Question

State Kohlrausch law, and write the mathematical expression of molar conductivity of the given solution at infinite dilution.

Answer 1

Hint: Molar conductivities of the compound are studied based on the number of anions and cations. The difference between the electrolytes is calculated for this. It involves infinite dilution.

Complete answer:
Kohlrausch studied the molar conductivities at infinite dilution \[{{\lambda }^{\circ }}_{m}\] for several pairs of strong electrolyte, each pair having a common cation or anion.
Based on his observation, Kohlrausch concluded that each ion makes a definite contribution to the total molar conductivity of an electrolyte at infinite dilution, irrespective of the nature of the other ions of the electrolyte. This individual contribution of an ion towards the total molar conductivity of the electrolyte is called molar ionic conductivity.
As a result, it states that:
The limiting molar conductivity of the electrolyte (i.e. molar conductivity at infinite dilution) is the sum of the limiting ionic conductivities of the cation and the anion each multiplied with the number of ions present in one formula unit of the electrolyte.

Mathematically,
\[{{\lambda }^{\circ }}_{m}\text{ for }{{\text{A}}_{\text{x}}}{{\text{B}}_{\text{y}}}=x{{\lambda }^{\circ }}_{+}+y{{\lambda }^{\circ }}_{-}\]
Where \[{{\lambda }^{\circ }}_{m}\] is the limiting molar conductivity of the electrolyte, \[{{\lambda }^{\circ }}_{+}\] and \[{{\lambda }^{\circ }}_{-}\] are the limiting molar conductivities of the cation (\[{{\text{A}}^{y+}}\]) and the anion (\[{{\text{B}}^{x-}}\]) respectively.

For example,
\[{{\lambda }^{\circ }}_{m}\text{ for NaCl}=x{{\lambda }^{\circ }}_{Na+}+y{{\lambda }^{\circ }}_{Cl-}\]
The equivalent conductivity of an electrolyte at infinite dilution is the sum of two values one depending upon the cation and the other upon the anion,
\[{{\lambda }^{\circ }}_{eq}={{\lambda }^{\circ }}_{c}+{{\lambda }^{\circ }}_{a}\]
Where \[{{\lambda }^{\circ }}_{c}\] and \[{{\lambda }^{\circ }}_{a}\] are called the limiting ionic conductivities for the cation and the anion respectively.

Note: This law is applicable only for the salts of the compounds that can split into cations and anions. While calculating the limiting molar conductivities do not forget to multiply with the number of ions present.