The √t law in solid-phase reactions verification of the √t law stability in h-atom abstraction reactions

The law c = c₀ exp(? K √t) in the alkyl radical abstraction reaction is affected by neither the matrix annealing nor the way of the radical generation. If the reaction runs at varying temperature, a dimensionless time τ which does determine unambiguously the degree of conversion can be introduced.     

A discrete stochastic model of diffusion controlled reactions. The rate constant

Diffusion controlled chemical reaction is modelled as random walk on a cubic lattice. The rate coefficient is shown to depend on the spatial distribution of the reactants.

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Derivation of rate constant ratios for consecutive second‐order irreversible reactions

The determination of rate constants for consecutive irreversible reactions is a difficult and time‐consuming problem, especially when the research extends up to many subsequent products. Thus, the derivation of proper mathematical expressions would greatly facilitate the determination of these rate constants when only the rate constant of the first consecutive reaction is known. Many authors have dealt with this problem in the past but the issue is still of interest to the scientific community judging from recent publications. This paper aims at extending our knowledge of mathematical expressions for rate constant ratios of consecutive reactions to more than three reactions, as is the situation now, and offering a simple graphical estimation of the rate constant ratios exploiting the maxima of each intermediate product. Furthermore, the method extends to the derivation of a generic formula for the estimation of the rate constant ratios based on this graphical approach. This approach for the estimation of rate constant ratios based on mathematical expressions and graphical estimations was validated against experimental data found in the literature.     

The hydroxyl radical reaction rate constant and atmospheric transformation products of 2‐propoxyethanol

The relative rate technique has been used to measure the hydroxyl radical (OH) reaction rate constant of 2‐propoxyethanol (2PEOH, CH₃CH₂CH₂OCH₂CH₂(OH)). 2PEOH reacts with OH with a bimolecular rate constant of (21.4 ± 6.0) × 10⁻¹² cm³molecule⁻¹s⁻¹ at 297 ± 3 K and 1 atm total pressure, which is a little larger than previously reported [1]. Assuming an average OH concentration of 1 × 10⁶ molecules cm⁻³, an atmospheric lifetime of 13 h is calculated for 2PEOH. In order to more clearly define this hydroxy ether's atmospheric reaction mechanism, an investigation into the OH + 2PEOH reaction products was also conducted. The OH + 2PEOH reaction products and yields observed were: propyl formate (PF, 47 ± 2%, CH₃CH₂CH₂OC(O)H), 2 propoxyethanal (CH₃CH₂CH₂OCH₂C(O)H 15 ± 1%), and 2‐ethyl‐1,3‐dioxolane (5.4 ± 0.4%). The 2PEOH reaction mechanism is discussed in light of current understanding of oxygenated hydrocarbon atmospheric chemistry. The findings reported here can be related to other structurally similar alcohols and may impact regulatory tools such as ground‐level ozone‐forming potential calculations (incremental reactivity) [2]. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 315–322, 1999     

The hydroxyl radical reaction rate constant and products of 3,5‐dimethyl‐1‐hexyn‐3‐ol

A bimolecular rate constant,k_DHO, of (29 ± 9) × 10^?12 cm³ molecule^?1 s^?1 was measured using the relative rate technique for the reaction of the hydroxyl radical (OH) with 3,5‐dimethyl‐1‐hexyn‐3‐ol (DHO, HC?CC(OH)(CH₃)CH₂CH(CH₃)₂) at (297 ± 3) K and 1 atm total pressure. To more clearly define DHO's indoor environment degradation mechanism, the products of the DHO + OH reaction were also investigated. The positively identified DHO/OH reaction products were acetone ((CH₃)₂C?O), 3‐butyne‐2‐one (3B2O, HC?CC(?O)(CH₃)), 2‐methyl‐propanal (2MP, H(O?)CCH(CH₃)₂), 4‐methyl‐2‐pentanone (MIBK, CH₃C(?O)CH₂CH(CH₃)₂), ethanedial (GLY, HC(?O)C(?O)H), 2‐oxopropanal (MGLY, CH₃C(?O)C(?O)H), and 2,3‐butanedione (23BD, CH₃C(?O)C(?O)CH₃). The yields of 3B2O and MIBK from the DHO/OH reaction were (8.4 ± 0.3) and (26 ± 2)%, respectively. The use of derivatizing agents O‐(2,3,4,5,6‐pentalfluorobenzyl)hydroxylamine (PFBHA) and N,O‐bis(trimethylsilyl)trifluoroacetamide (BSTFA) clearly indicated that several other reaction products were formed. The elucidation of these other reaction products was facilitated by mass spectrometry of the derivatized reaction products coupled with plausible DHO/OH reaction mechanisms based on previously published volatile organic compound/OH gas‐phase reaction mechanisms. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 534–544, 2004     

Kinetics of the surface catalyzed reactions: Application of power rate law

Oxidative dehydrogenation of cyclohexane to benzene, catalyzed by copperchromia catalyst, has been carried out. Data was analyzed according to the first order rate law. It is concluded that the rate is affected by changes in the volume flow rate due to changes, in the value of the contact time as well as the distribution of the molecules transformed over a larger or smaller volume.     

The temperature dependence of the rate coefficients for β-hydroxyperoxy radical self reactions

A laser-flash photolysis/UV absorption technique has been used to study the temperature dependence (from T = 300 - 470 K) of the self-reaction kinetics of representative primary secondary and tertiary β-hydroxyperoxy radicals The following Arrhenius expressions were derived for the rate coefficients of reactions (1)-(3) (in cm³ molecule ⁻¹s⁻¹) and for the product branching ratios of reactions (1) and (2) as a function of temperature (all errors 1σ) The calculated rate coefficients for reactions (1)-(3) at 298 K are therefore (in 10⁻¹³ cm³molecule ⁻¹s ⁻¹ 23 ± 2, 6.7 ± 1.3, and 0.040 ± 0.012, respectively which compare well with the values measured elsewhere at this temperature using a similar technique. The product branching ratios and the Arrhenius parameters are compared with those for other substituted and unsubstituted peroxy radical self reactions. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 323–331, 1997     

The rate constant of NO + O3 → NO2 + O2 in the temperature range of 283–443 K

The reaction NO + O₃ → NO₂ + O₂ has been studied in a 220-m³ spherical stainless steel reactor under stopped-flow conditions below 0.1 mtorr total pressure. Under the conditions used, the mixing time of the reactants was negligible compared with the chemical reaction time. The pseudo-first-order decay of the chemiluminescence owing to the reaction of ozone with a large excess of nitric oxide was measured with an infrared sensitive photomultiplier. One hundred twenty-nine decays at 18 different temperatures in the range of 283–443 K were evaluated. A weighted least-squares fit to the Arrhenius equation yielded k = (4.3 ± 0.6) × 10^?12 exp[-(1598 ± 50)/T] cm³/molecule sec (two standard deviations in brackets). The Arrhenius plot showed no curvature within experimental accuracy. Comparison with recent results of Birks and co-workers, however, suggests that a nonlinear fit, as proposed by these authors, is more appropriate over an extended temperature range.     

β‐Ionone reactions with the nitrate radical: Rate constant and gas‐phase products

The bimolecular rate constant of k (9.4 ± 2.4 × 10^?12 cm³ molecule^?1 s^?1 was measured using the relative rate technique for the reaction of the nitrate radical (NO₃?) with 4‐(2,6,6‐trimethyl‐1‐cyclohexen‐1‐yl)‐3‐buten‐2‐one (β‐ionone) at (297 ± 3) K and 1 atmosphere total pressure. In addition, the products of β‐ionone + NO₃? reaction were also investigated. The identified reaction products were glyoxal (HC(?O)C(?O)H), and methylglyoxal (CH₃C(?O)C(?O)H). Derivatizing agents O‐(2,3,4,5,6‐pentafluorobenzyl)hydroxylamine and N,O‐bis(trimethylsilyl)trifluoroacetamide were used to propose the other major reaction products: 3‐oxobutane‐1,2‐diyl nitrate, 2,6,6‐trimethylcyclohex‐1‐ene‐carbaldehyde, 2‐oxo‐1‐(2,6,6‐trimethylcyclohex‐1‐en‐1‐yl)ethyl nitrate, pentane‐2,4‐dione, 3‐oxo‐1‐(2,6,6‐trimethylcyclohex‐1‐en‐1‐yl)butane‐1,2‐diyl dinitrate, 3,3‐dimethylcyclohexane‐1,2‐dione, and 4‐oxopent‐2‐enal. The elucidation of these products was facilitated by mass spectrometry of the derivatized reaction products coupled with plausible β‐ionone + NO₃? reaction mechanisms based on previously published volatile organic compound + NO₃? gas‐phase mechanisms. The additional gas‐phase products 5‐acetyl‐2‐ethylidene‐3‐methylcyclopentyl nitrate, 1‐(1‐hydroxy‐7,7‐dimethyl‐2,3,4,5,6,7‐hexahydro‐1 H‐inden‐2‐yl)ethanone, 1‐(1‐hydroxy‐3a,7‐dimethyl‐2,3,3a,4,5,6,‐hexahydro‐1 H‐inden‐2‐yl)ethanone, and 5‐acetyl‐2‐ethylidene‐3‐methylcyclopentanone are proposed to be the result of cyclization through a reaction intermediate. © 2009 Wiley Periodicals, Inc. *

1 This article is a U.S. Government work and, as such, is in the public domain of the United States of America.

Int J Chem Kinet 41: 629–641, 2009     

The rate constant for H + i-C4H8 → t-C4H9 in the range of 298–563 K

The overall rate constant for hydrogen-atom addition to isobutene has been measured in the temperature range of 298–563 K in a flow discharge system coupled to a quadrupole mass spectrometer. Previously published results allow the determination of where the error limits are 95% confidence limits.      

The rate constant of polymer reversal inside a pore

Translocation of biopolymers through pores is implicated in many biological phenomena. Confinement within a pore often breaks ergodicity on experimental and/or biological time scales by creating large entropic barriers to conformational rearrangements of the chain. Here, we study one example of such hindered rearrangement, in which the chain reverses its direction inside a long pore. Our goal is twofold. First, we study the dependence of the time scale of polymer reversal on the pore size and on the polymer length. Second, we examine the ability of simple one-dimensional theories to quantitatively describe a transition in a system with a complex energy landscape by comparing them with the exact rate constant obtained using brute-force simulations and the forward flux sampling method. We find that one-dimensional transition state theory (TST) using the polymer extension along the pore axis as the reaction coordinate adequately accounts for the exponentially strong dependence of the reversal rate constant on the pore radius r and the polymer length N, while the transmission factor, i.e., the ratio of the exact rate and the TST approximation, has a much weaker power law r and N dependence. We have further attempted to estimate the transmission factor from Kramer's theory, which assumes the reaction coordinate dynamics to be governed by a Langevin equation. However, such an approximation was found to be inadequate. Finally, we examine the scaling behavior of the reversal rate constant with N and r and show that finite size effects are important even for chains with N up to several hundreds.     

Chemisorption of thiol‐functionalized metallocene molecules on Si(111)‐ Ag√3×√3 surface: A density functional theory study

Herein, chemical adsorption properties of the thiol‐functionalized metallocene molecules [M(C₅H₄SH)₂] on Si(111)‐Ag√3×√3 surface were investigated using density functional theory calculation. For this purpose, thiol‐modified ferrocene [Fe(C₅H₄SH)₂], osmocene [Os(C₅H₄SH)₂], and ruthenocene [Ru(C₅H₄SH)₂] molecules were attached on the surface via two different binding models. The more favorable chemical binding energies of [Fe(C₅H₄SH)₂], [Os(C₅H₄SH)₂], and [Ru(C₅H₄SH)₂] molecules were calculated as ?3.42, ?2.15, and ?2.00 eV, respectively. The results showed that the adsorption energies of metallocene molecules change independently by increasing the radius of metal ions where on going down the group of the periodic table. The calculated adsorption energies showed that [Fe(C₅H₄SH)₂] molecule was more stable on the Si(111)‐Ag√3×√3 surface. By calculating the electronic band structure for metallocene/Si(111)‐Ag√3×√3 surfaces, we identified a flat dispersion band in a part of the surface Brillouin zone. © 2015 Wiley Periodicals, Inc.     

Ferrous ion oxidations by √H, √OH and H2O2 in aerated FBX dosimetry system

In the ferrous ion, benzoic acid and xylenol orange (FBX) dosimetric system, benzoic acid (BA) increases the G(Fe³⁺) value. Xylenol orange (XO) controls the BA sensitized chain reaction as well as forms a complex with Fe³⁺. In the aerated FBX system each √H, √OH and H₂O₂ oxidizes 8.5, 6.6 and 7.6 Fe²⁺ ions, respectively; and these values respectively increase to 11.3, 7.6 and 8.6 in oxygenated solution. About 8% √OH reacts with XO and the remaining with BA. The above fractional values are due to this competition. This √OH reaction with XO oxidizes 1.8% and 2.1% ferrous ions only in aerated and oxygenated solutions, respectively. There is a competition between √H reactions with O₂ and with BA, but both lead to the production of H₂O₂. The oxidation of Fe²⁺ by √OH reactions at different concentrations of H₂O₂ is linear with absorbed dose while the √H reactions make the oxidation of Fe²⁺ non-linear with dose. This is due to competition reaction of H-adduct of BA between O₂ and Fe³⁺.     

Standard reactions for comparative rate studies: Experiments on the dehydrochlorination reactions of 2‐chloropropane,chlorocyclopentane, and chlorocyclohexane

Single pulse shock tube studies of the thermal dehydrochlorination reactions (chlorocyclopentane → cyclopentene + HCl) and (chlorocyclohexane → cyclohexene + HCl) at temperatures of 843–1021 K and pressures of 1.4–2.4 bar have been carried out using the comparative rate technique. Rate constants have been measured relative to (2‐chloropropane → propene + HCl) and the decyclization reactions of cyclohexene, 4‐methylcyclohexene, and 4‐vinylcyclohexene. Absolute rate constants have been derived using k(cyclohexene → ethene + butadiene) = 1.4 × 10¹⁵ exp(?33,500/T) s^?1. These data provide a self‐consistent temperature scale of use in the comparison of chemical systems studied with different temperature standards. A combined analysis of the present results with the literature data from lower temperature static studies leads to

• k(2‐chloropropane) = 10^{(13.98±0.08)} exp(?26, 225 ± 130) K/T) s^?1; 590–1020 K; 1–3 bar
• k(chlorocylopentane) = 10^{(13.65 ± 0.10)} exp(?24,570 ± 160) K/T) s^?1; 590–1020 K; 1–3 bar
• k(chlorocylohexane) = 10^{(14.33 ± 0.10)} exp(?25,950 ± 180) K/T) s^?1; 590–1020 K; 1–3 bar

Including systematic uncertainties, expanded standard uncertainties are estimated to be about 15% near 600 K rising to about 25% at 1000 K. At 2 bar and 1000 K, the reactions are only slightly under their high‐pressure limits, but falloff effects rapidly become significant at higher temperatures. On the basis of computational studies and Rice–Ramsperger–Kassel–Marcus (RRKM)/Master Equation modeling of these and reference dehydrochlorination reactions, reported in more detail in an accompanying article, the following high‐pressure limits have been derived:

• k_∞ (2‐chloropropane) = 5.74 × 10⁹T^1.37 exp(?25,680/T) s^?1; 600–1600 K
• k_∞ (chlorocylopentane) = 7.65 × 10⁷T^1.75 exp(?23,320/T) s^?1; 600–1600 K
• k_∞ (chlorocylohexane) = 8.25 × 10⁹T^1.34 exp(?25,010/T) s^?1; 600–1600 K

© 2011 Wiley Periodicals, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain of the United States of America.

Int J Chem Kinet 44: 351–368, 2012     

The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics

The rates of formation and concentration distributions of a dimer reaction showing hysteresis behavior are examined in an ab initio chemical reaction designed as elementary and where the hysteresis structure precludes the formation of transition states (TS) with pre-equilibrium and internal sub-reactions. It was discovered that the the reactivity coefficients, defined as a measure of departure from the zero density rate constant for the forward and backward steps had a ratio that was equal to the activity coefficient ratio for the product and reactant species. This surprising result, never formally incorporated in elementary rate expressions over approximately one and a half centuries of quantitative chemical kinetics measurement and calculation is accepted axiomatically and leads to an outline of a theory for the form of the rate constant, in any one given substrate—here the vacuum state. A major deduction is that the long-standing definition of the rate constant for elementary reactions is not complete and is nonlinear, where previous works almost always implicitly refer to the zero density limit for strictly irreducible elementary reactions without any attending concatenation of side-reactions. This is shown directly from MD simulation, where for specially designed elementary reactions without any transition states, density dependence of reactants and products always feature, in contrast to current practice of writing rate equations. It is argued that the rate constant expression without reactant and product dependence is due to historical conventions used for strictly elementary reactions. From the above observations, a theory is developed with the aid of some proven elementary theorems in thermodynamics, and expressions under different state conditions are derived whereby a feasible experimental and computational method for determining the activity coefficients from the rate constants may be obtained under various approximations and conditions. Elementary relations for subspecies equilibria and its relation to the bulk activity coefficient are discussed. From one choice of reaction conditions, estimates of activity coefficients are given which are in at least semi-quantitative agreement with the data for non-reacting Lennard-Jones (LJ) particles for the atomic component. The theory developed is applied to ionic reactions where the standard Brönsted-Bjerrum rate equation and exceptions to this are rationalized.     

The effect of heating rate upon the coupling of complex reactions. I. Independent and competitive reactions

Theoretical curves of the rate of conversion vs. temperature at constant heating rate for first-order reactions with activation energies of 80, 160, 240 and 320 kJ mole^?1 are compared over a range of heating rates from 10^?9 to 10⁵ K s^?1 for independent and competitive reactions. Independent reactions with different activation energies may be separated from one another by either increasing or decreasing the rate of heating. The spectrum of derivative peaks for two competing reactions at various heating rates has a dispersion effect in the region of change from low to high activation energy reactions. The practical range of heating rates in thermal analytical experiments and the application of these model cases to the understanding of the kinetics of complex systems at high and low temperatures are discussed.