 10 21 33 23 16 11 15
x
sumed to be infinite, (NO2)= 0 (providing it is not added in excess), and the term V N O j V / V is simply equivalent to an inlet (OH),,. Since it was not possible to measure the residual (NO2) in this experiment, a direct test of this assumption could not be made. A large number of experiments were performed at room temperature with (NOz) taken to be zero, however, so that kg could be evaluated simply from the metered flow rate of NO2 and V , together with an esr measurement of (OH). The results were not very satisfactory, as shown in Table 111. The values of ks tend to be higher than our earlier value" of 1.5 X 10l2and to increase with decreasing V N O ~This . is the behavior to be expected when neglect of the (NO2) in eq 9 is not justified; ie., a residual (NO2)would be more significant at low values of V T N so~that ~ its neglect would lead to a relatively larger apparent IC,. I n other words, the effect of finite combined with appreciable mixing time for the entering NO2 means that the frequent practice of computing initial (OH), from the inlet NOz rate may tend to overestimate the effective (OH),,. I n
10-10
(E/ W ) o
mol/cm'
0.57 0.29 0.67 0.32 0.32 0.59 0.56 0.35 0.47
87 X 10-l2 86 56 70 93 89 88 90 37
ks, cma mol-& 800-1
0.77 X 10la 2.7 1.5 3.5 3.2 1.4 1.o 1.1 4.1
the present experiments this leads to a high apparent lcs, while in linear reactor experiments an overestimate of (OH)o would tend to underestimate k6 for a given measured (OH)-' slope. The latter point had been noted earlier1' in attempting to understand the discrepancy between our value of ks obtained in a linear reactor and the lower values of Kaufman and Del Greco.20 The overestimate of (OH),, by the NO2 rate has also been noted by Breen and Glassn22 Another possible cause of the difficulty might be loss of OH on the walls, particularly due to the deposit NO2 formation which is known to occur with the H system. This deposit (presumably ",NO1) was noted previously11 in this laboratory and elsewhere, and was again apparent in the present work. It tended to concentrate around the central injector. Since the deposit is known to accentuate OH loss, it may have been a contributor to the high values of k6 measured. have also invoked a wall loss in the Breen and analysis of their linear reactor data, which gave a kt, lower than either ref 20 or 11.
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The JOUTWEof Physical Chemistry, Vol. 74, No. 19, 1970
A. A. WESTENBERG, N. DEHAAS,AND J. M. ROSCOE
3438 Method I I . Addition of eq 7 and 8 gives
Table IV: Total Partition Functions for OH and NO as Functions of Temperature Temp,
which is an alternate form not requiring a value for initial (OH),,. The initial (H),,was obtained by esr with the NOz off, while (H) and (OH) were obtained with KOz on. No assumption was necessary about the rapidity of reaction VI, since this term cancels out. This method was also unsatisfactory, giving erratic values of i& depending on $“oa (see Table 111). It seems most likely that deposit formation and serious wall loss of OHwerelargely responsible for this behavior. Thus, the homogeneous reactor is suitable only for radical-radical reactions which are fast enough in the gas phase so that wall losses are negligible. Establishing this in a given case is difficult, and lacking independent evidence, perhaps the best indication that wall losses are not important would be a set of results consistent with an analytical model derived for zero wall loss which are independent of flow variables over as wide a range as possible. , I n some cases finite wall losses can be canceled out, as noted earlier.
Appendix For operation of the reactor at other than room temperature, in the case of reaction IV the temperature dependence of the calibration relation for determining absolute (OH) is required. The general procedure for calibrating electric dipole species such as OH against NO has been described in detaiLZ3 The integrated esr intensity is given by
OK
ZOH
ZNO
100 200 300 400 500 600 700 800 900 1000
28.4 54.2 82.8 113 143 175 206 236 268 296
292 704 1160 1632 2124 2630 3154 3702 4284 5103
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G at 8765 Mc) of the set of six -P - transitions for Let us designate it as line C. For this J = 3/2, line l(p,)ijlz = 0.634 and geff = 0.935, so that eq 11 gives
(OH)
= 1.47
(3 Lm - TOHZOH
XI’
(OH, line C) d H (12)
I n a similar manner, the relation for line “a” of NO may be derived (line “a” is the lowest field line of the nine-line J = 3/2, z ~ s / , set of NO transition^,^^ lying at 7944 G for v0 = 8765 Mc). The Boltzmann factor for the desired level is not unity in this caselZ3so the result is TNOZNO eXp(-180/TNo)
x
rrm
J0 where the terms have been defined previously.2a The last factor in eq 11 contains all of the temperaturedependent quantities. The OH lines best suited for practical intensity measurements are those for the lowest rotational level J = 3//z of the 2 ~ a / , ground state, for which the Boltzmann factor is unity. The total partition function Z for OH as function of T was derived from the appropriate thermodynamic tablesz6 and is given in Table IV. For present purposes the single OH line M , = ‘/z -t 3/2, M I = I/Z, (J = 3//2, state) of the -+ - A doubling transition was more convenient than the composite OH lines (lines A and B in the notation of ref 23) used previously. This is the lowest field line (7926
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The Journal of Physical Chemistry, Vol. 74, No. 19, 1970
XI’
(NO, line a) d H (13)
Normally the NO calibration is carried out with pure NO in the reactor at a pressure P N O , and the calibration temperature TNO may be different than the temperature TORa t which OH is measured. Combining eq 12 and 13 gives the working relation
- 180 [exp(K)l
J
XI’
(OH, line C) d H
x’I
(NO, line a) d H
(14)
(26) “JANAF Thermochemical Tables,” Dow Chemical Co., Midland, Mich., 1960.
