Pseudo-orders

The published quantification of the rate of hydrogenation of the dienes COD and NBD of a large number of cationic rhodium(I) chelate complexes allows a good estimation of expected effects on the rate of enantioselective hydrogenation of prochiral alkenes. From the first-order pseudo-rate constants the time needed for complete hydrogenation of the diene introduced as part of the rhodium precursor can be easily calculated as six- to seven-fold the half life. It is recommended that the transfer into the solvent complex be followed by NMR spectroscopy. 

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. 

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

A good example of a first-order (pseudo-first-order) chemical reaction is the hydration of CO2 to form carbonic acid. Reaction l-7f, C02(aq) + H20(aq) H2C03(aq). Because this is a reversible reaction, the concentration evolution is considered in Chapter 2. 

Pakalapati, S., Yavuz, I., Elizalde-Blancas, F. and Celik, I. (2006) Comparison of a multidimensional model with a reduced order pseudo three-dimensional model for simulation of solid oxide fuel ells, in Proceedings of the 4th International ASME Conference on Fuel Cell Science, Engineering and Technology, Irvine, CA, June 19-21. 

Figure 1.10. (a) Second-order spin-rotation interaction occurring via L. (b) Second-order pseudo-contact hyperfine interaction occurring via L. (c) Electron coupled nuclear spin-spin interaction, (d) Second-order interaction of R and L. 

If some of the reactant or product species are present in excessive quantities, then the fractional changes in their concentrations over the entire duration of the reaction may be immeasurably small. In such cases the concentrations of the reactants present in excess remain approximately constant and may be absorbed into the rate constant fe. A measurement of the order of the reaction from concentration-time plots then does not reveal the dependence of the rate on the concentrations of the overabundant species the measurement yields the pseudo molecularity of the reaction, that is, the sum of the orders with respect to the species that are not present in excess. Thus a number of higher-order reactions are found to be pseudounimolecular under certain conditions. This observation provides the basis for the isolation method of determining the order of a complex reaction with respect to a particular reactant in this method, the apparent overall order (pseudo-molecularity) of the reaction is measured under conditions in which all of the reactants except the one of interest are present in excess. 

Zero-order, pseudo, 23 Zero-order approximation, 450... 

The temperature dependence of the rate of reactions is particularly Important for the pyrolytic processes. Relation (5) can be used for the understanding of the common choices for the pyrolysis parameters. As an example, we can take the pyrolysis of cellulose [8]. Assuming a kinetics of the first order (pseudo first order), the activation energy in Arrhenius equation was estimated E = 100.7 kJ / mol. The frequency factor was estimated 9.60 10 s These values will lead to the following expression for the weight variation of a cellulose sample during pyrolysis ... 

The kinetics of cellulose pyrolysis was extensively studied, mainly for practical purposes. As shown in Sections 3.2 and 3.3, cellulose pyrolysis can be approximated either by a reaction of first order (pseudo first order) or by more elaborate models. Assuming a first order reaction for example, the weight variation of a cellulose sample during pyrolysis is given by the relation (see rel. 15, Section 3.2) ... 

In a majori of chemical treatment processes the differential rate laws describing zero-order, first-order, pseudo first-order, and second-order reactions have the widest applications (11,14,26,33,38,61,63). These include many complex reactions, which involve a number of different steps. In such cases, one step is normally slower than ail the rest. This step controls the overall rate of reaction (the rate-limiting step), and it can generally be described by one of the afore-mentioned rate laws. 

I. N. Bazanova, O. V. Lefedova, V. P. Gostikin, and L. V. Kudryashova [Kinet. Catal., 28, 1177-1182 (1988)] studied the kinetics of the catalytic reduction of 2-(2 -hydroxy-5 -methylphenyl)benzotriazole over Raney nickel in 1 M NaOH. Several successive hydrogenation reactions occur such that the reaction network of interest can be regarded as a series of apparent first-order pseudo-homogeneous reactions of the form... 

In the absence of the terms oc these equations represent two uncoupled harmonic oscillators with frequencies (1 2/+), analogous to the zeroth-order pseudo-Renner-Teller system of Section IV,C. The diagonal terms oc distort these potentials, especially near the origin, whereas the corresponding oif-diagonal terms provide a coupling. Both of these terms... 

As the large excess of methanol, it could be safely assumed to be a first-order pseudo-homogeneous reaction. The esterification reaction was carried out using 15 wt% TPA/SnOa as catalyst (wa Wcai=5 l) in the temperature range of 45-65°Cand the kinetic data were measured. 

Since the zero order pseudo wave functions are plane waves, each one of these zero order terms contains a uniform contribution I/O to the density. This gives a uniform distribution outside the core region ... 

Three kinetic models, pseudo-first-order, pseudo-second-order, and intra-particle diffusion model are used to fit the experimental data The mathematical description of these models is given below. The conformity between data predicted by arty of these models and the experimental data is indicated by the correlation coefficient R. The model of higher values of R means that it successfully describes the adsorption kinetics. 

In this ion exchange reaction, we have identified the sodium ion concentration in the resin phase on a volumetric basis. Car, as well as on a per unit resin weight basis, <7ar correspondingly, the H ion concentrations are Car - Car and q - exchange capacities for Na". The net rate of transfer of Na+ ions to the resin phase may be written for this second-order (pseudo) reaction as (see expression (3.4.39b) or (3.4.39d))... 

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