Which ions remain in solution, unreacted, after each of the following pairs of solutions is mixed? \begin{equation} \begin{array}{l}{\text { (a) potassium carbonate and magnesium sulfate }} \\\ {\text { (b) lead nitrate and lithium sulfide }} \\ {\text { (c) ammonium phosphate and calcium chloride }}\end{array} \end{equation}

Precipitation reactions occur when two solutions containing soluble salts are mixed, leading to the formation of an insoluble compound. These reactions are essential to many processes in chemistry and are often depicted in chemical equations.

For instance, when mixing solutions of potassium carbonate and magnesium sulfate, we observe the outcome of a precipitation reaction. Two new compounds can form: potassium sulfate (K2SO4) and magnesium carbonate (MgCO3). However, the solubility rules tell us that magnesium carbonate is insoluble in water and therefore precipitates out of the solution as a solid.

Applying these principles helps identify which ions will remain in solution and which will form the precipitate. Soluble ions, like the potassium (K⁺) and sulfate (SO₄²⁻) ions in our example, will not participate in the precipitate formation and will remain in the solution as spectator ions.

Ionic equations provide a deeper understanding of the reactions happening in a solution by showing which ions are involved and their states. The process begins by writing the complete ionic equation, which lists all ions in their dissociated form. For example, lead nitrate and lithium sulfide dissociate into their constituent ions Pb²⁺, NO₃⁻, Li⁺, and S²⁻ when dissolved in water.

In an ionic equation, the ions that do not participate in the formation of the precipitate are termed 'spectator ions'. These ions do not change state and are not part of the net ionic equation. For instance, when lead nitrate reacts with lithium sulfide, the net ionic equation would only include the ions that form the lead sulfide precipitate, not the spectator ions Li⁺ and NO₃⁻ which are soluble and remain in the solution.

Understanding the concept of solubility is essential for predicting the outcome of reactions in aqueous solutions. Solubility rules are guidelines that allow us to predict whether a compound will dissolve in water (soluble) or form a precipitate (insoluble).

Compounds containing alkali metal ions and the ammonium ion are typically soluble. Hence, potassium sulfate and ammonium chloride remain in solution in the given examples. On the other hand, many carbonates, phosphates, and sulfides, such as magnesium carbonate, calcium phosphate, and lead sulfide, are generally insoluble, except when paired with specific ions that can make them soluble.

These solubility rules come in handy when predicting which ions will remain unreacted in a solution, such as Ca²⁺ and PO₄³⁻ ions forming the insoluble compound calcium phosphate, whereas NH₄⁺ and Cl⁻ remain in solution as they form the soluble compound ammonium chloride.