Kinetic analysis activation energy

Experiments in which catalyst wafers are used may suffer from reactant mass transfer problems, which limit the validity of the data or complicate their analysis. To determine the reaction kinetics and activation energies, mass transfer effects have to be understood (Burcham and Wachs, 1999). These difficulties can be avoided if a conventional fixed-bed reactor is mimicked closely and the catalyst is used in powder form and the reactant gases flow through the bed. It is also important to prevent homogeneous gas-phase reactions by reducing the dead volume. 

Statistical analysis using a one step non-linear regression metliod was applied in order to estimate kinetic parameters. Activation energies and rate constants estimated at the reference temperature of 40°C and corresponding 95% confidence intervals are reported in Table I. 

The reaction kinetic constants activation energy E and frequency factor A, can only be correlated with the concentration of paraffinic carbon, CP (from structural group analysis) with the concentration of dispersion medium (fiom colloid analysis) and with the H/C ratio (from elemental analysis). These functions show correlation coefficients of an acceptable magnitude. Examination of the correlation of the concentration of maltenes revealed a similar tendency but with very low coefficients of correlation. It is well known that the dispersion medium contains the highest concentration of chemical bonds, which can be cracked under the chosen reaction conditions [4-20]. In the pyrolysis experiments from distillation residues, about 92 % of the dispersion medium was converted, whereas conversion of the petroleum resins was only 83 %, despite the fact that the kinetic coefficients are of nearly the same magnitude for the two components. 

There are two main applications for such real-time analysis. The first is the detemiination of the chemical reaction kinetics. Wlien the sample temperature is ramped linearly with time, the data of thickness of fomied phase together with ramped temperature allows calculation of the complete reaction kinetics (that is, both the activation energy and tlie pre-exponential factor) from a single sample [6], instead of having to perfomi many different temperature ramps as is the usual case in differential themial analysis [7, 8, 9, 10 and H]. The second application is in detemiining the... 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

Figure 12-11. Self-heat rate analysis. ARC data are shown along with a fitted model obtained by assuming the following kinetic parameters reaction order = 1, activation energy = 31.08 kcal/mol, and frequency factor = 2.31 El 2 min ...

The paper by Dawson and Peng (98) can be quoted as an example of applying Eq. (58) to a kinetic analysis of both the first-order and second-order desorptions with an activation energy varying linearly with the surface coverage. 

Dynamic DSC scans of resole resins show two distinguishable reaction peaks, which correspond to formaldehyde addition and die formation of edier and metiiy-lene bridges characterized by different activation energies. Kinetic parameters calculated using a regression analysis show good agreement widi experimental values.75... 

As the reaction proceeds higher sulfanes and finally Ss are formed. The reaction is autocatalytic which makes any kinetic analysis difficult. The authors discussed a number of reaction mechanisms which are, however, obsolete by today s standards. Also, the reported Arrhenius activation energy of 107 17 kJ mol is questionable since it was derived from the study of the decomposition of a mixture of disulfane and higher sulfanes. Nevertheless, the observed autocatalytic behavior may be explained by the easier ho-molytic SS bond dissociation of the higher sulfanes formed as intermediate products compared to the SS bond of disulfane (see above). The free radicals formed may then attack the disulfane molecule with formation of H2S on the one hand and higher and higher sulfanes on the other hand from which eventually an Ss molecule is split off. 

The hydrolytic depolymerisation of PETP in stirred potassium hydroxide solution was investigated. It was found that the depolymerisation reaction rate in a KOH solution was much more rapid than that in a neutral water solution. The correlation between the yield of product and the conversion of PETP showed that the main alkaline hydrolysis of PETP linkages was through a mechanism of chain-end scission. The result of kinetic analysis showed that the reaction rate was first order with respect to the concentration of KOH and to the concentration of PETP solids, respectively. This indicated that the ester linkages in PETP were hydrolysed sequentially. The activation energy for the depolymerisation of solid PETP in a KOH solution was 69 kJ/mol and the Arrhenius constant was 419 L/min/sq cm. 21 refs. 

This study presents kinetic data obtained with a microreactor set-up both at atmospheric pressure and at high pressures up to 50 bar as a function of temperature and of the partial pressures from which power-law expressions and apparent activation energies are derived. An additional microreactor set-up equipped with a calibrated mass spectrometer was used for the isotopic exchange reaction (DER) N2 + N2 = 2 N2 and the transient kinetic experiments. The transient experiments comprised the temperature-programmed desorption (TPD) of N2 and H2. Furthermore, the interaction of N2 with Ru surfaces was monitored by means of temperature-programmed adsorption (TPA) using a dilute mixture of N2 in He. The kinetic data set is intended to serve as basis for a detailed microkinetic analysis of NH3 synthesis kinetics [10] following the concepts by Dumesic et al. [11]. 

Kinetic analysis shows that the formation of tropone through a hydroxyphenyl-carbene intermediate (which exhibits the lowest activation energy 69.3 kcal/mol) dominates o-QM decomposition process up to 1500 K, with fulvene + CO formation becoming competitive at higher temperatures. In fact, the latter decomposition mode although disfavored by its higher activation enthalpy (75.4 versus 69.3 kcal/mol) becomes competitive due to its more positive activation entropy. 

Sharma et al. [153] have devised a gentle accelerated corrosion test using a kinetic rate equation to establish appropriate acceleration factors due to relative humidity and thermal effects. Using an estimate for the thermal activation energy of 0.6 eV and determining the amount of adsorbed water by a BET analysis on Au, Cu and Ni, they obtain an acceleration factor of 154 at 65°C/80% RH with respect to 25 °C/35-40% RH. 

Analysis of the kinetic parameters showed that the apparent activation energy for the reaction was reduced from 105 to 57 kj mol-1 (Tab. 3.2). This observation is consistent with the polar mechanism of this reaction implying the development of a dipole in the transition state (Fig. 3.8) even when the reaction was performed in a polar solvent. 

Thermogravimetric analysis (TGA) has often been used to determine pyrolysis rates and activation energies (Ea). The technique is relatively fast, simple and convenient, and many experimental variables can be quickly examined. However for cellulose, as with most polymers, the kinetics of mass loss can be extremely complex (8 ) and isothermal experiments are often needed to separate and identify temperature effects (9. Also, the rate of mass loss should not be assumed to be related to the pyrolysis kinetic rate ( 6 ) since multiple competing reactions which result in different mass losses occur. Finally, kinetic rate values obtained from TGA can be dependent on the technique used to analyze the data. 

A comparative analysis of the kinetics of the reactions of atoms and radicals with paraffinic (R1 ), olefinic (R2H), and aromatic alkyl-substituted (R3H) hydrocarbons within the framework of the parabolic model permitted a new important conclusion. It was found that the tt-C—C bond occupying the a-position relative to the attacked C—H bond increases the activation energy for thermally neutral reaction [11]. The corresponding results are presented in Table 6.9. 

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