First-order apparent

Table 6.8 First-order apparent reaction constant for benzene alkylation with propylene.

In a water-filled porous medium. As soon as diffusion in a water-filled porous medium is considered, the effects of porosity, tortuosity, permeability as well as any interaction with the porous medium must also be considered. This enables us to define the first order apparent diffusion coefficient. Da (cm /s), where ... 

In this type of process one may expect quasi first order apparent kinetics, since mixing and diffusion, in first approximation, are first order rate processes. The first order apparent rate constant may be assumed to be the same as the volumetric mass transfer coefficient / , introduced in section 4.232,... 

The first order apparent rate constant k in this model can be found from experiments, and used as a "fitting parameter". 

First order apparent rate constants (k,pp) for various PLLA polymerizations are shown in Table 1 k,pp was obtained from the slope of a plot of In ([M]o/[M]) versus time (Figure 2). 

Figure 35. First-order apparent spacings for the three-component interstratifications that can be formed from 10, 12.4, 14, and 15.4 A spacings (from Jonas and Brown [1959]).

Herein k js is the observed pseudo-first-order rate constant. In the presence of micelles, analogous treatment of the experimental data will only provide an apparent second-order rate constant, which is a weighed average of the second-order rate constants in the micellar pseudophase and in the aqueous phase (Equation 5.2). 

The effect of micelles of SDS, CTAB and C12E7 on the apparent second-order rate constants of the Diels-Alder reaction between nonionic 5.1a, anionic 5.1 f and cationic 5.1g with 5.2 is reported in Table 5.1. These apparent rate constants are calculated from the observed pseudo-first-order rate constants by dividing the latter by the overall concentration of 5.2. 

The kinetics of the reactions were complicated, but three broad categories were distinguished in some cases the rate of reaction followed an exponential course corresponding to a first-order form in others the rate of reaction seemed to be constant until it terminated abruptly when the aromatic had been consumed yet others were susceptible to autocatalysis of varying intensities. It was realised that the second category of reactions, which apparently accorded to a zeroth-order rate, arose from the superimposition of the two limiting kinetic forms, for all degrees of transition between these forms could be observed. 

Even when there is a transport disguise, the reaction order remains one for a first-order reaction. But for reactions that are not intrinsically first order, the transport disguise changes the observed reaction order for an intrinsically zero-order reaction, the observed order becomes 1/2 and for an intrinsically second-order reaction it becomes 3/2 when 0 10. For all reaction orders the apparent activation energy is approximately half the intrinsic... 

An apparent first-order specific rate increases with liquid rate as the fraction of wetted surface improves. Catalyst effectiveness of particles 3 to 5 mm (0.12 to 0.20 in) diameter has been found to be about 40 to 60 percent. 

There are relatively few kinetic data on the Friedel-Crafts reaction. Alkylation of benzene or toluene with methyl bromide or ethyl bromide with gallium bromide as catalyst is first-order in each reactant and in catalyst. With aluminum bromide as catalyst, the rate of reaction changes with time, apparently because of heterogeneity of the reaction mixture. The initial rate data fit the kinetic expression ... 

For example, a temperature-measuring device, having its sensor placed in a protecting rube, is a system of second order. For such a system no single rime constant exists in the same way as a first-order system. The behavior of such a system is often given by a response time. Another concept is to give the apparent time constant t, which can be constructed by placing a line in the inflection point of the step response curve see Fig. 12.14. 

We have next to consider the measurement of the relaxation times. Each t is the reciprocal of an apparent first-order rate constant, so the problem is identical with problems considered in Chapters 2 and 3. If the system possesses a single relaxation time, a semilogarithmic first-order plot suffices to estimate t. The analytical response is often solution absorbance, or an electrical signal proportional to absorbance or to another physical property. As shown in Section 2.3 (Treatment of Instrument Response Data), the appropriate plotting function is In (A, - Aa=), where A, is the... 

When acetone is treated with hydroxylamine in aqueous solution near neutral pH, the carbonyl UV absorption intensity decreases very rapidly this fast spectral change is followed by a much slower absorption increase that is due to the appearance of the oxime product. This suggests that, at such pH values, the initial addition is very rapid and the second step, dehydration of the carbinolamine, is the rds. Figure 5-12 is a plot of the apparent first-order rate constant against pH for this reaction. As the pH is decreased from neutrality, the rate increases, indicating that the rds... 

This bimolecular process is called the S/ 2 mechanism. It yields overall second-order kinetics (unless the nucleophile is the solvent, in which case apparent first-order kinetics are seen). 

Despite the utmost importance of physical limitations such as solubility and mixing efficiency of the two phases, an apparent first-order reaction rate relative to the olefin monomer was determined experimentally. It has also been observed that an increase of the nickel concentration in the ionic phase results in an increase in the olefin conversion. 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

Even if the peak behavior fits well for a given apparent desorption order, the real kinetic situation may be a different one. As a rate controlling step in a second-order desorption, random recombination of two particles is assumed most frequently. However, should the desorption proceed via a nonrandom recombination of neighboring particle pairs into an ordered structure, the resulting apparent first-order desorption kinetics is claimed to be possible (36). The term pseudo-first-order kinetics is used in this instance. Vice versa, second-order kinetics of desorption can appear for a nondissociative adsorption, if the existence of a dimer complex is necessary before the actual desorption step can take place (99). A possibility of switching between the apparent second-order and first-order kinetics by changing the surface coverage has also been claimed (60, 99, 100). 

N02 addition [both (1.3 2,6) x lCf4 moles] acts the same way. In the absence of salt, however, 2.6 x lO 4 moles of N02 first slow down the 171° decompn, and then make it faster than first order. With 1.3 x 1CT4 moles of added N02, the decompn (lower dashed line in Fig 13) is pseudo first order with an apparent induction time, or more probably a much slower decompn in its initial stages... 

De Tar and Day [498] considered problems which arise in applying the first-order expression [eqn. (15)] to kinetic data of limited accuracy. If a is known to a high degree of accuracy (e.g. 0.1%), then small components (5—10%) of higher or lower order behaviour are detectable. When the accuracy of a is reduced to 1%, a second-order component of 25% could escape detection, and perhaps an even larger contribution might be missed within a limited a interval. Using exact values of a from known kinetic behaviour, the apparent rate coefficient, ft, was found to depend on both the proportion of the non-first-order component and on the extent of reaction considered. 

From non-isothermal measurements, based on apparent first-order obedience, values of E for the overall reactions were 528 and 302 kJ mole-1 for the Na and K salts, respectively. During dehydration at 450 K, Rochelle salt formed [1104] a mixture of separate crystallites of the Na and K salts which then decomposed as above. 

The first kinetic study appears to have been that of Martinsen148, who found that the sulphonation of 4-nitrotoluene in 99.4-100.54 wt. % sulphuric acid was first-order in aromatic and apparently zeroth-order in sulphur trioxide, the rate being very susceptible to the water concentration. By contrast, Ioffe149 considered the reaction to be first-order in both aromatic and sulphur trioxide, but the experimental data of both workers was inconclusive. The first-order dependence upon aromatic concentration was confirmed by Pinnow150, who determined the equilibrium concentrations of quinol and quinolsulphonic acid after reacting mixtures of these with 40-70 wt. % sulphuric acid at temperatures between 50 and 100 °C the first-order rate coefficients for sulphonation and desulphonation are given in Tables 34 and 35. The logarithms of the rate coefficients for sulphonation... 

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