Second-order reactions pseudo

Figure 2.3 Comparison of the Michaelis-Menten model for a minimal kinetic scheme (bottom equation) with the pseudo second-order format (top equation). Relationship between the kinetic barriers for the formation of the Michaelis complex and the chemical transformation S -> P, and the Gibbs free energy of the (virtual) barrier for the pseudo second-order reaction S + —> P + E.

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. 

When drug D reacts reversibly with A to form P according to a pseudo-second-order reaction, the rate expression for the loss of D is given by... 

The progress of the Diels-Alder reaction was assessed by contact angle measurements performed at room temperature (Fig. 19.7). Again, the reaction was studied systematically at six different temperatures. We observed that the Diels-Alder reaction could be described as a pseudo-second-order reaction (Fig. 19.8). Similarly to the Diels-Alder reaction on monolayers, the third-order rate constants koA. calculated from the least-squares fits shown in Fig. 19.8 for the Diels-Alder reaction in the polymer thin film, obey the Arrhenius equation (Fig. 19.9). The activation energy 3 = 48.1 3.7 kj moh and the activation entropy AS = -538.2 16.4 J mol at 298 K (Table 19.2) are determined at the polymer surface in the same way as for the monolayers. 

A general analytical solution for a nonlinear (Langmuir) system with a pseudo second-order reaction kinetic rate law has been found by Thomas. His model is summarized in Table 8.3. The numerical values of t( j8) have... 

The adsorption properties of natural clinoptilolite toward Co were investigated by batch equilibration technique [07S2], The kinetic data were fitted by pseudo-second-order reaction model, and the adsorption isotherms were defined by the Langmuir equation. The adsorption capacity of the natural clinoptilolite was decreased by the competition among the metal ions in solution. The adsorption capacity reached 2.34 mg/g for Co. The adsorption of Co was low, at low pH, but increased remarkably with increasing pH and precipitated at pH > 8. The presence of EDTA hindered the adsorption of Co on clinoptiloUte. 

Initially, a pseudo-first-order deactivation of A is assumed, while a pseudo second-order reaction is assumed for A + B reaction ... 

Furthermore, during the cracking process there is an increase in the number of moles of products being formed from the gas oil. In a riser, which is normally modeled as a plug flow reactor, this results in a decrease in the massic vapour density. If the concentration of the reactants is defined at a constant volumetric flow, the apparent order also increases because the actual concentration decreases much faster than expected as the conversion increases. A pseudo-second-order reaction has been normally used to account for these non-linear effects (Weekman, 1968). However, the reaction order should be independent of the reaction system used and an additional term to account for the increased vapour velocity in a flow unit should be used to define the formal kinetics (Shaikh and Carberry, 1984). 

Figure 3.2 Simulated pseudo second order reactions A+ R AR 1, Cr= 1 and in (a) Ca = 5 and in (b) Ca=2. The exponentials fitted for the two cases give 1/t of 4.710 s and 1.712 s". The deviations from true pseudo second order are discussed in the text. Residuals between the simulated reaction and the fitted exponential are shown across the graph.

Thomas (1944) has provided a general analytical solution for a non-linear Langmuir system with a pseudo second-order reaction kinetic law. The results, which are given in graphical form by Hiester and Vermeulen (1952), provide a means of assessing the importance of a mass transfer resistance in any system for which the rate constant and equilibrium parameters are... 

The expression in Eq. 33.1 is not simple, as the concentration of one of the reactants [ArNH2] appears in both, numerator and denominator. Frequently, complex rate laws can be simplified by making assumptions, like considering extreme concentrations (very high or very low) of reagents or assuming that some individual constants are negligible. In these cases a complex rate law is converted into a pseudo first- or pseudo second-order reaction. In other cases, however, the simplification is not possible. 

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