Intrinsic pseudo-first-order rate constant

Fig. 10. The time-on-stream behavior of the pseudo-first-order intrinsic rate constant for Pt and PtFe catalysts on alumina.

Figure 6.18.14 shows the influence of NO conversion on the pseudo-first-order intrinsic rate constant and on the effectiveness factor for pore diffusion. 

Reactions catalyzed by hydrogen ion or hydroxide ion, when studied at controlled pH, are often described by pseudo-first-order rate constants that include the catalyst concentration or activity. Activation energies determined from Arrhenius plots using the pseudo-first-order rate constants may include contributions other than the activation energy intrinsic to the reaction of interest. This problem was analyzed for a special case by Higuchi et al. the following treatment is drawn from a more general analysis. ... 

The material balance was calculated for EtPy, ethyl lactates (EtLa) and CD by solving the set of differential equation derived form the reaction scheme Adam s method was used for the solution of the set of differential equations. The rate constants for the hydrogenation reactions are of pseudo first order. Their value depends on the intrinsic rate constant of the catalytic reaction, the hydrogen pressure, and the adsorption equilibrium constants of all components involved in the hydrogenation. It was assumed that the hydrogen pressure is constant during... 

The consequence of Equation (3) is that the relaxation process is related to the sum of the rate constant for the pseudo-first-order association process and the rate constant for the dissociation process. The association process can be influenced by changes in the concentration of H, but the value of k is intrinsic to the system and cannot be manipulated by external parameters, such as concentrations of reactants. The relaxation process can be dominated by the association or dissociation process depending on the relative value of k+[H] compared to k. The lifetime for the relaxation process is the inverse of the observed rate constant (r0bs — l/kefe). 

Samples 1-4 correspond to VPO treated in steam for 92, 312h, in N2 and activated base catalysts, respectively, k, are pseudo-first-order rate constants for the disappearance of butane. The constants are measured in a microreactor on a larger amount ( 1 g) of catalyst at 633 K. k (intrinsic) are based on the BET surface area. 

Bertole et al.u reported experiments on an unsupported Re-promoted cobalt catalyst. The experiments were done in a SSITKA setup, at 210 °C and pressures in the range 3-16.5 bar, using a 4 mm i.d. fixed bed reactor. The partial pressures of H2, CO and H20 in the feed were varied, and the deactivation, effect on activity, selectivity and intrinsic activity (SSITKA) were studied. The direct observation of the kinetic effect of the water on the activity was difficult due to deactivation. However, the authors discuss kinetic effects of water after correcting for deactivation. The results are summarized in Table 1, the table showing the ratio between the results obtained with added water in the feed divided by the same result in a dry experiment. The column headings refer to the actual experiments compared. It is evident that adding water leads to an increase in the overall rate constant kco. The authors also report the intrinsic pseudo first order rate-coefficient kc, where the overall rate of CO conversion rco = kc 6C and 0C is the coverage of active... 

In a typical experiment, the sample is a solution (e.g., in benzene) of both the ferf-butoxyl radical precursor (di-tert-butylperoxide) and the substrate (phenol). The phenol concentration is defined by the time constraint referred to before. The net reaction must be complete much faster than the intrinsic response of the microphone. Because reaction 13.23 is, in practical terms, instantaneous, that requirement will fall only on reaction 13.24. The time scale of this reaction can be quantified by its lifetime rr, which is related to its pseudo-first-order rate constant k [PhOH] and can be set by choosing an adequate concentration of phenol, according to equation 13.25 ... 

The optical rotation of the mixture approaches zero (a racemic mixture) over time, with apparent first-order kinetics. This observation was supported by the semi-log plot [ln(a°D/ aD) vs time], which is linear (Figure 1). It has been shown that this racemization process does in fact follow a true pseudo-first-order rate equation, the details of which have been described by Eliel.t30 Therefore, these processes can be described by the first-order rate constant associated with them, which reflects precisely the intrinsic rate of racemization. Comparison of the half-lives for racemization under conditions of varying amino acid side chain, base, and solvent is the basis for this new general method. 

Pure component in gas phase and saturated liquid phase First-order kinetics in A In this case, the gas phase is a pure component A (CAG is constant) and the liquid phase is considered to be saturated with A (C is constant). Furthermore, the intrinsic rate is considered to be of fust order with respect to A -rm = /cmCAS, per unit mass of catalyst. Under these conditions, the material balances for the gas component A in the gas and liquid phases (eqs. (3.365) and (3.367)) are not needed CAL is constant and equal to CAl q = CAG/HA. The same analysis is valid for reactions of fu st order for both components, if Cbl -> > Cal and thus CBS = const (pseudo-first order) (Smith, 1981). Then (eq. (3.369))... 

All the polymers show marked catalytic effects on the decarboxylation in the water solvent. In the polymer environment the intrinsic first-order rate constant k2 can be 103-fold greater than the pseudo-first-order rate constant in the aqueous solvent alone (B and E, respectively, in Table X). 

Consider a species A whose removal from the atmosphere can be expressed as a first-order reaction, that is, RA = —kAcA. If the removal of A is the result of reaction with background species B, then kA can be a pseudo-first-order rate constant that includes the concentration of B in it. The intrinsic rate constant is given by the Arrhenius expression kA = Aq exp(—Ea/RT). 

Table 11.6 Pseudo-First-Order Rate Constants and Intrinsic Activity of the Catalysts Applied...

Given the intrinsic rate expression kfCC), Eq. 7.15 can be solved for the surface concentration Q, which upon inserting into Eq. 7.14 3rields the global rate in terms of Qq, the rate constant, and the mass transfer coefficients. A pseudo-first-order rate expression is often adequate when the gaseous reactant dissolves slightly in the liquid reactant. In such a case, the global rate is simply ... 

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