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

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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.

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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.

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Authors and Affiliations

  1. Department of Inorganic and Analytical Chemistry, University of Debrecen, P.O.B. 21, Debrecen, 4010, Hungary

    Gábor Lente

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  1. Gábor Lente
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Correspondence to Gábor Lente.

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Lente, G. Analytical solutions for the rate equations of irreversible two-step consecutive processes with mixed second order later steps. J Math Chem 55, 832–848 (2017). https://doi.org/10.1007/s10910-016-0712-x

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  • DOI: https://doi.org/10.1007/s10910-016-0712-x

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