Studies on the reaction N + N3 → N2(B 3Πg) + N2(X 1Σ+g)

Strongly enhanced N₂ first positive emission N₂(B ³Π_g → A ³Σ⁺_u) has been observed on addition of N atoms into a flowing mixture of Cl and HN₃. The dependence of the emission intensity on N atom concentration gave a rate constant for the reaction N + N₃ → N₂(B ³Π_g) + N₂(X ¹Σ⁺_g) of _i(1.6 ± 1.1) × 10^?11 cm³ molecule^?1 s^?1. That for the reaction Cl + HN₃ → HCl + N₃ is (8.9 ± 1.0) × 10^?13 cm³ molecule^?1 s^?1 from the decay of the emission. Comparison of the emission intensity in ClHN₃ with that in ClHN₃N gave the rate constant of the reaction N₃ + N₃ → N₂(B ³Π_g) + 2N₂(X ¹Σ⁺_g) as 1.4 × 10^?12 cm³ molecule^?1 s^?1 on the assumption that N + N₃ yields only N₂(B ³Π_g) + N₂(X ¹Σ⁺_g).     

A laser flash photolysis/IR diode laser absorption study of the reaction of chlorine atoms with selected alkanes

A high‐resolution IR diode laser in conjunction with a Herriot multiple reflection flow‐cell has been used to directly determine the rate coefficients for simple alkanes with Cl atoms at room temperature (298 K). The following results were obtained: k(Cl + n‐butane) = (1.91 ± 0.10) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + n‐pentane) = (2.46 ± 0.12) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + iso‐pentane) = (1.94 ± 0.10) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + neopentane) = (1.01 ± 0.05) × 10^?10 cm³ molecule^?1 s^?1, k(Cl + n‐hexane) = (3.44 ± 0.17) × 10^?10 cm³ molecule^?1 s^?1 where the error limits are ±1σ. These values have been used in conjunction with our own previous measurements on Cl + ethane and literature values on Cl + propane and Cl + iso‐butane to generate a structure activity relationship (SAR) for Cl atom abstraction reactions based on direct measurements. The resulting best fit parameters are k_p = (2.61 ± 0.12) × 10^?11 cm³ molecule^?1 s^?1, k_s = (8.40 ± 0.60) × 10^?11 cm³ molecule^?1 s^?1, k_t = (5.90 ± 0.30) × 10^?11 cm³ molecule^?1 s^?1, with f( ? CH₂^? ) = f (? CH₂^? ) = f (?C?) = f = 0.85 ± 0.06. Tests were carried out to investigate the potential interference from production of excited state HCl(v = 1) in the Cl + alkane reactions. There is some evidence for HCl(v = 1) production in the reaction of Cl with shape n‐hexane. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 34: 86–94, 2002     

Rate constants for the reactions of chlorine atoms with hydrochloroethers at 298 k and atmospheric pressure

The relative rate technique has been used to determine the rate constants for the reactions Cl + CH₃OCHCl₂ → products and Cl + CH₃OCH₂CH₂Cl → products. Experiments were carried out at 298 ± 2 K and atmospheric pressure using nitrogen as the bath gas. The decay rates of the organic species were measured relative to those of 1,2‐dichloroethane, acetone, and ethane. Using rate constants of (1.3 ± 0.2) × 10^?12 cm³ molecule^?1 s^?1, (2.4 ± 0.4) × 10^?12 cm³ molecule^?1 s^?1, and (5.9 ± 0.6) × 10^?11 cm³ molecule^?1 s^?1 for the reactions of Cl atoms with 1,2‐dichloroethane, acetone, and ethane respectively, the following rate coefficients were derived for the reaction of Cl atoms (in units of cm³ molecule^?1 s^?1) with CH₃OCHCl₂, k= (1.04 ± 0.30) × 10^?12 and CH₃OCH₂CH₂Cl, k= (1.11 ± 0.20) × 10^?10. Errors quoted represent two σ, and include the errors due to the uncertainties in the rate constants used to place our relative measurements on an absolute basis. The rate constants obtained are compared with previous literature data and used to estimate the atmospheric lifetimes for the studied ethers. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 420–426, 2005     

Rate constant and a detailed error analysis for C2H3 + H reaction

The production and reactions of vinyl radicals and hydrogen atoms from the photolysis of vinyl iodide (C₂H₃I) at 193 nm have been examined employing laser photolysis coupled to kinetic-absorption spectroscopic and gas chromatographic product analysis techniques. The time history of vinyl radicals in the presence of hydrogen atoms was monitored using the 1,3-butadiene (the vinyl radical combination product) absorption at 210 nm. By employing kinetic modeling procedures a rate constant of 1.8 × 10^?10 cm² molecule^?1 s^?1 for the reaction C₂H₃ + H has been determined at 298 K and 27 KPa (200 torr) pressure. A detailed error analysis for determination of the C₂H₃ + H reaction rate constant, the initial C₂H₃ and H concentrations are performed. A combined uncertainty of ±0.43 × 10^?10 cm² molecule^?1 s^?1 for the above measured rate constant has been evaluated by combining the contribution of the random errors and the systematic errors (biases) due to uncertainties of each known parameter used in the modeling. © 1995 John Wiley & Sons, Inc.     

Ab initio chemical kinetics for the NH2 + HNOx reactions,part II: Kinetics and mechanism for NH2 + HONO

The kinetics and mechanism for the reaction of NH₂ with HONO have been investigated by ab initio calculations with rate constant prediction. The potential energy surface of this reaction has been computed by single‐point calculations at the CCSD(T)/6‐311+G(3df, 2p) level based on geometries optimized at the CCSD/6‐311++G(d, p) level. The reaction producing the primary products, NH₃ + NO₂, takes place via precomplexes, H₂N???c‐HONO or H₂N???t‐HONO with binding energies, 5.0 or 5.9 kcal/mol, respectively. The rate constants for the major reaction channels in the temperature range of 300–3000 K are predicted by variational transition state theory or Rice–Ramsperger–Kassel–Marcus theory depending on the mechanism involved. The total rate constant can be represented by k_total = 1.69 × 10^?20 × T^2.34 exp(1612/T) cm³ molecule^?1 s^?1 at T = 300–650 K and 8.04 × 10^?22 × T^3.36 exp(2303/T) cm³ molecule^?1 s^?1 at T = 650–3000 K. The branching ratios of the major channels are predicted: k₁ + k₃ producing NH₃ + NO₂ accounts for 1.00–0.98 in the temperature range 300–3000 K and k₂ producing OH + H₂NNO accounts for 0.02 at T > 2500 K. The predicted rate constant for the reverse reaction, NH₃ + NO₂ → NH₂ + HONO represented by 8.00 × 10^?26 × T^4.25 exp(?11,560/T) cm³ molecule^?1 s^?1, is in good agreement with the experimental data. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 678–688, 2009     

Ab initio chemical kinetics for the NH2 + HNOx reactions,part III: Kinetics and mechanism for NH2 + HONO2

The kinetics and mechanism for the reaction of NH₂ with HONO₂ have been investigated by ab initio calculations with rate constant prediction. The potential energy surface of this reaction has been computed by single‐point calculations at the CCSD(T)/6‐311+G(3df, 2p) level based on geometries optimized at the B3LYP/6‐311+G(3df, 2p) level. The reaction producing the primary products, NH₃ + NO₃, takes place via a precursor complex, H₂N…HONO₂ with an 8.4‐kcal/mol binding energy. The rate constants for major product channels in the temperature range 200–3000 K are predicted by variational transition state or variational Rice–Ramsperger–Kassel–Marcus theory. The results show that the reaction has a noticeable pressure dependence at T < 900 K. The total rate constants at 760 Torr Ar‐pressure can be represented by k_total = 1.71 × 10^?3 × T^?3.85 exp(?96/T) cm³ molecule^?1 s^?1 at T = 200–550 K, 5.11 × 10^?23 × T^+3.22 exp(70/T) cm³ molecule^?1 s^?1 at T = 550–3000 K. The branching ratios of primary channels at 760 Torr Ar‐pressure are predicted: k₁ producing NH₃ + NO₃ accounts for 1.00–0.99 in the temperature range of 200–3000 K and k₂ + k₃ producing H₂NO + HONO accounts for less than 0.01 when temperature is more than 2600 K. The reverse reaction, NH₃ + NO₃ → NH₂ + HONO₂ shows relatively weak pressure dependence at P < 100 Torr and T < 600 K due to its precursor complex, NH₃…O₃N with a lower binding energy of 1.8 kcal/mol. The predicted rate constants can be represented by k_?1 = 6.70 × 10^?24 × T^+3.58 exp(?850/T) cm³ molecule^?1 s^?1 at T = 200–3000 K and 760 Torr N₂ pressure, where the predicted rate at T = 298 K, 2.8 × 10^?16 cm³ molecule^?1 s^?1 is in good agreement with the experimental data. The NH₃ + NO₃ formation rate constant was found to be a factor of 4 smaller than that of the reaction OH + HONO₂ producing the H₂O + NO₃ because of the lower barrier for the transition state for the OH + HONO₂. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 42: 69–78, 2010     

Azide mechanisms for the production of NCl metastables

The production of both the b¹Σ⁺ and a¹Δ states of NCl has been observed from the reaction of HN₃ with flowing streams of Cl and F atoms. The results suggest that a two-step reaction sequence is responsible for the production of excited NCl, as follows: The rate contant (all products) for the first step is k(F + HN₃) > 1 × 10^?11 cm³/molecule sec. Comparison of this value to results obtained in a previous study of the F + HN₃ system yields a value k(F + N₃) = 2 × 10^?12 cm³/molecule sec. The rate constant for the reaction of chlorine atoms with HN₃ was determined to be k(Cl + HN₃) 1 × 10^?12 cm³/molecule sec. The difference between the Cl + HN₃ and F + HN₃ rates is interpreted in terms of an addition–elimination mechanism.     

Production of electronically excited NF by the reaction of fluorine atoms with HN3

Electronically excited NF in both the a¹Δ and b ¹Σ⁺ states hasbeen observed from the reaction of fluorine atoms with HN₃. The results suggest that fluorine atoms first abstract the hydrogen atom from HN₃, then react with the remaining N₃ to form NF^≠(a¹Δ). NF^*(b¹Σ⁺) is produced by a subsequent energy pooling reaction between NF^≠(a¹Δ) and vibrationally excited HF. The rate of the F + N₃ reaction is estimated to be ≈ 10¹² and ³ mole^?1 s^?1.     

Rate constant for the reaction NH3 + OH → NH2 + H2O over a wide temperature range

The rate constant for the reaction or NH₃ + OH → NH₂ + H₂O has been measured in a high temperature fast flow reactor over the range 294–1075 K k = (5.41 ± 0.86) × 10^-12 exp[?(2120 ± 143) cal mole^?1/RT cm³ molecule^?1 s^?1. This result is compared with literature values and discussed.     

Direct rate measurements on the reactions N + OH → NO + H And O + OH → O2 + H

Rate constants for the radical-radical reactions N + OH → NO + H (1), and O + OH → O₂ + H (2) have been measured for the first time by a direct method. In each experiment, a known concentration of N or O atoms is established in a discharge-flow system. OH radicals are then created by flash photolysis of H₂O present in the flowing gas, and the disappearance of OH is monitored by time-resolved observations of its resonance fluorescence. The experiments yield K₁ = (5.0 = 1.2) × 10^?11 cm³ molecule^?1 s^?1 and k₂ = (3.8 = 0.9) × 10^?11 cm³ molecule^?1 s^?1, for the reactions at 298 = 5 K.     

Kinetics and mechanism of the reaction of Cl atoms with HO2 radicals

The kinetic and mechanism of the reaction Cl + HO₂ → products (1) have been studied in the temperature range 230–360 K and at total pressure of 1 Torr of helium using the discharge‐flow mass spectrometric method. The following Arrhenius expression for the total rate constant was obtained either from the kinetics of HO₂ consumption in excess of Cl atoms or from the kinetics of Cl in excess of HO₂: k₁ = (3.8 ± 1.2) × 10^?11 exp[(40 ± 90)/T] cm³ molecule^?1 s^?1, where uncertainties are 95% confidence limits. The temperature‐independent value of k₁ = (4.4 ± 0.6) × 10^?11 cm³ molecule^?1 s^?1 at T = 230–360 K, which can be recommended from this study, agrees well with most recent studies and current recommendations. Both OH and ClO were detected as the products of reaction (1) and the rate constant for the channel forming these species, Cl + HO₂ → OH + ClO (1b), has been determined: k_1b = (8.6 ± 3.2) × 10^?11 exp[?(660 ± 100)/T] cm³ molecule^?1 s^?1 (with k_1b = (9.4 ± 1.9) × 10^?12 cm³ molecule^?1 s^?1 at T = 298 K), where uncertainties represent 95% confidence limits. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 317–327, 2001     

Kinetics and mechanism of the reaction of propylene oxide with chlorine atoms and hydroxy radicals

The kinetics and mechanism of gas‐phase propylene oxide (PPO) reactions were studied in a 142‐L reaction chamber by long‐path Fourier transform infrared spectroscopy at atmospheric pressure and 298 K. Rate coefficients for the reaction of PPO with ozone (O₃), chlorine atoms (Cl), and hydroxyl radicals (OH) were measured using the relative rate technique. Product yields of acetic acid, acetic formic anhydride, formic acid, and carbon monoxide were determined for the following reactions: PPO with Cl both in the presence and absence of NO, PPO with OH and NO, methyl acetate with Cl both in the presence and absence of NO, and ethyl formate with Cl both in the presence and absence of NO. The measured rate coefficients for PPO with O₃, Cl, and OH are <3.5 × 10^?21 cm³ molecule^?1 s^?1, (3.0 ± 0.7) × 10^?11 cm³ molecule^?1 s^?1, and (3.0 ± 1.0) × 10^?13 cm³ molecule^?1 s^?1, respectively. The carbon balance for the products measured ranged from 10% (for OH + PPO) to 100% (for Cl + methyl acetate in the absence of NO). The mechanistic and atmospheric implications of these measurements are discussed. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 507–521, 2011     

Absolute rate constants for the reaction of O(3P) aroms with n-butane and NO(M  Ar) over the temperature range 298–439 K

Absolute rate constants for the reaction of O(³P) atoms with n-butane (k₂) and NO(M  Ar)(k₃) have been determined over the temperature range 298–439 K using a flash photolysis-NO₂ chemiluminescence technique. The Arrhenius expressions obtained were k₂ = 2.5 × 10^?11exp[-(4170 ± 300)/RT] cm³ molecule^?1 s^?1, k₃ = 1.46 × 10^?32 exp[940 ± 200)/ RT] cm⁶ molecule^?2 s^?1, with rate constants at room temperature of k₂ = (2.2 ± 0.4) × 10^?14 cm³ molecule^?1 s^?1 and k₃ = (7.04 ± 0.70)×10^?32 cm⁶ molecule^?2 s^?1. These rate constants are compared and discussed with literature values.     

Different effects of active minor admixtures on hydrogen and methane ignitions

The methane combustion inhibitor CCl₄ exerts no effect on the first ignition limit of hydrogen; therefore, the role of hydrogen atoms in hydrocarbon oxidation consists at least of participating in longer reaction chains than are observed in hydrogen oxidation. The upper limits of the rate constants of the reactions of hydrogen atoms with propylene and isobutylene molecules were estimated by the self-ignition limit method to be (1.0 ± 0.3) × 10^?11 exp(?1450 ± 400/T) and (0.8 ± 0.3) × 10^?11 exp(?550 ± 200/T) cm³ molecule^?1 s^?1, respectively, in the temperature range of 840–950 K. These data are evidence that the stronger inductive effect of the two methyl groups in isobutylene lowers the energy barrier to the H + iso-C₄H₈ reaction. It has been demonstrated experimentally that chemiluminescence in the hydrocarbon flame front at atmospheric pressure precedes heat evolution. Throughout the pressure and temperature ranges examined (5–750 Torr, 298–950 K), the chain mechanism determines the basic laws of combustion.     

Kinetics of the reaction of NH2 with NO2

The absolute rate constant of the reaction of NH₂ with NO₂ has been measured using a flash-photolysis laser resonance-fluorescence technique. The value obtained at room temperature is k₁ = 2.3 (± 0.2) × 10^?11 cm³ molecule ^?1 s^?1. A negative temperature coefficient has been found between 298 and 505 K for this reaction, k₁ = 3.8 × 10^?8 × T^?1.30 cm³ molecule^?1 s^?1. It is thought that this is the major reaction of NH₂ in the troposphere.     

Kinetic study of the reactions of atomic chlorine with several volatile organic compounds at 240–340 K

The rate constant for the reactions of atomic chlorine with 1,4‐dioxane (k₁), cyclohexane (k₂), cyclohexane‐d₁₂(k₃), and n‐octane (k₄) has been determined at 240–340 K using the relative rate/discharge fast flow/mass spectrometer (RR/DF/MS) technique developed in our laboratory. Essentially, no temperature dependence for these reactions was observed over this temperature range, with an average of k₁ = (1.91 ± 0.20) × 10^?10 cm³ molecule^?1 s^?1, k₂ = (2.91 ± 0.31) × 10^?10 cm³ molecule^?1 s^?1, k₃ = (2.73 ± 0.30) × 10^?10 cm³ molecule^?1 s^?1, and k₄ = (3.22 ± 0.36) × 10^?10 cm³ molecule^?1 s^?1, respectively. The kinetic isotope effect of the reaction of cyclohexane with atomic chlorine has also been determined to be 1.14 by directly monitoring the decay of both cyclohexane and cyclohexane‐d₁₂ in the presence of chlorine atoms, which is consistent with the literature value of 1.20. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 386–398, 2006     

UV absorption spectrum of CF3CFClO2 and kinetics of the self reaction of CF3CFCl and CF3CFClO2 and the reactions of CF3CFClO2 with NO and NO2

The ultraviolet absorption spectrum of CF₃CFClO₂ and the kinetics of the self reactions of CF₃CFCl and CF₃CFClO₂ radicals and the reactions of CF₃CFClO₂ with NO and NO₂ have been studied in the gas phase at 295 K by pulse radiolysis/transient UV absorption spectroscopy. The UV absorption cross section of CF₃CFCl radicals was measured to be (1.78 ± 0.22) × 10^?18 cm² molecule^?1 at 220 nm. The UV spectrum of CF₃CFClO₂ radicals was quantified from 220 nm to 290 nm. The absorption cross section at 250 nm was determined to be (1.67 ± 0.21) × 10^?18 cm² molecule^?1. The rate constants for the self reactions of CF₃CFCl and CF₃CFClO₂ radicals were (2.6 ± 0.4) × 10^?12 cm³ molecule^?1 s^?1 and (2.6 ± 0.5) × 10^?12 cm³ molecule^?1 s^?1, respectively. The reactivity of CF₃CFClO₂ radicals towards NO and NO₂ was determined to (1.5 ± 0.6) × 10^?11 cm³ molecule^?1 s^?1 and (5.9 ± 0.5) × 10^?12 cm³ molecule^?1 s^?1, respectively. Finally, the rate constant for the reaction of F atoms with CF₃CFClH was determined to (8 ± 2) × 10^?13 cm³ molecule^?1 s^?1. Results are discussed in the context of the atmospheric chemistry of HCFC-124, CF₃CFClH. © 1994 John Wiley & Sons, Inc.     

Kinetic study of the reaction of chlorine atoms with CF3I and the reactions of CF3 radicals with O2, Cl2 and NO at 296 K

The kinetics of the gas-phase reaction of Cl atoms with CF₃I have been studied relative to the reaction of Cl atoms with CH₄ over the temperature range 271–363 K. Using k(Cl + CH₄) = 9.6 × 10^?12 exp(?2680/RT) cm³ molecule^?1 s^?1, we derive k(Cl + CF₃I) = 6.25 × 10^?11 exp(?2970/RT) in which E_a has units of cal mol^?1. CF₃ radicals are produced from the reaction of Cl with CF₃I in a yield which was indistinguishable from 100%. Other relative rate constant ratios measured at 296 K during these experiments were k(Cl + C₂F₅I)/k(Cl + CF₃I) = 11.0 ± 0.6 and k(Cl + C₂F₅I)/k(Cl + C₂H₅Cl) = 0.49 ± 0.02. The reaction of CF₃ radicals with Cl₂ was studied relative to that with O₂ at pressures from 4 to 700 torr of N₂ diluent. By using the published absolute rate constants for k(CF₃ + O₂) at 1–10 torr to calibrate the pressure dependence of these relative rate constants, values of the low- and high-pressure limiting rate constants have been determined at 296 K using a Troe expression: k₀(CF₃ + O₂) = (4.8 ± 1.2) × 10^?29 cm⁶ molecule^?2 s^?1; k_∞(CF₃ + O₂) = (3.95 ± 0.25) × 10^?12 cm³ molecule^?1 s^?1; F_c = 0.46. The value of the rate constant k(CF₃ + Cl₂) was determined to be (3.5 ± 0.4) × 10^?14 cm³ molecule^?1 s^?1 at 296 K. The reaction of Cl atoms with CF₃I is a convenient way to prepare CF₃ radicals for laboratory study. © 1995 John Wiley & Sons, Inc.     

Kinetics and products of the gas-phase reactions of the OH radical and O3 with allyl chloride and benzyl chloride at room temperature

The kinetics of the gas-phase reactions of allyl chloride and benzyl chloride with the OH radical and O₃ were investigated at 298 ± 2 K and atmospheric pressure. Direct measurements of the rate constants for reactions with ozone yielded values of ??(O₃ + allyl chloride) = (1.60 ± 0.18) × 10^?18 cm³ molecule^?1 s^?1 and ??(O₃ + benzyl chloride) < 6 × 10^?20 cm³ molecule^?1 s^?1. With the use of a relative rate technique and ethane as a scavenger of chlorine atoms produced in the OH radical reactions, rate constants of ??(OH + allyl chloride) = (1.69 ± 0.07) × 10^?11 cm³ molecule^?1 s^?1 and ??(OH + benzyl chloride) = (2.80 ± 0.19) × 10^?12 cm³ molecule^?1 s^?1 were measured. A study of the OH radical reaction with allyl chloride by long pathlength FT-IR absorption spectroscopy indicated that the co-products ClCH₂CHO and HCHO account for ca. 44% of the reaction, and along with the other products HOCH₂CHO, (ClCH₂)₂CO, and CH₂ ? CHCHO account for 84 ± 16% of the allyl chloride reacting. The data indicate that in one atmosphere of air in the presence of NO the chloroalkoxy radical formed following OH radical addition to the terminal carbon atom of the double bond decomposes to yield HOCH₂CHO and the CH₂Cl radical, which becomes a significant source of the Cl atoms involved in secondary reactions. A product study of the OH radical reaction with benzyl chloride identified only benzaldehyde and peroxybenzoyl nitrate in low yields (ca. 8% and ?4%, respectively), with the remainder of the products being unidentified.     

A spectrokinetic study of CH2I and CH2IO2 radicals

The UV absorption spectrum and kinetics of CH₂I and CH₂IO₂ radicals have been studied in the gasphase at 295 K using a pulse radiolysis UV absorption spectroscopic technique. UV absorption spectra of CH₂I and CH₂IO₂ radicals were quantified in the range 220–400 nm. The spectrum of CH₂I has absorption maxima at 280 nm and 337.5 nm. The absorption cross-section for the CH₂I radicals at 337.5 nm was (4.1 ± 0.9) × 10^?18 cm² molecule^?1. The UV spectrum of CH₂IO₂ radicals is broad. The absorption cross-section at 370 nm was (2.1 ± 0.5) × 10^?18 cm² molecule^?1. The rate constant for the self reaction of CH₂I radicals, k = 4 × 10^?11 cm³ molecule^?1 s^?1 at 1000 mbar total pressure of SF₆, was derived by kinetic modelling of experimental absorbance transients. The observed self-reaction rate constant for CH₂IO₂ radicals was estimated also by modelling to k = 9 × 10^?11 cm³ molecule^?1 s^?1. As part of this work a rate constant of (2.0 ± 0.3) × 10^?10 cm³ molecule^?1 s^?1 was measured for the reaction of F atoms with CH₃I. The branching ratios of this reaction for abstraction of an I atom and a H atom were determined to (64 ± 6)% and (36 ± 6)%, respectively. © 1994 John Wiley & Sons, Inc.