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Sample text
At this point we are going to break into the narrative of rate forms to discuss three particular aspects of kinetic formulations that pertain to most of the situations we discuss, at least for simple reactions. The ®rst of these are the concepts of relaxation time and reaction half-life. The rate equations we have written incorporate the constant k to express the proportionality between the rate and the state variables of the system, and, as such, it is some measure of a characteristic time constant for the reaction.
A ®nal, interesting type of chain mechanism is the branching chain reaction. In this case one of the chain steps (branching) yields two active centers from the reaction of a single center: Á Á Á 3 mR R ÁÁÁ 3 R ÁÁÁ R Á Á Á 3 2R XIV R ÁÁÁ 3 The pssh gives for the concentration of R: R mri = rt À rb 1-136 where rb is de®ned for the branching step in the same manner as ri and rt for initiation and termination. The propagation rate is rp R mri rp = rt À rb 1-137 * The same distribution occurs in catalytic synthesis of hydrocarbons from CO and H2 (Fischer-Tropsch synthesis).
Christiansen, Kgl. Danske Videnskab. F. Herzfeld, Ann. Physik. , 59, 635 (1919); M. Polanyi, Z. , 26, 50 (1920)]. A through discussion of this is given in the text by Frost and Pearson. Because of their commercial importance, we still need to do more work on thermal cracking reactions, since their scope and complexity extend considerably beyond the world of Rice-Herzfeld mechanisms. J. Laidler, Chemical Kinetics, McGraw-Hill, New York, 1965). W. K. J. Pitz, Int. J. Chem. , 18, 655 (1986). Apparent Reaction Kinetics 45 is probably easier to have recourse to the nearest available computer and solve the set of dierential equations numerically.