A New Approach to Balance the Chemical Reaction Equations by Applying Gauss,Gauss-Jordan Methods and Cramer’s Rule and Verification of the Same by Computational Programming Softwares

A New Approach to Balance the Chemical Reaction Equations by Applying Gauss,Gauss-Jordan Methods and Cramer’s Rule and Verification of the Same by Computational Programming Softwares | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A New Approach to Balance the Chemical Reaction Equations by Applying Gauss,Gauss-Jordan Methods and Cramer’s Rule and Verification of the Same by Computational Programming Softwares Majid Ali Choudhary, Md Ajmal Khan, Mohammed Arifuddin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5929827/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study is undertaken to balance the chemical reaction, i.e., combustion of hydrocarbons, by using a system of linear equations with the Gauss and Gauss-Jordan elimination method and Cramer’s Rule. It was earlier reported that these reactions are not possible to balance mathematically. The results of the present study show that these reactions can be balanced by using the linear equations protocol. Furthermore, the results of the present study were verified by using various computational programming tools or software, such as MATLAB, Python (Jupyter Notebook), and Lindo. The above methods are also applied to get the various hydrocarbon combustion reactions to prove the generality of the present study. Thus, it is anticipated that the present study results will open a gateway in the area of balancing chemical reactions by using mathematical protocols 1 and their computational counterparts, and in the future, it may be possible to mathematically handle any chemical reaction with given reactants and products. MSC Classification: 15A06 , 15A52 , 15A12 , 65F05 , 65F3 Chemical Reaction Linear Equations Balancing Chemical Equations Gauss Elimination Method Gauss-Jordan Elimination Method Cramer’s Rule Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5929827","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":409413980,"identity":"be1d4647-112e-47c6-9d0c-6b1736c41faf","order_by":0,"name":"Majid Ali Choudhary","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYDACdsYGZiDFuAHE+cDAkAAVl8CthRlJC+MM4rSAEUQLMw9CC27A38zc+Lmg4rDsdvazz6Rt2+zy+NkbGD98YLDIw6VF4jBjs/SMM4eNd/akm0nntiUXS/YcYJacwSBRjNOaw4xtzLxthxM3HEhjA2phTtxwI4EN6EKJxAYcOuThWs4/Y5O2bKsnrMUAruUG0BZGMIOAFkOQX3jOpBtvuPGM2bLn3PHEmT0HmyVnGODWIne8/eFnngpr2Q3n0xhv/CirTuxnbz744UNFHU4tyIBFgpENRDMCFRsQoR4ImD8w/CFO5SgYBaNgFIwsAAAyPFaRhJEGMQAAAABJRU5ErkJggg==","orcid":"","institution":"Maulana Azad National Urdu University","correspondingAuthor":true,"prefix":"","firstName":"Majid","middleName":"Ali","lastName":"Choudhary","suffix":""},{"id":409413981,"identity":"72b5bab4-22d6-463a-aa09-1617d90a4684","order_by":1,"name":"Md Ajmal Khan","email":"","orcid":"","institution":"Maulana Azad National Urdu University","correspondingAuthor":false,"prefix":"","firstName":"Md","middleName":"Ajmal","lastName":"Khan","suffix":""},{"id":409413986,"identity":"7ff8d399-83f1-4b4c-b250-3e8b64699510","order_by":2,"name":"Mohammed Arifuddin","email":"","orcid":"","institution":"Maulana Azad National Urdu University","correspondingAuthor":false,"prefix":"","firstName":"Mohammed","middleName":"","lastName":"Arifuddin","suffix":""}],"badges":[],"createdAt":"2025-01-30 11:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5929827/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5929827/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":77719296,"identity":"caa98955-076a-4710-bc70-faf47c67e2eb","added_by":"auto","created_at":"2025-03-04 15:39:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":415194,"visible":true,"origin":"","legend":"","description":"","filename":"ArticleTitle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5929827/v1_covered_26b1a1e4-951f-4adc-8786-715db1d2bc6c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A New Approach to Balance the Chemical Reaction Equations by Applying Gauss,Gauss-Jordan Methods and Cramer’s Rule and Verification of the Same by Computational Programming Softwares","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Chemical Reaction, Linear Equations, Balancing Chemical Equations, Gauss Elimination Method, Gauss-Jordan Elimination Method, Cramer’s Rule","lastPublishedDoi":"10.21203/rs.3.rs-5929827/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5929827/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study is undertaken to balance the chemical reaction, i.e., combustion of hydrocarbons, by using a system of linear equations with the Gauss and Gauss-Jordan elimination method and Cramer’s Rule. 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