[Byrne]

This stuff is pretty simply, but my question lies within the solubility of one of the reactants...

Now, the question states:

Write the net ionic equation when the following solutions form a precipitate:

BaS(aq) and ZnSO4(aq)

Now, according to the solubility rules I have, barium sulphide has low solubility (solubility < 0.1 mol/L).  According to my rules, sulphide ionic compounds that are soluble in water include Group 1 ions, NH4+, and Group 2 ions.  So why is it that my teacher would give a problem where BaS is soluble?  Is BaS soluble in water?

So, would I be correct if I my net equation looked like this:

Ba+2(aq) + S-2(aq) + Zn+2(aq) + ZnSO4-2(aq) ---> BaSO4(s) + ZnS(s)

My solubility rules claim BaSO4 and ZnS have low solubility in water.

[Borek]

Now, according to the solubility rules I have, barium sulphide has low solubility (solubility < 0.1 mol/L).

0.1M for a sulphide is a lot

You may safely assume that it is soluble. Note, that "soluble" is very imprecise term. Saturated solution of ZnS is about 10^-12M, while saturated CaSO₄ is almost 10^-2M, yet they are in the same drawer with insoluble salts.

Depending on your further education you may later learn that solubilities can be described precisely by so called solubility product, which gives quantitative information about how much salt can be dissolved. For now you may safely assume 2nd group sulphides are soluble 'enough'.