About

In quantitative chemistry, precision is binary: an equation is either perfectly balanced, or it is useless. This tool transcends simple "guess-and-check" methods by employing a deterministic Algebraic Matrix Solver. Whether you are calculating industrial yields or solving complex redox half-reactions for a thesis, this engine guarantees adherence to the Law of Conservation of Mass.

Why this tool is different: Unlike basic calculators that simply output coefficients, this application includes a full Stoichiometry Suite. It automatically calculates Molar Masses, identifies reaction types (Synthesis, Decomposition, Combustion), and - if you provide masses - determines the Limiting Reagent and theoretical yield instantly. It supports polyatomic ions (e.g., SO4^2-) and provides a visualization of the molecular geometry.

Formulas

The core algorithm converts chemical symbols into a linear algebra problem Ax = 0. We define the conservation vector for every element E as:

n∑j=1 c_j ⋅ a_ij = 0

Where c_j is the stoichiometric coefficient for compound j, and a_ij is the number of atoms of element i in compound j (positive for reactants, negative for products). The solver computes the Null Space of this matrix to find the integer coefficients.

Reference Data

Reaction Category	Equation Example	Stoichiometric Ratios	Technique Used
Hydrocarbon Combustion	C₃H₈ + O₂ → CO₂ + H₂O	1 : 5 : 3 : 4	CH-O Balancing Method
Double Displacement	Pb(NO₃)₂ + KI → PbI₂ + KNO₃	1 : 2 : 1 : 2	Ion Exchange Tracking
Synthesis (Redox)	Fe + O₂ → Fe₂O₃	4 : 3 : 2	Electron Transfer / LCM
Decomposition	KClO₃ → KCl + O₂	2 : 2 : 3	Oxygen Balance
Acid-Base Neutralization	H₂SO₄ + NaOH → Na₂SO₄ + H₂O	1 : 2 : 1 : 2	Proton Transfer
Complex Ion / Redox	MnO₄^- + Fe²⁺ + H⁺ → Mn²⁺ + Fe³⁺ + H₂O	1 : 5 : 8 : 1 : 5 : 4	Half-Reaction Method (Charge Balance)

Frequently Asked Questions

Algebraically, the solution to a chemical matrix often yields fractions. However, standard chemistry convention requires "Whole Number Integers." Our algorithm finds the Lowest Common Multiple (LCM) of all denominators and multiplies the entire equation by that number to ensure the final result is clean and standard-compliant.

Yes. After balancing the equation, switch to the "Stoichiometry" tab. Enter the mass (in grams) for your reactants. The tool will calculate moles, compare the mole ratios to the balanced coefficients, and highlight exactly which reactant will run out first and how much product will be formed.

Absolutely. Use the caret symbol (^) for charges. Example: `Fe^3+ + e^- -> Fe^2+`. The solver treats "Charge" as a distinct element that must be conserved between the left and right sides of the equation.

This means you are trying to create matter that doesn't exist (Alchemy). For example, if you input `H2 + O2 -> Au` (Gold), the system cannot balance Hydrogen or Oxygen against Gold. Check that every element on the left appears on the right.