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)].     

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 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.     

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.     

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     

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 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.     

Kinetics and mechanism of electron transfer from phenolate anion to hexacyanoferrate (III) in aqueous alkaline media

A kinetic reinvestigation of the title redox system in aqueous alkaline media at 35°C and an ionic strength of 0.5 mol dm^?3 shows that the reaction follows a pseudosecond-order Fe(CN) disappearance. While varying [phenol]₀ and [OH^?] exhibit a linear influence on the pseudo-second-order rate constant, varying[Fe(CN)]₀ and [Fe(CN)]₀, initially taken, have a complicated inhibitory effect on the same. The major phenoloxidation products isolated under a chosen condition are 2,2′- and 4,4′- dihydroxydiphenyl. Results are interpreted in terms of a probable mechanism which envisages a reversible formation, by the first one-electron transfer, of a reactive phenoxy radical (PhO^˙) which on the second one-electron transfer forms a less reactive ion-pair intermediate (stabilized by the Fe(CN) produced) to decompose rate-determiningly to phenoxonium cation (PhO⁺) and Fe(CN), the product-formation steps being very rapid and kinetically indistinguishable.     

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.     

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.     

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     

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.     

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.     

Kinetics and thermochemistry of electron attachment to SF6

Thermochemical analysis of the electron capture process of SF₆ leads to a rate constant for the reverse process \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm SF}_6^ - \mathop \to \limits^2 {\rm SF}_6 + e^ -,k_2 = 1.5 \times 10^{13 - 31.4/\theta } {\rm s}^{{\rm - 1}} $\end{document}, where θ = 2.303RT, in kcal/mol. The electron affinity of 32±3 kcal/mol is deduced from the observed bimolecularity of the capture process down to 0.1 torr Ar bath gas and estimated entropies of SF₆ and SF. The capture process is discussed from the view point of the formation of a metastable SF electron (SF₆·e) Langevin complex which appears to have a lifetime of about 2 × 10^?13 s. Curve crossing from the SF₆·e complex to vibrationally excited (SF)* appears to have a normal rate and A factor. This is interpreted to indicate near-resonant coupling between the orbiting electron and the vibronic motions of SF₆, together with similarity in structure of SF₆ and SF. It is shown that the apparent slowness of thermal electron ejection from SF is a result of an unfavorable equilibrium constant rather than a slow rate.     

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.     

Kinetics and equilibria of the reaction between bromine and ethyl ether. The C?H bond dissociation energy in ethyl ether

The kinetics and equilibria of the reaction: have been studied in the temperature range 298–333 K by using the very low pressure reactor (VLPR) technique. Combining the estimated entropy change of reaction (1), ΔS = 8.1 ± 1.0 eu, with the measured ΔG, we find ΔH = 4.2 ± 0.4 kcal/mol; ΔH(CH₃CHOC₂H₅) = ?20.2 kcal/mol, and DH° [Et OCH(Me)-H] = 91.7 ± 0.4 kcal/mol. We find: where θ = 2.3 RT in kcal/mol. It has been shown that the reaction proceeds via a loose transition state and the “contact TS” model calculation gives a very good agreement with the observed value.     

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.     

Comparison of the kinetics of cathodic H2 evolution from the unhydrated H3O+ ion and its hydrated form H9O: Frequency factor effects and modes of activation

Experiments are described in which the kinetics of cathodic hydrogen evolution from the unhydrated H₃O⁺ ion in pure CF₃SO H₃O⁺ are compared with those from an aqueous solution of CF₃SO₃H where the proton is mainly in a fully hydrated state as H₉O. From the acid hydrate, which exists mainly as the ionic compound CF₃SOH₃O⁺, rates of H₂ evolution at Ni, Pt, and Hg electrodes, measured at a given overpotential or expressed as exchange current densities, are between about 3.5 and 20 times slower than those from the same electrolyte in dilute (1.0M) aqueous solution. Allowing for the concentration differences in these two types of system and double-layer effects, the rate constants are between about 9.4 and 216 times smaller for the reaction from H₃O⁺ than from H₉O at the above electrodes. The evaluation of apparent heats of activation for H₂ evolution from the two types of proton sources allows ratios of real frequency factors to be calculated for discharge from H₃O⁺ and H₉O. These data have a bearing on the theoretical conclusions regarding proton discharge mechanisms and show that frequency factor effects can be as important as activation energy differences in determining the rates of proton discharge from different proton sources. The results are discussed in terms of current ideas about electron and proton transfer in electrochemical reactions, the state of hydration of H⁺, and the role of discharge from paired CF₃SO and H₃O⁺ ions. In particular, the molecular mechanics of discharge of the proton from the molecular ion H₃O⁺ can be different from that from the fully hydrated H⁺ ion where many more HO- vibrational and librational modes can be involved in the process of activation of the H₉O entity.     

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.     

Kinetic study of hydroxylamine-bromate ion reaction in acid sulfate solution—a competitive consecutive reaction

A kinetic study of oxidation of hydroxylamine by bromate ion in acid sulfate solution using spectrophotometric and potentiometric methods is reported. Oxidation of hydroxylamine to nitrate is quantitative and followed competitive, consecutive, and auto catalytics steps characterized by induction periods. In the slow rate limiting step, hydroxylamine on reaction with HOBr (k) forms an intermediate I, which further reacts fast with second molecule of HOBr (k) giving nitrite. Nitrite reacts with HOBr (k) yielding the final product nitrate. Nitric acts as an autocatalyst also and its initial addition decreased the induction periods. In excess of hydrogen ion concentration all the reaction steps follow second-order kinetics. All the second-order rate constants are reported and the reaction mechanism is proposed.