Question

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

Answer 1

Hint: We need to define and understand the Kohlrausch’s law along with molar conductivity. Molar conductivity is studied for electrolytic solutions based on their ions. Conductivity is defined as the rate at which heat passes through a specified material. The molar conductivity of an electrolyte solution is defined as its conductivity divided by its molar concentration. The Kohlrausch Law is used to study the molar conductivities at infinite dilution.

Complete answer:
We have to remember that in an electrolytic solution, the Kohlrausch’s Law is used to study the contribution of molar conductivities of the ions of an electrolyte to the total molar conductivity of the electrolyte. This individual contribution of the ions of an electrolyte is called molar ionic conductivity. The total molar conductivity of an electrolyte at infinite dilution is symbolized as \[\lambda {^\circ _m}\] . The total molar conductivity at infinite dilution is also known as Limiting molar conductivity.
Hence, the Kohlrausch Law states that the limiting molar conductivity of an electrolyte is the sum of the limiting ionic conductivities of the anion and the cation each multiplied by the number of ions present in one formula unit of the electrolyte.
Mathematical expression of molar conductivity of the given solution at infinite dilution: Let \[{A_x}{B_y}\] be the formula unit of an electrolyte where \[{A^{x + }}\] is the cation and \[{B^{y - }}\] is the anion and \[{\lambda ^ \circ }_ + \] is the limiting molar conductivity of the cation and \[{\lambda ^ \circ }_ - \] is the limiting molar conductivity of the anion. Hence the limiting molar conductivity of the electrolyte is given mathematically by\[{\lambda ^ \circ }_m = x{\lambda ^ \circ }_ + + y{\lambda ^ \circ }_ - \]

Note:
 It must be noted that weak electrolytes have lower molar conductivities and lower degrees of dissociation. Hence the Kohlrausch’s Law can be used to determine the extent of dissociation by finding the value of the dissociation constant. It can also be used to calculate the solubility of a sparingly soluble salt. This law is only applicable for electrolytes.