Which of these is the strongest acid? #"HCl"#, #"H"_3"PO"_4#, #"CH"_3"COOH"#

#"HCl"# is the only strong acid in this selection of acids.

The highest #["H"^(+)]# comes from the acid, #"HA"#, that dissociates into #"H"^(+)# and #"A"^(-)# (its conjugate base) the most:

#"HA"(aq) + "H"_2"O"(l) rightleftharpoons "H"_3"O"^(+)(aq) + "A"^(-)(aq)#

(note that #"H"_3"O"^(+)# and #"H"^(+)# are different representations for equivalent species.)

By definition, a strong acid dissociates pretty much completely, so it must give the most #"H"^(+)# into solution.

This can be quantified by their acid dissociation constants, #K_a#:

#"HCl"#: #K_a ~~ 10^7#

#"H"_3"PO"_4#: #K_(a1) = 6.9 xx 10^(-3)#

#"CH"_3"COOH"#: #K_a = 1.76 xx 10^(-5)#

Based on the values of the #K_a#'s, which do you think is the weakest acid (considering only the first proton)?

When we talk of the strength of an acid, we refer to the following equilibrium reaction in water:

#HX(aq) rightleftharpoons H^(+) + X^-#

The further the equilibrium lies to the right hand side as we face the page, the STRONGER is the acid. (Sometimes we represent #H^+# as the hydronium ion, #H_3O^+#, i.e. protonated water:

#HX(aq) + H_2O(l) rightleftharpoons H_3O^+ + X^-#)

For the LOWER hydrogen halides, #HCl#, #HBr#, #HI#, (but not for #HF)#, the given equilibrium lies almost quantitatively to the right. Thus #1*mol*L^-1# solutions of #HCl#, #HBr#, are almost quantitative in #H^+#, i.e. #H^(+)=1.0*mol*L^-1#

For acetic acid and phosphoric acid, the equilibrium would not go to completion:

#H_3"CCO"_2H(aq) rightleftharpoons H_3"CCO"_2^(-) +H^+#

Mind you phosphoric acid has a lower #pK_(a1)# than acetic acid.