Reaction rate constants pressure effect

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. 

The reaction rate constant and the diffusivity may depend weakly on pressure (see previous section). Because the temperature dependence is much more pronounced and temperature and pressure often co-vary, the temperature effect usually overwhelms the pressure effect. Therefore, there are various cooling rate indicators, but few direct decompression rate indicators have been developed based on geochemical kinetics. Rutherford and Hill (1993) developed a method to estimate the decompression (ascent) rate based on the width of the break-dovm rim of amphibole phenocryst due to dehydration. Indirectly, decompres-... 

Another m3d h arises from the intuition that pressure effect is opposite to the temperature effect. This is not true in kinetics. Therefore, kinetic constants (reaction rate constants, diffusion coefficients, etc.) almost always increase with increasing temperature, but they may decrease or increase with increasing pressure. Both positive and negative pressure dependences are well accounted for by the transition-state theory and are not strange. 

Supercritical solvents can be used to adjust reaction rate constants (k) by as much as two orders of magnitude by small changes in the system pressure. Activation volumes (slopes of In k vs P) as low as —6000 cm3/mol were observed for a homogeneous reaction (97). Pressure effects can also be pronounced on reversible reactions (17). In one example the equilibrium constant was increased from two- to sixfold by increasing the solvent pressure. The choice of supercritical solvent can also dramatically affect an equilibrium constant. An obvious advantage of using supercritical fluid solvents as a media for chemical reactions is the adjustability of the reaction kinetics and equilibria owing to solvent effects. 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

The effect of pressure on the reaction rate constant can be interpreted by both the collision-, and the transition state or activated complex theories. However, it has generally been found that the role of pressure can be evaluated more clearly by the transition state approach [3]. 

Rates of Gas-Phase Reactions. Reaction rates have been reported for only a few CVD gas-phase reactions, and most reports are primarily for the silane system. Because of the high temperatures and low pressures used in CVD, the direct use of reported gas-phase rate constants must be done with care. In addition to mass-transfer and wall effects, process pressure may be another factor affecting reaction rates. Process pressure affects major CVD processes, such as the deposition of Si from SiH4 and GaAs from Ga(CH3)3, reactions that involve unimolecular decomposition. The collisional activation, deactivation, and decomposition underlying these reactions can be summarized qualitatively by the following reactions (139, 140) ... 

While studies of reactions in supercritical fluids abound, only a few researchers have addressed the fundamental molecular effects that the supercritical fluid solvent has on the reactants and products that can enhance or depress reaction rates. A few measurements of reaction rate constants as a function of pressure do exist. For instance, Paulaitis and Alexander (1987) studied the Diels Alder cycloaddition reaction between maleic anhydride and isoprene in SCF CO2. They observed bimolecular rate constants that increased with increasing pressure above the critical point and finally at high pressures approached the rates observed in high pressure liquid solutions. Johnston and Haynes (1987) found the same trends in the... 

The thermodynamic pressure effect on the reaction rate constant can be explained in terms of transition state theory (Evans and Polanyi, 1935), when the reactants are in thermodynamic equilibrium with a transition state. Once the transition state complex is formed it proceeds directly to products. With this analysis the pressure effect on the reaction rate constant can be given as follows ... 

Figure 9 Values of the pressure effect on the reaction rate constant of benzophenone triplet + isopropanol in SCF CO2 predicted from the Peng-Robinson equation of state at various alcohol concentrations.

In principle, the fundamental equation for the effect of high pressure on a reaction rate constant was deduced by Evans and Polanyi on the basis of transition state theory ... 

Not only the internal pressure of a solvent can affect chemical reactions (see Section 5.4.2 [231, 232]), but also the application of external pressure can exert large effects on reaction rates and equilibrium constants [239, 429-433, 747-750]. According to Le Chatelier s principle of least restraint, the rate of a reaction should be increased by an increase in external pressure if the volume of the activated complex is less than the sum of the volumes of the reactant molecules, whereas the rate of reaction should be decreased by an increase in external pressure if the reverse is true. The fundamental equation for the effect of external pressure on a reaction rate constant k was deduced by Evans and Polanyi on the basis of transition-state theory [434] ... 

The reaction rate constant k is not truly a constant, but is merely independent of the concentrations of the sp ies involved in the reaction. The quantity k is also referred to as the specific reaction rate (constant). It is almost always strongly dependent on temperature. In gas-phase reactions, it depends on the catalyst and may be a function of total pressure. In liquid systems it can also be a fiinction of total pressure, and in addition can depend on other parameters, such as ionic strengfli and choice of solvent. These other variables normally exhibit much less effect on the specific reaction rate than does temperature, so for the purposes of the material presented here it will be assumed that kf depends only on ten erature. This assumption is valid in most laboratory and industrial reactions and seems to work quite well. 

TABLE 1. Values for the rate parameters of the elementary steps in our MC model, p stands for pressure, u for prefaotors, Eact for activation energy, and So for the initial sticking coefficient. For the reactions which have zero activation barriers, we have considered the rate constants as effective, temperature-independent parameters. 

Pressure Transition-state theory accounts for pressure effects on solution reaction rates through the effect of pressure on the equilibrium constant K. At constant temperature and electrolyte concentration (constant ionic strength),... 

Effect of H2S on Reaction Rate. As the desulfurization reaction proceeds, H2S is produced. This material, although mainly in the vapor phase, is in equilibrium with a concentration of dissolved H2S in the liquid. Under certain conditions the mass action effect of this material can strongly influence the overall rate of the desulfurization reaction. Figure 3 shows the effect for one set of circumstances of H2S partial pressure on the pseudo second-order reaction rate constant. Again the constant shown is not a true reaction rate constant— which would be independent of such parameters— but is an overall representation of several simultaneously occurring forward and reverse desulfurization reac-... 

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