Measurement of Conductivity of Ionic Solutions

Measuring the resistance of a metallic wire with a metre bridge, built on the Wheatstone bridge principle, is a familiar technique from physics practicals; the very same principle, with one crucial modification, is used to measure the resistance — and hence the conductivity — of an electrolytic solution.

The modification is necessary because a metre-bridge measurement of a metallic wire normally uses a DC power supply, but passing DC current through a conductivity cell would electrolyse the solution being measured, permanently altering its composition and corrupting the reading. To avoid this, an AC source, typically in the range 550 Hz to 5 kHz, is used instead — alternating the current direction fast enough that no net electrolysis occurs, while still allowing the bridge balance to be found.

The bridge itself is built from two known resistances P and Q, a variable resistance S, and the conductivity cell (carrying the unknown solution resistance R) wired as the fourth arm, with the AC source connected across one diagonal (junctions A and C) and a sensitive detector — classically a telephone earpiece — connected across the other diagonal (junctions B and D). The variable resistance S is adjusted until no current flows through the detector, meaning the bridge is balanced; at that exact balance point, the standard Wheatstone bridge relationship holds:

so R can be calculated immediately from the known P and Q and the measured balancing value of S. Once R is known, the specific conductance follows from $\kappa = \dfrac{1}{R}\cdot\dfrac{l}{A}$ — but rather than measuring the cell's physical dimensions l and A directly (which is difficult to do precisely for a real electrode assembly), the cell constant l/A is instead determined once, by calibrating the same cell against a KCl solution of known concentration and known specific conductance, and then reused for every subsequent measurement made with that cell. …