Initiator concentration, first-order

For each initiator there is a useful temperature range for which the initiator decomposition rate constant, kd, will produce radicals at suitable rates for polymerization. The initiation rate is usually controlled by the decomposition rate of the initiator, which depends directly on its concentration (first-order reaction). The temperature window can be enlarged by the use of catalysts such as a tertiary amine (Eq. (2.80)), or an organometallic compound in a redox reaction (Eqs (2.81) and (2.82)). 

Ans. Since propagation does not change the free radical concentration, the rate of initiation must equal the rate of termination. If the rate of initiation is first-order in P and proportional to the light intensity, fc,[P]7, and the rate of termination is a bimolecular reaction with a rate, kt[R ]1/2, then at the steady state,... 

The first step in this direction is to correlate the permeability values obtained in the Caco-2 cell lines (apical-basolateral direction, Pay) with the fraction of dose absorbed in vivo in rat For this proposal eight fluoroquinolones were assayed and the results found with Caco-2 cell lines were compared with those obtained in vivo in rat In the Caco-2 cell lines the permeability of the quinolones was evaluated at different initial concentration, in order to test for no linearities in the absorption process. For some of them, it was observed that a secretion system worked in the opposite direction to passive diffusion for this reason the permeability value used for the correlations, in the case of secretion, was the one obtained at the highest concentration of the quinolone, which corresponds to saturation of the secretion process. 

As an alternative to using the rate constant k, the course of first order reactions may be expressed in terms of a half-life, thaime- The half-life of a reaction is the time required for reactant concentration to reach half of its initial value. First order rate constants and half-lives are inversely proportional ... 

The effect of pH is shown in Figure 12, and that of surfactant concentration In Figure 13. In both cases, log Cj./c is plotted as a function of t, where c denotes the initial concentration of cobalt(III) acetylacetonate, and Cj. denotes its concentration after a time t. The linearity of these plots shows that the decomposition of the initiator is first order over a wide range of reaction conditions. Figure 12 shows that the first-order rate coefficient for the decomposition rises sharply as the... 

The addition of trace levels (> 10 M) of bis(bipyri-dine)cobalt(ll) to 02-saturated solutions of aldehydes in acetonitrile initiates their rapid autoxidation to carboxylic acids. The initial reaction rates appear to be first order in catalyst concentration, first order in substrate concentration, and first order in O2 concentration. However, within one hour the autoxidation process is almost independent of catalyst concentration. 

Keeping the factors such as pH, temperature and enzyme concentration at optimum levels, if the substrate concentration is increased, the velocity of the reaction recorded a rectangular hyperbola. At very low substrate concentration the initial reaction velocity (v) is nearly proportional to the substrate concentration (first order kinetics). However, if the substrate concentration is increased the rate of increase slows down (mixed order kinetics). With a further increase in the subshate concentration the reaction rate approaches a constant (zero order-reaction where velocity is independent of substrate concentration). 

The addition of trace levels (>1M) of bis(bipyridine)cobalt(II) to O2-saturated solutions of aldehydes in acetonitrile initiates their rapid autooxidation to carboxylic acids. 0 Figure 6-1 illustrates the CoIKbpy)2 -induced autooxidation of hexanal [CH3(CH2)4CH(O)] for 02-saturated (8.1 mM) and air-saturated (1.6 mM) acetonitrile. The apparent reaction dynamics for the catalyzed auto-oxidation of PhCH(O) and of CH3(CH2)4CH(O) during the first hour of their auto-oxidation is summarized in Table 6-1. The initial reaction rates appear to be first order in catalyst concentration, first order in substrate concentration, and first order in O2 concentration (Fig. 6-1). However, within one hour the autooxidation process is almost independent of catalyst concentration. Although the Fellfbpy) and Mnii(bpy)complexes also induce the auto-oxidation of aldehydes, they are much less effective initiators, and the propagation dynamics are much slower. 

Fig. 26. Dependence of the initial rate of initiation of polymerization on the concentration of f-BuLi. Solvent benzene. Lower curve styrene, [t-BuLi] = 4.5 10 4 M. Upper curve isoprene, [f-BuLi] = 1.37 10 3 M. Note the plateau of isoprene curve (— 3.5) is higher than that oif the styrene curve (- 4,5) after adjustment to the concentration [r-BuLi] = 1.37 10-3 M. The initiation is first order in f-BuLi...

Since the initiator concentration remains fairly unchanged in the course of vinyl polymerization, if the initiator efficiency is independent of monomer concentration, first-order kinetics with respect to the monomer is expected. This is indeed observed over a wide extent of reaction for the polymerization of styrene in toluene solution with benzoyl peroxide as initiator (Figure 7.3). The polymerization of certain monomers, either undiluted or in concentrated solution, shows a marked deviation Irom such first-order kinetics. At a certain stage in the polymerization process, there is a considerable increase in both the reaction rate and the molecular weight. This observation is referred to as autoacceleration or gel effect and is illustrated in Figure 7.4 for polymerization of methyl methacrylate at various concentrations of the monomer in benzene. 

The effect of a, a -azobisisobutyronitrile initiator concentration [1] on the rate of polymerization of methyl methacrylate at 50°C has been stndied by Arnett (1952). Use the following data to show that the termination reaction is second order with respect to the growing chains and initiation is first order with respect to the initiator concentration. ... 

Figure 8. Reduction of nitrobenzene (NB) in aqueous suspensions containing 200 mgL magnetite and 1.5 mM Fe at pH 7. Plot of ln(C/Co) versus time. C and Cq are the concentrations of NB at time zero and t, respectively. The initial pseudo-first order rate constant, kobs, is obtained by a linear least-squares fit of ln(C/Co) = - kobs t, using only the first few data points. Data from (38).

The decomposition of most organic free radical initiators follows first order kinetics. With certain peroxides, however, higher order deeompositions are observed. Generally, the higher order reaetion is caused by a reaction of radicals with the initiator (indueed decomposition). The value of the rate for unimoleeular decomposition m be determined either by extrapolation of the rate back to zero initiator concentration or by use of a monomer or other radical trap . Some of the peroxides may also decompose by non-radical routes. Acids, bases, and polar solvents favor ionic intermediates. Koenig (296) presents an excellent discussion of dw and peroxide decomposition pathways. 

Bromide ion acts as an inliibitor through step (9) which competes for HBr02 with the rate detennining step for the autocatalytic process described previously, step (4) and step (5). Step (8) and Step (9) constitute a pseudo-first-order removal of Br with HBr02 maintained in a low steady-state concentration. Only once [Br ] < [Br ] = /fo[Br07]//r2 does step (3) become effective, initiating the autocatalytic growth and oxidation. 

When the concentration of 2-phenylethanesulphonate anion was >0-5 mol 1, or when 2-mesitylethanesulphonate anion (v), " mesitylene-a-sulphonate anion, or iso-durene-a -sulphonate anion were nitrated, the initial part of the reaction deviated from a first-order dependence on the concentration of the aromatic towards a zeroth-order dependence. 

Under conditions in which benzene and its homologues were nitrated at the zeroth-order rate, the reactions of the halogenobenzenes ([aromatic] = c. o-1 mol 1 ) obeyed no simple kinetic law. The reactions of fluorobenzene and iodobenzene initially followed the same rates as that of benzene but, as the concentration of the aromatic was depleted by the progress of the reaction, the rate deviated to a dependence on the first power of the concentration of aromatic. The same situation was observed with chloro- andjbromo-benzene, but these compounds could not maintain a zeroth-order dependence as easily as the other halogenobenzenes, and the first-order character of the reaction was more marked. 

The effect of nitrous acid on the nitration of mesitylene in acetic acid was also investigated. In solutions containing 5-7 mol 1 of nitric acid and < c. 0-014 mol of nitrous acid, the rate was independent of the concentration of the aromatic. As the concentration of nitrous acid was increased, the catalysed reaction intervened, and superimposed a first-order reaction on the zeroth-order one. The catalysed reaction could not be made sufficiently dominant to impose a truly first-order rate. Because the kinetic order was intermediate the importance of the catalysed reaction was gauged by following initial rates, and it was shown that in a solution containing 5-7 mol 1 of nitric acid and 0-5 mol 1 of nitrous acid, the catalysed reaction was initially twice as important as the general nitronium ion mechanism. 

The evidence outlined strongly suggests that nitration via nitrosation accompanies the general mechanism of nitration in these media in the reactions of very reactive compounds.i Proof that phenol, even in solutions prepared from pure nitric acid, underwent nitration by a special mechanism came from examining rates of reaction of phenol and mesi-tylene under zeroth-order conditions. The variation in the initial rates with the concentration of aromatic (fig. 5.2) shows that mesitylene (o-2-0 4 mol 1 ) reacts at the zeroth-order rate, whereas phenol is nitrated considerably faster by a process which is first order in the concentration of aromatic. It is noteworthy that in these solutions the concentration of nitrous acid was below the level of detection (< c. 5 X mol... 

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