Chemical kinetics pseudo first-order reactions

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 reaction kinetics of ozonation can be determined after the Osac is reached, and the resistance of the ozone transfer from gas phase to liquid phase becomes insignificant where the concentrations of ozone are uniform in the liquid, in this case, the ozone consumption rate is determined solely by the rate of chemical reaction in the bulk (Charpentier, 1981). The reaction kinetics of dye ozonation, therefore, was studied under this circumstance, and the rate constants of dye decay were determined at various initial dye concentrations and pHs. From Figure 15, the results of dye ozonation at different pHs have shown that the reaction followed a pseudo first-order reaction. Since the oxidizing ability of ozone comes from either molecular ozone or hydroxyl free radicals, the rate of dye disappearance can be formulated as follows ... 

On the first part of this research, Advanced Chemical Oxidation, a quantitative estimation of direct ozonation and indirect free radical oxidation of dyes with assorted chromophores was studied through the examination of reaction kinetics in the ozonation process. The reaction kinetics of dye ozonation under different conditions was determined by adjusting the ozone doses, dye concentration, and reaction pH. The ozonation of dyes was found dominant by pseudo first-order reaction, and the rate constants decreased as the dye/ozone ratio increased. For all selected azo dyes, the dye decay rates increased as the initial pH of the solution increased, yet the decay rates of anthraquinone dyes would decrease in the same situation because of their insensible structure for ozone oxidation, formation of leuco-form, and higher solubility at a lower pH. The ozonation of dyes at a high pH contributed by hydroxyl free radicals was qualitatively verified by the use of a free radical scavenger. A proposed model, in another way, quantitatively determines the fraction of contribution for dye decomposition between free radical oxidation and direct ozonation. 

The field has a well-developed nomenclature and symbolism. The one-electron electrode reaction is designated by E and a chemical reaction by C. There are extensions of this system, such as E+E for a two-electron electrode reaction, and for reduction and oxidation. Cl and C2 for first- and second-order reactions and Cl for a pseudo-first-order reaction. Cyclic voltammetry is the most widely used technique because of the availability of appropriate instrumentation, and the number of 2q>pIications is likely to increase with the recent availability of software to simulate cyclic voltammograms. Such simulations generally are essential for the determination of meaningful kinetic parameters. 

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 ... 

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. 

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,... 

A distinction between "molecularity" and "kinetic order" was deliberately made, "Mechanism" of reaction was said to be a matter at the molecular level. In contrast, kinetic order is calculated from macroscopic quantities "which depend in part on mechanism and in part on circumstances other than mechanism."81 The kinetic rate of a first-order reaction is proportional to the concentration of just one reactant the rate of a second-order reaction is proportional to the product of two concentrations. In a substitution of RY by X, if the reagent X is in constant excess, the reaction is (pseudo) unimolecular with respect to its kinetic order but bimolecular with respect to mechanism, since two distinct chemical entities form new bonds or break old bonds during the rate-determining step. 

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) ... 

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 ... 

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 ... 

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. 

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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