Kohlrausch's Law of Independent Migration of Ions

Kohlrausch's law (1876) states:

'At infinite dilution, the molar conductivity of an electrolyte is the sum of the individual contributions of its constituent ions, regardless of the nature of the counter-ion.'

Mathematical expression: Λm° = ν+ λ°+ + ν− λ°−

Where:

• Λm° = limiting molar conductivity of the electrolyte
• λ°+ = limiting molar conductivity of the cation
• λ°− = limiting molar conductivity of the anion
• ν+ = number of cations per formula unit
• ν− = number of anions per formula unit

At infinite dilution, inter-ionic interactions become negligible and each ion conducts electricity independently.

Weak electrolytes (such as acetic acid, CH3COOH) do not fully dissociate in solution. Their molar conductivity increases steeply with dilution and cannot be directly measured at infinite dilution by extrapolation (the graph does not give a clear intercept).

Kohlrausch's law allows calculation of Λm° for weak electrolytes using the known values of strong electrolytes:

Example: For acetic acid (CH3COOH): Λm°(CH3COOH) = Λm°(HCl) + Λm°(CH3COONa) − Λm°(NaCl)

This is because:

• HCl provides λ°(H+) and λ°(Cl−)
• CH3COONa provides λ°(CH3COO−) and λ°(Na+)
• NaCl provides λ°(Na+) and λ°(Cl−)

Subtracting NaCl removes the Na+ and Cl− contributions, leaving only H+ and CH3COO−.

Kohlrausch's law enables calculation of the degree of dissociation (α) of a weak electrolyte at a given concentration:

α = Λm / Λm°

Where:

• Λm = molar conductivity at given concentration c
• Λm° = limiting molar conductivity (calculated using Kohlrausch's law)
• α = fraction of electrolyte that has dissociated

The dissociation constant Ka can then be calculated: Ka = cα² / (1 − α)

This provides a way to experimentally determine Ka for weak acids and bases through conductivity measurements.

Limiting molar ionic conductivities (λ°) at 298 K in S·cm²·mol−1:

Cations:

• H⁺: 349.6
• Na⁺: 50.1
• K⁺: 73.5
• Ca²⁺: 119.0
• Mg²⁺: 106.0

Anions:

• OH⁻: 198.6
• Cl⁻: 76.3
• NO3⁻: 71.4
• SO4²⁻: 160.0
• CH3COO⁻: 40.9

H⁺ and OH⁻ have abnormally high conductivities due to the Grotthuss mechanism (proton hopping through the hydrogen-bonded water network).

Kohlrausch's law has broad applications in electrochemistry:

1. Determining Λm° of weak electrolytes that cannot be measured directly.
2. Calculating degree of dissociation (α) of weak acids and bases.
3. Finding dissociation constants (Ka, Kb) of weak electrolytes from conductivity data.
4. Verifying ionic mobility values and understanding transport phenomena in solutions.
5. Used in industrial processes such as water quality monitoring (conductivity measurements detect ion concentration).
6. Basis for designing conductometric titrations used in analytical chemistry.