Titration Calculator
Find an unknown acid or base concentration from the titrant volume at the equivalence point.
Mole ratio 1:1 (titrant:analyte). Volumes in mL cancel in the ratio — no conversion needed.
At the equivalence point the moles of H⁺ and OH⁻ are equal, so Mₐ·Vₐ·nₐ = M_b·V_b·n_b. If 20 mL of 0.1 M NaOH neutralizes 25 mL of a monoprotic acid (1:1), then M_acid = (0.1 × 20) ÷ 25 = 0.08 M. Volumes in mL cancel, so no unit conversion is needed.
What a titration measures
A titration finds an unknown concentration by reacting it with a solution of known concentration — the titrant — added until the reaction is exactly complete. For an acid–base titration, that equivalence point is where the moles of H⁺ donated equal the moles of OH⁻ available, so neither reactant is left over.
Counting moles is the whole trick: moles = molarity × volume. The factor n accounts for how many H⁺ or OH⁻ each formula unit contributes — 1 for a monoprotic acid like HCl, 2 for a diprotic acid like H₂SO₄.
At the equivalence point; n is the number of H⁺ (acid) or OH⁻ (base) per formula unit
Worked example
20 mL of 0.1 M NaOH neutralizes 25 mL of an unknown monoprotic acid. Find the acid’s concentration.
- 1 Write the equivalence-point balance. Moles of base = moles of acid: M_b · V_b · n_b = Mₐ · Vₐ · nₐ. Here both are monoprotic, so nₐ = n_b = 1.
- 2 Rearrange for the unknown. Mₐ = (M_b × V_b × n_b) ÷ (Vₐ × nₐ). The known titrant values go on top.
- 3 Substitute the numbers. Mₐ = (0.1 × 20 × 1) ÷ (25 × 1). The mL units cancel because they appear on both sides.
- 4 Compute. Mₐ = 2 ÷ 25 = 0.08 mol/L — the acid is 0.08 M.
Rearranging the titration equation
Mₐ·Vₐ·nₐ = M_b·V_b·n_b. Volumes may stay in mL as long as both sides use the same unit.
| Solve for | Rearrangement | Note |
|---|---|---|
| Unknown acid molarity | Mₐ = (M_b × V_b × n_b) ÷ (Vₐ × nₐ) | Most common case |
| Unknown base molarity | M_b = (Mₐ × Vₐ × nₐ) ÷ (V_b × n_b) | Swap which side is known |
| Titrant volume needed | V_b = (Mₐ × Vₐ × nₐ) ÷ (M_b × n_b) | Predict the burette reading |
| Diprotic acid (e.g. H₂SO₄) | nₐ = 2 | Each acid unit gives 2 H⁺ |
Equivalence point vs endpoint
The equivalence point is the theoretical instant where moles of acid and base match exactly. The endpoint is what you actually observe — usually the colour change of an indicator. A well-chosen indicator changes colour right at the equivalence point, so the two nearly coincide; a poorly matched one introduces a small titration error.
Polyprotic acids. Acids like H₂SO₄ (diprotic) or H₃PO₄ (triprotic) release more than one H⁺, so set n to the number released in the reaction. With n = 2, twice as much base is needed for the same amount of acid. Multi-step titrations can even show more than one endpoint, one per dissociation.