J. Phys. Chem. 1994,98, 2105-2109
2105
Kinetics of the C a s + NO Association Reaction T. Yu and M. C . Lin' Department of Chemistry, Emory University, Atlanta, Georgia 30322 Received: October 5, 1993; In Final Form: December 14, 1993"
+
-
The rate constants for the C6Hs N O C6HsNO reaction have been measured with the cavity-ring-down method between 298 and 500 K to be k = 10-11.3s*0.06exp[(+433 f 11 l ) / q cm3/s. The effect of pressure was examined at 388 K by sextupling of the total pressure from 20 to 120 Torr, with no significant increase in the measured rate constants within the scatter of the data. This is consistent with the k/k" ratio predicted for 388 K using the known literature value of k" for the unimolecular decomposition of nitrosobenzene. Our result for CaH5 NO compares reasonably with t h e values for other R' N O association reactions.
+
+
Introduction OPTICS
The reactivity of phenyl (CsH5) radical is poorly characterized. The radical has noknown fluorescing electronicstates, wherewith the standard laser-inducedfluorescencemethod might be utilized for its detection and kinetic studies. Only limited kinetic data for its reactions in the gas phase are available in the literature; these data are based primarily on relative rate mea~urements.l-~ The reactions of C ~ Hwith S combustion species(0,Oz. OH, C ~ H Z , etc.) are believed to be critical to thechemistry of soot f ~ r m a t i o n , ~ which is still poorly understood. In a recent communication, we reported the first successful measurement of absolute rate constants for C6H5 reactions at room temperature with a variety of molecules in the gas phase.5 We employed a novel multiple-pass absorption method, referred to as the "cavity-ringdown" technique by its original developers, O'Keefe et al.6.7 The technique utilizes a high-quality optical cavity consistingof a pair of highly reflectivemirrors which allow an injected pulse of photons to oscillate within the cavity up to 2 1 X 104 timeslpulse, depending on the quality of the cavity. The technique was originally developed for spectroscopic studies of weak transitions which cannot be readily measured by the conventional multipass absorption method.6 We extended the technique for time-resolved kinetic measurements; the basic principle and the experimental procedure have been described in some detail in our recent publications.5.8 The validity of the technique for kinetic applications has also been tested with the NH2 NO reaction, whose rate constants at various temperatures have been measured by several group^.^ We will compare our data with the recently recommended value. The major focus of the present study, however, is placed on the effect of temperature on the analogous NO association reaction, C6H5 NO, the fastest phenyl reaction we have measured so far.5 The rateof this process will be compared with those of the alkyl and alkoxy radical reactions. The reactions of NO with hydrocarbon radicals in general play an important role in nitric oxide inhibited hydrocarbon decomposition reactions.
+
+
Experimental Section A. Experimental Setup. The experimental arrangement and the data acquisitionmethod are essentiallythe same as previously described588 except for the minor modification depicted below. In order to avoid coating of the photodissociation laser windows and the cavity mirrors (which sbaled the reactor tube), a small fraction of the Ar carrier gas was diverted to purge these optics. The photodissociation laser beam was split into two, crossing with the probing dye laser beam at the center of the cavity at a 15O angle 0
Abstract published in Advance ACS Abstracts, February 1, 1994.
~
LASER I RESONANT CAVITY
I
I
Figure 1. Schematic diagram of the cavity-ring-down absorption measurements.
(instead of 90' used previously). The schematic diagram of the experimental layout is shown in Figure 1. Reaction mixture was continuouslypumped through the reactor via four inlet and opposing outlet tubes, as indicated in Figure 1 by the four circles. In this manner, the photolyzed and reacted mixture could be efficientlypumped off the probed region between two laser shots. The lasers were operated at 2 Hz to assure the total removal of the reacted mixture from the reactor which has a volume of about 570 cm3. B. Data Acquisition. The basic principle of the cavity-ringdown (CRD) method, using a multimode Nz-pumped dye laser (Laser Photonics) for kinetic studies, has also been described previou~ly.~.8The method lies in measuring the cavity decay time (tc) of a dye laser pulse (FWHM = 5 ns) injected into the reactor cavity at different time intervals after the generation of the radical of interest (NHzor C6H5in the present case) employing a second, photodissociation laser (Lambda Physik, LPX 100 Excimer Laser). In the absence of resonance absorption, the photons inside the cavity have a longer decay time ( t c o )than that measured with resonance absorption by the radical ( t c ) . It can be readily shown that if thechemical decay time ( t )' of the radical is long compared with the photon decay time, the following relationship holds:5,8 l n ( l / & - l / t c o ) = B - k't'
(1)
The photon decay times are typically in the range of 10 ns (total absorption) to 30 ps (no absorption), Le., 10 ns Itc ItCo,with tco = 30 ps at 500 nm, whereas the chemical decay time of the radical usually varied between 500 and 5000 ps, depending on the concentration of molecular reactants used. In eq 1, the experimental constant B contains cavity length (50 cm), the extinction coefficient and initial concentration of the radical, and the refractive index of the reaction medium, et^.^.* The k'is the pseudo-first-order decay constant of the radical in the presence of the known concentration of the molecular reactant, [XI. k'is related to the bimolecular rate constant, k", by the equation
0022-365419412098-2105$04.50/0 0 1994 American Chemical Society
Yu and Lin
2106 The Journal of Physical Chemistry, Vol. 98, No. 8, 1994
538
~
-7
“.I”
537
Wavelength (nm)
600
300
900
1200
1500
t’(psec)
-
Figure 2. Spectrum of the NH2 A AI- 2 2B1 absorption band. The strong peak at 537.6 nm corresponds to the (1,7,0) (O,O,O) vibronic band.
k’= ko + k”[X]
0
539
538
(2)
where X = NO in the present study. ko in the above equation is the chemical decay constant of the radical measured in the absence of NO; it is a convoluted decay constant which may depend on the pumping speed of the reaction medium and on the recombination rates of the radical with itself or other photofragments. By varying the concentration of NO at a constant total pressure regulated with the Ar carrier gas (so as to maintain a constant pumping speed), one can obtain the second-order, bimolecular rate constant k”from the slope of a k‘vs [XI plot according to eq 2.58a C. Chemicals. All chemicals used in the present study were obtained from Aldrich. Both C6HsN0 and C ~ H S C O C H were ~ employed as the C6H5 radical source using 248-nm (KrF) and 193-nm(ArF) photodissociationlasers,respectively. For the NH2 NO test experiment,NH3 was photolyzed at 193nm to generate the NH2 radical. These radical sources were purified before use by standard trap-to-trap distillation employing appropriate cold baths. Themolecular reactant (NO) was purified bypassing it through a silica gel trap maintained at dry ice temperature. Ar, acquired from Specialty Gases (99.995%),was mostly used without further purification. In several experimental runs, the carrier gas was passed through a hot tube containing Cu filings to remove the trace amount of O2 which is usually present in commercially available noble gases. The purification procedure was found to be necessary for a lower grade Ar because the 0 2 impurity reacted with NO to produce NO2 in the foreline, which shortens the photon decay time pronouncedly.
+
+ NO reaction under different,excess NO concentrationconditions: ( 0 )[NO] = 0, (A) [NO] = 1.51 X 1014,(0) [NO] = 3.32 X loi4,(0)[NO] = 6.04 X lOI4, all in molecules/cm3. The slopes of these plots give the first-order decay constants, k’. Figure 3. Typical pseudo-first-order decay plots for the NHz
72
-
-
8 -
0
m
0
6 -
7
-s
100
0
200
300
400
500
600
700
[NO)(1Oi2molec/cm’)
Figure 4. k’versus [NO] at 297 I(. Linear least-squares fit yields the second-order rate constants for the NH2 + NO reaction, k”. The solid circles were obtained by varying the fraction of the Ar carrier gas to
purge the optics (see text).
+
for the NH2 NO reaction, varying amounts of NO measured accurately with a calibrated flow meter were employed with the Ar carrier gas to give a constant total pressure. Figure 3 presents some of the pseudo-first-order plots measured for the decay of NH2 in the presence of the different amounts of NO as indicated in the caption of the figure. The good linear quality of the In( 1/ t , - 1/ t c o )vs t’plots illustrates the linear relationship predicted by eq l.5 The slopes of these straight lines obtained by a standard least-squaresanalysisgive the pseudo-first-order rate coefficients, k’, for the NH2 NO reaction in the presence of the known amount of [NO]. The slope of the k’vs {NO] plot as shown in Figure 4 gives the second-order rate constant for the NH2 NO reaction, k’hH2 = (1.4 f 0.2) X cm3/s at room temperature (297 K) and 60 Torr Ar pressure. This result will be compared later with the recently recommended value. The filled circles given in Figure 4 were obtained from a test with different fractions of the total Ar carrier gas diverted for purging of the cavity mirrors and the laser photolysis windows at a constant total pressure. The purging of these optics, as mentioned before, is essential to avoid coating of these components by aromatic materials generated by the photolysis laser. The result of this test indicates that the measured NH2 decay rates are not affected by the diversion of the Ar flow by as much as 30%, as long as the concentration of NO was calculated exactly from the measured flow rate into the reaction zone through the four inlets as shown in Figure 1. B. Kinetics of the C& + NO Reaction. In the present study of the C6H5 reaction with NO, both nitrosobenzene (CsHsNO) and acetophenone (C&COCH3) were used as the C6H5 radical
+
Results A. Test of the CRD Method for Kinetic Applications. Aside from the room-temperaturerate measurementsfor C6H5reactions with a variety of molecules,S covering the values of rate constants from 2 X to 1 X lO-’5 cm3/s, we have also performed a test measurement for the kinetic applicationof the CRD method using theNH2 + NO reaction. Theoverall rateconstant for thereaction has been determined by several groups,g as alluded to earlier. Figure 2 shows the absorption spectrum of the NH;! radical formed by the 193-nm photolysis of NH3 in the narrow spectral region between 536 and 539 nm, conveniently covered by the same set of the cavity mirrors used for the C6H5 radical study. The relative absorption intensity plotted in the figure corresponds to the normalized value of l/tc to l/tco, where tc and tco,as defined above, represent the photon decay times measured in the presence and absence of resonance absorption, respectively. The strong absorption p k appearing at 237.6 nm corresponds to the band head of the A ZAl(1,7,0) X 2B1(0,0,0) vibronic transition of the NH2 radical.12 To measure the rate constant
-
+
Kinetics of C6Hs + N O Association
-
$ .-
-m Q
0.85
The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2107
. -I
0.80 ’
U
-7
-8
503
1”“* .oo
504
505
506
L
‘
I
0
507
600
300
900
1200
15CO
t (wet)
Figure 6. Typical pseudo-first-order decay plots for the C& + NO reaction under different, excess NO concentrationconditions: ( 0 )[NO] = 0, (A) [NO] = 3.27 X lo”, (0)[NO] = 6.52 X lo”, ( 0 )[NO] 2.17 x 1014, all in molecules/cm3. The s l o p of these plots give the first-order decay constants, k’. 6000 r 6ooo
0.80
-
I
-.
4500
C,H,COCH, at 193 nm h
‘0 Y
-x
2 9 8 ~ ‘OT
0
4000
3000
’
’ 60
.
‘
120
J
’
180
240
300
I
‘0
g
2000
Y
-x
1000
0
m
0
30
60
80
120‘
150
[NO](lO” molecules/cm3)
Figure 7. k’versus [NO] at 298 K (top) and 388 K (bottom). Radical sources: (0)CsH5N0, (A)CsH&OCHn. Linear least-squaresfit yields the second-order rate constants for the C,& + NO reaction, k‘’,
where the error limits represent 2ds, directly evaluated from the averaged values of the data points. In order to examine the effect of pressure, we have varied the total pressure of the system a t 388 K, with different amounts of the Ar carrier gas (whose flow rate was also accurately measured with a calibrated flow meter) from 20 to 120Torr. No significant change in the value of kJ$ was noted in the test within the scatter of the data as presented in Table 1. Also included in Figure 8 is the result of Preidel and Zellner,14 presumably for the C& NO reaction: k’$ = 1611.4exp(+300/T) cm3/s, which is about a factor of 2 smaller than our value throughout the range of temperature studied. Preidel and Zellner employed the conventional multipass absorption method to monitor CsHs with a C W Ar+ laser operating a t 488 nm, a t which no absorption peak was reported by Porter and Ward.” The species monitored by Preidel and Zellner, therefore, might not be the phenyl radical. These authors also failed to measure
+
2108 The Journal of Physical Chemistry, Vol. 98, No. 8,199‘4 TABLE 1: Measured Bimolecular Constants for C a s + NO T/K P I T o r f IN01/(lO+I3molec/cm3) k”d(lO-I1 ~ m ’ / s ) ~ 298‘ 323‘ 35OC 388 388 388 423c 463d 500f
20 20 20 2W.d 60d 12od 20 20 20
0-25 0-14 0-30 0-12 0-2 1 0-2 1 0-2 5 0-1 1 0-30
Yu and Lin
TABLE 2 Comparison of the Rate Constants for R Reactions at Room Temperature R
1.87 f 0.16 1.84 f 0.28 1.56 f 0.18 1.39 f 0.38 1.70 f 0.38 1.85 f 0.46 1.06 f 0.14 1.44 f 0.34 0.98 f 0.15
3
Total pressure, mostly Ar. Errors represent 2u’s. C6HsNO at 248 nm. C6HsCOCH3 at 193 nm. a le-10
I
le-12’ 1
I
3
2
4
1000/T
Figure 8. Arrhenius plot for C6Hs
k/(10-ll cm3/s)
+ NO:
(0)20 Torr, (A) 60 Torr, (0)120 Torr. Dashed curve: result of ref 14.
the kinetics for seven of nine reactions investigated (except NO and N02).14 Several of the seven reactions which they failed to measure could be determined with the CRD method.5
Discussion
In this work, we have tested the applicabilityof the CRD method for kinetic investigations using a well-studied system: NH2 NO.9 We have also measured the absolute rate constant for the reaction of the phenyl radical with N O in the temperature range 298-500 K. At 297 K, the rate constant for the NH2 N O reaction was determined to be (1.4 f 0.2) X 10-11cm3/s, which agrees closely with the recently recommended value: 1.6 X 10-11 cm3/s with a reliability limit of f0.3 for A log k at room temperature, independent of p r e s ~ u r e .This ~ agreement is most reassuring and has, thus, confirmed the general applicability of the CRD method not only to spectros~opic6*~ but also to kinetic studies, as has already been demonstrated in our earlier communicationss.8 for phenyl radical reactions. For the kinetics of the CsH5 N O reaction, we have shown that at 20 Torr Ar pressure the bimolecular rate constant can be effectively represented by the Arrhenius equation
+
+
+
with a “negative activation energy” of about 0.8 kcal/mol. The observation of a small negative activation energy for association and recombination processes is nowadays quite common on account of the improved reliability in acquiring more accurate kinetic data through the use of laser diagnostics.9J5 The negative activation energy observed for a radical recombination reaction occurring without an energy barrier arises from the variation in its transition-state structure which becomes tighter at higher temperatures.16 We have also investigated the effect of pressure on the CaHS + N O reaction at 388 K by varying the total pressure of the
1.87 f 0.16 1.40 f 0.2 3.6 4.4 3.4 1.2 1.7 f 1.0 1.1 1.83 f 0.20 1.76 f 0.20
M*(eu). -2.81 -3.38 -1.51 -1.11 -1.62 -3.69 -3.00 -3.85 -2.85 -2.93
+ NO ref
this work this work 9 9 9 18 19 20 19 19
The standard state is 1 mol/cm3 of the ideal gas.
system from 20 to 120 Torr. Within the scatter of our data, no strong effect was observed in the pressure range investigated at this temperature. This is consistent with the result of an RRKM calculation using the high-pressure rate constant for the unimolecular decomposition of nitrosobenzene reported by Choo et al.,17 km = 1015.4exp(-24700/T) S-I; at 388 K, the calculated value is k / k m = 0.9998 at 20 Torr Ar pressure. Experimentally, the absence of pressure effect and the independence of the precursors suggest that the phenyl radical, which might be internally excited in its nascent states, had been effectively thermalized within SO ps after photodissociation when kinetic measurements were initiated. In theory, the recombination rate constant for the reaction of vibrationally excited phenyl radicals would exhibit a stronger pressure effect than the thermalized ones because of the expected larger redissociation rates a t lower pressures. The magnitude of our rate constant for C ~ H S N O compares reasonably with other rate constants for the R N O R N O association reactions, as summarized in Table 2. Our roomtemperature value, k = 10-10.73 cm!/s, agrees closely with that predicted by Choo et al.17 based on the nitrozobenzene decomposition data, k = 10-10.8*0.5 cm3/s. The values of the listed rate constants give the entropies of activation, A S ,from -1.1 to -3.9 eu, based on the well-known relationshiplo
+ +
-
assuming E, = 0 for all cases. The values of pS* are typical for radical-radical association/recombination reactions. It should be noted that pS* for reactions with gas-kinetic collision rates is approximately +2 eu.
Acknowledgment. The authors gratefully acknowledge the support of this work by the Division of Chemical Sciences, Office of Energy Sciences, DOE, under contract no. DE-FGOS9 1ER14192. References and Notes (1) Kerr, J. A.; Moss, S. J. CRC Handbook of Bimolecular and Termolecular Gas Reactions; CRC Press: Boca Raton, FL, 1981; Vol. I, p 369. (2) Fahr, A.; Mallard, W. G.; Stein, S.E. 21st Symp. Int. on Combustion [Proceedings]; The Combustion Institute: Pittsburgh, PA, 1986, p 825. (3) Fahr, A.; Stein, S. E. 22ndSymp. Int. on Combustion [Proceedings]; The Combustion Institute: Pittsburgh, PA, 1988, p 1023. (4) Glassman, I. Combustion, Znded.;AcademicPress: New York, 1986. ( 5 ) Yu, T.; Lin, M.C. J . Am. Chem. Soc. 1993, 115, 4371. (6) O’Keefe, A.; Deacon, D. A. G. Reu. Sci. Instrum. 1988, 59,2544. (7) OKeefe, A.; Scherer, J. J.; Cooksy, A. L.; Sgeeks, R.; Heath, J.; Saykally, R. J. Chem. Phys. Lett. 1990, 172, 214. (8) Lin, M. C.; Yu,T. Inr. J. Chem. Kinet. 1993, 25, 875. (9) Baulch, B. L.; C o b , C. b.; Cox,R. A.; Esscr, C.; Frank, P.; Just, Th.; Kerr, T. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J. Phys. Chem. Ref. Data 1992, 21, 411. (10) Laidler, K. J. Chemical Kinetics, 3rd ed.;Harper and Row: New York, 1987. (11) Back, M. H.; Laidler, K. J. Can. J. Chem. 1966, 44, 215. (12) Dressler, K.; Ramsay, D. A. Phil. Trans.Roy. SOC.1959,A251,553.
Kinetics of C6Hs + NO Association (13) Porter, G.;Ward, B. Proc. Roy. SOC. 1965, A287,457. (14) Preidel, M.;Zellner, R. Ber. Bunsenges. Phys. Chem. 1989, 93, 1417. (15) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr, J. A.: Troe. J. J . Phvs. Chem. R e t Dutu 1992. 21. 1125. (16) Wardlaw, D. M.;Marc&, R. A. J . Phys. Chem. 1985, 83, 3462; 1986, 90, 5383.
The Journal of Physical Chemistry, Vo1. 98, No. 8, 1994 2109 (17) Choo, K.Y.;Golden, D. M.; Benson, S.W. Int. J. Chem. Kinet.1975, 7, 713. (18) Davits, J. W.; Green, N. J. B.; Rlling, M. J. J . Chem. SOC.,Furaduy Trans. 1991,87, 2317. (19) Vakhtin. A. B.: Petrov. A. K.Chem. Phvs. 1991. 149. 427. (20) Jodkowski, J. T.;Rata&ak, E.; Sillme& A.; Pagssbcrg,P. Chem. Phys. Lett.1993, 203, 490.
