Potentiometric titration is an electroanalytical technique that determines the endpoint of a titration by monitoring the potential difference between two electrodes immersed in the analyte solution. Unlike visual indicator methods, potentiometric detection is not affected by the sample’s color, turbidity, or the presence of suspended solids, making it ideal for challenging matrices. The potential is measured under near-zero current conditions, ensuring that the measurement does not disturb the chemical equilibrium of the titration reaction.
The fundamental relationship governing the electrode potential is the Nernst equation. For a reduction half-reaction Ox + ne⁻ ⇌ Red, the potential is given by E = E° - (RT/nF)lnQ, where E° is the standard electrode potential, R is the gas constant (8.314 J·mol⁻¹·K⁻¹), T is the absolute temperature, n is the number of electrons transferred, F is the Faraday constant (96485 C·mol⁻¹), and Q is the reaction quotient. At 25 °C, the equation simplifies to E = E° - (0.05916/n)logQ. This logarithmic relationship produces the characteristic S-shaped titration curve observed in potentiometric titrations.
The measurement setup consists of an indicator electrode whose potential responds to the analyte concentration and a reference electrode that maintains a constant potential. For acid-base titrations, the glass electrode (a pH-sensitive membrane electrode) serves as the indicator. For redox titrations, inert metal electrodes such as platinum or gold are used. Common reference electrodes include the calomel electrode (Hg₂Cl₂/Hg) and the silver-silver chloride electrode (Ag/AgCl/KCl). The two electrodes are connected via a salt bridge or combined into a single combination electrode for convenience.
Potentiometric titration curves plot measured potential (mV) against titrant volume (mL). The curve is S-shaped, with the inflection point corresponding to the equivalence point. The endpoint is most accurately identified using the first derivative method (ΔE/ΔV versus V), where the peak maximum indicates the endpoint. For greater precision, the second derivative (Δ²E/ΔV²) crosses zero at the endpoint. These numerical methods are readily implemented by modern titration software and eliminate subjective interpretation.
The Gran plot is an alternative graphical method for endpoint determination in potentiometric titrations, particularly useful for weak acid-strong base titrations and for determining equilibrium constants. A Gran plot linearizes the data before and after the equivalence point by plotting V × 10^(±pH) against titrant volume V. The intersection of the two linear segments gives the equivalence point volume with high precision. Gran plots are especially valuable when the titration curve is asymmetrical or when the endpoint is poorly defined due to sample dilution.
Potentiometric titration finds broad application across analytical chemistry. In acid-base titrations, it provides accurate determination of weak acids and bases where visual indicators give indistinct endpoints. Redox titrations of species such as Fe²⁺/Ce⁴⁺, I₂/S₂O₃²⁻, and MnO₄⁻/Fe²⁺ are routinely monitored potentiometrically. Precipitation titrations, including halide determination with AgNO₃, benefit from silver ion-selective electrodes. The method is also employed in the pharmaceutical industry for assay determination of active ingredients, in environmental analysis for measuring acidity and alkalinity, and in quality control of industrial processes.
