How to Use This Balancing Equations Calculator
- Arrow:
->,=, or → between reactants and products, and+between substances. - Formulas: capital letters matter (Co is cobalt, CO is carbon monoxide). Parentheses, brackets, and hydrates such as CuSO4·5H2O all work.
- Charges: write Fe^3+, SO4^2-, or MnO4^-. Na+, Cl-, NH4+, and single-element ions such as Fe3+ or Ca2+ are also read correctly. Write electrons as e-.
- States: (s), (l), (g), and (aq) are kept in the answer. Any coefficients you type are checked, then ignored.
How the Calculator Balances an Equation With Algebra
Every element gives one equation, because the number of its atoms must be the same on both sides. For iron rusting, a Fe + b O2 → c Fe2O3:
- Fe: a = 2c
- O: 2b = 3c
Setting c = 1 gives a = 2 and b = 3/2. Multiplying all three by 2 clears the fraction: 4 Fe + 3 O2 → 2 Fe2O3, with 4 Fe and 6 O on each side. The calculator solves the same kind of system with exact fractions, so it never rounds, and it can balance long equations with eight or more substances that are hard to do by trial and error.
Balancing by Inspection on the AP Exam
On the exam you balance by inspection: adjust one coefficient at a time, starting with the element that appears in the fewest formulas and leaving hydrogen and oxygen for last. Polyatomic ions that stay intact, such as SO42−, can be counted as one unit. The method is worked through with four examples and practice problems in AP Chemistry balancing equations; use the calculator to check your answers. Once an equation is balanced, its coefficients give the mole ratios for stoichiometry and the percent yield calculator.
How to Balance Ionic and Redox Equations by Charge
The AP course describes balanced equations as showing that both mass and charge are conserved. When ions are involved, total charge is one more equation to satisfy. For permanganate oxidizing iron(II) in acid:
MnO4− + 5 Fe2+ + 8 H+ → Mn2+ + 5 Fe3+ + 4 H2O
Total charge on the left is (−1) + 5(+2) + 8(+1) = +17, and on the right (+2) + 5(+3) = +17. Without the charge equation, MnO4− + Fe2+ + 8 H+ → Mn2+ + Fe3+ + 4 H2O would look balanced in atoms but not in charge. For writing these equations from scratch, see the half-reaction method and net ionic equations.
Why Some Equations Cannot Be Balanced
- An element appears on only one side. A formula is mistyped or a product is missing, for example NaCl → Na with no chlorine product.
- A substance is on the wrong side. H2O2 + O2 → H2O only balances with O2 as a product.
- There is more than one answer. H2 + O2 → H2O + H2O2 combines two reactions, so the ratio of water to peroxide is not fixed.
Balancing equations is one skill among many on the exam. To see how your practice scores across all nine units translate into a 1–5 estimate, use the AP Chem Score Calculator.
Related Resources
- AP Chem Score Calculator
- All AP Chemistry Calculators
- AP Chemistry Balancing Equations
- How to Write Net Ionic Equations
- How to Balance Redox Equations Using Half-Reactions
- AP Chemistry Stoichiometry
- Percent Yield Calculator
- Unit 4 Review: Chemical Reactions
Frequently Asked Questions
How do you balance a chemical equation?
Change only the coefficients in front of each formula until every element has the same number of atoms on both sides. Start with the element that appears in the fewest formulas, leave hydrogen and oxygen for last, and finish by reducing the coefficients to the smallest whole numbers.
What does it mean for an equation to be balanced?
It has the same number of atoms of every element on both sides of the arrow, and the same total charge. Atoms are rearranged in a reaction, not created or destroyed, so a balanced equation shows that mass and charge are conserved.
Can you change subscripts to balance an equation?
No. Subscripts are part of the formula, so changing H2O to H2O2 turns water into hydrogen peroxide, a different substance. Only the coefficients in front of the formulas can change.
How do you balance an ionic or redox equation?
Balance the atoms first, then make the total charge the same on both sides. For example, MnO4^- + 5 Fe^2+ + 8 H^+ -> Mn^2+ + 5 Fe^3+ + 4 H2O has a total charge of +17 on each side. For longer redox reactions, balancing the oxidation and reduction half-reactions separately is usually easier.
Why can’t my equation be balanced?
Usually a formula is wrong or a substance is missing, so some element appears on only one side. An equation can also fail if a substance is on the wrong side of the arrow, or if two separate reactions are written together, which allows more than one set of coefficients.
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