INDUCTION PERIOD SERIES REACTIONS

Concentration-time curves. Much of Sections 3.1 and 3.2 was devoted to mathematical techniques for describing or simulating concentration as a function of time. Experimental concentration-time curves for reactants, intermediates, and products can be compared with computed curves for reasonable kinetic schemes. Absolute concentrations are most useful, but even instrument responses (such as absorbances) are very helpful. One hopes to identify characteristic features such as the formation and decay of intermediates, approach to an equilibrium state, induction periods, an autocatalytic growth phase, or simple kinetic behavior of certain phases of the reaction. Recall, for example, that for a series first-order reaction scheme, the loss of the initial reactant is simple first-order. Approximations to simple behavior may suggest justifiable mathematical assumptions that can simplify the quantitative description. 

Induced reactions, 102 Induction period, 72 Inhibitor competitive, 92 noncompetitive, 93 Initial rates, method of, 8, 32 from power series, 8 Initiation step, 182 Inverse dependences, 130-131 Isokinetic relationship, 164—165 Isokinetic temperature, 163, 238 Isolation, method of (see Flooding, method of)... 

A series of 2- and 4-nitroaniline derivatives and analogues when heated with cone, sulfuric acid to above 200°C undergo, after an induction period, a vigorous reaction. This is accompanied by gas evolution which produces up to a 150-fold increase in volume of a solid foam, and is rapid enough to be potentially hazardous if confined. 

Using this form of the rate equation, with A0 = 100, the /3-resin data obtained at 800°, 825°, and 850°F (430°, 440°, and 450°C, respectively) are plotted in Figure 1. The first-order rate equation produces a series of reasonably straight lines, but only after the reaction has passed through what appears to be some form of induction period. The data obtained at 980°F (530°C) (not shown in Figure 1 because of the much smaller time interval involved) produces a plot with similar character-... 

The generation sequence of the most intense photoproduct series is shown in Fig. 5 by the integral absorptions of the individual photoproducts as a function of the irradiation time. Only the photoproduct A is generated without any delay. In the sequence B, C, D,. .. the induction period increases continuously. This corresponds to the expected polymerization reaction starting with the formation of the dimer A followed by subsequent addition reaction steps to the trimer B and tetramer C molecules etc. The curves are calculated using the kinetic expressions described below. 

Reaction began without appreciable induction period (except in the case of iso-butyl amine) and the rate accelerated smoothly to a maximum. In the series Me-, Et-, n-Pr-, n-Bu-amine the oxidation rate increased with lengthening hydrocarbon chain, while secondary amines were more readily oxidized than the corresponding primary compounds. 

In order to clarify the autocatalysis by carbon, a series of runs was carried out with carbon samples of different origin (Fig. 10). Primary interest was on hexa carbon. Curve 1 represents the normal reaction in AR-glass. The reactions 2 and 3 were conducted in an apparatus in which a reaction had previously taken place. The volatile reaction products were removed by pumping, without letting the carbon film come into contact with air. For this, the apparatus was baked at 400° for 4 hrs. (curve 2) or 20 days (curve 3). It is apparent that the hexa carbon shortens the induction period, and that an increase in the baking time increases its activity. Brief exposure to air prior to baking increases the activity of the carbon film (curve 4). 

A series of papers has appeared on the gelation of Konjac D-mannan. On reaction with either sodium hydroxide or sodium carbonate, an induction period occurred before gelation due to the requirement for deacetylation. The rate of the induced reaction was of the form V = 4.8[OH ]° where V is the reaction rate (min ). ° The power value of 0.61 suggested that the rate of deacetylation was proportional to the concentration of hydroxide ion and that gelation of the deacetylated molecules was inhibited by the hydroxide ion. The degree of deactylation, calculated from the Arrhenius equation, increased with a decrease in the concentration of D-mannan and an increase in the concentration of hydroxide ion, but was not influenced by temperature or the nature of the cation (Na or K ). Deacetylation was an induced reaction which was essential for gelation and occurred after the equilibrium of the deacetylation and peptization reactions by hydroxide ion. 

Precatalytic Reactions and Xpre. The catalyst precursor must transform under reaction conditions into intermediates to obtain an active system. This transformation may involve, in a small number of cases, only a single elementary step, for example, the dissociation of a ligand from a transition-metal complex. However, a series of elementary reaction steps are usually required to convert the catalyst precursor. Useful examples include (1) the degradation of a polynuclear precursor to mononuclear intermediates, (2) the modification of a precursor with a ligand L which is used to control selectivity, and (3) the transformation of finely divided metal. The characteristic time scale for the precatalytic reaction will be denoted tpre, and the instantaneous reaction rate will be denoted Ppre- Precatalytic phenomena and the associated induction periods have been directly monitored in a number of in situ spectroscopic studies using a variety of mononuclear, dinuclear, polynuclear, and metallic precursors (11). 

The induction periods observed, the inhibition by traces of 2,6-di-r-butyl-4-methyl-phenol, and the fractional reaction orders appearing in the rate laws suggested a series of radical chain processes. 

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