Chain reaction, rate

Figure 6.3 (a) Concentrations of the species involved in the reaction and (b) reaction rates as a function of time. Kinetics in the absence (dashed lines) and presence (solid lines) of bimolecular termination. Concentrations R = active chains X = active chains Pc = terminated chains. Reaction rates Ra = activation = deactivation Rt = bimolecular termination... 

With eqns 9.6, a free-radical population proportional to the initiator concentration gives a chain-reaction rate that is first order instead of half order in initiator. However, for chain transfer to outrun coupling, its rate must be high, and species S then acts essentially as an inhibitor (see also Section 9.7). 

In general, the activation energy for kp is small (8 it 3 kcal), while that for kt is zero, and E is very large, 80 to 100 kcal. In consequence, A will appear to have a large negative activation of the order of Ep — E = —37 kcal/mole. This places some very severe restraints on the use and accurate measurement of chain reaction rates. At the very lowest temperatures where chain lengths can be very long (—102 to 103), the rates can be extremely sensitive to adventitious impurities such as 02 and wall effects. There is a natural floor imposed, however, on the use of low temperatures since at temperatures below about 750°K, initiation rates are so slow that chain rates are too slow to measure. 

For the chain termination of the second order, the chain reaction rate is V = const [RHl... 

Ad 5.1 eV/mol is the H2O dissociation energy. The total chain reaction rate obviously depends on the chain length, which can be numerically estimated as v >= 100 at vibrational temperature 7(, = 0.5 eV and water vapor density [H2O] = 3 10 cm . The total chain reaction rate can be calculated by taking into account both the chain initiation rate (5-115) and the chain length as follows ... 

Computer studies of the course of macroscopic ignition in shocked Hg-Og mixtures containing an excess of either reactant have revealed the occurrence under certain conditions of short-lived excursions of intermediate species concentrations significantly above the quasi-stable N = I partial equilibrium levels. These so-called spikes occur between the time of the peak chain reaction rate, which occurs when the lesser reactant is about 50% depleted, and the time of establishment of partial equilibrium proportions among the major intermediates. In an excess of H2, the partial equilibrium 0-atom concentration is quite... 

Figure 1.4.Time dependence for chain reaction rate (consumption of initial reagents is not taken into account) (/ = O) (1) - no branching < O) (2) = 0)(3)

In the system where the chain reaction can develop, initiation with the known specified rate is created by either the introduction of an initiator, which decomposes to radicals with the known rate constant, or photochemically, or under the action of penetrating radiation (y beams, P beams). The dependence of the chain reaction rate V on the initiation rate v, allows one to judge about the character of chain termination. If V v chain termination has the first order with respect to the concentration of active centers if v v/, it has the second order. In the liquid phase in the absence of an inhibitor, chains termination is monomolecular, and the rate of the chain reaction, e.g., polymerization of the monomer M, is... 

The experiment is performed as follows (Fig. 13.1). The reaction mixture is placed in a thermostatted vessel 6 with transparent planar-parallel walls. The vessel is irradiated with the light with such a wavelength that generates radicals. Disk 4 is placed in the point where the beams are focused and is rotated. The reaction rate is measured by this or another method from experiment to experiment, and the empirical dependence of the v/v ratio on logrj is plotted, td is found from the rotation velocity of the disk and the ratio between the sizes of the dark and light sectors (usually r - 3). This empirical dependence is compared with the theoretical one, and 2k, is determined by comparison, and from this 2k, is calculated. The initiation rate is measured by the methods of inhibitors (see above) or through the chain reaction rate and the kp/2k, ratio. 

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