A Vector-Based Algorithm for Generating Complete Balanced Reaction Sets with Arbitrary Numbers of Reagents

TL;DR

This paper introduces a vector-based algorithm for automatically balancing chemical reactions, capable of handling complex cases like redox and providing clear, minimal integer coefficients without special-case rules.

Contribution

The paper presents a novel geometric vector formulation for reaction balancing that is deterministic, general, and supports visualizations and extensions beyond traditional methods.

Findings

Successfully balances various reaction types including redox and displacement

Produces minimal integer coefficients and handles multiple solutions consistently

Provides a foundation for future algorithmic improvements and reaction network analysis

Abstract

We present a vector-based method to balance chemical reactions. The algorithm builds candidates in a deterministic way, removes duplicates, and always prints coefficients in the lowest whole-number form. For redox cases, electrons and protons/hydroxide are treated explicitly, so both mass and charge are balanced. We also outline the basic principles of the vector formulation of stoichiometry, interpreting reactions as integer vectors in composition space, this geometric view supports compact visualizations of reagent-product interactions and helps surface distinct reaction families. The method enumerates valid balances for arbitrary user-specified species lists without special-case balancing rules or symbolic tricks, and it provides a clean foundation for developing new algorithmic variants (e.g., alternative objectives or constraints). On representative examples (neutralization, double displacement, decomposition, classical redox, small multicomponent sets) and a negative control, the method produced correct integer balances. When multiple balances exist, we report a canonical one - minimizing the total coefficient sum with a simple tie-breaker - without claiming global optimality beyond the solutions the search enumerates. The procedure applies per reaction and extends to reaction networks via consistent per-reaction application. We do not report runtimes, broader benchmarking and code/data release are planned.