Arrhenius parameters interpretation

Equations 3.1-6 to -8 are all forms of the Arrhenius equation. The usefulness of this equation to represent experimental results for the dependence of kA on Tand the numerical determination of the Arrhenius parameters are explored in Chapter 4. The interpretations of A and EA are considered in Chapter 6 in connection with theories of reaction rates. 

If pt is used in the rate law instead of c,-, there are two ways of interpreting rt and hence kt. In the first of these, the definition of r, given in equation 1.4-2 is retained, and in the second, the definition is in terms of rate of change of p,. Care must be taken to identify which one is being used in a particular case. The first is relatively uncommon, and the second is limited to constant-density situations. The consequences of these two ways are explored further in this and the next section, first for the rate constant, and second for the Arrhenius parameters. 

We wish to account for (i.e., interpret) the Arrhenius parameters A and EA, and the form of the concentration dependence as a product of the factors c (the order of reaction). We would also like to predict values of the various parameters, from as simple and general a basis as possible, without having to measure them for every case. The first of these two tasks is the easier one. The second is still not achieved despite more than a century of study of reaction kinetics the difficulty lies in quantum mechanical... 

Interpretation of the mechanisms of the hydrocarbon desorption reactions mentioned above was considered (31,291) with due regard for the possible role of clay dehydration. While this water evolution process is not regarded as a heterogeneous catalytic reaction, it is at least possible that water loss occurs at an interface (293) so that estimations of preexponential factors per unit area can be made. On this assumption, Arrhenius parameters (in the units used throughout the present review) were calculated from the available observations in the literature and it was found (Fig. 9, Table V, S) that compensation trends were present in the kinetic data for the dehydration reactions of illite (+) (294), kaolinite ( ) (293,295 298), montmorillonite (x) (294) and muscovite (O) (299). If these surface reactions are at least partially reversible,... 

Study of the hydrolysis of adenosine triphosphate acid (ATP) showed that the temperature gradient during the reaction under microwave conditions can reach ca. 30°C, therefore reliable temperature measurement is the key factor for interpretation and comparison of rate of any reaction under conventional and microwave conditions. In this case, the Arrhenius parameters were estimated for the reaction under conventional conditions. Then taking into account the temperature gradient in investigated samples, the concentrations of the reagents were calculated for the experiments carried out under microwave conditions to show that both theoretical and experimental values fell within the range of the experimental error [23]. 

We return to the microscopic interpretation of the Arrhenius parameters, i.e., the pre-exponential factor (A) and the activation energy (Ea) known from classical chemical kinetics. 

In Chapter 2, the first chapter of the gas-phase part of the book, we began the transition from microscopic to macroscopic descriptions of chemical kinetics. In this last chapter of the gas-phase part, we will assume that the Arrhenius equation forms a useful parameterization of the rate constant, and consider the microscopic interpretation of the Arrhenius parameters, i.e., the pre-exponential factor (A) and the activation energy (Ea) defined by the Arrhenius equation k(T) = Aexp(—Ea/kBT). 

In Chapter 7 we turn to the other basic type of elementary reaction, i.e., uni-molecular reactions, and discuss detailed reaction dynamics as well as transition-state theory for unimolecular reactions. In this chapter we also touch upon the question of the atomic-level detection and control of molecular dynamics. In the final chapter dealing with gas-phase reactions, Chapter 8, we consider unimolecular as well as bimolecular reactions and summarize the insights obtained concerning the microscopic interpretation of the Arrhenius parameters, i.e., the pre-exponential factor and the activation energy of the Arrhenius equation. 

Heterogeneous or surface effects have been found to complicate the interpretation of kinetic experiments, which lead to erroneous Arrhenius parameters. However, with special precautions involving the use of seasoned vessels and the presence of a free-radical suppressor, the errors are minimized. Consequently, the present chapter will cover mostly homogeneous gas-phase processes. Studies on chemical activation, the use of catalysts, the bimolecular gas phase and heterogeneous reactions are not included. As an attempt to describe important pyrolyses data from 1972 to 1992, this review does not pretend to offer a complete coverage of the literature. 

Robinson, 1969a). It is probable that the hydrophobic nature of the phenyl groups of p-nitrophenyl diphenyl phosphate results in deep penetration of the neutral ester in the Stern layer, thus shielding the phosphoryl group from nucleophilic attack. Unlike other reactions between nucleophiles and neutral substrates catalyzed by cationic micelles (Bunton and Robinson, 1968, 1969a) and the hydrolysis of dinitrophenyl phosphate dianions in the presence of cationic micelles (Bunton et al., 1968), the catalysis of the hydrolysis of -nitrophenyl diphenyl phosphate by CTAB arises from an increase in the activation entropy rather than from a decrease in the enthalpy of activation. The Arrhenius parameters for the micelle-catalyzed and inhibited reactions are most probably manifestations of the extensive solubilization of this substrate. However, these parameters can be composites of those for the micellar and non-micellar reactions and the eifects of temperature on the micelles themselves are not known. Interpretation of the factors which affect these parameters must therefore be carried out with caution. In addition, the inhibition of the micelle-catalyzed reactions by added electrolytes has been observed (Bunton and Robinson, 1969a Bunton et al., 1969, 1970) and, as in the cases of other anion-molecule reactions and the heterolysis of dinitrophenyl phosphate dianions, can be reasonably attributed to the exclusion of the nucleophile by the anion of the added salt. 

Using the same approach and interpretation, values of — jq-ii.io o.44 jjj3 molecule s and Eub = 161.2 6.4 kJ mol were obtained [45] from studies of isobutene oxidation, as predicted by the similar thermochemistry and inert nature of methylallyl radicals due to electron delocalization. The agreement is good, and moreover the Arrhenius parameters are entirety consistent with Aif= 10 " cm molecule s and Elf = 163 kJ mot , which were obtained from studies of HCHO oxidation under conditions where the chain length was reduced virtually to zero. In the initial stages of reaction, the mechanism in KCl-coated vessels, where HO2 and H2O2 are efficiently destroyed at the vessel surface, is very simple. 

For rate processes in which the Arrhenius parameters are independent of reaction conditions, it may be possible to interpret the magnitudes of A and ii, to provide insights into the chemical step that controls the reaction rates. However, for a number of reversible dissociations (such as CaCOj, Ca(OH)2, LijSO Hp, etc.) compensation behaviour has been foimd in the pattern of kinetic data measured for the same reaction proceeding under different experimental conditions. These observations have been ascribed to the influence of procedural variables such as sample masses, pressure, particle sizes, etc., that affect the ease of heat transfer in the sample and the release of volatile products. The various measured values of A and cannot then be associated with a particular rate controlling step. Galwey and Brown [52] point out that few studies have been specifically directed towards studying compensation phenomena. However, many instances of compensation behaviour have been recognized as empirical correlations applicable to kinetic data... 

The kinetics of dehydration [128] of Na2S203.5H20 were difficult to interpret because the course of the reaction was markedly influenced by the perfection of the initial reactant surface and the reaction conditions. No reliable Arrhenius parameters could be obtained. The mechanism proposed to account for behaviour was the initial formation of a thin superficial layer of the anhydrous salt which later reorganized to form dihydrate. The first step in the reaction pentahydrate - dihydrate was satisfactorily represented by the contracting area (0.08 < or, < 0.80) expression. The second reaction, giving the anhydrous salt, fitted the Avrami-Erofeev equation (n = 2) between 0.05 < 2< 0.8. The product layer offers no impedance to product water vapoiu escape and no evidence of diffusion control was obtained. The mechanistic discussions are supported by microscopic observations of the distributions and development of nuclei as reaction proceeds. 

Reports of compensation behaviour appear to have been mainly empirical findings which have not contributed much to the theory of solid state reactions. Identification of the effect as a direct consequence of isokinetic behaviour [57,58] does, however, offer a theoretical foimdation for interpretation of the observed correlated changes in apparent Arrhenius parameters. The fit of Arrhenius parameters for crystolysis reactions to the expression ... 

Interpretation of the rate constants and Arrhenius parameters for thermal ,Z-isomeriza-tion is not always straightforward mechanistically, however, since sequential electrocyclic ring closure/ring opening reactions can often provide a lower energy route to the same products as formal rotation about a single C=C bond. This can be illustrated by Brauman and coworkers classic study of the thermal isomerization of E,E-, E,Z- and Z,Z-1,4-dideuterio-1,3-butadiene At 637 °C, the E,E- and Z,Z-isomers intercon-... 

Thermogravimetry is an attractive experimental technique for investigations of the thermal reactions of a wide range of initially solid or liquid substances, under controlled conditions of temperature and atmosphere. TG measurements probably provide more accurate kinetic (m, t, T) values than most other alternative laboratory methods available for the wide range of rate processes that involve a mass loss. The popularity of the method is due to the versatility and reliability of the apparatus, which provides results rapidly and is capable of automation. However, there have been relatively few critical studies of the accuracy, reproducibility, reliability, etc. of TG data based on quantitative comparisons with measurements made for the same reaction by alternative techniques, such as DTA, DSC, and EGA. One such comparison is by Brown et al. (69,70). This study of kinetic results obtained by different experimental methods contrasts with the often-reported use of multiple mathematical methods to calculate, from the same data, the kinetic model, rate equation g(a) = kt (29), the Arrhenius parameters, etc. In practice, the use of complementary kinetic observations, based on different measurable parameters of the chemical change occurring, provides a more secure foundation for kinetic data interpretation and formulation of a mechanism than multiple kinetic analyses based on a single set of experimental data. 

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