Reaction rate pressure dependence

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. 

As propagation rates of gassy reactions are pressure dependent, so are gasless reactions temp dependent. This temp dependence has been... 

In this case the reaction rate will depend not only on the system temperature and pressure but also on the properties of the catalyst. It should be noted that the reaction rate term must include the effects of external and intraparticle heat and mass transfer limitations on the rate. Chapter 12 treats these subjects and indicates how equation 8.2.12 can be used in the analysis of packed bed reactors. 

The influence of hydrogen pressure, substrate and catalyst concentration has briefly been mentioned. The reaction rate is dependent upon the catalyst concentration and hydrogen pressure, but appears to be independent of substrate concentration. The mechanism is proposed to involve the activation of the parent [Pd(allyl)] species producing an unstable hydrido-Pd(II) species (71), ensued by a fast reaction with the diene to restore the [Pd(allyl)] moiety (72) (Scheme 14.21). The observation that most of the starting material is isolated after the reaction suggests that only a small portion of the catalyst is active under the reaction conditions. Although a complete selectivity for the monoene is observed (even after full conversion), the presence of catalytically active colloidal palladium has not been completely excluded. 

The second key process design parameter is the reaction rate, which depends on temperature, pressure, and concentrations. Rates of reaction... 

Ignition is dependent on various physicochemical parameters, such as the type of reactants, reaction rate, pressure, the heat transfer process from the external heat source to the reactants, and the size or mass of the reactants. The rate of heat production is dependent on the heats of formation of the reactants and products, the temperature, and the activation energy. As the process of ignition includes an external heating and an exothermic reaction of the reactants, there is a non-steady heat balance during these phases. 

Termolecular Reactions and Pressure Dependence of Rate Constants... 

When a solid is reacting with a gas stream flowing over its surface and the reaction rate is dependent on the partial pressure of the reacting gas, the over-all picture of the process of reaction may be represented as shown in Fig. 6. The general over-all rate and mass transfer relations can be expressed as follows ... 

The selective oxidation of propene to acrolein on supported vanadia catalysts was recently investigated by combined Raman, IR, and UV-vis DR spectroscopies (Zhao and Wachs, 2006). The surface vanadia species became more reduced under these reaction conditions as compared to those of alkane ODH (vide supra) because of the greater reducing power of alkenes relative to alkanes. Consequently, the reaction rates were dependent on the O2 partial pressures, because the surface vanadia sites were... 

In this text, the conversion rate is used in relevant equations to avoid difficulties in applying the correct sign to the reaction rate in material balances. Note that the chemical conversion rate is not identical to the chemical reaction rate. The chemical reaction rate only reflects the chemical kinetics of the system, that is, the conversion rate measured under such conditions that it is not influenced by physical transport (diffusion and convective mass transfer) of reactants toward the reaction site or of product away from it. The reaction rate generally depends only on the composition of the reaction mixture, its temperature and pressure, and the properties of the catalyst. The conversion rate, in addition, can be influenced by the conditions of flow, mixing, and mass and heat transfer in the reaction system. For homogeneous reactions that proceed slowly with respect to potential physical transport, the conversion rate approximates the reaction rate. In contrast, for homogeneous reactions in poorly mixed fluids and for relatively rapid heterogeneous reactions, physical transport phenomena may reduce the conversion rate. In this case, the conversion rate is lower than the reaction rate. 

When carbon dioxide is heated beyond its critical point, with a critical temperature of tc = 31.0 °C, a critical pressure of pc = 7.38 MPa, and a critical density of Pc = 0.47 g cm , the gaseous and the liquid phase merge into a single supercritical phase (SC-CO2) with particular new physical properties very low surface tension, low viscosity, high diffusion rates, pressure-dependent adjustable density and solvation capability ( solvation power ), and miscibility with many reaction gases (H2, O2, etc.). It can dissolve solids and liquids. The relative permittivity of an sc-fluid varies linearly with density, e.g. for SC-CO2 at 40 °C, r = 1.4 1.6 on going from 108 to 300 bar. This... 

For reactions with pressure-dependent rate constants this formalism developed by Troe and his co-workers is now most widely used. The rate constant k T, [M]) is written as,... 

In this model, the first step is the dissociation of C02 at a carbon free active site (Cfas), releasing CO and forming an oxidized surface complex [C(O)]. In the second step, the carbon-oxygen complex subsequently produces CO and a new free active site. The reverse reaction is relatively slow compared with the forward reaction, so the second reaction can be treated as an irreversible reaction. In this model, desorption of the carbon-oxygen surface complex is the rate-limiting step. The rate for this mechanism can be described by the Lang-muir-Hinshelwood rate equation. Furthermore, the C/C02 reaction rate is dependent on the CO and C02 partial pressures and is inhibited by the presence of carbon monoxide. A widely utilized reaction rate equation based on this mechanism is... 

Evidently, this initial rate pressure dependence gives a quick insight into which kinetic model describes best the experimental results of the reaction under consideration. Initial rate experiments are ideal for model discrimination purposes where one tries to select the best kinetic description of a process. However, two important aspects must be realised ... 

We recall from Chapter 1 and Part 1 of this chapter that the kinetic rate law e.g.. —= kC ) is a function solely of the intensive properties of the reacting system (e.g., temperature, pressure, concentration, and catalysts, if any). The reaction rate, usually depends on the concentration of the... 

MTBE is eliminated with pseudo-first order reaction kinetics [108-111]. The reaction rate is dependent on the frequency and power density of the ultrasound. At higher frequency, the elimination of MTBE is much faster. For each frequency the power density shows an optimum, since the interaction of and influence on cavitation bubble size, collapse time, transient temperature and internal pressure is very complex. Initial MTBE concentration was also observed to be of influence the reaction rate decreased with increasing MTBE concentration. This indicates that the reaction is limited by OH radical diffusion. 

In the case where X is H20, that is, for the water-exchange reaction, the pressure-dependence of the rate has been measured and the volume of activation found to be +1.2 ml per mole. This result definitely excludes a predominantly SN2 mechanism, but it does not agree satisfactorily with an extreme 5N1 mechanism either. It is most consistent with a transition state in which the initial Co—OH2 bond is stretched quite far while formation of a new Co—bond is only beginning to occur, that is, a predominantly dissociative mechanism. 

The conversion data fit second order kinetics for Ni removal reactions and first order kinetics for V removal reactions. The pressure dependence of the rate constants at 375°C was 1.39 for Ni and 1.82 for V and the activation energies 94.30 and 45.53 kcal/mol, respectively. 

Batt and Milne (1976) studied the thermal decay of the r-C4H90 radical in comparison with its reaction with NO in the pyrolysis of r-C4H90NO. This reaction was pressure dependent at 0.025-0.9 atm and 160°C. Over the temperature range of 119-158 C, the high-isessure limiting rate coefficient for... 

As illustrated in Fig. 5.1, the steady state of a catalytic reaction depends (apart from transport processes) on the external parameters, temperature T and partial pressures of reactants and products. Pi, pj, respectively. These parameters determine the surface concentrations of the reaction intermediates, which in turn are governed by the overall reaction mechanism. Description of the reaction rate r depending on the external parameters is achieved on various levels ... 

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