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Titration Curve Simulator
In short: This titration curve simulator plots pH against the volume of titrant for strong acids, weak acids, weak bases and polyprotic acids such as H₃PO₄. It marks the initial pH, each equivalence point, half-equivalence points where pH = pKa and buffer regions, then suggests an indicator. It is free and works in your web browser.
Pick the analyte in the flask, enter its concentration and volume and the concentration of the titrant. The curve updates as you type. The results panel lists the equivalence and half-equivalence points, and the indicator table rates each common indicator by its end point error. Save the plot with Export PNG or the data with Export CSV.
pH at chosen volumes
How the titration curve is calculated
The simulator does not switch between separate formulas for each region. It solves one charge balance at every volume, so the curve is correct at the start, in the buffer region, at each equivalence point and beyond:
[H⁺] + [Na⁺] = [OH⁻] + [A⁻] + 2[A²⁻] + 3[A³⁻] + [Cl⁻] Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴
The textbook shortcuts below give almost the same numbers and are what you use in an exam.
| Region | Weak acid HA + NaOH | Example: 25.00 mL 0.100 M CH₃COOH |
|---|---|---|
| Start (0 mL) | [H⁺] = √(Ka × C) | pH 2.88 |
| Buffer region | pH = pKa + log(n A⁻ / n HA) | 20.00 mL: pH 5.36 |
| Half-equivalence | pH = pKa | 12.50 mL: pH 4.76 |
| Equivalence | [OH⁻] = √(Kb × C salt), Kb = Kw / Ka | 25.00 mL: pH 8.73 |
| After equivalence | [OH⁻] = excess NaOH ÷ total volume | 30.00 mL: pH 11.96 |
Equivalence point pH by titration type
| Titration | pH at equivalence | Good indicator |
|---|---|---|
| Strong acid + strong base | 7.00 | Phenolphthalein, methyl red, bromothymol blue, methyl orange |
| Weak acid + strong base | Above 7 (8.73 for 0.1 M acetic acid) | Phenolphthalein |
| Weak base + strong acid | Below 7 (5.28 for 0.1 M ammonia) | Methyl red, methyl orange |
| Weak acid + weak base | Near 7, no sharp jump | None; use a pH meter |
Indicator colour ranges
| Indicator | pH range | Acid colour | Base colour |
|---|---|---|---|
| Methyl orange | 3.1 to 4.4 | Red | Yellow |
| Methyl red | 4.4 to 6.2 | Red | Yellow |
| Litmus | 4.5 to 8.3 | Red | Blue |
| Bromothymol blue | 6.0 to 7.6 | Yellow | Blue |
| Phenolphthalein | 8.2 to 10.0 | Colourless | Pink |
The verdict for each indicator comes from the end point error: the volume at the middle of its colour range compared with the true equivalence volume. Within 0.1% is excellent, within 0.5% is good. Litmus changes colour too gradually for titrations.
Worked examples
HCl with NaOH
25.00 mL of 0.100 M HCl, 0.100 M NaOH. After 10.00 mL: 2.50 − 1.00 = 1.50 mmol H⁺ in 35.00 mL.
[H⁺] = 0.0429 M, pH 1.37. At 25.00 mL pH 7.00. At 30.00 mL: 0.500 mmol OH⁻ in 55.00 mL.
pH 1.37, 7.00 and 11.96
Acetic acid with NaOH
25.00 mL of 0.100 M CH₃COOH (pKa 4.76), 0.100 M NaOH.
Start pH 2.88. Half-equivalence 12.50 mL, pH 4.76. Equivalence 25.00 mL: 0.0500 M acetate.
Equivalence pH 8.73: use phenolphthalein
Ammonia with HCl
25.00 mL of 0.100 M NH₃ (pKb 4.75), 0.100 M HCl.
Start pH 11.12. Half-equivalence pH 9.25 (pKa of NH₄⁺). Equivalence: 0.0500 M NH₄⁺.
Equivalence pH 5.28: use methyl red
Phosphoric acid with NaOH
25.00 mL of 0.100 M H₃PO₄, 0.100 M NaOH. Steps at 25.00 and 50.00 mL.
pH at 37.50 mL = pKa₂ = 7.20. The third step (pKa₃ 12.38) shows no jump.
Equivalence pH 4.70 and 9.67
Sodium carbonate with HCl
25.00 mL of 0.0500 M Na₂CO₃, 0.100 M HCl.
CO₃²⁻ → HCO₃⁻ at 12.50 mL, then HCO₃⁻ → H₂CO₃ at 25.00 mL.
pH 8.34 then 3.98: methyl orange for the second
Oxalic acid with NaOH
25.00 mL of 0.100 M H₂C₂O₄ (pKa 1.25 and 4.27), 0.100 M NaOH.
The pKa values are too close and too low for a first jump. Both protons are titrated together.
One clear end point at 50.00 mL, pH 8.40
Common mistakes
- Assuming pH 7 at every equivalence point. Only strong acid with strong base gives pH 7.00.
- Forgetting the total volume. Concentrations after mixing use the analyte volume plus the titrant volume.
- Using Henderson-Hasselbalch at 0 mL or at equivalence. It only works when both HA and A⁻ are present in useful amounts.
- Choosing the indicator by "pH 7". Pick an indicator whose colour range falls on the steep part of your curve.
- Counting every proton as a visible step. A proton with pKa above about 11, or two pKa values less than about 3 units apart, does not give a separate clear jump.
- Mixing mL and L. Moles = mol/L × volume in L. Using mL directly gives millimoles, which is fine if you stay consistent.
Drawing acids, bases and their conjugates? Sketch structures and reaction schemes for your lab report in MolDraw, a free online chemical structure editor.
Open MolDraw editorFrequently asked questions
Why is the pH at the equivalence point not always 7?
At the equivalence point the flask holds the salt of the acid and base. For a strong acid and strong base the salt is neutral, so pH = 7.00. A weak acid gives a basic conjugate base (0.050 M acetate gives pH 8.73). A weak base gives an acidic conjugate acid (0.050 M NH4+ gives pH 5.28).
What is the pH at the half-equivalence point?
Half of the weak acid has been turned into its conjugate base, so [HA] = [A−] and pH = pKa. For acetic acid this is pH 4.76. The exact value differs slightly when the acid is strong-ish or very dilute, which the simulator shows.
Which indicator should I use for a weak acid and strong base titration?
Phenolphthalein. Its colour change (pH 8.2 to 10.0) sits on the steep part of the curve near the equivalence pH of about 8.7. Methyl orange changes colour far too early and gives a large error.
How many equivalence points does phosphoric acid show?
Two clear ones. With 0.100 M H3PO4 and 0.100 M NaOH they appear near pH 4.7 and pH 9.7. The third proton has pKa 12.38, so the third equivalence point gives no visible jump in water.
What is the difference between the equivalence point and the end point?
The equivalence point is where moles of titrant exactly match the analyte. The end point is where the indicator changes colour. A good indicator makes the end point fall within a fraction of a percent of the equivalence point.
How do I calculate the pH before the equivalence point of a weak acid?
Find moles of HA left and moles of A− formed, then use pH = pKa + log(moles A− / moles HA). For 25.00 mL of 0.100 M acetic acid after 20.00 mL of 0.100 M NaOH: pH = 4.76 + log(2.00 / 0.50) = 5.36.
Related chemistry tools
Want the full method with more examples? Read the titration curve guide. Need to sketch molecules for a report? Draw chemical structures online with MolDraw.
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