Oxidation kinetics linear rate equation

In both of these equations, x is the film thickness, t is the time of the oxidation, and k and are experimentally determined constants. The constant fep is called the parabolic rate constant. A linear rate is usually found when the film is porous or cracked. The parabolic equation is found when the film forms a coherent, impenetrable layer. As the rate of film growth, dx/dt, diminishes with time for the parabolic rate law, this equation is associated with protective kinetics. The parabolic rate law arises when the reaction is controlled by diffusion. The species with the lowest diffusion coefficient plays the most important role in this case. 

In principle, the rate equations for surface reaction kinetics are linear and describe a linearly time-dependent growth of the corrosion layer. However, during this growth the oxygen activity on the surface increases and gradually approaches the value for equilibrium of gas phase and oxide surface. Because of the dependence on ao with a negative exponent, the rate gradually decreases, and several authors have misinterpreted this kinetics as parabolic kinetics (see Sect. G.2.3.2). 

Equation (65) demonstrates that decreasing rates are to be expected in the transition from linear to parabolic kinetics. Therefore, the kinetics of oxidation, sulfidation, and so on cannot be exactly linear, even in the start of reaction, but the rate must decrease. This decreasing linear rate often has been misinterpreted, for example, in... 

Assuming that the contribution made by the free oxygen was controlled by boundary layer diffusion [35] whereas those made by carbon dioxide and water vapour were controlled by the rates of surface reactions [57], the authors derived separate equations to calculate the components on the right-hand side of Equation (8.8). Based on laboratory examination results, the authors believed that when the steel was oxidized in dilute O2-N2 atmospheres, the oxidation rate followed a linear kinetics law until the scale thickness was 400-500 microns. Thereafter, the oxidation kinetics gradually changed from linear to parabolic. 

The kinetics of the contributory rate processes could be described [995] by the contracting volume equation [eqn. (7), n = 3], sometimes preceded by an approximately linear region and values of E for isothermal reactions in air were 175, 133 and 143 kJ mole-1. It was concluded [995] that the rate-limiting step for decomposition in inert atmospheres is NH3 evolution while in oxidizing atmospheres it is the release of H20. A detailed discussion of the reaction mechanisms has been given [995]. Thermal analyses for the decomposition in air [991,996] revealed only the hexavanadate intermediate and values of E for the two steps detected were 180 and 163 kJ mole-1. 

On the basis of kinetic data, it was suggested that appreciable charge separation in the activated complex (equation 13) could be avoided by means of such proton transfers, where HA is a general acid (H2O, ROH, RO—OH). Upon change from a polar protic solvent to the nonpolar solvent dioxane, the reaction was observed to be second-order in hydrogen peroxide and the second molecule of H2O2 obviously played the role of HA in the 1,4-proton shift. The rate of oxidation was shown to increase linearly with the pfsTa of solvent HA. In general, it was concluded that solvent interactions provide a... 

Equation E is consistent with linear dependence of oxidation rate on [AIBN], l/[ZnP], and [RH] as shown in Figures 1, 2, and 3, respectively, but it does not adequately describe the observed kinetics since it requires that the intercepts on the rate axis in Figures 2 and 3 should be equal. Equation D cannot be similarly ruled out since it is also clearly consistent with the linear dependence of rate on [AIBN] and 1/ [ZnP], while the dependence on [RH] is less obvious. Because of the illogical nature of the oxidation rate of Tetralin as a function of the zinc... 

Mechanistic Interpretation of Results. The kinetic experiments we performed have made possible an expansion of the empirical rate constant, k in Equation 1, as shown in Equation 9. However, Equation 9 is only an empirical approximation of the linear expression suggested by Equation 13, and the terms atmospheric oxidation and oxygen-independent describe experimental manifestations only. It is possible that these processes are the sum of other subprocesses and that Equation 9 might be expanded further. 

The present view is that cytochrome a is the acceptor of electrons from cytochrome c, but that a simple linear electron-transfer sequence from cytochrome a to Cua and then to the cytochrome 03/Cub centre is unlikely. Instead the sequence shown in equation (63) holds, where cytochrome a is in rapid equilibrium with Cua. These views depend largely upon pre-steady-state kinetics of the redox half reactions of the enzyme with its two substrates, ferrocytochrome c and O2. However, these conclusions are not in accord with kinetic studies under conditions when both substrates are bound to the enzyme, and which show maximal rates of electron transfer from cytochrome c to O2. In particular some of the cytochrome c is oxidized at a faster rate than a metal centre in the oxidase. In contrast, at high ionic strength conditions, where the cytochrome c and the cytochrome oxidase are mainly dissociated, oxidation of cytochrome c occurs only slowly following the complete oxidation of the oxidase. These results for the fast oxidation of cytochrome c have been interpreted in terms of direct electron transfer from cytochrome c to the bridged peroxo intermediate involving 03 and Cub, or to a two-electron transfer to O2 from cytochromes a and 03 during the initial phase of the reaction. 

For maximal sensitivity 0.1 ml of 2.5 M potassium fluoride in 0.1 M borate buffer, pH 9.8, containing 5 x 10 Af EDTA, are added to 0.4 ml of sample to be assayed. The enzyme concentration can be calculated once R, the molar relaxivity of the enzyme, in the range 10 - 10 M enzyme, where F relaxation rate is linearly dependent on enzyme concentration is known. R, a second-order kinetic rate constant (M sec ), is calculated measuring the Ti of F in the presence of a known concentration of the oxidized form of a pure enzyme sample, according to the equation... 

Application of equation (4) to the organic cocktail oxidation profiles, given in Fig. 6(a), yields straight line plots. Two of these kinetic plots for current densities of 0.14 and 0.40 A cm are presented in Fig. 8. The linear relationships obtained demonstrate that pseudo first-order kinetics are obeyed. This relationship directly supports the heterogeneous bimolecular reaction mechanism proposed for the electrochemical oxidation of organics in the electrochemical reactor. The slopes of the linear plots yield the pseudo first-order rate constants, which are summarized in Table 2 for each value of the current density (i.e. the anodic electrode potential) used. It can be seen from the table that, with increasing current... 

Deep knowledge of the enzymatic reaction is necessary for a proper selection of the variables that should be considered in the reaction model. In this case, two variables were selected Orange n concentration, as the dye is the substrate to be oxidized, and H2O2 addition rate, as the primary substrate of the enzyme (Lopez et al. 2007). The performance of some discontinuous experiments at different initial values of both variables resulted in the definition of a kinetic equation, defined using a Michaelis-Menten model with respect to the Orange II concentration and a first-order linear... 

Generally, adsorption steps were taken as temperature independent, whereas the rate parameters of surface reactions and desorption steps were described by Arrhenius equations. The kinetic rate parameters for CO oxidation (steps 1-10) and the catalyst properties were taken from [24] with minor adaptation as mentioned. The rate parameters, e.g. activation energies and pre-exponential factors, for steps 11-28 were determined by non-linear regression. It was found [25] that the rates for NO reactions on ceria are independent of the oxidation state of ceria, so the rate parameters for the corresponding steps were taken as the same (i.e. steps 11 and 12 for oxygen, steps 25-28 for NO). 

This almost trivial conclusion may, however, become invalid if the kinetics of a more complex reaction are no longer governed by a set of linear ordinary differential equations. Such a case is, for example, given by the CO oxidation reaction at a Pt(llO) single crystal surface where for certain sets of control parameters (p02, pCO, T) and by operation in a flow system the kinetics may become oscillatory or even chaotic, lliis is illustrated by Fig. 4 which shows the variation of the work function (which is a measure for the O-coverage as well as for the reaction rate) as a function of time for three slightly differing sets of control parameters [15]. le this quantity varies periodically with time in a), it is chaotic in b) and even more in c). The latter data reflect in fact a case of hyperchaos, in which Lyapounov exponents are positive. 

The oxidation rate was also dependent on the concentration of hypotaurine in the incubation medium. The reaction appeared to obey simple Michaelis-Menten kinetics (Fig. 2). The kinetic constants were estimated from a linear transformation of the Michaelis-Menten equation in a t against v/s plot. The apparent Michaelis constant ( ) was about 0.2 ramol/1 and the maximal velocity (F) about 0.1 ymol/s X kg. In our crude liver homogenate the apparent for hypotaurine oxidation was of the same order of magnitude as for the partially purified L-cysteine sulphinate decarboxylase (Jacobsen et al., 1964), the preceding enz3nne in the biosynthesis pathway. 

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