Question

State and explain Kohlrausch’s law of independent migration of ions. Give the application of kohlrausch's law of independent migration of ions.

Answer 1

.Kohlrausch observed some regularities when associating the values of limiting molar conductivities of some strong electrolytes in a solution. On the base of his remarks, Kohlrausch proposed that ‘molar conductivity of an electrolyte in a solution can be represented as the sum of the individual conductivity of the anions and cations generated from the electrolyte.

Complete answer:
Kohlrausch's law of independent migration of ions explains about the limiting molar conductivity of an electrolyte can be denoted as the sum of the amounts of individual contributions of its cations and anions. The conductivity of the solution decreases with dilution because fewer ions are only present for conduction.
We can represent the above definition in the form of following formula
${{\Lambda }_{0}}=\lambda _{+}^{0}+\lambda _{-}^{0}$
Here,
${{\Lambda }_{0}}$= the molar conductivity of the electrolyte at zero concentration
$\lambda _{+}^{0}$​= the molar conductivity of cation at zero concentration
$\lambda _{-}^{0}$= the molar conductivity of anion at zero concentration
The representation of Kohlrausch's law of independent migration of ions to the solution of Hydrochloric acid solution is as follows.
${{\Lambda }_{0}}(HCl)={{\lambda }_{0}}({{H}^{+}})+{{\lambda }_{0}}(C{{l}^{-}})$
Here,
${{\Lambda }_{0}}(HCl)$= the molar conductivity of HCl at zero concentration
${{\lambda }_{0}}({{H}^{+}})$ = the molar conductivity of protons (${{H}^{+}}$) at zero concentration
${{\lambda }_{0}}(C{{l}^{-}})$ = the molar conductivity of chloride ions ($C{{l}^{-}}$) at zero concentration.

Application of Kohlrausch's law
It is used to calculate the degree of dissociation of weak electrolyte at a specific concentration.
The formula is as follows
Degree of dissociation of weak electrolyte $\begin{aligned} & (\alpha )=\dfrac{\Lambda _{m}^{e}}{\Lambda _{m}^{\infty }} \\\ & \\\ \end{aligned}$
$\Lambda _{m}^{e}$= molar conductivity of weak electrolyte at a specific concentration
$\Lambda _{m}^{\infty }$ = molar conductivity of weak electrolyte at infinite dilution

Note:
Kohlrausch's law used to
Calculation the Degree of dissociation of an electrolyte.
Calculation of the solubility of sparingly soluble salt in a solvent.
Calculate the Dissociation Constant for weak electrolytes in a solvent.
Calculate the Molar Conductivity of weak electrolytes at infinite dilution.