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Pré-Publication, Document De Travail Année : 2023

Pivotal condensation and chemical balancing

Résumé

I present a universal method, called pivotal condensation, for calculating stoichiometric factors of chemical reactions. It can be done by hand, even for rather complicated reactions. The main trick, which I call \emph{kernel pivotal condensation} (ker pc), to calculate the kernel of a matrix might be of independent interest. The discussion is elaborated for matrices with entries in a principal ideal domain $R$. The ker pc calculates a basis with coefficients in $R$ for the kernel of a matrix, seen as e $Q$-vector space, where $Q$ is the quotient field of $R$. If $W$ is a free saturated $R$-submodule of $R^n$ I address the question how to modify an $R$-basis of the $Q$-vector subspace $Q\otimes _R W$ over the quotient field $Q$ to obtain a basis of the $R$-module $W$. I also indicate how one can solve inhomogeneous linear systems, invert matrices and determine the four subspaces using pivotal condensation. I formulate the balancing by inspection method that is widely used to reduce the size of a linear system arising in chemical balancing in mathematical language.
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Dates et versions

hal-04091017 , version 1 (07-05-2023)

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Paternité

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  • HAL Id : hal-04091017 , version 1

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Hans-Christian Herbig. Pivotal condensation and chemical balancing. 2023. ⟨hal-04091017⟩
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