Chemical reactions pseudo-first-order

We finally consider the EC catalytic mechanism in which the product of the electrode reaction transforms back to the initial electroactive reactant by means of a pseudo first-order chemical reaction [ 15,53,55] ... 

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. 

Let us first consider the case in which the initial electron transfer in Eq. (190) is sufficiently rapid to be nernstian (i.e., A = k (5/D 1) but is followed by an irreversible, pseudo-first-order, chemical reaction (that is, k may include the concentration of other reagent, when constant). 

Interestingly, under such circumstances the electrochemical consumption of the species is equivalent to a pseudo-first-order chemical reaction taking place into the bulk solution, with a rate constant kgiec in Eq. (4) [6]. 

Figure 2.12 Concentration profiles for mass transfer with pseudo first order chemical reaction (fiim model) (a) slow chemical reaction Ha <03 (b) moderate chemical...

A simple procedure for studying pseudo first order chemical reactions has been described by Albery coworkers [22, 23]. A constant current is applied to the disc, and the ring current is monitored. Plots of —/r vs /q are found to be linear, but the slopes are a function of co and the rate constant is found from an analysis of the slopes. Such procedures allow the determination of second order rate constants in the range 3 X 10 to lO dm mol" s ... 

Oxygen diffusing into a solid polymer film through both surfaces is being consumed by a first-order or pseudo-first-order chemical reaction [571, 643, 1591]. 

In case of pseudo-first order chemical reaction in absorption of CO2 in NaOH solution, the constant / is given the equation ... 

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. 

A number of processes that have been studied show a linear relationship between the log of the amount of substance present versus the time. Many of these processes do not arise from simple first-order chemical reactions, or the chemistry of the process may be unclear. Nevertheless, since they empirically fit the model for a first-order chemical reaction, they are commonly called pseudo first order processes. The slope of the log (concentration) versus time plot is called the apparent first order... 

In direct analogy to the Michaelis-Menten mechanism for reaction of enzyme with a substrate, the inactivator, I, binds to the enzyme to produce an E l complex with a dissociation constant K. A first-order chemical reaction then produces the chemically reactive intermediate with a rate constant k. The activated species may either dissociate from the active site with a rate constant to yield product, P, or covalently modify the enzyme ( 4). The inactivation reaction should therefore be a time-dependent, pseudo-first-order process which displays saturation kinetics. This is verified by measuring the apparent rate constant for the loss of activity at several fixed concentrations of inactivator (Fig. lA). The rate constant for inactivation at infinite [I], itj act (a function of k2, k, and k4), and the Ki can be extracted from a double reciprocal plot of 1/Jfcobs versus 1/ 1 (Fig. IB) (Kitz and Wilson, 1962 Jung and Metcalf, 1975). A positive vertical... 

The mass balance with diffusion and first-order chemical reaction, given by (24-12), is classified as a frequently occurring second-order linear ordinary differential equation (i.e., ODE) with constant coefficients. It is a second-order equation because diffusion is an important mass transfer rate process that is included in the mass balance. It is linear because the kinetic rate law is first-order or pseudo-first-order, and it is ordinary because diffusion is considered only in one coordinate direction—normal to the interface. The coefficients are constant under isothermal conditions because the physicochemical properties of the fluid don t change... 

Danckwerts et al. (D6, R4, R5) recently used the absorption of COz in carbonate-bicarbonate buffer solutions containing arsenate as a catalyst in the study of absorption in packed column. The C02 undergoes a pseudo first-order reaction and the reaction rate constant is well defined. Consequently this reaction could prove to be a useful method for determining mass-transfer rates and evaluating the reliability of analytical approaches proposed for the prediction of mass transfer with simultaneous chemical reaction in gas-liquid dispersions. 

Within the strictly chemical realm, sequences of pseudo-first-order reactions are quite common. The usually cited examples are hydrations carried out in water and slow oxidations carried out in air, where one of the reactants... 

In the case of 0-pipettes, the collection efficiency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-first-order reaction a semiquantita-tive description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efficiency approaches zero when the dimensionless rate constant (a = 2kr /D, where k is the first-order rate constant of the homogeneous ionic reaction) becomes 1. 

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. 

The rate of photolytic transformations in aquatic systems also depends on the intensity and spectral distribution of light in the medium (24). Light intensity decreases exponentially with depth. This fact, known as the Beer-Lambert law, can be stated mathematically as d(Eo)/dZ = -K(Eo), where Eo = photon scalar irradiance (photons/cm2/sec), Z = depth (m), and K = diffuse attenuation coefficient for irradiance (/m). The product of light intensity, chemical absorptivity, and reaction quantum yield, when integrated across the solar spectrum, yields a pseudo-first-order photochemical transformation rate constant. 

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 ... 

Isopropylbenzene (A) is alkylated with propylene (P) using HF catalyst. The mono (B), di (C), tri (D) and tetra (E) derivatives are formed. Relative specific rates are given by Rodiguin Rodiguina (Consecutive Chemical Reactions, 1964) for the case of a large excess of propylene which makes the reactions pseudo first order. The relative specific rates used here are kx = 1.0, k2 = 0.5, k3 = 0.3 and k4 0.2. The system of linear differential... 

A waste stream of 20,000 liters/day contains chemical A in concentration 0.01 kg/llter which can be hydrolyzed in aqueous solution to give chemical B which has a value of 1.00/kg. The reaction is pseudo first order with k = 6/day. A CSTR is contemplated. Cost data are... 

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,... 

Catalytic regeneration of the reagent following a reversible electron transfer. A particular case of following chemical reaction is constituted by that in which the product of the electrode reaction undergoes a homogeneous, irreversible, first-order (or pseudo-first-order)... 

Note that the chemical step (2.75) is totally irreversible, attributed with a pseudo first-order rate constant (s ) defined as Atc =, rCx, where cx has the same meaning as for the CE and EC mechanisms (Sect. 2.4.1). Although this is the simplest case of an electrode mechanism involving chemical reaction, it has particular analytical utihty [53]. The mass transport of the redox species is described by the following model ... 

The rate of a chemical reaction depends on temperature. A rule of thumb for many organic reactions in solution is that a 10 °C change in temperature causes a two- to three-fold change in rate of reaction [25]. To study the temperature dependence of solid-phase reactions, the cleavage reaction of resin (35) with n-butyla-mine at 20, 40 and 60 °C were carried out. The cleavage time courses and pseudo-first-order rate fits at these three temperatures are shown in Fig. 12.20. The rate constants from single bead FTIR analysis are Hsted in Tab. 12.4. Compared with the reaction at 20 °C, the solid-phase cleavage reaction of resin 3b was two times faster at 40 °C and four times faster at 60 °C. 

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) ... 

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