Question

The degree of ionization (or dissociation) of any weak electrolyte is inversely proportional to the square root of concentration and directly proportional to the square root of dilution. Which law states this and explain it?

Answer 1

Hint:We must be first knowing about the Ostwald’s dilution law. Ostwald’s dilution law will give the relationship between the dissociation constant of the weak electrolyte with the degree of dissociation and the concentration of the weak electrolyte.

Complete step-by-step answer:Let us first understand about what an Ostwald’s dilution law is. Ostwald’s dilution law will give the relationship between the dissociation constant of the weak electrolyte with the degree of dissociation and the concentration of the weak electrolyte. In other words, it can be stated that at infinite dilution, the weak electrolyte will undergo complete dilution.
Let us now consider a binary electrolyte solution \[AB\] which will dissociate reversibly into \[{A^ + }\]and \[{B^ - }\]ions. The reaction of binary electrolyte solution \[AB\]is given below.
\[AB \rightleftharpoons {A^ + } + {B^ - }\]
The dissociation constant for a binary electrolyte solution \[AB\]is given below:
\[K = \dfrac{{[{A^ + }][{B^ - }]}}{{[AB]}}\]
\[K = \dfrac{{{\alpha ^2}{C^2}}}{{(1 - \alpha )C}}\]
As \[\alpha < < < 1\]
Therefore, \[1 - \alpha = 1\]
Hence,
 \[K = {\alpha ^2}C\]
\[\alpha = \sqrt {\dfrac{K}{C}} \]
Where K is the dissociation constant
\[\alpha \]is the degree of the dissociation.

Additional information:
Let us understand about the weak and strong electrolytes.
- Weak electrolyte is the electrolyte which will undergo dissociation only partially when dissolved in water.
- Strong electrolyte is the electrolyte which will undergo dissociation completely when dissolved in water.

Note:We have to remember that the Ostwald’s dilution law has certain limitations, that is this law is applicable for weak electrolyte. This law is not applicable for strong electrolyte and saturated solutions. Only a portion of the electrolyte will be dissociated at an ordinary dilution. But the complete electrolyte will be dissociated at the infinite dilution.