J . Phys. Chem. 1990, 94, 3286-3290
3286
contrast, if the transition state were at the limit of extreme looseness, still with Eo equal to 2.43 eV, the rate (at 308 nm) would be faster than that observed by a factori4of IO5. I t is curious that the Eo value measured for the reaction is equal, within experimental uncertainty, to the reaction endoergicity; this would be cxpected for a loose transition state but has no reason to be true for the tight transition state which seems indisputable for this reaction. We suggest that this is purely coincidental and that the tight transition state by chance has an energy equal to that of thc dissociation products. Since the tight transition state has an energy not less than that of products, it is always rate limiting by virtue of its low frequency factor, and transition-state switching to thc loose transition state would not be expected at any cncrgy.
-
Conclusions Among cncrgy-selected unimolecular dissociations of polyatomic ions, thc styrene ion dissociation is perhaps the one with the (14) The rate in the limit of a loose orbiting complex is conveniently calculated from the equations derived by Klots from microscopic reversibility of Langevin orbiting collision rates: Klots, C. E.Z . Nufurforsch. 1972, A27, 553.
best-known kinetic parameters. The accuracy with which the rate-energy curve follows the RRKM predicted shape, with very reasonable parameters in the RRKM calculation, is a good indication of the validity of this theoretical framework for understanding the reaction. It does not appear that kinetic parameters for the corresponding neutral dissociation have been reported, but the fact that the reaction rate can be measured in a shock tubei5 gives reason to hope that they will be determined soon. I t will also be of interest to try to map out the potential hypersurface along the reaction path by theory to identify the structure of the transition state at 2.43 eV. Acknowledgment. Appreciation is expressed to the National Science Foundation and to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Registry No. Styrene molecular, 34504-74-0.
( 1 5 ) Dudek, D.; Glanzer, K.; Troe, J. Ber. Bumen-Ges. Phys. Chem. 1979,
83, 776.
Kinetic Energy and Temperature Dependences of the Rate Constants for Electron Detachment of NO- by N,O, CO,, N,, CH,, C2H8,and C3H8 A. A. Viggiano,* Robert A. Morris,+ and John F. Paulson Ionospheric Physics Division (LID), Geophysics Laboratory (AFSC). Hanscom AFB, Massachusetts 01731 -5000 (Receiued: October 6 , 1989: I n Final Form: February 7 , 19901 Rate constants were measured as a function of average center-of-mass kinetic energy, (KE,,), at several temperatures for thc reactions of NO- with N20, C02, C2H6, and C3Hs. In addition, temperature dependences were measured for the rate
constants of the reactions of NO- with N2 and CH4. In the reactions of C2H6, C3H8,N2, and CH4, the only channel observed was electron detachment. N,O and C 0 2 reacted both by electron detachment and, at low temperature and low (KE,,), by association. The rate constants for electron detachment were found to have positive temperature dependences and, in most cases, positive dependences on (KE,,). An exception is that the rate constants for electron detachment for C2H6 and C3Hs at the higher temperatures showed negative dependenceson (KE,). Rate constants for the association reaction channels wcrc found to have negative temperature dependences. Rate constants for electron detachment from NO- in collisions with C 0 2 and N 2 0 in the L' = 0 and L' = 1 levels of the bending mode were derived from the data as a function of (KE,,). Rate constants for the c = 1 level are approximately an order of magnitude larger than those for the L' = 0 level.
Introduction The reaction of 0- with N 2 0 produces NO0- + N2O
--t
NO-
+ NO
(1)
A recent valuc of thc rate constant for reaction 1 is 2 X cm3 s-I at 300 K.' The electron affinity of N O is extremely low. The most recent measured value is 0.026 f 0.005 eV,2slightly higher than thc bcst prcvious value of 0.024 The electron affinity is thcrefore lower than thermal energy (0.038 eV) at 300 K. The low clcctron affinity cnables NO- to lose its electron easily. In fact, almost no NO- is seen as a product of reaction 1 in flow tube experiments using a helium buffer. In the early 1970s McFarland et uL4 discovered that NO-detaches only slowly in an argon buffer, enabling them to measure electron detachment rate constants of NO- with several neutrals as a function of temperature. They found the thermal detachment rate constants to follow an Arrhenius expression with activation energies in the range 0.046-0.107 eV. They also found that plyatomic neutrals with low-frcquency vibrational modes were the most efficient detachers. 'On contract io thc Geophysics Laboratory (AFSC) from Systems Integration Engineering, Inc.. Lexington, MA. 0022-3654/90/2094-3286$02.50/0
In addition to undergoing electron detachment, NO- has long been known to undergo chemical reaction with O2 and HCI. Rinden et aL5 have recently studied reactions of NO- with a number of compounds. They found that the reactions proceeded by four pathways: electron detachment, charge transfer, dissociative charge transfer/nucleophilic displacement, and adduct formation. Maricq et al. have recently studied the vibrational autodetachment of NO-.6 In the present study we have measured rate constants for electron detachment of NO- with several neutrals as a function of ion-neutral average center-of-mass kinetic energy ( ( KE,,)) at several temperatures. This technique also allows information to be derived on the dependence of the rate constants on the ( I ) Morris, R. A.; Viggiano, A. A.; Paulson, J. F. J . Chem. Phys. 1990, 92. 3448. (2) Travers. M. J.; Cowles, D. C.; Ellison, G.B. Chem. Phys. Left. 1989, 164, 449. (3) Siege], M. W.; Celotta, R. J.; Hall, J. L.; Levine, J.; Bennett, R. A. Phys. Rev. A 1972. 6 , 607. (4) McFarland, M.; Dunkin, D. B.; Fehsenfeld, F. C.; Schmeltekopf, A. L.; Ferguson, E. E. .I. Chem. Phys. 1972, 56, 2358. ( 5 ) Rinden, E.; M a r i q , M. M.; Grabowski, J. J. J. Am. Chem. Soc. 1989, 111, 1203. (6) Maricq, M. M.; Tanquay, N . A,; O'Brien. J. C.; Rodday, S . M.; Rinden, E. J. Chem. Phys. 1989, 90. 3136.
0 I990 American Chemical Society
Rate Constants for Electron Detachment of NO10"
N O + N20 + products
A
T
-E, d
n
10
"'
'00
e
e!
A
mV.
A
g
V
. 0
0
A A
00
10 .'' .
O O
B
I
A
0 0
..
]
Te
V
A
N O + CO2 + products
A
A
A
0 0
V 0
0
0
10
O 0 142K
B
.
0 0
0
V
0 A
v i n .ii I"
0
30
20 (KE.,)-~
40
50
0
60
0
10
The experiments were performed in a variable temperatureselected ion flow drift tube (VT-SIFDT). This instrument has been described in detail and only details pertinent to the present experiments will be given. NO- is generated in a high-pressure ion source from N 2 0 . N 2 0 attaches electrons to form 0-, which further reacts with N 2 0 to form NO-. The generation of NO- required the ion source to be run for several days before a stable signal could be obtained. We attribute this behavior to the source cleansing itself of previous source gases; NO- is very reactive and would react or detach with almost any impurity . Normally He is used as a buffer in the VT-SIFDT. For these experiments, an Ar buffer was used. As noted above, NO- undergoes rapid electron detachment at room temperature in a ~ only little NOhelium buffer but not in an Ar b ~ f f e r .While can be detected at room temperature, we have found that NOcan survive injection in a He buffer below room temperature and that useful signal levels can be detected at the downstream end of the flow tube. At higher energies (-0.1-0.2 eV) Ar also detaches electrons from NO-. This detachment is observed as a decrease in the detected NO- signal at higher drift fields. The usual case for nondetaching ions is that ion signals increase with increasing electric field. The occurrence of detachment at high field strengths dictated the highest energies at which we could perform the experiments. Rate constants were derived from declines in the NO- signal upon addition of the neutral reactant. Energies were derived from the Wannier formulalo using measured drift velocities. All gases were used without further purification. The rate constants are believed to be accurate to f25%. The relative accuracy (the uncertainty in the ratio of any two rate constants for the same reaction) is f 15%. A 15% relative error bar is shown in Figures 1-4 and represents the maximum allowed variation (in either direction) of a rate constant relative to another rate constant plotted in the same figure. Branching ratios were measured by comparing the increase in the ionic product signal level to the ( 7 ) Viggiano. A. A.: Morris, R. A.; Paulson, J. F. J . Chem. Phys. 1988, 89. 4848. (8) Viggiano, A. A.; Morris, R. A.; Paulson, J . F. J . Chem. Phys. 1989, 90, 681 1. (9)Viggiano, A. A.; Morris, R. A.; Dale, F.; Paulson, J. F.; Giles, K.; Smith, D.; Su,T.J . Chem. Phys., submitted for publication. (IO) Wannier, G. H. Bell. Sysr. Tech. J . 1953, 32, 170.
30
20
(KE,.,Y~
40
50
(evy'
Figure 2. Total rate constants for the reaction of NO- with C 0 2 as a
function of inverse (KE,,).
Open circles, open squares, open triangles,
and solid squares represent data taken at 173, 212, 297, and 465 K, respectively. NOAA data are shown as inverted triangles. The NOAA data are pure temperature data converted to (KE,,). Only electron detachment was seen in the NOAA experiment. A relative error bar is shown (see text). 10
vibrational energy of the detacher. At low temperatures and low (KE,,) association was also found to be important, and the association rate constants are reported. Experimental Section
0
V
(evrl
Figure 1. Total rate constants for the reaction of NO- with NzO as a function of inverse (KE,). Solid circles, open circles, open squares, open triangles, and solid squares represent data taken at 142, 173, 212, 298, and 465 K. respectively. NOAA data are shown as inverted triangles. The NOAA data are pure temperature data converted to (KE,,). Only electron detachment was seen in the NOAA experiment. A relative error bar is shown (see text).
0
.I
I
10
0
173K 212K 297K 165K NOAA 18' only. T oolyl
1
N O + C3H8 + NO + C3H8 + e
..
%-
e n
E,
1
E 10'". d
A
10
1
30
20
40
50
(KE~,,)-~eV.1
Figure 3. Rate constants for the detachment reaction of NO- with C3Hs as a function of inverse (KE,,). Open circles, open squares, open triangles, and solid squares represent data taken 173, 212, 298, and 465 K, respectively. A relative error bar is shown (see text). 10."
N O + Nz, CHg, C2H6 + NO + Np, CHq, C2H6 + e
A m E
I
A
A
0
10
10
20
I
30
(KE~,,)-~(evy'
Figure 4. Rate constants for the detachment
reactions of NO- with N2, CH4, and C2H6 plotted as a function of inverse (KE,,). Open circles and open squares represent data for N2and CH,, and open triangles and solid triangles represent data for C,H6 at 298 and 480 K, respectively. For N, and CH4 the data are pure temperature data converted to (KE,,). A relative error bar is shown (see text). decline in the NO- signal level. No attempt was made to detect the electron product. No correction for mass discrimination was
Viggiano et al. N O + N20 + NO'(N20) N O + C02 --t NO(C02) O
0 -
I
U
a
: .
0 0 0
a m A
n
0 A
0
A
I
0 142K 173K
AN20 212K
WE,,,,)
(W
Figure 5. Rate constants for the association channel of the reaction of NO- with N20and with C 0 2 as a function of (KE,,) at several temperatures. Data for C 0 2 and N20are represented by open and closed symbols, respectively. Circles, squares, and triangles represent data for 173. 212. and 297 K for C 0 2 and 142, 173, and 212 K for N 2 0 , respect ivel y.
made. Mass discrimination effects are expected to be small since the data were taken with low mass resolution. The branching ratios are accurate to f30%. Relative branching ratios are believed to be accurate to within 10%. since they are not affected by mass discrimination.
Results Rate constants were measured for reactions of NO- with N20, C o 2 , and C3H8as a function of average center-of-mass kinetic energy with respect to the reactant ( ( KE,,)) at several temperatures. For N 2 0 and C02, clustering was observed, in addition to electron detachment, at low temperatures and low kinetic energies. The overall rate constants for N 2 0 , C 0 2 , and C3H8 reacting with NO- are shown in Figures 1-3, respectively. At all temperatures, detachment is the dominant channel. The data are plotted as the logarithm of the rate constant versus the reciprocal of the kinetic energy, i.e., as quasi-Arrhenius plots. The lowest energy point at each temperature represent data taken with no drift field and together represent the pure temperature dependence. Temperature dependences were also measured for the rate constants for detachment of NO- with N2, CHI, and CzH6. For C2H6,an energy dependence was also measured at 480 K. The rate constants for detachment of NO- by these three neutrals are shown in Figure 4. The rate constants for the detachment reactions with N2 and CHI were too small to measure as a function of kinetic energy. The rate constants for the reactions of NO- with N 2 0and C 0 2 have been measured previously at the NOAA laboratories as a function of temperat~re.~ The NOAA data are shown as inverted triangles in Figures I and 2 . The present data are in excellent agreement with the previous work at higher temperatures and agree within the combined error for low temperature. The fact that the NOAA workers did not observe the association channel, seen in the present study at low temperature, may account for the difference between the measurements. As stated earlier, both N 2 0 and COz associate with NO-. The rate constants for these reactions are shown in Figure 5. These data are plotted as the logarithm of the rate constant versus logarithm of the kinetic energy. This type of plot is usually linear for ion-molecule association reactions." The rate constants for the association channel are derived from the overall rate constants and the branching fraction. Competition between detachment and association in reactions of NO- has been observed previ~usly.~ The binding energy of N 2 0 to NO- has been measured and has been found to be 0.2 eV.'* ( I I ) Adams. N . G.;Smith, D. In Reactions of Small Transient Species; Fontijn. A.. Clyne. M . A . A , . Eds.; Academic Press: New York. 1983.
Two other minor channels were observed for the reaction of NO- with N 2 0 . A small amount of charge transfer to produce N,O- was observed, as well as a small amount of NO< production. These channels are discussed The rate constants for all the electron detachment reactions showed a positive temperature dependence, indicative of an activation energy. The activation energies derived from the data range from 0.043 to 0.121 eV. The electron affinity of NO, and therefore the endothermicity of all the detachment reactions, is 0.026 f 0.005 eV.2 Positive temperature dependences are to be expected for detachment reactions and have been observed previously for this type of reaction4 The activation energies are all larger than the endothermicity of the reaction, indicating that the electron attachment reaction has a positive activation energy as well. The reason that the activation energies vary is unknown. Curiously, the rate constants do not show a positive energy dependence in all cases. For the detachment of NO- in collisions with COS and N 2 0 , a positive energy dependence is seen at the lower temperatures, but at 465 K the rate constants are approximately independent of kinetic energy. The situation is even more extreme for detachment in collisions with C3H8. In this case, at the lowest temperature, 173 K, the rate constants show no kinetic energy dependence, while at all the higher temperatures the rate constants show negative kinetic energy dependences. The rate constant for the reaction of NO- with C2H6also has a negative kinetic energy dependence at 480 K. The rate constants for CzH6 were too small to measure as a function of kinetic energy at the other temperatures. This negative energy dependence is quite unexpected, as one would expect that any type of energy increase would increase the rate constants for an endothermic reaction. We have no detailed explanation of this behavior, and it is especially difficult to understand why some reactions show this trend and others do not. The fact that the dependences of the rate constants on kinetic energy and on temperature are so different is intriguing. One possible explanation is that it is the internal energy of the neutral reactants that causes the differences. We have previously presented a procedure for deriving dependences of rate constants on the internal temperature of the reactant neutral from data such as those presented The procedure has several restrictions and is strictly applicable only to atomic reactant ion species. However, the differences between the effects of temperature and (KE,,) in the present data are so large that at least qualitatively the procedure may be applicable. (KE,) in a VT-SIFDT is given byi3-15
where mi, mb, and mn are the masses of the reactant ion, buffer gas, and reactant neutral, respectively, ud is the ion drift velocity, and T i s the temperature. A particular (KE,,) can be obtained with varying contributions from the drift tube component (first term) and the thermal component (second term). If the reactant ion is monatomic, then at a particular (KE,,), any difference between the rate constants measured at different temperatures can be attributed to the internal temperature of the neutral. For neutrals having such large vibrational frequencies that vibrational excitation can be neglected at the temperatures used, the temperature dependence of the rate constants at a particular (KE,) can only be a dependence on rotational temperature of the reactant neutral. Because the internal modes of polyatomic ions can be excited in a drift tube, the analysis is strictly limited to monatomic ions. If polyatomic reactant ions were used, the temperature dependence of the rate constants at a particular (KE,,) would (12) Cw,J. C.;Snodgrass. J . T.; Freidhoff, C. B.; McHugh, K. M.; Bowen, K. H.J . Chem. Phys. 1987,87, 4302. (13) McFarland, M.; Albritton, D. L.; Fehsenfeld, F. C.; Ferguson, E. E.; Schmeltekopf, A. L. J . Chem. Phys. 1973, 59, 6610. (14) McFarland, M.; Albritton, D. L.; Fehsenfeld, F. C . ; Ferguson, E. E.; Schmeltekopf, A. L. J . Chem. Phys. 1973, 59, 6620. ( 1 5 ) McFarland, M.; Albritton, D. L.; Fehsenfeld, F. C.; Ferguson, E. E.; Schmeltekopf. A . L.J . Chem. Phys. 1973, 59, 6629.
Rate Constants for Electron Detachment of NOreflect varying amounts of internal excitation of the ion, as well as the rotational temperature dependence of the neutral, a situation that is difficult to interpret. Average ion rotational energies in a drift tube have been found to be equal to the average ion-buffer center-of-mass kinetic energy.'6 In the present case, the buffer mass and the neutral reactant masses are similar, Ar having a mass of 40 amu and N20, C 0 2 , and C,Hs all having masses of 44 amu. This similarity ensures that the average ion-buffer center-of-mass kinetic energy is similar to (KE,,) and therefore that the rotational excitation of NO- at a particular (KE,,) is approximately independent of temperature for each of these three neutral reactants. Rotational temperature effects on rate constants for ion-molecule reactions are generally mall,^-^ and therefore the slight differences in the rotational energy distribution should not severely affect the measured rate constants. In contrast to rotational excitation, vibrational excitation cannot be assumed to reach equilibrium in drift tubes.17 However, the vibrational frequency of NO- is high enough6 that little vibrational excitation should occur at low collision energies. In addition, NOis unstable with respect to detachment by vibrational excitation6 and is therefore not expected to live long enough to react. A significant problem in deriving internal temperature dependences for the present data is that non-Maxwellian kinetic energy distributions are found in drift tubes when an Ar buffer is sed.'^*'^ This means that, at a particular (KE,,), different energy distributions are found at different temperatures. The magnitude of this effect is usually small. Even for an extreme case where the rate constant increases by a factor of 85 over an energy range of 0.2-1 eV, an increase of only a factor of 3 has been observed for rate constants in an Ar buffer over that expected for a Maxwellian distribution at a given ( KE,,).20 The present data show much larger differences than this. The differences in rate constants measured in an Ar buffer and those derived for a Maxwellian ion speed distribution from rate constants measured in a He buffer have been attributed to the fact that the high-energy tail of the ion speed distribution in an Ar buffer is more pronounced than is that for a Maxwellian distribution.,O Most likely, it is the NO- ions in the high-energy part of the NO- speed distribution that detach most readily. Therefore, the high-energy tail of the distribution is likely to be truncated as the result of electron detachment by the Ar buffer. We suggest that the rate constants measured here, Le., for reactions with species other than the buffer, are therefore less likely to be affected by the non-Maxwellian distributions found in an Ar buffer than would otherwise be the case. Another argument may be offered against non-Maxwellian energy distributions as an explanation for the difference we observe in the effects of temperature and kinetic energy on the rate constants for collisional detachment. This argument is that, for N,O and CO,, the rate constants at a particular (KE,,) are independent of temperature at low temperatures. We suggest that at least part of the difference observed in the rate constants at higher temperatures but at a particular (KE,,) is due to the internal temperature of the reactant neutral. Additional evidence is given below. As noted above, only minor differences are observed between the temperature dependence and the kinetic energy dependence of the rate constants for detachment of NO- in collisions with CO, and N 2 0 at low temperatures. At higher temperatures large differences are observed. For C,Hs, differences are observed at all temperatures. The most likely explanation of this observation is that at the low temperatures no significant vibrational excitation (16) Duncan, M. A.; Bierbaum, V. M.; Ellison, G . 8.; Leone, S. R. J . Chem. Phys. 1983, 79, 5448. ( 1 7) Kriegel, M.; Richter, R.; Lindinger, W.; Barbier, L.;Ferguson, E. E. J . Chem. Phys. 1988, 88, 2 13. (18) Dressler, R. A.; Meyer, H.; Langford, A. 0.;Bierbaum, V. M.; Leone, S. R. J . Chem. Phys. 1987, 87, 5578. (19) Dressler, R. A.; Beijers, J. P. M.; Meyer, H.; Penn. S. M.; Bierbaum, V . M.; Leone, S. R. J . Chem. Phys. 1988, 89, 4707. ( 2 0 ) Albritton, D. L. I n Kinetics of Ion-Molecule Reactions; Ausloos, P., Ed.; Plenum Press: New York, 1979.
The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 3289 10
N O + N20 + NO + N20 + e
142K
0 0 A
173K 212K 23SK
465K
"
-1 ""' 165 K m a l -2212KMel
J '
\
10
1
''SO
30
10
40
50
60
20
(KE~,,,)-~ (evrl
Figure 6. Rate constants for the detachment channel for the reaction of NO- and N 2 0 as a function of inverse (KE,). Solid circles, open circles, open squares, open triangles, and solid squares represent data taken at 142, 173, 212, 298, and 465 K, respectively. The solid line is the derived rate constant for the u = 1 level of the bending mode. The dashed and dashed-dotted lines represent fits to the data at 465 and 212 K, respec-
tively. of N 2 0 and CO, occurs. Therefore, any internal temperature dependence can result only from rotational excitation of the neutral reactant. The fact that little internal temperature dependence is in fact observed indicates that rotational energy does not have a large effect on the rate constants, at least at low temperatures. This absence of rotational energy dependence may hold at higher temperatures as well, since even at 142 K fairly large values of J are populated. For both N 2 0 and CO,, the most highly populated J level at 142 K is 5-6, and significant (10% of the maximum) excitation is found for J equal to 16.,' At room temperature and above, however, the vibrational bending modes of both of these molecules are excited enough to affect the rate constants; Le., the fraction of the population excited is on the order of the reaction efficiency.21 Propane has even lower lying bending vibrations than does either CO, or N 2 0 and has some vibrational excitation at all temperatures used here. At 465 K, other vibrational modes in propane become significantly populated as well. Thus, while it appears that rotational energy has little effect on the rate constants, vibrational energy has a substantial effect. Enhancement of the rate constants for electron detachment of NOin collisions with vibrationally excited neutral molecules has also been postulated by McFarland et ale4 Their analysis was based on the fact that molecules with low-frequency vibrational modes showed large rate constants and large preexponential factors. A similar trend is found in the present data. Assuming that the difference in rate constants for collisional detachment at different temperatures but at a particular (KE,) is due to vibrational excitation of the neutral reactant, rate constants for the detachment of NO- by C 0 2 and N 2 0 in the u = I bending mode can be derived as a function of (KE,,). The derivation is done in the following manner. The fraction of vibrational excitation at each temperature is calculated according to the Boltzmann equation, neglecting anharmonicity. The detachment rate constants at 298 K are given by k298 = froko + fr,kl (3) where k298are the measured detachment rate constants at 298 K, fro 2nd frl are the fractions of molecules (C02or N20) in the zeroth and first excited vibrational level, respectively, and ko and k , are the detachment rate constants for u = 0 and u = 1, respectively. Rate constants for the detachment channel are obtained by multiplying the overall rate constants by the branching fraction into the detachment channel. Inherent in this derivation is the assumption that the small percentage of molecules with u > 1 does (21) Herzberg, G . Molecular Spectra and Molecular Structure III. Electronic Spectra and Electronic Structure of Polyatomic Molecules; Van Nostrand Reinhold: New York, 1966.
3290 The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 10
NO- + CO1+ NO+ C o p + e
0 173K 0 h 12 10 27 K Y 165K
IV
0
10
20
30
40
50
1
60
(KE~,,,)-~(evy'
Figure 7. Rate constants for the detachment channel for the reaction of NO- with C 0 2 as a function of inverse (KE,). Open circles, open squares, open triangles, and solid squares represent data taken at 173, 212, 298, and 465 K, respectively. The solid line is the derived rate constant for the u = 1 level of the bending mode. The dashed and dashed-dotted lines represent fits to the data at 465 and 212 K , respectively.
not affect the analysis. The small fraction of states with higher vibrational excitation is included in the u = 1 population in this analysis. The data are not of sufficient accuracy to warrant inclusion of terms of higher u levels in eq 3. The rate constants for the lowest temperatures (1 42 K for N 2 0 and 173 K for C02) are set equal to ko, Le., to the rate constants for u = 0. The only unknown in eq 3 is then k , . The rate constants for the detachment channel for N 2 0 and C 0 2 are shown in Figures 6 and 7 . Rate constants are plotted versus the reciprocal of (KE,,). The derived rate constants for u = I are given as the solid lines. For detachment by either N 2 0 or C 0 2 , the rate constants for u = 1 are approximately an order of magnitude larger than are those for u = 0. Considering the low value of the electron affinity of NO, it is not surprising that vibrational energy greatly increases the detachment efficiency. To test the validity of the procedure described here, rate constants at 465 and 212 K were derived from the Boltzmann distributions a t those temperatures and from the values for ko and k , obtained at 298 K . The results of these derivations are shown as dashed and dashed-dotted lines for 465 and 21 2 K, respectively, in Figures 6 and 7 . For both N 2 0 and C 0 2 , the derived values of the rate constants agree very well with the measured values at 465 K. At 21 2 K the derived values for N 2 0 are either in good agreement or slightly high, depending on the (KE,,). For C 0 2 the agreement at 21 2 K is not so good but still satisfactory. These checks suggest that the model is correct and that the bending mode vibrations of COz and N 2 0 do in fact substantially increase the
Viggiano et al. rate constants for collisional detachment. The data for C3Hs also indicate that vibrational energy increases the rate constants for detachment, but the derivation of rate constants for a particular mode is not possible due to the many vibrational modes of C3H8. While the above analysis strongly indicates that the major part of the increase in rate constant with temperature at a particular average kinetic energy is due to vibrational excitation in the neutral, it cannot be ruled out that some of the increase arises from the different kinetic energy distributions that are expected in the Ar buffer. The most puzzling aspect of the data is the fact that increasing kinetic energy leads to decreasing rate constants for detachment at higher temperatures for C3Hsand C2H6. As stated previously, we are unable to provide a reasonable explanation of this effect. While the rate constants for detachment show a positive dependence on temperature and, in most cases, on kinetic energy, those for association show negative dependences, as shown in Figure 5. This is to be expected for association reactions that depend on a stabilizing collision to remove excess energy. For both N 2 0 and C 0 2 , the rate constants for association at the two lowest temperatures have similar dependences on (KE,,). Very little association was observed at the higher temperatures; the effective bimolecular rate constants are on the order of to cm3 s-l. The temperature dependences of these reactions are F 3and T-4,6for C 0 2 and NzO, respectively. Simple theory predicts temperature dependences of approximately T2.'for both reaction^.^) Thus, for C 0 2 the experimental and theoretical temperature dependences are in reasonable agreement, while for N 2 0 the agreement is poor. However, the agreement is improved if the high-temperature data are excluded. In any case, the theory applies to low-pressure association with no competing channels. In summary, rate constants for the reactions of NO- with several neutrals were measured as a function of (KE,,) at several temperatures. The main channel in every case studied here is electron detachment. For N 2 0 and C 0 2 , association was also observed at low temperatures. The rate constants for detachment were found to have positive activation energies, as expected for an endothermic process. The dependences of the detachment rate constants on (KE,) were found to vary greatly with temperature. This variation has been explained by rate constants that increase greatly with vibrational excitation of the neutral. A simple model has allowed us to calculate detachment rate constants for the u = 0 and u = 1 levels of the bending modes of N 2 0 and C 0 2 . For detachment in collisions with C3Hs and C2H6. rate constants that decreased with increasing (KE,,) were found. This decrease is surprising and remains unexplained. The association channels show inverse temperature dependences, in reasonable agreement with theory. (22) Viggiano, A. A. J . Chem. Phys. 1986,84,244and references therein. (23) Morris, R . A,; Viggiano, A. A,; Paulson, J. F. J . Chem. Phys. 1990, 92. 2342.
