Kinetics, chemical pseudo-first-order

The reactant R2 can also be considered to be a solvent molecule. The global kinetics become pseudo first order in Rl. For a SNl mechanism, the bond breaking in R1 can be solvent assisted in the sense that the ionic fluctuation state is stabilized by solvent polarization effects and the probability of having an interconversion via heterolytic decomposition is facilitated by the solvent. This is actually found when external and/or reaction field effects are introduced in the quantum chemical calculation of the energy of such species [2]. The kinetics, however, may depend on the process moving the system from the contact ionic-pair to a solvent-separated ionic pair, but the interconversion step takes place inside the contact ion-pair following the quantum mechanical mechanism described in section 4.1. Solvation then should ensure quantum resonance conditions. 

In classical kinetics, intemiolecular exchange processes are quite different from the uniniolecular, first-order kinetics associated with intramolecular exchange. However, the NMR of chemical exchange can still be treated as pseudo-first-order kinetics, and all the previous results apply. One way of rationalizing this is as... 

In the experiments carried out, the rate of hydrogenation was first order with respect to [C=C] from 30 to 90% conversion. Pseudo first order rate constants (k ) were determined for experiments over a range of conditions in order to measure the effect of different reaction parameters. The maximum hydrogenation rate constant recorded in this study was an order of magnitude less than the rate of H2 mass transfer10 and so gas uptake measurement reflected the inherent chemically controlled kinetics of the system. 

For some organic compounds, such as phenols, aromatic amines, electron-rich olefins and dienes, alkyl sulfides, and eneamines, chemical oxidation is an important degradation process under environmental conditions. Most of these reactions depend on reactions with free-radicals already in solution and are usually modeled by pseudo-first-order kinetics ... 

We start with the case where the initial electron transfer reaction is fast enough not to interfere kinetically in the electrochemical response.1 Under these conditions, the follow-up reaction is the only possible rate-limiting factor other than diffusion. The electrochemical response is a function of two parameters, the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic parameter, 2, that measures the competition between chemical reaction and diffusion. In cyclic voltammetry,... 

RP-HPLC found application in the monitoring of the alkali hydrolysis kinetics of alkali-clearable azo disperse dyes containing a fluorosulphonyl group. The chemical structures of dyes included in the experiments are shown in Fig. 3.85. Samples for RP-HPLC analysis were neutralized to pH 4.0 - 4.5 with diluted HC1 mixed with five volumes of ACN and injected without any other sample preparation step. Separation was carried out in an ODS column at ambient temperature. The isocratic mobile phase consisted of ACN-water (80 20, v/v) and dyes were detected at their absorption maxima. HPLC measurements indicated that dyes are easily hydrolysed under relatively mild alkaline conditions, and the hydrolysis follows a pseudo first-order kinetics [148],... 

The L-dopa esters were also examined for their enzymatic hydrolysis in human plasma and/or by purified pig liver carboxylesterase (EC 3.ELI Table 8.1). In human plasma under the conditions of study, hydrolysis again followed pseudo-first-order kinetics. In all but two cases examined, enzymatic hydrolysis was slightly faster than chemical hydrolysis. For the methyl ester, rates of chemical and enzymatic hydrolysis were comparable, whereas the /erf-butyl ester was not hydrolyzed in plasma and was protected from chemical hydrolysis presumably by becoming bound to plasma proteins. 

V = V max [S]// m- A reaction of higher order is called pseudo-first-order if all but one of the reactants are high in concentration and do not change appreciably in concentration over the time course of the reaction. In such cases, these concentrations can be treated as constants. See Order of Reaction Half-Life Second-Order Reaction Zero-Order Reaction Molecularity Michaelis-Menten Equation Chemical Kinetics... 

The ratio of the enantiomeric benzyl amide products was determined by analyzing a diluted aliquot of the quenched reaction mixture by HPLC using a chiral stationary phase column (Chiralcel OD, Daicel Chemical Co.). Since racemization is a pseudo-first-order kinetic process, these data (along with the time zero value) are sufficient for determination of the intrinsic rate of racemization kR. The half-life for racemization lRU2 can be directly calculated from the l/d ratio (or % enantiomeric excess, %ee) where t was the time of benzylamine addition (the delay time) ... 

After a fire in a chemical storehouse at Schweizerhalle, Switzerland, in November 1986, several tons of various pesticides, solvents, dyes, and other raw and intermediate chemicals were flushed into the Rhine River (Capel et al., 1988 Wanner et al., 1989). Among these chemicals was the insecticide disulfoton, of which 3500 kg were introduced into the river water (11°C, pH 7.5). During the 8 days travel time from Schweizerhalle to the Dutch border, 2500 kg of this compound were eliminated from the river water. Somebody wants to know how much of this elimination was due to abiotic hydrolysis. Since in the literature you do not find any good kinetic data for the hydrolysis of disulfoton, you make your own measurements in the laboratory. Under all selected experimental conditions, you observe (pseudo)first-order kinetics, and you get the results given below. 

The influence of the chemical follow-up reaction depends on the ratio of the rate constant kc of the C step and the sweep rate v. The higher that v is, the less influence does the follow-up reaction have for chemical reactions with first-order rate constants kc 104, it is possible to outrun the reaction and obtain a reversible cyclic voltammogram at high v. The p(red) for a given system with first-order (or pseudo first-order) kinetics is then shifted 30 mV in the negative direction when v is increased tenfold.11-15 By plotting Ep versus log v, one can get curves from which the value of kc can be obtained. This is illustrated in Fig. 3 for a reaction where the chemical step is a cleavage. 

So the product, R, of the electrochemical reduction reacts in the solution with an electroinactive oxidizer, Ox, to regenerate O, etc. If Ox is present in large excess, the chemical reaction is pseudo-first-order in R and O. For thermodynamic reasons, Rc can only proceed if the standard potential of the redox couple Ox/Red is more positive than that of O/R. Then, for Ox to be electroinactive, it is required that its electroreduction proceeds irreversibly, in a potential range far negative to the faradaic region of the 0/R reaction. Thus, Ox being stable for reasons of the slow kinetics of its direct reduction, it can be said that, in the presence of O, it is being catalytically reduced. 

As pointed out in Section 8.2, most physical and chemical processes, not just the chemical transformation of reactants into products, are accompanied by heat effects. Thus, if calorimetry is used as an analytical tool and such additional processes take place before, during, or after a chemical reaction, it is necessary to separate their effects from that of the chemical reaction in the measured heat-flow signals. In the following, we illustrate the basic principles involved in applying calorimetry combined with IR-ATR spectroscopy to the determination of kinetic and thermodynamic parameters of chemical reactions. We shall show how the combination of the two techniques provides extra information that helps in identifying processes additional to the chemical reaction which is the primary focus of the investigation. The hydrolysis of acetic anhydride is shown in Scheme 8.1, and the postulated pseudo-first-order kinetic model for the reaction carried out in 0.1 M aqueous hydrochloric acid is shown in Equation 8.22 ... 

There are many tricks and shortcuts to this process. For example, rather than compiling all of the transformation rate equations (or conducting the actual kinetic experiments yourself), there are many sources of typical chemical half-lives based on pseudo-first-order rate expressions. It is usually prudent to begin with these best estimates of half-lives in air, water, soil, and sediment and perform a sensitivity analysis with the model to determine which processes are most important. One can return to the most important processes to assess whether more detailed rate expressions are necessary. An illustration of this mass balance approach is given in Figure 27.5 for benzol a Ipyrene. This approach allows a first-order evaluation of how chemicals enter the environment, what happens to them in the environment, and what the exposure concentrations will be in various environmental media. Thus the chemical mass balance provides information relevant to toxicant exposure to both humans and wildlife. 

It is known from the theory of chemical kinetics that a system of S chemical substances in dynamic equilibrium can be described by rate constants of the pseudo-first order, K, a (i = 1, 2,..., S a= 1,2,..., Q). Some of the rates may assume zero values. The rate of depletion of substance A-t in the reaction co(er), Vrw(o), and that of its formation in the reverse reaction a, Vj+tt, must equal each other at equilibrium ... 

The single pulse voltammograms of a pseudo-first-order catalytic process are easily characterized by the increase of the limiting current with the time or the chemical kinetic constants, whereas its half-wave potential remains unchanged. 

For a first-order or pseudo-first-order CE mechanism with a reversible electrode reaction, the SWV response is determined by the thermodynamic and kinetic parameters of the chemical reaction. So, the peak current y6 wv ancl the peak potential are notably dependent on them. 

Solution of the coupled mass-transport and reaction problem for arbitrary chemical kinetic rate laws is possible only by numerical methods. The problem is greatly simplified by decoupling the time dependence of mass-transport from that of chemical kinetics the mass-transport solutions rapidly relax to a pseudo steady state in view of the small dimensions of the system (19). The gas-phase diffusion problem may be solved parametrically in terms of the net flux into the drop. In the case of first-order or pseudo-first-order chemical kinetics an analytical solution to the problem of coupled aqueous-phase diffusion and reaction is available (19). These solutions, together with the interfacial boundary condition, specify the concentration profile of the reagent gas. In turn the extent of departure of the reaction rate from that corresponding to saturation may be determined. Finally criteria have been developed (17,19) by which it may be ascertained whether or not there is appreciable (e.g., 10%) limitation to the rate of reaction as a consequence of the finite rate of mass transport. These criteria are listed in Table 1. 

When the process pN- n-> pv in the mobile phase or stationary phase can be represented by first-order or pseudo-first-order interconversion kinetics and as a reversible binding event, the resolution of the interconverting species can be evaluated319 by treating the column as a chemical reactor with properties specified by the corresponding Damkohler number Da and the corresponding interconversion rate constants derived. Thus,... 

Dissolution Kinetics. Pseudo first-order reactions are widely employed in the field of soil-water environmental science for evaluating physical, chemical, or biochemical events. A pseudo first-order dissolution example is given below to demonstrate the use of kinetics in identifying or quantifying minerals in simple or complex systems. Consider a metal carbonate solid (MC03s) reacting with a strong acid (HC1) ... 

The parameters that are extricated from a line shape analysis are the reciprocal mean lifetimes, l/rsp(sp = species), between successive exchanges via each particular step. In chemical usage l/rsp is preferably written as kj, the pseudo-first-order rate constant. The results of NMR line shape analysis provide kinetic information via the well-known relationship given in equation 57. A term such as in equation 5 is used for each separate exchange step. 

In the case of quenching the reduction (shortening of the o-Ps lifetime) is explained by the chemical reaction of positronium and the quenching species (which in many cases are additives present in the polymer matrix). The chemical rate constant for the reaction between the Ps and quenching species can be expressed in terms of the concentration of the quenching species [M], and it is found that it can be described by pseudo-first order kinetics as [42, 80] ... 

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