Any fast reaction can enhance mass transfer. Consider a very fast, second-order reaction between the gas-phase component A and a liquid component B. The concentration of B will quickly fall to zero in the vicinity of the freshly exposed surface and a reaction plane, within which b = Q, will gradually move away from the surface. If components A and B have similar liquid-phase diflusivities, the enhancement factor is [Pg.411]

In the text, we used the film theory to show that for a fast irreversible second-order reaction, [Pg.511]

As discussed later, the reaction-enhancement factor ( ) will be large for all extremely fast pseudo-first-order reac tions and will be large tor extremely fast second-order irreversible reaction systems in which there is a sufficiently large excess of liquid-phase reagent. When the rate of an extremely fast second-order irreversible reaction system A -t-VB produc ts is limited by the availabihty of the liquid-phase reagent B, then the reac tion-enhancement factor may be estimated by the formula ( ) = 1 -t- B /VCj. In systems for which this formula is applicable, it can be shown that the interface concentration yj will be equal to zero whenever the ratio k yV/k B is less than or equal to unity. [Pg.1363]

For a dilute system in which the liquid-phase mass-transfer limited condition is valid, in which a veiy fast second-order reaction is involved, and for which Nna E veiy large, the equation [Pg.1368]

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides [Pg.2947]

Ultrasonic absorption is used in the investigation of fast reactions in solution. If a system is at equilibrium and the equilibrium is disturbed in a very short time (of the order of 10"seconds) then it takes a finite time for the system to recover its equilibrium condition. This is called a relaxation process. When a system in solution is caused to relax using ultrasonics, the relaxation lime of the equilibrium can be related to the attenuation of the sound wave. Relaxation times of 10" to 10 seconds have been measured using this method and the rates of formation of many mono-, di-and tripositive metal complexes with a range of anions have been determined. [Pg.411]

For many reaction mechanisms, the rate-determining step occurs after one or more faster steps. In such cases the reactants in the early steps may or may not appear in the rate law. Furthermore, the rate law is likely to depart from simple first- or second-order behavior. Fractional orders, negative orders, and overall orders greater than two, all are signals that a fast first step is followed by a slow subsequent step. [Pg.1085]

Notice that in the region of fast chemical reaction, the effectiveness factor becomes inversely proportional to the modulus h2. Since h2 is proportional to the square root of the external surface concentration, these two fundamental relations require that for second-order kinetics, the fraction of the catalyst surface that is effective will increase as one moves downstream in an isothermal packed bed reactor. [Pg.446]

The first of these reactions was carried out in 1,4-cyclohexadiene over a temperature range of 39 to 100 °C. It is fairly slow the half-times were 20 h and 3.4 min at the extremes. Reaction (7-11) is quite fast the second-order rate constant, kn, was evaluated over the range 6.4 to 47.5 °C. Values of feio and fen are presented in Table 7-1. The temperature profiles are depicted in Fig. 7-1 from their intercepts and slopes the activation parameters can be obtained. A nonlinear least-squares fit to Eq. (7-1) or [Pg.157]

In this case, the rate law has been experimentally determined to be first order with respect to CO and also first order with respect to the Pt surface sites available for reaction (second order overall). Since we would like to know how fast the Pt surface is poisoned, we write the rate law in terms of the CO surface coverage, 3> [Pg.76]

Similar expressions can be written for third-order reactions. A reaction whose rate is proportional to [A] and to [B] is said to be first order in A and in B, second order overall. A reaction rate can be measured in terms of any reactant or product, but the rates so determined are not necessarily the same. For example, if the stoichiometry of a reaction is2A-)-B—>C- -D then, on a molar basis, A must disappear twice as fast as B, so that —d[A]/dt and -d[B]/dr are not equal but the former is twice as large as the latter. [Pg.291]

First-order and second-order rate constants have different dimensions and cannot be directly compared, so the following interpretation is made. The ratio intra/ inter has the units mole per liter and is the molar concentration of reagent Y in Eq. (7-72) that would be required for the intermolecular reaction to proceed (under pseudo-first-order conditions) as fast as the intramolecular reaction. This ratio is called the effective molarity (EM) thus EM = An example is the nu- [Pg.365]

There are obviously many reactions that are too fast to investigate by ordinary mixing techniques. Some important examples are proton transfers, enzymatic reactions, and noncovalent complex formation. Prior to the second half of the 20th century, these reactions were referred to as instantaneous because their kinetics could not be studied. It is now possible to measure the rates of such reactions. In Section 4.1 we will find that the fastest reactions have half-lives of the order 10 s, so the fast reaction regime encompasses a much wider range of rates than does the conventional study of kinetics. [Pg.133]

This mechanism is consistent with all the observations except the variation in rate with initial aluminium chloride concentration. With very reactive aromatics the ionisation step (80) is rate-determining, leading to second-order kinetics, but with less reactive aromatics the ionisation is fast compared with the subsequent reaction of the ionised complex with the aromatic (81), so that this latter then becomes rate-determining. [Pg.80]

In hydroxylation, quinones are usually obtained since the initial hydroxyl product is further oxidised. Kinetic studies on the hydroxylation of 1,3,5-tri-methoxybenzene with perbenzoic acid gave second-order rate coefficients (Table 29) which remained fairly constant for a wide variation in concentration of aromatic and acid thus indicating that the rate-determining step is bimolecular133. The variation was considered to be within the rather large experimental error for the reaction which was very fast and, therefore, studied at low temperature (—12.4 °C). Since more than one mole of acid per mole of aromatic was eventually consumed, the mechanism was formulated as [Pg.54]

Because the cyanide ion is so easily oxidized its apparent ability to react with aromatic cation radicals instead of being oxidized by them reflects the competition so often encountered in cation radical chemistry between nucleophilicity and oxidizability of a nucleophile. The subject has not been treated analytically yet. In the present context, the tri-p-anisylaminium ion is reduced by cyanide ion (Papouchado et al., 1969) in a very fast overall second-order reaction (Blount et al., 1970). The cation radicals of thianthrene, pheno-thiazine, and phenoxathiin are also reduced by cyanide ion (Shine et al., 1974). In none of these cases, incidentally, is the fate known of the cyano radical presumed to be formed. Perylene cation radical perchlorate, on the other hand, reacts with cyanide ion in acetonitrile solution to give low (13%) yields of both 1- and 3-cyano-perylene (Shine and Ristagno, 1972). [Pg.233]

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