Titration calculator
Enter the titrant concentration, the volume used to reach the endpoint and the volume of the sample to get the sample’s concentration. Or switch to the equivalence volume to see how much titrant a sample of known concentration will need. Coefficients from the balanced equation handle acids like H₂SO₄, and a pKa gives the pH at the equivalence point.
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How to use it
- Choose what to find: the analyte concentration (you know the titrant volume used) or the equivalence volume (you know the analyte concentration).
- Enter the titrant concentration in mol/L and the volumes in mL.
- Set the coefficients from the balanced equation (1 and 1 for HCl + NaOH).
- Pick the acid–base pair. For a weak acid or base, enter its pKa to see the pH at the equivalence and half-equivalence points.
How it works
At the equivalence point:
n(analyte) ÷ a = n(titrant) ÷ b, with n = C × V.
- Analyte concentration: C(a) = C(t) × V(t) × a ÷ (b × V(a))
- Equivalence volume: V(t) = C(a) × V(a) × b ÷ (a × C(t))
For the pH at equivalence the salt concentration is c = n(analyte) ÷ (V(a) + V(t)). A weak acid’s anion has Kb = 10⁻¹⁴ ÷ Ka, and [OH⁻] is the positive root of x² + Kb·x − Kb·c = 0; a weak base’s conjugate acid gives [H₃O⁺] from the same equation with Ka. At half-equivalence the acid and its salt are equal, so pH = pKa (Henderson–Hasselbalch).
Worked example
25 mL of hydrochloric acid needs 23.5 mL of 0.1 M NaOH. Titrant: 0.1 × 23.5 = 2.35 mmol. The coefficients are 1 and 1, so the sample holds 2.35 mmol too, and its concentration is 2.35 ÷ 25 = 0.094 mol/L. The total volume at equivalence is 48.5 mL and the pH there is 7.
Now 25 mL of 0.1 M acetic acid (pKa 4.76) with 0.1 M NaOH: the equivalence volume is 25 mL, the acetate concentration 2.5 ÷ 50 = 0.05 M, Kb = 5.754 × 10⁻¹⁰, [OH⁻] = 5.364 × 10⁻⁶ M and the pH at equivalence is 8.73. Halfway, at 12.5 mL, the pH is 4.76.
Tips and common mistakes
- Keep the units together. Millilitres on both sides cancel out; mixing mL and L gives a result 1000 times off.
- Use the balanced equation. Diprotic acids (H₂SO₄, oxalic acid) and bases such as Ca(OH)₂ need coefficients other than 1.
- Average several runs. Use the mean titrant volume of concordant titrations, usually within 0.1 mL of each other.
- Pick the indicator by the pH at equivalence. Phenolphthalein suits weak acid–strong base titrations (basic endpoint); methyl orange suits weak base–strong acid ones.
Frequently asked questions
How do you calculate concentration from a titration?
At the equivalence point the moles of titrant and analyte match the balanced equation: n(analyte) = n(titrant) × a ÷ b. With moles = concentration × volume, the analyte concentration is C(titrant) × V(titrant) × a ÷ (b × V(analyte)). For HCl with NaOH a = b = 1, so it is simply C₁V₁ = C₂V₂.
What are the coefficients for?
They are the numbers in front of the analyte and the titrant in the balanced equation. Sulfuric acid needs two NaOH: H₂SO₄ + 2 NaOH → Na₂SO₄ + 2 H₂O, so the analyte coefficient is 1 and the titrant coefficient is 2. Without them a diprotic acid would come out twice as concentrated as it is.
Why is the pH at equivalence not 7 for a weak acid?
At the equivalence point of acetic acid with NaOH the flask holds sodium acetate, and acetate is a weak base: it takes protons from water and the solution turns basic, around pH 8.7 for 0.05 M acetate. A weak base titrated with a strong acid ends acidic for the same reason. Only a strong acid with a strong base gives pH 7 at 25 °C.
What is the difference between the endpoint and the equivalence point?
The equivalence point is where the amounts match the equation exactly; the endpoint is where you see the indicator change or the pH jump. A well-chosen indicator changes colour close to the equivalence point, so the endpoint volume is used as the equivalence volume.
When is the pH at equivalence not shown?
The pH formulas here assume a monoprotic acid or base reacting 1 : 1. When either coefficient is not 1 the concentration and volumes are still calculated, but the pH rows are left out.