Conductance of electrolytic solutions

The essentials

Electrolytic solutions conduct electricity through the movement of ions. Resistance R = ρ(l/A), where ρ is resistivity. Conductance G = 1/R, and conductivity κ = 1/ρ. The ratio l/A for a conductivity cell is the cell constant G*, so κ = G*/R.

Key points

• Units: conductance in siemens (S); conductivity in S m⁻¹ or S cm⁻¹; cell constant in cm⁻¹ or m⁻¹.
• Molar conductivity Λm = κ ÷ c. With κ in S cm⁻¹ and c in mol L⁻¹, Λm = (κ × 1000) ÷ M in S cm² mol⁻¹.
• Conductivity decreases on dilution because fewer ions are present per unit volume.
• Molar conductivity increases on dilution. For strong electrolytes it rises slowly and follows Λm = Λ°m − A√c. For weak electrolytes it rises steeply at low concentration because the degree of dissociation increases.
• Λ°m (limiting molar conductivity) of a strong electrolyte is found by extrapolating the straight-line graph of Λm against √c to zero concentration. For a weak electrolyte this extrapolation does not work.
• Kohlrausch's law: the limiting molar conductivity of an electrolyte is the sum of the limiting ionic conductivities of its cation and anion, Λ°m = ν₊λ°₊ + ν₋λ°₋.
• Uses: Λ°m of weak electrolytes, e.g. Λ°(CH₃COOH) = Λ°(CH₃COONa) + Λ°(HCl) − Λ°(NaCl); degree of dissociation α = Λm ÷ Λ°m.

Exam tips

• Example: κ = 0.012 S cm⁻¹ for 0.1 M solution gives Λm = 0.012 × 1000 ÷ 0.1 = 120 S cm² mol⁻¹.

Common mistakes

• Saying both κ and Λm increase on dilution; only Λm does.