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Balancing Chemical Equations Using Matrix Algebra

Author(s): John Jungck1, Jennifer Spangenberg1

Beloit College

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Summary:
This Excel workbook introduces using matrix algebra to balance chemical reactions. The workbook allows the user to set up their own matrices for chemical reactions involving 2-7 elements.

Licensed under these terms

Version 1.0 - published on 09 Aug 2024 doi:10.25334/KBHZ-1567 - cite this

Keywords

  1. chemical reactions
  2. Inverse matrix method
  3. matrix algebra

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  2. Subdiscipline
  3. Audience Level
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Contents:
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Overview

This Excel workbook introduces using matrix algebra to balance chemical reactions. The user can follow several instructional buttons and examples to learn how to set up the required matrices and how to interpret the results. The workbook allows the user to set up their own matrices for chemical reactions involving 2-7 elements. Several sample equations are available for the user to select. See the tutorial for a more detailed description of the matrix algebra.

Popular Text Citations

Grimaldi RP. 1980. Balancing Chemical Reactions with Methods and Computer Assistance. Module 339. UMAP (Modules in Undergraduate Mathematics and Its Applications).

Research Articles

Bottomley J. 1878. Method of indeterminate coefficients (algebraic method). J Chem News. 37:110.

Krishamurthy E V. 1978. General matrix methods for chemical equations. International Journal of Mathematical Education in Science and Technology. 9:323-328.

Herndon W C. 1997. On Balancing Chemical Equations: Past and Present. Journal of Chemical Education. 74: 1359-1362.

Brown J P, Brown L P, Redd R M. 1972. Matrix algebra method. Journal of Chemical Education. 49: 754.

Copley, George Novello. 1968. Linear algebra of chemical formulas and equations. Chemistry 41: 22-27.

Alberty, R. A. 1996. Calculation of biochemical net reactions and pathways by using matrix operations. Biophysical Journal 71:507-515.

Tutorial & Background Materials

Chemical Equation Calculators. Witek Mozga (Note: Some browsers will fail to load required JavaScript)

Citation

Researchers should cite this work as follows:

Fundamental Mathematical Concepts

Fundamental Mathematical Concepts
Inverse matrix method

Developed By

Developed by
Arthur Cayley

Primary Reference

Cayley, A. R. 1853. Note on the Porism of the in-and-circumscribed Polygon. Philosophical Magazine

Cayley, A. R. 1858. A memoir on the theory of matricies. Philosophical Transactions of the Royal Society of London 148:17-37.