Matrix method for balancing chemical equations of few significant inorganic reactions
- 
            			            				
            			
            			            			
            					
            						
            							https://doi.org/10.14419/8g6xtb36
            						
            					
            				Received date: April 28, 2025
Accepted date: June 2, 2025
Published date: June 7, 2025
 - 
            			            			            			
Augmented Matrix; Chemical Equations; Gauss Elimination Method; Linear Equations; Matrix Method  - 
            			            			            				
Abstract
Balancing chemical equations provides a unified framework on understanding and quantifying chemical reactions, making it a fundamental tool in chemistry. The prime objectives to balanced chemical equations are to make both sides of the reaction, the reactants as well as the products, possess the same number of atoms per element. It is worth mentioning that understanding how and in what amounts certain mole-cules are created is made easier with the use of chemical reactions. It also indicates the quantity of reactants required to complete the reaction. These two identities of a chemical reaction are specified by balancing the reaction, which also helps in understanding how to speed up or stop the process. However, balancing long chemical reactions is a difficult and time-consuming task. Employing the principles of mathematical computation to the balancing of chemical equations may come as a remedy to this problem. Thus, in the current paper, we use a matrix-based method, Gauss Elimination mathematical model to balance the chemical equations of a few specific inorganic reactions. Computation work was performed and validated with the help of Python software.
 - 
            			            			            				
References
- Udawat B, Begani J, Mansinghka M, Bhatia N, Sharma H, & Hadap A (2022), Gauss Jordan method for balancing chemical equation for different materials. Materials Today: Proceedings 51, 451-454. https://doi.org/10.1016/j.matpr.2021.05.576.
 - Hamid, I. (2019), Balancing chemical equations by systems of linear equations. Applied Mathematics 10, 521-526. https://doi.org/10.4236/am.2019.107036.
 - Risteski, I. B. (2014), A new generalized algebra for the balancing of chemical reactions. Materials and Technology 48, 215-219. https://doi.org/10.4236/am.2019.107036.
 - Soleimani F, Stanimirovi PS, & Soleymani F (2015), Some matrix iterations for computing generalized inverses and balancing chemical equations. Algorithms 8, 982-998. https://doi.org/10.3390/a8040982.
 - Charnock NL (2016), Teaching method for balancing chemical equations: An inspection versus an algebraic approach. American Journal of Educa-tional Research 4, 507-511. https://pubs.sciepub.com/education/4/7/2.
 - Risteski IB (2009), A new singular matrix method for balancing chemical equations and their stability. Journal of the Chinese Chemical Society 56 65-79. https://doi.org/10.1002/jccs.200900011.
 - Shaikh MM, & Yousaf M (2023), On mathematical methods to balance equations of chemical reactions - a comparison and way forward. Journal of Mechanics of Continua and Mathematical Sciences 18(1), 1-20. https://doi.org/10.26782/jmcms.2023.01.00001.
 - Yousaf M, Shaikh MM, & Shaikh, AW (2020), Efficient mathematical programming techninques for balancing equations of complex chemical reac-tions. Journal of Mechanics of Continua and Mathematical Sciences 15(10), 53-66. https://doi.org/10.26782/jmcms.2020.10.00004.
 - Sen, S. K., Agarwal, H., & Sen, S. Chemical equation balancing: An integer programming approach. Mathematical and Computer Modelling 44 (2006) 678–691. https://doi.org/10.1016/j.mcm.2006.02.004.
 - Pandichelvi V & Saranya S (2022), Application of system linear diophantine equations in balancing chemical equations. International Journal for Research in Applied Science and Engineering Technology 10(10), 917-920. https://doi.org/10.22214/ijraset.2022.47111.
 - Udawat B (2022), Gauss Jordan method for balancing chemical equation for different materials. Materials Today: Proceedings 51, 451-454. https://doi.org/10.1016/j.matpr.2021.05.576.
 - Zhang Z, Zhang X, Zhao YX & Yang SA (2024), Balancing chemical equations: form the perspective of Hilbert basis. Physics.chem-ph. arXiv:2410.06023:1-4.
 - Phan TL, Weinbauer K, Gärtner T, Merkle D, Andersen JL, Fagerberg R, & Stadler PF (2024), Reaction rebalancing: a novel approach to curating reaction databases. Journal of Cheminformatics 16, Article No. 82. https://doi.org/10.1186/s13321-024-00875-4.
 - Mohialden YM, Hussien NM, & Al-Rada WAA (2023), Automated chemical equation balancing using the Apriori algorithm. Journal La Multiapp 4(3), 92-97. https://doi.org/10.37899/journallamultiapp.v4i3.852.
 - Johar DA (2020), Application of the concept of linear equation systems in balancing chemical reaction equations. International Journal of Global Operations Research 1(4), 130-135. https://doi.org/10.47194/ijgor.v1i4.48.
 - Barrett E (2019), Using matrices to balance chemical reactions and modelling the implications of a balanced reaction. Undergraduate Journal of Mathematical Modeling: One + Two 10(1), 5. https://doi.org/10.5038/2326-3652.10.1.4910.
 - Kong Q, Siauw T, & Bayen AM (2021), Chapter 14 - Linear algebra and systems of linear equations, Editor(s): Qingkai Kong, Timmy Siauw, Al-exandre M. Bayen, Python Programming and Numerical Methods, Academic Press, pp. 235-263. https://doi.org/10.1016/B978-0-12-819549-9.00024-5.
 - Luo H, Wu S, & Xie N (2021), Three methods for solving systems of linear equations: Comparing the advantages and disadvantages. Journal of Physics: Conference Series 2012, 012061. https://doi.org/10.1088/1742-6596/2012/1/012061.
 - Vishwambharrao KR, Raju NI, & Shivarudrappa HS (2013), Balancing chemical equations by using mathematical model. International Journal of Mathematical Research and Science 1(4), 129-132.
 - Krishna YH, Bindu P, Yaragani V, Vijaya N, & Makinde OD (2020), Application of Gauss-Jordan elimination method in balancing typical chemi-cal equations. International Journal of Scientific and Technology Research 9 (1), 465-468.
 
 - 
            			            				
Downloads
 - 
	
How to Cite
Sharma, G., Bhattacharyya, S. ., & Bora, N. (2025). Matrix method for balancing chemical equations of few significant inorganic reactions. International Journal of Basic and Applied Sciences, 14(2), 22-28. https://doi.org/10.14419/8g6xtb36 
