Rate constant pressure dependent

The attenuation of ultrasound (acoustic spectroscopy) or high frequency electrical current (dielectric spectroscopy) as it passes through a suspension is different for weU-dispersed individual particles than for floes of those particles because the floes adsorb energy by breakup and reformation as pressure or electrical waves josde them. The degree of attenuation varies with frequency in a manner related to floe breakup and reformation rate constants, which depend on the strength of the interparticle attraction, size, and density (inertia) of the particles, and viscosity of the Hquid. 

The variation in rate constant (which depends on the concentration of the transition state) with pressure can be expressed as... 

Pressure effects The diffusion through liquids is governed by the number of defects or atomic-sized holes in the liquid. A high external pressme can reduce the concentration of holes and slow diffusion. Therefore, in a liquid, a diffusion-controlled rate constant also depends on the pressure. 

Chloryl fluoride is stable at ambient temperature in well-passivated and dry containers. Its thermal decomposition in quartz was studied by Schumacher et al. 24, 137). It reaches a measurable rate only above 300°C. The decomposition reaction is monomolecular and its rate is pressure-dependent. The actiyation energy was calculated to be 45 2 kcal mole and the rate constant was determined as = 2.3 x 10 X sec . The following decomposition mechanism was... 

In addition to temperature, the rate constant also depends on pressure, but this dependence... 

Previous studies of the reactions of guaiacol (orthomethoxy-phenol) (3 ), dibenzyl ether (4 ), and benzyl phenyl amine (5) in dense water elucidated parallel hydrolysis and pyrolysis pathways, the selectivity to the latter increasing with water density. Reactant decomposition kinetics were interestingly nonlinear in water density and consistent with two mechanistic interpretations. The first involved "cage" effects, as described for reactions in liquid solutions (6 ). The second led to parallel pyrolysis and solvolysis reaction pathways wherein associated rate constants were dependent upon pressure. These two schemes are probed herein through the reactions of benzyl phenyl amine (BPA) in water and methanol. 

For different polymers the results can be more readily appredated by examining the change in pressure with extrusion ratio R for a constant extrudate velocity. Results for different polyethylenes are shown in Fig. 17, where the rapid upturn occurs at comparatively low extrusion ratios. For different polymers results are shown in Fig. 18, together with the best analytical Gts based on modifled Hoffman-Sachs analysis, which incorporates the strain, strain rate and pressure dependent flow stress according to Eq. (4) and the Avitzur strain rate field of Eq. (5). Figure 17... 

Effect of Pressure on Reaction Rate Constant Pressure can have a direct impact on the reaction rate through its effect on the reaction rate constant. The pressure dependence of the reaction rate constant and unusual partial molar behavior of a solute in a SCF can result in enhancement of the reaction rate in the critical region of the mixture (136). According to the transition state theory (172, 173), pressure enhances the rate of a reaction if the activation volume (difference in the partial molar volumes of the activated complex and the reactants) is negative, whereas the reaction is hindered by pressure if the activation volume is positive. 

Like equilibrium constants, rate constants also depend on environmental factors such as pressure and, especially, temperature. An increase in temperature usually gives rise to an increase in the chemical reaction rate, because molecules are moving faster and colliding more frequently with greater energy. If rate constants are known for two different temperatures, the rate constant for any other temperature can be calculated using the Arrhenius rate law,... 

The various procedures for obtaining rate constants from experimental data are next considered. In most of these, the ionic yields are deduced solely from their power absorption from the observing rf field. Expressions for the rate constant thus depend on the nature of the power absorption, according to whether (1) the ion is in free flight (zero collisions in the limit of zero pressure), (2) it is experiencing elastic, nonreactive collisions, or (3) it is undergoing chemically reactive collisions. The three different procedures which have been developed are now considered in turn. 

Figure 7. Plots of apparent rate constant (k ) depending on pressure in SCCO2...

All the above-described reactions take place simultaneously in a polymerization reactor. However, the rate of each reaction depends on the concentration of the reactants and on the individual reaction rate constants kj. These rate constants largely depend on pressure and temperature. 

The correct treatment of the mechanism (equation (A3.4.25), equation (A3.4.26) and equation (A3.4.27), which goes back to Lindemann [18] and Hinshelwood [19], also describes the pressure dependence of the effective rate constant in the low-pressure limit ([M] < [CHoNC], see section A3.4.8.2). 

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

Figure A3.4.9. Pressure dependence of the effective unimolecular rate constant. Schematic fall-off curve for the Lindemaim-FIinshelwood mechanism. A is the (constant) high-pressure limit of the effective rate constant...

Figure A3.6.1. Pressure dependence of imimolecular rate constant...

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

Borkovec M, Straub J E and Berne B J The influence of intramolecular vibrational relaxation on the pressure dependence of unimolecular rate constants J. Chem. Phys. 85 146... 

The chemically activated molecules are fonned by reaction of with the appropriate fliiorinated alkene. In all these cases apparent non-RRKM behaviour was observed. As displayed in figure A3.12.11 the measured imimolecular rate constants are strongly dependent on pressure. The large rate constant at high pressure reflects an mitial excitation of only a fraction of the total number of vibrational modes, i.e. initially the molecule behaves smaller than its total size. However, as the pressure is decreased, there is time for IVR to compete with dissociation and energy is distributed between a larger fraction of the vibrational modes and the rate constant decreases. At low pressures each rate constant approaches the RRKM value. 

Mies F H and Krauss M 1966 Time-dependent behavior of activated molecules. High-pressure unimolecular rate constant and mass spectra J. Cham. Phys. 45 4455-68... 

Lu D-H and Hase W L 1989 Monoenergetic unimolecular rate constants and their dependence on pressure and fluctuations in state-specific unimolecular rate constants J. Phys. Chem. 93 1681-3... 

Song K and Hase W L 1998 Role of state specificity in the temperature- and pressure-dependent unimolecular rate constants for H02->H+02 dissociation J. Phys. Chem. A 102 1292-6... 

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