It is tempting to assume that #HO^-# and #H_3O^+# are actual species in aqueous species. As far as anyone knows these species are CLUSTERS of water molecules LESS or PLUS a proton...
And so #HO^(-)"/"H^+# or #HO^(-)"/"H_3O^+# are likely to be #H_5O_3^(+)# or #H_7O_4^-# or ...or something...we use the #HO^(-)"/"H_3O^+# as a label of convenience...the acidium species is a water cluster associated with an extra proton, and the hydroxide species is a water cluster LESS a proton. And if you play rugby think of #H^+# as the ball in a maul.
But certainly, when we do acid-base titrations, we can find the equivalence of acids and bases, straightforwardly and quantitatively, using very simple equipment, calibrated burettes, and standard indicatos.
And we use the brackets to designate a concentration term: #[H_3O^+][HO^-]=10^(-14)# under standard conditions. And for simplicity, when we see #[H_3O^+]# or #[NO_3^(-)]# or #[Cl^-]#, we mean the concentration of acidium ion, or nitrate ion, or chloride in #mol*L^-1#...
