Pseudo-second-order

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

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 ... 

OS 12] [reactor given in [84]] [P 11] In [84], the scale-down from a 250 ml batch reactor to a 10 ml batch reactor is described. The validity of applying a pseudo-second-order kinetic model for the scaled-down processing was confirmed (Figure 4.41). 

Regarding submerged plants, sorption of Cu(II) by Myriophyllum spicatum L. (Eurasian water milfoil) has been shown to be fast and fits isotherm models such as Langmuir, Temkin, and Redlich-Peterson. The maximum sorption capacity (c/lll l j ) of copper onto M. spicatum L. was 10.80 mg/g, while the overall sorption process was best described by the pseudo-second-order equation.115 Likewise, Hydrilla verticillata has been described as an excellent biosorbent for Cd(II). In batch conditions, the qmsx calculated was 15.0 mg/g. Additionally, II. verticillata biomass was capable of decreasing Cd(II) concentration from 10 to a value below the detection limit of 0.02 mg/L in continuous flow studies (fixed-bed column). It was also found that the Zn ions affected Cd(II) biosorption.116... 

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). 

Loukidou et al. (2005) fitted the data for the equilibrium sorption of Cd from aqueous solutions by Aeromonas caviae to the Langmuir and Freundlich isotherms. They also conducted, a detailed analysis of sorption rates to validate several kinetic models. A suitable kinetic equation was derived, assuming that biosorption is chemically controlled. The so-called pseudo second-order rate expression could satisfactorily describe the experimental data. The adsorption data of Zn on soil bacterium Pseudomonas putida were fit with the van Bemmelen-Freundlich model (Toner et al. 2005). 

Experiments were then designed in which absorbance readings were acquired over the full time course of the reaction. These experiments employed a low concentration of PyO as the limiting reagent and a large excess of phosphine. The data fit a precise pseudo-second-order analysis, and gave kcat = 1.5xl04Lmol 1 s-1 in benzene at 298 K a precision of 5% was estimated. 

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. 

The reaction obeys pseudo-second-order kinetics that are first order in thiol, cycloalkenone, and catalyst. 

Abstract Removal of catechol and resorcinol from aqueous solutions by adsorption onto high area activated carbon cloth (ACC) was investigated. Kinetics of adsorption was followed by in-situ uv-spectroscopy and the data were treated according to pseudo-first-order, pseudo-second-order and intraparticle drfiusion models. It was fotmd that the adsorption process of these compotmds onto ACC follows pseudo-second-order model. Furthermore, intraparticle drfiusion is efiective in rate of adsorption processes of these compoimds. Adsorption isotherms were derived at 25°C on the basis of batch analysis. Isotherm data were treated according to Langmuir and Freundhch models. The fits of experimental data to these equations were examined. 

Three kinetic models were applied to adsorption kinetic data in order to investigate the behavior of adsorption process of adsorbates catechol and resorcinol onto ACC. These models are the pseudo-first-order, the pseudo-second-order and the intraparticle diffusion models. Linear form of pseudo-first-order model can be formulated as... 

The hnear form of pseudo-second-order equation can be formulated as... 

Table 21.1 Experimental and calculated values, rate eonstants of pseudo-first-order, pseudo-second-order and intrapartiele diffusion models...

Comparison of the observed pseudo-first-order decay of biological activity with a half-life of 30 sec at normal oxygen tensions versus decomposition via nitrogen dioxide by pseudo-second-order kinetics predicted by Reaction 4. The loss of nitric oxide through formation of nitrogen oxide is twice as fast as calculated by Reaction 4 because each nitrogen dioxide formed rapidly attacks a second nitric oxide to form nitrite. 

Pseudo second-order kinetic model In this model, the kinetic rate in differential form... 

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 ... 

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.

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 reactions can be described using a pseudo-second-order treatment. 

Each of the three approaches has been used to describe hydrodesulfurization of residua under a variety of conditions with varying degrees of success, but it does appear that pseudo-second-order kinetics are favored. In this particular treatment, the rate of hydrodesulfurization is expressed by a simple second-order equation ... 

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. 

Chromatograms of degraded aspartame solutions also showed irregular, low intensity, strongly retained peaks which were more prominent in solutions with higher initial aspartame concentrations [26]. These may be due to polymerization products from pseudo-second order intermolecular self-aminolysis of aspartame. 

Develop a pseudo-second-order rate law for the formation of Al-fulvic acid complexes according to the reaction in Eq. 2.44 and the parallel reaction ... 

---