Question

Write the definition of Kohlrausch law of independent migration of ions.

Answer 1

Hint: When we talk about this law,we must remember that it's applications are seen in the case of weak electrolytes. As these electrolytes cannot dissociate completely into ions ,and thus it is difficult to obtain certain quantities, this law comes into play there.

Complete step by step solution:
First let us try to understand few law related terms here:
- Conductivity: It is defined as the ability of an electrolyte to conduct electricity. It is represented by $\text{ }\!\!\kappa\!\!\text{ }$.
- Molar conductivity: The ratio of conductivity by molar concentration of a solution is molar conductivity.It is represented by ${{\text{ }\!\!\Lambda\!\!\text{ }}_{\text{m}}}$
- limiting molar conductivity: As the molar conductivity increases with decrease in concentration, the value at which concentration approaches to zero,it is known as limiting molar conductivity. It is represented by ${{\text{ }\!\!\Lambda\!\!\text{ }}^{\text{o}}}_{\text{m}}$ .
So now let's know when is the Kohlraush law applied:
- The equivalent conductance of a solution like acetic acid increases with dilution and thus we cannot accurately obtain a limiting value of molar conductivity, when the dissociation is complete (at $\text{ }\!\!\alpha\!\!\text{ =1}$ )even when the conductance of such electrolytes approaches to zero.
- And in case of strong electrolytes, this law helps in determining the limiting molar conductivity. So Kohlraush law helps in determining the limiting molar conductivity of strong electrolytes like NaCl, KCl etc.
- It is given by the equation: ${{\text{ }\!\!\Lambda\!\!\text{ }}^{\text{o}}}_{\text{m}}$$\text{=}{{\text{ }\!\!\nu\!\!\text{ }}_{\text{+}}}{{\text{ }\!\!\lambda\!\!\text{ }}^{\text{o}}}_{\text{+}}\text{+}{{\text{ }\!\!\nu\!\!\text{ }}_{\text{-}}}{{\text{ }\!\!\lambda\!\!\text{ }}^{\text{o}}}_{\text{-}}$ ,where ${{\text{ }\!\!\nu\!\!\text{ }}_{\text{+}}}$are cations and${{\text{ }\!\!\nu\!\!\text{ }}_{\text{-}}}$are anions on dissociation of strong electrolytes. ${{\text{ }\!\!\nu\!\!\text{ }}_{\text{-}}}$ ${{\text{ }\!\!\nu\!\!\text{ }}_{\text{+}}}$
- Thus in order to determine the equivalent conductance at infinite dilution of electrolytes ,we have devised a method known as Kohlraush law.
- This law states that at infinite dilution, when the dissociation gets completed,each ion of the electrolyte makes a definite contribution in the equivalent conductance irrespective of its nature with which it is associated and the value of the equivalent conductance obtained here is the sum of the contribution by each of its ions,which are anions and cations.
Now let's check the formulas of determining the limiting molar conductivity by this law:
- It is given by the equation: ${{\text{ }\!\!\Lambda\!\!\text{ }}^{\text{o}}}_{\text{m}}$$\text{=}{{\text{ }\!\!\nu\!\!\text{ }}_{\text{+}}}{{\text{ }\!\!\lambda\!\!\text{ }}^{\text{o}}}_{\text{+}}\text{+}{{\text{ }\!\!\nu\!\!\text{ }}_{\text{-}}}{{\text{ }\!\!\lambda\!\!\text{ }}^{\text{o}}}_{\text{-}}$, where ${{\text{ }\!\!\nu\!\!\text{ }}_{\text{+}}}$ are cations and ${{\text{ }\!\!\nu\!\!\text{ }}_{\text{-}}}$ are anions on dissociation of strong electrolytes.
At a concentration c, the degree of dissociation $\text{ }\!\!\alpha\!\!\text{ }$ is given by: ${{\text{ }\!\!\nu\!\!\text{ }}_{\text{-}}}$$\text{ }\!\!\alpha\!\!\text{ =}\dfrac{{{\text{ }\!\!\Lambda\!\!\text{ }}_{\text{m}}}}{{{\text{ }\!\!\Lambda\!\!\text{ }}^{\text{o}}}_{\text{m}}}$
Now,in case of weak electrolytes like acetic acid we use the following formula: ${{\text{K}}_{\text{a}}}\text{=}\dfrac{\text{c}{{\text{ }\!\!\alpha\!\!\text{ }}^{\text{2}}}}{\left( \text{1- }\!\!\alpha\!\!\text{ } \right)}\text{=}\dfrac{\text{c }\!\!\Lambda\!\!\text{ }_{\text{m}}^{\text{2}}}{{{\text{ }\!\!\Lambda\!\!\text{ }}^{\text{o}}}_{\text{m}}\left( {{\text{ }\!\!\Lambda\!\!\text{ }}^{\text{o}}}_{\text{m}}\text{-}{{\text{ }\!\!\Lambda\!\!\text{ }}_{\text{m}}} \right)}$,
Where ${{\text{K}}_{\text{a}}}$ is the dissociation constant of acid and c is the concentration.

Note: By using the Kohlraush law of independent migration of ions, it is possible to calculate the limiting molar conductivity for any electrolyte by it's individual ions, and in case of weak electrolytes it is possible to determine the dissociation constant, once we are able to determine the molar and limiting molar conductivity at a concentration c.