Question

Explain Ostwald's dilution law.

Answer 1

Ostwald's dilution law relates the dissociation constant of the weak electrolyte with the degree of dissociation and the concentration of the weak electrolyte. Consider the dissociation equilibrium of $C{H}_{3}COOH$ which is a weak electrolyte in water.
$C{H}_{3}COOH\rightleftharpoons C{H}_{3}CO{O}^{-}+H^{+}$
$K_a=\frac{\left[C{H}_{3}CO{O}^{-}\right]\left[H^{+}\right]}{\left[C{H}_{3}COOH\right]}$
$\alpha$=degree of dissociation of acetic acid.
$\therefore K_a=\frac{\alpha C\times \alpha C}{(1-\alpha )C}$

$K_a=\frac{{\alpha }^{2}C}{1-\alpha }$

Ostwald's dilution law
If $\alpha$ is too small, $K_a={\alpha }^{2}C$
${\alpha }^{2}C=K_a$
${\alpha }^2=\frac{K_a}{C}$
$\alpha =\sqrt{\frac{K_a}{C}}$
$\left[H^1\right]=C\alpha$
$=C\sqrt{\frac{K_a}{C}}$
$=\sqrt{\frac{K_a{C}^2}{C}}=\sqrt{K_{a}C}$
$\therefore \left[H^{+}\right]=\sqrt{K_{a}C}$
$K_a={\alpha }^{2}C-$Ostwald's dilution law for weak acid.
$K_b={\alpha }^{2}C-$Ostwald's dilution law for weak base.