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Journal of Mathematical Chemistry

, Volume 55, Issue 3, pp 832–848 | Cite as

Analytical solutions for the rate equations of irreversible two-step consecutive processes with mixed second order later steps

  • Gábor Lente
Original Paper

Abstract

A general strategy was developed to solve the ordinary differential equations defined by two-step chemical processes with a mixed second order later process for all possible cases of parameter values (initial concentrations and rate constant values). As the earlier process, first order, second order, mixed second order and zeroth order cases were considered. For the scheme with a mixed second order first step, several different variations were considered. The analytical solutions contain moderately advanced, but still elementary functions such as the error function, the incomplete gamma function, the hypergeometric function or the Legendre functions. When coupling between the two steps or some reversibility is present in the system, no analytical solutions are found.

Keywords

Mixed second order kinetics Rate equation Reaction kinetics Mathematical modelling Intermediate Biphasic process 

Notes

Acknowledgements

The research was supported by the EU and co-financed by the European Regional Development Fund under the project GINOP-2.3.2-15-2016-00008.

Supplementary material

10910_2016_712_MOESM1_ESM.docx (40 kb)
Supplementary material 1 (docx 39 KB)

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Inorganic and Analytical ChemistryUniversity of DebrecenDebrecenHungary

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