The Chemical Educator
ISSN: 1430-4171 (electronic version)
Abstract Volume 15
(2010) pp 304-308
An Innovative Approach to Balancing Chemical-Reaction Equations: A Simplified Matrix-Inversion Technique for Determining The Matrix Null Space
Lawrence R. Thorne
Sandia National Laboratories, Livermore, CA 94550,
Published: 31 July 2010
Abstract. I propose a novel approach to balancing equations that is applicable to all chemical-reaction equations; it is readily accessible to students via scientific calculators and basic computer spreadsheets that have a matrix-inversion application. The new approach utilizes the familiar matrix-inversion operation in an unfamiliar and innovative way; its purpose is not to identify undetermined coefficients as usual, but, instead, to compute a matrix null space (or matrix kernel). The null space then provides the coefficients that balance the equation. Indeed, the null space contains everything there is to know about balancing any chemical-reaction equation!
Key Words: In the Classroom; general chemistry; physical chemistry
(*) Corresponding author. (E-mail: firstname.lastname@example.org)
Supporting Materials:An Appendix containing A Manual Approach To Determining The Rank Of A Chemical-Composition Matrix is available for download (16 KB).