Ion-Selective Electrode: Nernstian Potentiometry & Interference

Primary Ion

Primary ion conc. 1.0×10⁻³ M

Interfering Na⁺ conc. 1.0×10⁻⁵ M

Selectivity coeff. K_ij 1.0×10⁻²

Temperature 25 °C

Electrode Readout

Potential E

–177.5 mV

Slope S

59.2 mV/dec

True [ion]

1.00e-3 M

Apparent [ion]

1.00e-3 M

Interference error

+0.0 %

How it works

An ion-selective electrode (ISE) develops a membrane potential that follows the Nernst equation. When a second ion the membrane is not perfectly selective for is also present, the response follows the Nikolsky-Eikman equation:

E = E₀ + S · log₁₀( a_i + K_ij · a_j^(z_i/z_j) )
S = 2.303 · R · T / (z_i · F)   [mV per decade]

where a_i is the primary-ion activity, a_j the interfering-ion activity, K_ij the Nikolsky selectivity coefficient, z_i / z_j the ion charges, R the gas constant, F the Faraday constant and T the absolute temperature. Activities are approximated here as concentrations (dilute solution, activity coefficient ≈ 1).

Primary ion — K⁺ gives a full 59 mV/decade Nernstian slope at 25°C (z=1); Ca²⁺ gives roughly half that (z=2), since the same charge is carried by half as many ions per mole.
Interfering Na⁺ concentration & K_ij — a real electrode is never perfectly selective. When the interference term K_ij·a_j^(z_i/z_j) becomes comparable to a_i, the electrode reports too high a concentration — this is exactly the low-concentration "detection-limit" curvature seen on a real ISE calibration curve.
Apparent [ion] is what you would back-calculate from the measured E using an ideal (interference-free) calibration line — the gap between it and the true concentration is the analytical error the interference causes.
Temperature scales the slope S directly, which is why potentiometric methods are always run at controlled temperature in a real lab.

Real-world relevance: this is the working principle behind blood-gas Ca²⁺/K⁺ analyzers, water-quality fluoride and nitrate probes, and soil-nutrient field meters.

–177.5 mV

membrane potential

Primary ion Interfering Na⁺ ISE membrane

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