When an acid dissolves in a solvent it is conceived to increase the concentration of the CHARACTERISTIC CATION solvent of the solvent. And we commonly use water as a solvent....and so should we dissolve #HX# in water, protonolysis of the solvent is conceived to occur......to give the hydronium ion.
#HX(g) +H_2O(l) rarr underbrace(H_3O^+)_"hydronium ion" + X^-#
or more simply we designate the acid principle as #"protium ion":#
#HX(g) stackrel(H_2O)rarr underbrace(H^+)_"protium ion" + X^-#
And note that this is a conception rather than an actuality, the actual acid species, is probably #H_9O_4^+#; a cluster of 3-4 water molecules WITH an EXTRA PROTON, that passes rapidly, tunnels if you like from cluster to cluster. We use #H_3O^+# or #H^+# interchangeably to represent this species in solution.
#HX(g) +H_2O(l) rightleftharpoons underbrace(H_3O^+)_"hydronium ion" + X^-#
The strength of the acid is defined by the completeness of the equilibrium. For strong mineral acids, #H_2SO_4#, #HClO_4#, #HX#, #(X!=F)#, the equilibrium LIES to the right as we face the page.
For weaker acids, #HOAc#, #HF#, #NH_4^+#, the equilibrium lies to the left as written.....