Acid or base strength describes how extensively a substance reacts with water to produce its characteristic ions. It is not the same as concentration.

A strong acid transfers essentially all available acidic protons to water under ordinary dilute aqueous conditions. For a monoprotic strong acid represented as $\mathrm{HA}$,

$$\mathrm{HA+H_2O\rightarrow H_3O^+ + A^-}$$

is treated as going essentially to completion.

Likewise, a soluble strong base produces hydroxide essentially completely. Sodium hydroxide, for example, dissociates as

$$\mathrm{NaOH(aq)\rightarrow Na^+(aq)+OH^-(aq)}.$$

A weak acid ionizes only partially:

$$\mathrm{HA+H_2O\rightleftharpoons H_3O^+ + A^-},$$

so appreciable amounts of both $\mathrm{HA}$ and its ions coexist at equilibrium. A weak base behaves analogously, accepting protons from water only partially.

Strength is not concentration

A solution can be:

• concentrated and weak, such as a relatively concentrated acetic-acid solution;
• dilute and strong, such as a very dilute hydrochloric-acid solution.

Concentration tells how much acid or base was supplied per volume. Strength tells how far its proton-transfer reaction proceeds.

The distinction also explains why writing a single arrow or an equilibrium arrow matters. Strong acids and bases are normally represented as essentially complete ionization in introductory aqueous calculations; weak acids and bases require an equilibrium treatment.

Strength is also relative to the solvent. Water reacts so completely with sufficiently strong acids that their individual strengths are effectively hidden: they all produce hydronium as the strongest acid that can persist in appreciable amount in water. An analogous leveling occurs for strong bases, which produce hydroxide.

The extent of ionization of weak acids and bases is quantified by acid- and base-ionization equilibrium constants.