Proofwell
Menu

Chemical Equation Balancer

Type an unbalanced equation and get the smallest whole-number coefficients, with an atom count to prove it balances. It handles ions, electrons and redox reactions in acidic or basic solution, and shows which elements are oxidised and reduced.

Chemistry · ReactionsUpdated Sources cited

Separate species with + and use -> or = for the arrow. Write charges with ^ (Fe^3+, SO4^2-) and electrons as e-.
Reaction medium
Examples:

Result

Balanced

2KMnO₄ + 16HCl → 2KCl + 2MnCl₂ + 8H₂O + 5Cl₂

ElementReactantsProducts
K22 ✓
Mn22 ✓
O88 ✓
H1616 ✓
Cl1616 ✓

Redox reaction

Cl is oxidised: −1 → 0 (in Cl₂)

Mn is reduced: +7 → +2 (in MnCl₂)

Electrons transferred: 10

Oxidation states in each species
  • KMnO₄: K +1, Mn +7, O −2
  • HCl: H +1, Cl −1
  • KCl: K +1, Cl −1
  • MnCl₂: Mn +2, Cl −1
  • H₂O: H +1, O −2
  • Cl₂: Cl 0
Assumptions behind this result
  • Species are taken exactly as written; state symbols such as (aq) are ignored for balancing.

Step-by-step solution

  1. Assign an unknown coefficient to each species

    Write a coefficient in front of every formula.

    a KMnO4+b HCl+c KCl+d MnCl2+e H2O+f Cl2a\,\mathrm{KMnO_{4}} + b\,\mathrm{HCl} + c\,\mathrm{KCl} + d\,\mathrm{MnCl_{2}} + e\,\mathrm{H_{2}O} + f\,\mathrm{Cl_{2}}

  2. Write a conservation equation for each element

    The number of atoms of each element must be the same on both sides.

    K:a=cMn:a=dO:4a=eH:b=2eCl:b=c+2d+2f\begin{aligned} \text{K}: a &= c \\ \text{Mn}: a &= d \\ \text{O}: 4a &= e \\ \text{H}: b &= 2e \\ \text{Cl}: b &= c + 2d + 2f \end{aligned}

  3. Solve the equations exactly

    The system has a single family of solutions. Choosing the smallest whole numbers gives a = 2, b = 16, c = 2, d = 2, e = 8, f = 5.

    2KMnO4+16HCl→2KCl+2MnCl2+8H2O+5Cl22\mathrm{KMnO_{4}} + 16\mathrm{HCl} \rightarrow 2\mathrm{KCl} + 2\mathrm{MnCl_{2}} + 8\mathrm{H_{2}O} + 5\mathrm{Cl_{2}}

  4. Check that every element balances

    Counting atoms on each side gives the same totals for every element.

    K:2=2Mn:2=2O:8=8H:16=16Cl:16=16\begin{aligned} \text{K}: 2 &= 2 \\ \text{Mn}: 2 &= 2 \\ \text{O}: 8 &= 8 \\ \text{H}: 16 &= 16 \\ \text{Cl}: 16 &= 16 \end{aligned}

  5. Identify oxidation and reduction

    Cl is oxidised from −1 to 0 (in Cl₂); Mn is reduced from +7 to +2 (in MnCl₂). In the balanced equation, 10 electrons are transferred.

What the balancer does

  • Finds the smallest whole-number coefficients that conserve every element and the total charge.
  • Adds H₂O and H⁺ (acidic) or H₂O and OH⁻ (basic) for redox reactions in solution, on whichever side they are needed.
  • Shows an atom count for each side as proof.
  • Gives the oxidation state of each element in every species, and identifies redox changes and the electrons transferred.
  • Explains why an equation cannot be balanced, when that happens.

How to enter an equation

Separate species with + and use ->, → or = for the arrow. Write charges with ^ (Fe^3+, SO4^2-), or simply NH4+ and OH-, and electrons as e-. State symbols such as (aq) and (s) are ignored.

How balancing works

Give each species an unknown coefficient. For every element, the atoms on the left must equal the atoms on the right. For propane burning, a C₃H₈ + b O₂ → c CO₂ + d H₂O:

C:  3a=cH:  8a=2dO:  2b=2c+d\begin{aligned} \text{C}: \; 3a &= c \\ \text{H}: \; 8a &= 2d \\ \text{O}: \; 2b &= 2c + d \end{aligned}

This is a system of linear equations with no constant terms. Its solutions form a family, and the smallest whole numbers in that family are the balanced coefficients. The balancer solves the system exactly, without trial and error. That approach also tells it when there is no solution or more than one independent solution.

For ionic equations, the total charge on each side gives one more equation.

Worked example: combustion of propane

  1. Carbon: c = 3a. Hydrogen: d = 4a.
  2. Oxygen: 2b = 2(3a) + 4a = 10a, so b = 5a.
  3. Smallest whole numbers: a = 1 gives b = 5, c = 3, d = 4.

The balanced equation is C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. Check: 3 C, 8 H and 10 O on each side.

Common mistakes

  • Changing subscripts instead of coefficients. Changing H₂O to H₂O₂ changes the substance; only the coefficients may change.
  • Forgetting the charge in ionic equations. Atoms can balance while charge does not.
  • Leaving fractional coefficients. ½O₂ is fine in thermochemistry, but a standard balanced equation uses whole numbers.
  • Writing a wrong product formula, such as NaCl₂, which makes balancing impossible or misleading.

Practical applications

  • Stoichiometry. Mole ratios for yield calculations come from the balanced coefficients.
  • Titrations. The 5 : 1 ratio of Fe²⁺ to MnO₄⁻ is the basis of a classic redox titration.
  • Combustion and fuels. Balanced equations give the oxygen needed and the CO₂ produced.
  • Electrochemistry. Balanced half-equations give the electrons transferred in batteries and electrolysis.

Assumptions and limitations

Species are used exactly as entered; the balancer does not predict products. It finds a balanced form whenever one exists. When the species describe several independent reactions it says so, instead of choosing one of the infinitely many answers.

Frequently asked questions

Why do some equations have no balanced form?

If an element appears on only one side, or the species given cannot be combined to conserve every element, no coefficients work. This usually means a formula is wrong or a product is missing, and the balancer tells you which element is the problem.

What does "balanced in infinitely many ways" mean?

Some lists of species contain two or more independent reactions, such as H₂ + O₂ → H₂O + H₂O₂, which combines the formation of water and of hydrogen peroxide. Any mixture of the two is balanced, so there is no single answer. Split the equation into separate reactions.

When should I choose acidic or basic solution?

Choose one when balancing a redox reaction in water where H₂O, H⁺ or OH⁻ take part but you have not written them. The balancer adds them and decides which side each belongs on.

Does a balanced equation mean the reaction happens?

No. Balancing only ensures that atoms and charge are conserved. Whether a reaction actually occurs depends on thermodynamics and kinetics.

Why does the balancer ignore the coefficients I typed?

It always balances from scratch, so a mistake in a typed coefficient cannot carry through. It tells you when it has done this.

References

  1. Atkins, P., Jones, L. & Laverman, L. (2016). Chemical Principles (7th ed.), Fundamentals sections H and K. W. H. Freeman.
  2. Smith, W. R. & Missen, R. W. (1979). What is chemical stoichiometry? Chemical Engineering Education, 13(1), 26–32.
  3. Strang, G. (2016). Introduction to Linear Algebra (5th ed.), section 3.2 (the null space). Wellesley-Cambridge Press.

Related calculators

Chemistry

Stoichiometry Calculator

Limiting reactant, excess left over, and theoretical and percentage yield from any reaction.

Chemistry

Oxidation State Calculator

Oxidation states of every element in a compound or ion, with the rule behind each one.

Chemistry

Molar Mass Calculator

Molar mass and percent composition of any formula, including brackets, hydrates and ions.

Mathematics

System of Linear Equations Solver

Solve simultaneous linear equations by Gaussian or Gauss–Jordan elimination, with every row operation shown.