8470
J. Phys. Chem. A 1997, 101, 8470-8479
Reaction Kinetics of Muonium with N2O in the Gas Phase James J. Pan,* Donald J. Arseneau, Masayoshi Senba,† Mee Shelly,‡ and Donald G. Fleming TRIUMF and Department of Chemistry, UniVersity of British Columbia, 4004 Wesbrook Mall, VancouVer, BC, Canada V6T 2A3 ReceiVed: May 20, 1997; In Final Form: August 8, 1997X
The thermal reaction Mu + N2O has been studied by the muon spin rotation (µSR) technique at temperatures from 303 to 593 K and pressures up to 60 atm. The overall reaction rate coefficient depends on the N2O pressure quadratically in pure N2O and is proportional to both the N2O partial pressure and the total pressure in mixtures, confirming the theoretical prediction of Diau and Lin that the analogous H atom reaction proceeds through two channels in this temperature range, forming different products, MuN2O and MuO + N2. The measured total rate coefficients are much larger than those reported by Marshall et al. for H(D) + N2O, indicating a dramatic kinetic isotope effect, which is mainly due to the enhanced quantum tunneling of the ultralight Mu atom. Even at room temperature (and low pressure), kMu/kH ≈ 120, the largest yet seen in comparisons of gas-phase Mu and H reactivity at such relatively high temperatures. The addition reaction forming MuN2O (and by implication, HN2O) contributes significantly to the total reaction rate at higher pressures but with the thermal rate coefficient remaining in the termolecular regime even at the highest pressures measured.
1. Introduction The H + N2O reaction has long been of interest in combustion chemistry.1-8 Nitrous oxide is an important intermediate formed during propellant combustion9 and is known to contribute to the depletion of stratospheric ozone.10 The H + N2O reaction, a key reaction in N2O flames, is one of the few that can convert N2O into N2 thus avoiding production of undesirable nitrogen oxides in the atmosphere.11 The development of chemical kinetic models to control N2O formation is therefore highly desirable. To this end, it is essential to understand the temperature and pressure dependence of these reactions so that appropriate rate coefficients can be included in combustion models. Furthermore, the H + N2O reaction has a very large activation barrier despite being highly exothermic, spin allowed, and symmetry allowed, and therefore is of fundamental interest.4-7 The H(D) + N2O reactions have been extensively studied experimentally,1-3,12 but all of these, as well as earlier studies, were carried out at high temperatures (400-3000 K, some involved hot H/D atoms) and low pressures (mostly less than 1 atm). There are also several theoretical calculations of the rate coefficients for this reaction with different techniques.1,3-6 Despite the wealth of information available on this key reaction, the overall reaction mechanism and thus the dependence of the rate on pressure at different temperatures has yet to be established and confirmed by experiments.1,5,6 At the relatively low pressures that have characterized the H(D) + N2O experiments to date, no pressure dependence has been observed,1 in contrast to recent theoretical predictions.5,6 However, any expected pressure dependence would have been obscured by the small pressure ranges covered (55-430 Torr), especially in light of the tunneling effect which exhibits the opposite pressure dependence.5 Furthermore, although significant isotope effects attributed to quantum tunneling were observed with H and D,1 * To whom all correspondence should be addressed. E-mail: jjpan@ triumf.ca. Fax: (604) 222-1074. † Present address: Department of Physics, Dalhousie University, Halifax, NS, Canada. ‡ Present address: Department of Chemistry, Miami University, Oxford, OH 45056. X Abstract published in AdVance ACS Abstracts, October 15, 1997.
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these atoms differ only by a factor of 2 in mass. A much greater tunneling effect can be expected for the analogous muonium reaction, Mu + N2O, where the muonium atom, Mu, consisting of a positive muon (µ+) and an electron, behaves chemically as an ultralight H isotope with only one-ninth the mass (mMu/ mH ) 1/9). The main distinction of Mu reaction kinetics compared with traditional hydrogen isotopes is the remarkable range and magnitude of kinetic isotope effects (KIEs) it is sensitive to. Because of its remarkably low mass, the quantum tunneling effect of the Mu atom, alluded to above, can be greatly enhanced relative to H(D), enabling observation of tunneling effects at easily accessible temperatures, indeed even at room temperature. Zero-point energy (ZPE) shifts, both at the transition states (TSs) and, in the present case, in the intermediate adduct, MuN2O*, also make significant contributions to the KIE. Another advantage in the study of Mu reactivity lies in the ease with which Mu atoms are formed by charge exchange in the gas,13 which in turn facilitates measurements at high pressures. The wide and unprecedented pressure variation undertaken in the present study provides an invaluable probe of the total pressure dependence of H isotope + N2O kinetics and enables us to distinguish contributions from different reaction channels. This is of considerable importance in comparison with current theoretical calculation of this reaction system.5,6 Moreover, the muon spin rotation/relaxation (µSR) technique (see below) monitors Mu atoms individually, thereby eliminating the selfinteractions that often plague H atom experiments.12,14 The experimental Mu rate coefficients can thus be more accurate than those of their heavier atom counterparts (see, e.g., ref 15) and can, in principle, be used to predict H atom reaction rates, provided an accurate theory and potential energy surface are available. The only previous measurement of the Mu + N2O reaction was carried out in aqueous solution (H2O saturated with N2O) by Venkateswaran et al.16 who reported a KIE on the order of 1000 in favor of the Mu atom at room temperature. © 1997 American Chemical Society
Reaction Kinetics of Muonium with N2O
J. Phys. Chem. A, Vol. 101, No. 45, 1997 8471
Figure 1. Reaction coordinates and energetics for H + N2O, adopted from refs 1 and 5 (cf. text). The zero-point energies are included.5
2. The Reaction Mechanisms and the µSR Technique A. Reaction Pathways of H(Mu,D) + N2O. The H + N2O reaction17 has four possible products as shown in the potential energy diagram of Figure 1, adapted from the energetics given in refs 1 and 5, which suggests that the major reaction channels, particularly at lower temperatures, would be those forming N2 + OH or HNNO.The reaction forming HNNO involves addition of H to the N end of N2O and passing through the HNNOq transition state (TS1) to form the excited HNNO* intermediate which is then stabilized by collisions, M
H + N2O h HNNO* 98 HNNO
(1)
Both HNNO* and HNNO may undergo a 1,3-hydrogen shift to form (via TS2, assisted by tunneling) the unstable NNOH intermediate, which dissociates to N2 + OH, but the rate depends strongly on internal excitation, with stabilized HNNO reacting much more slowly. Depending on the time scale of the experiment, HNNO may be regarded either as a relatively stable reaction intermediate or as a “final” product. Consistent with the calculations in ref 5, the results presented in this article are interpreted by regarding HNNO (and MuNNO) as a final product and hence with addition and stabilization considered as a distinct reaction channel. The addition channel has an enthalpy barrier of 38 kJ/mol at 300 K and is exothermic, ∆H0 ) -61 kJ/mol, for forming stable HNNO (though much less so for MuNNO). It is unusual in that the formation of HNNO has a higher effective Arrhenius A factor than the reverse unimolecular dissociation, a result of the low entropy of the reactant H atom combined with loss of a rotor in the dissociation.1,6 Thus, with a relatively small dissociation coefficient, HNNO* can be expected to have a high probability of either stabilization or tunneling through the second barrier (TS2). The recent theoretical calculations have shown that the addition channel is important at even 200 Torr total pressures,5,6 in contrast to earlier experiments which concluded that it is not a major pathway based on a reported pressure independence of the reaction rate coefficient.1 The present results for the Mu + N2O reaction, however, clearly establish the importance of pressure-dependent pathways in the overall mechanism. The reaction forming N2 + OH, with ∆H0 ) -261 kJ/mol, is highly exothermic overall,5 but also exhibits high reaction barriers. There are two pathways for this reaction to proceed, a “direct” pathway and an “indirect” one, shown by the longdashed and solid lines, respectively, in Figure 1. The direct pathway is the addition of an H atom to the O end of N2O (with the transition state NNOHq) to form the unstable NNOH intermediate which immediately dissociates to N2 and OH. The
calculated enthalpy barrier relative to the reactants for this direct process is 76 kJ/mol at 300 K.5 Note that this direct mechanism is distinct from simple abstraction, where the initial H attack at the O atom with simultaneous weakening of the N-O bond would lead to a large preexponential factor in the Arrhenius expression due to the loose transition state.1 This channel should have no pressure dependence since NNOH is not a stable product. At temperatures above 1000 K, calculations show that this channel contributes significantly to the overall reaction rate coefficient but it is not expected to account for the observed rate coefficient at lower temperatures.1,6 The alternate indirect mechanism shares the first step with the addition channel that forms the HNNO* intermediate. This step is followed by a 1,3-hydrogen shift to form the unstable NNOH intermediate (via TS2), which dissociates with an enthalpy barrier of 64 kJ/mol relative to H + N2O. At lower temperatures, the indirect pathway is favored over the direct one since it is much easier to tunnel through the lower first barrier (TS1) and particularly the narrower second barrier (TS2) of the indirect process.1,4,6,8,18 The H data, despite the absence of any moderator pressure dependence, agree much better with the indirect model than the direct model calculations below 1000 K.1,6 The tunneling effect is dramatic because the intermediate (HNNO*) precursor to the 1,3-hydrogen shift transition state gives rise to a large (but narrow) internal barrier of 126 kJ/mol relative to the HNNO ground state. The formation rate of N2 + OH through this indirect channel is dependent on the total pressure because the collisional activation/deactivation of HNNO* affects both the classical overbarrier and quantum tunneling reaction rates for forming NNOH. The reactions forming NH + NO and NNH + O are both highly endothermic with reaction enthalpies of about 147 and 203 kJ/mol at 300 K, respectively,5 and thus are not important contributions to the thermal reaction rates near room temperature. The isotopic reaction Mu + N2O is expected to proceed in the same fashion as that for H + N2O, represented by the following scheme: k′d
Mu + N2O 9q8 MuO + N2 MuONN ka
Mu + N2O 9q8 MuNNO* MuNNO k-a
MuNNO* 9q8 Mu + N2O MuNNO
βks[M]
MuNNO* + M 98 MuN2O + M kd
MuNNO* 9q8 MuO + N2 Mu-O | | N- N
(2) (3) (4)
(5) (6)
where the ks are rate coefficients for each particular process and β is the efficiency of collisional stabilization in the “strong collision” model.19 From either an eigenvalue solution or the steady-state approximation, the total thermal rate coefficient for the overall chemical reaction of Mu is found20 to have the form:
kc ) k′d +
ka(kd + βks[M]) k-a + kd + βks[M]
(7)
where kc is defined by -d[Mu]/dt ) kc[N2O][Mu]. This expression exhibits the usual expected chemical kinetics limits.
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Pan et al.
Figure 2. Schematic of a µSR experiment. TM is the muon counter. B, L, F, and R are positron counters. The arrows under the column labeled “muon spin” indicate the muon spin direction while the arrows under the column “field” show the direction of the applied magnetic field. The gas target positioned in the center of the counters is actually much larger than indicated in the figure.
Thus, when k-a is much larger than βks[M] + kd (the lowpressure limit, indicated over the range of pressures run), and k′d, the contribution from the direct pathway, is small (this is as expected from the earlier discussion for H, and ZPE conceivably could raise the barrier height further for Mu), eq 7 reduces to
kc ) k1 + k2[M]
(8)
with
k1 )
kakd k-a
(9)
k2 )
kaβks k-a
(10)
where k1 is the overall bimolecular rate coefficient for MuO + N2 formation and k2 the termolecular rate coefficient for MuN2O stabilization. Note that the moderator “M” here can be either N2O itself or some added inert gas (N2 or Ar in this study). B. µSR Technique. The gas chemistry time-differential µSR techniques20-22 utilize 100% spin-polarized muons produced in the parity-violating pion decay processes. When these spin-polarized muons (with a few MeV initial energy) enter a reaction cell filled with gases, they slow down and thermalize. Some muons emerge as thermalized Mu atoms, also spinpolarized.13,20,24 In a µSR experiment, the reaction rate is measured by monitoring the disappearance of spin-polarized Mu atoms via the detection of muon decay positrons (µ+ f e+νeνjµ), which are emitted along the muon spin direction in either a transverse (TF) or longitudinal (LF) magnetic field (see Figure 2). A clock is started by an incoming muon and stopped by the detection of a positron in any of the counters. The electronic logic of the data acquisition system ensures that there is only one muon in the target at a time so the muon that created each decay positron is unambiguously identified. The time histogram of detected positrons, N(t), from a single counter can be fit to the following form
N(t) ) N0e-t/τµ[1 ( A(t)] + NB
(11)
where N0 is a normalization factor, τµ is the muon lifetime (2.197 µs), NB is a constant to account for time-independent background, and A(t) is the muon decay asymmetry which accounts
Figure 3. A typical TF experimental µSR signal after removal of normalization, decay, and background. The spectrum was obtained in 22 atm pure N2O at 303 K and 5 G TF. The solid line is a fit to eq 12. It is primarily the relaxation rate “λ” which is of interest.
for the time dependence of the muon polarization and contains the kinetics information of the reaction. In general, A(t) has the form
A(t) )
∑i Aie-λ t cos(ωit + φi) i
(12)
where the index i labels each magnetic environment of the muon: paramagnetic Mu (i ) Mu), a diamagnetic molecule (i ) D), or a paramagnetic Mu-containing radical (i ) R). The parameters Ai, λi, ωi, and φi are, respectively, the initial asymmetry, the relaxation rate, the Larmor precession frequency (equals zero in a LF), and the initial phase of the spin polarization of muons in the i-th environment.20-24 A typical µSR signal obtained in a weak TF is shown in Figure 3, giving the relaxation rate, λ, of principal interest in the present experiments. µSR is essentially a spin-depolarizing technique: any mechanism which perturbs the coherent precession of triplet Mu spin in a weak TF or causes “spin flip” in a LF gives rise to relaxation of the signal.20 Most of the work in the present study was carried out in a weak TF environment, where polarization loss is essentially one of spin dephasing, described by eq 12. Since N2O has no unpaired electron, there is no intermolecular spin exchange interaction causing relaxation as there is, for example, in the case of Mu + NO.22 However, in a transverse magnetic field, when Mu enters one of the two long-lived product species MuO and MuN2O, both free radicals, it rapidly loses phase coherence with the reactant Mu ensemble (T2) because either the hyperfine interaction with nuclear moments splits the precession frequency, similar to the case of MuC2H4,27-29 and/ or concurrently it undergoes rapid collisional spin relaxation (T1), primarily due to the electronic spin-rotation interaction.20,28 The OH radical is difficult to observe even in liquid-phase electron spin resonance (ESR) due to its large spin rotation interaction.30 Current studies in our research group,20,28,31-34 as well as theoretical studies of spin relaxation of muonium free radicals,29 have demonstrated extremely fast relaxation rates (extrapolated) in weak magnetic fields, particularly for small radical systems. The spin relaxation of free radicals can only be followed in a LF of appreciable strength (J1 kG).20,28,31 Nonetheless, the spin-rotation coupling in the MuNNO radical is not as strong as in some smaller radicals, e.g., MuO and MuCO. Unlike the reaction of Mu + CO,32 the Mu relaxation rate due to spin-rotation coupling in the short-lived intermediate MuNNO* is much smaller than the chemical reaction rate (kc) and can be neglected. The above assessment is confirmed by the fact that the measured relaxation rates have no field
Reaction Kinetics of Muonium with N2O
J. Phys. Chem. A, Vol. 101, No. 45, 1997 8473
dependence in up to 100 G TF (see below). Thus, the Mu spin relaxation rate observed in a weak TF (
