Titration Calculator
Enter the titrant concentration and the volume used to reach the endpoint and get the unknown concentration, with any mole ratio. Or plot the full pH curve for a strong or weak acid or base, with the equivalence point, the half-equivalence point and a choice of indicator. Runs entirely in your browser. Free, no sign-up.
From the balanced equation, a analyte + b titrant: 1 and 1 for HCl + NaOH.
Adds the concentration in g/L.
Results
0.09740 mol/L
Analyte concentration
0.002435 mol
Moles of titrant
0.002435 mol
Moles of analyte
Rounded to 4 significant figures, the fewest in the measurements you entered. The coefficients are exact.
The working
n(titrant) = 0.10000 mol/L × 24.350 mL × 10⁻³ L/mL = 0.0024350 mol
n(analyte) = 0.0024350 mol × 1 ÷ 1 = 0.0024350 mol
c(analyte) = 0.0024350 mol ÷ (25.000 mL × 10⁻³ L/mL) = 0.097400 mol/L
How to Use the Titration Calculator
- 1. Choose what to work out. Pick Unknown concentration to analyse a result, Titrant volume at equivalence to plan one, or Titration curve to see the pH throughout.
- 2. Enter your measurements. Use mol/L for concentrations and mL for volumes. Set the mole ratio from the balanced equation: 1 : 1 for HCl + NaOH, 1 : 2 for H₂SO₄ + 2NaOH, and so on.
- 3. For a curve, say what is in the flask. Choose a strong or weak acid or base. For a weak one pick it from the list or type its Ka or Kb at 25 °C.
- 4. Read the answer and the working. Concentration and volume answers come with each line of arithmetic; the curve comes with a table of key points and a guide to indicators.
Finding an Unknown Concentration
At the equivalence point the titrant has reacted with exactly all of the analyte, in the ratio of the balanced equation. The endpoint is where the indicator changes colour, which a good choice of indicator puts very close to equivalence. For a reaction of a analyte with b titrant, the moles of titrant used divided by b equal the moles of analyte divided by a.
Moles of titrant
n(titrant) = c(titrant) × V(titrant)
Moles of analyte
n(analyte) = n(titrant) × a ÷ b
Concentration
c(analyte) = n(analyte) ÷ V(analyte)
| Reaction | Analyte : titrant (a : b) |
|---|---|
| HCl + NaOH → NaCl + H₂O | 1 : 1 |
| H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O | 1 : 2 |
| 5Fe²⁺ + MnO₄⁻ + 8H⁺ → 5Fe³⁺ + Mn²⁺ + 4H₂O | 5 : 1 |
Worked example. A 25.00 mL sample of hydrochloric acid needs 24.35 mL of 0.1000 M sodium hydroxide to reach the endpoint. The titrant is 0.1000 mol/L × 0.02435 L = 0.002435 mol, the ratio is 1 : 1, so the acid is 0.002435 mol in 0.02500 L, which is 0.09740 mol/L. All four measurements have four significant figures, so the answer has four.
Reading a Titration Curve
A titration curve plots pH against the volume of titrant added. The calculator solves the charge balance (the charges of all ions must sum to zero) at every point, including the effect of water, so it needs no separate formula for the buffer region, the equivalence point or the excess. That is the exact answer for a monoprotic acid or base at 25 °C, with Kw = 1.0 × 10⁻¹⁴.
| Titration | pH at equivalence | Why |
|---|---|---|
| Strong acid + strong base | 7.00 | Neither ion reacts with water |
| Weak acid + strong base | Above 7 | The conjugate base of the acid reacts with water |
| Weak base + strong acid | Below 7 | The conjugate acid of the base reacts with water |
The calculator opens on 25.00 mL of 0.100 M acetic acid (Ka = 1.8 × 10⁻⁵) with 0.100 M sodium hydroxide, a standard textbook case. The equivalence volume is 25.00 mL. The pH is 2.88 at the start, 4.75 at half-equivalence (12.50 mL, where pH = pKa up to rounding), 8.72 at equivalence and 12.30 at 37.50 mL. Some books print 2.87 and 4.74 because they round along the way; the exact values here differ by that last digit.
Choosing an Indicator
The curve is nearly vertical around equivalence, so one drop of titrant moves the pH through several units. An indicator works when its colour change falls inside that steep region. The calculator takes the pH reached at 0.5 % before and after the equivalence volume as the steep region and marks an indicator suitable when the middle of its colour-change range lies inside it. For a weak acid, that rules out methyl red and bromothymol blue and leaves indicators that change above about pH 7, such as phenolphthalein; for a strong acid with a strong base, all the listed indicators fit at 0.1 M. Ranges are from OpenStax Chemistry 2e, Figure 14.19.
What this tool does not cover
Curves are for monoprotic acids and bases titrated with a strong titrant at 25 °C. Polyprotic acids such as phosphoric acid have several equivalence points, and weak-acid with weak-base titrations have no sharp jump. Use the Ka or Kb for your own temperature if you need it.
Frequently Asked Questions
- How do you calculate the concentration of an unknown in a titration?
- Multiply the titrant's concentration by the volume used to get moles of titrant, scale by the mole ratio of the equation to get moles of analyte, then divide by the analyte's volume. The calculator shows each of these lines.
- What is the difference between the equivalence point and the endpoint?
- The equivalence point is the theoretical moment when the reactants are in exactly the ratio of the balanced equation. The endpoint is what you actually observe, usually an indicator colour change. A well-chosen indicator makes the two very close.
- Why is the equivalence point of a weak acid titration above pH 7?
- At equivalence all the weak acid has become its conjugate base, which reacts with water to make hydroxide. For 0.100 M acetic acid titrated with 0.100 M NaOH, the acetate left at 0.0500 M gives a pH of 8.72.
- What is the half-equivalence point?
- It is the point where half the weak acid has been neutralised, so [HA] ≈ [A⁻]. By the Henderson–Hasselbalch equation the pH then equals the pKa, so you can read the pKa straight off the curve. The Henderson–Hasselbalch Calculator covers buffers in general.
- How do I choose an indicator?
- Pick one whose colour-change range lies on the steep part of the curve. Phenolphthalein, which changes at about pH 8 to 10, suits weak acid with strong base; methyl red, near pH 4.2 to 6.3, suits weak base with strong acid. The table in the curve view marks which suit your case.
- What if the acid has more than one acidic hydrogen?
- Use the mole ratio. Sulfuric acid titrated with sodium hydroxide to the second equivalence point is a 1 : 2 ratio, so choose that preset. The curve view handles only one acidic or basic site, because a polyprotic curve has several steps.