Q.A weak monobasic acid $\text{HA}$ has $K_a = 1.8 \times 10^{-5}$. Using Ostwald's dilution law, calculate its degree of ionization $\alpha$ in a $0.1\ \text{M}$ solution.

Ostwald's dilution law quantifies exactly how the degree of ionization $\alpha$ of a weak electrolyte

depends on its concentration, by applying the equilibrium law to the ionization equilibrium itself.

For a weak monobasic acid $\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$ at initial

concentration $C$ and degree of ionization $\alpha$, the equilibrium concentrations are

$[\text{HA}] = C(1-\alpha)$ and $[\text{H}^+] = [\text{A}^-] = C\alpha$, so

For a weak acid, $\alpha \ll 1$ so $1 - \alpha \approx 1$, simplifying this to $K_a \approx C\alpha^2$

and hence

Because $\alpha$ varies as $1/\sqrt{C}$, dilution increases the degree of ionization: the same weak

acid ionizes to a noticeably larger fraction in a more dilute solution, even though its ionization

constant $K_a$ — a genuine equilibrium constant — stays exactly the same at fixed temperature. The …