Limiting Rate Coefficients Research Articles

Determination of the High-Pressure Limiting Rate Coefficient and the Enthalpy of Reaction for OH + SO2

The kinetics of the association reaction OH + SO2 have been studied using laser flash photolysis at 248 nm to generate OH radicals and laser-induced fluorescence to monitor their decay under pseudo-first-order conditions, [OH] ≪ [SO2]. The removal kinetics of OH(v = 1) + SO2 have been measured over the temperature range of 295 to 673 K. Master equation calculations were performed to demonstrate that, provided intramolecular vibrational redistribution is fast, OH(v = 1) + SO2 is a good approximation for the high-pressure rate coefficient of the OH(v = 0) + SO2 + M reaction, giving k1∞(T) = (2.04 ± 0.10) × 10-12 (T/300 K)-0.27 ± 0.11 cm3 molecule-1 s-1. This temperature dependence of the rate coefficient suggests that the reaction occurs on a barrierless surface. The kinetics of the reaction OH(v = 0) + SO2 + M, k1, were also studied. At room temperature, the kinetic data were in good agreement with literature values. At elevated temperatures, 523 to 603 K, equilibrium behavior was observed between OH + SO2 and HOSO2. This represents the first direct observation of equilibration, and an analysis of the data, using a Third-Law method, with ΔrS0298 = −142 ± 10 J mol-1 K-1 gives a reaction enthalpy of ΔrH0298 = −113.3 ± 6 kJ mol-1, and ΔfH0298(HOSO2) = −373 ± 6 kJ mol-1. These numerical values are significantly lower than literature values. k1∞(T) has been used to generate a consistent set of parameters to describe k1([M], T) for OH + SO2 for use in atmospheric modeling, and ΔrH0298 has been used to assess the role of HOSO2 in the oxidation of SO2 at elevated temperatures.

The Recombination of Propargyl Radicals: Solving the Master Equation

We have investigated theoretically the recombination reaction between two propargyl (C3H3) radicals using previously published BAC-MP4 calculations (supplemented by DFT-B3LYP results) to characterize the potential energy surface, RRKM theory to compute microcanonical rate coefficients, and solutions to the time-dependent, multiple-well master equation to predict thermal rate coefficients and product distributions as a function of temperature and pressure. The thermal rate coefficient k(T,p) drops off precipitously at high temperature, regardless of the pressure. Below 500 K, k(T,p) ≈ k∞(T), the high-pressure limit rate coefficient for initial complex formation, independent of p. For 500 K < T < 2000 K, the rate coefficient increases with increasing pressure, as one would normally expect. At 2000 K, the “coalescence temperature” for this reaction, k(T,p) = k0(T), the zero-pressure rate coefficient, and only bimolecular products (phenyl + H) are predicted, no matter how high we make the pressure. The latter effect is a consequence of all the intermediate complexes reaching their “stabilization limits,” a concept discussed extensively in the text. Below 800 K, many C6H6 isomers are formed as products, and the pressure and temperature dependence of the branching fractions is easily understood from conventional reasoning. Above 800 K, the product distributions begin to be dominated by isomers reaching their stabilization limits and disappearing as important products. Above 1200 K, the only significant products are fulvene, benzene, and phenyl + H. Beyond 1700 K fulvene disappears, and for T > 2000 K the only products are phenyl + H. We discuss our results in terms of the eigenvalues and eigenvectors of G, the transition matrix of the master equation. A “good” rate coefficient exists only when the rate is controlled by a single eigenvalue of G. A jump of the k(T,p) curve for any pressure from one eigenvalue to another is triggered by the reaching of critical stabilization limits, producing “avoided crossings” of the eigenvalue curves. It is at such avoided crossings that biexponential reactant decays occur.

Kinetic Studies of the Reactions CH3+ NO2→ Products, CH3O + NO2→ Products, and OH + CH3C(O)CH3→ CH3C(O)OH + CH3, over a Range of Temperature and Pressure

The title reactions were investigated using pulsed laser photolysis combined with pulsed laser induced fluorescence detection of CH3O to determine the rate coefficients for CH3 + NO2 → products (3) and CH3O + NO2 → products (5) as a function of temperature and pressure, and to estimate the yield of CH3 (and thus the yield of CH3C(O)OH) from the reaction of OH with CH3C(O)CH3 (2) at two different temperatures. Reaction 3 has both bimolecular and termolecular components: a simplified falloff parametrization with Fcent = 0.6 gives = (3.2 ± 1.3) × 10-28(T/297)-0.3 cm6 s-1 and = (4.3 ± 0.4) × 10-11(T/297)-1.2 cm3 s-1 with CH3NO2 the likely product. The rate constant for the bimolecular reaction pathway to form CH3O + NO (3a) was found to be 1.9 × 10-11 cm-3 s-1. The low- and high-pressure limiting rate coefficients for reaction between CH3O and NO2 to form CH3ONO2 (5b) were derived as = (5.3 ± 0.3) × 10-29(T/297)-4.4 cm6 s-1 and = (1.9 ± 0.05) × 10-11(T/297)-1.9 cm3 s-1, respectively. Although the final resul...

Kinetics of the Reactions of N(4S) Atoms with O2 and CO2 over Wide Temperatures Ranges

Rate coefficients for the depletion of ground-state nitrogen atoms by O2 have been measured using a high-temperature photochemistry reactor. The N atoms were generated by VUV flash photolysis of N2O, and the relative concentrations were monitored by resonance fluorescence. The data are best fitted by the expression k(400−1220 K) = 2.0 × 10-18(T/K)2.15 exp(−2557 K/T) cm3 molecule-1 s-1 with 2σ precision limits varying from ±7% to ±20% depending upon temperature, and corresponding 2σ accuracy limits of ±23% to ±30%. Good agreement is found with earlier, electrical discharge initiated, rate coefficient measurements for the 280−910 K domain. Semiempirical theory-based calculations are presented that lead to a plot nearly indistinguishable from those of the present results and the Baulch et al. recommendation for the 300−5000 K temperature range. These yield a classical barrier E0⧧ of 27.4 kJ mol-1. No reaction with CO2 could be observed; upper limit rate coefficients were obtained from 285 to 1140 K. These up...

A shock tube study of the pyrolysis of NO2

NO2 concentration profiles in shock-heated NO2/Ar mixtures were measured in the temperature range of 1350–2100 K and pressures up to 380 atm using Ar+ laser absorption at 472.7 nm, IR emission at 6.25±0.25 μm, and visible emission at 300–600 nm. In the course of this study, the absorption coefficient of NO2 at 472.7 nm was measured at temperatures from 300 K to 2100 K and pressures up to 75 atm. Rate coefficients for the reactions NO2+MNO+O+M (1), NO2+NO22NO+O2 (2a), and NO2+NO2NO3+NO (2b) were derived by comparing the measured and calculated NO2 profiles. For reaction (1), the following low- and high-pressure limiting rate coefficients were inferred which describe the measured fall-off curves in Lindemann form within 15% [FORMULA] The inferred rate coefficient at the low- pressure limit, k1o, is in good agreement with previous work at higher temperatures, but the energy of activation is lower by 20 kJ/mol than reported previously. The pressure dependence of k1 observed in the earlier work of Troe [1] was confirmed. The rate coefficient inferred for the high pressure limit, k1∞, is higher by a factor of two than Troe's value, but in agreement with data obtained by measuring specific energy-dependent rate coefficients. For the reactions (2a) and (2b), least-squares fits of the present data lead to the following Arrhenius expressions: [FORMULA] For reaction (2), the new data agree with previously recommended values of k2a and k2b, although the present study suggests a slightly higher preexponential factor for k2a. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 483–493, 1997.

Conventional transition state theory/Rice–Ramsperger–Kassel–Marcus theory calculations of thermal termolecular rate coefficients for H(D)+O2+M

Several ab initio studies have focused on the minimum energy path region of the hydroperoxyl potential energy surface (PES) [J. Chem. Phys. 88, 6273 (1988)] and the saddle point region for H-atom exchange via a T-shaped HO2 complex [J. Chem. Phys. 91, 2373 (1989)]. Further, the results of additional calculations [J. Chem. Phys. 94, 7068 (1991)] have been reported, which, when combined with the earlier studies, provide a global description (but not an analytic representation) of the PES for this reaction. In this work, information at the stationary points of the ab initio PES is used within the framework of conventional Transition State Theory (TST)/RRKM. Theory to compute estimates of the thermal termolecular rate coefficients for the reaction between the H(D) atom and O2 in the presence of two different bath gases, argon and nitrogen, as a function of pressure and temperature. These calculations span a pressure range from 1.0 Torr to the high-pressure limit and a temperature range from 298.15 to 6000.0 K. Conventional TST/RRKM Theory was utilized within the framework of two models: an equilibrium model employing the strong collision assumption (model I), [R. G. Gilbert and S. C. Smith, Theory of Unimolecular and Recombination Reactions (Blackwell, Oxford, 1990), as implemented in the UNIMOL program suite]; and a steady-state model that includes chemical activation (model II), using the collisional energy transfer approximation proposed by J. Troe [J. Chem. Phys. 66, 4745, 4758 (1977); 97, 288 (1992)]. In this work we first summarize the pressure-dependent fall-off curves (calculated with model I) and the high-pressure limit rate coefficients (calculated with models I and II) over the entire temperature range, and then focus on the fall-off behavior for temperatures between 298.15 and 2000.0 K. Direct comparisons are made between the experimentally determined termolecular rate coefficients (either from direct measurements or based on recommended pressure/temperature-dependent expressions) and the estimates of these rate coefficients calculated in this work as a function of pressure at 298.15 and 500.0 K. In the fall-off region, we find better agreement between the theoretical and experimental values at low pressures than at pressures approaching the high-pressure limit. Significant deviations are observed between theory and experiment as the high-pressure limit is approached. The disagreement at 298.15 K is greater for N2 than for Ar.

The pressure dependence of the thermal decomposition of N2O

The pressure dependence of the thermal decomposition of nitrous oxide was investigated behind shock waves at temperatures between 1570 K and 3100 K and pressures from 0.3 atm to 450 atm. Nitrous oxide concentration profiles were measured using IR emission from the 4.5-μm ν1 band of N2O. The pressure dependence of the measured rate constant was described using simple Lindemann fits, resulting in the following low- and high-pressure limiting rate coefficients: These values were used to extrapolate current measurements of the rate coefficient to lower temperatures, where the agreement with past work is excellent. Therefore the limiting rate coefficients given above should be suitable for kinetic modeling over a temperature range of 800–2000 K and pressures up to 450 atm. © 1996 John Wiley & Sons, Inc.

The pressure dependence of the thermal decomposition of N2O

The pressure dependence of the thermal decomposition of nitrous oxide was investigated behind shock waves at temperatures between 1570 K and 3100 K and pressures from 0.3 atm to 450 atm. Nitrous oxide concentration profiles were measured using IR emission from the 4.5-μm ν1 band of N2O. The pressure dependence of the measured rate constant was described using simple Lindemann fits, resulting in the following low- and high-pressure limiting rate coefficients: These values were used to extrapolate current measurements of the rate coefficient to lower temperatures, where the agreement with past work is excellent. Therefore the limiting rate coefficients given above should be suitable for kinetic modeling over a temperature range of 800–2000 K and pressures up to 450 atm. © 1996 John Wiley & Sons, Inc.

Kinetics of the cross reaction between amidogen and methyl radicals

For the title reaction, the pressure dependent rate coefficients were studied at 298 K using two complementary experimental techniques. Pulse radiolysis combined with UV absorption was employed at pressures between 500 and 1000 mbar, while a fast-flow system with a quadrupole mass spectrometer (at low ionization energies) was applied at pressures in the range of 0.7–5.1 mbar. The fall-off curve was constructed in terms of Troe's analysis, and the following high- and low-pressure limiting rate coefficients were derived: k rec,∞ = (1.3 ± 0.3) × 10 −10 × ( T/300) 0.42 cm 3 molecule −1 s −1 and k rec,0/[ He] = (1.8 ± 0.5) × 10 −25 × ( T/300) −3.85 cm 6 molecule −2 s −1.

Direct measurement of the reaction CH 3+OH and its pathways between 300 and 480 K

In an extension of our earlier room temperature study [2] the title reaction was measured directly in a flow reactor at 480 K and in the pressure range between 1.05 and 9.1 mb. OH was used in an excess over CH 3 . Both reactants along with some products were monitored by mass spectrometry. CH 3 profiles served as the major observable quantity for the extraction of rate data. This had to be done by using computer simulation since it was impossible to work under pseudo-first order conditions. Under the conditions used, the CH 3 profiles are most sensitive to the association channel CH 3 +OH→CH 3 OH (1a), and by variation of the pressure it was possible to cover a considerable portion of the fall-off region. The 480 K data were fitted along with the 300 K measurements. If the high pressure limiting rate coefficient k ∞ 1a (298 K)=9.3·10 −11 cm 3 molec −1 s −1 of Hochanadel et al. [1] is assumed to be temperature independent, as suggested by Tsang and Hampson [8] only a poor fit is achieved yielding k 0 1a values in He at 300 and 480 K of (2.5 ± 1.0)·10 −27 and (6.5±1.0)·10 −28 cm 6 molec −2 sec −1 respectively. However, a much better fit is found by increasing K ∞ 1a to 1.7·10 −10 cm 3 molec −1 s −1 , with k 0 1a (300 K) and k 0 1a (480 K) having values of 2.0·10 −27 and 5.5·10 −28 cm 6 molec −2 sec −1 respectively. 1 CH 2 concentrations formed through the channel CH 3 +OH→ 1 CH 2 +H 2 O (1d) reach a steady state early in the reaction through the presence of H 2 , CH 4 or water (D 2 O). Channel (1d) could be quantitatively assessed by the measurement of HDO when OD was used instead of OH. The results show k 1 d .0D (480 K)=4·10 −12 cm 3 molec −1 sec −1 . In combination with further measurements at 300 K and 370 K an expression for k 1d (T) was derived. The temperature dependence provides evidence that the reaction enthalpy for the 1 CH 2 channel may differ by over 2.0 kcal mol −1 from the value obtained from the current Sandia data [6], giving ΔH f.300k ( 1 CH 2 )=103.9 kcal mol −1 . The reaction channels to CH 2 OH +H (1b) and to CH 3 O+H (1c) could not be detected.

The metals-HTP technique: Kinetics of the Cr/O 2/Ar reaction system from 290 to 1510 K

The recently developed Metals-HTP (high-temperature photochemistry) technique for kinetic measurements on gas-phase elementary combustion reactions of metallic species is described. This technique complements the HTFFR (high-temperature fast-flow reactor) technique and extends the achievable pressure range: 15 to 615 mbar has been covered in the present work. The reactions between ground state ( 7 S 3 ) Cr atoms and O 2 have been studied. The observed Cr-consumption rate coefficients are pressure dependent over the entire 290–1510 K range. For T ≤700 K only recombination is observed, while above that temperature O-atom abstraction is also evident. The low-pressure limiting rate coefficients for Cr+O 2 +Ar→CrO 2 +Ar are well described by log 10 [ k 0 (290–1510 K)/(cm 6 molecule −2 s −1 )]=−24.4 −1.56log 10 (T/K), with 2σ precision limits varying from ±10% to ±21%, depending on temperature, and corresponding estimated 2σ accuracy limits of ±22% to ±29%. The rate coefficients for the Cr+O 2 → CrO+O reaction are well fitted by k 2 (855−1510 K)=2.2×10 −10 exp (−3560 K/T) cm 3 molecule −1 s −1 with estimated 2σ accuracy limits of ±28%. Chromium is a health hazard in its hexavalent form to which it is partially converted in waste incinerators. The present results indicate that over the approximately 700 to 1600 K range, of prime interest to that problem, the ratio k 2 / k 0 [M] increases, for atmospheric pressure, by over two orders of magnitude, i.e. the competition between the two described precursor pathways for Cr 6+ compound formation is very temperature-sensitive.

An investigation of temperature and pressure dependence of the reaction of CF2ClO2 radicals with nitrogen dioxide by flash photolysis and time resolved mass spectrometry

AbstractRate coefficients of the termolecular reaction were determined over the temperature range of 248–324 K and at pressures from 1 to 10 torr by time resolved mass spectrometry. CF2ClO2 radicals were generated by flash photolysis of CF2ClBr in the presence of oxygen. Their rate of decay was measured by following (CF2O2)+ fragment ions formed in the ion source. With 2 to 40 mtorr of NO2 present the dominant removal pathway is addition to form the peroxynitrate. The third order rate coefficients are wholly within the falloff over the experimental pressure range, and have a negative temperature coefficient. Rate constants for the reverse reaction, the unimolecular dissociation of CF2ClO2NO2, D. Koppenkastrop and F. Zabel, Int. J. Chem. Kinet., 23, 1 (1991) were employed to calculate equilibrium constants, from which a 600 torr value of the combination rate coefficient was obtained at each temperature. From the temperature dependence of the equilibrium constants, the average enthalpy of reaction over the experimental temperature range was found to be 106.1 ± 0.3 kJ/mol. Extrapolation of the combination rate constants to lower and higher pressures, and estimates of low and high pressure limiting rate coefficients, k0 and k∞ were done by nonlinear least squares fit of the experimental data, using the empirical Fc equations developed by Troe.

Association reactions of atoms and radicals

AbstractThe pressure and temperature dependences of association reactions involving atoms and/or radicals is discussed and illustrated by reference to the reactions CH3 + CH3 → C2H6, CH3 + O2 → CH3O2, CH3 + H → CH4, and H + C2H4 → C2H5. Recent experimental measurements of the rate coefficients, k([M], T) are described, particular attention being paid to experiments designed to measure the rate coefficient over wide ranges of pressure and temperature. Methods of fitting the experimental data, to obtain estimates of the limiting rate coefficients, k0 and k∞, and to permit extrapolation to regions beyond the experimental range, are discussed. These methods include the Troe factorization technique, a combination of master equation and variational RRKM theory, and recent calculations by Wagner and Wardlaw using the technique developed by Wardlaw and Marcus to describe loose transition states.

Pressure and temperature dependence of the gas-phase recombination of hydroxyl radicals

Rate constants for the reaction OH + OH + M ..-->.. H/sub 2/O/sub 2/ + M (M = N/sub 2/, H/sub 2/O) have been determined by using flash photolysis of H/sub 2/O vapor in combination with quantitative OH resonance spectrometry. For M = N/sub 2/ experiments were performed at 253, 298, and 353 K and at pressures between 26 and 1100 mbar. Under these conditions the reaction is found to be primarily in the low-pressure limit with k/sub 1,N/sub 2///sup 0/ (T = 298 K) = (6.9/sub -2.5//sup +1.4/) x 10/sup -31/ cm/sup 6//s and a temperature dependence of T/sup -0.8/. Both the absolute value of k/sub 1,N/sub 2// and its temperature variation are in very satisfactory agreement with theoretical predictions and extrapolations from high-temperature dissociation data. A pressure falloff of k/sub 1,N/sub 2// is also observed. On the basis of a theoretical analysis of the falloff behavior, a high-pressure limiting rate coefficient of k/sub 1/infinity = 1.5 x 10/sup -11/ cm/sup 3//s, independent of temperature, is predicted. From experiments in N/sub 2//H/sub 2/O mixtures with /kappa cur//sub H/sub 2/O/ = 0.11 at pressures up to 140 mbar a low-pressure limiting rate coefficient for H/sub 2/O as a third bodymore » of k/sub 1,H/sub 2/O//sup 0/ (T = 298 K) = (4.0 /sub -2.0//sup +1.3/) x 10/sup -30/ cm/sup 6//s is obtained.« less

Dynamics of unimolecular dissociation of silylene

The semiempirical valence-bond surface formulated by Viswanathan et al. [J. Phys. Chem. 89, 1428 (1985)] for the unimolecular dissociation of SiH2 has been fitted to an analytical function of the type suggested by Murrell and co-workers [J. Phys. Chem. 88, 4887 (1984)]. The fitted surface accurately represents most of the experimental and CI results. The dynamics of the unimolecular dissociation of SiH2 to form Si and H2 have been investigated by classical trajectory methods on this fitted surface. The effect of describing the initial state of the molecule using normal and local mode approximations has been studied. In spite of the presence of the heavier atom, no bond or mode specificity is observed. The product energy distribution is found to be statistical. Using the RRK model, the high-pressure limiting rate coefficient is found to be k(T,∞)=3.38×1012 exp[−61.6 kcal mol−1/RT] s−1, which is less than the dissociation rate for SiH4. This has been attributed to the higher activation energy for SiH2 and to a statistical factor.

Theoretical Prediction of CH3O and CH2OH Gas-Phase Decomposition Rate Coefficients

Theoretical predictions are made for the pressure and temperature dependences of two reactions involved in methanol combustion: (A) CH3O → CH2O + H and (B) CH2OH → CH2O + H. The calculations are carried out by using RRKM theory with a Gorin model for the activated complexes, with fall-off effects being taken into account by using the master equation. Results for the high-pressure rate coefficients (s-1) are (A) 3×1014 exp(-108 kJ mol-1 /RT), (B) 7×1014 exp(-124 kJ mol-1 /RT) at 1000 K. For the low-pressure limiting rate coefficient (cm3 s-1) over the range 600- 1000 K (A) 8×10-9 exp(-90 kJ mol-1 /RT); (B) 2×10-8 exp(-108 kJ mol-1 /RT). At 1000 K, the pressure at which the fall-off rate coefficients are one-half of their limiting high-pressure values are 3x108 Pa for both reactions. Formulae for inclusion of these reactions (including fall- off effects) over the range 300-2000 K and 10-2-106 Pa in modelling complex kinetic schemes are presented.

Theoretical investigations of elementary processes in the chemical vapor deposition of silicon from silane. Unimolecular decomposition of SiH4

The rates and mechanism for the unimolecular decomposition of SiH4 have been investigated using quasiclassical trajectory methods to follow the dynamics and Metropolis sampling procedures to average over the initial SiH4 phase space. The semiempirical potential-energy surface has been fitted to scaled SCF calculations and to a variety of experimental data. It gives the correct SiH4 equilibrium structure, reaction endothermicities, and bond energies for SiH4, SiH3, and SiH2. All hydrogen atoms are treated in an equivalent fashion. Excellent first-order decay plots are obtained for the microcanonical rates for the total SiH4 decomposition as well as for the separate decomposition channels. The low-energy pathway is found to be a three-center elimination to form SiH2+H2. The decomposition channel forming SiH3+H becomes important only at internal SiH4 energies in excess of 5.0 eV. Comparison of computed falloff curves with RRKM calculations fitted to experimental results indicates that the critical threshold energy for the three-center reaction lies in the range 2.10&amp;lt;E0&amp;lt;2.20 eV. The calculated high-pressure limiting rate coefficient is k(T,∞)=(1.08±0.02)×1013 exp(−49 600±1200/RT) s−1. The calculated distributions of relative translational energies for SiH2 and H2 reflect the fact that there is no barrier to the back reaction. Both concerted three-center eliminations and processes that resemble ‘‘half-collisions’’ of SiH3+H are found to be important decomposition pathways.

Rate coefficients for the reaction HS+NO+M→HSNO+M (M=He, Ar, and N2) over the temperature range 250–445 K

HS radicals were generated by photodissociation of H2S at 193 nm and their disappearance monitored by LIF. The three-body recombination of HS with NO has been studied over the temperature range 250–445 K using He, Ar, and N2 as diluent gases. The temperature dependences of the low-pressure, three-body rate coefficients are given by 10−(22.56±0.60)T−(3.28±0.27), 10−(23.27±0.50)T−(2.98±0.20), and 10−(24.43±0.94)T−(2.48±0.36) cm6 molecule−2 s−1 for He, Ar, and N2, respectively. A tentative value of (2.7±0.5)×10−11 cm3 molecule−1 s−1 for the high pressure limiting rate coefficient over the range 250–300 K is suggested on the basis of extrapolation. These kinetic data are evaluated in terms of unimolecular rate theory.

On the Mechanism of Reversible Unimolecular Reactions and the Canonical (“High Pressure”) Limit of the Rate Coefficient at Low Pressures*)

AbstractJost's [1] treatment of generalized first order kinetics is used for a new discussion of the mechanism of reversible unimolecular reactions. A detailed analysis of time dependent average microscopic rate coefficients and level populations is presented using exact solutions for a realistic model of an isomerization reaction. It is shown that unimolecular fall‐off for the macroscopic relaxation is not mainly due to a reduced population of reactive levels as suggested by the irreversible Lindemann mechanism, but rather due to a fast reverse reaction even at early times. It is furthermore shown that the average microscopic rate coefficients can be measured directly, in principle. At equilibrium they are equal to the canonical (“high pressure”) limit of the rate coefficient even for arbitrarily low pressures. Practical experimental schemes are suggested for thus obtaining high pressure limiting rate coefficients without extrapolation procedures.