Reactant bulk

Use of dilute solutions/emulsions or suspensions rather than bulk reactants ... 

Changes in bulk reactant concentration during the limiting current measurement, due, for example, to variations in gas pressure (oxygen reduction) or to the presence of other species susceptible to reduction at the... 

MeOH and MeOAc carbonylation reactions lend themselves particularly well to mechanistic investigation by spectroscopic methods, particularly IR and NMR. There are a number of reasons for this. Firstly the species involved, both the bulk reactants and the catalysts, are structurally relatively simple. This means that there is a reasonable possibility of resolving, identifying and quantifying components by either or both methods. 

By contrast, in the case of PCH, a much higher yield of Flavan, 15.3%, was obtained. The limitation of the diffusions of the bulk reactant and product (flavan) were in some way overcome by the PCH. Obviously, the formation of mesoporosity in PCH does appreciably alter the accessibility of reactants and this increases its ability of shape selectivity to catalyze the alkylation reaction. 

This relation emphasizes that only part of the double-layer correction upon AG arises from the formation of the precursor state [eqn. (4a)]. Since the charges of the reactant and product generally differ, normally wp = ws and so, from eqn. (9) the work-corrected activation energy, AG orr, will differ from AG. [This arises because, according to transition-state theory, the influence of the double layer upon AG equals the work required to transport the transition state, rather than the reactant, from the bulk solution to the reaction site (see Sect. 3.5.2).] Equation (9) therefore expresses the effect of the double layer upon the elementary electron-transfer step, whereas eqn. (4a) accounts for the work of forming the precursor state from the bulk reactant. These two components of the double-layer correction are given together in eqn. (7a). 

Although the foregoing electron-transfer theory is preoccupied with describing the electron-transfer step itself, in order to understand the kinetics of overall reactions it is clearly also important to provide satisfactory models for the effective free energy of forming the precursor and successor states from the bulk reactant and product, wv and ws, respectively. As outlined in Sect. 2.2, it is convenient to describe the influence of the precursor and successor state stabilities upon the overall activation barrier using relations such as... 

Although the presence of merely thermodynamic, rather than additional intrinsic, inner-sphere catalysis can yield substantial rate enhancements, these will be limited inevitably by the availability of surface coordination sites. Thus, for example, a bulk reactant concentration of ImM and a maximum (i.e. monolayer) surface concentration of 5 x 10 10mol cm-2 yields a maximum rate enhancement of 5 x 104 fold resulting from "thermodynamic catalysis if Sr = 1 A for the alternative outer-sphere pathway. Greater inner-sphere rate accelerations require pathways yielding increases in /ce) or decreases in AG. ... 

Inhibition [77]. An inhibitor is itself being consumed as it traps free radicals. To be effective, it must therefore be present in an excess over the initiator. In practice, this limits effective inhibition to chain reactions apt to be set off by small amounts of an initiator other than the bulk reactant. The most common application of inhibition is for protection of sensitive chemicals whose decomposition or polymerization by chain mechanisms may easily be triggered. 

The observed rate will appear to be first-order with respect to the bulk reactant concentration, regardless of the intrinsic rate expression applicable to the surface reaction. This is a clear example of how external diffusion can mask the intrinsic kinetics of a catalytic reaction. In a catalytic reactor operating under mass transfer limitations, the conversion at the reactor outlet can be calculated by incorporating Equation (6.2.20) into the appropriate reactor model. 

The theoretical treatment of electron transfer at metal electrodes has much in common with that for homogeneous electron transfer described in 12.2.3. The role of one of the reactants is taken by the electrode surface, which provides a rigid two-dimensional environment where reaction occurs. In some respects, electrode reactions represent a particularly simple class of electron-transfer reactions because only one redox center is required to be activated prior to electron transfer, and the proximity of the electrode surface often may yield only a weak, nonspecific influence on the activation energetics of the isolated reactant. As with homogeneous electron transfer, it is useful to consider that simple electrochemical reactions occur in two steps (1) formation from the bulk reactant of a precursor state with the reacting species located at a suitable site within the interphasial region where electron transfer can occur (2) thermal activation of the precursor species leading to electron transfer and subsequent deactivation to form the product successor state. 

Because the formation of an inner-sphere precursor state involves specific chemical interactions between the reactant and the electrode surface, it is difficult to calculate the precursor-complex equilibrium constant. However, such states can be sufficiently stable so that the electrode coverage by the precursor complex approaches unity (i.e., a monolayer of adsorbed reactant is formed). In these circumstances, the observed rate becomes independent of the bulk reactant concentration, and k, can be obtained directly from combined with the estimated close-packed surface concentration. An analogous situation exists for stable precursor complexes formed in homogeneous solution ( 12.3.3.1). 

Figure 1. Free-energy profile for simple electrochemical reaction + e - Y plotted against the nuclear-reaction coordinate. Fig. lA shows the overall electrochemical free-energy profile I, bulk reactant P, precursor state S, successor state 11, bulk product. Figs. IB and C show the components of the free-energy profile arising from the solution species (Y, Y ), and transferring electron, respectively.

The kinetics of inner-sphere reactions are generally expected to be sensitive to the nature of the electrode material Variations in may arise from several sources. First, the work term, Wp, and hence the precursor stability, Kp, is expected to depend strongly upon the electrode material in view of the specific reactant-electrode interactions involved. Therefore, k p increases as the strength of the reactant-electrode bond increases [Eq. (n) in 12.3.7.2]. However, there is an upper limit to the catalysis thereby induced, corresponding to the onset of monolayer formation. For example, if the adsorbate concentration, corresponding to a monolayer equals 10 mol cm , for the typical bulk-reactant concentration, C, of 10 M, K = F /C = 3 X 10 cm. By comparison, the statistical value of Kp when Wp = 0, is expected to be ca. 10 cm ( 12.3.7.2). Consequently, stabilization of the precursor state via reactant-electrode interactions corresponds to a maximum rate acceleration of ca. 10 under these conditions. 

If the reactive-collision model (Eq. e) rather than the preequilibrium model is employed for outer-sphere reactions, then the first term on the right side of Eq, (n) is replaced by RT In KjiZ,..] The final bracketed terms in Eq. (n) can be thought of as thermodynamic influences upon the electrochemical reactivity because they determine how k is influenced by inequalities in the free energies of the bulk reactant, precursor and... 

This is the expression for the global rate in terms of the bulk-reactant concentration. The concentration profile in this case is shown by the solid line in Fig. 7-1. It is a very restricted illustration of a global rate, since heat-transfer resistances were not considered (constant temperature was assumed) and only external mass transfer is involved (the catalyst particle is non-porous). These restrictions are removed in the detailed treatment in Chaps. 10 and 11, but this simple example illustrates the meaning of global rates of reaction for heterogeneous systems. 

The limiting current density is an important parameter for the analysis of mass transfer controlled electrochemical processes and represents the maximum possible reaction rate for a given bulk reactant concentration and fluid flow pattern. During anodic metal dissolution, a mass transfer limiting current does not exist because the surface concentration of the dissolving ion (e.g., Cu + when the anode is composed of copper metal) increases with increasing current density, eventually leading to salt precipitation that blocks the electrode surface. 

Identifying the limiting current density (ij) during electrodeposition is important since it represents the maximum rate of metal plating for a given bulk reactant concentration and hydrodynamic flow pattern. Also, the stracture of the electrodeposit varies with current density see Figure 26.23 [92]. 

Here, Cb is the bulk reactant (copper) concentration, and 8c is the equivalent, Nemst-type, boundary layer thickness. The transport number for the copper, tcu, is defined by ... 

The treatment of many process liquors often results in an electrochemical reaction which is under mass transport control due to the restricted convective-diffusion of species to (or from) the electrode (figure 4). This is particularly true in dilute liquors, where the bulk reactant concentration, Cg is low. The situation may be characterised by a mass transport coefficient,... 

Effect of the Damkohler Number on Conversion in Square Ducts. More conversion is predicted at higher Damkohler numbers because the rate of surface-catalyzed chemical reaction is larger. At a given axial position z, reactant conversion reaches an asymptotic limit in the diffusion-controlled regime, where oo. Actual simulations of I Abuik vs. f at /i = 20 are almost indistinguishable from those when p = 1000. The effect of p on bulk reactant molar density is illustrated in Table 23-5 for viscous flow in a square duct at = 0.20, first-order irreversible chemical reaction, and uniform catalyst deposition. These results in Table 23-5 for the parameter A, as a function of the Damkohler number p can be predicted via equations (23-80) and (23-81) when C = A and... 

The key feature is always that phase boundaries move during solid-state reactions. Defects and grain boundaries influence both the mechanisms and the rates of solid-state reactions, but with bulk reactants you do not know where to start. The volume probably changes during... 

The diversity of reactions that are considered to be surface mediated has also increased over the past decade. It is not only strict sorption/desorption and precipitation/dissolution processes that are important but also the surface mediation of reactions such as electron transfer (eg. 14-17), hydrolysis 18) and various photochemical transformations. In addition certain solid phases, in particular metallic iron, iron oxides and smectitic clays, are capable of transferring electrons in and out of their bulk structure (eg. 19-23), When viewed in this context, minerals should not be considered as passive solids, or even as simple sources of a reactive surface but must be considered as bulk reactants. 

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