Balance Chemical Equation Calculator

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Reviewed by: David Chen, PhD in Chemical Engineering

Use this tool to automatically balance complex chemical equations by solving the underlying system of linear algebraic equations based on the conservation of mass (atoms).

Balance Chemical Equation Calculator

Enter an equation and click ‘Calculate’ to see the balanced result.

Detailed Balancing Steps

Steps will appear here after a successful calculation.

Chemical Equation Balancing Formula

Chemical equations are balanced based on the principle of the conservation of atoms (mass). This calculator uses a matrix algebra method to solve the system of linear equations derived from the count of each element on both sides of the reaction.

Reactants Atoms Matrix (R) $\times$ Coefficients Vector (X) = Products Atoms Matrix (P) $\times$ Coefficients Vector (Y)

For a generic reaction $C_1 + C_2 \rightarrow C_3 + C_4$ with coefficients $x_1, x_2, x_3, x_4$, and elements $E_1, E_2, \dots, E_m$:

$\sum_{i \in \text{Reactants}} (\text{Atoms}(E_j, C_i) \cdot x_i) = \sum_{k \in \text{Products}} (\text{Atoms}(E_j, C_k) \cdot x_k)$
Source 1: LibreTexts Chemistry – Balancing Equations Source 2: IUPAC Gold Book – Chemical Reaction

Variables (Inputs)

  • Unbalanced Chemical Equation: The string representation of the reaction, separated by ‘+’ (plus) for compounds and ‘=’ (equals) for reactants/products boundary. Elements must be correctly capitalized (e.g., ‘O’ not ‘o’, ‘Fe’ not ‘fE’).

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What is Chemical Equation Balancing?

Balancing a chemical equation is the process of ensuring that the number of atoms of each element is the same on both the reactant side (left) and the product side (right) of the reaction arrow. This is a fundamental requirement rooted in the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.

The balancing process involves placing integer coefficients in front of the chemical formulas. These coefficients represent the relative number of molecules or formula units involved in the reaction. Finding the correct, simplest set of whole-number coefficients is the goal of balancing.

How to Balance a Chemical Equation (Example: $C_2H_5OH + O_2 \rightarrow CO_2 + H_2O$)

  1. Identify the compounds: Reactants are $C_2H_5OH$ and $O_2$. Products are $CO_2$ and $H_2O$.
  2. List the elements: C, H, and O.
  3. Set up algebraic equations: Assign variables ($x_1, x_2, x_3, x_4$) to the coefficients.
    • C: $2x_1 = 1x_3$
    • H: $6x_1 = 2x_4$ (5+1=6 H atoms in $C_2H_5OH$)
    • O: $1x_1 + 2x_2 = 2x_3 + 1x_4$
  4. Solve the system: Set $x_1 = 1$ to find the relative integers.
    • $x_3 = 2(1) = 2$
    • $2x_4 = 6(1) \implies x_4 = 3$
    • $1(1) + 2x_2 = 2(2) + 1(3) \implies 1 + 2x_2 = 7 \implies 2x_2 = 6 \implies x_2 = 3$
  5. Write the balanced equation: The coefficients are 1, 3, 2, 3. Balanced equation: $C_2H_5OH + 3O_2 \rightarrow 2CO_2 + 3H_2O$.

Frequently Asked Questions (FAQ)

Why must chemical equations be balanced?
They must be balanced to satisfy the Law of Conservation of Mass, ensuring that all atoms are accounted for and converted, but not created or destroyed, during the reaction.
Can coefficients be fractions?
While the algebraic solution may yield fractions, the final coefficients in a balanced equation must be the lowest possible set of whole numbers. If fractions occur, you multiply the entire equation by the denominator to clear them.
Is the state of matter (s, l, g, aq) required for balancing?
No. The state symbols (e.g., (s) for solid) are important for describing the reaction but do not affect the stoichiometric coefficients needed for balancing.
What is the difference between a coefficient and a subscript?
A coefficient is a large number placed *in front* of a compound (it changes the number of molecules). A subscript is a small number *within* a compound (it changes the number of atoms in that molecule) and cannot be altered when balancing.
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