Application of Matrix Methods in Balancing Chemical Equations: A Systematic Approach
DOI:
https://doi.org/10.65486/yrw8p569Keywords:
Chemical equations, linear algebra, matrix methods, row reduction, stoichiometryAbstract
Purpose:
Balancing chemical equations is essential to maintain reaction stoichiometry and the principle of mass conservation. Traditional balancing methods, such as inspection and trial-and-error, often become inefficient and error-prone for complex reactions. The purpose of this study is to introduce a systematic and reliable matrix-based approach that improves the efficiency and accuracy of balancing chemical equations.
Method:
The proposed method reformulates chemical equations into systems of linear equations, which are then solved using linear algebraic techniques. Tools such as Gaussian elimination and row reduction are applied to determine stoichiometric coefficients systematically. The study also evaluates the pedagogical value of incorporating matrix-based approaches into chemistry education to strengthen interdisciplinary connections between mathematics and chemistry.
Results:
The findings show that the matrix method simplifies the balancing of chemical equations, particularly in cases where conventional approaches are cumbersome. The method ensures accuracy and reduces human error by providing an algorithmic solution. Furthermore, its application in education demonstrates that students gain both improved problem-solving efficiency and a deeper conceptual understanding of the mathematical underpinnings of chemical processes.
Practical Implications:
The matrix-based approach provides chemists and educators with a reliable tool to balance complex reactions quickly and accurately. For academic contexts, integrating this method into curricula can foster interdisciplinary learning and enhance student engagement. In professional applications, the method supports computational chemistry tools and can be further optimized for large-scale or automated chemical process simulations.
Originality/Novelty:
This study contributes originality by bridging linear algebra techniques with practical chemistry applications. Unlike conventional methods, the matrix-based approach introduces an algorithmic and scalable framework for balancing chemical equations. It also highlights the innovative educational dimension of connecting mathematics and chemistry, while opening avenues for future advancements through artificial intelligence and advanced matrix methods.
Downloads
References
[1]. Angelis, D., Sofos, F., & Karakasidis, T. E. (2023). Artificial intelligence in physical sciences: Symbolic regression trends
and perspectives. Archives of Computational Methods in Engineering, 30(6), 3845-3865.
[2]. Anton, H., & Rorres, C. (2013). Elementary linear algebra: applications version. John Wiley & Sons.
[3]. Bronson, R., & Costa, G. B. (2008). Matrix methods: Applied linear algebra. Academic Press.
[4]. Chen, W. K. (2016). Active network analysis: feedback amplifier theory (Vol. 15). World Scientific.
[5]. Gilbert, J., & Gilbert, L. (2014). Linear algebra and matrix theory. Elsevier.
[6]. Goel, A., & Manocha, A. K. (2024). A schematic study of dimension reduction techniques for complex high-order
integer, fractional and interval systems. Electrical Engineering, 1-41.
[7]. Kumar, R., Chaudhary, M. P., Shah, M. A., & Mahajan, K. (2020). A mathematical elucidation of separation membrane
operations and technology of chemical and physical processes: An advanced review. Journal of Integrated Science and
Technology, 8(2), 57-69.
[8]. Lay, D. C. (2003). Linear algebra and its applications. Pearson Education India.
[9]. Meyer, C. D. (2023). Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics.
[10]. Potgieter, M., Harding, A., & Engelbrecht, J. (2008). Transfer of algebraic and graphical thinking between mathematics
and chemistry. Journal of Research in Science Teaching: The Official Journal of the National Association for Research
in Science Teaching, 45(2), 197-218.
[11]. Shores, T. S. (2007). Applied linear algebra and matrix analysis (Vol. 2541). New York: Springer.
[12]. Smith, J. (2012). AAAR 31st Annual Conference Symposium Focusing on Topics of Interest to the US DOE
Atmostpheric System Research Program, Oct 8-12, 2012 (No. DOE Grant 2012). American Association for Aerosol
Research, Mount Laurel, NJ (United States).
[13]. Strang, G. (2022). Introduction to linear algebra. Wellesley-Cambridge Press.
