Chemistry · Ch 9 — Electrochemistry
Conductivity of Electrolytic Solution
Conductivity of Electrolytic Solution
An electrolyte such as sodium chloride or potassium chloride, once dissolved in a solvent like water, dissociates almost completely into its constituent cations and anions. When an external electric field is applied across the solution, these free ions migrate toward the oppositely-charged electrode and, by carrying charge across the solution, allow it to conduct electricity — quite unlike the metallic conduction that happens through a fixed lattice of atoms, where only electrons move.
The conductivity of an electrolytic solution is measured with a conductivity cell: two platinum electrodes of cross-sectional area A, separated by a distance l, immersed face-to-face in the solution. A conductivity cell behaves exactly like a metallic conductor with respect to Ohm's law — at a fixed temperature, the current I flowing through it is directly proportional to the applied voltage V:
Here R is the resistance of the enclosed solution, measured in ohms (Ω) — the opposition the solution offers to the flow of current through it. This single relationship, R = V/I, is the starting point for everything else in the section: resistivity, conductivity, and eventually molar and equivalent conductance are all built from it by relating R to the geometry and concentration of the solution.
Resistivity. Just as for a metallic conductor, the resistance of the electrolyte column between the two electrodes is directly proportional to the length l separating them and inversely proportional to their cross-sectional area A:
where ρ (rho) is the specific resistance, or resistivity, a property that depends only on the nature of the electrolyte and not on the cell's geometry. When l/A = 1 m⁻¹ (unit length, unit area), ρ becomes numerically equal to R — so resistivity is defined as the resistance of an electrolyte confined between electrodes of unit cross-sectional area, separated by unit distance. The ratio l/A itself is called the cell constant, and the SI unit of resistivity is the ohm metre (Ωm).
Conductance and conductivity. Because working with conductance is usually more convenient than working with resistance, the reciprocal of resistance, , is defined as the conductance of the solution, with SI unit the siemen (S). Substituting gives . The reciprocal of resistivity, , is called the specific conductance or conductivity, symbol κ (kappa), so that
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What this figure shows. A conductivity cell consists of two platinum electrodes, each of cross-sectional area A, held a fixed distance l apart and dipped face-to-face into the electrolytic solution whose conductance is to be measured. Because the electrodes and the solution between them form a column of fixed geometry, the cell behaves like a resistor: at constant temperature the current I flowing through the cell is directly proportional to the applied voltage V, so V = IR, where R is the resistance of the enclosed solution in ohms. Real cells use platinum (often platinised, i.e. coated with finely divided platinum black) because it resists chemical attack by the electrolyte …
What this figure shows. This figure pictures a 1 m × 1 m × 1 m cube of electrolytic solution held between two electrodes that exactly cover two opposite faces of the cube, so that l = 1 m and A = 1 m^2. Substituting these values into R = ρ(l/A) makes R numerically equal to ρ, which is exactly how resistivity is defined — the resistance of an electrolyte of unit length and unit cross-sectional area. Taking the reciprocal, the conductance of this same unit cube is numerically equal to the specific conductance κ, giving κ a clean physical picture: it is the conductance of exactly one cu …