Pseudo second-order constant

The second-order rate constant 2 is, in reality, a pseudo-second-order constant of complexity. The shape of the plot of k2 (Figure 4) vs. chloride is exponential as expected. 

The equilibrium adsorption capacity q and the initial sorption rate Qi) along with the pseudo-second-order constant kg can be determined from the slope and the intercept of the plot of t/q versus t. The adsorption capacity depends upon the initial sorbate concentration, Cq, system temperature, T, solution, pH, sorbate particle size, sorbate dose, w, sorbate characteristics and so on. The kinetic model is concerned only with the effect of observable parameters on the overall rate (Ho, 2006). 

The kinetic law of the reaction will be v = A i [DNFB] [ArNH2] and the complex expression of obs in Eq. 33.1 has been transformed into a simple pseudo second-order constant. 

If the dominant contributions /r,[M.] are approximately constant, this leads to pseudo second-order kinetics with an effective rate constant... 

This form is indeed found. It is easy to show that the maximum rate occurs at pH = pKa, 7.78 in this case. The maximum value of the pseudo-second-order rate constant is... 

Kennedy and co-workers10 studied model cationic polymerization initiation and termination. They determined the effect of halogens in f-BuX and MeX on the rate of reaction between f-BuX and Me3Al. The pseudo second order rate constant decreased (Table 1) as ... 

Note that k and /c3 are second-order constants, whereas k2 is a pseudo-first-order constant. The pH versus rate profile can be constructed by considering, in turn, that one of the three kinetic terms is predominating, thus ... 

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

Specificity constant Defined as kcJKm. It is a pseudo-second-order rate constant which, in theory, would be the actual rate constant if formation of the enzyme-substrate complex were the rate-determining step. 

Selectivity is an intrinsic properly of enzymatic catalysis. [3] Following the nomenclature proposed by Cleland [24, 25], the pseudo second-order rate constant for the reaction of a substrate with an enzyme, kml/KM, is known as the specificity constant, ksp. [26] To express the relative rates of competing enzymatic reactions, involving any type of substrates, the ratio of the specificity constants appears to be the parameter of choice [3]. Since the authoritative proposition by Sih and coworkers [27], the ratio of specificity constants for the catalytic conversion of enantiomeric substrates, R and S, is commonly known as the enantiomeric ratio or E -value (Equation 1) ... 

It can be readily shown that the specificity constant ksp = kcat/KM can be taken to act as a (pseudo) second-order rate constant in the rate equation for an enzymatic reaction that follows minimal Michaelis-Menten kinetics ... 

The rate law for the hydride-catalyzed system can be written as —d[CO]/dt = k [RuT] [pip], where k is a pseudo-second-order rate constant which includes the CO dependence. A mechanism which incorporates slow steps corresponding to Reactions 5 and 6 will lead to a rate law of the kind shown in Equation 11 which satisfies all the... 

The predicted kinetic behavior under these circumstances is therefore first-order, with a first-order koba related to the microscopic second-order constant k1 by Equation 2.36. Such reactions are said to follow pseudo first-order kinetics. 

Kinetic traces are now exponential and the first-order treatment yields /cv, which will exhibit a linear dependence on [B]. The true rate constant k can then be easily obtained from the relationship/c Ar, (/ B. A similar treatment is applicable to other reaction types as well. A third-order reaction, for example, can be run under pseudo-first- or pseudo-second-order conditions, depending on the precise rate law and the chemistry involved. 

At 80 °C, the value of the pseudo second order rate constant, k, was 2.05 X 10 mole" hr" (gram cat)" These observed kinetics provide firm quantitative support for a Rideal mechanism, which requires fast, reversible, and noncompetitive adsorption of the olefin on the catalyst acid sites see Scheme 5 above). The strictly first order dependency of toluene proves freedom from intracrystalline diffusion problems with respect to ethylene. Likewise, the product distribution, which contains only traces of disubstituted toluenes, shows absence of diffusion limitation for the product, ethyltoluene. Intracrystalline diffusion problems may, however, exist in the isopropylation experiments with extremely active catalysts. 

Most of the literature indicated that the RHDS reaction is pseudo second order, Shah (ref, 7) has reported that the apparent reaction rate constant can be determined by the following equation... 

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-... 

When n equals 0, 1, or 2, the reaction is said to be a pseudo-zero-, pseudo-first-, or pseudo-second-order reaction (pseudo-nth-order for higher order reactions), respectively. If the concentration of an additional reactant other than drug D is not constant during the reaction, the reaction order becomes n + 1. 

Pseudo second-order rate constant at ambient pressure. 

Actual experimental data on the pressure variation of the pseudo-second-order rate constant k exhibit a broader transition between the two limits than is predicted by... 

Actual experimental data on the pressure variation of the pseudo-second-order rate constant k do not conform with (3.71). The reason is that the elementary rate constants k , and should have been defined for each individual quantized vibrational level of AB, and the individual rates summed to give the total rate. Also, vibrations and rotations can interconvert in the newly formed molecule. A widely used modification of the treatment of pressure-dependent reactions is due to Troe (1983). In the Troe theory, the right-hand side of (3.71) is multiplied by a broadening factor F that is itself a function of ko/k. ... 

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