Conductance of solutions

Some solutions carry electricity. Put two wires from a battery and a bulb into pure water and the bulb stays dark; add salt and it lights. The salt gives ions, and moving ions carry the current. How well a solution conducts is described by a family of quantities, built from ones you met in physics:

• Resistance R (ohm, Ω) depends on the length l and cross-section A of the conductor: R = ρl/A, where ρ is the resistivity.
• Conductance G = 1/R. Its unit is the siemens, S (once called the mho).
• Conductivity κ = 1/ρ, measured in S cm⁻¹ (or S m⁻¹).

Solutions are measured in a conductivity cell: two platinum electrodes a fixed distance apart. Since l and A never change, l/A is a constant for that cell, the cell constant G∗ = l/A. Turning R = ρl/A upside down gives a handy link:

κ = G∗ × G = G∗/R

So when the cell constant is 1, conductivity and conductance are equal. In practice the cell constant is found with a KCl solution of known κ.

To compare solutions of different strengths, divide by the concentration. This is the molar conductivity:

Λ_m = κ/c, and with κ in S cm⁻¹ and c in mol L⁻¹, Λ_m = 1000κ/M in S cm² mol⁻¹.

What happens on dilution (adding water)?

• κ goes down, because there are fewer ions in each cm³ to carry the current.
• Λ_m goes up, because it counts the conductance of a whole mole, and the ions have more room to move.

Electrolytes come in two kinds. A strong electrolyte (NaCl, KCl, HCl) breaks up completely into ions. A weak electrolyte (acetic acid, ammonium hydroxide) breaks up only a little: most of its molecules stay whole.

The graph of Λ_m against √c shows the difference. For a strong electrolyte it is a gentle straight line: Λ_m = Λ°_m – A√c. Extend the line back to c = 0 and you read off Λ°_m, the limiting molar conductivity (at infinite dilution). For a weak electrolyte, Λ_m shoots up steeply at low concentration, because dilution makes more molecules break into new ions. That curve cannot be extended to c = 0.