Conductance of Electrolytic Solutions: Specific Conductivity

An electrolyte solution, like a metal wire, resists the flow of electric current to some degree, and this resistance, $R$, can be measured by placing two fixed electrodes in the solution (forming a conductivity cell) and applying a known voltage. The reciprocal of resistance is conductance, $G = 1/R$, measured in siemens (S), with a larger conductance meaning the solution carries current more easily.

Just as the resistance of a metal wire depends not only on the material but on its length and cross-sectional area, the measured resistance of a solution in a conductivity cell depends not only on the solution's own composition and concentration but also on the geometry of that particular cell — the distance $l$ between its two electrodes and their cross-sectional area $A$. To strip away this cell-dependent geometric factor and obtain a property that describes the solution alone, chemists define specific conductivity (or simply conductivity), $\kappa$, as: $\kappa = G \times \frac{l}{A} = \frac{l/A}{R}$ where the purely geometric ratio $l/A$ is called the cell constant of that particular conductivity cell.

Because directly measuring the tiny electrode separation and area of a real conductivity cell with sufficient precision is impractical, the cell constant is instead determined once, indirectly: a standard solution of precisely known $\kappa$ (traditionally a $\text{KCl}$ solution of standard concentration, whose $\kappa$ has been established by careful prior calibration) is placed in the cell, its resistance is measured, and the cell constant is computed as $\text{cell constant} = \kappa\times R$. Once known for that specific cell, the same cell constant is then used, together with the measured resistance of any other solution placed in it, to find that solution's own specific conductivity via $\kappa = (\text{cell constant})/R$. …