Potentiometric Titrations

In a potentiometric titration, you don’t watch for a colour change at all. Instead, you place an electrode in the solution and record its electrical potential (voltage) as the titrant is added. The potential depends on the concentration of a particular ion, so it changes sharply at the equivalence point. The result is a curve from which the equivalence point can be located precisely, without any judgement about colour.

Potentiometric titrations are the standard method in pharmaceutical, food and industrial quality-control labs, usually carried out by automatic titrators.

The basic set-up

Two electrodes are dipped into the solution being titrated:

1. An indicator electrode, whose potential depends on the concentration (strictly, the activity) of a particular ion in the solution.
2. A reference electrode, whose potential stays constant (usually a silver/silver chloride electrode).

A high-resistance voltmeter (a pH meter or potentiometer) measures the potential difference between them. Very little current flows, so the solution isn’t changed by the measurement.

The indicator electrode’s potential follows the Nernst equation: it changes by about 59 mV (at 25 °C) for every tenfold change in the concentration of a singly charged ion. So a steep change in concentration at the equivalence point produces a steep change in potential.

Choosing the indicator electrode

Titration type	Indicator electrode	What it responds to
Acid–base	glass pH electrode	H⁺ (pH)
Redox	platinum (or gold) electrode	ratio of oxidised to reduced forms
Precipitation (halides)	silver electrode, or silver/halide ion-selective electrode	Ag⁺ or halide ions
Complexometric	ion-selective electrode (e.g. calcium) or mercury electrode	the metal ion
Specific ions	ion-selective electrodes (fluoride, nitrate, etc.)	one particular ion

Acid–base potentiometric titrations

This is simply a titration followed with a pH meter. The pH curve shows the classic S-shape, with a steep rise at the equivalence point. It’s especially useful for:

• weak acids and weak bases where indicators give poor end points
• coloured or cloudy samples
• polyprotic acids, where several equivalence points can be seen
• measuring pKa from the half-equivalence point

The details, with a full data set, are in plotting a pH curve with a pH meter. See also how a pH meter works.

Redox potentiometric titrations

In a redox titration, the potential of an inert platinum electrode depends on the ratio of oxidised to reduced forms of the species in solution.

Example: iron(II) titrated with cerium(IV)

Fe²⁺ + Ce⁴⁺ → Fe³⁺ + Ce³⁺

• Before the equivalence point: the solution contains both Fe²⁺ and Fe³⁺, so the platinum electrode potential is controlled by the Fe³⁺/Fe²⁺ couple. It changes slowly as the ratio [Fe³⁺]/[Fe²⁺] rises.
• At half-equivalence, [Fe³⁺] = [Fe²⁺], and the potential equals the standard potential of the Fe³⁺/Fe²⁺ couple (about +0.68 V in 1 mol/dm³ sulfuric acid).
• At the equivalence point, the potential jumps sharply.
• After the equivalence point, the potential is controlled by the Ce⁴⁺/Ce³⁺ couple and levels off near its standard potential (about +1.44 V in sulfuric acid).

The size of the jump depends on the difference between the two standard electrode potentials. A large difference gives a large, sharp jump. See oxidation and reduction for the background to redox reactions.

This approach also works for permanganate, dichromate and iodine titrations.

Precipitation potentiometric titrations

A silver electrode responds to the concentration of Ag⁺ ions. When chloride is titrated with silver nitrate:

• Before the equivalence point, [Ag⁺] is very low (limited by the solubility of AgCl in the presence of excess Cl⁻).
• At the equivalence point, [Ag⁺] rises rapidly.
• The potential of the silver electrode jumps.

A big advantage over indicator methods: a mixture of chloride, bromide and iodide can be titrated in one run, giving three separate jumps (iodide first, because AgI is least soluble, then bromide, then chloride). See precipitation titrations.

Finding the equivalence point precisely

From the curve of potential (or pH) against volume, the equivalence point can be found in several ways.

1. Midpoint of the steep section

Draw the curve and find the point halfway up the steepest part. Simple, but less precise.

2. First derivative plot

Calculate the change in potential per unit volume, ΔE/ΔV, between successive readings, and plot it against the average volume. The peak of this graph is the equivalence point.

Example:

Volume (cm³)	E (mV)	ΔE/ΔV (mV/cm³)	Average volume (cm³)
24.0	520
24.5	545	50	24.25
24.8	580	117	24.65
25.0	700	600	24.90
25.2	820	600	25.10
25.5	850	100	25.35

The largest ΔE/ΔV values are centred on about 25.0 cm³, the equivalence point.

3. Second derivative plot

The second derivative, Δ²E/ΔV², crosses zero at the equivalence point. Automatic titrators often use this method.

4. Gran plot

A linearised method that uses data before the equivalence point, useful when the jump is small.

A worked example: equivalence point to concentration

25.00 cm³ of an iron(II) solution is titrated with 0.0200 mol/dm³ potassium manganate(VII), following the potential with a platinum electrode. The first derivative plot peaks at 18.60 cm³. Calculate [Fe²⁺].

The reaction is MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺, a 1 : 5 ratio.

• n(MnO₄⁻) = 0.0200 × 0.01860 = 3.72 × 10⁻⁴ mol
• n(Fe²⁺) = 5 × 3.72 × 10⁻⁴ = 1.86 × 10⁻³ mol
• [Fe²⁺] = 1.86 × 10⁻³ ÷ 0.02500 = 0.0744 mol/dm³

Once the equivalence volume is found from the electrode data, the calculation is exactly the same as for any titration. See titration calculations.

Automatic titrators

Modern labs use autotitrators: instruments that add titrant from a motor-driven burette, record the electrode signal continuously, adjust the size of additions automatically (small increments near the equivalence point), detect the equivalence point mathematically and calculate the result. They’re used for:

• pharmaceutical assays (active ingredient content)
• food analysis (acidity of wine and juices, salt content)
• water analysis (alkalinity, chloride)
• petroleum products (acid number of oils)
• Karl Fischer titration (a related electrochemical method for measuring water content)

Advantages and disadvantages

Advantages:

• No indicator needed; works for coloured, cloudy or opaque samples.
• Objective and reproducible; easily automated.
• Can resolve several equivalence points in mixtures and polyprotic acids.
• Can also give thermodynamic data, such as pKa values and standard potentials.

Disadvantages:

• Requires electrodes and meters, which need calibration and maintenance.
• Slower than a simple indicator titration when done manually.
• Electrodes can be affected by fouling or interfering ions.
• Reference electrode junctions can become blocked, causing drifting readings.

Key takeaways

• A potentiometric titration follows the potential of an indicator electrode against a reference electrode.
• The potential changes sharply at the equivalence point because it depends logarithmically on ion concentration (Nernst equation).
• Glass electrodes are used for acid–base, platinum for redox and silver for halide titrations.
• The equivalence point is found from the steepest point, the peak of the first derivative, or where the second derivative crosses zero.
• Automatic potentiometric titrators are the standard in quality-control labs.
• Once the equivalence volume is known, the mole calculation is identical to that of an ordinary indicator titration.