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Euler algorithm to solve reaction kinetic equations: Mathematical formulation, programing, and applications
Author(s) -
Coto Baudilio,
Suárez Inmaculada
Publication year - 2018
Publication title -
computer applications in engineering education
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.478
H-Index - 29
eISSN - 1099-0542
pISSN - 1061-3773
DOI - 10.1002/cae.21858
Subject(s) - differential equation , computer science , computation , rate equation , euler equations , mathematical model , mathematics , numerical analysis , set (abstract data type) , interpretation (philosophy) , algorithm , mathematical analysis , kinetics , physics , statistics , quantum mechanics , programming language
Integration of rate laws to obtain the several concentrations in terms of time is well described in books of General Chemistry, Physical Chemistry, or Chemical Engineering including mathematical and graphical descriptions. When several reactions have to be considered simultaneously, the mathematical solution of involved differential equations became difficult for students and is a good task from the mathematical point of view. Qualitative interpretation has interest from the chemical and engineering point of view and it is usually related with the change of concentrations along reactions which in turns modifies the rate of the several processes involved. In this work, no differential equations are solved analytically and no functions are obtained in order to reduce the mathematical complexity for students but a numerical solution is obtained by using the differential method and the computation of changes in concentration. A general formulation of the involved equations is presented including the effect of reactant concentration in the rate laws and an arbitrary number of simultaneous reactions. Details for numerical solution of involved equations are indicated and the task for students is to create their own program to solve the rate laws. Student should be able to input a set of compounds and reactions, to compute the evolution of concentrations of the several species with time and to plot such concentrations. Some applications with increasing complexity were computed and analyzed. In order to show the quantitative obtained results, comparison with analytical functions was carried out for simple systems.