Pressure dependence kinetic rate constants

Checking the absence of external mass transfer limitations is a rather easy procedure. One has simply to vary the total volumetric flowrate while keeping constant the partial pressures of the reactants. In the absence of external mass transfer limitations the rate of consumption of reactants does not change with varying flowrate. As kinetic rate constants increase exponentially with increasing temperature while the dependence of mass transfer coefficient on temperature is weak ( T in the worst case), absence... 

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. 

PllC-2 Given the proposed rate equation on page 296 of the article in Ind. Eng. Chem. Process Des. Dev., 19, 294 (1980), determine whether or not the Icon-centration dependence on sulfur, Cj, is really second-order. Also, determine if the intrinsic kinetic rate constant, K2p, is indeed only a function of temperature and partial pressure of oxygen and not of some other variables as well. 

Now it is possible to develop a strategy for analyzing the time dependence of total pressure for gas-phase reactions when the sum of stoichiometric coefficients does not vanish. Since the order of the forward and backward reactions is known for elementary steps, linear least-squares analysis via the differential approach is useful to determine the forward kinetic rate constant if the equilibrium constant can be calculated from thermodynamics. The logical sequence of steps is as follows ... 

The forward kinetic rate constant kforvmrd, p T) exhibits Arrhenius temperature dependence and has dimensions of moles/volume time atm". The equilibrium constant based on gas phase partial pressures has dimensions of (atm), where S = —2. Since N2 and H2 are present in their standard states, the enthalpy and free energy of formation for NH3 at 298 K allow one to construct the temperature dependence of /Cequii, p as follows ... 

This matches the functional form of the BET isotherm when the parameter k is given by the ratio of adsorbate partial pressure pa to its saturation vapor pressure at the experimental temperature T, PA,saturation(P)- Let s consider the parameter f), which was defined above as the ratio of kq to k. If the adsorption and desorption kinetic rate constants for chemisorption follow Arrhenius temperature dependence, then kq for chemisorption on the bare surface is expressed as... 

The initial reactant product conversion rate should increase at higher temperature because kinetic rate constants for elementary steps, particularly the desorption of gas D, increase at higher temperature. In summary, there is no total pressure dependence of the initial reactant product conversion rate when (1) A -h B C -h D, (2) single-site adsorption is appropriate for each component, and (3) desorption of one of the products controls the Hougen-Watson kinetic rate law. 

PRESSURE DEPENDENCE OF THE KINETIC RATE CONSTANT VIA ELEMENTS OF TRANSITION STATE THEORY... 

Since the pressure dependence of this unusual standard-state chemical potential of species i at constant temperature and composition yields the partial molar volume of species i, Wi, one obtains the final result for the pressure dependence of kinetic rate constants ... 

Figure 15-1 Total pressure dependence of the best pseudo-first-order kinetic rate constant when a first-order rate law approximates a Hougen-Watson model for dissociative adsorption of diatomic A2 on active catalytic sites. Irreversible triple-site chemical reaction between atomic A and reactant B (i.e., 2Acr - - Bcr -> products) on the catalytic surface is the rate-limiting step. The adsorption/desorption equilibrium constant for each adsorbed species is 0.25 atm. ...

Figure 22-1 Pressure dependence of the best pseudo-first-order kinetic rate constant ki with units of min" is calculated from 0.03 to 100 atm at 325 K for the synthesis of methanol from carbon monoxide and hydrogen. The original heterogeneous catalytic mechanism is postulated as five-site chemicai reaction rate controiiing, whrae H2 unda--goes dissociative adsorption and CO and CH3OH each adsorb on singie active sites. In each case, all adsorption/desorption equilibrium constants are either 0.25 or 2.5 atm. ...

In Section 8.2 we discuss the main ideas behind the formalism and illustrate some of the features based on predictions from integral equation calculations involving simple binary mixtures modeled as Lennard-Jones systems (Section 8.2.1), to guide the development of, and provide molecular-based support to, the macroscopic modeling of high-temperature dilute aqueous-electrolyte solutions (Section 8.2.2), as well as to highlight the role played by the solvation effects on the pressure dependence of the kinetic rate constants of reactions in near-critical solvents (Section 8.2.3). 

Now, we interpret the effect of species-solvent molecular asymmetries on the pressure dependence of the kinetic rate constants for reacting systems studied by Roberts et al. (1995) according to the solvation formalism. The system under consideration consists of triplet benzophenone ( BP) as an infinitely dilute reactant, O2 as an infinitely dilute reactive cosolvent, and the infinitely dilute transition state (TS) species all immersed in near aitical CO2 solvent, where all species are described in terms of Lennard-Jones interactions (see Table 8.3) and unlike-pair interactions based on the Lorentz-Berthelot combining rules. 

To perform a kinetic analysis of pressure-dependent reactions is in practice a straightforward task, since many codes are available. The major problem is to obtain the required input parameters. The following sections give short descriptions of several programs that allow the calculation of pressure-dependent rate constants, followed by a discussion of methods to obtain the input data. 

From the viewpoint of modeling, the ultimate goal of the kinetic analysis of pressure-dependent reaction systems is to provide reliable time-independent rate expressions k(T, p) which can be incorporated into large kinetic models. The functional forms of these rate expressions can be rather complicated for multi-channel multiple wells systems, since—as we saw from the examples—the competition of product channels leads to strongly non-Arrhenius behavior. On the other hand, pressure-dependent rate constants for single-well single-channel reaction systems are comparably easy to describe. Therefore, we will divide this discussion into two sections going from simple fall-off systems to complex systems. 

Even though the kinetic analysis of pressure-dependent reactions can clearly be improved, even at this point the kineticist is already in the position to provide relatively accurate pressure-dependent rate constants. We hopefully showed that such calculations are straightforward to perform, and we anticipate that k T, p) data for many more important reactions will soon be available for modeling studies. 

Properties associated with a chemical reaction includes thermodynamic quantities (e.g., equilibrium constants, electrode potentials), kinetic rate constants, and activation energies (see Rates of Chemical Reactions). These are often very sensitive functions of temperature and may depend on pressure as well. 

In high-pressure ethylene polymerization, the kinetic rate constants are also dependent on pressure. For example, the propagation rate constant is given by... 

The kinetic data fit a mechanism of successive reactions sequent to only one primary ion equally well, provided that the first step can yield 1.37 methyl radical/100 e.v. and is pressure dependent and that the succeeding pressure independent step yields methyl radicals with a lesser efficiency and leads to a pressure independent yield of 0.58 methyl radicals/100 e.v. If the first step is either Reaction 9a or Reaction 17b, one can once more use the rate constant ratios given earlier to estimate the yields of the possible primary precursor ions. Hence, either G-(C2H2+) = 1.9 ions/100 e.v., or G(C2H4+) = 1.52 ions/100 e.v. The... 

Kinetic examination of the methane yield shows behavior quite similar to that of methyl radical a pressure dependent yield of 0.406 molecule/100 e.v., a pressure independent yield of 0.126 molecule/100 e.v., and a rate constant ratio of kq/kf = 1.5 X 106 mole-1 cc. for the competing steps. 

Calculation of kinetic parameters - In the experiments carried out in the single autoclave the H2 pressure was not maintained and the consumption of H2 controlled the conversion of AcOBu, which could be described by pseudo-first order rate constant. In the activity tests performed in SPR16 the conversion of AcOBu increased linearly up to ca. 50 % with reaction time. Initial reaction rates were calculated from AcOBu conversion vs. reaction time dependence, the initial concentration of substrate and the amount of catalyst or the amount of promoters in 1 g of catalyst. 

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