Question

What is Kohrausch law of independent migration of ions? How is it useful in obtaining molar conductivity at zero concentration of a weak electrolyte ? Explain with an example.

Answer 1

(A) Statement of Kohlrausch’s law : This states that at infinite dilution of the solution, each ion of an electrolyte migrates independently of its co-ions and contributes independently to the total molar conductivity of the electrolyte, irrespective of the nature of other ions present in the solution.

(B) Explanation : Both the ions, cation and anion of the electrolyte make a definite contribution to the molar conductivity of the electrolyte at infinite dilution or zero concentration (∧₀).

If \(\lambda^0_+\) and \(\lambda^0_-\) are the molar ionic conductivities of cation and anion respectively at infinite dilution, then

∧₀ = \(\lambda^0_+\) + \(\lambda^0_-.\)

This is known as Kohlrausch’s law of independent migration of ions.

For an electrolyte, \(B_xA_y\) giving x number of cations and y number of anions,

 ∧₀ = x\(\lambda^0_+\) + y\(\lambda^0_-.\)

(C) Applications of Kohlrausch’s law : 

(1) With this law, the molar conductivity of a strong electrolyte at zero concentration can be determined. 

For example,

(2) ∧₀ values of weak electrolyte with those of strong electrolytes can be obtained. 

For example,

Molar conductivity of a weak electrolyte at infinite dilution or zero concentration cannot be measured experimentally.

Consider the molar conductivity (∧₀) of a weak acid, CH₃COOH at zero concentration. By Kohlrausch s law,

where \(\lambda^0CH_3COO^-\) and \(\lambda^0{_{H+}}\) are the molar ionic conductivities of CH₃COO^- and H⁺ ions respectively.

If ∧_0CH3COONa, ∧_0HCl and ∧_NaCl are molar conductivities of CH₃COONa, HCl and NaCl respectively at zero concentration, then by Kohlrausch’s law,

Hence, from ∧₀ values of strong electrolytes, ∧ of a weak electrolyte CH₃COOH, at infinite dilution can be calculated.