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.     

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.     

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.     

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.     

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     

Disproportionation-to-combination ratios for cyclohexyl-h11 and -d11 radicals in the gas phase as determined by the radiolysis of water vapor–cyclohexane mixtures

In the radiolysis of water vapor containing small concentrations of cyclohexane, the principal products which account for about 98% of all end products are found to be hydrogen, cyclohexene, and bicyclohexyl. Cyclohexene and bicyclohexyl yields were determined over a range of temperatures (70–200°C), total pressures (50–2400 torr), and total doses (0.15–2.0 Mrad). The disproportionation–combination ratio k/k for c-C₆H₁₁ radicals could be determined as 0.56 ± 0.01 from the ratio of cyclohexene to bicyclohexyl yield. By using c-C₆D₁₂, the ratio k/k for c-C₆D₁₁ radicals is found to be 0.38 ± 0.01. Comparison of the reactivity pattern of C₆H₁₁ and C₆D₁₁ radicals leads to (k)/(k)/(k/k) = 1.47 ± 0.02. The corresponding values for the reactions of c-C₆H₁₁ with c-C₆D₁₁ were also determined.     

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.     

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.     

Reactions of NO3-naphthalene adducts with O2 and NO2

The kinetics of the gas-phase reaction of the NO₃ radical with naphthalene have been investigated at 150 torr O₂ + 590 torr N₂ and 600 torr O₂ + 140 torr N₂ at 298 ± 2 K. Relative rate measurements were carried out in reacting NO₃? N₂O₅-naphthalene-propene-O₂? N₂ mixtures by longpath Fourier transform infrared absorption spectroscopy. A rate constant ratio for the reactions of O₂ and NO₂ with the NO₃-naphthalene adduct of k/k < 4 × 10^?7 was obtained from the competition between O₂ and NO₂ for reaction with the NO₃-naphthalene adduct and thermal decomposition of the adduct back to reactants. Atmospheric pressure ionization MS/MS measurements of the nitronaphthalene products of the NO₃ radical-initiated reaction of naphthalene are consistent with the proposed reaction mechanism, and the atmospheric implications of the data are discussed. © 1994 John Wiley & Sons, Inc.     

The reaction of methyl p-nitrophenyl sulfate with hydrogen peroxide anion determination of pKa of hydrogen peroxide in methanol by a kinetic spectrophotometric procedure

A kinetic spectrophotometric investigation of the reaction of the hydrogen peroxide anion with methyl p-nitrophenyl sulfate in methanol solvent resulted in the evaluation of the pK_a of HOOH in methanol at 25°C as 15.8 ± 0.2. Since normal kinetic procedures for the determination of the equilibrium constant K for the process CH₃O^? + H₂O₂ ? CH₃OH + HO were found to be associated with high uncertainty, another procedure was devised to establish the magnitude of K. This method is based on an analysis of the changing slopes of plots of pseudo-first-order rate constants against the total base concentration as the stoichiometric amount of hydrogen peroxide is varied. The method is applicable to any system in which anionic nucleophiles generated in situ compete with solvent anions. Such a corroboration of kinetically determined equilibrium constants is believed essential. The kinetic data allow the specific rate constant k_HOO-for the reaction of methyl p-nitrophenyl sulfate with hydrogen peroxide anions to be evaluated and yield the rate constant ratio k/k = 8.8 ± 2.2. This confirms the existence of an α effect at saturated carbon in this system.     

Rate constants for the gas‐phase reactions of nitrate radicals with geraniol,citronellol, and dihydromyrcenol

Terpenes and terpene alcohols are prevalent compounds found in a wide variety of consumer products including soaps, flavorings, perfumes, and air fresheners used in the indoor environment. Knowing the reaction rate of these chemicals with the nitrate radical is an important factor in determining their fate indoors. In this study, the bimolecular rate constants of k (16.6 ± 4.2) × 10^?12, k (12.1 ± 3) × 10^?12, and k (2.3 ± 0.6) × 10^?14 cm³ molecule^?1 s^?1 were measured using the relative rate technique for the reaction of the nitrate radical (NO₃?) with 2,6‐dimethyl‐2,6‐octadien‐8‐ol (geraniol), 3,7‐dimethyl‐6‐octen‐1‐ol (citronellol), and 2,6‐dimethyl‐7‐octen‐2‐ol (dihydromyrcenol) at (297 ± 3) K and 1 atmosphere total pressure. Using the geraniol, citronellol, or dihydromyrcenol + NO₃? rate constants reported here, pseudo‐first‐order rate lifetimes (k′) of 1.5, 1.1, and 0.002 h^?1 were determined, respectively. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 669–675, 2010     

Reactions of Cl2P3/2: Absolute rate constants for reaction with H2, CH4, C2H6, CH2Cl2, C2Cl4, and c?C6H12

The absolute rate constants have been measured for several gas-phase chlorine atom-molecule reactions at 25°C by resonance fluorescence. These reactions and their corresponding rate constants in units of cm³ mole^?1 sec^?1 are: The effects of varying the substrate pressure, total pressure, light intensity and chlorine-atom source on the value of the bimolecular rate constants have been investigated for all these reactions. Conditions under which no competing side reaction occurs were established and the reported rate constants were measured under these conditions. For reactions (2), (5), (6), (7), and 8, there is a discrepancy of a factor of two between the rate constants measured in this work and values in the literature; it is suggested that this is due to an error in the previously measured value of k/k upon which the relative measurements in the literature ultimately depend.     

Consistency of theory and experiment in the ethane–methyl radical system

The thermal decomposition of ethane has been reinvestigated using the single pulse, reflected shock technique. Reflected shock temperatures were corrected for boundary layer-induced nonidealities using the thermal decomposition of cyclohexene as a kinetic standard. The rate constant for the reaction was calculated from the rate of formation of methane under conditions of very low extent of reaction, over a temperature range of 1000–1241 K. Ethane compositions of 1% and 3% in argon at total reaction pressures of 3 and 9 atm were used, and a small pressure dependence of k₁ was observed. An RRKM model is described which gives excellent agreement with this and other recent dissociation and recombination rate constant data in light of a recent revision to the thermochemistry of the methyl radical. In the range of 1000–1300 K an RRKM extrapolated k is given by the expression, log k = 17.2 ? 91,000/2.3RT, while at 298 K the calculation gives log k (l/mol sec) = 10.44, where k is calculated from k and the equilibrium constant.     

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     

Linear free energy relationships for peroxy radical-phenol reactions. Influence of the para-substituent,the ortho-di-tert-butyl groups and the peroxy radical

Calculations were carried out on several data sets to study the mechanism of hydrogen abstraction from phenols by peroxy radicals: (1) Rate constants, k values, were collected for the reactions of cumyl-, 1-phenylethyl- and tert-butyl-peroxy radicals with ortho-para-substituted phenol inhibitors. The rate constants were recalculated for the same temperature. Solvent effects were neglected because the solvents used were similar in nature. The phenol ortho substituents were characterized by an indicator variable I_tBu accounting for the presence or absence of di-tert-butyl groups. The phenol para substituents were characterized by Charton's σ_I, σ_R, and σ substituent constants. The dependence of log k values on I_tbu, σ_I, σ_R, σ was investigated using stepwise linear regression analysis. The combined data set of 32 reactions gives: and The results suggest that hydrogen abstraction from phenols by peroxy radicals proceeds by an electrophilic mechanism, and that neither the peroxy-radical nor the ortho-di-tert-butyl groups have considerable effect on the rate of reaction (1).     

Effect of olefins on the thermal decomposition of propane part I. The model reaction

Study of the thermal decomposition of propane at very low conversions in the temperature range 760–830 K led to refinement of the mechanism of the reaction. The quotient V/V characterizing the two decomposition routes connected with the 1- and 2-propyl radicals proved to depend linearly on the initial propane concentration. This suggested the occurrence of intermolecular radical isomerization: in competition with decomposition of the 2-propyl radical: The linearity led to the conclusion that the selectivity of H-abstraction from the methyl and methylene groups by the methyl radical is practically the same as that by the H atom. The temperature-dependence of this selectivity ( μ = kCH₃/kCH₂) was given by Further evaluation of the dependence gave the Arrhenius representation for the ratio of the rate coefficients of the above isomerization and decomposition reactions. Steady-state treatment resulted in the rate equation of the process, comparison of which with measurements gave further Arrhenius dependences.     

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.     

Kinetics of oxidation of benzyl alcohol by sodium N-chloro-p-toluenesulfonamide

The kinetics of oxidation of benzyl alcohol and substituted benzyl alcohols by sodium N-chloro-p-toluenesulfonamide (chloramine-T, CAT) in HClO₄ (0.1–1 mol/dm³) containing Cl^? ions, over the temperature range of 30–50°C have been studied. The reaction is of first order each with respect to alcohol and oxidant. The fractional order dependence of the rate on the concentrations of H⁺ and Cl^? suggests a complex formation between RNCl^? and HCl. In higher acidic chloride solution the rate of reaction is proportional to the concentrations of both H⁺ and Cl^7hyphen;. The observed solvent isotope effect (k/k) is 1.43 at 30°C. The reaction constant (p = ?1.66) and thermodynamic parameters are evaluated. Rate expressions and probable mechanisms for the observed kinetics have been suggested.     

The kinetics of the reaction: Br + C3H6 ⇌ HBr + C3H5

Studies of the reaction of Br + propylene to produce HBr and allyl radical were made using VLPR (Very Low Pressure Reactor) over the range 263–363 K. Apparent bimolecular rate constants k were found to vary in an inverse manner with the initial concentration of bromine atoms introduced into the reactor. Plots of k against [Br] give straight lines whose intercepts were taken to be the true bimolecular, metathesis rate constant k₁. The reaction scheme is where k₂ ? k₁ and k_?1 [HBr] is negligibly small under our conditions. Arrhenius parameters for k₁ were assigned for linear and bent transition states and shown to give excellent fits to the observed intercepts. where θ = 2.303 RT (kcal mol^?1). The dependence of k on [Br] is accounted for in terms of the reactivity of Br* (²P_1/2) produced in the microwave discharge. The activation energy for the metathesis reaction of Br* with propylene is shown to be very small.