Answer
First column (Solubles): $K_2S, K_2SO_4, NH_4Cl, Na_2CO_3, Li_2S, BaS$ and $SrS$.
Second column (Insolubles): $Cu_3(PO_4)_2, PbSO_4, CaSO_4, Hg_2I_2, PbCl_2, Hg_2Cl_2$ and $MgS$
Work Step by Step
1. Classify each compound as soluble or insoluble:
$K_2S$, $K_2SO_4$, $NH_4Cl$, $Na_2CO_3$ and $Li_2S$:
Any $K^+$, $NH_4^+$, $Na^+$ or $Li^+$ compound is soluble.
$Cu_3(PO_4)_2$:
Most $PO_4$ compounds are insoluble.
$PbSO_4$ and $CaSO_4$:
$SO_4^{2-}$ compounds with $Pb^{2+}$ or $Ca^{2+}$ are insoluble.
$Hg_2I_2$, $PbCl_2$ and $Hg_2Cl_2$:
$Hg^{2+}$ or $Pb^{2+}$ compounds with $Cl^-$ or $I^-$ are insoluble.
$MgS$:
Most $S^{2-}$ compounds are insoluble.
$BaS$ and $SrS$:
$S^{2-}$ compounds with $Ba^{2+}$ or $Sr^{2+}$ are soluble.
2. Now, create a column with all the soluble compounds, and another one with the insoluble ones.
First column: $K_2S, K_2SO_4, NH_4Cl, Na_2CO_3, Li_2S, BaS$ and $SrS$.
Second column: $Cu_3(PO_4)_2, PbSO_4, CaSO_4, Hg_2I_2, PbCl_2, Hg_2Cl_2$ and $MgS$
