What is the Arrhenius concept of acidity?

And the autoprotolysis reaction of water was proposed to be:

#H_2O(l) rightleftharpoons H^(+) + HO^-#

And so for the stoichiometric equation:

#Ba(OH)_2(s) + 2HCl(aq) rarr BaCl_2(aq) + 2H_2O#

We could write the net ionic equation:

#HO^(-) + H^(+) rarr H_2O#

Clearly, stoichiometry requires that we add 2 equiv hydrochloric acid per equiv barium hydroxide.

In Arrhenius' view, the HCl solution would be a mixture of #H^+# and #Cl^-# ions.

Barium hydroxide is slightly soluble, so you could write is in aqueous form or as a solid. Here is the former:

#H^+ + Cl^- ##+ Ba^(2+) + OH^-## rarr Ba^(2+) + Cl^- + H_2O#

To balance this, you note that #Ba(OH)_2# has two hydroxide ions, and requires two hydrogen ions for complete reaction:

#2H^+ + 2Cl^- ##+ Ba^(2+) + 2OH^-## rarr Ba^(2+) + 2Cl^- + 2H_2O#

Or, if the net ionic equation is desired, leave out the #Ba^(2+)# and #Cl^-# ions. (They do not change during the reaction.)

#2H^+ +2OH^-## rarr 2H_2O#

which of course, is the neutralization reaction.

If you write the reaction showing barium hydroxide as a solid, it looks like this:

#2H^+ + 2Cl^- ##+ Ba(OH)_2(s) rarr Ba^(2+) + 2Cl^- + 2H_2O#