Cage effect and inverse temperature dependence of the kinetic isotope effect in the c‐C₆H₁₂/c‐C₆D₁₂ reaction with OH radicals in fenton and HOONOH₂O systems

Abstract

Recently, we have discovered the unusual inverse temperature dependence of the kinetic isotope effect (KIE) for the OH + c -C 6 H 12 /c -C 6 D 12 reaction in water. Temperature increase causes a KIE increase; this is valid for both the Fenton system (I) and the HOONO H 2 O system (II) (a new source of OH radicals in alkane reactions), whereas in the gas phase KIE decreases with increasing temperature. Results of these studies are considered. The KIE temperature dependences for both reactions in solution,The anomalous temperature behavior of KIE in water is described by a cage effect model at the step of the reactant encounter, which was proposed earlier by Rudakov. The model can be represented in a concise form:H 2 O, where RH··OH * is the oriented encounter complex in the water cage. It is suggested that elementary acts of H-abstraction (step 2) are identical for both gas phase and solution. It allows calculation of the competition parameter between steps 2 and -1 (the alkane leaves the cage via diffusion), by using the experimental KIEs.Correspondence to: E. S. Rudakov; e-mail: rudakove@ukr.net; V. L. Lobachev; e-mail: lmarvl@ivc.com.ua. c 2011 Wiley Periodicals, Inc. RUDAKOV, LOBACHEV, AND VOLKOVAA temperature-dependence average for systems I and II was found as (k −1 /k 2H ) = (245 ± 35) exp[(18.5 ± 0.5)/RT]. The hypothetical dependence of (k H /k D ) w on T was calculated within the overall temperature range (by extrapolations outside the experimental area, 278-328 K), and its connection with that of (k H /k D ) g on T is considered.

What Controls Selectivity of Hydroxyl Radicals in Aqueous Solution? Indications for a Cage Effect

“…Equation can be resolved toward k chem , yielding eq We call the term in bold in eq , i.e., 1/(1 – k obs / k diff ) , the “amplification factor” because it increases the true chemical rate constant. Now one can check to what extent the diffusion limitation attenuates the true KIE chem = k chem,H / k chem,D toward an observable diffusion-affected AKIE predicted = k obs,H / k obs,D on the basis of the example C 6 D 12 vs C 6 H 12 with the following rate constants (values from refs , , and , all in terms of 10 9 L/(mol s)): k diff = 11.5, k obs,C6H12 = 6.0, k obs,C6D12 = 5.2, AKIE experimental = 1.15; see also the SI). The calculation shows that partial diffusion control of hydrogen abstraction from cyclohexane by • OH can only explain about a 15% attenuation of the true KIE.…”

“…This cage model is similar to the model of Minakata et al where an initial van der Waals complex between the reactants with a significant energy sink is postulated. Rudakov et al based their cage model on kinetic isotope effects (KIEs) measured in aqueous- and gas-phase oxidation of cyclohexane isotopologues: KIE = k C6H12 / k C6D12 = 1.18 in water and 2.57 in the gas phase, both at 298 K, where k C6H12 and k C6D12 are observed (apparent) second-order rate coefficients of cyclohexane oxidation. Therefore, these ratios are named apparent KIEs (AKIEs) .…”

“…4,8−17 This could be attributed to (i) different inherent reactivities of • OH in the two media (e.g., due to solvation effects in the water phase) or (ii) a diffusion limitation of reaction events due to very high rate coefficients. 17 Rudakov et al 18 interpret the selectivity pattern of • OH in aqueous solution by means of a cage effect according to eq 1…”

DFT analysis of the mechanism for the gas-phase chlorination of methane in the HOCL–H2O system

“…Thus, the ratio of the rate constants ethane : propane : isobutane is 0.14 : 1 : 3.6, while the KIE = 2.9 ± 0.2 for HOCl in water at 70°C and 0.24 : 1 : 2.1 and KIE = 2.6 ± 0.2 for OH • in the gas phase at 25°C. We note that the reaction of RH + OH • in water is complicated by a cage effect [4,5] and is not suitable for comparison with reaction (1).…”

“…Thus, the ratio of the rate constants ethane : propane : isobutane is 0.14 : 1 : 3.6, while the KIE = 2.9 ± 0.2 for HOCl in water at 70°C and 0.24 : 1 : 2.1 and KIE = 2.6 ± 0.2 for OH • in the gas phase at 25°C. We note that the reaction of RH + OH • in water is complicated by a cage effect [4,5] and is not suitable for comparison with reaction (1).These findings permit us to exclude species Cl • , Cl 2 , Cl + , Cl -¼Hg 2+ , and Cl + ¼OH 2 as possible reagents and conclude that reaction (1) proceeds as a molecular chlorination by HOCl and begins with reagent preactivation entailing the conversion of singlet HOCl into triplet HO • Cl • , while the C-H bond is broken by the action of the OH • group of the HO • Cl • diradical [4].In the present work, for a comparison with the kinetic data for reaction (1) in water and to check the hypothesis of a singlet-triplet preactivation of the reagent, we studied the mechanism of the chlorination of methane by HOCl molecules in the gas phase by the density functional (DFT) method for variants with a bimolecular (reaction (1)) and trimolecular reaction (with the participation of a water molecule)(2) RH + HOCl + H 2 O ® RCl + 2H 2 O. …”