Titration Curve Calculator

The equivalence point is not neutral

This is the most common misconception in the topic, and the curve above makes it hard to keep believing. The horizontal line is pH 7. Watch where a weak acid’s curve crosses the vertical equivalence line: well above it.

The reason is that equivalence does not mean neutral, it means the moles match. At that point every molecule of ethanoic acid has become an ethanoate ion, and ethanoate is a base. So the flask holds a solution of a weak base, and a solution of a weak base is not pH 7. For 0.1 M ethanoic acid it is about 8.7.

Switch the acid to strong and the crossing lands exactly on the line. The conjugate base of a strong acid, chloride for instance, is not basic at all, so it contributes nothing and only water sets the pH.

Reading the pKa off the curve

At half the equivalence volume, exactly half the acid has been converted, so [HA] ≈ [A⁻]. The log term in pH = pKa + log([A⁻]/[HA]) is then near log 1 = 0, and the pH is close to the pKa.

This is how a pKa is measured in practice: find the equivalence volume, halve it, read the pH. It holds while the free [H⁺] and [OH⁻] are small beside the acid left, as they are for the default ethanoic acid. A fairly strong acid dissociates enough on its own to read above its pKa, so pKa 1 at 0.1 M reads 1.67, and the conjugate base of a very weak, dilute acid takes enough H⁺ back from water to read below it, so pKa 12 with acid and base both at 0.001 M reads 10.5. The calculator’s hint points out when the reading is not the pKa.

Why the shortcut cannot draw this curve

Nearly every titration curve online comes from the Henderson-Hasselbalch equation, which has two failure regions, and they are the two regions people look up.

• Before any base is added. No conjugate base exists, so the ratio is zero and the logarithm is minus infinity. The equation cannot produce the starting pH.
• At the equivalence point. No acid remains, so the ratio is infinite and it fails the other way.

It also assumes the amount dissociated is negligible against the starting concentration, which breaks for a strong weak acid or a dilute one. This calculator instead solves the full charge balance, [H⁺] + [M⁺] = [A⁻] + [OH⁻], at every point by bisection on pH. Water’s own contribution is included, so it stays correct at 10⁻⁴ M where the shortcut drifts, and it handles a strong acid, where there is no pKa to put in the equation at all.

The four regions of the curve

• The start. Weak acid alone. The pH is set by the dissociation equilibrium, which is why a weak acid starts several pH units above a strong one at the same concentration.
• The buffer region. Both the acid and its conjugate base are present in quantity, so added base is absorbed with little pH change. The flattest point is at half equivalence, and that flatness is what buffering is.
• The jump. The last of the acid runs out and there is nothing left to absorb the base, so a fraction of a millilitre moves the pH by several units. This is why an endpoint can be detected at all.
• Past equivalence. Excess strong base sets the pH directly, and the identity of the original acid stops mattering. A weak and a strong acid give identical curves out here.

Choosing an indicator

The indicator has to change colour on the steep part of the curve, which means its range must bracket the equivalence pH. Get this wrong and the colour changes at the wrong volume, so the titration is precise and inaccurate at the same time.

A weak acid against a strong base needs phenolphthalein, which changes between pH 8.3 and 10.0. A strong acid against a strong base suits bromothymol blue at 6.0 to 7.6. Methyl orange, at 3.1 to 4.4, is the habit to unlearn for weak acids: it changes several pH units early, on the shallow buffer region, and gives a reading well below the true equivalence volume.

What this model leaves out

The acid is monoprotic and donates one proton. A diprotic acid such as carbonic acid gives two equivalence points and two buffer regions, which needs a coupled pair of equilibria. Activity coefficients are ignored, so concentrations are treated as activities; this is a good approximation at these dilutions and drifts at high ionic strength. And everything is at 25 °C, where the ion product of water is 10⁻¹⁴; that value changes with temperature and moves the whole curve with it.

Common mistakes

• Assuming equivalence means pH 7. Only for a strong acid.
• Confusing the endpoint with the equivalence point. Equivalence is the chemistry; the endpoint is where your indicator happens to change. A good indicator makes them nearly the same.
• Thinking a weaker acid needs more base. The equivalence volume comes from the mole ratio alone. Strength changes the shape of the curve, not where it jumps.
• Reading the pKa at the equivalence point. It is at half the equivalence volume.
• Using methyl orange for a weak acid. Several pH units too early.
• Believing the buffer region means nothing is happening. The reaction is proceeding the whole time; the pH is being held steady, which is a different statement.