Rate constants general order

For all samples, including the treated celluloses, Wilkinson s approximation generally gave unrealistic rate constants, reaction orders, and especially Ea s. Although this method is easy and requires no assumption of order, values obtained by this technique should be viewed cautiously. 

Before concluding this section, we should briefly explain the averaging procedure which is implicit in the derivation of parabolic rate constants. In order to simplify without loss of generality, we assume that DA>DB. Integration of Eqn. (6.27) yields... 

General symbol for reaction rate constant (n = order). 

The extreme influence water can exert on the Diels-Alder reaction was rediscovered by Breslow in 1980, much by coincidence . Whale studying the effect of p-cyclodextrin on the rate of a Diels-Alder reaction in water, accidentally, the addition of the cyclodextrin was omitted, but still rate constants were observed that were one to two orders of magnitude larger than those obtained in organic solvents. The investigations that followed this remarkable observation showed that the acceleration of Diels-Alder reactions by water is a general phenomenon. Table 1.2 contains a selection from the multitude of Diels-Alder reactions in aqueous media that have been studied Note that the rate enhancements induced by water can amount up to a factor 12,800 compared to organic solvents (entry 1 in Table 1.2). 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

As with the case of energy input, detergency generally reaches a plateau after a certain wash time as would be expected from a kinetic analysis. In a practical system, each of its numerous components has a different rate constant, hence its rate behavior generally does not exhibit any simple pattern. Many attempts have been made to fit soil removal (50) rates in practical systems to the usual rate equations of physical chemistry. The rate of soil removal in the Launder-Ometer could be reasonably well described by the equation of a first-order chemical reaction, ie, the rate was proportional to the amount of removable soil remaining on the fabric (51,52). In a study of soil removal rates from artificially soiled fabrics in the Terg-O-Tometer, the percent soil removal increased linearly with the log of cumulative wash time. 

Many researchers have correlated the overall decomposition as an nxh. order reaction, with most paraffins following the first order and most olefins following a higher order. In general, isoparaffin rate constants are lower than normal paraffin rate constants. The rate constants are somewhat dependent on conversion due to inhibition effects that is, the rate constant often decreases with increasing conversion, and the order of conversion is not affected. This has been explained by considering the formation of aHyl radicals (38). To predict the product distribution, yields are often correlated as a function of conversion or other severity parameters (39). 

Reactions catalyzed by hydrogen ion or hydroxide ion, when studied at controlled pH, are often described by pseudo-first-order rate constants that include the catalyst concentration or activity. Activation energies determined from Arrhenius plots using the pseudo-first-order rate constants may include contributions other than the activation energy intrinsic to the reaction of interest. This problem was analyzed for a special case by Higuchi et al. the following treatment is drawn from a more general analysis. ... 

The general rate equation for the first-order rate constants, k, is given by Eq. (4) ... 

The rate constants for unimolecular dissociation of the intermediate ions suggested earlier indicate that all ions containing seven or more carbon atoms arise from reactions of the dissociation products of Steps 9, 13, and 17 when pressures are of the order of a few torr and of Step 20 and its analogues at pressures in excess of a few hundred torr. The product ions are generally quite complex, and the simple exothermicity rule given earlier will not apply. Thus, we may well expect that there will be inefficient ion-molecule reactions in the sequences originating with these ions as well. 

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