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The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

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,
Received September 2, 2009. Accepted December 26, 2009.

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

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Article in PDF format (154 KB) HTML format

Supporting Materials:

An Appendix containing A Manual Approach To Determining The Rank Of A Chemical-Composition Matrix is available for download (16 KB).

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