Kohlraush’s Law and its Applications

Kohlrausch's law states that at infinite dilution, each ion contributes a definite amount to an electrolyte's molar conductance, regardless of its counter ion. The total molar conductance at infinite dilution (Λ°m) is the sum of individual molar ionic conductances. This principle applies because ion contributions become independent of other ions present when the solution is highly diluted and dissociation is complete.

Kohlrausch's law enables transport number calculation because molar ionic conductance at infinite dilution is directly proportional to ion mobility. Since each ion's conductance contribution is known and independent, the transport number of cations and anions can be expressed in terms of their individual molar ionic conductances. This relationship allows quantification of how much electrical charge each ion carries in solution.

Weak electrolytes do not completely dissociate in solution, so their molar conductance cannot be directly measured at infinite dilution. Kohlrausch's law solves this by enabling indirect calculation using known Λ°m values of strong electrolytes. For example, acetic acid's Λ°m is found by adding the Λ°m values of HCl and sodium acetate, then subtracting the Λ°m of NaCl to isolate the required ionic contributions.

Once Kohlrausch's law provides the molar conductance at infinite dilution (Λ°m) for a weak electrolyte, the degree of dissociation can be determined as the ratio of measured molar conductance (Λm) to Λ°m. This ratio indicates what fraction of the electrolyte molecules have dissociated into ions. The add-subtract approach using strong electrolyte values cancels common ions and isolates the weak electrolyte's true conductance contribution.

The add-subtract method calculates Λ°m for sparingly soluble salts like silver chloride by combining known Λ°m values of strong electrolytes. For AgCl, add the Λ°m values of NH4Cl and AgNO3, then subtract the Λ°m of NH4NO3. This approach isolates the ionic contributions of Ag+ and Cl- while canceling the NH4+ and NO3- ions that appear in multiple salts but not in the target compound.

For sparingly soluble salts like silver chloride, Kohlrausch's law allows solubility calculation by first measuring the conductivity of a saturated solution. The difference between solution conductivity and water conductivity, multiplied by the cell constant, gives the specific conductance of dissolved salt. Since sparingly soluble salts have extremely low solubility, their molar conductance approximates Λ°m, enabling solubility determination through Kohlrausch's law.

Kohlrausch's law provides the theoretical foundation for conductometric titrations by establishing that ionic conductance contributions are additive and independent. Understanding molar ionic conductances at infinite dilution allows prediction of conductivity changes during conductometric titrations strong acid base and weak acid base titrations, where ion concentrations change as reactants are neutralized and products form.