J . Phys. Chem. 1989, 93, 8162-8170
8162
probe field (eq 3. IC) varies slowly in time compared to its optical frequency, i.e.
a
--E(w,,t) at
O). Incoming arrows represent photon absorption while outgoing arrows represent photon emission. (vi) An incoming arrow on the left or an outgoing arrow on the right represents a photon annihilation (wj) and will contribute a factor E(w,,t) exp(-iw,t) to the diagram. Conversely, an outgoing arrow on the left or an incoming arrow on the right represents a photon creation (-wj) and contributes a factor E*(wj,t) exp(iwjt) to the diagram. The overall frequency of the term is the sum of the three interactions wj, ok,and w / with their appropriate signs. In the Feynman diagrams of Figure 2 we include also the fourth interaction at time t with E*(02,t)by an incoming arrow on the right. This represents probing the final absorption signal (eq 3.4). Registry No. ICN, 506-78-5.
Temperature Dependence of the Electronic-to-Vibrational Quenching Rate Constants of NF(b'x') X. Y. Bao and D. W. Setser* Department of Chemistry, Kansas State University, Manhattan, Kansas 66506 (Received: December 22, 1988; I n Final Form: June 9, 1989)
The temperature dependence of the quenching rate constants of NF(b) by 18 different reagents has been measured in a flow reactor over the 530-200 K range. The rate constants for 02,H2, D2, HCI, C02,and CO were fitted to an Arrhenius dependence on temperature, but the rate constants for the other molecules generally have a weaker dependence on temperature. The temperature dependence of the rate constant and the hydrogen-deuterium isotope effect for several pairs of molecules are discussed in terms of the expected exit channels for quenching by electronic-to-vibrational energy transfer.
I. Introduction There has been continued interest in the chemistry of NF(aiA;l 1435 cm-I) and NF(b1Z+;18905 cm-') because of their potential for utilization as chemical energy storage source^.^-^ In particular, the NF(b) state has been considered as a candidate for excitation-transfer laser system^.^^^ The NF(a) state can be efficiently produced by two reactions, H + NF2 and F + N3.396 Subsequent formation of NF(b) can be achieved by energy-pooling reactions from I(2P,,2),HF(v=2), or 0,(aiA).4v7-9 In addition ( I ) (a) Clyne, M. A. A.; White, I. F. Chem. Phys. Lett. 1970,26,465. (b) Cheah, C. T.; Clyne, M. A. A. J . Photochem. 1981, 15, 21. (2) Herbelin, J. M.; Cohen, N. Chem. Phys. Lett. 1973, 20, 605. (3) Malins, R . J.; Setser, D. W. J . Phys. Chem. 1981, 85, 1342. (4) (a) Pritt, A. T., Jr.; Patel, D.; Benard, D. J. Chem. Phys. Lett. 1983, 97,471. (b) Pritt, A. T., Jr.; Benard, D. J. J . Chem. Phys. 1986,85, 7159. ( 5 ) Cha, H.; Setser, D. W. J . Phys. Chem. 1987, 91, 3758. (6) (a) Coombe, R. D.; Pritt, A. T., Jr. Chem. Phys. Lett. 1978, 58, 606. (b) Habdas, J.; Wategaonkar, S.; Setser, D. W. J . Phys. Chem. 1987, 91,451. (7) Herbelin, J. M.; Kwok, M. A.; Spencer, D. J. J . Appl. Phys. 1978,19, 3750. The observations given here must be adjusted for the currently accepted NF(a) lifetime. (8) Habdas, J.; Setser, D. W. J . Phys. Chem. 1989, 93, 229. (9) (a) Hack, A.; Horie, 0. Chem. Phys. Lett. 1981, 82, 327. (b) Patel, D.; Pritt, A . T.; Benard, D. J. Chem. Phys. Lett. 1984, 107, 105.
0022-3654/89/2093-8 162$01.50/0
to these practical considerations, the NF(a) and NF(b) states offer the opportunity to study reactions of electronically excited singlet molecules. A general understanding of electronic-to-vibrational (E-V) energy transfer is particularly lacking, and the NF(a and b) states can be systematically studied and compared with the isoelectronic O2 states (a1A,;7918 cm-' and b1Z,+;13 195 cm-I) to generate a data base. Our laboratory has utilized a NF(b) source based upon the metastable Ar flowing afterglow t e c h n i q ~ e . ~ *Quenching '~ rate constants for halogens and inter-halogens5 and a comprehensive study of quenching by diatomic and small polyatomic molecules at 300 K have been reported.I0 Except for the halogens, there was no evidence for quenching by chemical reaction and the quenching mechanism was assigned as E-V transfer with formation of NF(a). In this paper, we have extended the quenching measurements to both higher (1530 K) and lower (200 K) temperature for diatomic, triatomic, and small polyatomic molecules. The deuterium isotope effect on the quenching rate constants also was studied for the following pairs of molecules: H2 vs D2, H 2 0 vs D20, C H 3 0 H vs CH30D, (CH3)2C0 vs (CD&CO, and CH2C12 vs CD2C12. The temperature dependence of the rate (10) Cha, H.; Setser, D. W. J . Phys. Chem. 1988, 93, 235
0 1989 American Chemical Society
E-V Quenching Rate Constants of NF(b'Z+) constants is generally small in accord with an E-V quenching mechanism."-14 Our data can be used to discuss the mechanism of E-V quenching for NF(b) by comparison with 02(b).11-15 Two or more quanta are likely to be activated in the acceptor molecule upon quenching of NF(b) to NF(a). The kinetic isotope effects and the temperature dependence of the rate constants are interpreted by using a modification of the formalism employed by Maier and co-workersI6 for 0 2 ( a and b) in an attempt to identify the exit channels for E-V quenching of NF(b). 11. Experimental Techniques
The NF(b) radicals were prepared by the dissociative excitation-transfer reaction between Ar(3Po,2)atoms and NF2 in a p r e r e a c t ~ r ; ~ the - I ~ quenching of NF(b) was studied by adding reagents to the NF(b) flow in a 41-mm-diameter tublar flow reactor. The Ar metastable atoms ( 1Olo atoms ~ m - were ~) generated by passing Ar through a weak discharge maintained between two hollow Ta electrodes. The NF2 was obtained from thermal dissociation of a flow of N2F4. The reaction time, At, in the flow reactor was calculated by the plug flow approximation; At = & / t u ) . To achieve temperatures above 300 K, the reactor was wrapped with heating tape plus a small amount of insulation. Low temperature was achieved by enclosing the reactor in a small rectangular box filled with solid C 0 2 . The reagent molecules were introduced into the reactor through a ring-shaped Pyrex glass inlet, which was placed -15 cm downstream from the entrance of the NF(b) flow to the reactor. Since the entire reactor, but not the prereactor, was heated (or cooled), the NF(b) and Ar carrier gas reached the desired temperature before the reagent was added to the reactor. The flow rates of reagents were measured by monitoring the pressure rise in a calibrated volume with a 0-10-Torr MKS Baratron transducer. The reliability of the Ar and reagent flow calibrations was estimated as flO%.IO The reagents used in the experiments were degassed, distilled, and stored in reservoirs as pure gases. Those gases which could not be condensed at liquid N 2 temperature were passed through traps filled with molecular sieve and cooled to liquid nitrogen temperature to remove impurities before being stored. The reagent concentration in the flow reactor were calculated from the reagent flow rate, the Ar carrier gas flow rate, the temperature in the reactor, and the total pressure in the reactor. The NF(b-X) emission was detected with a photomultiplier tube (Hamamatsu R-212) and a 530-nm interference filter with 10-nm band-pass. The photomultiplier tube was placed immediately after the furnace and masked to ensure that the gas was viewed as close to the edge of the furnace as physically possible. The signal from the photomultiplier tube was measured with an electrometer and displayed on a strip chart recorder. The interference filter viewed the (O), (1-I), and (2-2) bands at 528.9, 527.3, and 525.8 nm, respectively. The NF(b) vibrational distribution was close to Boltzmann for the present experiments.I0 The background emission intensity was established for each quenching measurement by turning off the dc discharge. Three variable-voltage transformers were used to drive the heating tapes, which were wrapped around the whole reactor and then covered with a layer of insulation. By use of the variablevoltage transformers, stable temperatures of 300-530 K were obtainable. A 2-mm-diameter Pyrex tube extended along the axis of the reactor to accommodate a chromel-alumel thermocouple. A potentiometer was used to read the thermocouple voltage
-
The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 8163 referenced to the room-temperature junction. The calibration of the thermocouple was confirmed from the boiling and freezing points of several fluids. The temperature from the reagent inlet to the end of the furnace was constant to f5 K. Before data were taken for a given reagent, the reactor was baked for 3 h at 500 K under vacuum. The reactor was then cooled to 300 K, and the first run was made at room temperature. After a series of high-temperature measurements were made, the reactor was cooled and a room-temperature measurement was repeated to confirm the validity of that set of experiments. The final and initial room-temperature rate constants usually were in good agreement. For the low-temperature measurements, solid CO, was placed in a cardboard box surrounding the flow reactor. Usually it took about 2 h for the reactor to reach a stable temperature after the box was filled and the Ar flow started. Weaker NF(b) signals were obtained in the low-temperature experiments because of the longer residence time (vide infra). The lowest temperature attainable was 190 K; the temperature variation along the reactor was f8 K. As the temperature was raised or lowered from 300 K, the pressure in the flow reactor remained approximately constant for a fixed Ar flow rate. This means that the stream velocity, (o), increased (for higher temperature) because the gas density in the flow reactor is smaller. Conversely, for low temperature the stream velocity must decrease since the density increased. It follows that the reaction time, At = & / ( u ) , changes with temperature. Young and c o - ~ o r k e r s found '~ the same behavior in their NF(b) flow reactor of a similar design. This effect has a rather dramatic effect upon the NF(b-X) intensity observed at the exit of the furnace with no added reagent, because the total time for radiative decay is shortened or lengthened for the higher and lower temperatures, respectively. The stream velocity (cm SI) in the plug flow approximation is given by (0)= FA,(RT/P)/7r2(1cm) where FAr is the Ar flow rate in mol s-I and P is the pressure in the flow reactor of radius r. If FAr and P are constant then ( u ) 0: T. The reagent flow rate measured at room temperature also must be converted to concentration at the temperature of the reactor for computation of the rate constants. To obtain a quenching rate constant at a given temperature, the decay of the NF(b) emission intensity was monitored at the end of the furnace for six to seven different concentrations, after the system reached a fixed stable temperature. As already mentioned, a room-temperature measurement was made before proceeding to the higher temperatures and also at the end of the experiment. If the initial or final room-temperature result was suspicious, the data for the other temperatures were disregarded. Some reagents react with the F atoms generated by Ar(3Po,2) + NF, to give products, which seem to introduce complications to the NF(b) quenching kinetics. As noted in our earlier work,1° this problem can be circumvented by adding a small amount of C2H6 before the reagent inlet part. The C2H6 removes F atoms but does not cause appreciable quenching of NF(b). This approach was necessary for experiments with H2, D2, and HCl. 111. Experimental Results 1 . Room- Temperature Experimental Results. The [NF(b)] decreases along the flow reactor because of radiative decay, wall quenching, collisional deactivation by Ar, NF,, and added reagent, Q. The interaction of NF(b) with itself (or with NF(a) and with F atoms) can be ignored at the low concentration, -7 X IO9 molecules ~ m - in ~ ,the flow reactor. The NF(b) decay follows a pseudo-first-order differential rate law.
(11) Kohse-Hoinghaus, K.; Stuhl, F. J . Chem. Phys. 1980, 72, 3720. (12) Borrell, P. M.; Borrell, P.; Grant, K. R.; Pedley, M. D. J. Phys. Chem. 1982, 86, 700; J . Chem. Phys. 1983, 78, 748. (1 3) Boodaghians, R. B.; Borrell, P. M.; Borrell, P. J . Chem. Soc., Faraday Trans. 2 1983, 79, 907. (14) Borrell, P.; Borrell, P. M.; Richards, D. S.; Boodaghians, R. B. J . Photochem. 1984, 25, 399; 1985, 31, 29. ( 1 5 ) Wayne, R. P. In Singlet Oxygen; Frimes, A. A,, Ed.; CRC Press:
Equation 1 assumes no complications from the interaction of the
Cleveland, OH, 1984. (16) (a) Wild, E.; Klingshirn, H.; Maier, M. J . Phorochem. 1984,25, 131. (b) Plotz, J.; Maier, M. Chem. Phys. Lett. 1987, 138, 419. (c) Shin, H. K. J. Chem. Phys. 1981, 74, 2866.
(17) Young, R. A,; Blauer, J.; Bower, R.; Lin, C. L. J . Chem. Phys. 1987, 87, 4634.
8164
Bao and Setser
The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 100
100
90
90
8a
80
70
70
60
60
50
50 c
n
h
v
40
L
z
U Z
-
> .-
E
VI
C
-K L
40
21 c ,-
3
30
30
%
Y
T498
20
20
10
0.0
4.0
EQI
8.0
:
12.0
Id4Molecule c E 3
Figure 1. Quenching plots of [NF(b)] vs the concentration of O2 and C 0 2 for fixed reaction time over the temperature range of 195-500 K. The typical reaction times were 47,31, and 18 ms at -195, -300, and -500 K, respectively. The NF@) concentrations at zero time have been scaled to a common value for each reagent for convenience in plotting.
added reagent with NF2 or F atom; 7 N p - I is the radiative decay constant, kw is the wall quenching rate constant, and kAr,kNF2, and kQ are the quenching rate constants for Ar, NF2,and reagent, Q. Since the kAr[Ar]and kNF2[NF2] terms are very small,43'0the integrated rate law can be simplified.
IO
,
0.4
0.i2
0.8
f
CQ1 : I d 4 Molecule cS3 Figure 2. Quenching plots of [NF(b)] vs the concentration of CH,OD and CH30H for fixed reaction time at 300, -385, and 492 K. The NF(b) concentrations at zero times have been scaled to a common value for each reagent for convenience in plotting. 100
90
T:300 80 70
In a clean reactor kw is insignificant relative to TNF*-', which is 52 f 3 s - ~ , ' O However, after extended use the walls of the flow reactor tend to become activated and kw becomes sufficiently large that useful experiments cannot be done. During the course of the measurements reported here, the reactor was replaced two times. The NF(b-X) emission intensity can be used to monitor the relative NF(b) concentration. Since most of the reactor was enclosed in a furnace, INF(b) was observed 47 cm downstream from reagent inlet, At = 31 ms at 300 K, while the reagent concentration was varied. Figures 1-5 show some typical results obtained by this method. The linearity of the In (INF(b))vs [Q] plots confirms the expected pseudo-first-order kinetics for fixed At. The slope of these plots gives the product of kQAt. The data in Figures 1, 2, and 5 give kcOl = (0.14 f 0.20) X lO-I4, kol = (2.4 f 0.3) X kcH, = (16.0 f 2.5) X and kCH,OH= (67.5 f 7.0) X cm3 s-' at 300 K, which illustrate the range of rate constants that can be measured. The reproducibility of the rate constant measurements with no special complications was typically *lo%. Table I summarizes the NF(b) quenching rate constants at 300 K. The uncertainty is the standard deviation from multiple experiments. The most general problem was the presence of impurities, mainly H20, in gases with small quenching rate constants. Obtaining reproducible results with COz, NO, and CO at high temperature was especially difficult even for gases stated by the suppliers to be of high purity and were further purified by passage through cooled traps filled with molecular sieve. As discussed by Cha and Setser,Io quenching plots for H2, D2, and HCI are poorly behaved and exhibit two first-order decay regimes.
D20 T:401
60
c
50
D "
2 .-cVI7.
40
a,
c
30
20 H20 T:480 10 I
l:o
2.0
[Q] Molecule cm-3 Figure 3. Quenching plots of [NF(b)] vs the concentration of H20and D20for fixed reaction time at 300,401, and 480 K. The decay rate for H 2 0 at 480 K is slower than at 401 K, but allowance must be made for change in A?; see Figure 1.
Therefore, rate constant measurements for H2, DZ,and HCI were done in the presence of C2H6. For HCI and (CH3)#20, some difficulty was encountered with obtaining the original NF(b) signal when the reagent flow was stopped. With these reagents 230 min
E-V Quenching Rate Constants of NF(bLZ+)
The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 8165
100 90
80
6C
T193 50 A
0 Y
40
.-
2,
4-
C
E
Quenching Rate Constants for NF(b) (XlO-" c d
reaeent H2
300 K 400 K 2.5 f 0.3 6.0 0.5 0.25 0.07 0.64 f 0.08 2.4 f 0.3 7.0 0.5 0.09 f 0.03 0.14 f 0.04 0.21 f 0.05 0.29 f 0.06 1.30 f 0.40 2.20 i 0.45 0.14 f 0.02 0.23 f 0.04 5.0 f 1.0 1.8 f 0.7 85.8 f 8.0 133 f 15 2.2 f 0.3 3.8 f 0.5 16.0 f 2.5 25.0 f 3.5 18.5 f 2.5 14.0 f 1.5 19.5 f 2.0 14.0 f 1.5 0.47 f 0.05 3.0 f 0.6b 26.1 f 4.0 19.8 f 4.0 1.10 0.15 0.55 f 0.06 67.5 f 7.0 85.6 f 8.6 20.5 f 2.1 17.2 f 1.8 30.6 f 4.6 35.1 f 5.3 5.1 f 1.1 8.8 f 0.9 11.5 1.2 2.5 f 0.5c 31.4 f 3.8 6.0 f 1.5d 48.4 f 5.0
I
70
5
TABLE I: S-9
200 K 0.26 f 0.04 0.02 f 0.01 0.70 f 0.10 0.09 f 0.02 0.08 f 0.02 1.75 f 0.30 0.10 f 0.02
*
* *
*
30
*
20
I
5.0
10.0
15.0
20.0
25.0
CQI : 10'4Molecule crri3 Figure 4. Quenching plots of [NF(b)] vs the concentration of H2 and D2 for fixed reaction time at 193,300,and -495 K. These experiments were done with added C2H, to remove F atoms (and the fast NF(b) decay component); see text.
T:2 16
T:300
1lo
0.b
CQI
2 lo
: 10'4Molecule cm-3
Figure 5. Quenching plots for [NF(b)] vs the concentration of CH,, (CH,),CO, and (CD3)*COat fixed reaction time for different temperatures. The NF(b) concentrations at zero time have been scaled to a common value for convenience in plotting.
was required for [NF(b)] to return to the level expected for [Q] = 0. We associate this difficulty with adsorption/desorption of Q on the reactor walls or possibly with absorption by the O-rings for (CH3)2C0. This problem was so serious with HCl at 200 K that experiments could not be done. For these cases rate constants were measured by adding successively larger [Q] in a single series of measurements. There seemed to be fewer problems associated with (CD3)$0 data. The acetones were selected in order to have an inexpensive source of fully deuterated reagent for examination
500 K 9.4 f 1.2 0.88 f 0.10 11.2 f 1.0 0.23 0.05 0.65 0.10 3.20 0.50 0.33 f 0.06 7.7 f 1.5 99 f 10 6.2 & 1.0 23.0 f 3.0 23.5 f 2.5
* *
25.6 f 4.0 1.65 0.40 105 f 12 13.7 f 1.4 24.1 f 3.6 14.3 1.5
*
*
'The 300 K rate constant for CH2CI2is (15f 2) X 1O-I' cm3s-I. 'This rate constant seems anomalously low and probably should be disregarded; see text. 'This rate constant was measured in a different set of experiments;I0 however, the kNHlfrom ref 10 agrees with the value measured here at 300 K. dThis rate constant is suspiciously low and should be used with caution; see text.
of the temperature dependence of the C-H/C-D kinetic isotope effect. In retrospect a different choice would have been preferable. A few molecules were selected for study only at room temperature in order to extend rate constant survey of Cha'O or to test trends known to exist for quenching of 02(b).15 The amines and Bi(CH3)3were selected for the latter purpose. The increase in rate constant for CH3NH2,relative to NH3, is about as expected from the additional contribution to quenching from the C-H bonds of the CH3 group. The quenching by Bi(CH3)3also appears to be normal, but the quenching constant for N(CH3)3 seems anomalously low. Although the data from three experiments were reproducible, reservation should be maintained since samples were taken from the same tank. The room-temperature study of CD2C12 was done in order to have another measure of the kinetic isotope for C-H vs C-D bonds. From Cha's work kCHZcll = (1 5 f 2) X cm3 s-l, which gives (k~/kD)cHzclz = 33 f 5. This is in modest agreement with the ratio of 40 found for acetone. Trifluoroacetic acid was selected to provide another molecule with an OH bond for comparison with CH30H and H20. For the pressure range used to measure the flow rate, no correction for equilibrium with the dimerL8was needed to obtain the correct CF3COOH concentration in the reactor. The rate constant for ND3 was part of an earlier series of measurements, but the rate constant is included here for comparison with NH3. 2. High- and Low-Temperature Results. An initially surprising observation was the increase, about a factor of 1.3, in the emission intensity of NF(b) as the temperature was raised from room temperature to -400 K. The intensity decreased with further increase of temperature from 400 to 500 K. As the temperature is raised, the residence time in the reactor is reduced and a smaller fraction of the [NF(a)] decays by radiation (see eq 2), which is the dominant NF(b) removal term in absence of [Q], providing that kw is insignificant. Quenching by the wall presumably becomes more important above 400 K, since the intensity typically would decrease by a factor of 1.4 over the 400-500 K range. This implies that kw was 25% of T ~ ~ over . - ~this temperature range. Some typical quenching data are shown in Figures 1-5 for various temperatures. The quality of the quenching plots a t higher and lower temperature generally was similar to those at room temperature. The rate constant data are summarized as plots of k, (18)Taylor, M.D.;Templeman, M. B. J. Am. Chem. Soc. 1956,78,2950.
8166 The Journal of Physical Chemistry, Vol. 93, No. 25, 1989
Bao and Setser
-60
'0
3
-60
-0m0 2 -4 0
3..-
$0
-
P
-2 0
Temperature :
K
Figure 6. Plot of quenching rate constants for H2, D2, and O2vs temperature. The D2 data also are shown on an expanded scale in Figure 8. Each plot is fitted to an Arrhenius expression: D2, 9.0 X IO-', exp(-1070/T); H2, 9.1 X exp(-1084/T); 02,7.2 X IO-!, exp(945/T). The various symbols for each molecule represent a separate series of experiments
00 li0
Lo 0 240
350
450
Temperature
550
K
Figure 8. Plots of quenching rate constants vs temperature for N2, NO, and D2. The D2 data are fitted to both Arrhenius and linear forms: k = 9.0 X exp(-l070/T) and k = (-0.24 1.75 X lO-,T) X The NO data are fitted to a linear plot: k = (1.10 0.3 X 10-T) X although the 300 K result is below the calculated line. The N2 data, are fitted to a linear and modified Arrhenius plots: k = (0.01 3.4 X 104T) X and k = 1.8 X 10-I2T1exp(-460/T). The temperature dedependence for N2 and N O also could be approximated by a pendence.
+
+
+
0 04 150
250
360
450
550
Temperature : K
Figure 7. Plot of quenching rate constants vs temperature for C 0 2 and CO. The experimental uncertainty for each rate constant is shown for CO. The C 0 2 data were fitted to a linear plot (solid line), k = (-0.035 + 7.0) X lo-") X and to an Arrhenius plot (dashed curve), k = 8.2 X exp(-474/T); the data for CO were fitted to an Arrhenius plot (not shown), k = 1.5 X lo-" exp(dOO/T), and to a modified Arrhenius plot (solid curve), k = T 1X 1.38 X lo-" exp(-890/T). The different symbols for each molecule represent a separate series of experiments.
vs Tin Figures 6-1 1 and in Table I. The results at 400 and 500 K in Table 1 are average results obtained from interpolation of the data points near 400 and 500 K. The residence time in the reactor increased with reduction of temperature, and the NF(b-X) intensity decreased by a factor of 0.6-0.7 upon cooling to 200 K, even with [Q] = 0. The lower NF(B) signal reduced the range of [Q]for which quenching could be studied, but there was no evidence that kw was enhanced. Experiments at 200 K were attempted for reagents that had sufficiently high vapor pressure, and generally good data were obtained. Although the equilibrium vapor pressure of (CH3),C0 should have been adequate, the observed rate constant was surprisingly small. Possibly chemisorption on the reactor walls at 200 K reduced the concentration below the value expected from the measured (CH3)+20 flow rate. On the other hand, the quenching plots appeared to be well-behaved. The situation for (CH3)2C0at 190 K is unresolved, and further work is needed before the small rate constant is accepted. We believe the data for CH4 and C2H6better represent the 200 K rate constants for E-V quenching by molecules containing C-H bonds. 3. Analysis of Temperature Dependence. The temperature dependence of the quenching rate constants are summarized in two ways. For ease of comparison, the average values of kQ(T ) are presented in Table I for 200, 300, 400, and 500 K. A more complete presentation is given by plots of kQ(T ) vs T in Figures
I
150
250
,
55
460
350
Temperature : K
Figure 9. Plots of quenching rate constants vs temperature for NH,, CH,, and CzH6. The data for NH, can be fitted to linear (shown) and Arrhenius (not shown) functions: k = 2.67 X IO-', exp(-3OO/T) and k = (0.46 + 2.8 X 10-2T) X to a similar degree; the CH, data are fitted to k = T 3exp(-15.27 0.009737'); the C2H6 data are represented by a linear plot, k = (5.42 + 3.63 X lo-*?") X IO-',, the near equality of kczH6(200)and kczH6(300) prevents fitting by an Arrhenius form.
+
6-1 1. Data points that were obviously suspect have been deleted; otherwise, all kQ(T ) measurements are included in Figures 6-1 1. For each molecule one or more functional fits to the data are shown, and the functional forms are given in the figure captions. The temperature dependence of the rate constants was monotonic for all cases except CH4 and HzO, which seemed to have a minimum at -300 K and a maximum a t -425 K, respectively. A smooth curve is shown in Figure 10 for the H20data, because the apparent decline in kQ(T)from 13 X to 10 X cm3 s-' may be just experimental error. All other cases had a positive dependence on temperature, with the exception of CH30D. Although the decline of kCHPDwith T i s not strong, the general trend does seem to be definitivei With the exception of O2(and perhaps H2) the data from 300 to 500 K could be fitted by either linear or Arrhenius type functions. However, the addition of the 200 K data point frequently showed that a strictly linear fit was no longer applicable over the extended temperature range. Six cases were fitted to an Arrhenius law from 200 to 500 K, and HCl was fitted from
-
-
E-V Quenching Rate Constants of NF(b12+)
The Journal of Physical Chemistry. Vol. 93, No. 25, 1989 8167 TABLE II: Arrhenius Parameters for Selected Reseents
reagent 0 2
HZ D2 HCI
co2 Cob "
NH3d
I
N p
C2H6c'd I
0 350
250
150
460
550
Temperature K
Plots of quenching rate constants vs temperature for CH30D, (CH,),CO, CHIOH, and H20. The uncertainty in the rate constants is shown for HzO data. The CH30H and CH30D data can be fitted to both Arrhenius (not shown) and linear plots: CH30H, k = 1.86 X exp(-310/T) and k = (1.56 + 1.76 X 10-zT) X lo-"; CH,OD, k = 4.47 X exp(560/T) and k = (28.2 - 2.9 X X If the 200 K data point is ignored, the (CH&CO data are essentially independent of temperature. The curve that is shown corresponds to 8.2 X exp(350/T). The k H sresults were not fitted to a functional dependence on temperature; the curve is a hand-drawn smooth fit ignoring the four highest temperature points. Figure 10.
I
0.04 300
350
'
400
450
500
Temperature K
Plots of quenching rate constants vs temperature for (CD3)2C0,DzO, and HCI. The data are fitted to linear plots: HCI, k = (-5.66 + 2.69 X 10-2T) X (CD3),C0, k = (-1.1 + 0.55 X 1W2T) X D20,k = (-5.3 + 2.4 X IF2?")X Arrhenius forms also could be used; for example, kHCl= 4.78 X exp(-900/T) gives as good a fit as the linear plot. Figure 11.
300 to 500 K; the Arrhenius parameters are summarized in Table 11. However, the results for COz, HC1, NH3, and Dz also fit a linear dependence equally well. For the sake of comparison with H2, the Arrhenius fit to the Dz data is emphasized. Two other cases gave better fit to a modified Arrhenius form, k( T ) = T ' B exp(-EJRT), and these also are included in Table 11. The fit to the high-temperature data for CO is poor, but the data are badly scattered. Linear or even TI/*fits to the Nz and CzH6 results also are possible. The kNo(300) data points were not fully weighted in drawing the linear plot for NO. The figure captions should be consulted for the functional fit selected for each molecule. The 200 K rate constants for Nz, NO, COz, and C2H6 are nearly the same as for 300 K. However, three independent experiments showed that kcH,(200) was 50% larger than kcH,(300), and the kch( r ) plot suggests a minimum near 300 K. In contrast, kc,H6(200) was the same as kc,H6(300)to within the experimental uncertainty. The 200 K result for (CH3)2C0is not considered to be reliable, and that point was ignored in drawing the line shown in Figure 5. The temperature dependence of the rate constants for C-H-containing molecules is certainly small based upon the CHI, C2H6, and (CH3),C0 data. The collective viewpoint from
temp range, K 195-500 195-500 195-500 300-500 195-500 195-500 195-500 195-500 195-500
E,, cm-l 660 f 30 740 f 40 750 f 80 630 f 80 330 f 60 340 f 50 230 f 35 320 f 85 290 f 40
preexponential factof 7.2 x
10-13
9.1 x 10-13 7.1 x 10-14
4.8 x 10-13 8.2 x 10-15 1.5 x 2.7 x
10-14 10-13
'In units of cm3 molecule-I s-!. bThe CO data also could be fitted by T I B exp(-E,/RT) with E, = 620 f 60 cm-'. CThesemolecules were fitted to a modified Arrhenius plot of the form k ( T ) = T ' B exp(-E,/RT). dThe data also be fitted to a linear dependence on temperature, and the results for CzH6and NH, can be represented as a
T'12 dependence.
the H,O, C H 3 0 H , and CF3COOH data suggests that E-V transfer to the O H bond also has a small positive temperature coefficient. Four pairs of molecules were investigated to ascertain how the kinetic isotope effect changed with temperature: Hz:Dz, H20:D20, (CH3)2CO:(CD3)zC0,and CH30H:CH30D. The kinetic isotope effect for H2/D2 remained approximately constant at 10.6 f 0.9. The ratio for water declined from 40 to 20 with increasing temperature, and the ratio for acetone decreased from 47 to about 20 with increasing temperature. Because of the negative temperature coefficient for kCH,OD( T), the ratio for methanol increased from 3 to 8 from 300 to 500 K. The small isotope effect for methanol arises because quenching occurs by E-V transfer to both the C-H bonds and the 0-H or 0-D bonds, and the CH3 group makes a larger contribution than does OD to the total quenching by CH30D. The room-temperature kinetic isotope effects for CH3CN:CD3CN,IoCHC13:CDC13,10and CH2Cl2:CDzCl2are 60 f 10, 21?i0, and 33 f 5, respectively. The room-temperature isotope effect for the NH3:ND3 pair is only 3.5, substantially smaller than for the C-H/C-D or 0-H/O-D cases. It should be remembered that the quenching rates for the deuterated molecules are slow; the presence of impurities would lead to overestimates of the true rate constants, and these kinetics isotope effects probably are lower limits.
IV. Discussion 1. Room- Temperature Quenching Rate Constants. The rate constants at 300 K should be compared to the independent measurements of Cha and Setser for consistency. The results for the test molecules, CH4, C&, and 02,agree well with the earlier data, 15.5 f 0.7, 13.1 f 1.2, and 2.4 f 0.4, respectively, all in units of cm3 s-l. The results in Table I for HzO and CH30H are lower than the earlier measurements of (145 f 15) X and (81 f 4) X cm3 s-I. Cha's upper limit value for kN of 0.2 X cm3 S-I has been lowered to (0.09 f 0.02) X cm3 s-I. The general level of agreement for molecules that were examined in both studies seems to be adequate. If there are differences, the present work is favored, because more effort was put into determining the 300 K results. The correlation of k, with the highest frequency in a molecule rather than with the density of vibrational states in the 7470-cm-I energy range strongly suggests that the acceptor states are the stretch modes associated with individual bonds in a molecule. The 300 K rate constant values assigned to individual C-H, N-H, and 0-H bonds by Cha were 4-6, 2-3, and -45 in units of cm3 s-l, respectively.1° These assignments give rate constants that are in approximate agreement for (CH3),C0(24-36), CH3COOH(31), CH3NH,(24), and Bi(CH3)3(36-54) with the new experimental results. According to these arguments the experimental N(CH3)3 rate constant is anomalously low. Although the kQ values do correlate with the highest frequency in a polyatomic molecule, the results do not follow Davidson and Ogryzlo's suggestion made for 02(b) that kQ = k(AE'/vmax)+
8168 The Journal of Physical Chemistry, Vol. 93, No. 25, 1989
C with k and C having common values for certain classes of m~lecules.’~If definite classes exist for the quenching of NF(b), they are not simply polyatomic, triatomic, or diatomic molecules. For example, U N H > UCH but k N H , 5 k q and UNO v~~ 5 vco but kNO > kco > kN2. Also, substitution Of D for H in CH or O H bonds results in reduction of rate constants by a factor of -40, which is much larger than predicted. Thus, a model is needed that includes more specific reference to the properties of individual molecules than permitted by a correlation with just the highest vibrational frequency. As a step toward this goal, we will examine the temperature dependence of the rate constants in an attempt to identify exit channel from E-V quenching. 2. Exit Channels and Temperature Dependence of kQ. Except for 02,we assume that quenching occurs by collision-induced conversion from the V(NF(b)-Q) potential to the V(NF(a)-Q) potential, with Q acquiring vibrational energy. The entrance channel ‘A’ potential arises from the r 2 + r; configuration of NF(b), whereas the lA” exit channel arises from the biradical rxruconfiguration of the NF(aiA) state. Both potentials are repulsive, and for thermal collisions quenching probably occurs without a formal crossing of electronic potential surfaces. At a purely empirical level, the probability for E-V quenching per collision should consist of three main terms. p
OC
Bao and Setser the temperature dependence of F(AEv,T) for the well depth, t(103 K), and the range parameter a (4.5 X lo-* cm-’) values adopted for O2with AEv = 100, 200, and 400 cm-I. The relative magnitudes of F(AEv,T) were 1.0,9.7 X 1P2,and 2.1 X l P 3 for AEv = 100, 200, and 400 cm-I, respectively, at 300 K. The values of F(AEV,T) increased by factors of 1.8, 3.1, and 7.6 from 200 to 500 K for these three AEv. For AEv = 100 cm-’ the functional dependence of F(AEv,T) on temperature was linear, but for AEv = 400 cm-’ the dependence increased to a higher order over this temperature range. More exoergic AEv values lead to smaller rate constants but larger temperature coefficients. Therefore, assigning rate constants with modest positive temperature coefficients to endoergic exit channels must be done with caution. If the exit channels are endoergic, the F(AEv,T) factor is augmented by the Boltzmann term. In the following discussion of exit channels, we will assume that NF(b,u’=O) is quenched to NF(a,u”). The available energies are 7470 and 6303 cm-’ for u“ = 0 and 1. (i) 02.Quenching of NF(b) by O2probably occurs by excitation transfer via diabatic potential surface crossing. There are two likely exit channels. NF(b)
I(J/(a,~’31I“~IJ/(b,~’=o))I2I(J/(Q,u)(~~l~(Q,O))IZ x
+ Oz(X)
-
-
+ 02(a) - 412 cm-’ NF(X) + 02(b) + 5784 cm-’ NF(a)
(la) (1b)
F ( U v , T ) (1) The temperature dependence is contained in the last factor, which is a function of the energy defect. As a guide to relating the exoergic energy defect, AEV,to the temperature dependence of a rate constant for quenching of NF(b,O) to NF(a,d), we will follow the model advocated by Plotz and Maier’6b in their interpretation of the temperature dependence of the quenching of 0 2 ( a ) and 02(b) by 02(X). Maier et al. used the SSH vibrational-to-vibrational relaxation model for the matrix elements describing the change in electronic change (first term), as well as the acquisition of vibrational energy (second term). However, we prefer to write the first matrix element as a product of an electronic-state collision-induced coupling factor (unknown) between the NF(b,u’=O) and NF(a,u”) states and the FranckCondon factors for formation of NF(a,u”), which are 0.9888, 0.0098, and 0,0010 for u ” = 0, 1, and 2.1° The matrix elements for the vibrational excitation of Q for a repulsive intermolecular potential are as follows.2o
The ko2(T ) values fit an Arrhenius plot (see Figure 6) over the entire 200-500 K range with E, = 660 f 60 cm-I, and (la) seems to be the favored channel. Since E, is larger than AHoo, the V(02(a)-NF(a)) exit channel potential probably interacts with the V(02(X)-NF(b)) potential on the repulsive wall of the entrance channel. This expected result for quenching by O2provides some confidence in the reliability of the data. (ii) H2 and 4. Although the Arrhenius fits (see Figures 6 and 8) may not be exact, especially for the D2 data, the nominal activation energies correspond to 740 f 40 and 750 f 80 cm-’ for Hz and D2, respectively. This analysis implies that the kinetic isotope effect should be nearly constant and independent of temperature, and indeed kH2/kD2 is 12.4 f 2.5, 10.0 f 2.0,9.4 f 1.9, and 10.7 f 2.0 at 200, 300,400, and 500 K, respectively, and the isotope effect is primarily the ratio of the preexponential factors. The following plausible exit channels are given without specification of the H2 and D2 rotational energies.
V Q ~ ( Q=) a 2 ~ 2 / 2 r
(114
= a4A4/8r2
(IIb)
V”*3(Q) = a6A6/48r3
(IIC)
+ H2(1) + 994 cm-I NF(a,O) + H2(2) - 604 cm-l NF(b) + D2 NF(a,l) + D2(2) + 442 cm-’ NF(a,2) + D2(2) - 707 cm-’ NF(a,O) + D2(3) - 1135 cm-I
V‘s2(Q)
NF(b)
+ H2
-
-
-
NF(a,3)
+ H2(1) - 139 cm-’
NF(a,2)
-
(2a) (2b) (2c) (3a)
The constants a,A, and I’ are the range parameter of the exponential intermolecular repulsion, the vibrational amplitude coefficient, and 4u2u/h, respectively. The numerical values of the matrix elements for the accepted parameters of H2 (N2)mare 5X (5.9 X 1.0 X (1.8 X and 1.6 x lo-$ (3.5 X lo-*) for u = 1-3. For our purpose the two important aspects of (11) are the rapid decline with multiplequanta excitation and the effect of substitution of H for D. According to eq 11, the change in the matrix element upon substitution of H for D is not large for the same number of quanta, but the number of quanta and the energy defect usually do change, since uD < uH. These empirical aspects of eq I suggest that the quenching rate constant should decline by an order of magnitude for each quantum of vibrational energy added to either NF(a) or Q(u). Plotz and Maier used the translational factor, F(AEv,T), developed for vibrational-to-vibrational (or translational) energy transfer with a Morse potential to model the temperature dependence for quenching of different isotopes of 02.We calculated
(3c) Reaction 3c is too endoergic and can be dismissed. Based upon the similar activation energies for H2 and Dz, the dominant channels could be (2c) and (3b). Adjustment for the difference in collision frequency between H2 and D2 would give a quenching cross section ratio of q+,/a&= 7.7, which would be just a measure of the ease of forming NF(a,O) vs NF(a,2). This is much smaller than expected from the NF(b,O-a,u”) Franck-Condon factors. This contradiction suggests that (3a) must play a role for D2 and the apparent match between the Arrhenius energies for D2 and H2 is fortuitous. The temperature dependence of the F(AEV,T) factor for AEv = 442 cm-’ could match the D2data, and we favor (3a) as the main exit channel for quenching by D2 and (2c) for
(1 9) (a) Davidson, J. A.; Ogryzlo, E.A. Chemiluminescence and Bioluminescence; Plenum Press: New York,1973; p 1 1 1 . (b) Kear, K.; Abrahamsen, E. W. J . Phorochem. 1975, 3, 409. (20) Lambert, J. D. Vibrational and Rotational Relaxation in Gases; C . Krendon Press: Oxford, 1977; p 46.
NF(b)
-
-+
(3b)
H2.
(iii) H 2 0 and 40.Near-resonant transfer involving two quanta of OH stretch excitation is consistent with the weak temperature dependence for quenching by H20.
+ H20
-
-
NF(a,O)
NF(a,O)
+ H20(200) + 269 cm-I
+ H20(002) + 25 cm-’
(4a) (4b)
The Journal of Physical Chemistry, Vol. 93, No. 25, 1989 8169
E-V Quenching Rate Constants of NF(blZ+) Quenching by H F has a rate constant of (70 f 15) X cm3 s-l *JO and probably proceeds by two-quanta excitation with an endoergic defect of 282 cm-'. Thus, H 2 0 and H F set the upper limit for the E-V quenching rate constants of NF(b) with excitation of two quanta of vibrational energy. Excitation of HzO with one quantum in the symmetric and antisymmetric stretch modes has a 220-cm-I defect, but simultaneous excitation of two different stretching modes seems improbable. If simultaneous excitation of independent normal modes were common, the quenching rate constants for hydrocarbons would increase more than linearly with the number of C-H bonds, which is not the case. It also is possible that local stretch modes participate in energy transfer rather than normal modes. Two HzO bending quanta are nearly equivalent to u I , but multiple excitation of v2 in combination with single excitation of v l or v2 seems less likely than (4a) and (4b). The CH30H and CF3COOH data also show a very weak positive temperature dependence for quenching by the O H bond in accord with a nearly resonant process. The likely channels giving NF(a,O) for quenching by DzO involve three or more quanta of excitation, and they are endoergic: (300, -419 cm-I), (003, -707 cm-I), (022, -370 cm-I), (220, -72 cm-I), and (1 21, -223 cm-I). The D 2 0 bending frequency (1 179 cm-l) almost exactly matches the NF(a) frequency and formation of NF(a,l) D,0(012, 210, and 111) have the same energy defects as the last three entries in the preceding list. The endoergic nature of the probable D 2 0 exit channels is consistent with the larger temperature coefficient, relative to H20. The large isotope effect, -35, is associated with the need to excite three or four quanta in DzO, as well as the endoergic nature of the expected D,O channels. (iu ) HCI, CH,, and NH3. These molecules have similar 300 K rate constants (if considered on the basis of individual C-H or N-H bonds) and similar vibrational stretch frequencies (2885, 301 9, and 3400 cm-I, respectively); however, the temperature coefficient of kHCl is the largest. These frequencies are reduced sufficiently, relative to H20, that energy resonance can no longer be achieved by excitation of two quanta, and this is one reason that the rate constants are smaller than for kHF or kH20. Quenching by HCI has the following probable exit channels.
+
NF(b)
+ HCI
-
-
-
NF(a,2)
+ HCl(2) - 512 cm-'
+ HCl(2) + 638 cm-l NF(a,O) + HCl(3) - 869 cm-l
NF(a,l)
(sa) (5b) (5c)
Based upon E, = 630 cm-I from the 300-500 K data, (5c) is excluded. The small Franck-Condon (FC) factor for NF(a,2) suggests that (5b) is the major channel; the 10-fold reduction in kHClvs kHFmust largely arise from the FC factor for formation of NF(a,u=l) vs NF(a,u=O). A 638-cm-I exoergic energy defect would be compatible with the data according to the calculated F(AEV,T) factors. The rate constants for NH3 were fitted to an Arrhenius law from 200 to 500 K with an E, of -230 cm-'. Likely channels are two quanta in v I or u3, the symmetric (3336 cm-I) and antisymmetric (3444 cm-I) stretching modes with formation of NF(a,l). The addition of one quantum to v,, the umbrella mode (950 cm-I), gives slightly less endoergic channels with NF(a,O). NF(b)
-
+ NH3
NF(a,l)
+ NH3(2000) - 303 cm-'
(6a)
+ NH3(O020) - 490 cm-l (6b) NF(a,O) + NH3(2100) - 86 cm-' (6c) NF(a,O) + NH3(0120) - 283 cm-l (64 The NF(a,O) + NH3(0020) + 677-cm-l channel can be excluded NF(a,l)
-
by the temperature dependence of kNH, unless transfer to rotational energy reduces AEv. There are several other vibrational states in the 6600-6800-cm-l range because two quanta of N H bend (1626 cm-l) are nearly equivalent to single excitation of a N-H stretch. These states interact with the (0020) and (2000) states by Fermi resonance.*Ib Indentification of a single major channel
is not possible, and perhaps NH3 quenching involves several exit channels. Discussion of quenching by C-H-containing compounds is complicated by the uncertainty of the temperature coefficient. Nevertheless, the temperature dependence for CH,, C2H6,and (CH3),C0 is weaker than for NH3 or HCI and the energy defect presumably is smaller. The symmetric (vl = 2917 cm-I) and antisymmetric ( v 3 = 3019 cm-I) C-H stretches modes of CH4 must be involved in quenching. NF(b)
-
+ CH4
-
NF(a,O)
+ CH4(O120) - 24 cm-I
(7a)
+ CH,(OO2l) + 197 cm-I NF(a,O) + CH4(2100) + 102 cm-I NF(a,O) + CH4(2001) + 488 cm-I NF(a,O)
(7b) (7c)
(74 The defects for (7a)-(7c) are consistent with the weak temperature dependence. Since v2 and v4 are close to %F, formation of NF(a,l) without excitation of v2 and v4 also is possible. These combinations of C-H stretch and C-H bending mode excitation with formation of NF(a,O) or formation of NF(a,l) without C-H bending mode excitation will be typical for molecules containing C-H bonds. Quenching by molecules with C-D bonds can be examined by inspection of the frequencies for CD4. Excitation of 3v3 corresponds to AEv of -750 cm-l. Adding one quantum to the lowest bending frequency, v4, gives AEv = -250 cm-I. The utilization of an additional quantum, which leads to small endoergic defect, can explain the large isotope effect for C-D bonds vs C-H bonds. In contrast, excitation of three N-D stretch quanta gives a nearly energy resonant channel, and this explains why the kNHl/kND3 isotope effect is smaller than for hydrocarbons. (u) N,, CO, NO, and CO,. These molecules will be considered together because their rate constants have a similar weak positive dependence on temperature and their vibrational frequencies are similar. As noted in the figure captions, the temperature dependence for quenching by N O and N 2 could be just the temperature dependence of the collision frequency; Le., the quenching cross section is independent of temperature. Although quenching by CO has the largest activation energy, 340 cm-' (or 640 cm-l for the modified Arrhenius fit), formation of NF(a,O) CO(4) requires 943 cm-I more energy, and this channel is ruled out, as is NF(a,O) CO(3) which is 1120 cm-' exoergic. The following are probable exit channels for CO:
+
+
- + - + + CO
NF(b)
NF(a,l)
+ CO(3) - 47 cm-I
NF(a,3)
CO(2) - 240 cm-I
NF(a,2)
CO(2)
(8a) (8b)
+ 893 cm-l
(8c) If the calculated temperature dependence from the F( AEv,T ) factor is reliable, (8c) also can be excluded because a stronger temperature dependence would be expected. It is not possible to choose between formation of CO(3) with one quantum of NF(a) excitation vs CO(2) with three quanta of NF(a) excitation. There are no channels with small defects for N2. NF(b)
+ N2
-
-
NF(a,l)
+ N2(3) - 601 cm-I
+ N,(3) + 566 cm-I NF(a,3) + N2(2) - 61 1 cm-l NF(a,2) + N2(2) + 521 cm-I NF(a,O)
(9a) (9b) (9c)
(94 The endoergic channels would seem to be excluded by the weak temperature dependence. The calculated F(AEV,T) factors for (9b) and (9d) give somewhat larger temperature coefficients than the experimental result unless a is increased (or e decreased). Excitation of N 2 rotational states could reduce the exoergic translational energy defects, and (9b) or (9d) seems to be the best choice. (21) (a) The vibrational energies of excited molecules were taken from standard compilations except for NHJ;see ref 21b. (b) Lehmann, K. K.; Coy, S. L. J . Chem. SOC.,Faraday Trans. 2, in press.
8170 The Journal of Physical Chemistry, Vol. 93, No. 25, 1989
The 3-fold increase in kc02 from 200 to 500 K can be fitted by a linear dependence, although an Arrhenius form also can be used with E, = 330 cm-I. The asymmetric stretch is assumed to act as the acceptor mode with one or two quanta placed in v 2 or in NF(a) to achieve small energy defects. The temperature dependence of kCO2could be consistent with the following three channels, providing CO, accepts some rotational energy to reduce AEv for (loa). NF(b)
-
+ CO,
NF(a,O)
+ Co2(O03) + 497 cm-'
+ Co2(013) - 170 cm-' NF(a,l) + CO2(O22) + 190 cm-l NF(a,O)
(loa) (lob) (10c)
Several N O exit channels have small energy defects. NF(b)
+ NO
-
-
NF(a,O)
+ N O ( 4 ) + 136 cm-l
+ NO(3) - 390 cm-I NF(a,3) + NO(2) + 297 cm-' NF(a,2)
(lla) (1 1b) (1 IC)
The larger rate constant, relative to CO and N,, and the actual small increase in kNOat 200 K suggest the importance of (1 la). The interaction of NF(b) with the unpaired electron of NO(X2111/2,3/2) could provide a more attractive potential than for N 2 or CO. V. Summary The small experimental temperature coefficients for the NF(b) quenching rate constants and the remarkably large H / D kinetic isotope effects serve to focus attention upon exit channels with small energy defects (H2, D2, and 0, are special cases).23 The cm3 s-l, to the quenching rate constants upper limit, -50 X by H F or H O bonds is associated with near-energy-resonant events for which two quanta of excitation are received by the stretching mode. Reduced rate constants are associated with activation of a larger number of vibrational quanta in the acceptor molecule, formation of vibrationally excited NF(a), or large energy defects. The rate constants (per bond) for molecules with N-H, C-H, or CI-H bonds are an order of magnitude lower than for H F or H O bonds because excitation of three stretch quanta is endoergic and either two quanta of stretch plus one quantum of bend or two quanta of stretch and one quantum of vibration in NF(a) are required to achieve small energy defects. For molecules with stretch frequencies of -2000 cm-I, three or more quanta of excitation and/or formation of NF(a,l) or NF(a,2) are required to achieve small defects, and the rate constants are 2 orders of magnitude less than for H F or H O bonds. However, k, varies considerably among molecules in this class because of different vibrational energy level pattern or difference in the interaction potentials. Substitution of D for H in C-H or 0-H bonds tends to place the deuterated molecules in the 2000-cm-' category just mentioned. For H2 two quanta of excitation is endoergic by -600 cm-I, but the rate constants have a temperature dependence consistent with this exit channel. The preexponential factor for cm3 s-l, which resembles the k H 2is approximately 100 X result for kHFand koH. Although the NF(a) state has not been positively identified, we are confident that this is the product state based upon the close analogy to the trends for O,(b) quenching.22including the modest
Bao and Setser temperature Unfortunately, identification of the nascent product vibrational state is not feasible in our flow reactor, except possibly for NO, because of the low NF(b) concentration and the large [Q] required to measure small rate constants. Theoretical guidelines for the entrance and exit channel potentials would be helpful, but most of all definitive experiments to identify product states in a different experimental system are needed. In principle, detailed comparison with quenching studies of O,(b), which releases 5239 cm-I, should be worthwhile. However, even for the reactions of 02(b) the product vibrational states generally are not known with certainty. One exception is HBr, which seems to give HBr(2) with near energy re~onance;,~ the rate constant is 20 X cm3 s-I, and the temperature coefficient is small.25 The close resemblance to quenching of NF(b) by H F and H 2 0 is significant. Quenching of 02(b) by H F gives HF(u=l) with a defect of 1280 cm-', but the rate constant is large, 110 X cm3 s-I. Possibly, the rotational energy of H F is involved in this one-quantum E-V process. The CH4/CD4 results with 02(b) are quite interesting because the isotope effect is small, 1.O at 200 K and 1.4 at 350 K, but the rate constants increase from 3X to I O X cm3 s-' over this range." These results suggest that one C-H stretch quantum and one C-H bend quantum are excited in CHI but that two C-D stretch quanta are excited with CD4 and, fortuitously, the AEv values are similar. The isotope effect is -4 for the HCI/DCI pair.]' The isotope effects for these two examples were much smaller than the ratios for NF(b) with molecules having H-C/D-C and H-O/D-0 bonds, but similar to kNH,/kND3.In contrast, the isotope effect11322 is nearly 50, for quenching of O,(b) by H2 and D,, whereas it is only 10 for NF(b). The H2 quenching rate constant,, is larger cm3 s-' vs k,,(NF*) = 2.5 for 02(b), e.g. kH2(02*) = 61 X X cm3 s-l, but the temperature coefficients are comparable for both O,(b) and NF(b). The larger kH2for O,(b) vs NF(b) presumably reflects the ease of Av = 1 vs 2 excitation; the large isotope probably arises because of the need to reduce the potentially large energy defect for single-quantum excitation of D2 (-2000 cm-I) by vibrational excitation of 02(a,u"). Observation of the nascent product-state distributions is required to confirm these suggestions about exit channels. The importance of vibrational states with small energy defects has been emphasized in this discussion. However, several exit channels frequently seem probable even within this restriction. A distribution of product vibrational states with not all of the available energy being released as vibrational energy of the reagent is consistent with the general conclusions about the E-V quenching of 02(b), based upon direct observations of product states by Thomas and Thrushz6 and our l a b ~ r a t o r y . ~ ~
-
-
-
Acknowledgment. This work was supported by the US.Air Force Weapons Laboratory and by AFOSR (Grant-88-0279). We are pleased to acknowledge discussions of endoergic exit channels and the F(AEV,T) factor with Professor H. K. Shin. We thank Dr. K. Y. Du for assistance with some of the measurements and Dr. Vern Schlie for his interest in this work. Registry No. NF, 13967-06-1; H2, 1333-74-0; D2, 7782-39-0; 02, 7782-44-7; N2, 7727-37-9; CO, 630-08-0; NO, 10102-43-9; C02, 12438-9; HCI, 7647-01-0; H20, 7732-18-5; D20, 7789-20-0; CH4, 74-82-8; C2H6. 74-84-0; CDzCI2, 1665-00-5; (CHj)&O, 67-64- 1; (CDj)ZCO, 666-52-4; CHjOH, 67-56-1; CHSOD, 1455-13-6; CF,COOH, 76-05-1; NH,, 7664-41-7; ND,, 13550-49-7; NH*CHp, 74-89-5; N(CH3)j, 7550-3; Bi(CH3)3,593-91-9; CH2CI,, 75-09-2.
(22) Wildt, J.; Bednarek, G.; Fink, E. H.; Wayne, R. P. Chem. Phys. 1988,
122, 463.
(23) The quenching constants of NF(b) by IF, 12, and F, also have small temperature coefficients (see ref 17), but chemical reaction probably is the quenching mechanism.
(24) Singh, J. P.; Setser, D. W. J . Phys. Chem. 1985, 89, 5353. (25) Braithwaite, M.; Ogryzlo, E. A. Chem. Phys. Leu. 1976, 42, 158. (26) Thomas, R. G. 0.;Thrush, B. A. Proc. R . SOC.London 1977, 356, 295, 307.
