Oxidation equations expressing rate

Kirk et al. (1990b) and Kirk and Solivas (1994) used the above understanding of oxidation kinetics to develop a model of soil oxygenation. The model allows for the diffnsion of O2 into the soil, the diffnsion of Fe + towards the oxidizing surface, the rate of formation and concentration profile of the Fe(OH)3 formed, and the diffusion by acid-base transfer of the acidity formed H3O+ diffusing away from the zone of acidification and HCOs (derived from CO2) towards it. The principal equations are as follows, expressed in planar geometry so as to be able to test the predictions against experimentally measnred reactant profiles. 

Initial rates of oxidation were estimated from tangents at the origin of the oxygen absorption plots (Table II). The equation expressing the dependence of these rates on temperature is... 

This mechanistic scheme leads to a system of differential equations expressing the build-up or consumption rate of the reactive species. P°, P02°, POOH, O2 and PH concentrations can be derived from the above mechanistic scheme in which the only adjustable parameter is the initial hydroperoxide concentration. Oxygen diffusion and consumption can be coupled (see Colin et al. in the same Issue) but in the case under study here, the low sample thickness (70 pm) leads to a quasi uniform oxidation within that thickness. POOH build up (5) and oxygen consumption (7) can be measured, allowing us to partially verify this model. Carbonyl build-up can also be simulated by assuming that carbonyls result mainly from rearrangements of P0° radicals and by using a new adjustable parameters 72, that accounts for the yield of carbonyl buil-up in initiation and termination steps of the mechanistic scheme. 

For low conversions (less than 20%) of organic, the assumption of a differential reactor (dc/ct Ac/At=([C]in-[C]out)/ is a good one and rates are calculated on this basis. For higher conversions (greater than 20%), the lobal stoichiometric oxidation equation is numerically integrated and the inetic parameters are obtained by regression to conversion data. Rates are then calculated from the global rate expression. 

Table VII shows the data obtained for parathion-KMn04 oxidations at diflFerent pH values. The observed rate constants in Table VII were obtained with initial concentrations of 8 X lO M KMn04 and 3.95 X lO M parathion. Ten- and hundred-fold dilutions of these concentrations obey the same rate expression (Equation 13), as shown by constant observed rate constants in Table VIII. Table VII shows that the observed rate constant of the parathion-KMn04 varies with pH. The rate constant of the oxidation reaction decreases as the pH value of the solution was increased from 3.1 to 7.4. A sharp increase in the oxidation rate constant occurred as the pH value was further increased from 7.4 to 9.0. For paraoxon-KMn04 oxidations, the overall rate of reaction at pH 9.0 is approximately 4,000 times faster compared with that determined at pH 7.4 (Table IX). However, the p-nitrophenol oxidation reaction proceeds faster under acidic, rather than alkaline conditions (Table X).

As so far described, photolysis of nitrogen dioxide can give rise to small steady-state concentrations of ozone, which are limited by the reaction with nitric oxide. Concentrations of ozone in city centers tend to be lower than those in adjacent rural areas due to fresh emissions of NO from traffic reacting with ozone, as above. Equating the rate of NO2 loss by photolysis to the rate of NO2 formation leads to the following expression for the concentration of ozone ... 

The release and the oxidation processes of the encapsulated D-limonene are closely related to the structural changes in the capsule matrices. Physico-chemical changes caused by the phase transition of carbohydrate from amorphous glass to rubbery are commonly expressed with the temperature difference between the storage temperature, T, and the glass transition temperature, Tg, of the carrier matrices, T — Tg. The idea is based on the fact that the viscosity (or relaxation time) of the carrier matrices follows the Wflliams-Landel-Ferry (WLF) equation expressed as a function of T — Tg (Williams et al., 1955). Therefore, the release rate constants k and the oxidation rate... 

The free energy on the right-hand side of both of the above equations can be considered as the chemical component of the activation free-energy change that is, it is only dependent upon the chemical species and not the applied voltage. We can now substitute the activation free energy terms above into the expressions for the oxidation and reduction rate constants, which give... 

Many organic compounds can either accept or donate electrons, forming reduced or oxidized species. This is environmentally significant since the oxidized and reduced forms of an organic compound may have totally different biological and ecological properties. The rate of loss of a chemical by oxidation or reduction is generally a second-order kinetic reaction. For example, oxidation is expressed by equation (2) ... 

As tire reaction leading to tire complex involves electron transfer it is clear that tire activation energy AG" for complex fonnation can be lowered or raised by an applied potential (A). Of course, botlr tire forward (oxidation) and well as tire reverse (reduction) reaction are influenced by A4>. If one expresses tire reaction rate as a current flow (/ ), tire above equation C2.8.11 can be expressed in tenns of tire Butler-Volmer equation (for a more detailed... 

This is the general expression for film growth under an electric field. The same basic relationship can be derived if the forward and reverse rate constants, k, are regarded as different, and the forward and reverse activation energies, AG are correspondingly different these parameters are equilibrium parameters, and are both incorporated into the constant A. The parameters A and B are constants for a particular oxide A has units of current density (Am" ) and B has units of reciprocal electric field (mV ). Equation 1.114 has two limiting approximations. 

For definiteness, the oxidation of copper to copper(l) oxide may be considered. Our picture of the process is that cation vacancies and positive holes formed at the Cu O/Oj interface by equation, 1.166 are transported to the Cu/CujO interface where they are destroyed by copper dissolving in the non-stoichiometric oxide. We require an expression for the rate of oxidation. 

CO Stripping Chronoamperometiy Before discussing experimental results, let us examine what the LH mechanism predicts for the chronoamperometric response of an experiment where we start at a potential at which the CO adlayer is stable and we step to a final potential E where the CO adlayer will be oxidized. We will also assume that the so-called mean field approximation applies, i.e., CO and OH are well mixed on the surface and the reaction rate can be expressed in terms of their average coverages dco and qh- The differential equation for the rate of change of dco with time is... 

In every case, large particles of metal are more active in oxidation than the smallest ones. CO oxidation is moderately structure-sensitive (less than one order of magnitude between metal foil and much dispersed catalysts). By contrast, propane oxidation (and in general oxidation of small alkanes) are strongly stmcture-sensitive (two orders of magnitude between large and small particles). Rate equations were also expressed as... 

Kinetic orders in CO oxidation on M/A1203 can be explained by the classical Langmuir-Hinshelwood expression for the rate equation, as a function of the rate constant k, the adsorption constants K and the partial pressures P ... 

Reactions. Reactions are expressed by fir t order equations in chemical concentration (rate constant k.h ) such that the rates of processes such as hydrolysis, oxidation, photolysis, or biolysis can be combined by adding the k terms to yield a total rate constant kT-... 

When inhibited oxidation is quasistationary with respect to hydroperoxide, the induction period t can be expressed through [InH]0, [RH], v , and the rate constants of key reactions (see Equations [8.8] [8.14]). Parametric equations make it possible to derive simple expressions for t. Table 14.8 summarizes expressions for log x in terms of k2 and k2, T, /, and /3 = k2/kd. 

If the activation energies for the epoxidation and combustion reactions on silver oxide equal E, then the rate coefficients k in equations (14) can be expressed as... 

The Mallard-Le Chatelier development for the laminar flame speed permits one to determine the general trends with pressure and temperature. When an overall rate expression is used to approximate real hydrocarbon oxidation kinetics experimental results, the activation energy of the overall process is found to be quite high—of the order of 160kJ/mol. Thus, the exponential in the flame speed equation is quite sensitive to variations in the flame temperature. This sensitivity is the dominant temperature effect on flame speed. There is also, of course, an effect of temperature on the diffusivity generally, the dif-fusivity is considered to vary with the temperature to the 1.75 power. 

---