Internal oxidation equation

Maak (1961) has obtained the equation governing the oxidation rate of a metal to form both an external oxide and an internally oxidized dilute solute, as for example in Cu-Be alloys, coiTesponding to tire equation given earlier... 

Naphthalene derivatives 158 were also prepared by the oxidative coupUng of benzoic acids 156 with internal alkynes such as diphenylacetylene 157 in the presence of [Cp lrCl2]2 complex combined with Ag2C03 as oxidant (Equation 10.42) [71]. 

How does the anionic alkyl of the original trialkylaluminum or of the dialkylaiuminum chloride, which has sufficient anionic character to undergo anionic hydride exchange or CH3OT reaction, form a catalyst which becomes cationic under certain polymerization conditions No studies of this have been reported. One possibility is an internal oxidation-reduction reaction that converts an anionic alkyltitanium trichloride to a cationic alkyltitanium trichloride (Equation 10). Basic and electrophilic catalyst components would determine the relative contributions of the anionic and cationic forms. This type of equilibrium or resonance structures could also explain the color in transition metal compounds such as methyltitanium trichloride (73). 

The rate of alkene oxidation depends on the substitution pattern of the alkene. For a series of alkenes oxidized in aqueous solution, with benzoquinone as oxidant for the PdCl2, the relative rates are ethene (850) > propene(450) > 1-butene (380) > tra i-2-pentene (90) > cfr-2-pentene (80) > cyclohexene (8) > cycloheptene (1). Thus, selective oxidation of terminal alkenes to methyl ketones can occur in the presence of internal alkenes (equation 84). 

The quasi-steady approximation requires the assumption that the dissolved oxygen concentration varies linearly across the zone of internal oxidation. Therefore, the oxygen flux through the internal oxidation zone (lOZ) is given by Pick s first law as Equation (5.3),... 

Figure 5.5 Simplified concentration profiles for the internal oxidation of A-B. Equation (5.4),...

The latter gives the penetration depth of the internal oxidation zone as a function of oxidation time. The following points concerning Equation (5.9) are of interest. 

The effect of particle-matrix interfacial free energy is often overlooked but is particularly important in the nucleation and coarsening of internal oxides. Consider the classical nucleation problem of forming a spherical nucleus. If strain is neglected, the free energy of formation of a nucleus of radius r is given by Equation (5.31),... 

Accelerated transport along the interfaces between internal oxides and the alloy matrix producing oxide needles and deeper penetrations than those predicted from Equation... 

If/represents the mole fraction of BOv in the internal oxidation zone and Vm the molar volume of the alloy, then//Em will be the concentration in moles per volume and the number of moles in a volume element, AdX, will be (/7Em)AdX, where A is the cross-sectional area for diffusion. This quantity must be equal to the number of moles of B arriving at x = X in the time dt by diffusion from within the sample, i.e., from x > X. Therefore, we obtain Equation (5.21) ... 

When a is large, we expect the accumulation and lateral growth of the internal oxides to form a continuous layer, i.e., the transition to external oxidation. Figure 5.12 shows this occurring in a Co-7.5 wt% Ti alloy. Wagner states that, when the volume fraction of oxide, g = /(Vox/ Tm), reaches a critical value, g, the transition from internal to external scale formation should occur. Insertion of/, in terms of g, in a in Equation (5.23) then gives the criterion for external oxidation as shown... 

Earlier work on the reactions of vinyl halides with tertiary phosphine platinum(0) compounds showed that complexes such as [Pt( y -vinyl halide)(PPh3)2] are formed initially, and the kinetics and mechanism of the oxidative addition (isomerization) were examined. Corresponding work on halogenoalkynes has now been carried out. Thus when c/5 -[PtCl2(PPh3)2] is reduced with hydrazine in the presence of PhC=CX (X =Br or I") the product obtained is [PtX(C= CPhXPPhs). ]. However, with PhC = Cl the intermediate substitution product [Pt(jj -PhC CCl)(PPh3)2] could be isolated and its internal oxidative addition examined mechanistically [see equation (8)]. 

For steels with less Si, the carburisation at high temperatures >1050 °C is not hindered by any oxide layer and its rate is just determined by the inward diffusion of carbon. This process was studied by carburisation in CH4/H2 mixtures which avoids oxidation [2, 3]. The progress of internal carbide formation can be described by an equation which corresponds to the equation for internal oxidation... 

The parameter /expresses the ratio between the lengths 8 and 5 that characterize respectively, the rates of selective external and internal oxidation. These lengths are given by equations (9.69) and (9.62). 

On the other hand, the carbonylation reactions discussed in Sect. VI.7 generally require external oxidants. In some reactions, however, reactants are derivatized such that they can serve as internal oxidants. Conversion of alcohols into nitrites prior to carbonylation is a representative example. In such cases, the question of redox versus nonredox is a matter of precisely what chemical equation one deals with. For example, carbonylation... 

Figure 5.6 is a transmission electron micrograph showing a Ti02 precipitate that has formed on the grain boundary of an internally oxidized Cu-Ti alloy [5]. Measurement of the dihedral angle of numerous precipitates yielded values of ycu/Tic>2 ranging from 400 to 700 mjW when ygb was approximated as 450 mj/m in Equation (5.6). The reason for... 

The presence of oxygen in the gas mixture provides the possibility of internal conversion of hydrocarbons through their partial oxidation [equation (11.4)]. 

X in this equation is the penetration depth of the internal corrosion zone, which is a function of the square route of time. is the initial solute concentration and y is a stoichiometric factor. Dq is the diffusivity of the oxidant in metal A. NqDq is also called the oxygen permeability in metal A. The considerations covered so far show that, even under a dense oxide scale BX, internal oxide CX can be formed if the latter has a higher stability than the surface scale oxide BX. The reason for this is that the equilibrium oxygen partial pressure of the outer scale oxide BX is higher than the Pq needed for the formation of the more stable internal oxide CX, i.e., according to Eq. (2-30) sufficient oxygen is dissolved in A for CX formation. 

Using equation [16.16], we obtain the variation of penetration depth of internal oxidation as a function of the time ... 

In this case, the internal oxidation reaction is determining by both steps diffusion of oxygen and of the oxidizable element in the alloy. We will see below, as a result, that there is a greater amount of oxide in the zone of internal oxidation than the amount of A initially contained in this zone (equation [16.22]). 

It results finm inequality (equation [16.23]) that for a very low oxygen solubility of oxygen (x ), the minimum concentration of A to expect an internal oxidation becomes very low. 

The criterion for the minimum solute concentration, Ng, of a binary A B alloy required for the second transition process has been derived based on thermodynamic and kinetic analyses. Using this equation the effects of oxygen partial pressure, addition of rare earth elements, surface micro-crystallization, and the gettering effects on the transition between external and internal oxidations can be explained. 

Rapp (1961) has confirmed this equation in a study of the oxidation in air of Ag-In alloys at 550°C. The reaction proceeds with tire internal formation of In203 particles over a range of indium concenuations, but at a critical mole fraction of indium in the alloy, external oxidation occurs with the growdr of a layer of In203 covering the alloy. The n airsitioir from internal to external oxidation was found by Rapp to occur at the mole fraction of indium cone-sponding to... 

Claisse40 has made a comprehensive attack on mineral analysis. He realized that fusion to give a glass disk could be used at once to remove Class II deviations. (7.8) and to give samples in which a (Equation 6-6) varies very little from one sample to another. Accordingly, he developed the fusion of minerals (other than sulfide minerals) with fluxes based on borax (100 mg of sample to 10 grams of borax) when graphite or sulfides are present, oxidation must precede the borax fusion. Internal standards or materials intended to fix the value of a may be added before... 

One strategy in limiting the formation of ozone and other photochemical oxidants has been the use (in the past) of low reactivity fuels in internal combustion engines. More recently, alternate fuels (methanol, for instance) have been proposed for regions that suffer from elevated levels of photochemical air pollution. The effect of switching to such a low-reactivity fuel may be seen in Equation E2 for methanol, which has a simple atmospheric reaction mechanism. 

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