The products of the unbalanced reaction are as follows:
Ba(OH)₂ (aq) + H₃PO₄(aq) → Ba₃(PO₄)₂(s) + H₂O(l)
This is an acid base reaction where Ba(OH)₂ is the base and H₃PO₄ is the acid. Acid base reaction is also known as neutralization reaction where the acid and base react with each other to form salt and water. In this reaction Ba₃(PO₄)₂ is the salt. Also barium phosphate (Ba₃(PO₄)₂) is insoluble in water and forms a solid precipitate.
The balanced reaction is as follows:
3Ba(OH)₂ (aq) + 2H₃PO₄(aq) → Ba₃(PO₄)₂(s) + 6H₂O(l)
There are three Ba from Ba₃(PO₄)₂ on the product side of the equation, so to balance 3 coefficient was placed before Ba(OH)₂. Similarly, 2 coefficient was placed before H₃PO₄ on the reactant side to balance the two phosphate from Ba₃(PO₄)₂ on the product side. Finally, 6 coefficient was placed before H₂O on the product side, to balance the number of H and O atoms on both side of the equation.