Kohlraush's Law - Application with example

KOHLRAUSH'S LAW

This law states that, ''at infinite dilution wherein the ionisation of all electrolytes is complete, each ion migrates independently and contributes a definite value to the total equivalent conductance of the electrolyte''. Consider an electrolyte AB in aqueous solution. It dissociates as

A_mB_n --- --- > mAⁿ⁺   +  nB^m-

Then at infinite dilution, according to Kohlrausch's law, the total equivalent conductance of the electrolyte, λ ∞ = (1/n⁺ ) λ_A+ + (1/m- ) λ_B-  where λ_∞⁺  and λ_∞^- are the cationic and anionic equivalent conductances at infinite dilutions and n+ and m- correspond the valency of cations and anions furnished from each molecule of the electrolyte.

Application of Kohlraush's law : The important use of Kohlraush's law is to deduce the l_¥ value of the weak electrolytes correctly by arithmetically combining the l_¥ values of strong electrolyte in appropriate manner.

For example λ_∞ of CH₃COOH which is a weak electrolyte is deduced from λ_∞ values of NaCl, HCl, and CH₃COONa in such a manner that λ_∞ of CH₃COOH is obtained. Sodium acetate (CH₃COONa) is a strong electrolyte and it ionises to acetate (CH₃COO^- ) and sodium (Na⁺) ions at all concentrations in water. Applying Kohlraush's law,

Molar conductances at infinite dilution : (m_¥) when an electrolyte dissociates into g₊ number of cations and g_- number of anions then total molar conductance at infinite dilution m_¥ of the electrolyte is given by

A _γ+ B _{γ -}  ---- >  g₊ A⁺ + γ _- B^-

The common ion effect

When a soluble salt (say A⁺C^- ) is added to a solution of another salt (A⁺B^- ) containing a common ion (A+), the dissociation of AB is suppressed.

AB  < --- > A⁺ + B^-

By the addition of the salt (AC), the concentration of A⁺ increases. Therefore, according to Le Chatelier's principle, the equilibrium will shift to the left, thereby decreasing the concentration of A⁺ ions or the degree of dissociation of AB will be reduced.

The reduction of the degree of dissociation of a salt by the addition of a common-ion is called the Common-ion effect.