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 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.     

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 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     

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.     

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 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.     

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.     

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.     

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.     

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     

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.     

Effects of CH3OH‐H2O and CH3OH solvents on rate of reaction of phthalimide with piperidine

Pseudo‐first‐order rate constants (k_obs) for the cleavage of phthalimide in the presence of piperidine (Pip) vary linearly with the total concentration of Pip ([Pip]_T) at a constant content of methanol in mixed aqueous solvents containing 2% v/v acetonitrile. Such linear variation of k_obs against [Pip]_T exists within the methanol content range 10%–∼80% v/v. The change in k_obs with the change in [Pip]_T at 98% v/v CH₃OH in mixed methanol‐acetonitrile solvent shows the relationship: k_obs = k[Pip]_T + k[Pip], where respective k and k represent apparent second‐order and third‐order rate constants for nucleophilic and general base‐catalyzed piperidinolysis of phthalimide. The values of k_obs, obtained within [Pip]_T range 0.02–0.40 M at 0.03 M NaOH and 20 as well as 50% v/v CH₃OH reveal the relationship: k_obs = k₀/(1 + {k_n[Pip]/k_OX[⁻OX]_T}), where k₀ is the pseudo‐first‐order rate constant for hydrolysis of phthalimide, k_n and k_OX represent nucleophilic second‐order rate constants for the reaction of Pip with phthalimide and for the XO⁻‐catalyzed cyclization of N‐piperidinylphthalamide to phthalimide, respectively, and [⁻OX]_T = [NaOH] + [⁻OX_re], where [⁻OX_re] = [⁻OH_re] + [CH₃O_re⁻]. The reversible reactions of Pip with H₂O and CH₃OH produce ⁻OH_re and CH₃O_re⁻ ions. The effects of mixed methanol‐water solvents on the rates of piperidinolysis of PTH reveal a nonlinear decrease in k with the increase in the content of methanol. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 33: 29–40, 2001     

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.     

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.     

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.     

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.     

Kinetics of the reaction O(3P) + SO2 + M → SO3 + M over the temperature range of 299°–440°K

Rate constants for the reaction O(³P) + SO₂ + M have been determined over the temperature range of 299°–440°K, using a flash photolysis–NO₂ chemiluminescence technique. For M?Ar, the Arrhenius expression was obtained. At room temperature k₂^Ar = (1.05 ± 0.21) × 10^?33 cm⁶/molec²·sec. In addition, the rate constants k₂ = (1.37 + 0.27) × 10^?33 cm⁶/molec²·sec, k₂ = (9.5 ± 3.0) ± 10^?33 cm⁶/molec²·sec, k₃ = (1.1 ± 0.2) ± 10^?31 cm⁶/molec²·sec, and k₃ = (2.6 ? 0.9) ± 10^?31 cm⁶/molec²·sec were obtained at room temperature where k₃^M is the rate constant for the reaction O + NO + M → NO₂ + M. The rate data are compared and discussed with literature values.     

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.     

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.