Propagation of a chain reaction

The propagation reaction often has the function of producing the products of the reaction, or at least to regeneration of the active centers. This is the most fiequently repeated stage during the reaction. Propagation reactions are classified in four categories  

If the synthesis of the reaction product requires several steps, the propagation rate will be the rate of the last step. If the propagation sequence is in a pseudo-steady state mode, the propagation rate is the rate from any step divided by its multiplying 

The rate of disappearance of the reactants is the sum of the initiation and propagation rates. This is the propagation phase consuming the vast majority of the reactants (and that also synthesizes the majority of the products). The rate of initiation will therefore be much lower than the rate of propagation, so that 

Breaking reactions lead to the disappearance of active centers. Breaking can be caused by  

Both quadratic reactions and reactions between active centers and impurities occur in the reactor volume and are called bulk breakings as opposed to a type of breaking that frequently occurs at the surface of the reactor walls, which concentrates the active centers by adsorption. 

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Not infrequently, however, a difficult initial formation of free atoms or radicals leads to the propagation of a chain reaction which greatly multiplies the effect. Sometimes the chains may branch, when special phenomena of inflammation and explosion may occur at sharply defined limits of concentration. 

Intermediate species bearing an active site for the propagation of a chain reaction. 

V, volumetric rate of the initiation of a chain reaction p. volumetric rate of the propagation of a chain reaction Va)A- absolute rate of a reaction with respect to component N... 

An important descriptor of a chain reaction is the kinetic chain length, ie, the number of cycles of the propagation steps (eqs. 2 and 3) for each new radical introduced into the system. The chain length for a hydroperoxide reaction is given by equation (10) where HPE = efficiency to hydroperoxide, %, and 2/ = number of effective radicals generated per mol of hydroperoxide decomposed. For 100% radical generation efficiency, / = 1. For 90% efficiency to hydroperoxide, the minimum chain length (/ = 1) is 14. 

Chain reaction (Section 5.3) A reaction that., once initiated, sustains itself in an endlessly repeating cycle of propagation steps. The radical chlorination of alkanes is an example of a chain reaction that is initiated by irradiation with light and then continues in a series of propagation steps. 

Bond energy considerations indicate that the initiation reaction (4.2.2) should be quite slow because its activation energy must be quite high (at least equal to the bond dissociation energy). If one were dealing with an open sequence reaction mechanism, such a step would imply that the overall reaction rate would also be low because in these cases the overall reaction becomes approximately equal to that of the rate limiting step. In the case of a chain reaction, on the other hand, the overall reaction rate is usually much faster because the propagation steps occur many times for each time that an initiation step occurs. 

The essential characteristic of a chain reaction mechanism is the existence of a closed cycle of reactions in which unstable or highly reactive intermediates react in propagation steps with stable reactant molecules or other intermediates and are regenerated by the sequence of reactions... 

To write down the differential equation for the rate of a chain reaction we employ the law of mass action, but the simple application of this involves the concentration of the transitorily formed activated molecules which propagate the chain, and as this concentration is unknown the equation written down would be useless unless some other relations are established by means of which the unknown quantities can be eliminated. These relations are provided by the condition that the chains shall be stable, or the Egerton and Gates, J. Inst. Petroleum, Tech., 1927, 13, 281. 

But occurrence of a chemical reaction along one or even several mean free paths is quite surprising, and to explain such a large reaction rate and large velocity of propagation, these authors resorted to electrons and radiation, quantum-mechanical resonance of collectively moving particles and direct impact of rapid active centers of a chain reaction. 

The conception of a chain reaction in which the breaking off of the chains on the walls depends on the dimensions of the vessel or on the location of the point of ignition is untenable, since the chemical reaction in the propagation of a flame takes place in a narrow zone, the thickness of which is thousands of times less than the dimensions of the vessel and the reaction time of an individual volume element and even of the entire explosive mixture in the vessel is many times less than the time of diffusion of active centers to the walls of the vessel. 

As the reaction equations show, the last propagation step supplies the initiating radical consumed in the first propagation step. From this you also see that the mass conversion of a chain reaction is described by an equation that results from the propagation steps alone they are added up, and species that occur on both sides of the reaction arrow are dropped. 

Propagation steps A radical chain reaction often has several propagation steps. In each of these steps, a radical reacts with a normal compound to produce a new radical. The final propagation step of a chain reaction produces the same radical that reacts in the initial propagation step, so the process can begin anew. 

Although the initiation and termination steps are important in the mechanism of a chain reaction, almost all of the products are formed as the result of the propagation steps because there are so many more of them. An equation for the overall reaction can be obtained by summing the propagation steps and canceling species that appear on both sides of the equation ... 

This step forms only one of the final products the molecule of HC1. A later step must form chloromethane. Notice that the first propagation step begins with one free radical (the chlorine atom) and produces another free radical (the methyl radical). The regeneration of a free radical is characteristic of a propagation step of a chain reaction. The reaction can continue because another reactive intermediate is produced. 

QUESTION What factors characterize the propagation steps of a chain reaction ... 

As mentioned at the outset, chain reactions, relying on free radicals as chain carriers, are sensitive toward any substances that can destroy or trap such radicals. The interference with chain propagation can assume two forms. An added substance can reduce the reaction rate to almost nil or bring it to essentially a complete and permanent stop. This is called inhibition. It occurs if the inhibitor catches practically all free radicals produced by the initiator. Under different conditions, an added substance or impurity can delay the start of a chain reaction for some period of time, called an induction period, without affecting its later course. 

Both of these reactions are propagation reactions, and if they are considered as a pair it is to be seen that the radical (or atom) that disappears in one is formed in the other this is the essential feature of a chain reaction. 

Inhibitor A general term for any compound which will inhibit (i.e. slow down or stop) a reaction, generally by preventing propagation of the chain reaction or by passivation of surfaces, etc. The term is often used to describe any additive which will prevent a particular tendency during working operations (e.g. antioxidants, anticorrosion agents). 

When dealing with catalysis it is best, however, to classify polymerization reactions according to the mechanism of chain propagation (2). One may distinguish in this way between chain-reaction polymerization and step-reaction (stepwise) polymerization. The essential features of these classes are shown in Table I (15). The diflFerences between the two types of polymerization are also evident from equations of rate (Rp) and average degree of polymerization (DP). For a free-radical polymerization of vinyl compounds (an example of a chain reaction), Rp and DP are functions of monomer and catalyst concentration (Equations 9 and 10) ... 

Common error alert Although it is possible for an initiator to participate in the propagation part of a chain reaction, it is bad practice to write a mechanism in this way. The concentration of initiator is usually very small, and the probability that a radical will encounter it is considerably smaller than the probability that the radical will encounter a stoichiometric starting material. 

Discussion. The rate of a chain reaction of long chain length may be represented symbolically by a chain initiating step I, a chain propagating step P, and a chain terminating step T ... 

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