We represent the general reaction of an acid in water by the following equilibrium.......
#HX(g) + H_2O(l) rightleftharpoonsH_3O^+ + X^-#
The extent to which this equilibrium lies to the RIGHT, specifies the STRENGTH of the acids. Acids such as #H_2SO_4,HClO_4, HX(X!=F)#, are all strong acids. And this #H_3O^+#, the hydronium ion, is CONCEIVED to be a protonated water molecule.........i.e. #H^+ + H_2O rarr H_3O^+# (mass and charge are conserved as always!) The #HX# molecule has been IONIZED, and we get charge-separated ions, formally #H^+# or #X^-#.
And thus #HCl(g)# (for instance) is a source of hydronium ion, #H_3O^+# in aqueous solution.........
We may take a tank of #HCl(g)#, a room temperature gas, and we can bleed it in to water to give an AQUEOUS solution that we could represent as #HCl(aq)# OR #H_3O^+# and #Cl^−#.
#HCl(g) stackrel(H_2O)rarrunderbrace(H_3O^(+))_("hydronium ion") +Cl^-#
In each case this is a REPRESENTATION of what occurs in solution. If we bleed enuff gas in, we achieve saturation at a concentration of approx. #10.6*mol*L^-1# with respect to hydrochloric acid - of course the acid has been #"ionized"#.
As far as anyone knows, the actual acidium ion in solution is #H_3O^+#, or #H_5O_2^+#, or #H_7O_3^+#, i.e. a cluster of 2 or 3 or 4 water molecules with an EXTRA #H^+# tacked on. We represent it in solution (without loss of generality) as #H_3O^+#, the #"hydronium ion"#, which is clearly the conjugate acid of #H_2O#. Sometimes, especially when we are first introduced to the concept, we represent it simply as the #"protium ion"#, i.e. #H^+#, which is perhaps a bit simpler, but ignores the water solvent.
Note that the #H^+# is quite mobile, and passes, tunnels if you like, the extra #H^+# from cluster to cluster. If you have ever played rugby, I have always liked to compare this to when the forwards form a maul, and can pass the pill from hand to hand to the back of the maul while the maul is still formed.
Of course, tunnelling, proton transfer, is more likely in a cluster of water molecules, so the analogy might not be particularly apt in that there is definite transfer of a ball in a maul, but a charge in a water cluster is conceivably tunnelled. The same applies to the transfer of an hydroxide ion. For this reason both #H^+"/"H_3O^+# and #HO^-# have substantial mobility in aqueous solution.
And we know that hydroxide/hydronium ions obey the following equilibrium in aqueous solution at #298*K#.......
#H_3O^+ + HO^(-) rarr2H_2O#; #K_w=[H_3O^+][HO^-]=10^(-14)#.
Depending at which level you are at (and I don't know!, which is part of the problem in answering questions on this site), you might not have to know the details at this level of sophistication. The level I have addressed here is probably 1st/2nd year undergrad.........
