Of course, it would be nice to get the symbols correct. Barium is Ba. And "yes", it is possible for some acid/base reactions to produce an insoluble product. A better definition of a double replacement reaction, of which acid/base reactions are a part, is that it produces an undissociated product. Now, that can easily mean a solid precipitate, since it is undissociated. But H2O is also an undissociated product and water is frequently the only product of an acid/base reaction. So in essence H2O is the 'precipitate". Your lecturer is being a bit overzealous in discounting liquid products.
HCl(aq) + NaOH(aq)
NaCl(aq) + H2O(l) .... water is the "precipitate", the undissociated product.
In your reaction there are two undissociated products.
2H3PO4(aq) + 3Ba(OH)2(aq)
Ba3(PO4)2(s) + 6H2O(l)
When we write the net ionic equation we must remind ourselves that phosphoric acid is a weak acid and not dissociated to any great extent. Ba(OH)2 is a strong base and what little dissolves dissociates completely. The catch is that barium hydroxide is not very soluble in water.
The net ionic equation will look like this:
2H3PO4(aq) + 3Ba^2+(aq) + 6OH-(aq)
Ba3(PO4)2(s) + 6H2O(l)
=========== Follow up =============
Trevor is quite correct in that reacting two salts can more easily produce barium phosphate, but I think that somewhat deviates from the intent of the question. The question, as I interpret it, deals with a precipitate forming in an acid/base reaction.
Another possibility is the reaction between sulfuric acid and barium hydroxide. Sulfuric acid is a strong acid, and of course, barium hydroxide is a strong base. Not a very soluble base, but what little dissolves dissociates completely. H2SO4 and Ba(OH)2 will make insoluble BaSO4.
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