Open AccessDetermination of the number of radicals in the initial chain reactions by mathematical methods
Author(s) -
Branko Pejović,
B Milovan Jotanovic,
M Vladan Micic,
V Milorad Tomic,
S Goran Tadic
Publication year - 2009
Publication title -
hemijska industrija
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.147
H-Index - 19
eISSN - 2217-7426
pISSN - 0367-598X
DOI - 10.2298/hemind0902121p
Subject(s) - radical , series (stratigraphy) , chemical equation , chain (unit) , chain reaction , mathematics , basis (linear algebra) , computational chemistry , chemistry , organic chemistry , physics , photochemistry , quantum mechanics , paleontology , biology , geometry
Starting from the fact that the real mechanism in a chemical equation takes places through a certain number of radicals which participate in simultaneous reactions and initiate chain reactions according to a particular pattern, the aim of this study is to determine their number in the first couple of steps of the reaction. Based on this, the numbers of radicals were determined in the general case, in the form of linear difference equations, which, by certain mathematical transformations, were reduced to one equation that satisfies a particular numeric series, entirely defined if its first members are known. The equation obtained was solved by a common method developed in the theory of numeric series, in which its solutions represent the number of radicals in an arbitrary step of the reaction observed, in the analytical form. In the final part of the study, the method was tested and verified using two characteristic examples from general chemistry. The study also gives a suggestion of a more efficient procedure by reducing the difference equation to a lower order