Balancing chemical equations

Hydrogen and oxygen make water only in the ratio 2 : 1 : 2, because one O₂ molecule carries enough oxygen for two water molecules.

Write hydrogen burning as H₂ + O₂ → H₂O and count. On the left there are two hydrogen atoms and two oxygen atoms. On the right there are two hydrogen atoms but only one oxygen atom. One oxygen atom has gone missing, which cannot happen. An equation that obeys the conservation of matter must have the same number of atoms of each element on both sides. Such an equation is called balanced.

Change coefficients, never subscripts

There is a tempting shortcut: change H₂O to H₂O₂ and the oxygen balances at once. But H₂O₂ is hydrogen peroxide, a different substance, so the equation would now describe a reaction that is not happening. Subscripts belong to the identity of each substance. The only numbers you may change are the coefficients. Put a 2 in front of H₂O and the right side now has 4 hydrogen and 2 oxygen atoms. Oxygen is fixed, hydrogen is not, so put a 2 in front of H₂ as well: 2H₂ + O₂ → 2H₂O. Four hydrogen and two oxygen on each side.

Balancing by inspection

Most school equations can be balanced by inspection, which means trying coefficients in a sensible order and counting after each change. A few habits make it quicker. Start with an element that appears in only one substance on each side. Leave elements that appear on their own, such as O₂, H₂ or Fe, until last, because changing their coefficient affects nothing else. If a group of atoms such as NO₃ or SO₄ goes through the reaction unchanged, count it as one unit. Finally, check every element again and make sure the coefficients are the smallest whole numbers possible.

Try propane, a fuel sold in camping gas cylinders, often mixed with butane: C₃H₈ + O₂ → CO₂ + H₂O. Carbon first: three carbon atoms on the left need 3CO₂. Hydrogen next: eight hydrogen atoms need 4H₂O. Now count oxygen on the right: 3 × 2 + 4 × 1 = 10 atoms, so the left needs 5O₂. The balanced equation is C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. OpenStax works through nitrogen and oxygen forming dinitrogen pentoxide the same way and arrives at 2N₂ + 5O₂ → 2N₂O₅.

When fractions appear

Sometimes the quickest route gives a fraction. Burning hydrogen to make one mole of water can be written H₂ + ½O₂ → H₂O, and tables of combustion energies often use this form because they are quoted per mole of fuel. To turn it into whole numbers, multiply every coefficient by 2. The same trick works for ethanol: C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O is already whole, but iron rusting worked out as 2Fe + 1½O₂ → Fe₂O₃ becomes 4Fe + 3O₂ → 2Fe₂O₃.

The lab reports when an equation is balanced but not in lowest terms. 4H₂ + 2O₂ → 4H₂O is balanced, yet every coefficient can be divided by 2, so the accepted form is 2H₂ + O₂ → 2H₂O. Both describe the same ratio; the smaller set is simply the convention.