Analytical solutions for the rate equations of irreversible two-step consecutive processes with mixed second order later steps
- 167 Downloads
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.
KeywordsMixed second order kinetics Rate equation Reaction kinetics Mathematical modelling Intermediate Biphasic process
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.
- 1.P. Érdi, J. Tóth, Mathematical Models of Chemical Reactions (Manchester University Press, Manchester, 1989)Google Scholar
- 2.J.H. Espenson, Chemical Kinetics and Reaction Mechanisms, 2nd edn. (McGraw-Hill, New York, 1995)Google Scholar
- 3.G.B. Marin, G.S. Yablonsky, Kinetics of Chemical Reactions (Wiley, Weinheim, 2011)Google Scholar
- 5.P. Érdi, G. Lente, Stochastic Chemical Kinetics. Theory and (Mostly) Systems Biological Applications (Springer, New York, 2014)Google Scholar
- 11.Z. Szabó, in Comprehensive Chemical Kinetics, Volume 2: Theory of Kinetics, ed. by C.H. Bamford, C.F.H. Tipper (Elsevier, Amsterdam, 1969), pp. 2–80Google Scholar
- 13.F.G. Helfferich, Comprehensive Chemical Kinetics, Volume 38: Kinetics of Homogeneous Multistep Reactions (Elsevier, 2000)Google Scholar
- 14.F.G. Helfferich, Comprehensive Chemical Kinetics, Volume 40: Kinetics of Multistep Reactions, 2nd edn, (Elsevier, 2004)Google Scholar
- 31.G. Lente, J. Math. Chem. 53, 1175–1183 (2015)Google Scholar