The molecular form of the equation is the easiest to understand: The salts swap partners driven by precipitation, the formation of a molecule (like water from an acid-base reaction, or a gas that leaves the solution by bubbling away making the reaction go forward). In words:
potassium carbonate + barium nitrate → potassium nitrate + barium carbonate(ppt)
We know that barium carbonate is insoluble from the rule: all carbonates are insoluble except ammonium and !A metal carbonates.
Write in formula form and balance:
K2CO3(aq) + Ba(NO3)2(aq) ⇒ 2KNO3(aq) + BaCO3(s)
Because the aqueous salts are actually dissociated ions in solution, we can write the net ionic equation (K+ and NO3- are spectator ions) as
Ba2+ + CO3- ⇒ BaCO3
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