An acid $HB$ is called weak if its proton exchange with water (protolysis, dissociation) reaction to give the corresponding base $B$ $HB$ $+$ $H_2O$ $\rightleftarrows$ $ H_3O^+$ $+$ $B$ is incomplete, therefore limited to an equilibrium.
- Note the double arrow for this reaction $\rightleftarrows$ - Eventual charges of $HB$ and $B$ are not shown in this general formula.
The aqueous solution of strong acid is formed by the corresponding base and hydronium ions, while the weak acid solution containing both acid and the corresponding base and also hydronium ions.
The aqueous solution of acetic acid (a weak acid) contains both of the acetic acid molecules $CH_3COOH$, $CH_3COO^-$ acetate ions and hydronium $H_3O^+$ ions
$HF$ $+$ $H_2O$ $\rightleftarrows$ $H_3O^+$ $+$ $F^-$ (Fluorhydric acid / fluoride ion) $NH_4^+$ $+$ $H_2O$ $\rightleftarrows$ $H_3O^+$ $+$ $NH_3$ (Ammonium ion/ammonia) $HCO_3^-$ $+$ $H_2O$ $\rightleftarrows$ $H_3O^+$ $+$ $CO_3^{2-}$ (Hydrogencarbonate ion/carbonate ion)