Titration: Concentration of an Unknown

At the equivalence point the moles of titrant delivered, CbVb, exactly match the moles of analyte present, CaVa, scaled by the balanced equation's mole ratio n. Everything else in a titration — the burette, the indicator, the swirling — exists only to find that point precisely. Titrate a 25.00 mL aliquot of hydrochloric acid with 0.1000 M sodium hydroxide and take 23.45 mL to reach the endpoint: with n = 1, Ca = (1 × 0.1000 × 23.45)/25.00 = 0.09380 M, good to four figures from nothing but glassware.

The mole ratio is where marks are lost. For a diprotic acid such as H₂SO₄ titrated with NaOH, one mole of acid consumes two of base, so n = 0.5: a 25.00 mL aliquot needing 30.00 mL of 0.100 M NaOH is 0.5 × 0.100 × 30.00/25.00 = 0.0600 M. Karl Friedrich Mohr systematised the whole technique in his 1855 Lehrbuch der chemisch-analytischen Titrirmethode, introducing the burette clamp and the pinchcock that made reproducible volumetric analysis possible; his methods still underpin water-hardness and chlorine testing today. Note the difference between the endpoint (where the indicator changes) and the equivalence point (where the stoichiometry balances) — the gap between them is the indicator error, which is why the indicator is chosen to change colour on the steep part of the titration curve.