If you know the concentration of one solution, and the volumes of two solutions that react completely together, you can find the concentration of the other. There are three steps. First, moles of the known solution = concentration (mol/dm3) × volume (dm3). Second, use the balanced equation to find the moles of the other substance from the ratio. Third, concentration = moles ÷ volume (dm3).
Example: 25.0 cm3 of sodium hydroxide is neutralised by 20.0 cm3 of 0.10 mol/dm3 hydrochloric acid. The equation is HCl + NaOH → NaCl + H2O, so one mole of acid reacts with one mole of alkali and the moles are equal. Moles of HCl = 0.10 × 0.0200 = 0.0020 mol. So moles of NaOH = 0.0020 mol. Concentration of NaOH = 0.0020 ÷ 0.0250 = 0.080 mol/dm3.
The ratio is not always 1 : 1. In H2SO4 + 2NaOH → Na2SO4 + 2H2O, one mole of sulfuric acid reacts with two moles of sodium hydroxide, so the moles of alkali are double the moles of acid. The same method can find an unknown volume, using volume = moles ÷ concentration.