Ostwald's Dilution Law

Since a weak electrolyte sets up a genuine ionization equilibrium, its degree of ionization $\alpha$

can be derived quantitatively from the ionization constant using an equilibrium (ICE) table, exactly

as for any other equilibrium — this quantitative relationship is called Ostwald's dilution law.

Consider a weak monobasic acid $\text{HA}$ at an initial molar concentration $C$, ionizing as

$\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$. If $\alpha$ is the degree of ionization at

equilibrium, the equilibrium concentrations are $[\text{HA}] = C(1-\alpha)$, $[\text{H}^+] = C\alpha$

and $[\text{A}^-] = C\alpha$. Substituting into the equilibrium-constant expression,

For a weak acid, $\alpha$ is small enough that $1 - \alpha \approx 1$ to a good approximation, which

simplifies the expression to $K_a \approx C\alpha^2$, and rearranging gives Ostwald's dilution law in

its most-used form:

This single relation has an immediate, testable consequence: since $\alpha$ is inversely proportional

to $\sqrt{C}$, diluting a weak electrolyte's solution (decreasing $C$) increases its degree of

ionization $\alpha$ — the same weak acid ionizes to a noticeably greater fractional extent when more

dilute, even though the ionization constant $K_a$ itself, being a true equilibrium constant, stays

exactly the same at a fixed temperature. Physically, dilution reduces the concentration of ions

already in solution, so by Le Chatelier's principle the ionization equilibrium shifts further forward

to partially replace them.

For example, a weak acid with $K_a = 1.8 \times 10^{-5}$ ionizes to about $1.3\%$ in a $0.1\ \text{M}$ …