How to balance chemical equations

The short version

1. Write the unbalanced equation with the correct formula for every substance.
2. Count the atoms of each element on both sides.
3. Add coefficients in front of formulas, never change subscripts, until every element matches.
4. Check and reduce recount every element and make sure the coefficients are the smallest whole numbers.

Example: burning propane

Unbalanced: C₃H₈ + O₂ → CO₂ + H₂O. Balance carbon, then hydrogen, then oxygen last.

A strategy that works

• Balance elements that appear in only one substance on each side first.
• Leave oxygen and hydrogen until last, since they often appear in several substances.
• If a polyatomic ion such as SO₄ or OH appears unchanged on both sides, balance it as one unit instead of counting its atoms.
• If you end up with a half (such as ½O₂), double every coefficient to clear it.

Never change the subscripts

Subscripts say what a substance is: H₂O is water, H₂O₂ is hydrogen peroxide. Changing a subscript changes the substance. Only coefficients, the numbers in front, can be adjusted.

When trial and error fails: the algebra method

Give every substance a letter for its coefficient and write one equation per element saying atoms in equals atoms out. For propane: a C₃H₈ + b O₂ → c CO₂ + d H₂O gives carbon 3a = c, hydrogen 8a = 2d, oxygen 2b = 2c + d. Set a = 1 and solve: c = 3, d = 4, b = (6 + 4) ÷ 2 = 5. This always works, even for equations with many substances such as KMnO₄ + HCl → KCl + MnCl₂ + H₂O + Cl₂ (2, 16, 2, 2, 8, 5), and is how the balancer on this site works.

Mistakes to avoid

• Changing subscripts instead of adding coefficients.
• Balancing a polyatomic ion's atoms separately when it should stay together.
• Stopping when atoms match but the coefficients can still be reduced.
• Writing the wrong formula for a substance, which makes the equation impossible to balance.