Titration Curve Simulator
Equations in this simulation
| C_a | Analyte concentration C_a (mol/L) | what a titration is done to find; here it is set, so you can check the result | |
|---|---|---|---|
| V_a | Analyte volume V_a (mL) | measured into the flask with a pipette | |
| C_b | Titrant concentration C_b (mol/L) | the solution in the burette: NaOH for an acid, HCl for a base | |
| n | protons given up per molecule | 1 for HCl and acetic acid; phosphoric acid has three, and the first two show as separate steps in the curve | |
| V_e | equivalence volume | the titrant added when it has exactly neutralized the analyte |
With the current values:
| [H₃O⁺] | concentration of hydronium ions | found at every drop by solving the charge balance below | |
|---|---|---|---|
| [OH⁻] | concentration of hydroxide ions | water keeps the product of the two at 10⁻¹⁴ at 25 °C | |
| pH | pH of the flask | the curve rises slowly, then steeply around the equivalence point, then levels off |
With the current values:
| [A⁻] | anions of the weak acid | C × Ka ÷ (Ka + [H₃O⁺]) for each proton; the solution must stay electrically neutral, which fixes [H₃O⁺] exactly | |
|---|---|---|---|
| [Na⁺], [Cl⁻] | ions of the strong base and acid | they never react, so they are just the moles added divided by the total volume |
| pKa | acid dissociation constant, as −log₁₀ Ka | at half the equivalence volume [A⁻] = [HA], so the pH there is the pKa, which is how a titration measures it | |
|---|---|---|---|
| [A⁻] ÷ [HA] | ratio of base to acid form | the Henderson–Hasselbalch equation holds in the buffer region, the flat part of a weak acid curve |
With the current values:
| pK_In | the indicator's own pKa | the middle of its color range; a good indicator changes within the steep part of the curve | |
|---|---|---|---|
| changed | share of the indicator in its base color | the end point is where it is half changed; the gap between end point and equivalence point is the titration error |
With the current values:
How to use the titration simulator
- Choose the analyte in the flask, its concentration and volume, and the concentration of the titrant in the burette: sodium hydroxide for an acid, hydrochloric acid for a base. Pick an indicator. The tap opens at once and the titrant drips into the flask while the stirrer mixes it.
- Watch the pH meter and the color of the flask. The chart draws the titration curve as you go, over the full curve in gray; the red lines mark the equivalence volume and the pink line the middle of the indicator's range. With Close the tap when the indicator changes color ticked, the tap shuts at the end point; press Play to carry on past it, or add single drops near the end.
- Compare the end point with the equivalence point to see the titration error, and read the pH at half equivalence, which equals the pKa of a weak acid. The pH Calculator and Molarity Calculator do the same arithmetic for a single solution, and the Buffer Calculator works out the buffer region.
Frequently asked questions
What is the equivalence point?
The moment the titrant has exactly neutralized the analyte: moles of base added equal moles of acid present, C_a V_a = C_b V_e. For a strong acid with a strong base the pH there is 7. For a weak acid it is above 7, because the conjugate base left behind is weakly basic; for a weak base it is below 7.
What is the difference between the end point and the equivalence point?
The equivalence point is a fact of the chemistry; the end point is what you see, the moment the indicator changes color. A well-chosen indicator changes within the steep part of the curve, so the two are a fraction of a drop apart. Phenolphthalein suits weak acids with strong bases; methyl orange suits strong acids with weak bases; for a strong acid with a strong base almost any of them works, because the jump runs from about pH 3 to 11.
How does a titration find the pKa?
Halfway to the equivalence point, half the weak acid has been turned into its conjugate base, so [A⁻] = [HA], and by the Henderson–Hasselbalch equation pH = pKa. Read the pH at half the equivalence volume and you have the pKa. That flat stretch of the curve is the buffer region.
Why does phosphoric acid show two jumps?
It has three protons, which come off at very different pH values (pKa 2.15, 7.20 and 12.35). Each one makes its own step in the curve, at one and two times the first equivalence volume. The third proton is too weak to show a jump in water.
How is the pH worked out?
Exactly, at every drop: the simulation solves the charge balance of the solution, [H₃O⁺] + [Na⁺] = [OH⁻] + [Cl⁻] + [A⁻], with the acid dissociation constants and the water constant 10⁻¹⁴. That one equation covers the start, the buffer region, the equivalence point and the excess titrant, without switching between approximations.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.