A Localized Linear Substitution Algorithm for Balancing Complex Chemical Systems: Efficiency and Computational Complexity of the EFN Method

Balancing complex chemical equations, particularly high-order redox reactions, is a fundamental yet computationally demanding task in chemistry. Conventional techniques, such as the standard algebraic method and the ion-electron method, often lead to overwhelming systems of linear equations or tedious multi-step procedures that are prone to human error. This paper proposes the EFN (Efficiency-Focused Normalization) method, a streamlined algorithmic approach designed to optimize the balancing process. While the EFN method shares its foundation with the classical algebraic method, it significantly diverges by employing a selective variable assignment strategy that reduces the number of unknowns. By prioritizing key elements and using localized substitution, the EFN method minimizes mathematical complexity and accelerates the solving process, making it possible to balance highly intricate equations within minutes. The efficiency of the proposed method is validated through several complex case studies, highlighting its potential for both educational purposes and computational chemistry applications.