Which ions remain in solution, unreacted, after each of the following pairs of solutions is mixed? (a) potassium carbonate and magnesium sulfate (b) lead nitrate and lithium sulfide (c) ammonium phosphate and calcium chloride

Step 1: Write the molecular equation Potassium carbonate reacts with magnesium sulfate to form potassium sulfate and magnesium carbonate. The balanced molecular equation is: \[K_2CO_3(aq) + MgSO_4(aq) \rightarrow 2 K^+SO_4^-(aq) + MgCO_3(s)\] Step 2: Write the complete ionic equation \[2K^+(aq) + CO_3^{2-}(aq) + Mg^{2+}(aq) + SO_4^{2-}(aq) \rightarrow 2K^+(aq) +SO_4^{2-}(aq) + MgCO_3(s)\] Step 3: Cancel the spectator ions and write the net ionic equation The spectator ions are \(K^+\) and \(SO_4^{2-}\). The net ionic equation is: \[CO_3^{2-}(aq) + Mg^{2+}(aq) \rightarrow MgCO_3(s)\] Step 4: Identify the ions that remain in solution and unreacted The ions that remain in solution and unreacted are \(K^+\) and \(SO_4^{2-}\).

Step 1: Write the molecular equation Lead nitrate reacts with lithium sulfide to form lead sulfide and lithium nitrate. The balanced molecular equation is: \[Pb(NO_3)_2(aq) + 2Li_2S(aq) \rightarrow PbS(s) + 2LiNO_3(aq)\] Step 2: Write the complete ionic equation \[Pb^{2+}(aq) + 2NO_3^-(aq) + 4Li^+(aq) + 2S^{2-}(aq) \rightarrow PbS(s) + 4Li^+(aq) + 2NO_3^-(aq)\] Step 3: Cancel the spectator ions and write the net ionic equation The spectator ions are \(Li^+\) and \(NO_3^-\). The net ionic equation is: \[Pb^{2+}(aq) + S^{2-}(aq) \rightarrow PbS(s)\] Step 4: Identify the ions that remain in solution and unreacted The ions that remain in solution and unreacted are \(Li^+\) and \(NO_3^-\).

Step 1: Write the molecular equation Ammonium phosphate reacts with calcium chloride to form calcium phosphate and ammonium chloride. The balanced molecular equation is: \[(NH_4)_3PO_4(aq) + 3CaCl_2(aq) \rightarrow Ca_3(PO_4)_2(s) + 6NH_4Cl(aq)\] Step 2: Write the complete ionic equation \[3NH_4^+(aq) + PO_4^{3-}(aq) + 3Ca^{2+}(aq) + 6Cl^-(aq) \rightarrow Ca_3(PO_4)_2(s) + 6NH_4^+(aq) + 6Cl^-(aq)\] Step 3: Cancel the spectator ions and write the net ionic equation The spectator ions are \(NH_4^+\) and \(Cl^-\). The net ionic equation is: \[PO_4^{3-}(aq) + 3Ca^{2+}(aq) \rightarrow Ca_3(PO_4)_2(s)\] Step 4: Identify the ions that remain in solution and unreacted The ions that remain in solution and unreacted are \(NH_4^+\) and \(Cl^-\).