Careful experiment established the following equilibrium in aqueous solution:
#H_2O rightleftharpoons H^(+) + HO^-#
Which has an alternative representation:
#2H_2O rightleftharpoons H_3O^(+) + HO^-#
#K_w=[H_3O^+][HO^-]=10^(-14)# under standard conditions.......
So what is the #"acidium ion"#? As far as anyone knows it is a cluster of 3 or 4 or so water molecules with an extra #H^+#, to give, say...........
#H_7O_3^+# or #H_9O_4^+#; the extra #H^+# can tunnel between clusters of water molecules VERY rapdidly - think of a maul when you play rugby.
When acids are added to water solvent, we conceive that the acid protonates the solvent to give hydronium ions:
#HX(aq) + H_2O(l) rightleftharpoonsH_3O^+ + X^-#
The #H_3O^+# ion, the #"hydronium ion"# is thus a conceptual species, but this conception allows us to solve quantitative problems in stoichiometry. We write #H^+# or #H_3O^+# as a shorthand. The completion of the equilibrium, i.e. how far to OUR right as we read the page, is a measure of the strength of the acid. For strong acids, #HClO_4#, #H_2SO_4#, #HX# #(X!=F)#, the equilibrium lies almost entirely to the right.