First, you must recognize that this is a double displacement reaction.
Next you must write the ionic formulas for the products.
You know that
After the cations have changed partners, the formulas of the products are
Next, you use the solubility rules to determine if there are any precipitates.
In this case, the important rules are:
- All nitrates are soluble.
- All sulfides are insoluble except those of Groups 1 and 2.
#"BaS"#is soluble, because #"Ba"#is in Group 2.
#"B"_2"S"_3#is insoluble, because #"Bi"#is in group 15.
The unbalanced molecular equation is
The balanced molecular equation is
The total ionic equation is
To get the net ionic equation, we cancel the spectator ions.
Here's a good video on solubility rules and net ionic equations.