Conductometric Titrations

What if a solution is too darkly coloured to see an indicator change? Or too cloudy? Or what if no indicator gives a sharp colour change for the reaction you need? One elegant answer is to stop looking and start measuring: track the solution’s electrical conductivity as the titrant is added. The end point shows up as a sharp change in the graph, no colour needed. This is a conductometric titration.

What conductivity measures

A solution conducts electricity because it contains ions that move when a voltage is applied. Its conductivity depends on:

• how many ions are present (concentration)
• the charge on each ion
• how fast each type of ion moves (its ionic mobility)

A conductivity meter measures this using two electrodes and an alternating current (to avoid electrolysis at the electrodes). Conductivity is measured in siemens per metre (S/m) or, more commonly in the lab, microsiemens or millisiemens per centimetre (μS/cm or mS/cm).

The key fact: H⁺ and OH⁻ are unusually fast

Not all ions move equally fast. Hydrogen ions and hydroxide ions are far more mobile than any other ions in water:

Ion	Approximate molar ionic conductivity at 25 °C (S cm² mol⁻¹)
H⁺ (H₃O⁺)	350
OH⁻	198
K⁺	74
Cl⁻	76
Na⁺	50
CH₃COO⁻	41

H⁺ and OH⁻ are so fast because they don’t have to physically travel through the water. Instead, a proton can hop from one water molecule to the next along a chain of hydrogen bonds (the Grotthuss mechanism), a bit like a relay race in which the baton is passed rather than carried.

This large difference in mobility is what makes conductometric titrations work so well for acids and bases.

Strong acid titrated with a strong base

25 cm³ of hydrochloric acid is titrated with sodium hydroxide, and conductivity is measured after each addition.

Before the end point: H⁺ + Cl⁻ + Na⁺ + OH⁻ → Na⁺ + Cl⁻ + H₂O

Each OH⁻ added removes one fast H⁺ ion and replaces it with a much slower Na⁺ ion. Chloride ions are unchanged. So the conductivity falls steeply.

At the end point: only Na⁺ and Cl⁻ remain. Conductivity is at its minimum.

After the end point: extra NaOH adds fast OH⁻ ions (and Na⁺), so conductivity rises again.

Graph shape: a V, with two straight lines. The end point is where the lines meet.

Weak acid titrated with a strong base

Ethanoic acid titrated with sodium hydroxide.

At the start: ethanoic acid is weak and only slightly ionised, so conductivity is low.

Before the end point: NaOH converts ethanoic acid into sodium ethanoate: CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O This adds Na⁺ and CH₃COO⁻ ions, so conductivity rises slowly. (There may be a small initial dip as the few free H⁺ ions are neutralised first.)

After the end point: excess fast OH⁻ ions make conductivity rise more steeply.

Graph shape: a gentle upward line followed by a steeper upward line. The end point is where the gradient changes.

Weak acid titrated with a weak base

Ethanoic acid titrated with aqueous ammonia.

Before the end point, conductivity rises as ammonium ethanoate forms. After it, adding more ammonia (a weak base) adds very few ions, so the conductivity levels off. The end point is at the corner. This is useful because weak acid–weak base titrations have no sharp pH change and no good indicator. See titration curves.

Strong acid titrated with a weak base

Hydrochloric acid titrated with ammonia.

Conductivity falls as fast H⁺ ions are replaced by slower NH₄⁺ ions, then stays roughly constant after the end point because excess ammonia hardly ionises. The end point is where the falling line meets the flat line.

Summary of graph shapes

Titration	Before end point	After end point
Strong acid + strong base	steep fall	steep rise
Weak acid + strong base	slow rise	steeper rise
Strong acid + weak base	steep fall	roughly flat
Weak acid + weak base	rise	roughly flat

Precipitation titrations

Conductometric methods also work for precipitation reactions. For example, silver nitrate titrated against potassium chloride:

K⁺ + Cl⁻ + Ag⁺ + NO₃⁻ → AgCl(s) + K⁺ + NO₃⁻

Before the end point, chloride ions are removed as insoluble AgCl and replaced by nitrate ions of similar mobility, so conductivity stays roughly flat (or falls slightly). After the end point, excess Ag⁺ and NO₃⁻ ions accumulate, so conductivity rises. See precipitation titrations.

Similar methods work for sulfate with barium ions, and many other reactions.

Finding the end point from the graph

1. Plot conductivity (y-axis) against volume of titrant (x-axis).
2. Draw a straight line of best fit through the points before the end point.
3. Draw another straight line through the points after the end point.
4. Extrapolate both lines until they meet. The x-value where they intersect is the end point volume.

Points close to the end point often lie slightly off the lines (because of partial reactions or hydrolysis), so they’re usually left out when drawing the lines. That’s a big advantage: you don’t need to hit the end point exactly, because it’s found by extrapolation from points on either side.

Practical tips

• Use a concentrated titrant (roughly ten times more concentrated than the analyte). This keeps the total volume nearly constant, so dilution doesn’t distort the straight lines. Alternatively, correct each reading for dilution by multiplying by (V₀ + V) ÷ V₀.
• Keep the temperature constant: conductivity rises by about 2% per °C.
• Stir after each addition and wait for the reading to settle.
• Take readings at regular intervals on both sides of the end point.
• Rinse the conductivity cell with distilled water between samples.

Advantages and disadvantages

Advantages:

• No indicator needed; works for coloured, cloudy or opaque solutions.
• Works for very dilute solutions and weak acid–weak base titrations.
• The end point is found by extrapolation, so readings right at the end point aren’t needed.
• Easy to automate with a data logger.

Disadvantages:

• Less suitable when the solution contains a large excess of other ions, which swamp the changes.
• Needs temperature control.
• Requires a conductivity meter.

Why dilution matters here

In an ordinary indicator titration, adding water to the flask doesn’t change the answer. In a conductometric titration it does affect the readings, because conductivity depends on concentration, and every addition of titrant slightly dilutes all the ions in the flask. If the titrant is dilute and large volumes are added, the “straight” lines curve, making the intersection less precise. That’s the reason for using a titrant about ten times more concentrated than the analyte, or for applying the volume correction mentioned above.

Key takeaways

• Conductometric titrations find the end point from changes in electrical conductivity, without an indicator.
• H⁺ and OH⁻ ions are much more mobile than other ions, so acid–base titrations give sharp changes.
• Strong acid + strong base gives a V-shaped graph with its minimum at the end point.
• The end point is where the two straight lines intersect; use a concentrated titrant to minimise dilution.
• The method works for weak acid–weak base and precipitation titrations, and for coloured or cloudy samples.