Reaction density

Also, from the definition of reactor conversion, for the special case of a constant density reaction mixture ... 

Thus, for a constant-density reaction in a BR, rA may be interpreted as the slope of the cA-t relation. This is illustrated in Figure 2.2, which also shows that rA itself depends on t, usually decreasing in nicgnitudc as the rcahon proceeds, with increasing t. ... 

If we combine this with the material-balance equation 2.2-10 for a constant-density reaction,... 

Consider a constant-density reaction with one reactant, A - products, as illustrated for a liquid-phase reaction in a CSTR in Figure 3.6. One experiment at steady-state generates one point value of (—rA) for the conditions (cA, q, T) chosen. This value is given by the material balance obtained in Section 2.3.2 ... 

For an nth-order isothermal, constant-density reaction in a BR or PFR (n 1), equa-... 

For a second-order, constant-density reaction, A - products, carried out in the vessel in... 

Recently, Uneyama et al. have systematically investigated the anodic generation of CF3 radicals and their utilization (Scheme 7.3) [68-72], They have clarified that trifluoromethyl radicals can be generated almost quantitatively in the oxidation of TFA at 0 °C in an aq. MeOH/Pt system using an undivided cell [70]. They have also found that the trifluoromethylation of electron-deficient olefins can be controlled by the current density, reaction temperature, and the substituents of the olefins. Interestingly, anodic trifluoromethylation of fumar-... 

A type iii-d reaction leads to the formation of (69). Trifluoromethyl radicals generated electrochemically from triflu-oroacetate can attack electron-deficient olefins leading to trifluoromethylated carbon radicals whose chemical and electrochemical follow-up reactions can be controlled by current density, reaction temperature, and substituents of the olefins. With fumaronitrile (86) at 50 °C the monotri-fluoromethylated compound (87) was obtained in 65% yield (Scheme 31) [110]. 

When we mention the constant-volume batch reactor we are really referring to the volume of reaction mixture, and not the volume of reactor. Thus, this term actually means a constant-density reaction system. Most liquid-phase reactions as well as all gas-phase reactions occurring in a constant-volume bomb fall in this class. 

Such processes are frequently bimolecular, irreversible, hence second-order ki-netically. When occurring in the liquid phase they are also essentially constant-density reactions. 

Table 2.9 Conversion, power density, reaction temperature and reformate composition for various fuels [131].

In the lower current density region, reaction (15.7) is rate determining and at the higher current densities, reaction (15.5) is rate determining. 

Fig. 4 shows a simple phase diagram for a metal (1) covered with a passivating oxide layer (2) contacting the electrolyte (3) with the reactions at the interfaces and the transfer processes across the film. This model is oversimplified. Most passive layers have a multilayer structure, but usually at least one of these partial layers has barrier character for the transfer of cations and anions. Three main reactions have to be distinguished. The corrosion in the passive state involves the transfer of cations from the metal to the oxide, across the oxide and to the electrolyte (reaction 1). It is a matter of a detailed kinetic investigation as to which part of this sequence of reactions is the rate-determining step. The transfer of O2 or OH- from the electrolyte to the film corresponds to film growth or film dissolution if it occurs in the opposite direction (reaction 2). These anions will combine with cations to new oxide at the metal/oxide and the oxide/electrolyte interface. Finally, one has to discuss electron transfer across the layer which is involved especially when cathodic redox processes have to occur to compensate the anodic metal dissolution and film formation (reaction 3). In addition, one has to discuss the formation of complexes of cations at the surface of the passive layer, which may increase their transfer into the electrolyte and thus the corrosion current density (reaction 4). The scheme of Fig. 4 explains the interaction of the partial electrode processes that are linked to each other by the elec-... 

In other cases, a push-me-pull-you situation arises the faster (as defined by the current density) reaction cannot produce current any faster than the slower reaction can consume it. Corrosion engineers use this principle in several ways including sacrificial anodes and corrosion inhibitors. Examples can be found throughout the text. 

The applied current density is the difference between the total anodic and the total cathodic current densities (reaction rates) at a given potential ... 

Solution Since this is a first-order constant-density reaction, Eqs. (4-7) and (4-8) give the conversions for single-stirred-tank and ideal tubular-flow reactors in terms of residence time VjQ. For multiple-stirred-tank reactors Eq. (A) of Example (4-9) is applicable. 

The form and shape of the electrodes are tailored for the specific reactor configuration. Typical shapes include flat metal sheets, perforated or expanded metal grids, metal foams and meshes, and three-dimensional packed bed electrodes formed by stacking metal meshes, pressing catalyst powders, or by use of microporous carbon felts and cloths (three-dimensional electrodes are particularly attractive for low-current density reactions because the electrode surface per unit reactor volume can be made very large) [28]. 

At the higher current density, Reaction 1.26 was rate determining. The adsorbed C02 ion present in the mechanism was discovered in the electrode in an early application of FTIR spectroscopy applied to mechanism analysis. 

Recently, anodic generation of the CF3 radical and its trapping reactions have been systematically studied by Uneyama and his coworkers (Scheme 24). "" This work has demonstrated that tri-fluoromethyl radicals can be generated almost quantitatively by the oxidation of TFA at 0 °C in an aqueous MeOH/Pt system using a divided cell." Also, it has been found that additions of the tri-fluoromethyl radical to electron-deficient olefin can be controlled by the choice of current density, reaction temperature, and olefin substituents. Notably, anodic trifluoromethylation of fumaronitrile leading to 31 (Scheme 25) is greatly affected by the reaction temperature. The... 

Consider a volume element of the reaction mixture in which the concentrations have unique values. For an irreversible first-order constant density reaction, Eqs. (1.1-6) and (l.M) lead to... 

From the background described, die reaction course at increasing cathodic polarization will be as follows at low current densities, reaction (4.2a) occurs under activation polarization. By increasing the current, this reaction becomes successively concentration polarized, and finally the reaction (4.2b) takes over. Since this reaction does not depend on diffusion, a current increase is allowed again. 

The general case of variable density reactions is applicable mostly to gas-phase reactions and seldom to liquid-phase reactions. Because the gas law gives the precise relationship between P, V, T, and N, we start with that equation. Based... 

Table 4.5 Analytical solutions (design equations) for some simple variable density reactions in a PFR...

BR (Table 4.2). Solutions to a few variable-density reactions are presented in Table 4.5. Graphical integration is straightforward and gives the reactor volume directly, as shown in Figure 4.9. The reciprocal rate is plotted as a function of either (Equation 4.61) or [ 4] (Equation 4.62). Alternatively, any of several numerical methods can be used, and this is perhaps the most attractive. 

Assuming that the incremental change in density, reaction enthalpy and surface heat transfer coefficient are not significant ... 

We generally do not conduct gas-phase reactions in batch reactors. For a constant liquid volume, constant density reaction or process, the component balance for a laboratory batch reactor is... 

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