Measured Rate Data Research Articles

High-temperature unimolecular decomposition of ethyl propionate

This work reports rate coefficients of the thermal unimolecular decomposition reaction of ethyl propionate (EP) behind reflected shock waves over the temperature range of 976–1300K and pressures of 825–1875Torr. The reaction progress was monitored by detecting C2H4 near 10.532μm using CO2 gas laser absorption. In addition, G3//MP2/aug-cc-pVDZ and master equation calculations were performed to assess the pressure- and temperature-dependence of the reaction. Our calculations revealed that C2H4 elimination occurs via a six-centered retro-ene transition state. Our measured rate data are close to the high-pressure limit and showed no discernable temperature fall off.

Controlled insertion of tin atoms into zeolite framework vacancies and consequences for glucose isomerization catalysis

The incorporation of tin heteroatoms within framework vacancy defects of dealuminated Beta zeolites via stannic chloride reflux in dichloromethane solvent (333K) enables preparing Sn-Beta zeolites comprising a wide range of Sn content (Si/Sn=30–144; 1.4–6.1wt% Sn) and >4× higher framework Sn densities than reported (Si/Sn>120) for reflux in isopropanol solvent (383K). Silanol defects form hydrogen bonds with isopropanol but not with dichloromethane under reflux conditions, evident in the evolution of adsorbed isopropanol (∼5× per vacancy) but not dichloromethane during temperature programmed desorption of dealuminated zeolites saturated with either solvent at ambient, and in IR features for perturbed hydroxyl stretches (∼3350cm−1) and CH stretches (∼2700–3000cm−1) that were retained after dealuminated zeolites were saturated with isopropanol and evacuated at 383K. Dichloromethane-assisted tin grafting provides a route to precisely control the density of framework Sn sites and residual vacancy defects in Sn-Beta, up to the point of grafting virtually every framework vacancy with Sn. Open Sn sites ((OSi)3Sn(OH), ν(CD3CN): 2316cm−1), quantified from IR spectra collected after CD3CN titration (303K), are preferentially incorporated over closed Sn sites (Sn(OSi)4, ν(CD3CN): 2308cm−1) at low Sn densities via grafting in dichloromethane solvent, suggesting that this preparation method can tune the open-to-closed framework Sn site ratio more systematically than hydrothermal synthesis methods. Open Sn sites are dominant active sites for aqueous-phase glucose-fructose isomerization; consequently, isomerization turnover rates (per total Sn) decrease systematically with increasing Sn content. Initial isomerization rates (per open Sn) are invariant (within ∼2×, 373K) among twelve Sn-Beta samples of varying Sn content (Si/Sn=30–144), the behavior expected of a single-site catalyst in which open framework Sn sites are the loci of catalytic reactivity. First-order isomerization rate constants are 15–50× lower (373K) when open Sn sites are confined within high-defect than within low-defect Beta micropores, consistent with previous reports that aqueous-phase sugar isomerization cycles turn over at faster rates within hydrophobic, low-defect micropores. These findings clarify the consequences of liquid-phase reflux procedures on the coordination of tin heteroatoms incorporated within zeolite framework vacancies, and underscore the requirement to quantify putative active site structures in order to rigorously normalize measured rate data prior to kinetic or mechanistic interpretation.

Solvent effects in the hydrogenation of 2-butanone

In liquid-phase reaction systems, the role of the solvent is often limited to the simple requirement of dissolving and/or diluting substrates. However, the correct choice, either pure or mixed, can significantly influence both reaction rate and selectivity. For multi-phase heterogeneously catalysed reactions observed variations may be due to changes in mass transfer rates, reaction mechanism, reaction kinetics, adsorption properties and combinations thereof. The liquid-phase hydrogenation of 2-butanone to 2-butanol over a Ru/SiO2 catalyst, for example, shows such complex rate behaviour when varying water/isopropyl alcohol (IPA) solvent ratios. In this paper, we outline a strategy which combines measured rate data with physical property measurements and molecular simulation in order to gain a more fundamental understanding of mixed solvent effects for this heterogeneously catalysed reaction. By combining these techniques, the observed complex behaviour of rate against water fraction is shown to be a combination of both mass transfer and chemical effects.

Nucleation Rates of Methanol Using the SAFT‐0 Equation of State

Classical and nonclassical calculations of nucleation rates are presented for methanol, an associating vapor system. The calculations use an equation of state (EOS) that accounts for the effects of molecular association based on the statistical association fluid theory (SAFT). Two forms of classical nucleation theory (CNT) were studied: a Gibbsian form known as the P-form and the standard or S-form. CNT P-form calculations and nonclassical gradient theory (GT) calculations were made using the SAFT-0 EOS. Calculated rates were compared to the experimental rates of Strey, et al. [J. Chem. Phys. 1986, 84, 2325-2335]. Very little difference was found between the two forms of CNT for either the temperature (T) or supersaturation (S) dependence of the rates. Nucleation rates based on GT showed improved T and S dependence compared to CNT. The GT rates were also improved by factors of 100-1000 compared to CNT. Despite these improvements, GT does not describe the reported T and S dependence of the nucleation rates. To explore this further, the GT and experimental rates were analyzed using Hale's scaled model [J. Chem. Phys. 2005, 122, 204 509]. This analysis reveals an inconsistency between the predictions of GT, which scale relatively well, and the experimental data, which do not scale. It also shows that the measured rate data have an anomalous T and S dependence. A likely source of this anomaly is the inadequate thermodynamic data base for small cluster properties that was used originally to correct the raw rate data for the effects of association.

Industrial fluidised bed direct reduction kinetics of hematite ore fines in H 2 rich gases at elevated pressure

Reduction kinetics of iron ore fines were investigated under fluidised bed conditions with hydrogen-rich gas mixtures in the temperature range from 400 to 700 °C at a pressure of 10 bar. Kinetic parameters were determined for the reactions hematite to magnetite, magnetite to wuestite and wuestite to iron from experimental data. To be able to investigate the influence of both temperature and reducing gas composition on the reaction rate, a laboratory scale pressurised fluidised bed reactor was used which is able to apply process conditions close to those in industrial plants. Appropriate to heterogeneous reactions, a rate expression considering the specific surface area was derived. The time dependent function for the transient evolution of specific surface area was generated from measured mercury porosimetry data. Kinetic parameters such as frequency factor, energy of activation and reaction orders were determined for the consecutive reactions from hematite to magnetite, magnetite to wuestite and wuestite to iron by numerical integration and parameter estimation from measured rate data. A comparison to the evaluation of kinetic parameters without considering specific surface area confirm the results of this work.

What can we learn about the mechanisms of thermal decompositions of solids from kinetic measurements?

Aspects of the theories that are conventionally and widely used for the kinetic analyses of thermal decompositions of solids, crystolysis reactions, are discussed critically. Particular emphasis is placed on shortcomings which arise because reaction models, originally developed for simple homogeneous reactions, have been extended, without adequate justification, to represent heterogeneous breakdowns of crystalline reactants. A further difficulty in the mechanistic interpretation of kinetic data obtained for solid-state reactions is that these rate measurements are often influenced by secondary controls. These include: (i) variations of reactant properties (particle sizes, reactant imperfections, nucleation and growth steps, etc.), (ii) the effects of reaction reversibility, of self-cooling, etc. and (iii) complex reaction mechanisms (concurrent and/or consecutive reactions, melting, etc.). A consequence of the contributions from these secondary rate controls is that the magnitudes of many reported kinetic parameters are empirical and results of chemical significance are not necessarily obtained by the most frequently used methods of rate data interpretation. Insights into the chemistry, controls and mechanisms of solid-state decompositions, in general, require more detailed and more extensive kinetic observations than are usually made. The value of complementary investigations, including microscopy, diffraction, etc., in interpreting measured rate data is also emphasized.

Atmospheric Hydroxyl Radical Production from Electronically Excited NO 2 and H 2 O

Hydroxyl radicals are often called the "detergent" of the atmosphere because they control the atmosphere's capacity to cleanse itself of pollutants. Here, we show that the reaction of electronically excited nitrogen dioxide with water can be an important source of tropospheric hydroxyl radicals. Using measured rate data, along with available solar flux and atmospheric mixing ratios, we demonstrate that the tropospheric hydroxyl contribution from this source can be a substantial fraction (50%) of that from the traditional O(1D) + H2O reaction in the boundary-layer region for high solar zenith angles. Inclusion of this chemistry is expected to affect modeling of urban air quality, where the interactions of sunlight with emitted NOx species, volatile organic compounds, and hydroxyl radicals are central in determining the rate of ozone formation.

Universal dynamic control law and rate feedbacks

A common approach to control problems is to look for a static control law through a detailed study of the known mathematical model of the system, assuming that the needed measurements of the state vector are available for closed-loop feedbacks. Recently, this author showed that a special universal dynamic control law can control a class of systems without the need of detailed knowledge of their mathematical models-provided good quality measured rate data of certain components of the state vector are available. The present paper shows that when additional knowledge beyond the minimum is available, the amount of needed rate data can be reduced. Numerical simulations are presented to elucidate the effects of measurement noises.

MALDI-TOF Characterization of Highly Cross-Linked, Degradable Polymer Networks

Multifunctional anhydride monomers were synthesized and photopolymerized to form highly cross-linked, degradable networks. The networks were synthesized from monomers and oligomers of dimethacrylated sebacic acid of varying molecular weight, as well as under varying reaction conditions. The cross-linked polymers were subsequently degraded in phosphate buffered saline, and the degradation products, sebacic acid and poly(methacrylic acid), were isolated. Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) was used to characterize the absolute molecular weight distribution of the linear poly(methacrylic acid) degradation product, especially as a function of the network evolution (i.e., double-bond conversion), rate of initiation, and monomer size. MALDI-TOF results, supported by 1H NMR, showed that the distribution of kinetic chain lengths was relatively narrow, with average lengths shorter than calculated from experimentally measured rate data, indicating the influenc...

Quantitative structure‐activity relationships for evaluating the influence of sorbate structure on sorption of organic compounds by soil

AbstractThe purpose of this work was to investigate the effect of sorbate structure, by using the quantitative structure‐activity relationship (QSAR) approach, on sorption of organic compounds by two soils with different amounts of organic matter. Miscible displacement experiments were performed with several organic contaminants representing six classes of nonpolar, nonionizable organic chemicals, including chlorinated aliphatics, chlorobenzenes, polycyclic aromatic hydrocarbons (PAHs), n‐alkylbenzenes, methylated benzenes, and polychlorinated biphenyls (PCBs). The breakthrough curves were analyzed by using a bicontinuum model wherein sorption is assumed to be instantaneous for a fraction of the sorbent and rate limited for the remainder. The QSAR approach was used to investigate the dependency of both equilibrium and nonequilibrium sorption coefficients on topological descriptors representing structural properties of the solutes. For both equilibrium and nonequilibrium parameters, the first‐order valence molecular connectivity (1Xv) was found to be the best topological descriptor. Most of the rate‐limited sorption behavior could be explained by accounting for the size and structure of the solute molecule, as indicated by the good correlation between the rate coefficient and 1Xv. This supports the contention that rate‐limited sorption in these systems is controlled by a physical diffusion mechanism, consistent with the polymer diffusion model. Based on this model, the calculated diffusion‐length ratios for the Borden and Mt. Lemmon soils, which have a large difference in organic‐matter contents, compare favorably to the values determined from the measured rate data.

Heat and mass transfer limitations in gasification of carbon by carbon dioxide

Rates of gasification of carbon by carbon dioxide were measured in the laboratory using a thermogravimetry apparatus. The experiments were conducted at various temperatures and sample bed depths using powders of graphite and coconut char as sources of carbon, under flowing gas of CO2. Various CO–CO2 mixtures were also employed for the study of coconut char. The measured rate data were subjected to a heat and mass transfer analysis to find out the values of isothermal and non‐isothermal effectiveness factors. These values were utilized to predict the intrinsic chemical reactivities of graphite and coconut char samples, free from heat and mass‐transfer limitations. Extrapolation of experimental data to hypothetical zero bed depth showed good agreements with the above at various temperatures, thus providing valuable cross‐checks. The activation energies were found to be 260 and 250 kJ/mol for graphite and coconut char, respectively, under CO2. Carbon monoxide was found to decrease the rate of gasification but not as drastically as some literature reports predict.

Rate constant for the reaction Na + O 2 + N 2 → NaO 2 + N 2 under mesospheric conditions

Measurement of the absolute third-order rate constant k R for the reaction constituting the major sink for atomic sodium under mesospheric conditions, namely Na + O 2 + N 2 → NaO 2 + N 2, has been extended to lower temperatures (415 – 1016 K) by the method of time-resolved atomic resonance spectroscopy at λ = 589 nm (Na(3 2P J) ← Na(3 2S 1 2 )). This has facilitated extrapolation of the measured rate data over a wide temperature range using the Tröe formalism of unimolecular rate theory to the temperature of the 90 km region, namely about 200 K. For the range T = 200 – 2000 K, k R (cm 6 molecule −2 s −1) can then be fitted to the expression ln k R = −0.3225(ln T) 2 + 2.133 ln T −69.211 The resulting value of k R(200 K) is found to be about three times greater than expected on the basis of recent measurements derived from atomic-laser-induced fluorescence experiments using a fast flow reactor, further substantiating the role of NaO 2 as a major sink.

Nonlinear evaluation of kinetic data of heterogeneous catalytic reactions: Application to the hydrogenation of phenol and of cyclohexanone

A method of evaluation of kinetic data for heterogeneous catalytic reactions is described which consists of a combination of linear regression of transformed rate data and nonlinear regression of the measured rate data by the grid search method. By this procedure it is possible to obtain the most probable estimates of kinetic constants and, if necessary, to determine their range of reliability, as well as to exclude unsuitable kinetic models on the basis of approximate statistical considerations, which is not possible when the evaluation is based on linear regression only. The procedure is illustrated by the treatment of kinetic data for the hydrogenation of phenol and of cyclohexanone, on a platinum catalyst, considering 26 kinetic models of the Langmuir-Hinshelwood type for competitive and noncompetitive adsorption of reactants and the powerlaw rate equation.

Spectrophotometric Measurements of the Vibrational Relaxation of CO in Shock-Wave and Nozzle Expansion-Flow Environments

Infrared and Na line-reversal spectrophotometric methods have been employed for the investigation of the vibrational relaxation of pure CO and 5% CO+95% Ar test-gas mixtures behind normal shock waves and in quasisteady expansion flows. The shock-wave studies were conducted over a range of equilibrium shocked-gas temperatures of about 1400°—3200°K and pressures of a few atmospheres. Vibrational relaxation times obtained by these two techniques were found to agree quite well and are consistent with other available shock-wave data for both test-gas mixtures. The expansion-flow results for 5% CO+95% Ar were obtained in a shock-driven conical nozzle for a range of reservoir temperatures of about 3500°—5000°K and reservoir pressures of about 45 atm. For these experiments, the Na line-reversal and CO infrared diagnostic techniques indicated vibrational temperatures much lower than those predicted by the Landau—Teller theory using the shock-wave measured rate data. In addition, the infrared measurements indicated somewhat lower vibrational temperatures than the Na line-reversal results. In terms of vibrational relaxation rates, the expansion-flow data indicate that the de-excitation process in the nozzle proceeds about two orders of magnitude faster than anticipated on the basis of the rates measured behind shock waves. These observations are consistent with previous results obtained for N2. While a conclusive explanation of these results is not presently available, the results of recent theoretical studies are discussed which suggest that the detailed mechanism of the relaxation process may depend on the gas-dynamic environment.