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** First-order irreversible reactions **

Example 16.3-1 Limits of a first-order heterogeneous reaction What is the overall rate for a first-order heterogeneous reaction under each of the conditions (a) fast stirring, (b) high temperature, and (c) an irreversible reaction Express this rate as T2- [Pg.462]

As discussed later, the reaction-enhancement factor ([) will be large for all extremely fast pseudo-first-order reactions and will be large for extremely fast second-order irreversible reaction systems in which there is a sufficiently large excess of hquid-phase reagent. When the rate of an extremely fast second-order irreversible reaction system A + vB — products is limited by the availability of the liquid-phase reagent B, then the reaction-enhancement factor may be estimated by the formula () = 1 -I- B /vc,. In systems for which this formula is applicable, it can be shown that the interface concentration y, will be equal to zero whenever the ratio k yv/klB is less than or equal to unity. [Pg.1367]

This expression is the same as that derived by LANGER (5) for a first order irreversible reaction in a chromatographic column, Thus a plot of experimental values of as a function of T provides a method for evaluating the kinetic constant if H is known from literature data. At the other extreme when the process is controlled by mass transfer from gas to liquid (fast reaction) the zero moment becomes [Pg.344]

For simplicity, assume fluid-phase mass transfer to be fast enough to maintain the bulk-fluid concentration of A up to the catalyst surface, the particle to be spherical, the reaction to be irreversible and first order, and mass transfer in the particle to obey Fick s law of diffusion. With the reaction as source-or-sink term, the differential material balance for A (change of content of a volume element = what enters minus what exits minus what reacts) is [Pg.291]

In this section we want to consider two examples of other chemistries that can alter the simple combinations of diffusion and reaction developed earlier. The first example is an irreversible second-order reaction. The second involves fast reactions of concentrated reagents and products. [Pg.469]

The kinetics of the C step are not always first order or pseudo-first order. A second-order reaction will produce qualitatively similar effects to those described above. However, the relative magnitude of the reverse peak current associated with the E step and hence the extent of reversibility and the shift in peak potential will depend on the concentration of the electroactive species for an EC2 mechanism. A process of this type will have a reversible E step at low concentrations or fast scan rates and an irreversible E step at high concentrations or slow scan rates. An example of an EQ-type reaction (Bond et al., 1983, 1989) is the electrochemical oxidation of cobalt (III) tris(dithiocarbamates) (Co(S2CNR2)3) at platinum electrodes in dichloromethane/0.1 M (C4H9)4NPp6 [equations (44) and (45)]. [Pg.37]

There are many reaction mechanisms for vinyl addition polymerizations. In approximate order of importance they are free radical polymerization, coordination metal catalysis (Ziegler-Natta), anionic polymerization, cationic polymerization, and group transfer polymerization. Regardless of specific mechanism, these polymerizations tend to be fast, essentially irreversible, highly exothermic and approximately first order with respect to monomer concentration. [Pg.126]

In Eq. 10.30, the first term corresponds to accumulation in the fluid and the surfaces, the second term describes convective transport, and the third term indicates the loss by the kinetic dissolution reaction defined by Eq. 10.28. Equation 10.30 applies to any chemical transport process that includes fast and reversible ion-exchange, and slow and irreversible dissolution of the mth-order kinetics. In reservoir sands, both fine silica and clay minerals dissolve under attack by the alkali, yielding a complex distribution of soluble solution products [Pg.412]

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. [Pg.391]

The problem raised by the saturation of the liquid can be avoided by using a solution which reacts with the dissolved gas in the slow reaction regime i.e. the reaction is too slow to affect the rate of absorption directly, but, on the other hand, the reaction is fast enough to reduce the bulk concentration of dissolved gas effectively to zero. If the considered reaction is irreversible and second-order (first order with respect to both components A and B) this leads to. [Pg.109]

The first step in heterogenous catalytic processes is the transfer of the reactant from the bulk phase to the external surface of the catalyst pellet. If a nonporous catalyst is used, only external mass and heat transfer can influence the effective rate of transformation. The same situation will occur for very fast reactions, where the reactants are completely consumed at the external catalyst surface. As no internal mass and heat transfer resistances are considered, the overall catalyst effectiveness factor corresponds to the external effectiveness factor, For a simple irreversible reaction of nth order, the following relation results [Pg.60]

If the intrinsic reaction rate is fast compared to the internal and/or external mass transfer processes, the reactant concentration within the porous catalyst and on its outer surface is smaller compared to the bulk concentration, whereas the concentration of the intermediate will be higher. Consequently, the consecutive reaction is promoted and the yield diminishes. The degree of yield losses depends on the ratio between transfer time and the intrinsic rate of the consecutive reaction, which is characterized by the corresponding Thiele moduli and Damkohler numbers referred to the consecutive reaction. For irreversible first-order reactions, the equations are as follows [Pg.338]

** First-order irreversible reactions **

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