Question
Derive the relationship between degree of dissociation and dissociation constant in weak electrolytes.

Answer


Expression of Ostwald’s dilution law in the case of a weak electrolyte :
Consider the dissociation of a weak electrolyte BA.
Let V dm$^3$ of a solution contain one mole of the electrolyte.
Then the concentration of a solution is, $C =\frac{1}{V} mol \ dm ^{-3}$.
Let α be the degree of dissociation of the electrolyte.

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Applying the law of mass action to this dissociation equilibrium, we have,

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As the electrolyte is weak, α is very small as compared to unity,
$\therefore (1 – \alpha ) ≈ 1.$
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This is the expression of Ostwald’s dilution law.
Thus, the degree of dissociation of a weak electrolyte is directly proportional to the square root of the volume of the solution containing $1$ mole of an electrolyte.

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