The formula
- Moles delivered by the buret
n(titrant) = M(titrant) × V(titrant)- Equivalence point, through the balanced equation
n(analyte) = n(titrant) × (coefficient of analyte / coefficient of titrant)- Unknown concentration
M(analyte) = n(analyte) / V(analyte)- Monoprotic acid against monoprotic base, one step
M_a·V_a = M_b·V_b
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
M(titrant), M_b | Known concentration of the solution in the buret | M |
V(titrant), V_b | Volume of titrant delivered to reach the end point | L |
M(analyte), M_a | Unknown concentration being measured | M |
V(analyte), V_a | Volume of the analyte sample taken | L |
n | Moles of titrant or analyte | mol |
coefficient | Stoichiometric coefficient of the analyte or titrant in the balanced neutralization equation | dimensionless |
When it applies
- The reaction is fast, complete and of known stoichiometry, which is why strong acid against strong base is the standard classroom case.
- The one-step M_a·V_a = M_b·V_b shortcut assumes a 1:1 reaction. Sulfuric acid against sodium hydroxide is 1:2, and the coefficients have to be carried through instead.
- The end point, where the indicator changes, is taken as the equivalence point, where the reaction is stoichiometrically complete. A well-chosen indicator makes the gap negligible.
- For a strong acid against a strong base the equivalence point is pH 7.00, but for a weak acid against a strong base it lands above 7, so the indicator has to match the system.
Worked example
Problem. A 25.00 mL sample of hydrochloric acid of unknown concentration requires 32.15 mL of 0.1000 M sodium hydroxide to reach the end point. What is the concentration of the acid?
- Write the reaction: HCl + NaOH → NaCl + H₂O. The coefficients are 1:1, so moles of base equal moles of acid at the equivalence point.
- Convert the titrant volume to liters and find its moles: n(NaOH) = 0.03215 L × 0.1000 M = 3.215 × 10⁻³ mol.
- Apply the 1:1 ratio: n(HCl) = 3.215 × 10⁻³ mol in the 25.00 mL sample.
- Divide by the sample volume in liters: M(HCl) = 3.215 × 10⁻³ / 0.02500 = 0.1286 M.
Answer. 0.1286 M hydrochloric acid, to four significant figures, matching the precision of the buret reading.
Common mistakes
- Leaving volumes in milliliters while concentrations are in moles per liter, which throws the moles out by a factor of a thousand.
- Using M_a·V_a = M_b·V_b on a reaction that is not 1:1. A diprotic acid needs twice the base, and the shortcut halves the answer.
- Dividing by the titrant volume instead of the analyte volume at the last step. The unknown concentration belongs to the sample in the flask.
- Assuming every equivalence point is at pH 7. That is true only when both the acid and the base are strong.
Related formulas
- pH formula:
pH = -log[H₃O⁺] - Henderson-Hasselbalch equation:
pH = pKa + log([A⁻] / [HA]) - Molarity formula:
M = mol solute / L solution