Finding an unknown concentration
A titration measures the concentration of a solution, the analyte, by adding a solution of known concentration, the titrant, from a burette until the reaction is complete. The moment when the amounts match the balanced equation exactly is the equivalence point. Acid-base, redox and complexation titrations all follow the same arithmetic.
The formulas
- Moles of titrant = titrant concentration × volume at equivalence (in L)
- Moles of analyte = moles of titrant × mole ratio (analyte : titrant)
- Analyte concentration = moles of analyte ÷ analyte volume (in L)
For a 1:1 reaction this reduces to the familiar C₁V₁ = C₂V₂.
Worked example
20.00 mL of hydrochloric acid is titrated with 0.100 mol/L sodium hydroxide. The indicator changes color after 25.00 mL.
- Moles of NaOH = 0.100 × 0.02500 = 2.50 mmol.
- HCl + NaOH → NaCl + H₂O is 1:1, so moles of HCl = 2.50 mmol.
- [HCl] = 2.50 mmol ÷ 20.00 mL = 0.125 mol/L.
- With a molar mass of 36.46 g/mol, that is 4.56 g/L, or 91.2 mg of HCl in the sample.
Mole ratios
| Reaction | Analyte : titrant |
|---|---|
| HCl + NaOH | 1 : 1 |
| H₂SO₄ + 2 NaOH (acid titrated) | 1 : 2 |
| 2 NaOH + H₂SO₄ (base titrated) | 2 : 1 |
| 5 Fe²⁺ + MnO₄⁻ + 8 H⁺ | 5 : 1 |
Always write and balance the equation first; the ratio comes straight from its coefficients.
Detecting the equivalence point
- Indicators change color over a pH range. Phenolphthalein (8.2 to 10) suits weak acids titrated with strong bases; methyl orange (3.1 to 4.4) suits weak bases titrated with strong acids.
- pH meter: plot pH against volume; the equivalence point is at the steepest part of the curve, found by the derivative or the tangent method.
- Self-indicating titrants: permanganate is purple and turns colorless as it reacts, so the first lasting pink tint marks the end point.
Good practice
- Rinse the burette with titrant and the pipette with analyte before use.
- Do a rough titration first, then at least two precise ones that agree within 0.1 mL.
- Read the burette at eye level at the bottom of the meniscus.
- Standardize sodium hydroxide against a primary standard such as potassium hydrogen phthalate, because NaOH absorbs CO₂ and water from the air.
Half-equivalence
For a weak acid, the pH at half the equivalence volume equals its pKa, which is a simple way to measure pKa from a titration curve.