Pressure dependence of reaction rate

For very fast reactions, as they are accessible to investigation by pico- and femtosecond laser spectroscopy, the separation of time scales into slow motion along the reaction path and fast relaxation of other degrees of freedom in most cases is no longer possible and it is necessary to consider dynamical models, which are not the topic of this section. But often the temperature, solvent or pressure dependence of reaction rate... 

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... 

Recently, Suzuki and Taniguchi93 hydrolyzed n-butylacetate, ethylacetate, and methylacetate with HPSt and 41 (PVA B) (partially-o-benzalsulfonated polyvinylalcohol). The volume of activation, A P+, was obtained from the pressure dependence of reaction rates [ F + = -kT(d Ink/dP)]. The A + increased with increasing hydro-phobidty of the substrate. 

When a reaction takes place under high pressures, however, the effect of pressure on the reaction rate may not be neglected. The description of the pressure dependence of reaction rates (15) Is based on the assunptlon that the reaction goes through a transition state Involving a volume change between reactants and the transi-... 

Figure 5. Partial pressure dependencies of reaction rate at 250°C for Rh catalyst [e.g., P(N0)var. NO partial pressure is variable and H2 partial pressure is constant].

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

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. 

A number of authors (29-32) have studied the dependence of reaction rate on pressure in the reaction mixture. Almost all of them [see, e.g., references (30-32) ] have obtained the first order with respect to hydrogen and deuterium. Pines and Ravoire (29) noted the order close to unity (0.7). 

Reaction of Ru(CO)g with H2 has been observed by high-pressure IR spectroscopy to produce H2Ru(CO)4 (18). The involvement of H2 in an equilibrium process such as step 2 could be the root of the observed non-integral dependence of reaction rate on H2 pressure. 

Because of the overall first-order dependence of reaction rate on pressure (specifically, on hydrogen partial pressure) in combination with the rather complex selectivity relationships among primary products, it is regarded as quite probable that all of the primary products (and the separate inter-... 

The measured rate constant for unimolecular reactions, association reactions, and certain bi-molecular reactions to be considered in the next section can have a complex dependence on total pressure, in addition to the strong temperature dependence of Eq. 9.83. This section introduces the theory of the pressure-dependence of the rate constant kmj the same theory follows to yield the pressure dependence of kassoc. Because kuni and kassoc are related by the equilibrium constant, which is independent of pressure, for a given reaction... 

The reaction was reinvestigated by Cvetanovic (21) who found that within a small analytical uncertainty the exclusive primary step was reaction (11). Formation in this reaction of oxygen atoms in their triplet ground state (OIP) is required by the spin conservation rule and there is now ample chemical evidence that this is indeed so. A primary formar tion of an electronically excited N20 molecule, ruled out in the early work on spectroscopic grounds, is also incompatible with the lack of a pressure dependence of the rate of decomposition. 

Fig. 3. A schematic picture of the dependence of reaction rate on partial pressure of CO. A case with a strong adsorption (7.5). (Reprinted with permission from Advances in Chemistry Series. Copyright by the American Chemical Society.)...

We can also investigate how the rate of deacfivafing C—C bond formation compares with the rate of initial C—H bond formation. These rates are a function of the strength of inferacfion befween adsorbed carbon atoms and the metal surface (28). When fhe mefhanation reaction expression is generalized such that it can be used to describe the chain-growth reaction, the resultant expression shows the complex CO pressure dependence of the rate of the chain-growth reaction. 

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