In an acid–base titration a solution of known concentration (the titrant) is added from a burette to a measured volume of the unknown until the reaction is exactly complete – the equivalence point, usually seen as the colour change of an indicator or the steepest jump on a pH curve. At that point the moles of H⁺ supplied by the acid equal the moles of OH⁻ supplied by the base, so the unknown concentration follows from the volumes.
The number of protons or hydroxide ions each formula unit provides matters: sulfuric acid gives two H⁺, so it needs twice as much NaOH as the same amount of HCl. The shape of the curve depends on strength. Strong acid with strong base gives an equivalence point at pH 7; a weak acid titrated with a strong base reaches equivalence above 7 (acetic acid with NaOH at about pH 8.7), and halfway there the pH equals the pKa of the acid – a classic way to measure pKa.
This calculator finds the unknown concentration, and in mixture mode it calculates the exact pH for any volumes you enter, draws the titration curve, marks the equivalence point and suggests an indicator whose colour change brackets it.
How to use the Titration Calculator
- Calculate
- Titrant (in the burette)
- Acid strength
- pKa of the acid
- Acid concentration
- Acid volume
- H⁺ donated per acid molecule
- Base strength
- pKb of the base
- Base concentration
- Base volume
- OH⁻ donated per base formula unit
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
For concentration problems the calculator applies n_a·M_a·V_a = n_b·M_b·V_b. For pH it computes the total acid and base concentrations in the combined volume and solves the charge balance exactly, including partial dissociation of weak acids (from pKa) and weak bases (from pKb) and the ionisation of water. The curve repeats this for titrant volumes up to twice the equivalence volume.
Worked example
Unknown acid: 25.0 mL of hydrochloric acid needs 21.4 mL of 0.100 M NaOH. Moles of OH⁻ = 0.100 × 0.0214 = 2.14 × 10⁻³ mol, so the acid concentration is 2.14 × 10⁻³ ÷ 0.0250 = 0.0856 M. Weak acid curve: 25.0 mL of 0.100 M acetic acid (pKa 4.76) titrated with 0.100 M NaOH reaches equivalence at 25.0 mL. After 12.5 mL the pH is 4.76 (= pKa); at 25.0 mL the solution is 0.050 M acetate and the pH is 8.73, so phenolphthalein is the right indicator.
Acid–base indicators
| Indicator | pH range | Colour change |
|---|---|---|
| Methyl orange | 3.1–4.4 | red → yellow |
| Bromocresol green | 3.8–5.4 | yellow → blue |
| Methyl red | 4.4–6.2 | red → yellow |
| Bromothymol blue | 6.0–7.6 | yellow → blue |
| Phenol red | 6.8–8.4 | yellow → red |
| Phenolphthalein | 8.2–10.0 | colourless → pink |
| Thymolphthalein | 9.3–10.5 | colourless → blue |
Tips
- Use the final volume of the solution, not the volume of solvent added, for molarity.
- For dilutions, C₁V₁ = C₂V₂ only holds when both concentrations use the same unit.
- Add acid to water, never water to acid.
- Everything is calculated in your browser.
Common mistakes to avoid
- Mixing w/w, w/v and v/v percentages.
- Forgetting that pH is logarithmic – one unit is a tenfold change in [H⁺].
- Using pKa where Ka is asked for (or the other way round).
Formula
At equivalence: n(H⁺) × M_a × V_a = n(OH⁻) × M_b × V_bUnknown acid: M_a = n(OH⁻) × M_b × V_b ÷ (n(H⁺) × V_a)Half-equivalence (weak acid): pH = pKapH from the charge balance [H⁺] + [cations] = [OH⁻] + [anions]Worked example
Inputs — Calculate: Unknown acid concentration (base titrant); Acid strength: Strong acid (HCl, HNO₃, H₂SO₄…); Acid volume: 25 mL; H⁺ donated per acid molecule: 1 (HCl, HNO₃, CH₃COOH); Base strength: Strong base (NaOH, KOH, Ba(OH)₂…); Base concentration: 0.1 mol/L (M); Base volume: 21.4 mL; OH⁻ donated per base formula unit: 1 (NaOH, KOH, NH₃).
Results — Acid concentration = 0.0856; Base concentration = 0.1; pH of the mixture = 7; Is the solution neutralized? = Yes – equivalence point reached (moles H⁺ = moles OH⁻); Titrant volume at the equivalence point = 0.0214; pH at the equivalence point = 7.
Key terms
- Titrant
- Solution of known concentration added from the burette.
- Analyte
- Solution of unknown concentration in the flask.
- Equivalence point
- Point where moles of H⁺ equal moles of OH⁻.
- End point
- Point where the indicator changes colour.
- Indicator
- Weak acid or base dye whose colour depends on pH.
Frequently asked questions
How do I calculate molarity from a titration?
M_a = M_b × V_b ÷ V_a for a 1:1 reaction. If 21.4 mL of 0.100 M NaOH neutralizes 25.0 mL of HCl, the acid is 0.100 × 21.4 ÷ 25.0 = 0.0856 M.
How do I account for sulfuric acid?
Each H₂SO₄ gives two H⁺, so set "H⁺ donated" to 2: M_a = M_b × V_b ÷ (2 × V_a).
What is the pH at the equivalence point?
7 for strong acid + strong base; above 7 for a weak acid + strong base (about 8.7 for 0.1 M acetic acid); below 7 for a weak base + strong acid.
Why is pH = pKa at half-equivalence?
Half the weak acid has been converted to its conjugate base, so [HA] = [A⁻] and the Henderson–Hasselbalch equation gives pH = pKa.
Which indicator should I use?
One whose colour-change range contains the equivalence pH: phenolphthalein (8.2–10.0) for weak acids with NaOH, methyl orange (3.1–4.4) or methyl red (4.4–6.2) for weak bases with strong acids, bromothymol blue for strong–strong titrations.
What is the difference between the equivalence point and the end point?
The equivalence point is where the stoichiometric amounts have reacted; the end point is where the indicator changes colour. A well-chosen indicator makes them almost the same.
Can I titrate a weak acid with a weak base?
It can be calculated, but the pH jump is small and gradual, so the end point is hard to see – that is why titrants are almost always strong acids or bases.
What formula does the Titration Calculator use?
At equivalence: n(H⁺) × M_a × V_a = n(OH⁻) × M_b × V_b.