Reaction rate constant | EPFL Graph Search

In chemical kinetics, a reaction rate constant or reaction rate coefficient (k) is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants. For a reaction between reactants A and B to form a product C, where :A and B are reactants :C is a product :a, b, and c are stoichiometric coefficients, the reaction rate is often found to have the form: r = k[\mathrm{A}]^m [\mathrm{B}]^{n} Here k is the reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution. (For a reaction taking place at a boundary, one would use moles of A or B per unit area instead.) The exponents m and n are called partial orders of reaction and are not generally equal to the stoichiometric coefficients a and b. Instead they depend

Incremental Identification of Kinetic Models by Online Spectroscopy and Multivariate Calibration

Laurent Brandinu

Extent-based kinetic identification is a modeling technique that uses number of moles / concentrations measurements to compute extents and identify reaction kinetics (partial orders of reactions and reaction rate constant) by the integral method of parameter estimation. This project uses infrared spectroscopic data with calibration models to predict moles / concentrations via a PLS1 regression method. The calibration set (design of experiment) is constructed from a seven-level design for multivariate calibration in molar fraction with reacting material. The extent-based kinetic identification using number of moles predicted from spectroscopic data is tested through experiments in a homogeneous liquid-phase reaction system. The experiments were conducted in an RC1 calorimeter from Mettler Toledo with two inlet streams, without outlet stream, and a ReactIR 10 FT-IR probe. The reaction studied was the transesterification of methanol and hexanol with acetic anhydride producing methyl, hexyl acetate and acetic acid. No solvents or catalyst were used, only pure species at a reaction temperature of 50°C. Results in terms of calibration design and model, computation of extents and extent-based kinetic identification are discussed.

2015

Water Oxidation Kinetics of Accumulated Holes on the Surface of a TiO2 Photoanode: A Rate Law Analysis

Florian Le Formal, Min Ling, Yimeng Ma

It has been more than 40 years since Fujishima and Honda demonstrated water splitting using TiO2, yet there is still no clear mechanism by which surface holes on TiO2 oxidize water. In this paper, we use a range of complementary techniques to study this reaction that provide a unique insight into the reaction mechanism. Using transient photocurrent and transient absorption spectroscopy, we measure both the kinetics of electron extraction (t(50%) approximate to 200 mu s, 1.5V(RHE)) and the kinetics of hole oxidation of water (t(50%) approximate to 100 ms, 1.5V(RHE)) as a function of applied potential, demonstrating the water oxidation by TiO2 holes is the kinetic bottleneck in this water-splitting system. Photoinduced absorption spectroscopy measurements under 5 s LED irradiation are used to monitor the accumulation of surface TiO2 holes under conditions of photoelectrochemical water oxidation. Under these conditions, we find that the surface density of these holes increases nonlinearly with photocurrent density. In alkali (pH 13.6), this corresponded to a rate law for water oxidation that is third order with respect to surface hole density, with a rate constant k(WO) = 22 +/- 2 nm(4).s(-1). Under neutral (pH = 6.7) and acidic (pH = 0.6) conditions, the rate law was second order with respect to surface hole density, indicative of a change in reaction mechanism. Although a change in reaction order was observed, the rate of reaction did not change significantly over the wide pH range examined (with TOFs per surface hole in the region of 20-25 s(-1) at similar to 1 sun irradiance). This showed that the rate-limiting step does not involve OH- nucleophilic attack and demonstrated the versatility of TiO2 as an active water oxidation photocatalyst over a wide range of pH.

Amer Chemical Soc2017

Fast temperature cycling of the catalytic CO oxidation using microstructure reactors

Martin Luther

The possibility to increase the performance (productivity or selectivity) of a chemical reactor by using periodic variations of reaction parameters (e.g. reactant concentration or temperature) has been theoretically envisaged since the beginning of the 70th. The experimental validation of the predicted positive effects was successful in the case of concentration variation but failed for temperature variation. This was mainly due to the high thermal inertia of the conventional chemical reactors used for the measurements which prevented to create variations having a sufficiently high frequency. Microstructure reactors own, at the contrary to conventional reactors, a very low thermal inertia and allow to generate temperature oscillations with an amplitude of about ten to hundred Kelvin at a frequency in the order of magnitude of 10-1 to 4 Hz. These properties, coupled with the possibility to introduce a catalytic active material within the devices, seem to make them well suited for the study of the effects of fast periodic temperature variations of a catalytic reaction. The objective of this work was to demonstrate that non-stationary temperature conditions may increase the reaction rate of a heterogeneously catalyzed reaction up to values not predicted by the classical Arrhenius dependency towards the temperature. Two different types of microstructure reactors have been used. The reaction was taking place in the first one (FTC-type 2) in microstructured channels on whose walls a catalytic layer was deposed. In the second one (FTC-type 3), the reaction was taking place on a piece of sintered metal fibres (SMF) plate placed in a reaction chamber. The catalytic active material was deposed on the SMF plate filaments. Both devices where permanently heated by electrical resistors and periodically cooled down with water flowing through cooling channels incorporated in the devices. The test reaction chosen for the experimental measurements was the CO oxidation reaction, heterogeneously catalyzed by platinum supported on alumina (Pt/Al2O3). The reaction behaviour under stationary thermal conditions was consistent with the one predicted by the Arrhenius law. The dependency of the reaction rate with the temperature was exponential with an apparent activation energy of 104 kJ·mol-1, a negative partial reaction order for CO and a positive one for O2. The measurements effectuated under quasi-stationary thermal conditions (slow temperature ramps) have shown that a temperature change rate between 7 and 14 K·min-1 was not sufficient to observe any non-trivial effect of the temperature. The reaction behaviour was always predicted by the Arrhenius law. The surface coverage of the reactive species is, in this case, always able to follow the slow temperature changes and the reaction behaves as being always under steady-state conditions. The experiments realized under non-stationary thermal conditions using the FTC-type 2 reactor have also failed to demonstrate any non-trivial effects of the temperature oscillations. This device allows indeed to generate temperature oscillations with an amplitude of up to 120 K with a frequency of 0.1 Hz but unfortunately correlated with a very high thermal inhomogeneity. A temperature difference of up to 80 K was measured between a cold spot and a hot spot inside the device. Due to their very low local reaction rate the colder areas of the reactor have attenuated the product concentration (CO2) oscillations which should have been created by the temperature variations. This attenuation prevented the temperature oscillations to have any positive effect compared to the stationary thermal conditions. The FTC-type 3 reactor allowed temperature changes of lower amplitude but the thermal homogeneity was much better. The maximal temperature difference measured between two points within the reactor was only 15 K. Under temperature oscillation conditions, the measured instantaneous CO2 concentration was higher for any temperature within the oscillation range compared to the one recorded under stationary thermal conditions. The increase obtained in the mean CO2 concentration was ranging from 34% for a frequency of the oscillations of 0.035 Hz to 85% for a frequency of 0.052 Hz. The amplitude of the oscillations was kept constant at approximately 40 K and the mean temperature value at 437 K. The simulations effectuated using a theoretical model for the catalytic CO oxidation including a feed-back step in the form of the oxidation-reduction of the catalyst have shown that the experimentally observed increase may be qualitatively explained. Above a certain frequency, the temperature oscillations are fast enough compared to the characteristic time of the feedback step and are able to perturb the stationary established reactive species surface coverage. The formation of a transient surface coverage more favourable for the reaction than the surface coverage at high temperature allows during the transient period to reach an instantaneous surface reaction rate values higher than the one at high temperature. This reaction rate peak is then responsible for the increase of the mean reaction rate under non-stationary thermal conditions and, thus, for an increased yield.

EPFL2008

Fast temperature cycling of the catalytic CO oxidation using microstructure reactors

Martin Luther

EPFL2008