Why is \(\mathrm{H}_{3} \mathrm{O}^{+}\) the strongest acid and \(\mathrm{OH}^{-}\) the strongest base that can exist in significant amounts in aqueous solutions?

In water, a small fraction of molecules undergo autoionization, a process where one water molecule donates a proton (H+) to another water molecule. This forms a hydronium ion, \(\mathrm{H}_{3} \mathrm{O}^{+}\), and a hydroxide ion, \(\mathrm{OH}^{-}\). The process can be represented by the chemical equation: \[2 \, \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}_3\mathrm{O}^+ + \mathrm{OH}^-\]

The equilibrium constant for the ionization of water (Kw) is defined as the product of the concentrations of the hydronium (\(\mathrm{H}_{3} \mathrm{O}^{+}\)) and hydroxide (\(\mathrm{OH}^{-}\)) ions in water: \[K_w = [\mathrm{H}_3\mathrm{O}^+][\mathrm{OH}^-]\] At 25°C, Kw is approximately equal to \(1.0 \times 10^{-14}\).

For an acid HA, the acid dissociation constant (Ka) represents the equilibrium constant for the dissociation of the acid in water: \[\mathrm{HA} \rightleftharpoons \mathrm{H}^+ + \mathrm{A}^-\] \[K_a = \frac{[\mathrm{H}^+][\mathrm{A}^-]}{[\mathrm{HA}]}\] A higher Ka value indicates a stronger acid, meaning it dissociates more completely in water.

A strong acid will completely dissociate in water and donate a proton to a water molecule, producing a hydronium ion (\(\mathrm{H}_{3} \mathrm{O}^{+}\)) in the process. The strong acid donates its proton to the strongest base, the hydroxide ion (\(\mathrm{OH}^{-}\)), forming two water molecules in the process. In this process, the reverse reaction is negligible. In aqueous solution, the hydronium ion (\(\mathrm{H}_{3} \mathrm{O}^{+}\)) and the hydroxide ion (\(\mathrm{OH}^{-}\)) are always present, formed by the autoionization of water. If a stronger acid or base than these two ions would exist in significant amounts, it would react with the respective other ion and form different species with a higher affinity for protons in equilibrium. Thus, for both, no stronger acid or base can exist in water in significant amounts, since the accumulation of either a stronger acid or base will cause the corresponding ions to react, immediately forming less reactive species that will reach equilibrium at some point.