For weak acid HA at concentration C: HA <=> H+ + A-. If degree of dissociation = alpha, then [H+] = Calpha, [A-] = Calpha, [HA] = C(1-alpha). Ka = Calpha^$\frac{2}{1-alpha}$. When alpha << 1 (less than 5%), the approximation gives Ka = C$alpha^2$, so alpha = sqrt$\frac{Ka}{C}$ and [H+] = sqrt(KaC). The pH formula becomes pH = $\frac{1}{2}$(pKa + pC) where pC = -log(C). Always verify the approximation: if alpha > 5%, use the quadratic formula. Ostwald's dilution law states that alpha increases upon dilution (alpha = sqrt$\frac{Ka}{C}$ — as C decreases, alpha increases). However, the actual [H+] = sqrt(KaC) decreases upon dilution (pH increases). These two trends seem contradictory but are both true.