Barium hydroxide, Ba(OH)_2Ba(OH)2, is a strong base, so it will react with hydrochloric acid, HClHCl, a strong acid, to produce water and barium chloride, a soluble salt.
Keep in mind that barium hydroxide is not very soluble in aqueous solution, but what does dissolve will dissociate completely to form barium cations, Ba^(2+)Ba2+, and hydroxide anions, OH^(-)OH−.
Ba(OH)_(2(aq)) -> Ba_text((aq])^(2+) + 2OH_((aq))^(-)Ba(OH)2(aq)→Ba2+(aq]+2OH−(aq)
Hydrochloric acid will dissociate completely in aqueous solution to give H^(+)H+ cations and Cl^(-)Cl− anions.
HCl_((aq)) -> H_((aq))^(+) + Cl_((aq))^(-)HCl(aq)→H+(aq)+Cl−(aq)
The chemical reaction between these two compounds will be
Ba(OH)_(2(aq)) + 2HCl_text((aq]) -> BaCl_(2(aq)) + 2H_2O_((l))Ba(OH)2(aq)+2HCl(aq]→BaCl2(aq)+2H2O(l)
The complete ionic equation will be
Ba_((aq))^(2+) + 2OH_((aq))^(-) + 2H_((aq))^(+) + 2Cl_((aq))^(-) -> Ba_((aq))^(2+) + 2Cl_((aq))^(-) + 2H_2O_((l))Ba2+(aq)+2OH−(aq)+2H+(aq)+2Cl−(aq)→Ba2+(aq)+2Cl−(aq)+2H2O(l)
The net ionic equation, which you get if you remove spectator ions, will be
cancel(Ba_((aq))^(2+)) + 2OH_((aq))^(-) + 2H_((aq))^(+) + cancel(2Cl_((aq))^(-)) -> cancel(Ba_((aq))^(2+)) + cancel(2Cl_((aq))^(-)) + 2H_2O_((l))
2OH_((aq))^(-) + 2H_((aq))^(+) -> 2H_2O_((l))
which is equivalent to
OH_((aq))^(-) + H_((aq))^(+) -> H_2O_((l))
