The mechanism of O(3P) atom reaction with ethylene and other simple olefins

Reactions of oxygen atoms with ethylene, propene, and 2-butene were studied at room temperature under discharge flow conditions by resonance fluorescence spectroscopy of O and H atoms at pressures of 0.08 to 12 torr. The measured total rate constants of these reactions are K = (7.8 ± 0.6)·10^?13cm³s^?1,K = (4.3 ± 0.4) ± 10^?12 cm³ s^?1, K = (1.4 ± 0.4) · 10^?11 cm³ s^?1. The branching ratios of H atom elimination channels were measured for reactions of O atoms with ethylene and propene. No H-atom elimination was found for the reaction of O-atoms with 2-butene. A redistribution of reaction O + C₂ channels with pressure was found. A mechanism of the O + C₂ reaction was proposed and the possibility of its application to other olefins is discussed. On the basis of mechanism the pressure dependence of the total rate constant for reaction O + C₂ was predicted and experimentally confirmed in the pressure range 0.08–1.46 torr.     

Recommendations for measuring second-order rate constants and kinetic solvent isotope effects on acid-catalyzed reactions

Kinetic solvent isotope effects (KSIE) were measured for the hydrolyses of acetals of benzaldehydes in aqueous solutions covering the pH (pD) range of 1–6. For p-methoxybenzaldehyde diethyl acetal, k/k = 1.8–3.1, depending on the procedure used to calculate the KSIE and on the pH (pD) range used as the basis for k(k). It is shown that this variation is an experimental artifact, and is a characteristic of KSIE measurements in general. It is recommended that k be calculated from a least-squares fit of data to the equation k_obs = k[L⁺], and that the KSIE be reported as k/k. The limitation remains, however, that the KSIE measured for a variety of substances over quite different pH (pD) ranges may not be comparable to more than ?20%. The source of these observations is discussed in terms of small changes in the activity coefficient ratios (a specific salt effect), including the solvent isotope effect on the activity coefficient ratio [eq. (3)].     

The kinetics of the reaction F + H2 → HF + H. A critical review of literature data

Published experimental studies concerning the determination of rate constants for the reaction F + H₂ → HF + H are reviewed critically and conclusions are presented as to the most accurate results available. Based on these results, the recommended Arrhenius expression for the temperature range 190–376 K is k = (1.1 ± 0.1) × 10⁻¹⁰ exp |-(450 ± 50)/T| cm³ molecule⁻¹ s⁻¹, and the recommended value for the rate constant at 298 K is k = (2.43 ± 0.15) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. The recommended Arrhenius expression for the reaction F + D₂ → DF + D, for the same temperature range, based on the recommended expression for k and accurate results for the kinetic isotope effect k/k is k = (1.06 ± 0.12) × 10^×10 exp |-(635 ± 55)/T|cm³ molecule⁻¹ s⁻¹, and the recommended value for 298 K is k = (1.25 ± 0.10) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 67–71, 1997.     

Kinetic characteristics of chloride-assisted oxidative dealkylation of alkylcobalamins

The recent experiments on the chloride-assisted dealkylation of alkylcobalamins by a variety of oxidants (IrCl, AuCl, Fe(H₂O)₅Cl²⁺, and PtCl), which are scattered in several previous publications, and their general kinetic characteristics are summarized. The kinetic studies are also extended to include the dealkylations of (methylaquo)?3,5,6-trimethylbenzimidazolylcobamide and protonated base-off ethylcobalamin by IrCl (1.0M Cl^?) and by Fe(III) ions at 0.1M Cl^?, and the demethylation of (methylaquo)?3,5,6-trimethylbenzimidazolylcobamide by AuCl (1.0M Cl^?). This extension is in an effort to substantiate the general mechanism which has been previously proposed for these oxidative dealkylations. The general kinetic characteristics are described in terms of a preassociation of the reactants, followed by a rate-determining electron-transfer process to yield the R-B radical, which then undergoes further reactions to produce the products observed. The overall reactions are discussed within the framework of chlorine-bridging inner sphere electron-transfer reactions.     

Kinetics and mechanism of the oxidation of some carboxylates by a nickel (III) oxime-imine complex

The kinetics of the oxidation of formate, oxalate, and malonate by |Ni^III(L¹)|²⁺ (where HL¹ = 15-amino-3-methyl-4,7,10,13-tetraazapentadec-3-en-2-one oxime) were carried out over the regions pH 3.0–5.75, 2.80–5.50, and 2.50–7.58, respectively, at constant ionic strength and temperature 40°C. All the reactions are overall second-order with first-order on both the oxidant and reductant. A general rate law is given as - d/dt|Ni^III(L¹)²⁺| = k_obs|Ni^III(L¹)²⁺| = (k_d + nk_s |R|)|Ni^III(L¹)²⁺|, where k_d is the auto-decomposition rate constant of the complex, k_s is the electron transfer rate constant, n is the stoichiometric factor, and R is either formate, oxalate, or malonate. The reactivity of all the reacting species of the reductants in solution were evaluated choosing suitable pH regions. The reactivity orders are: k_HCOOH > k; k > k > k, and k > k < k for the oxidation of formate, oxalate, and malonate, respectively, and these trends were explained considering the effect of hydrogen bonded adduct formation and thermodynamic potential. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 225–230, 1997.     

A pulse radiolysis study of I and (SCN) in aqueous solutions over the temperature range 15–90°C

The extinction coefficients and the decay kinetics of I and (SCN) have been characterized over the 15–90°C-temperature range. The extinction coefficients of I at 385 and 725 nm were determined to be 10,000 and 2560M^?1 cm^?1, respectively, based on the extinction coefficient of (SCN) at 475 nm being equal to 7600M^?1 cm^?1. At these three wavelengths, all extinction coefficients were constant over the temperature range studied. The rate of decay of both I and (SCN) was found to be a function of I^? and SCN^? concentration, respectively, as well as temperature.     

Kinetics and mechanisms of substitution reactions with sulfur-containing nucleophiles in aqueous acid solutions. I—rates of reactions of some tetrahalopalladate (II) anions with thiourea and selenourea

The activation energy parameters for the reaction of PdX (X=Cl^?, Br^?) in aqueous halide acid solution with thiourea (tu) and selenourea (seu) have been determined. High rates of reaction parallel low enthalpies and appreciable negative entropy of activation. The rate law in each case simplifies to k_obs=k[L] where L=tu or seu, and only ligand-dependent rate constants are observed at 25°C. The ligand-dependent rate constants for the first identifiable step in the PdCl + X system is (9.1±0.1) × 10³ M^?1 sec^?1 and (4.5±0.1) × 10⁴ M^?1 sec^?1 for X=tu and seu, respectively, while for the PdBr + X system it is (2.0±0.1) × 10⁴ M^?1 sec^?1 and (9.0±0.1) × 10⁴ M^?1 sec^?1 for X=tu and seu, respectively.     

Chemical actinometry at 147.0 nm

Hexafluoroacetone (HFA) and O₂ were photolyzed at 147.0 nm to investigate their use in chemical actinometry. The products, CO for the former and O₃ in the latter case, were monitored. For accurate comparison, both of these substances were irradiated by a single light source with two identical reaction cells at 180° to each other. The light intensities I were measured under the same integrated as well as instantaneous photon flux based on ? and ?_CO (quantum yield) as 2 and 1, respectively. Optimum conditions for maximum product yield were 5.0 torr HFA pressure and an O₂ flow rate of 200 ml/min at 1 atm pressure for a 20-minute photolysis period. For light intensity variations between 1.09 × 10¹⁴ and 2.10 × 10¹⁵ photons absorbed/sec, the ratio I/I_HFA was found to be unity. Calibration with the commonly used N₂O actinometer for a ? value of 1.41 showed that I/I_HFA and I/I are unity. Both HFA and O₂ are suitable chemical actinometers at 147.0 nm with ?_CO and ? of 1 and 2, respectively. The light intensity determination in the first case involves the measurement of only one product which is noncondensible at 77°K, whereas wet analysis for O₃, the only product, in the second actinometer is necessary. Both of these determinations are quite simple and are preferable over product analysis in N₂O actiometry, wherein N₂ separation from other noncondensibles at 77°K is required.     

The 13C and D kinetic isotope effects in the reaction of CH4 with Cl

The kinetic isotope effects in the reaction of methane (CH₄) with Cl atoms are studied in a relative rate experiment at 298 ± 2 K and 1013 ± 10 mbar. The reaction rates of ¹³CH₄, ¹²CH₃D, ¹²CH₂D₂, ¹²CHD₃, and ¹²CD₄ with Cl radicals are measured relative to ¹²CH₄ in a smog chamber using long path FTIR detection. The experimental data are analyzed with a nonlinear least squares spectral fitting method using measured high‐resolution spectra as well as cross sections from the HITRAN database. The relative reaction rates of ¹²CH₄, ¹³CH₄, ¹²CH₃D, ¹²CH₂D₂, ¹²CHD₃, and ¹²CD₄ with Cl are determined as k/k = 1.06 ± 0.01, k/k = 1.47 ± 0.03, k/k = 2.45 ± 0.05, k/k = 4.7 ± 0.1, k/k = 14.7 ± 0.3. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 37: 110–118, 2005     

Peculiar kinetics of the complex formation in the iron(III)–sulfate system

The results of comprehensive equilibrium and kinetic studies of the iron(III)–sulfate system in aqueous solutions at I = 1.0 M (NaClO₄), in the concentration ranges of T = 0.15–0.3 mM, and at pH 0.7–2.5 are presented. The iron(III)–containing species detected are FeOH²⁺ (=FeH_?1), (FeOH) (=Fe₂H_?2), FeSO, and Fe(SO₄) with formation constants of log β = ?2.84, log β = ?2.88, log β = 2.32, and log β = 3.83. The formation rate constants of the stepwise formation of the sulfate complexes are k_1a = 4.4 × 10³ M^?1 s^?1 for the ${\rm Fe}^{3+} + {\rm SO}_4^{2-}\,\stackrel{k_{1a}}{\rightleftharpoons}\, {\rm FeSO}_4^+The results of comprehensive equilibrium and kinetic studies of the iron(III)–sulfate system in aqueous solutions at I = 1.0 M (NaClO₄), in the concentration ranges of T = 0.15–0.3 mM, and at pH 0.7–2.5 are presented. The iron(III)–containing species detected are FeOH²⁺ (=FeH_?1), (FeOH) (=Fe₂H_?2), FeSO, and Fe(SO₄) with formation constants of log β = ?2.84, log β = ?2.88, log β = 2.32, and log β = 3.83. The formation rate constants of the stepwise formation of the sulfate complexes are k_1a = 4.4 × 10³ M^?1 s^?1 for the ${\rm Fe}^{3+} + {\rm SO}_4^{2-}\,\stackrel{k_{1a}}{\rightleftharpoons}\, {\rm FeSO}_4^+$ step and k₂ = 1.1 × 10³ M^?1 s^?1 for the ${\rm FeSO}_4^+ + {\rm SO}_4^{2-} \stackrel{k_2}{\rightleftharpoons}\, {\rm Fe}({\rm SO}_4)_2^-$ step. The mono‐sulfate complex is also formed in the ${\rm Fe}({\rm OH})^{2+} + {\rm SO}_4^{2-} \stackrel{k_{1b}}{\longrightarrow} {\rm FeSO}_4^+$ reaction with the k_1b = 2.7 × 10⁵ M^?1 s^?1 rate constant. The most surprising result is, however, that the 2 FeSO? Fe³⁺ + Fe(SO₄) equilibrium is established well before the system as a whole reaches its equilibrium state, and the main path of the formation of Fe(SO₄) is the above fast (on the stopped flow scale) equilibrium process. The use and advantages of our recently elaborated programs for the evaluation of equilibrium and kinetic experiments are briefly outlined. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 114–124, 2008     

Rate constants for some reactions of free radicals with haloacetates in aqueous solution

The kinetics of the acqueous-phase reactions of the free radicals ·OH, ·Cl, and SO· with the halogenated acetates, CH₂FCOO^?, CHF₂COO^?, CF₃COO^?, and with CH₂ClCOO^?, CHCl₂COO^?, CCl₃COO^? were investigated. Generally, the reactivity decreases with increasing halogen substitution and is in the order k(·OH) > k(SO·) > k(·Cl), but there is no general relation between the effect on reactivity of chlorine and fluorine substitution. © 1995 John Wiley & Sons, Inc.     

Kinetics of the solvolysis of [Co(3Rpy)4Cl2]+ ions (R = Me or Et) in water and in water + methanol mixtures

Rates of solvolysis of ions [Co(3Rpy)₄Cl₂]⁺ with R = Me and Et have been measured over a range of temperatures for a series of water-rich water + methanol mixtures to investigate the effect of changes in solvent structure on the solvolysis of complexes presenting a largely hydrophobic surface to the solvent. The variation of the enthalpies and entropies of activation with solvent composition has been determined. A free energy cycle relating the free energy of activation in water to that in water + methanol is applied using free energies of transfer of individual ionic species from water into water + methanol. Data for the free energy of transfer of chloride ions ΔG(Cl^?) from both the spectrophotometric solvent sorting method and the TATB method for separating ΔG(salt) into ΔG(i) for individual ions are used: irrespective of the source of ΔG(Cl^?), in general, ?ΔG(Co(Rpy)₄Cl²⁺) > ?ΔG(Co(Rpy)₄Cl₂⁺), where Rpy = py, 4Mepy, 4Etpy, 3Etpy, and 3Mepy, showing that changes in solvent structure in water-rich water + methanol mixtures generally stabilize the cation in the transition state more than the cation in the initial state for this type of complex ion. A similar result is found when the free energy cycle is applied to the solvolysis of the dichloro (2,2′,2″-triaminotriethylamine)cobalt(III) ion. The introduction of a Me or Et group on the pyridine ring in [Co(Rpy)₄Cl₂]⁺ has little influence on the difference {ΔG(Co(Rpy)₄Cl²⁺)?ΔG(Co(Rpy)₄Cl₂⁺)} in water + methanol with the mol fraction of methanol < 0.20.     

The acetyl radicals CH3CO· and CD3CO· studied by flash photolysis and kinetic spectroscopy

Ultraviolet absorption spectra have been characterized for the acetyl-h₃ and acetyl-d₃ radicals, which were generated by the flash photolysis of the corresponding acetones. The spectra are broad and intense, with values of the extinction coefficient at the respective maxima estimated as: ?CH₃CO(215) = (1.0 ± 0.1) × 10⁴ L/mol·cm and ?CD₃CO(207.5) = (1.0 ± 0.05) × 10⁴ L/mol·cm. Rate constants for the reactions of mutual interaction were estimated as: k = 3.5 × 10¹⁰ L/mol·s and k = 3.4 × 10¹⁰ L/mol·s. Rate constants for the reactions of cross interaction were estimated as: k = 8.6 × 10¹⁰ L/mol·s and k = 5.2 × 10¹⁰ L/mol·s. The related values of the cross interaction ratios k/(kk)^1/2 = 2.6 and k/(kk)^1/2 = 1.6 do not differ significantly from the statistical value of 2. The participation of the radical displacement reactions was estimated in terms of the fractions k/k = 0.38 and k/k = 0.47. Corroborative spectra were obtained from the flash photolysis of methyl ethyl ketone and biacetyl, and the relative rates of the competing primary processes were estimated from the relative peak heights of the acetyl and methyl radicals in each system.     

A kinetic study of the autocatalytic permanganate oxidation of formic acid

The kinetics of the permanganate oxidation of formic acid in aqueous perchloric acid has been studied. The results indicate that this reaction is autocatalyzed by both manganese(II) ion (formed as a reaction product) and colloidal manganese dioxide (formed as an intermediate). The apparent rate constants corresponding to the noncatalytic and autocatalytic reaction pathways are given, respectively, by the following equations The activation energies associated with the true rate constants, ??, ??, ??, ??, ??, and ?? are 37.2, 62.5, 70.9, 52.5, 40.8, and 59.9 kJ mol^?1, respectively. The percentage of the total reaction corresponding to each pathway is given for typical experimental conditions. Mechanisms in agreement with the kinetic data are proposed for the six different reaction pathways observed.     

The quantum efficiency of the primary processes in formaldehyde photolysis at 3130 Å and 25°C

The mechanism of the photolysis of formaldehyde was studied in experiments at 3130 Å and in the pressure range of 1–12 torr at 25°C. The experiments were designed to establish the quantum yields of the primary decomposition steps (1) and (2), CH₂O + hν → H + HCO (1): CH₂O + hν → H₂ + CO (2), through the effects of added isobutene, trimethylsilane, and nitric oxide on Φ_CO and Φ. The ratio Φ_CO/Φ was found to be 1.01 ± 0.09(2σ) and (Φ + Φ_CO)/2 = 1.10 ± 0.08 over the range of pressures and a 12-fold change in incident light intensity. Isobutene and nitric oxide additions reduced Φ to about the same limiting value, 0.32 ± 0.03 and 0.34 ± 0.04, respectively, but these added gases differed in their effects on Φ_CO. With isobutene addition Φ_CO/Φ reached a limiting value of 2.3; with NO addition Φ_CO exceeded unity. The addition of small amounts of Me₃SiH reduced Φ to 1.02 ± 0.08 and lowered Φ_CO to 0.7. These findings were rationalized in terms of a mechanism in which the “nonscavengeable,” molecular hydrogen is formed in reaction (2) with ?₂ = 0.32 ± 0.03, while the “free radical” hydrogen is formed in reaction (1) with ?₁ = 0.68 ± 0.03. In the pure formaldehyde system these reactions are followed by (3)–(5): H + CH₂O → H₂ + HCO (3); 2HCO → CH₂O + CO (4); 2HCO → H₂ + 2CO (5). The data suggest k₄/k₅ ? 5.8. Isobutene reduced Φ by the reaction H + iso-C₄H₈ → C₄H₉ (20), and the results give k₂₀/k₃ ? 43 ± 4, in good agreement with the ratio of the reported values of the individual constants k₃ and k₂₀.     

Studies on the composition and kinetics of chromium(III)-alanine system

Kinetics of the complex formation of chromium(III) with alanine in aqueous medium has been studied at 45, 50, and 55°C, pH 3.3–4.4, and μ = 1 M (KNO₃). Under pseudo first-order conditions the observed rate constant (k_obs) was found to follow the rate equation: Values of the rate parameters (k_an, k, K_IP, and K) were calculated. Activation parameters for anation rate constants, ΔH^≠(k_an) = 25 ± 1 kJ mol^?1, ΔH^≠(k) = 91 ± 3 kJ mol^?1, and ΔS^≠(k_an) = ?244 ± 3 JK^?1 mol^?1, ΔS^≠(k) = ?30 ± 10 JK^?1 mol^?1 are indicative of an (I_a) mechanism for k_an and (I_d) mechanism for k routes (‥substrate Cr(H₂O) is involved in the k route whereas Cr(H₂O)₅OH²⁺ is involved in k′ route). Thermodynamic parameters for ion-pair formation constants are found to be ΔH°(K_IP) = 12 ± 1 kJ mol^?1, ΔH°(K) = ?13 ± 3 kJ mol^?1 and ΔS°(K_IP) = 47 ± 2 JK^?1 mol^?1, and ΔS°(K) = 20 ± 9 JK^?1 mol^?1.     

The kinetics of the interaction of peroxy radicals. I. The Tertiary Peroxy Radicals

Existing data on the self-reactions of tertiary peroxy radicals RO₂ has been reanalyzed and corrected to deduce Arrhenius parameters for both termination and nontermination paths. For R = t-Butyl, these are logk_t(M^?1sec^?1) = 7.1 - (7.0/θ) and logk_nt(M^?1sec^?1) = 9.4 - (9.0/θ), respectively, different from those recommended by other authors. The higher magnitudes observed for termination processes of tertiary peroxy radicals like those of cumyl and 1,1-diphenylethyl have been discussed in terms of a much greater cage recombination of cumyloxy radicals as contrasted with t-butoxy radicals. It is shown that for benzyl peroxy radicals, the R—O bond dissociation energy is sufficiently low (18–20 kcal) that reversible dissociation into R^˙ + O₂ opens a competing second-order path to fast recombination R^˙ + RO → ROOR. This path is probably not important for cumyl peroxy radicals under usual experimental conditions but can become important for 1,1-diphenyl ethyl peroxy radicals at (O₂) < 10^?3M. At very low RO concentrations (<10^?5M), in the absence of added O₂, an apparent first-order disappearance of RO can occur reflecting the rate determining breaking of the cumyl—O bond followed by the second step above. The thermochemistry of RO is used to show that the reaction of R₂O₄ → 2RO + O₂ must be concerted and cannot proceed via RO which is too unstable and cannot form even from RO^˙ + O₂.     

Oxidation of thallium(I) by hexacyanoferrate(III) in aqueous acetic acid

The hexacyanoferrate(III)-thallium(I) reaction in aqueous acetic acid containing large concentrations of hydrochloric acid is considerably accelerated both by hydrogen and chloride ions as well as increasing acetic acid in the medium. The experimental results obey the rate law (1) where β₁ to β₆ are the cumulative stability constants of the species TlCl, TlCl, TlCl, HFe(CN), H₂Fe(CN) and H₃Fe(CN)₆ respectively and k_a and k_b are the rate constants associated with the mono- and di-protonated oxidant species. The main active species are H₂Fe(CN) and TlCl.     

2–Butoxyethanol and benzyl alcohol reactions with the nitrate radical: Rate coefficients and gas‐phase products

The bimolecular rate coefficients k and k were measured using the relative rate technique at (297 ± 3) K and 1 atmosphere total pressure. Values of (2.7 ± 0.7) and (4.0 ± 1.0) × 10^?15 cm³ molecule^?1 s^?1 were observed for k and k, respectively. In addition, the products of 2‐butoxyethanol + NO₃^? and benzyl alcohol + NO₃^? gas‐phase reactions were investigated. Derivatizing agents O‐(2,3,4,5,6‐pentafluorobenzyl)hydroxylamine and N, O‐bis (trimethylsilyl)trifluoroacetamide and gas chromatography mass spectrometry (GC/MS) were used to identify the reaction products. For 2‐butoxyethanol + NO₃^? reaction: hydroxyacetaldehyde, 3‐hydroxypropanal, 4‐hydroxybutanal, butoxyacetaldehyde, and 4‐(2‐oxoethoxy)butan‐2‐yl nitrate were the derivatized products observed. For the benzyl alcohol + NO₃^? reaction: benzaldehyde ((C₆H₅)C(?O)H) was the only derivatized product observed. Negative chemical ionization was used to identify the following nitrate products: [(2‐butoxyethoxy)(oxido)amino]oxidanide and benzyl nitrate, for 2‐butoxyethanol + NO₃^? and benzyl alcohol + NO₃^?, respectively. The elucidation of these products was facilitated by mass spectrometry of the derivatized reaction products coupled with a plausible 2‐butoxyethanol or benzyl alcohol + NO₃^? reaction mechanisms based on previously published volatile organic compound + NO₃^? gas‐phase mechanisms. © 2012 Wiley Periodicals, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain of the United States of America.

© 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 778–788, 2012     

Kinetics and mechanism of the reaction of CH3O with NO

The kinetics of the reaction of CH₃O with NO and the branching ratio for HCHO product formation, obtained as Γ_HCHO = (Rate of HCHO formation) / (Rate of CH₃O decay), have been studied using a discharge flow reactor. Laser induced fluorescence has been used to monitor the decay of the CH₃O radical and the build-up of the HCHO product. Overall rate constants and product branching ratios were measured at room temperature over the pressure range of 0.72–8.5 torr He. Three reaction mechanisms were considered which differed in the routes of HCHO formation: (i) direct disproportionation; (ii) via an energized collision complex; or (iii) both reaction routes. It has been shown that data on the pressure dependence of the overall rate constant are not sufficient to distinguish between these mechanisms. In addition, an accurate value of Γ is required. Analysis of the available experimental data provided 0.0 and about 0.1 as the lower and upper limit for Γ, respectively. Since the rate constants derived for CH₃ONO formation were not sensitive to the value assumed for Γ, k = (1.69 ± 0.69) × 10^?29 cm⁶ molecule^?2 s^?1 and k = (2.45 ± 0.31) × 10^?11 cm³ molecule^?1 s^?1 could be derived. The rate constant obtained for formaldehyde formation when extrapolated to zero pressure is k = (3.15 ± 0.92) × 10^?12 cm³ molecule^?1 s^?1. © 1994 John Wiley & Sons, Inc.