Journal of Mathematical Chemistry

, Volume 48, Issue 2, pp 305–312 | Cite as

Decomposition of reaction networks: the initial phase of the permanganate/oxalic acid reaction

  • Utz-Uwe Haus
  • Raymond Hemmecke
Original Paper


The determination of all chemical reaction networks composed of elementary reactions for a given net chemical reaction is one of the fundamental problems in chemistry, since the decomposition elucidates the reaction mechanism. It is essential in a wide range of applications: from the derivation of rate laws in physical chemistry to the design of large-scale reactors in process engineering where presence of unexpected side products can disturb operation. As an example we consider the well-known permanganate/oxalic acid reaction. We characterize all intermediate substances that can in principle act (auto-)catalytic, list all possible additional intermediate substances that would suffice to start the reaction without assuming presence of any autocatalyst. In particular, we propose for the first time a minimal network in which the well-known autocatalyst Mn2+ is produced. To derive our results we present an automatic method to determine whether a net chemical reaction can be explained by some reaction network with a given list of intermediate substances, how to generate all such networks, and how to suggest more intermediate substances if no network with the initially given substances exists.


Reaction networks Elementary reactions Reaction mechanisms Network decomposition 


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Supplementary material

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institut für Mathematische OptimierungOtto-von-Guericke Universität MagdeburgMagdeburgGermany
  2. 2.Zentrum MathematikTechnische Universität MünchenGarching bei MünchenGermany

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